Aspen Adsim
March 24, 2017 | Author: kiny81 | Category: N/A
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Description
Aspen Adsim 2004.1 Adsorption Reference Guide
Who Should Read this Guide
This guide contains reference information for use by experienced users of the Aspen Adsim application. The guide also describes the following Aspen Adsim features: •
Numerical methods for solving the partial differential equations.
•
Estimation module.
•
Cyclic Organizer.
•
Flowsheeting strategies.
Who Should Read this Guide
2
General Information
This section provides Copyright details and lists any other documentation related to the Aspen Adsim 2004.1 release.
Copyright Version: 2004.1 April 2005 Copyright © 1991-2005 Aspen Technology, Inc, and its applicable subsidiaries, affiliates, and suppliers. All rights reserved. This Software is a proprietary product of Aspen Technology, Inc., its applicable subsidiaries, affiliates and suppliers and may be used only under agreement with AspenTech. Aspen ACOL™, Aspen Adsim®, Aspen Advisor™, Aspen Aerotran®, Aspen Alarm & Event™, Aspen APLE™, Aspen Apollo Desktop™, Aspen Apollo Online™, Aspen AssetBuilder™, Aspen ATOMS™, Aspen Automated Stock Replenishment™, Aspen Batch Plus®, Aspen Batch.21™, Aspen BatchCAD™, Aspen BatchSep™, Aspen Calc™, Aspen Capable-to-Promise®, Aspen CatRef®, Aspen Chromatography®, Aspen Cim-IO for ACS™, Aspen Cim-IO for Csi VXL™, Aspen Cim-IO for Dow MIF™, Aspen Cim-IO for G2™, Aspen Cim-IO for GSE D/3™, Aspen Cim-IO for Hewlett-Packard RTAP™, Aspen CimIO for Hitachi PLC (H04E)™, Aspen Cim-IO for Intellution Fix™, Aspen Cim-IO for Melsec™, Aspen Cim-IO for WonderWare InTouch™, Aspen Cim-IO for Yokogawa Centum CS™, Aspen Cim-IO for Yokogawa Centum XL™, Aspen Cim-IO for Yokogawa EW3™, Aspen Cim-IO Interfaces™, Aspen Cim-IO Monitor™, Aspen Cim-IO™, Aspen Collaborative Demand Management™, Aspen Collaborative Forecasting™, Aspen Compliance.21™, Aspen COMThermo TRC Database™, Aspen COMThermo®, Aspen Cost Factor Manual™, Aspen Crude Manager™, Aspen Crude Margin Evaluation™, Aspen Custom Modeler®, Aspen Data Source Architecture™, Aspen Decision Analyzer™, Aspen Demand Manager™, Aspen DISTIL™, Aspen Distribution Scheduler™, Aspen DMCplus® Composite, Aspen DMCplus® Desktop, Aspen DMCplus® Online, Aspen DPO™, Aspen Dynamics®, Aspen eBRS™, Aspen Enterprise Model™, Aspen ERP Connect™, Aspen FCC®, Aspen FIHR™, Aspen FLARENET™, Aspen Fleet Operations Management™, Aspen Framework™, Aspen FRAN™, Aspen Fuel Gas Optimizer Desktop™, Aspen Fuel Gas Optimizer Online™, Aspen General Construction Standards™, Aspen Hetran®, Aspen HX-Net®, Aspen Hydrocracker®, Aspen Hydrotreater™, Aspen HYSYS Amines™, Aspen HYSYS Crude™, Aspen HYSYS Dynamics™, Aspen HYSYS
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OLGAS 3-Phase™, Aspen HYSYS OLGAS™, Aspen HYSYS OLI Interface™, Aspen HYSYS Tacite™, Aspen HYSYS Upstream Dynamics™, Aspen HYSYS Upstream™, Aspen HYSYS®, Aspen Icarus Process Evaluator®, Aspen Icarus Project Manager®, Aspen InfoPlus.21®, Aspen Inventory Balancing™, Aspen IQ Desktop™, Aspen IQ Online™, Aspen IQmodel Powertools™, Aspen Kbase®, Aspen LIMS Interface™, Aspen Local Security™, Aspen LPIMS™, Aspen MBO™, Aspen MIMI®, Aspen MPIMS™, Aspen Multivariate Server™, Aspen MUSE™, Aspen NPIMS™, Aspen OnLine®, Aspen Operations Manager Event Management™, Aspen Operations Manager - Integration Infrastructure™, Aspen Operations Manager - Peformance Scorecarding™, Aspen Operations Manager - Role Based Visualization™, Aspen Order Credit Management™, Aspen Orion Planning™, Aspen Orion™, Aspen PEP Process Library™, Aspen PIMS Blend Model Library™, Aspen PIMS Distributed Processing™, Aspen PIMS Enterprise Edition™, Aspen PIMS Mixed Integer Programming™, Aspen PIMS Simulator Interface™, Aspen PIMS Solution Ranging™, Aspen PIMS Submodel Calculator™, Aspen PIMS XNLP Optimizer™, Aspen PIMS™, Aspen PIPESYS™, Aspen PIPE™, Aspen Planning Accuracy™, Aspen Plant Planner & Scheduler™, Aspen Plant Scheduler Lite™, Aspen Plant Scheduler™, Aspen Plus OLI Interface™, Aspen Plus®, Aspen Polymers Plus®, Aspen PPIMS™, Aspen Process Data™, Aspen Process Explorer™, Aspen Process Manual™, Aspen Process Order™, Aspen Process Plant Construction Standards™, Aspen Process Recipe®, Aspen Process Tools™, Aspen Product Margin & Blending Evaluation™, Aspen Production Control Web Server™, Aspen ProFES® 2P Tran, Aspen ProFES® 2P Wax, Aspen ProFES® 3P Tran, Aspen ProFES® Tranflo, Aspen Properties®, Aspen Pumper Log™, Aspen Q Server™, Aspen RateSep™, Aspen RefSYS CatCracker™, Aspen RefSYS Spiral™, Aspen RefSYS™, Aspen Report Writer™, Aspen Resource Scheduling Optimization™, Aspen RTO Watch Cim-IO Server™, Aspen RTO Watch Server™, Aspen Scheduling & Inventory Management™, Aspen SmartStep Desktop™, Aspen SmartStep Online™, Aspen SQLplus™, Aspen Supply Chain Analytics™, Aspen Supply Chain Connect™, Aspen Supply Planner™, Aspen Tank Management™, Aspen TASCMechanical™, Aspen TASC™, Aspen Teams®, Aspen Terminals Management™, Aspen TICP™, Aspen Transition Manager™, Aspen Turbo PIMS™, Aspen Utilities™, Aspen Voice Fulfillment Management™, Aspen Watch Desktop™, Aspen Watch Server™, Aspen Water™, Aspen Web Fulfillment Management™, Aspen WinRace Database™, Aspen XPIMS™, Aspen Zyqad Development Version™, Aspen Zyqad™, SLM™, SLM Commute™, SLM Config Wizard™, the aspen leaf logo, and Plantelligence are trademarks or registered trademarks of Aspen Technology, Inc., Cambridge, MA. All other brand and product names are trademarks or registered trademarks of their respective companies. This document is intended as a guide to using AspenTech's software. This documentation contains AspenTech proprietary and confidential information and may not be disclosed, used, or copied without the prior consent of AspenTech or as set forth in the applicable license. Corporate Aspen Technology, Inc.
Phone: (1) (617) 949-1000
Ten Canal Park
Toll Free: (1) (888) 996-7001
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Cambridge, MA 02141-2201
Fax: (1) (617) 949-1030
USA
URL: http://www.aspentech.com
General Information
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Related Documentation In addition to this document, the following documents are provided to help users learn and use the Aspen Adsim applications. Title
Content
Aspen Adsim 2004.1 Library Reference Guide
Describes the models, streams, procedures and submodels available in Aspen Adsim.
AES 2004.1 Installation Guide
Full installation procedures for both server and client.
Aspen Engineering Suite 2004.1 What’s New Guide
An overview of new features and functionality within this release.
General Information
6
Technical Support
Online Technical Support Center AspenTech customers with a valid license and software maintenance agreement can register to access the Online Technical Support Center at: http://support.aspentech.com You use the Online Technical Support Center to: •
Access current product documentation.
•
Search for technical tips, solutions, and frequently asked questions (FAQs).
•
Search for and download application examples.
•
Search for and download service packs and product updates.
•
Submit and track technical issues.
•
Search for and review known limitations.
•
Send suggestions.
Registered users can also subscribe to our Technical Support e-Bulletins. These e-Bulletins proactively alert you to important technical support information such as: •
Technical advisories.
•
Product updates.
•
Service Pack announcements.
•
Product release announcements.
Technical Support
7
Phone and E-mail Customer support is also available by phone, fax, and e-mail for customers who have a current support contract for their product(s). Toll-free charges are listed where available; otherwise local and international rates apply. For the most up-to-date phone listings; please see the Online Technical Support Center at: http://support.aspentech.com Support Centers
Operating Hours
North America
8:00 – 20:00 Eastern time
South America
9:00 – 17:00 Local time
Europe
8:30 – 18:00 Central European time
Asia and Pacific Region
9:00 – 17:30 Local time
Technical Support
8
Contents GENERAL INFORMATION................................................................................. 3 Copyright................................................................................................................ 3 Related Documentation............................................................................................. 6
TECHNICAL SUPPORT...................................................................................... 7 Online Technical Support Center ................................................................................ 7 Phone and E-mail..................................................................................................... 8
INTRODUCING ASPEN ADSIM ....................................................................... 17 1 GAS ADSORPTION PROCESSES.................................................................. 18 About Gas Adsorption Processes............................................................................... 18 Bed Model Assumptions for Gas Adsorption Processes ................................................. 19 About Aspen Adsim's Bed Models ............................................................................. 20 Bed Model Ports ................................................................................................ 20 Configure Form (Gas) ............................................................................................. 21 Configure Form (gas): Bed Type.......................................................................... 22 Configure Form (gas): Spatial Dimensions ............................................................ 24 Configure Form (gas): Internal Heat Exchanger ..................................................... 25 Configure Layer Form (gas) ..................................................................................... 26 General Tab (gas) .................................................................................................. 26 General Tab (gas): Discretization Method to be used .............................................. 26 General Tab (gas): Number of Nodes ................................................................... 27 General Tab (gas): Number of Radial Nodes.......................................................... 27 General Tab (gas): Flux Limiter to be used ........................................................... 27 General Tab (gas): Gas Model Assumption ............................................................ 27 Material/Momentum Balance Tab (gas) ..................................................................... 28 About Axial Dispersion in Gas Adsorption Processes ............................................... 28 Material/Momentum Balance Tab (gas): Material Balance Assumption....................... 29 Material/Momentum Balance Tab (gas): Momentum Balance Assumption .................. 31 Material/Momentum Balance Tab (gas): 2-D Dispersive Properties ........................... 33 Kinetic Model Tab (gas) .......................................................................................... 37 Kinetic Model Tab (gas): Film Model Assumption.................................................... 37 Kinetic Model Tab (gas): Kinetic Model Assumption ................................................ 37
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Kinetic Model Tab (gas): Form of Lumped Resistance Model .................................... 50 Kinetic Model Tab (gas): Molecular Diffusivities ..................................................... 51 Kinetic Model Tab (gas): Form of Mass Transfer Coefficients.................................... 52 Kinetic Model Tab (gas): Apply Cyclic Correction.................................................... 55 Kinetic Model Tab (gas): Estimated Mass Transfer Coefficient Assumption ................. 56 Gas Adsorption Layer (gas): Particle Material Balance, Number of Nodes................... 56 Kinetic Model Tab (gas): Particle Material Balance, Effective Diffusivity ..................... 56 Isotherm Tab (gas) ................................................................................................ 57 About Adsorption Isotherms for Gas Adsorption Processes ...................................... 57 Guidelines for Choosing Aspen Adsim Isotherm Models (gas)................................... 58 About Multi-Component Mixture Isotherms (gas) ................................................... 58 Isotherm Tab (gas): Isotherm Assumed for Layer .................................................. 61 Isotherm Tab (gas): Adsorbed Solution Theory...................................................... 70 Isotherm Tab (gas): Isotherm Dependency........................................................... 70 Energy Balance Tab (gas)........................................................................................ 70 Energy Balance Tab (gas): Energy Balance Assumption .......................................... 70 Energy Balance Tab (gas): Consider Heat of Adsorbed Phase................................... 71 Energy Balance Tab (gas): Heat of Adsorption Assumption...................................... 72 Energy Balance Tab (gas): Form of Heat Transfer Coefficient................................... 73 Energy Balance Tab (gas): Form of Gas Thermal Conductivity ................................. 75 Energy Balance Tab (gas): Heat Transfer to Environment........................................ 76 Energy Balance Tab (gas): Form of Gas-Wall Heat Transfer Coefficient ..................... 78 Reaction Tab (gas) ................................................................................................. 79 About Gas Adsorption with Reaction Processes ...................................................... 79 Reaction Tab (gas): Reactions Present ................................................................. 80 Reaction Tab (gas): Homogeneous Rate Dependency ............................................. 80 Reaction Tab (gas): Number of Homogeneous Reactions......................................... 81 Reaction Tab (gas): Heterogeneous Rate Dependency ............................................ 81 Reaction Tab (gas): Number of Heterogeneous Reactions ....................................... 81 Reaction Tab (gas): Are Solid Reactants Present.................................................... 82 Reaction Tab (gas): Solid Reactant List ................................................................ 82 Procedures Tab (gas).............................................................................................. 82 Gas Adsorption: Summary of Mass and Energy Balance Equations................................. 82 Gas Adsorption: Mass Balance for Gas Phase......................................................... 83 Gas Adsorption: Mass Balance for Additional Solid Phase ........................................ 83 Gas Adsorption: Gas Phase Energy Balance........................................................... 84 Gas Adsorption: Solid Phase Energy Balance ......................................................... 84 Gas Adsorption: Wall Energy Balance ................................................................... 85 Gas Adsorption: Summary of Factors that affect the Mass Balance Equations............. 85 Gas Adsorption: Defining the Mass Balance for Additional Solid Phases ..................... 87 Gas Adsorption: Summary of Factors that affect the Energy Balance ........................ 87
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Gas Adsorption: Defining the Energy Balance in the Gas Phase ................................ 87 Gas Adsorption: Defining the Energy Balance for the Solid Phase ............................. 90 Gas Adsorption: Defining Energy Balance for the Wall ............................................ 92 Gas Adsorption: Explanation of Equation Symbols....................................................... 93
2 GAS CYCLIC STEADY STATE MODELING..................................................... 99 Introduction .......................................................................................................... 99 What is CSS Modeling…? ........................................................................................100 Discretization Techniques for Time and Space ...........................................................103 Connectivity between CSS Models ...........................................................................103 Bed Model Details .................................................................................................104 Material Balance ..............................................................................................104 Momentum Balance ..........................................................................................105 Kinetic Model...................................................................................................106 Energy Balance................................................................................................109 Adsorption Equilibrium Models ................................................................................112 Introduction ....................................................................................................112 Mathematical Equation Form for Extended Langmuir 1...........................................113 Mathematical Equation Form for Extended Langmuir 2...........................................113 Mathematical Equation Form for Extended Langmuir 3...........................................114 Mathematical Equation Form for Extended Langmuir 4...........................................115 Mathematical Equation Form for Extended Langmuir 5...........................................116 Mathematical Equation Form for Loading Ratio Correlation 1...................................117 Mathematical Equation Form for Loading Ratio Correlation 2...................................118 Mathematical Equation Form for Loading Ratio Correlation 3...................................119 Mathematical Equation Form for Loading Ratio Correlation 4...................................120 Mathematical Equation Form for Loading Ratio Correlation 5...................................121 Mathematical Equation Form for Extended Dual-Site Langmuir 1 .............................122 Mathematical Equation Form for Extended Dual-Site Langmuir 2 .............................123 I.A.S.T. (Ideal Adsorbed Solution Theory)............................................................123 Pure Isotherm List for the IAST Calculation of CSS................................................125 Langmuir 1 .....................................................................................................126 Langmuir 2 .....................................................................................................126 Langmuir 3 .....................................................................................................127 Langmuir 4 .....................................................................................................128 Langmuir 5 .....................................................................................................129 Dual-Site Langmuir 1........................................................................................130 Dual-Site Langmuir 2........................................................................................130 Sips (Langmuir-Freundlich) 1 .............................................................................131 Sips (Langmuir-Freundlich) 2 .............................................................................132 Sips (Langmuir-Freundlich) 3 .............................................................................133
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Sips (Langmuir-Freundlich) 4 .............................................................................134 Sips (Langmuir-Freundlich) 5 .............................................................................135 Henry 1 ..........................................................................................................136 Henry 2 ..........................................................................................................136 Henry 3 ..........................................................................................................137 Henry 4 ..........................................................................................................137 Freundlich 1 ....................................................................................................138 Toth 1 ............................................................................................................139 BET 1 .............................................................................................................139 User Guidelines.....................................................................................................140 How to Create a CSS Simulation Flowsheet ..........................................................140 How to Create a Dynamic Simulation Flowsheet using CSS Models ..........................158 How to Convert a CSS Flowsheet to a Dynamic Flowsheet ......................................174 How to Convert a Dynamic Flowsheet into a CSS Flowsheet ...................................177 Developer’s Tips to Get Better Convergence Property in CSS Simulation...................180
3 ION-EXCHANGE PROCESSES.....................................................................184 About Ion-Exchange Processes...........................................................................184 Bed Model Assumptions for Ion-Exchange............................................................185 Configure Form (ionx).......................................................................................185 Configure Layer Form (ionx) ..............................................................................185 General Tab (ionx) ...........................................................................................186 General Tab (ionx): Discretization Method to be Used............................................186 General Tab (ionx): Number of Nodes .................................................................186 Material/Momentum Balance Tab (ionx)...............................................................186 Material/Momentum Balance Tab (ionx): Material Balance Assumption.....................186 About Axial Dispersion in Ion-Exchange Processes ................................................188 Deciding When to Use Axial Dispersion in Ion-Exchange Processes ..........................188 Kinetic Model Tab (ionx)....................................................................................189 Kinetic Model Tab (ionx): Film Model Assumption..................................................189 Kinetic Model Tab (ionx): Kinetic Model Assumption ..............................................190 Kinetic Model Tab (ionx): Form of Lumped Resistance ...........................................190 Kinetic Model Tab (ionx): Form of Mass Transfer Coefficient ...................................191 Isotherm Tab (ionx) .........................................................................................191 About Adsorption Isotherms for Ion-Exchange Processes .......................................191 Isotherm Tab (ionx): Isotherm Assumed for Layer ................................................192 Summary of Mass Balance Equations for Ion-Exchange Processes ...........................194 Explanation of Equation Symbols for Ion-Exchange Processes.................................195
4 LIQUID ADSORPTION PROCESSES ...........................................................197 About Liquid Adsorption Processes......................................................................197 Bed Model Assumptions for Liquid Adsorption .......................................................198
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Configure Form (liq) .........................................................................................198 Configure Layer Form (liq).................................................................................198 General Tab (liq)..............................................................................................199 General Tab (liq): Discretization Method to be Used ..............................................199 General Tab (liq): Number of Nodes....................................................................199 Material/Momentum Balance (liq) .......................................................................199 Material/Momentum Balance Tab (liq): Material Balance Assumption .......................199 Material/Momentum Balance Tab (liq): Pressure Drop Assumption...........................201 Material/Momentum Balance Tab (liq): Velocity Assumption ...................................202 Material/Momentum Balance Tab (liq): Overall Material Balance Assumption.............202 Kinetic Model Tab (liq) ......................................................................................202 Kinetic Model Tab (liq): Film Model Assumption ....................................................203 Kinetic Model Tab (liq): Kinetic Model Assumption.................................................203 Kinetic Model Tab (liq): Form of Mass Transfer Coefficient......................................204 About Adsorption Isotherms for Liquid Adsorption .................................................205 Guidelines for Choosing Aspen Adsim Isotherm Models ..........................................205 The Ideal Adsorbed Solution Theory (IAS) ...........................................................206 Isotherm Tab (liq): Isotherm Assumed for Layer...................................................206 Energy Balance Tab (liq) ...................................................................................212 Energy Balance Tab (liq): Energy Balance Assumption...........................................212 Energy Balance Tab (liq): Consider Heat of Adsorbed Phase ...................................214 Energy Balance Tab (liq): Heat of Adsorption Assumption ......................................214 Energy Balance Tab (liq): Form of Heat Transfer Coefficient ...................................215 Energy Balance Tab (liq): Form of Fluid Thermal Conductivity.................................216 Energy Balance Tab (liq): Heat Transfer to Environment ........................................217 Procedures Tab (liq) .........................................................................................219 Liquid Adsorption: Summary of Mass and Energy Balance ......................................219 Liquid Adsorption: Mass Balance.........................................................................219 Liquid Adsorption: Solid Phase Energy Balance .....................................................220 Liquid Adsorption: Fluid Phase Energy Balance .....................................................220 Liquid Adsorption: Wall Energy Balance ...............................................................220 Liquid Adsorption: Explanation of Equation Symbols..............................................221
5 NUMERICAL METHODS .............................................................................224 About Numerical Methods..................................................................................224 Choosing the Discretization Method ....................................................................225 About the Discretization Methods........................................................................225 Upwind Differencing Scheme 1 ...........................................................................227 Upwind Differencing Scheme 2 ...........................................................................228 Central Differencing Scheme 1 ...........................................................................228 Central Differencing Scheme 2 ...........................................................................229 Leonard Differencing Scheme.............................................................................229
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Quadratic Upwind Differencing Scheme ...............................................................230 Mixed Differencing Scheme................................................................................232 Biased Upwind Differencing Scheme....................................................................233 Fromms’ scheme..............................................................................................234 Flux Limited Discretization Scheme .....................................................................235
6 ESTIMATION WITH ASPEN ADSIM............................................................236 Two Estimation Tools in Aspen Adsim 2004.1 .......................................................236 About the Estimation Module .............................................................................236 Defining Estimated Variables in the Estimation Module ..........................................238 Steady-State Estimation Using the Estimation Module ...........................................239 Manually Entering Steady-State Experimental Data ...............................................239 Steady-State Experimental Data from the Clipboard..............................................240 Dynamic Estimation Using the Estimation Module .................................................242 Manually Entering Dynamic Experimental Data .....................................................243 Dynamic Experimental Data from the Clipboard ....................................................244 Performing Estimation Using the Estimation Module ..............................................247 Converting Estimation Module Data ....................................................................247 Recommendations When Using the Estimation Module ...........................................247
7 CYCLIC OPERATION .................................................................................249 Cyclic Operations in Aspen Adsim 2004.1.............................................................249 About the Cycle Organizer .................................................................................249 Opening the Cycle Organizer..............................................................................250 Cycle Organizer Window....................................................................................250 Step Control ....................................................................................................252 Time Driven Step .............................................................................................252 Discrete Event Driven Step ................................................................................252 Step Variables .................................................................................................256 Adding Step Variables .......................................................................................256 Removing Step Variables...................................................................................257 Changing Step Variable Values...........................................................................257 Interaction Control ...........................................................................................258 Defining a Step Interaction ................................................................................258 Deleting Interaction Steps .................................................................................259 Adding Extra Interaction Steps...........................................................................259 Interacting Steps and Time Controls ...................................................................259 Additional Cycle Controls...................................................................................260 Maximum Cycles Box ........................................................................................260 Record Initial and Record Frequency Boxes ..........................................................261 Take Snapshot Box...........................................................................................261 Cyclic Steady State Testing Box .........................................................................261
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Additional Step Controls ....................................................................................262 Execute End of Step Script Box ..........................................................................262 Take Snapshot at End of Step Box ......................................................................262 Generating Cyclic Tasks ....................................................................................263 Activating and Deactivating Cyclic Tasks..............................................................263 Cyclic Reports..................................................................................................264 Preparing Aspen Adsim for Cyclic Reporting .........................................................264 Cyclic Stream Reports.......................................................................................265 Cyclic Recovery Reports ....................................................................................266
8 FLOWSHEETING .......................................................................................268 About Model Types ...........................................................................................268 General Model Types ........................................................................................269 Reversibility ....................................................................................................269 About Flowsheets in Aspen Adsim.......................................................................272 Connectivity on Flowsheets................................................................................273 Templates .......................................................................................................274 Demonstrations ...............................................................................................274 Types of Flowsheet in Aspen Adsim.....................................................................275 Types of Flowsheet: Simple Flowsheet ................................................................275 Intermediate Flowsheet.....................................................................................276 Full Flowsheet..................................................................................................277 Single Bed Approach.........................................................................................278 Pressure Interaction Diagram.............................................................................278 Interactions.....................................................................................................281 Specifications for Flowsheets .............................................................................283 Solver Options .................................................................................................283 Run Time Options.............................................................................................285 Model Specification...........................................................................................286 Consistency and Problem Definition Checks..........................................................287 Physical Properties ...........................................................................................288 Use of User Fortran ..........................................................................................289 Using a Physical Properties Application ................................................................290 Switching Between Methods...............................................................................290 Connecting to Aspen Dynamics Flowsheets ..........................................................291 Typical Workflows ............................................................................................291 Valid Flowsheet Combinations ............................................................................293 Connecting to a Single Bed Approach Flowsheet ...................................................296
9 REFERENCE LIST FOR ADSORPTION PROCESSES......................................298 INDEX ..........................................................................................................299
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Introducing Aspen Adsim
Aspen Adsim simulates gas processes with adsorption only, or adsorptive reaction gas processes where both reaction and adsorption occur simultaneously. Gas-phase adsorption is widely used for the large-scale purification or bulk separation of air, natural gas, chemicals and petrochemicals.
Introducing Aspen Adsim
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1 Gas Adsorption Processes
This chapter contains information on: •
About Gas Adsorption Processes.
•
Bed Model Assumptions for Gas Adsorption Processes.
•
About Aspen Adsim Bed Models.
•
Configure Form.
•
Configure Layer Form.
•
General Tab.
•
Material/Momentum Balance Tab.
•
Kinetic Model Tab.
•
Isotherm Tab.
•
Energy Balance Tab.
•
Reaction Tab.
•
Procedure Tab.
•
Summary of Mass and Energy Balance Equations.
•
Explanation of Equation Symbols.
About Gas Adsorption Processes Gas-phase adsorption is widely used for the large-scale purification or bulk separation of air, natural gas, chemicals and petrochemicals, where it is often better to use gas-phase adsorption rather than the older unit operations of distillation and absorption. Adsorbent attracts molecules from the gas, removing the molecules from the gas phase and concentrate on the surface of the adsorbent. Many process concepts have been developed to allow: •
Efficient contact of feed gas mixtures with adsorbent to carry out desired separations.
•
Efficient regeneration of the adsorbent for subsequent reuse.
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For gas phase applications, most commercial adsorbents are pellets, beads, or other granular shapes, typically about 1.5 to 3.2 mm in diameter. These adsorbents are usually packed into fixed beds through which the gaseous feed mixtures are passed. Normally, the process is cyclic. When the bed capacity is exhausted, the feed flow is stopped to finish the loading step of the process. The bed is then treated to remove the adsorbed molecules in separate regeneration steps, then the cycle is repeated. Gas phase adsorption processes have seen a growth in both variety and scale, especially since 1970. This is due mainly to improvements in adsorbents, for example the discovery of porous adsorbents with a large surface area, such as zeolites. These advances have encouraged parallel inventions of new process concepts. Increasingly, the development of new applications requires close cooperation in adsorbent design and process cycle development and optimization.
Bed Model Assumptions for Gas Adsorption Processes Aspen Adsim simulates gas processes with adsorption only, or adsorptive reaction gas processes where both reaction and adsorption occur simultaneously. For gas processes, the bed model makes the following assumptions: •
Isothermal or non-isothermal conditions apply. Terms in the energy balances include: − Thermal conductivity of gas and thermal conductivity of solid. − Compression. − Gas-solid heat transfer. − Heat of adsorption. − Enthalpy of adsorbed phase. − Heat exchange with environment. − Wall energy terms. − Enthalpy of mixing is negligible.
•
Plug flow or plug flow with axial dispersion occurs.
•
The system is fully mixed in the radial direction. Alternatively, radial dispersion and thermal conduction are used to account for radial material and temperature distributions.
•
The gas phase is ideal or non-ideal, the non-ideal behavior needing a compressibility factor.
•
Gas phase pressure is either constant (with velocity either constant, or varying according to mass balance and only applicable for breakthrough simulations), or the pressure varies according to a laminar or turbulent flow momentum balance.
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•
Mass transfer is described using a lumped overall resistance, or by a model that accounts separately for micropore and macropore effects. The driving force is based on a liquid or solid film, and is either linear, quadratic, or user-specified. Mass transfer coefficients are either constant, or vary with local conditions. A limited rigorous particle material balance functionality is provided.
•
Adsorption isotherms are either applicable for single or multi-component adsorption. IAS theory can be used for pure component isotherms.
About Aspen Adsim's Bed Models The table shows the classifications of adsorption bed models: Name
Type
Model type
Flow setter under compressible flow conditions.
Flow type
Reversible.
Time dependency
Dynamic.
Reversible models handle forward or reverse flow in the bed. They contain dummy variables associated with the input and output streams. The adsorption bed models are usually flow setters, but within the bed they can be both flow setters and pressure setters. This is because they determine internal pressure profiles and gas velocity profiles, provided the general compressible flow model is used. The nature of the process and its operating conditions determine the type of model to use. For example, a bulk separation process such as producing oxygen-rich gas from air requires a different model to that for a purification process for removing trace impurities. The adsorption column models use a set of partial differential equations to represent the momentum, heat, and material balances across the column. You can add further relationships, which are specific to the various options.
Bed Model Ports Bed models contain an input and an output port. Each port has associated variables that correspond to the material connection stream variables, and which allow for reversible flow.
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Configure Form (Gas) On the Configure form of the bed model: 1
Enter the number of layers within the bed (one or more).
2
Enter the bed type: Vertical, Horizontal or Radial. See Configure Form for Gas Process Bed Model, later.
3
For vertical beds only, define the spatial dimensions of the bed model: 1-D or 2-D. See Configure Form for Gas Process Bed Model: Spatial Dimensions, later.
4
For vertical and horizontal beds, specify whether an internal heat exchanger is present. See Configure Form for Gas Process Bed Model: Internal Heat, and See Configure Form for Gas Process Bed Model: Spatial Dimensions, later.
5
In the Description box for each layer, type a brief name or description.
6
Click Configure to open the
1 Gas Adsorption Processes
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Configure Layer Form (gas) dialog box. 7
Click Specify to open the Specify form for the layer model.
Configure Form (gas): Bed Type To choose the bed type: •
In the Bed Type box, choose vertical, horizontal or radial bed orientation.
Vertical Bed Type Typically, you use a vertical orientation for an adsorption bed. Vertical columns prevent variation in flow width because the flow is along the column axis.
Horizontal Bed Type Occasionally, you may need to choose horizontal orientation, for example, when a vertical bed may cause fluidization of the bed. Horizontal beds allow a much greater inflow area, keeping gas superficial velocities below the fluidization velocity. In the horizontal column orientation, the flow through the adsorbent packing is still vertical, but is now at right angles to the column axis so there is variation in the effective flow area of the column with height above the column base. The height of the start of the (first) adsorbent layer above the column base is the same thickness as the empty dead space and supporting grating.
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L HB,2 DB
HB,1 Layer 2
H0,1
H0,2
Layer 1 z W(z) The effective width W(z) of the bed is given as:
W ( z ) = [4 z (DB − z )]
0.5
Where:
DB
=
Column diameter
z
=
Height of adsorbent above column base
The effective cross-sectional flow area of the bed is the product of the width and the total horizontal length of the bed, that is, W(z)L.
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Radial Bed Type Use a radial bed type when the flow through the bed is in the radial direction, from a central core to the outer circumference of the packed bed. Product Adsorbent Layer 1
Inner Core
Adsorbent Layer 2
Bed Shell
Feed
The volumes of the central core and the bed shell are the dead volumes of the column. The positive radial co-ordinate runs from the center of the bed to the outer circumference.
Configure Form (gas): Spatial Dimensions If you select a vertical bed type, you need to specify either one- or twodimensional spatial discretization: •
One-dimensional discretization — Spatial derivatives are evaluated in axial (flow) direction only.
•
Two dimensional discretization — Second order spatial derivatives are evaluated in both the axial and radial direction, allowing the calculation of radial composition and temperature distributions.
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Configure Form (gas): Internal Heat Exchanger The adsorption columns used in some temperature swing adsorption processes are equipped with internal heat exchangers to improve adsorbent regeneration. Aspen Adsim can simulate this configuration through the following sub-options: •
None, that is, no heat exchanger
•
1-Phase, internal
•
1-Phase, jacket
•
Steam-Water, internal
•
Steam-Water, jacket
The heat exchanger operates either as a jacket encircling the adsorption column or is integrated into the packed bed of the adsorbent. The heat exchange medium remains in the phase it is supplied in, or is condensed in order to use its heat of evaporation to heat the bed.
Internal Heat Exchanger
Heat Exchange Jacket
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Configure Layer Form (gas) Use the options in the Configure Layer Form to specify the bed layers. The form has the following tabs: •
General tab
•
Material/Momentum Balance tab
•
Kinetic Model tab
•
Isotherm Tab
•
Energy Balance tab
•
Reaction tab
•
Procedures tab
General Tab (gas) Use the General tab to specify the numerical options for solving the partial differential equations, and to select the gas model assumption.
General Tab (gas): Discretization Method to be used These discretization methods are available for gas phase adsorption processes: •
UDS1
•
UDS2
•
CDS1
•
CDS2
•
LDS
•
QDS
•
MIXED
•
Flux Limiter
•
BUDS
•
FROMM
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General Tab (gas): Number of Nodes In the Number of Nodes box, choose an appropriate number of axial nodes for your chosen discretization method.
General Tab (gas): Number of Radial Nodes The Number of Radial Nodes option is available only if you selected a vertical bed with a 2-D spatial dimension. Choose an appropriate number of radial nodes. The derivatives in the component material balances and the gas phase energy balances are second order in radial co-ordinates, and are approximated by central differences.
General Tab (gas): Flux Limiter to be used If flux limiter is your discretization method, choose from: •
van Leer
•
OSPRE
•
SMART
General Tab (gas): Gas Model Assumption Gas flowing through the packed bed can be ideal or non-ideal. The gas model defines the relationship between pressure, temperature and molar density:
P = Z RTg ρ g (overall) or Pyi = Z RTg ci (component) Where: P
=
Pressure
Z
=
Compressibility factor
R
=
Universal gas constant
Tg
=
Gas phase temperature
ρg
=
Molar gas phase density
yi
=
Mole fraction of component i
ci
=
Molar concentration of component i
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In the Gas Model Assumption box, choose from: •
Ideal Gas Law (where Z=1)
•
Fixed Compressibility (where Z is constant)
•
User Procedure Compressibility (where Z is supplied through a user Fortran subroutine interfaced by the procedure pUser_g_Compressibility, or calculated using a selected physical properties package)
•
User Submodel Compressibility (where Z is supplied through the user submodel gUserCompressibility)
Material/Momentum Balance Tab (gas) Use the Material/Momentum Balance tab to specify the material and momentum balances, and the 2-D dispersive properties.
About Axial Dispersion in Gas Adsorption Processes As a fluid flows through a packed column, axial mixing tends to occur. This reduces the efficiency of separation so should be minimized in column design. However, if axial dispersion occurs, the model must account for its effects. In gases, there are three main sources of axial dispersion: •
From wall effects, due to non-uniformity of packing either at the wall (wall effects) or in the core section of the packing (channeling). You can avoid this type of dispersion by having a sufficiently large ratio of bed-to-particle diameters.
•
From molecular diffusion effects.
•
From turbulent mixing effects arising from the splitting and recombining of flows around the adsorbent particles.
In general, the molecular diffusion and turbulent mixing effect are additive and proportional to the second order spatial concentration derivative, so they can be lumped together into a single effective dispersion coefficient, E i . The dispersion term in the material balance is typically expressed as:
∂ 2 ck ∂z 2
− ε i E zk Where:
εi
=
Interparticle voidage
E zk
=
Axial dispersion coefficient of component k
The type of flow determines whether this term is included or omitted in the material balance.
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It is useful to work out the Peclet number Pe using a dispersion coefficient (effective bulk diffusivity E z ), typical bed velocities (ν g ), and bed height ( H b ):
Pe =
vgH b Ez
The Peclet number quantifies the degree of dispersion introduced into the system. It is dimensionless so is more convenient to use for this purpose than the dispersion coefficient. The following table shows the effect of different values of Peclet number: If the Peclet number is
The effect of axial dispersion on bed performance is
0
Infinite: the bulk gas is perfectly mixed and the gas is homogeneous through the entire bed.
< 30
Significant.
> 100
Very slight: The bed operates under near plug flow conditions.
∞
Zero: The bed operates under plug flow conditions.
Note: The numerical methods used to model the spatial derivatives in the general equations can also introduce an artificial form of dispersion.
Material/Momentum Balance Tab (gas): Material Balance Assumption The Material Balance Assumption option is available unless you previously chose vertical bed and two-dimensional bed discretization. Choose from these options: •
Convection Only
•
Convection with Constant Dispersion
•
Convection with Estimated Dispersion
•
Convection with User Submodel Dispersion
•
Convection with User Procedure Dispersion
Material Balance Assumption (gas): Convection Only The Convection Only option drops the dispersion term from the material balance, so the model represents plug flow with a zero dispersion coefficient (infinite Peclet number). Because the dispersion term is missing, you need not supply the dispersion coefficient.
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Material Balance Assumption (gas): Convection with Constant Dispersion The Convection with Constant Dispersion option assumes that the dispersion coefficient is constant for all components throughout the bed. You supply its value.
Material Balance Assumption (gas): Convection with Estimated Dispersion The Convection with Estimated Dispersion option assumes that the dispersion coefficient varies along the length of the bed. Aspen Adsim estimates the values during the simulation. Aspen Adsim estimates the components' dispersion coefficients using the following correlation, (Kast, 1988):
E zk = 0.73Dmk +
v g rp
ε i 1 + 9.49
ε i Dmk 2v g rp
Where:
νg
=
Gas velocity
Dmk
=
Molecular diffusivity
E zk
=
Axial dispersion coefficient
εi
=
Interparticle voidage
rp
=
Particle radius
Material Balance Assumption (gas): Convection with User Submodel Dispersion If you choose Convection with User Submodel Dispersion, the (varying) dispersion coefficient is estimated using the user submodel gUserDispersion.
Material Balance Assumption (gas): Convection with User Procedure Dispersion If you choose Convection with User Procedure Dispersion, the (varying) dispersion coefficient is estimated through a user-supplied Fortran subroutine, which Aspen Adsim interfaces through the procedure pUser_g_Dispersion.
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Material/Momentum Balance Tab (gas): Momentum Balance Assumption Use the Momentum Balance Assumption box to specify how the adsorption bed layer model treats gas velocity and pressure. Base your choice on the plant operating conditions and the envisaged scope of the simulation (constant pressure models are only applicable for breakthrough investigations). Choose from: Constant pressure options—The bed is driven by gas superficial velocity and the pressure is assumed constant in the bed. The bed is velocity-driven, and no momentum balance is needed. These models are applicable only for breakthrough investigations. The constant pressure options are: •
Constant Pressure and Velocity
•
Constant Pressure with Varying Velocity
Pressure driven options—The velocity is related to the overall or internal pressure gradients. In such cases, velocity and pressure gradient are related through a momentum balance. The pressure-drop relationships apply to local conditions inside the bed, so the momentum equations for entire beds can be used to determine local pressure gradients. No simplifying assumptions are made regarding the gas densities, gas velocities, or pressures. The pressure driven options are: •
Darcy's Law
•
Karman-Kozeny Equation
•
Burke-Plummer Equation
•
Ergun Equation
Momentum Balance Assumption (gas): Constant Pressure and Velocity Use the Constant Pressure and Velocity option only when using a simple flowsheet to simulate the breakthrough behavior of an adsorption column. The gas velocity and pressure are constant along the bed, whilst the gas density is essentially constant along the bed. These assumptions are valid only when dealing with the removal of trace components from a bulk carrier gas.
Momentum Balance Assumption (gas): Constant Pressure with Varying Velocity Use the Constant Pressure with Varying Velocity option only when using a simple flowsheet to simulate the breakthrough behavior of an adsorption column. Gas density is constant along the bed, so the pressure does not vary axially. Superficial velocity varies along the bed due to the rate at which the gas is adsorbed onto the solid, or desorbed from it.
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This option is applicable to bulk separation applications, in which case the axial velocity profile is determined by an overall material balance rather than an axial pressure gradient.
Momentum Balance Assumption (gas): Darcy's Law Use this option to apply a linear relationship between the gas superficial velocity and the pressure gradient at a particular point in a bed. Darcy's law states that pressure drop is directly proportional to flow rate. You have to set the proportionality constant. The relationship is given as:
∂P = − Kpνg ∂z Where:
Kp
=
Darcy’s law proportionality constant
νg
=
Gas velocity
Momentum Balance Assumption (gas): Karman-Kozeny Equation Choose this option to use the Karman-Kozeny equation to relate velocity to pressure drop. This is the laminar component of the Ergun equation:
∂P − 1.5 × 10 −3 µ (1 − ε i ) 2 = vg ∂z (2 rpψ )2 ε i3 For details of the Karman-Kozeny model see Bird et al. (1960). Where:
ψ
=
Shape factor
µ
=
Dynamic gas viscosity
Momentum Balance Assumption (gas): Burke-Plummer Equation This option uses the Burke-Plummer equation to relate velocity to pressure gradient:
Mρ g (1 − ε i ) 2 ∂P = −1.75 × 10 −5 vg ∂z 2rpψε i3 Where: M
=
Molecular weight
The equation is valid for fully turbulent conditions when the particle Reynolds number Re is:
Re =
Mρ g 2rp v g
µ
> 1000
For details of the Burke-Plummer model, see Bird et al. (1960).
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32
Momentum Balance Assumption (gas): Ergun Equation This option uses the Ergun equation, which combines the description of pressure drops by the Karman-Kozeny equation for laminar flow and the Burke-Plummer equation for turbulent flow.
1.5 × 10 −3 (1 − ε i ) 2 (1 − ε i ) 2 ∂P −5 µ ρ v M v = − + × 1 . 75 10 g g 2 3 3 g ∂z 2 ψε r ( ) ψ ε r 2 p i p i It is valid for both laminar and turbulent flow, and is the most popular option. For details of the Ergun model, see Bird et al. (1960).
Set Variables for Pressure-Drop Options (gas) This table shows the variables you need to specify for the pressure drop options: Equation Symbol
Variable
Definition
Kp
Kp
Proportionality constant
ψ
Sfac
Sphericity
rp
Rp
Particle radius
εi
Ei
Interparticle voidage
Material/Momentum Balance Tab (gas): 2-D Dispersive Properties The 2-D Dispersive Properties option is available only if you selected vertical bed and two-dimensional discretization. The axial dispersion is calculated from:
− ε i E zk
∂ 2 ck ∂z 2
Additionally, a radial dispersion term is also evaluated:
− ε i E rk
1 ∂ ∂c k r r ∂r ∂r
If you later specify the process as non-isothermal, equivalent dispersive terms are evaluated for the gas and solid phase energy balances. Namely: •
Gas phase thermal conduction in axial direction: − ε i k gz
•
Gas phase thermal conduction in radial direction: − ε i k gr
∂ 2Tg ∂z 2 1 ∂ ∂Tg r r ∂r ∂r
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•
∂ 2Ts Solid phase thermal conduction in axial direction: − k sz ∂z 2
•
Solid phase thermal conduction in radial direction: − k sr
1 ∂ ∂Ts r r ∂r ∂r
Choose from: •
Fixed
•
Estimated
2-D Dispersive Properties (gas): Fixed Choose this option if the dispersive properties are constant throughout the packed bed. You must supply values for: •
E zk : The dispersion coefficient of component k for the axial direction.
•
Erk : The dispersion coefficient of component k for the radial direction.
For non-isothermal operation, you must give values for the following thermal conductivities: •
k g : The effective thermal conductivity of the gas phase.
•
k s : The effective thermal conductivity of the solid phase.
2-D Dispersive Properties (gas): Estimated Choose this option when variables such as pressure, temperature and velocity are changing significantly through the column. These variables influence the values of dispersion coefficients and thermal conductivities. The axial dispersion coefficient is estimated using the following correlation, (Kast, 1988):
E zk = 0.73Dmk +
v g rp
ε i 1 + 9.49
ε i Dmk 2v g rp
Where:
νg
=
Gas Velocity
Dmk
=
Molecular diffusivity of component k
E zk
=
Axial dispersion coefficient of component k
εi
=
Interparticle voidage
rp
=
Particle radius
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The radial dispersion coefficient is evaluated according to (Carberry, 1976):
E rk =
rp v g 4
Where:
Erk
=
Radial dispersion coefficient of component k
Assuming the analogy between mass and heat transfer is valid, the effective gas phase thermal conductivity in the axial direction is: nc
k gz = ρ g C pg ∑ (Ez ,i yi ) i =1
Where:
k gz
=
Effective gas phase thermal conductivity in axial direction
ρg
=
Molar gas density
C pg
=
Molar specific heat capacity at constant volume
The effective gas phase thermal conductivity in the radial direction comprises a static and a dynamic contribution (Froment and Bischoff, 1990). The two contributions are additive. Assuming the validity of the analogy between heat and mass transfer, the dynamic contribution to the effective radial gas phase thermal conductivity is: nc
k grdyn = ε i ρ g C pg ∑ (Erk yk ) k =1
Where:
k grdyn
=
Dynamic contribution to the effective gas phase thermal conductivity in radial direction
As the adsorbent (a solid) is not in motion, it has no dynamic contribution to its effective thermal conductivity in the radial direction.
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35
The static contribution of the gas phase effective thermal conductivity in the radial direction is:
k grstat = ε i (k g + β 2rpα rg )
Where:
β = 1.0 α rg
= Factor
0.227 × 10 −3 T = ε 1 − p 100 1+ 2(1 − ε ) p
3
= Radiation contribution
p
=
Emissivity
kg
=
Thermal conductivity of the gas.
The total effective radial gas phase thermal conductivity is now given by:
k gr = k grdyn + k grstat The effective radial solid phase thermal conductivity comes from:
β (1 − ε i )
k sr = k srstat =
1 kg
φ
+ α rs 2rp
+
γ ks
Where:
α rs = 0.227 ×10 −3 φ = 0.28 γ =
2 3
ks
p T 2 − p 100
3
= Radiation contribution = Function of the packing density = Factor = Thermal conductivity of the solid
Aspen Adsim assumes that the effective solid thermal conductivity in the axial direction is not a function of any process variables, so k s is constant through the simulation.
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Kinetic Model Tab (gas) Use the Kinetic Model tab to specify the model kinetics, such as resistances, diffusivities and mass transfer coefficients.
Kinetic Model Tab (gas): Film Model Assumption In the Film Model Assumption box, choose from: •
Solid, where the mass transfer driving force is expressed as a function of the solid phase loading.
•
Fluid, where the mass transfer driving force is expressed as a function of the gas phase concentration.
Kinetic Model Tab (gas): Kinetic Model Assumption Typically, several mass transfer resistances occur in gas phase adsorption processes: •
Mass transfer resistance between the bulk gas phase and the gas-solid interface.
•
Mass transfer resistance due to the porous structure of the adsorbent. In cases where the adsorbent has two distinct pore size regions, such as macropores and micropores, the resistance can be subdivided to account separately for each region.
You can consider mass transfer resistances in one these ways: •
Lumped Resistance Separate mass transfer resistances are lumped as a single overall factor, or one resistance dominates all others.
•
Micro & Macro Pore The effects of the individual resistances to mass transfer in the micro- and macropores can be accounted for individually.
•
Particle MB Where all components are adsorbed and the adsorbent has a homogenous pore structure, you can use a rigorous particle material balance to determine the loading profile inside the adsorbent.
•
Particle MB 2 Where inert components are present, or the radial gas phase concentration profiles in the pores of the adsorbent particles are to be accounted for in addition to the loading profiles. The adsorbent should possess a homogenous pore structure. This option performs a rigorous particle material balance for both the adsorbed and the gas phases.
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In the Kinetic Model Assumption box, choose from these options: •
Lumped Resistance
•
Micro and Macro Pore Effects
•
Particle MB
•
Particle MB 2
•
User Procedure
•
User Submodel
Kinetic Model Assumption (gas): Lumped Resistance Here, the separate resistances to mass transfer is lumped as a single overall factor, or one mass transfer resistance dominates the others.
Kinetic Model Assumption (gas): Micro and Macro Pore Effects Two concentration gradients greatly affect the diffusion rate: •
Within the pores of the solid.
•
Within the void spaces between the particles (that is, within the crystallines).
Under practical conditions in gas separation, pore diffusion limits the overall mass transfer rate between the bulk flow and the internal surface of a particle. This gives importance to the effect of pore diffusion on the dynamics of absorbers. The following table shows the difference between modeling macropore and micropore resistance in composite and uniform adsorbents: Pore structure
Example(s)
Micropore diffusional resistance
Macropore diffusional resistance
Uniform
Activated carbon alumina silica molecular sieve carbon
High
Negligible
Composite
Zeolites
High
High
When modeling adsorbents with uniform pore structure, you can usually discount any macropore diffusional resistance. However, when modeling composite adsorbents, both resistances can be significant and should be accounted for. Qualitatively, a higher pore diffusion rate results in a sharper and steeper concentration wave front, giving a better separation. Quantitative prediction of behavior requires the simultaneous solution of the mass balance within the particle, as well as for the bulk flow in the bed. Solving the mass balance equation within the particle is usually complex. However, you can simplify the mass balance equation in two ways: •
Use expressions that relate the overall uptake rate to the bulk flow concentration:
J ads ,i ρ s =
∂w = f (ci ) ∂t i
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38
Where:
•
ρs
=
Adsorbent bulk density
wi J ads ,i
=
Loading of component i due to adsorption
=
Mass transfer rate of component i
If you know the concentration profile within the particle, you can make considerable savings in numerical computation because integration along the radial distance in the particle is no longer necessary. Several researchers have recently shown that profiles obtained by exact numerical solutions of both Pressure Swing and Thermal Swing Adsorption processes are usually parabolic in shape, so you can model pore diffusion by assuming a parabolic concentration profile within the particle.
The model developed for particle diffusion accounts for both interparticle (macropore) and intraparticle (micorpore) diffusion effects. The model assumes that material flows first from the bulk gas to the macropores (crystallines), and then from the macropores to the solid surface via the micropores:
Bulk: cbk, εB, w*bk
Macropores: w*msk, cmsk
Interpellet Voidage: εi
Pellet (macroparticle)
rP 2rc Intrapellet Porosity εP
Solid Microporous Particles: wk, ck* cbk, εB, w*bk Bulk Gas
* cmsk, (1-εi) εP, wmsk
c*k, wk
Macropore
Solid Surface
εi Interpellet porosity
Micropore
The material balance model assumes that: •
Radial concentration profile within the particle is parabolic.
•
Concentration profile within the particle is radially symmetric.
•
Radial dispersion is negligible.
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Gas Phase The component balance in the bulk gas phase is of the form:
∂ (cbk vg ) ∂z
+ εB
∂cbk ∂w ∂c + (1 − ε p )ρ s k + (1 − ε i )ε p msk = 0 ∂t ∂t ∂t
[Convection] + [accumulation] + [mass transfer (accumulation) to micropore] + [mass transfer (accumulation) to macropore] In the given example, the gas phase material balance is written for a convection only situation in a vertical, one-dimensional adsorption layer.
Macropore (Crystalline) The material balance in the macropore is given as: Fluid Film Model:
(1 − ε i )ε p ∂cmsk + (1 − ε p )ρ s ∂wk ∂t
∂t
= K mac (cbk − cmsk )
[accumulation] + [mass transfer to micropore] = [rate of mass transfer from bulk gas] Solid Film Model:
(1 − ε i )ε p
∂wk ∂c msk * * + (1 − ε p )ρ s = (1 − ε p )ρ s K mac wbk − wmsk ∂t ∂t
(
)
Micropore (Particle) Fluid Film Model:
(1 − ε )ρ p
s
∂wk = K mic c msk − c k* ∂t
(
)
[accumulation] = [rate of mass transfer from macropore] Solid Film Model:
(1 − ε )ρ p
s
∂wk = (1 − ε p )ρ s K mic wsk* − wk ∂t
(
)
[accumulation] = [rate of mass transfer from macropore]
Specifying Particle Resistance Coefficients If you choose Micro & Macro Pore Effects, you must specify the values of the macropore and micropore resistances: K mac and K mic . The following options are available in the Form of Mass Transfer Coefficient field.
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Constant This option forces the particle resistance coefficients to be constant throughout the bed. Set the coefficients in the variable arrays Kmac and Kmic. The macropore constant K mac is given by:
K mac = 15.0
DefP rP2
Where:
DefP
=
Component diffusivities in macropores
rp
=
Particle radius
The micropore constant K mic is given by:
K mic = 15.0
Defc rc2
Where:
Defc
=
Component diffusivities in micropores
rc
=
Microparticle radius
Estimated This option uses a submodel in which Aspen Adsim automatically estimates the coefficients.
User Procedure If you choose this option, the bed model is written so that the component rates of mass transfer are related to local conditions in the bed through the procedure type pUser_g_Kinetic.
∂wi = f (Tg , P, ci , Ts , wi , v g ) ∂t Note: Langmuir adsorption kinetics is quite a popular option, and can be applied with such a procedure.
User Submodel The name of the submodel is gUserKinetic.
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Kinetic Model Assumption (gas): Particle MB This option determines the loading and gas phase concentration profiles inside an adsorbent particle, by rigorously solving the particle material balance for both phases. For this to work, the following conditions must be met: •
Adsorbent has a uniform pore structure.
•
Effective gas phase diffusion coefficient is calculated from the molecular and the Knudsen diffusion coefficients.
•
Effective diffusivities for the gas and adsorbed phase are independent of the location inside the particle.
The Particle Material Balance option considers two mass transfer resistances: •
The intraparticle mass transfer resistance, which is the diffusional resistance inside the particle pore structure, caused by both gas and adsorbed phase diffusion.
•
The interparticle mass transfer resistance, which is the resistance to mass transfer posed by the boundary layer between particle surface and bulk gas.
The following figure illustrates these resistances:
1 Gas Adsorption Processes
42
Boundary Layer
Adsorbent Particle (Uniform Pore Structure)
Bulk Gas ∂w i wi* ∂r
r =rp
Ji = aρsDei
wi(r) ∂w i ∂r
Ji
ci
∂w i ∂r
(
= a(1 − ε )k f c i − c i*
)
r =rp
=0 r =0
c*i r
rp The particle material balance is expressed as:
2 ∂wk ∂ 2 wk ∂wk − Dek + =0 ∂t ∂r 2 r ∂r Where:
wk
=
Loading
Dek
=
Effective adsorbed phase diffusion coefficient
r
=
Radial particle co-ordinate
The effective diffusion coefficient is assumed constant throughout the particle. It is calculated from the particle location inside the adsorber (axial and radial column co-ordinate) using the procedure pUser_g_De or submodel gUserEffDiff.
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43
The boundary conditions for this partial differential equation come from both the symmetry condition at r=0:
∂wi ∂r
=0 r =0
and the material flux through the boundary layer at r = rp :
∂wk ∂r
aρ s Dek
(
= a(1 − ε i )k fk c k − c k*
)
r = rp
Where: a
=
Specific particle surface
ρs
=
Bulk density of solid
εi
=
Interparticle voidage
k fk
=
Boundary layer mass transfer coefficient
ck
=
Gas phase concentration
c k*
=
Interface gas phase concentration
The gas phase composition and the loading are coupled by the condition that thermodynamic equilibrium has been achieved at the interface between gas phase and particle:
wi* = wi
r = rp
( )
= f eq ci*
Where:
f eq
=
Isotherm equation
wi*
=
Loading at r = rp
The boundary layer mass transfer coefficient is expressed using the following Sherwood number correlation:
Shi = 2 + 1.1Sci1 / 3 Re 0.6 Where:
Shi = Sci = Re =
k fi 2rp Dmi
µ Dmi ρ g M v g 2rp Mρ g
µ
=
Sherwood number
=
Schmidt number
=
Reynolds number
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44
Dmi
=
Mean molecular diffusion coefficient
µ
=
Gas phase dynamic viscosity
ρg
=
Molar gas phase density
M
=
Mean molecular weight
νg
=
Superficial velocity
Kinetic Model Assumption (gas): Particle MB 2 This option determines the loading and gas phase concentration profiles inside an adsorbent particle, by rigorously solving the particle material balance for both phases. For this to work: •
Adsorbent has a uniform pore structure.
•
Effective gas phase diffusion coefficient is calculated from the molecular and the Knudsen diffusion coefficients.
•
Effective diffusivities for gas and adsorbed phase are independent of the location inside the particle.
The Particle Material Balance 2 option considers two mass transfer resistances: •
The intraparticle mass transfer resistance, which is the diffusional resistance inside the particle pore structure, caused by both gas and adsorbed phase diffusion.
•
The interparticle mass transfer resistance, which is the resistance to mass transfer posed by the boundary layer between particle surface and bulk gas.
The following figure illustrates these resistances:
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45
Boundary Layer
Adsorbent Particle (Uniform Pore Structure)
Bulk Gas ∂w i wi* ∂r
ρs ∂w Dei i (1 − ε ) ∂r
(
= k f ci − ci*
)
r = rp rp
∂c p ∂w 3 ∫ i r 2 dr 3 ∫ i r 2 dr ∂t ∂t + (1 − ε )ε p 0 3 Ji = ρs 0 3 rp rp
r =rp
∂w i ∂r
Ji ∂c c*i ∂r
r = rp
rp
wi(r) ci
+ D p ,i
∂cip ∂r
=0 r =0
p i
r
r = rp
c pi (r)
∂cip ∂r
rp
=0 r = rp
The particle material balance is given by:
εp
2 ∂ckp ∂ 2 ckp ρ ∂wk ρ ∂ckp + − Dek s + s − D pk 2 1− ε ∂t 1 − ε ∂t ∂r r ∂r
2 ∂wk ∂ 2 wk + =0 ∂r 2 r ∂r
Where:
ε
=
Interparticle voidage
εp
=
Intraparticle voidage
ρs
=
Bulk density
wk
=
Loading
ckp
=
Gas phase concentration
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46
Dek
=
Effective adsorbed phase diffusion coefficient
D pk
=
Effective pore gas phase diffusion coefficient
r
=
Radial particle co-ordinate
The effective adsorbed phase diffusion coefficient is assumed constant through the particle. You calculate it from the particle location inside the adsorber (given by the axial and radial column co-ordinate), using the procedure pUser_g_De or the submodel gUserEffDiff. The effective pore gas diffusion coefficient is calculated from the molecular diffusion coefficient and the Knudsen diffusion coefficient:
1 1 Tort 1 = + D pi ε p DKi Dmi and
T DKi = 97rPore Mi
0.5
Where: Tort
=
Tortuosity of adsorbent
D pi
=
Effective pore gas diffusion coefficient
DKi
=
Knudsen diffusion coefficient
Dmi
=
Molecular diffusion coefficient of component i in the mixture
rPore
=
Pore radius in adsorbent
T
=
Adsorbent temperature
Mi
=
Molecular weight of component i
The boundary conditions for this partial differential equation come from both the symmetry condition at r=0:
∂wi ∂r
=0 r =0
and
∂cip ∂r
=0 r =0
1 Gas Adsorption Processes
47
and the material flux through the boundary layer at r = rp :
ρs ∂w Dei i (1 − ε ) ∂r
+ D p ,i r = rp
∂cip ∂r
(
= k fi ci − ci*
)
r = rp rp
rp
∂wi 2 ∂cip 2 r dr r dr 3∫ 3∫ ∂t ∂t 0 0 + (1 − ε )ε p Ji = ρs rp3 rp3 Where:
ρs
=
Bulk density of solid
ε
=
Interparticle voidage
εp
=
Interparticle voidage
k fi
=
Boundary layer mass transfer coefficient
ci
=
Bulk gas phase concentration
ci*
=
Interface gas phase concentration
cip
=
Pore gas phase concentration
wi
=
Loading
Ji
=
Material flux
rp
=
particle radius
D pi
=
Effective gas phase pore diffusion coefficient
Dei
=
Effective adsorbed phase diffusion coefficient
The gas phase concentration and the loading are coupled by the condition that thermodynamic equilibrium has been at each radial location inside particle, so:
( )
wi = f eq cip Where:
f eq
=
Isotherm equation
cip
=
Pore gas phase concentration
wi
=
Loading
These calculations give the isotherm correlation at each radial node, which increases the computational effort.
1 Gas Adsorption Processes
48
The boundary layer mass transfer coefficient is given by the following Sherwood number correlation:
Shi = 2 + 1.1Sci1 / 3 Re 0.6 Where:
Shi = Sci = Re =
k fi 2rp Dmi
µ Dmi ρ g M v g 2rp Mρ g
µ
=
Sherwood number
=
Schmidt number
=
Reynolds number
Dmi
=
Mean molecular diffusion coefficient
µ
=
Gas phase dynamic viscosity
ρg
=
Molar gas phase density
M
=
Mean molecular weight
νg
=
Superficial velocity
Kinetic Model Assumption (gas): User Procedure With this option, the bed model relates component rates of mass transfer to local conditions in the bed through the procedure pUser_g_Kinetic.
∂wi = f (Tg , P, ci , Ts , wi , v g ) ∂t Note: Langmuir adsorption kinetics is quite a popular option, and can be applied with such a procedure.
Kinetic Model Assumption (gas): User Submodel With this option, the bed model relates component rates of mass transfer to local conditions in the bed through the submodel gUserKineticModel.
∂wi = f (Tg , P, ci , Ts , wi , v g ) ∂t Note: Langmuir adsorption kinetics is quite a popular option, and can be applied with such a procedure.
1 Gas Adsorption Processes
49
Kinetic Model Tab (gas): Form of Lumped Resistance Model Use the Lumped Resistance option to select the overall form of the mass transfer rate model. This option determines how the model relates the mass transfer rate due to adsorption ( J ads ,i ), to the local gas and solid states. The mass transfer rate is related to the adsorbent uptake, as follows:
ρs
∂wi = J ads ,i ∂t
If you chose Lumped Resistance as the kinetic model assumption, in the Form of the Lumped Resistance Model box, you need to choose between the following driving force expressions: •
Linear
•
Quadratic
Form of Lumped Resistance Model (gas): Linear The mass transfer driving force for component i is a linear function of the gas phase concentration (fluid film) or solid phase loading (solid film). Fluid:
ρs
∂wi = MTC gi ci − ci* ∂t
(
)
Solid:
∂wi = MTC si wi* − wi ∂t
(
)
Form of Lumped Resistance Model (gas): Quadratic The mass transfer driving force is a quadratic function of the fluid film concentration or solid film loading. Fluid:
( )
(c ) − ci* ∂w ρ s i = MTC gi i ∂t 2ci 2
2
Solid:
( )
∂wi wi* − (wi ) = MTC si ∂t 2 wi 2
2
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50
Kinetic Model Tab (gas): Molecular Diffusivities This option applies if you previously selected one of the following options: •
Particle MB as your kinetic model assumption.
•
Estimated as your form of mass transfer coefficient.
In either case, mean gas phase molecular diffusivities are required for the calculation of film mass transfer coefficients. These mass transfer coefficients describe the resistance against mass transfer posed by the boundary layer surrounding the adsorbent particle.
Bulk: cbk, εB, w*bk
Macropores: w*msk, cmsk
Interpellet Voidage: εi
Pellet (macroparticle)
rP 2rc Intrapellet Porosity εP
Solid Microporous Particles: wk, ck* cbk, εB, w*bk Bulk Gas
* cmsk, (1-εi) εP, wmsk
c*k, wk
Macropore
Solid Surface
εi Interpellet porosity
Micropore
Typically, the mass transfer coefficients are evaluated from Sherwood or Colburn j-factor correlations. Values and estimation equations for diffusion coefficients for various gases are given by Bird et al. (1960) and Reid et al. (1977), for example.
Molecular Diffusivities (gas): Fixed The mean molecular diffusion coefficients are fixed for each component. You supply a value for each component into the array Dm(*) of the adsorbent layer model.
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51
Molecular Diffusivities (gas): User Procedure You supply the mean gas phase diffusion coefficients using a Fortran subroutine, which Aspen Adsim interfaces through the procedure pUser_g_Diffusivity.
Kinetic Model Tab (gas): Form of Mass Transfer Coefficients If you selected either Lumped Resistance or Micro & Macropore for your kinetic model assumption then, in the Form of Mass Transfer Coefficients box, choose from these options: •
Arrhenius
•
Constant
•
Estimated
•
Pressure Dependent Arrhenius
•
User Procedure
•
User Submodel
Form of Mass Transfer Coefficients (gas): Arrhenius This option evaluates the mass transfer coefficient as a function of temperature from an Arrhenius type equation:
− E acti MTC i = k 0i exp RT To use this option, you must supply the pre-exponential factor k 0i and the activation energy E acti for each component i, as fixed variables in the Specify table for the adsorbent layer.
Form of Mass Transfer Coefficients (gas): Constant Here, the mass transfer coefficient for each component is constant throughout the bed. You must supply a constant value of mass transfer coefficient for each component in the Specify table for the adsorbent layer.
Form of Mass Transfer Coefficients (gas): Estimated If you have selected Lumped Resistance as your kinetic model assumption, and Estimated in the Form of Mass Transfer Coefficients box, choose the Estimated Mass Transfer Coefficient Assumption from: •
Micro and Macro Pores Considered
•
Macropore Only
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Methods exist in the literature for estimating the mass transfer coefficient as a function of the supplied isotherm. One such method is based on the Henry's Coefficient. These methods rarely provide exact values; they are approximations that serve only as rough guides. They usually need to be finetuned. You can fine-tune the values by adjusting the estimated values until the timing and shape of the simulated breakthrough curves match the experimentally measured breakthrough curves. In general, the adsorption rate model for component i can be expressed as:
∂wi = k i wi* − wi = k i K Ki ci − ci* ∂t
(
)
(
)
The effective mass transfer coefficient is given as a lumped term comprising the external film resistance term, the macropore diffusion term, and the micropore diffusion term:
rp rp2 rc2 1 = + + k i 3k fi 15ε p K pi 15 K Ki Dci The Henry's coefficient K Ki is obtained from the isotherm as:
K Ki =
∂wi* ∂w* = RT i ∂ci ∂Pi
The dimensionless Henry’s coefficient, K Ki , is obtained by:
K Ki = K Ki
ρs εi
The film resistance coefficient k fi is obtained from the Sherwood number as:
k fi = Shi
Dmi 2r p
Where:
Shi = 2.0 + 1.1Sci1 / 3 Re 0.6 Re
=
Reynolds number
Sci
=
Schmidt number
=
µ (Dmi ρ s )
The macropore diffusion coefficient K pi is obtained from:
1 1 1 = Tort + K pi DKi Dmi
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53
The Knudsen diffusion coefficient D Ki is:
T DKi = 97rPore Mi
0.5
Where:
ρg
=
Gas density
Dci
=
Micropore diffusion coefficient
DKi
=
Knudsen diffusion coefficient
Dmi
=
Multi-component molecular diffusion coefficient
ep
=
particle (macro) porosity
ki
=
effective mass transfer coefficient
K Ki
=
Henry's coefficient
k fi
=
Film resistance coefficient
K pi
=
Macropore diffusion coefficient
w
=
Loading
R
=
Universal Gas Constant
rc
=
Radius of crystalline or primary micropore
rp
=
Particle radius
Tort
=
Tortuosity factor
µ
=
Dynamic viscosity
To include the effect of the micropore resistance in the estimated values for the mass transfer coefficients: •
Give values for the micropore diffusion coefficients and the radius of the primary micropore.
To ignore the micropore effect: •
In the Estimated Mass Transfer Coefficient Assumption box, select Macropore only.
Form of Mass Transfer Coefficients (gas): Pressure Dependent Arrhenius This option is based on the Arrhenius model, but also accounts for changes in total pressure. As such it is especially suitable for PSA systems. The model was found to represent experimental data well.
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54
MTC i =
k 0 Pi − E acti exp P RT
You have to supply the pre-exponential factor k 0 Pi and the activation energy
E acti for each component i, as fixed variables in the Specify table for the adsorbent layer.
Form of Mass Transfer Coefficients (gas): User Procedure Here, the mass transfer coefficients are estimated using a Fortran subroutine, which Aspen Adsim interfaces through the procedure pUser_g_MTC.
Form of Mass Transfer Coefficients (gas): User Submodel If you choose this option, the mass transfer coefficients are estimated and then returned through the submodel gUserMTC.
Kinetic Model Tab (gas): Apply Cyclic Correction This option is available only if you selected Lumped Resistance as your kinetic model assumption, and either Constant or Estimated in the Form Of Mass Transfer Coefficient box. Furthermore, this option applies only to cyclic processes and especially PSA systems. The Glueckauf (see Yang, 1987 for example) approximation of a lumped mass transfer coefficient states:
MTC s ,i =
ΩDei rP2
with Ω=15. Nakao and Suzuki (1983) showed that the value of 15 underestimates the magnitude of the mass transfer coefficient for short adsorption times. Assuming that an adsorption column is in adsorbing mode for about half the total time of the adsorption cycle, the following time constant can be calculated:
θ = 0.5
De t Cycle rP2
The parameter Ω is a function of θ:
θ ≥ 0 .1
: Ω = 15
0.001 ≤ θ < 0.1 : Ω =
θ ≤ 0.001
5.14
θ
: Ω = 162.5
The above equations are evaluated automatically by Aspen Adsim when you select this option.
1 Gas Adsorption Processes
55
Kinetic Model Tab (gas): Estimated Mass Transfer Coefficient Assumption This option is available only if you selected Estimated as your estimated mass transfer coefficient.
Gas Adsorption Layer (gas): Particle Material Balance, Number of Nodes This option is available only if you selected Particle MB or Particle MB 2 as your kinetic model assumption. It determines how many nodes to use for the central finite difference discretization of the second order derivative in the particle material balance:
1 ∂ 2 ∂w 2 wk +1 − wk −1 wk +1 − 2 wk + wk −1 + r ≈ 2(∆r ) r 2 ∂r ∂r rk (∆r )2
Kinetic Model Tab (gas): Particle Material Balance, Effective Diffusivity This option is available only if you selcted Particle MB or Particle MB 2 as your Kinetic Model Assumption. With this option, the form of the effective adsorbed phase diffusion coefficient is determined. Choose one of three options: •
Fixed
•
User Procedure
•
User Submodel
Particle Material Balance, Effective Diffusivity (gas): Fixed With this option, the effective diffusion coefficients for each component in the adsorbed phase are given a constant value, which you supply through the array De(*) of the adsorbent layer model.
Particle Material Balance, Effective Diffusivity (gas): User Procedure You supply the mean adsorbed phase diffusion coefficients using a Fortran subroutine, which Adsim interfaces through the procedure pUser_g_De.
Particle Material Balance, Effective Diffusivity (gas): User Submodel You supply the mean adsorbed phase diffusion coefficients through the user submodel gUserEffDiff.
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56
Isotherm Tab (gas) Use the Isotherm tab to define the adsorption isotherms to be used in your gas adsorption process. The Aspen Adsim isotherm models are expressed as functions of either partial pressures or concentrations. When you use Aspen Adsim isotherm models for pure components or for multi-component mixtures, you must supply isotherm parameters consistent with the functional form. It is imperative that you convert isotherm parameters to Aspen Adsim's base units of measurement, which are listed in the following table: Variable
Unit of measurement
Loading (w)
kmol/kg
Gas phase concentration (c)
kmol/m3
Pressure (P)
bar
Temperature (T)
K
About Adsorption Isotherms for Gas Adsorption Processes Adsorption is the tendency of molecules from an ambient fluid phase (gas or liquid) to stick to the surface of a solid. Most of the important industrial applications of adsorption depend on differences in the affinity of the solid surface for different components. Adsorption isotherms describe the tendency for the components to adsorb onto the solid; they describe the amount of each component adsorbed onto the solid at thermodynamic equilibrium. The driving force behind all adsorptive gas separation processes is the departure from adsorption equilibrium, so adsorption isotherms are crucially important data in the design of adsorbers. If you know the adsorption isotherms for the components of the feed, you can create a bed model to predict the performance of the adsorber bed for the specified operating conditions. Aspen Adsim has a comprehensive list of adsorption isotherms. You choose these isotherms from the Configurure Layer forms for the layers making up the bed model. This section explains these choices for pure component, multicomponent, and user-supplied isotherms. For more information, see Chapters 2 through 4 in Ruthven, 1984, Chapters 2 and 3 in Yang, 1987, and Chapter 3 in Kast, 1988 (German language).
1 Gas Adsorption Processes
57
Guidelines for Choosing Aspen Adsim Isotherm Models (gas) Choose a model that is appropriate to the process you are investigating. The equilibrium specified by the isotherm model affects the driving force for mass transfer, so you can get significantly different simulation results when using different models, even if the model parameters are derived from exactly the same set of data. The isotherm model parameters are always set variables. You can estimate these parameters from experimental data, or use published literature values. Important: The expressions in this section are equilibrium equations. Depending on the mass transfer rate model you choose, the expressions compute either: •
w*, the loading which would be at equilibrium with the actual gas phase composition - or -
•
c*, the gas phase composition which would be at equilibrium with the actual loading.
The choice between w* and c* is automatically handled by Aspen Adsim. Aspen Adsim names the equilibrium variable arrays (of size n or n×m) either Ws or Cs. In bed models, these variables are distributed axially, or axially and radially, and have indices to identify their location in the bed.
About Multi-Component Mixture Isotherms (gas) In adsorber design, you are usually interested in the adsorption equilibria of mixtures, rather than those of pure components. This is because adsorbed gas components interact on the solid surface, so individual gas components adsorb in a different fashion when mixed with other components. Mixture adsorption equilibria data are not readily available. Although measurements can be made, they are tedious and time-consuming to perform, so it is common practice to predict mixture isotherms from pure component isotherms. Several methods for predicting mixture isotherms from pure component data have been proposed recently, including: •
Vacancy Solution
•
Extended Langmuir Approach
•
Ideal Adsorbed Solution
•
Real Adsorbed Solution Theory
Most of the physical adsorption models contain two or three parameters, and the parameters for mixture isotherms are written as a function of the pure component parameters and the composition of the adsorbed phase.
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58
Vacancy Solution (gas) The vacancy solution is the least popular of all the methods, but the approach has been developed in a limited number of cases for some single and multicomponent systems.
Extended Langmuir Approach (gas) This is an extension of the Langmuir isotherms for single components. Langmuir models use a weighting factor to account for the inter-species interaction in mixtures. The extended Langmuir approach takes a single component gas isotherm parameter and, depending on the components of the multi-component gas mixture, calculates a fitting parameter to account for the presence of other components. The values of the interaction parameters depend on all the species present. The value of the weighted inter-species interaction parameter is obtained from mixture experimental data.
Ideal Adsorbed Solution (gas) Recently, the Ideal Adsorbed Solution Theory (IAS) has become popular for multi-component mixtures. The method enables you to predict adsorption equilibria for components in a gaseous mixture. It requires data only for the pure-component adsorption equilibria at the same temperature and on the same adsorbent. The model treats the mixed adsorbate phase as an ideal solution in equilibrium with the gas phase. The Gibbs approach is used for vapor-liquid equilibria, in which the fundamental equations of thermodynamic equilibrium are developed, and applies this to the gas-adsorbed phase equilibria. At first sight, ideal behavior in the adsorbed phase seems improbable. However, many systems have shown strong correlation between experimental data and predictions by IAS theory, including binary and ternary mixtures on activated carbons, zeolites, and silica gel. For a full description of the IAS approach, see Chapter 4 of Ruthven (1984) or Chapter 3 of Kast (1988) (German language). IAS is available in Aspen Adsim. To use it, choose the appropriate isotherm on the Isotherm Tab of the layer configuration form. The basic requirements for thermodynamic equilibrium between two phases are that the pressure, temperature and chemical potential of each component are equal in both phases. The chemical potential for an adsorbed phase can be written as (Kast, 1988):
µ ads ,i (T , Π , xi ) = µ i0 (T ) + RT ln (Pi 0 (Π )) + RT ln (γ i xi )
The chemical potential for an ideal gas phase is given by:
µ gas ,i = µ i0 (T ) + RT ln ( yi P ) The equilibrium condition is:
µ gas ,i = µ ads ,i
1 Gas Adsorption Processes
59
Assuming ideal behavior in the adsorbed phase (that is,
γ i = 1 ), an expression
analogous to Raoult’s law can be derived:
yi P = xi Pi 0 (Π ) 0
The pressure Pi is a fictitious pure component gas phase pressure, which gives the same spread pressure in the adsorbed phase as the gas mixture at 0
pressure P. The relationship between Pi and the spreading pressure
Π i0
is
derived using the Gibbs-Duhem equation for a single adsorbed component:
(
)
AdΠ i0 = wi0 dµ i0 = wi0 RTd ln( Pi 0 (Π )
0
On integrating and using the pure component isotherm to replace wi :
AΠ i0 = RT
Pi0
∫ 0
f eq (T , P, IP ) dP P
The equation set is completed with the following conditions: n
∑x i =1
=1
i
n
∑y i =1
i
=1
Π i0 = Π 0j = Π k0 = ... The total loading and component loadings are calculated from: n
xi
∑w i =1
0 i
=
1 wtot
and
wi = xi wtot Real Adsorbed Solution Theory (gas) The derivation of the Ideal Adsorbed Solution Theory (see earlier) assumed ideal behavior in the adsorbed phase. This assumption resulted in the activity coefficient of each component being set to unity ( γ i = 1 ). Non-ideal behavior in the adsorbed phase can be accounted for by evaluating the activity coefficient using a suitable Gibbs excess enthalpy correlation (for E
example, Wilson or UNIQUAC). The binary parameters of the g models have to be determined from suitable experiments (Costa et al., 1981). Once those parameters are known, AspenTech’s Aspen Properties system is used to supply the value of γ i so that:
yi P = γ i xi Pi 0 (Π ) can be evaluated.
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60
Isotherm Tab (gas): Isotherm Assumed for Layer Aspen Adsim enables you to use a number of pure component isotherms and multi-component isotherms. In the Isotherm Assumed for Layer box, select from: •
Langmuir Models
•
Freundlich Models
•
Langmuir-Freundlich Model
•
Henry's Models
•
Toth Model
•
B.E.T. (Brunauer, Emmett & Teller) Models
•
B.E.T. Multilayer
•
Dubinin-Astakov Model
•
Linear Model
•
Volmer Model
•
Myers Model
•
Extended Langmuir Models
•
Extended Langmuir- Freundlich Model
•
Dual-Site Langmuir Model
•
Single Layer B.E.T
•
Dual Layer B.E.T
•
User Procedure
•
User Submodel
•
IAS
Isotherm Assumed for Layer (gas): Langmuir Models Langmuir isotherm models typically apply to the adsorption of a single molecule layer on completely homogeneous surfaces, with negligible interaction between adsorbed molecules. There are three standard sub-options for the pure component Langmuir isotherms supported in Aspen Adsim: Langmuir 1. The isotherm is a function of a partial pressure or concentration:
wi =
IP1 Pi 1 + IP2 Pi
(partial pressure)
IP1ci 1 + IP2 ci
(concentration)
or
wi =
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61
Langmuir 2. The isotherm is a function of temperature, and one of partial pressure or concentration:
IP1e IP2 / Ts Pi wi = 1 + IP3 e IP4 / Ts Pi
(partial pressure)
or
IP1e IP2 / Ts ci wi = 1 + IP3 e IP4 / Ts ci
(concentration)
Langmuir 3. The isotherm is a function of temperature, and one of partial pressure or concentration. Unlike Langmuir2, the maximum loading, expressed by (IP1 − IP2Ts ) , is a function of temperature, so reflects more accurately the physical reality of numerous adsorption processes:
wi =
(IP1 − IP2Ts )IP3 e IP / T Pi 4
s
1 + IP3 e IP4 / Ts Pi
(partial pressure)
or
wi =
(IP1 − IP2Ts )IP3 e IP / T ci 4
1 + IP3 e IP4 / Ts ci
s
(concentration)
Isotherm Assumed for Layer (gas): Freundlich Models Aspen Adsim has two sub-options for the pure component Freundlich isotherms: Freundlich 1. The isotherm is a function of partial pressure or concentration:
wi = IP1 Pi IP2
(partial pressure)
or
wi = IP1C iIP2
(concentration)
Freundlich 2. The isotherm is a function of temperature, and one of partial pressure or concentration:
wi = IP1e IP3 / Ts Pi IP2
(partial pressure)
or
wi = IP1e IP3 / Ts ciIP2
(concentration)
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62
Isotherm Assumed for Layer (gas): Langmuir-Freundlich Model This isotherm is a function of temperature, and one of partial pressure or concentration:
IP1 IP2 PiIP3 e IP4 / Ts wi = 1 + IP5 PiIP3 e IP6 / Ts
(partial pressure)
or
IP1 IP2 ciIP3 e IP4 / Ts wi = 1 + IP5 ciIP3 e IP6 / Ts
(concentration)
Isotherm Assumed for Layer (gas): Henry's Models Aspen Adsim has two sub-options of the pure component Henry's isotherms: Henry 1. The isotherm is a function of partial pressure or concentration:
wi = IP1Pi
(partial pressure)
or
wi = IP1ci
(concentration)
Henry 2. The isotherm is a function of temperature, and one of partial pressure or concentration:
wi = IP1e IP2 / Ts Pi
(partial pressure)
or
wi = IP1e IP2 / Ts ci
(concentration)
Isotherm Assumed for Layer (gas): Toth Model The isotherm is a function of partial pressure or concentration: 1
( IP1 Pi ) wi = IP2 1 + ( IP3 Pi ) IP2
IP2
(partial pressure)
or 1
( IP1ci ) IP2 IP2 wi = IP2 1 + ( IP3 ci )
(concentration)
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63
Isotherm Assumed for Layer (gas): B.E.T Use the B.E.T. (Brunauer, Emmett and Teller) type isotherm (or multilayer Langmuir relation) for gas-solid systems in which condensation is approached, and hence the number of adsorbed layers is extremely large. This isotherm is a function of temperature and one of partial pressure or concentration:
IP IP1 Pi exp 2 Ts wi = IP4 IP 1 − IP5 Pi exp 6 1 + IP3 Pi exp Ts Ts
(partial pressure)
or
IP IP1ci exp 2 Ts wi = IP4 IP 1 − IP5 ci exp 6 1 + IP3 ci exp Ts Ts
(concentration)
Isotherm Assumed for Layer (gas): BET Multilayer The BET Multilayer isotherm is similar to the BET isotherm, but has an additional parameter, IP4 , stating the number of layers adsorbed. Physically, it fills the gap between the Langmuir isotherm (single layer BET) and the BET isotherm with an infinite number of layers. Use it only for systems where the operating temperature is below the critical temperature of the adsorbate. The isotherm is always evaluated as a function of the relative pressure:
φi =
Pi Psat
If you selected concentration dependency, the following equation is used to calculate the partial pressure:
Pi = ci RTg The saturation pressure Psat is calculated according to a base 10 Antoine equation, using degrees Celsius or Kelvin as temperature units of measurement. The parameter IP8 is then a conversion factor for calculating
Psat in bar. Psat = IP8 × 10
IP5 −
IP6 IP7 + Ts
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64
The kinetic factor b is:
IP b = IP2 exp 3 Ts The isotherm is:
IP bφ 1 − (IP4 + 1)φ IP4 + IP4φ IP4 wi = 1 IP4 +1 1 − φ 1 + (b − 1)φ − bφ
Isotherm Assumed for Layer (gas): Dubinin-Astakov Model This isotherm is a function of temperature, and one of partial pressure or concentration:
[
]
[
wi = IP1 exp − ( AA / IP2 ) 2 + IP3 exp − ( AA / IP4 ) 2
]
Where:
P AA = RTs ln i Psat
(partial pressure)
or
c RT AA = RTs ln i s Psat
(concentration)
and
Psat = IP8 10
IP6 IP5 − Ts − IP7
IP8 is a conversion factor to convert the resulting partial pressure predicted by the Log10 base Antoine Equation, into bar (Aspen Adsim's base unit of measurement for pressure).
Isotherm Assumed for Layer (gas): Linear Model This isotherm is a function of partial pressure or concentration:
wi = IP1 Pi + IP2
(partial pressure)
or
wi = IP1ci + IP2
(concentration)
Isotherm Assumed for Layer (gas): Volmer Model The Volmer isotherm expresses concentration as a function of loading:
ci =
IP1 wi IP1 wi exp IP2 − IP1 wi IP2 − IP1 wi
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65
Isotherm Assumed for Layer (gas): Myers Model TheMyers isotherm expresses concentration as a function of loading:
w ci = IP1 exp IP2 i IP1 Isotherm Assumed for Layer (gas): Extended Langmuir Models There are three standard sub-options of the extended Langmuir isotherms supported in Aspen Adsim: Extended Langmuir 1. This isotherm is a function of partial pressure or concentration:
wi =
IP1i Pi 1 + ∑ (IP2 k Pk )
(partial pressure)
IP1i ci 1 + ∑ (IP2 k c k )
(concentration)
k
or
wi =
k
Extended Langmuir 2. This isotherm is a function of temperature, and one of partial pressure or concentration:
IP1i e IP2 i / Ts Pi 1 + ∑ IP3k e IP4 k / Ts Pk
(
)
(partial pressure)
IP1i e IP2 i / Ts ci wi = 1 + ∑ IP3k e IP4 k / Ts c k
)
(concentration)
wi =
k
or
(
k
Extended Langmuir 3. This isotherm is a function of temperature, and one of partial pressure or concentration:
( IP1i − IP2i Ts ) IP3i e IP4 i / Ts Pi wi = 1 + ∑ IP3k e IP4 k / Ts Pk
(
)
(partial pressure)
k
or
wi =
( IP1i − IP2i Ts ) IP3i e IP4 i / Ts ci 1 + ∑ IP3k e IP4 k / Ts c k
(
)
(concentration)
k
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66
Isotherm Assumed for Layer (gas): Extended LangmuirFreundlich Model This isotherm is a function of temperature, and one of partial pressure or concentration:
wi =
IP1i IP2i Pi IP3i e IP4 i / Ts 1 + ∑ IP5 k PkIP3 k e IP4 k / Ts
)
(partial pressure)
IP1i IP2i ciIP3i e IP4 i / Ts 1 + ∑ IP5 k c kIP3 k e IP4 k / Ts
)
(concentration)
(
k
or
wi =
(
k
Isotherm Assumed for Layer (gas): Dual-Site Langmuir Model This isotherm is a function of temperature, and one of partial pressure or concentration:
IP1i e IP2 i / Ts Pi IP5i e IP6 i / Ts Pi Wi = + 1 + ∑ ( IP3k e IP4 k / Ts Pk ) 1 + ∑ ( IP7 k e IP8 k / Ts Pk )
(partial pressure)
k
k
or
IP1i e IP2 i / Ts ci IP5i e IP6 i / Ts ci Wi = + 1 + ∑ ( IP3k e IP4 k / Ts ck ) 1 + ∑ ( IP7 k e IP8 k / Tk ck )
(concentration)
k
k
Isotherm Assumed for Layer (gas): Single Layer B.E.T. This isotherm is an extended B.E.T isotherm with a monolayer. It is equivalent to the extended Langmuir isotherm. The isotherm is a function of temperature, and one of partial pressure or concentration:
IP1i IP2i Pi e IP3i / Ts wi = 1 + ∑ IP2 k Pk e IP3 k / Ts
(
)
(partial pressure)
IP1i IP2i ci e IP3i / Ts wi = 1 + ∑ IP2 k ck e IP3 k / Ts
)
(concentration)
k
or
(
k
1 Gas Adsorption Processes
67
Isotherm Assumed for Layer (gas): Dual Layer B.E.T. This isotherm is a function of temperature, and one of partial pressure or concentration:
(
IP3 i / Ts
IP2i e IP3i / Ts IP4i ∑ IP2 k Pk e IP3 k / Ts
)
IP1i IP2i Pi e k + wi = 1 + ∑ IP2 k Pk e IP3 k / Ts IP3 k / Ts IP3 k / Ts k 1 + ∑ IP2 k Pk e 1 + IP4 k ∑ IP2 k Pk e k k
(
)
(
)
(
)
(partial pressure) or
(
)
IP2i e IP3i / Ts IP4i ∑ IP2 k ck e IP3 k / Ts IP1i IP2i ci e IP3i / Ts k + wi = 1 + ∑ IP2 k ck e IP3 k / Ts IP3 k / Ts IP3 k / Ts k 1 + ∑ IP2 k ck e 1 + IP4 k ∑ IP2 k ck e k k
(
)
(
)
(
)
(concentration)
Isotherm Assumed for Layer (gas): User Procedure You can supply your own proprietary isotherm relationships using a Fortran subroutine, which Aspen Adsim interfaces through either the procedure pUser_g_Isotherm_P (partial pressure dependent isotherm) or pUser_g_Isotherm_C (concentration dependent isotherm). The functional relationship is:
wi = f eq (T , P, y1 ... y nc , IP )
(partial pressure)
or
wi = f eq (T , c1 ...cnc , IP )
(concentration)
You can also supply pure component user-specified isotherms, for use as multi-component isotherms, using the IAS method. Here, you must supply two Fortran subroutines: •
The first subroutine is interfaced by the procedure pUser_g_Isotherm_Poi. This procedure relates the fictitious pure component partial pressure Pi
0
(resulting in the same spread pressure as the mixture at pressure P), to 0
the loading wi by means of a pure component isotherm:
(
wi0 = f eq T , Pi 0 , IP •
)
The second subroutine integrates the Gibbs isotherm to give the spread pressure. It is interfaced by the procedure pUser_g_Gibbs. The relationship to be evaluated is:
AΠ i0 = g T , Pi 0 , IP with g = RT
(
)
Pi0
∫ 0
f eq (T , P, IP ) P
dP
1 Gas Adsorption Processes
68
Isotherm Assumed for Layer (gas): User Submodel You can supply your own proprietary isotherm relationships using one of these two submodels: •
gUserIsothermPp (partial pressure dependent isotherm)
•
gUserIsothermC (concentration dependent isotherm)
The functional relationship is:
wi = f eq (T , P, y1 ... y nc , IP )
(partial pressure)
or
wi = f eq (T , c1 ...cnc , IP )
(concentration)
Pure component user specified isotherms may be supplied and used as multicomponent isotherms using the IAS method, in which case you must supply two submodels: •
The first submodel is gUserIsothermPoi. This relates the fictious pure 0
component partial pressure Pi (resulting in the same spread pressure as 0
the mixture at pressure P), to the loading wi by means of a pure component isotherm:
(
wi0 = f eq T , Pi 0 , IP •
)
The second submodel is gUserGibbs. This integrates the Gibbs isotherm to give the spread pressure. The relationship to be evaluated is:
AΠ i0 = g T , Pi 0 , IP with g = RT
(
)
Pi0
∫ 0
f eq (T , P, IP ) P
dP
Isotherm Assumed for Layer (gas): IAS The IAS facility in Aspen Adsim lets you calculate competitive, multicomponent adsorption behavior using pure component isotherms. Each pure component isotherm has the same expression as its pure component version. Aspen Adsim's standard pure component isotherms available with IAS are: •
Langmuir models
•
Freundlich models
•
Langmuir-Freundlich models
•
Henry's models
•
BET multilayer
•
User-specified isotherms (user procedure or user submodel)
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69
Isotherm Tab (gas): Adsorbed Solution Theory If you choose an IAS isotherm, you can then use either the ideal adsorbed solution theory (IAS) or the real adsorbed solution theory (RAST). The two options are: •
IAS
•
RAST
With RAST selected and with user procedures supplying the physical properties, you must write a Fortran procedure to supply the activity coefficients. The procedure is described by the type pUser_Act_Coeff. The procedure evaluates γ i as a function of temperature, pressure and the composition of the adsorbed phase:
γ i = f (T , p, x1 ,..., xnc )
Isotherm Tab (gas): Isotherm Dependency In the isotherm dependency box, choose from: •
Concentration — The adsorption isotherm model is a function of concentration.
•
Partial Pressure — The adsorption isotherm model is a function of partial pressure.
Energy Balance Tab (gas) Use the Energy Balance tab to specify how the energy balance is incorporated into the model for your gas adsorption process.
Energy Balance Tab (gas): Energy Balance Assumption In the Energy Balance Assumption box, choose your prefered type of energy balance, from: •
Isothermal
•
Non-Isothermal with No Conduction
•
Non-Isothermal with Gas Conduction
•
Non-Isothermal with Solid Conduction
•
Non-Isothermal with Gas and Solid Conduction
•
None
For a vertical bed type with 2-D spatial dimension, the conduction options are not available as conduction is automatically considered for all dimensions.
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70
Energy Balance Assumption (gas): Isothermal The Isothermal option completely ignores the energy balance. The gas temperature Tg and the solid temperature Ts are held constant and equal.
Energy Balance Assumption (gas): Non-Isothermal with No Conduction This option ignores the axial thermal conduction for the gas and solid phases.
Energy Balance Assumption (gas): Non-Isothermal with Gas Conduction This option includes the thermal conduction (axial thermal dispersion) term in the gas energy balance:
∂ 2T − εi k ∂z 2
g
gz
You need to define the form of the gas thermal conductivity.
Energy Balance Assumption (gas): Non-Isothermal with Solid Conduction This option includes the thermal conduction term in the solid energy balance:
− k sz
∂ 2Ts ∂z 2
You must supply a value for k sz in the Specify table for the layer.
Energy Balance Assumption (gas): Non-Isothermal with Gas and Solid Conduction This option includes the thermal conduction term for both gas and solid phases. You must define the form of the gas thermal conductivity. See Energy Balance Tab: Form of Gas Thermal Conductivity, later.
Energy Balance Tab (gas): Consider Heat of Adsorbed Phase Aspen Adsim models also let you include the enthalpy content of the adsorbed phase in the solid-phase energy balance. The Enthalpy of Adsorbed Phase term is optional. If the enthalpy content of the adsorbed phase is significant for your process, choose this option to include it in the solid phase energy balance. The term for each component is a function of the loading and the temperature in the solid phase, the adsorbed phase heat capacity, and the solid density:
H i = ρ s C pai wi
∂Ts ∂t
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71
The total contribution is the sum for all components:
∑(H ) i
i
This equation is quite rigorous, despite neglecting some second order terms such as enthalpy of mixing. In the Consider Heat of Adsorbed Phase box, choose from: •
None
•
Constant
•
User Procedure
•
User Submodel
Consider Heat of Adsorbed Phase(gas): None If you choose this option, the enthalpy of adsorbed phase term is ignored in the solid phase energy balance.
Consider Heat of Adsorbed Phase(gas): Constant Here, the heat capacities of the adsorbed phase components C pai are constant.
Consider Heat of Adsorbed Phase(gas): User Procedure With this option, the heat capacities of the adsorbed phase components C pai are calculated using a user-defined subroutine, which Aspen Adsim interfaces through the procedure pUser_g_Cpa.
Consider Heat of Adsorbed Phase(gas): User Submodel The heat capacities of the adsorbed phase components C pai are calculated through the user-defined submodel gUserCpa.
Energy Balance Tab (gas): Heat of Adsorption Assumption You must include the heat of adsorption in the solid-phase energy balance if it is significant for the process. The rate of heat generation by adsorption of each component i per unit mass of solid, depends on the local rate of mass transfer (the change in the amount of material adsorbed):
HTi =
∂w ∆H i ∂t i
These rates are held in vectors, HT, and summed for all components to obtain the total rate of heat generation by adsorption per unit volume of solid:
ρ
s
∑ (− HT ) i
i
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72
In the Heat of Adsorption Assumption box, choose from: •
None
•
Constant
•
User Procedure
•
User Submodel
Heat of Adsorption Assumption (gas): None The heat generation by adsorption term is omitted from the energy balance.
Heat of Adsorption Assumption (gas): Constant With this option, the heat of adsorption is constant for each component i. Choose it to set the heat of adsorption to constant values, which you supply in the Specify table for the layer for each component.
Heat of Adsorption Assumption (gas): User Procedure Here, the heat of adsorption is given by the Fortran procedure pUser_g_DH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms:
∆H ij = f (Tsj , Pj , wij ) Where i designates the component and j designates the node.
Heat of Adsorption Assumption (gas): User Submodel With this option, the heat of adsorption comes from the submodel gUserDH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms:
∆H ij = f (Tsj , Pj , wij ) Where i designates the component and j designates the node.
Energy Balance Tab (gas): Form of Heat Transfer Coefficient If you specify a non-isothermal energy balance, Aspen Adsim generates the solid and gas-phase energy balances with a film resistance to the heat transfer between the solid and the gas. Heat transfer is assumed to occur between the two phases according to the film resistance model:
rate of heat transferred per m 3 of bed = HTC a p (Tg − Ts ) If there is no such heat transfer resistance, the gas and solid temperatures are equal (lumped):
Tgj = Tsj for all nodes j = 1, m To get this condition, set the heat transfer coefficient to a large value (such as 1).
1 Gas Adsorption Processes
73
In the Form of Heat Transfer Coefficient box, choose from: •
Constant
•
Estimated
•
User Procedure
•
User Submodel
Form of Heat Transfer Coefficient (gas): Constant Choose this option to make the heat transfer coefficient a constant value, which you set through the variable HTC in the Specify table for the layer.
Form of Heat Transfer Coefficient (gas): Estimated The heat transfer coefficient is estimated as follows: 1
Calculate the Reynolds number:
Re =
2rp M ρ g v g
µ
If the calculated value falls below 1E-10, it is reset to this value. 2
Calculate the Prandl number:
Pr =
µ C pg kg M
If the calculated value falls below 1E-10, it is reset to this value. 3
Calculate the j-factor: If Re < 190 then j = 1.66 Re
4
−0.51
otherwise j = 0.983Re
−0.41
Calculate the heat transfer coefficient:
HTC = jC pg v g ρ g Pr
−2
3
If the calculated value falls below 1E-10, it is reset to a value of 1.
Form of Heat Transfer Coefficient (gas): User Procedure With this option, the user procedure pUser_g_HTC relates the local heat transfer coefficient to the state of the bed at a particular point in the bed. This means you can interface your own Fortran code to calculate the coefficients. Note that the heat transfer coefficient becomes a distributed variable when you select this option. The values are held in the variables HTC(1), HTC(2)……HTC(n). In general terms:
HTC j = f (Tgj , Pj , c j , vgj ) Form of Heat Transfer Coefficient (gas): User Submodel Here, the local heat transfer coefficient is defined through the user submodel gUserHTC, using the same dependencies as in the User Procedure option.
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74
Energy Balance Tab (gas): Form of Gas Thermal Conductivity If you selected non-isothermal with gas and/or solid conduction, you need to choose the form of gas thermal conductivity. In the Form of Gas Thermal Conductivity box, choose from: •
Constant
•
Based on Axial Dispersion
•
User Procedure
•
User Submodel
Form of Gas Thermal Conductivity (gas): Constant The thermal conductivity k g has a constant value, which you set in the layer Specify form.
Form of Gas Thermal Conductivity (gas): Based on Axial Dispersion This option assumes that the analogy between heat transfer and mass transfer is valid. The effective thermal conductivity coefficient is calculated as the product of the heat capacity of the gas, the axial dispersion coefficient, and the density of the gas:
k gz
=
(Heat capacity) x (Averaged Axial dispersion coefficient) x
(Molar density)
k gz = C pg ∑ (Ezk yk )ρ g k
Form of Gas Thermal Conductivity (gas): User Procedure The thermal conductivity varies axially along the bed. If you supply the necessary physical properties directly, Aspen Adsim interfaces a Fortran subroutine through the procedure pUser_g_Kg. If the physical properties come from a package such as PROPERTIES PLUS, Aspen Adsim handles the required calls automatically.
Form of Gas Thermal Conductivity (gas): User Submodel The thermal conductivity varies axially along the bed and is defined in the user submodel gUserKg.
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75
Energy Balance Tab (gas): Heat Transfer to Environment In the Heat Transfer to Environment box, choose from: •
Adiabatic
•
Thin Wall
•
Rigorous Model
Heat Transfer to Environment (gas): Adiabatic No heat transfer occurs between the bed and the wall.
Heat Transfer to Environment (gas): Thin Wall With this option, the heat exchange between the gas in the bed and the environment is included in the gas phase energy balance as:
4H w (Tg − Tamb ) DB The conductivity along the wall and the heat accumulation in the wall are neglected. H w combines the heat transfer resistances of: •
Boundary layer between gas and wall, on the inside of the column.
•
Material of the column wall, including insulation material.
•
Boundary layer between the outer column wall and the surroundings.
The following equation (Bird et al., 1960) calculates H w for the column cross section shown in the Heat Transfer to Environment figure (on the next page).
D ln D1 ln o D D 1 Di 1 i 1 + + + Hw = Do k2 k1 2 Di H H wo wi 2 2
−1
−1
1 Gas Adsorption Processes
76
Do D1 Di
Tg
Tamb
Hwi
k1
k2
Hwo
1 Gas Adsorption Processes
77
Heat Transfer to Environment (gas): Rigorous Model This option includes a wall energy balance equation that contains the following terms: •
Heat transfer from the gas in the bed to the inner wall.
•
Heat transfer from the outer wall to the environment (including the influence of any insulating material).
•
Axial thermal conduction along the wall.
•
Heat accumulation within the wall material.
The wall is assumed to be thin and conductive enough for the inner and outer wall temperatures to be equal. The adiabatic option, that is, ignoring the wall energy balance, is valid only when the wall is extremely thin and nonconductive.
Energy Balance Tab (gas): Form of Gas-Wall Heat Transfer Coefficient There are two options available for the definition of the gas-wall heat transfer coefficient H w : •
Constant
•
Estimated
Form of Gas-Wall Heat Transfer Coefficient (gas): Constant In the Specify table for the layer, set the heat transfer coefficient H w to be a fixed variable.
Form of Gas-Wall Heat Transfer Coefficient (gas): Estimated With this option, the gas-wall heat transfer coefficient is calculated from the local conditions inside the adsorbent layer. The correlation uses results from a graphical representation given by Kast, 1988:
C sphere H B Nu w 1 + DB Pe H
= −2 × 10 −6 (Pe H )2 + 0.0477 Pe H + 22.11
where:
C sphere = Nu w = Pe H = xchar
12 for a packed bed of spheres
H w xchar kg x char v g ρ g MC pg kg =
1.15(2 r p )
= Nusselt number for gas-wall heat transfer
= Gas wall heat transfer Peclet number = Characteristic length for a sphere
1 Gas Adsorption Processes
78
Reaction Tab (gas) Use the Reaction tab to generate a layer model that combines adsorption with reaction (heterogeneous and/or homogeneous). The mass and energy balances must include the reaction terms as well as the mass and heat transfer rates caused by adsorption. Furthermore, the formation of additional solid phases, such as coke, must be accounted for.
About Gas Adsorption with Reaction Processes Adsorptive reactors combine, into a single process unit, the unit operations of heterogeneous and/or homogeneous chemical reaction and adsorption. Such a hybrid process gives benefits over conventional catalytic reactors: •
Higher conversions, for example, when the product in an equilibrium reaction is removed by adsorption from the gas phase. An example of higher conversion is the catalytic dehydrogenation of methyl-cyclohexane to produce toluene. Adsorption of toluene greatly enhances the conversion.
•
Higher selectivity, when the desired product of an equilibrium reaction scheme is adsorbed.
Adsorptive reactors are also used in a number of gas purification processes: •
Removing sulfur compounds from gases by first contacting them with α or γ-ferric oxide monohydrates (Iron Sponge) to adsorb sulfur in the form of ferric sulfide, then periodically reoxidizing the surface to form elemental sulfur and to refresh the ferric oxides.
•
Removing mercury from natural gas streams by treatment in an ex-situ TSA regenerative process. The process uses an activated carbon adsorbent that contains sulfur, and which allows the formation of mercuric sulfide.
Adsorptive reactors are also useful in air purification processes. Careful selection of the adsorbent may allow one impurity to be adsorbed onto the adsorbent surface, while another impurity reacts on it. For example, modified activated carbon is used as an adsorbent for sulfur dioxide and a catalyst for NOx reduction. An important application of adsorptive reactors is the separation of radioactive wastes. Such applications usually require extremely high degrees of purification because of the high toxicity of many radioactive elements. Nuclear power plants generate radioactive xenon and krypton as products of the fission reactions, and these can leak out in small quantities into the coolant, to be released to the atmosphere with other gases. To prevent such release, off gases are treated in charcoal delay systems, which prevent the release of xenon and krypton until sufficient time has elapsed for the shortlived radioactivity to decay. Similarly, radioactive iodine from nuclear fuel reprocessing may be captured by chemisorption on molecular sieve zeolites containing silver.
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Reaction Tab (gas): Reactions Present In the Reactions Present box, choose a reaction type from: •
None
•
Homogeneous
•
Heterogeneous
•
Homogeneous and Heterogeneous
Reactions Present (gas): None No reactions are present in the gas or solid phases.
Reactions Present (gas): Homogeneous Reactions are present in the gas phase only.
Reactions Present (gas): Heterogeneous Reactions are heterogeneously catalyzed by a solid. The catalyst and adsorbent are assumed to be different, giving rise to two distinct solid phases. Solid reaction participants can be considered.
Reactions Present (gas): Homogeneous and Heterogeneous Reactions are present in both the gas phase and the solid phase.
Reaction Tab (gas): Homogeneous Rate Dependency In the Homogeneous Rate Dependency box, select the type of expression for homogeneous reaction rate. Choose from these options: •
Homogenous Rate Dependency: Partial Pressure
•
Homogenous Rate Dependency: Concentration
Homogeneous Rate Dependency (gas): Partial Pressure The reaction rate for components in the gas phase is related to the partial pressure of the component and gas phase temperature through the procedure pUser_g_Gas_Rx_Rate_Pp, which requires the user to supply the appropriate Fortran subroutine.
Homogeneous Rate Dependency (gas): Concentration The reaction rate for components in the gas phase is related to the concentration of the component and gas phase temperature through the procedure pUser_g_Gas_Rx_Rate_C, which requires the user to supply the appropriate Fortran subroutine.
1 Gas Adsorption Processes
80
Reaction Tab (gas): Number of Homogeneous Reactions In the Number of Homogeneous Reactions box, select the number of reactions that occur in the gas phase.
Reaction Tab (gas): Heterogeneous Rate Dependency In the Heterogeneous Rate Dependency box, select the type of expression for heterogeneous reaction rate. Choose from: •
Partial Pressure
•
Concentration
Heterogeneous Rate Dependency (gas): Partial Pressure With this option, the reaction rate for components on the surface of the catalytic adsorbent is related to the gas phase partial pressure of the component and gas phase temperature, through one of these procedures: •
pUser_g_Cat_Rx_Rate_Pp
•
pUser_g_Cat_Rx_Rate_Pp_Sol (for when solid reactants are present)
Both procedures require you to supply the appropriate Fortran subroutine.
Heterogeneous Rate Dependency (gas): Concentration With this option, the reaction rate for components on the surface of the catalytic adsorbent is related to the concentration of the component and gas phase temperature through one of these procedures: •
pUser_g_Cat_Rx_Rate_C
•
pUser_g_Cat_Rx_Rate_C_Sol (for when solid reactants are present)
Both procedures require you to supply the appropriate Fortran subroutine.
Reaction Tab (gas): Number of Heterogeneous Reactions In the Number of Heterogeneous Reactions box, select the number of reactions that occur on the surface of the catalytic adsorbent.
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81
Reaction Tab (gas): Are Solid Reactants Present This option is active only if heterogeneous reactions are present. Choose from: Yes. Here, solid reaction participants are present. The solids are formed either by the reaction (for example carbon in reaction networks that suffer from coking), or they represent catalytically active sites being deactivated or reactivated. You define, through Fortran subroutines, the way solid components interact with the gas phase. Aspen Adsim interfaces these subroutines through one of these two procedures: •
pUser_g_Cat_Rx_Rate_Pp - or -
•
pUser_g_Cat_Rx_Rate_Pp_Sol
No. Here, no solid reactants are present.
Reaction Tab (gas): Solid Reactant List In the Solid Reactant List box, choose a default list or a user-defined list of solid reactants.
Procedures Tab (gas) Use the Procedures tab to view a list of the user procedures in use within the current adsorption layer model.
Gas Adsorption: Summary of Mass and Energy Balance Equations This section summarizes the equations for mass and energy balances used for gas adsorption processes in Aspen Adsim.
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82
Gas Adsorption: Mass Balance for Gas Phase The overall mass balance for a multi-component gas phase accounts for the convection of material and mass transfer, from the gas to the solid phase. Aspen Adsim uses this equation only for constant pressure systems, and it is suitable only for simulating breakthrough curves at constant pressure and temperature. The governing partial differential equation is:
∂ (v g ρ g ) ∂w + ρs ∑ k = 0 k ∂t ∂z
For an explanation of the symbols used, see Explanation of Equation Symbols, later. Each component in the gas phase is governed by a similar equation, with extra terms for accumulation, and for axial and radial dispersion terms (if required):
− ε i E zk
∂ 2 ck 1 ∂ ∂c k ε E − r i rk r ∂r ∂r ∂z 2
∂c ∂ (v g c k ) + εB k + Jk = 0 + ∂z ∂t
In general, axial and radial dispersion needs to be considered, but the dispersion coefficient can be difficult to measure. Aspen Adsim sets the dispersion coefficient either to a constant value, or calculates it as a function of local conditions (that is, a distributed parameter).
Gas Adsorption: Mass Balance for Additional Solid Phase The concentration of each solid component i is calculated from its formation rate:
∂c sol ,i ∂t
− Rsol ,i = 0
1 Gas Adsorption Processes
83
Gas Adsorption: Gas Phase Energy Balance The gas phase energy balance includes terms for: •
Thermal conduction
•
Convection of energy, accumulation of heat
•
Compression
•
Heat transfer from gas to solid
•
Heat transfer from gas to the internal wall
•
Heat of reaction.
The governing partial differential equation is:
− k ga ε i
∂ 2Tg ∂T g ∂T g ∂v g + Cvg v g ρ g + ε B C vg ρ g +P 2 ∂z ∂t ∂z ∂z
+ HTCa p (Tg − Ts ) +
4H w (Tg − To ) + H r + ρ s,cat C p,cat ∂Tg + a Hx QHx = 0 ∂t DB
The above equation is in its most complete form, including axial thermal conduction, heat transfer to the environment, and the effect of heterogeneous and homogenous chemical reactions. The only term missing is the radial thermal conduction term, which is included for 2-dimensional, vertical beds. However, in this geometry, heat transfer to the environment is a boundary condition so is not part of the energy balance (it is in the 1-dimensional case).
Gas Adsorption: Solid Phase Energy Balance The solid phase energy balance includes terms for: •
Thermal conduction
•
Accumulation of heat
•
Accumulation of enthalpy in the adsorbed phase
•
Heat of adsorption
•
Gas-solid heat transfer from gas to solid (expressed in terms of a film resistance, where the heat transfer area is proportional to the area of the adsorbent particles)
The solid phase energy balance is: n ∂ 2Ts ∂Ts ∂Ts 1 ∂ 1 ∂Ts ρ ρ k C − + + sr s ps s ∑ (C pai wi ) 2 ∂z ∂t ∂t r ∂r r ∂r i =1 n ∂w + ρ s ∑ ∆H i i − HTCa p (Tg − Ts ) = 0 ∂t i =1
− k sa
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84
Gas Adsorption: Wall Energy Balance The wall energy balance includes terms for: •
Axial thermal conduction along the wall
•
Heat accumulation within the wall material
•
Heat transfer from the bed to the inner wall
•
Heat transfer from the outer wall to the environment
The governing equation is: 2 ∂ 2Tw ∂Tw 4 DB 4(DB + WT ) (T − T ) + H amb (T − T ) = 0 − kw + ρ w c pw − Hw ∂t ∂z 2 (DB + WT )2 − DB2 w amb (DB + WT )2 − DB2 g w
For a 2-dimensional bed model, Aspen Adsim replaces the third term with the sum of the conductive energy fluxes in the radial direction, which come from the solid phase energy balances. These fluxes are the boundary conditions for 2-dimensional bed models.
Gas Adsorption: Summary of Factors that affect the Mass Balance Equations This section lists the factors that affect the mass balance in the solid and gas phases.
Gas Adsorption: Axial Dispersion Term The axial dispersion term is:
∂ 2 ck − ε i E zk ∂z 2 Gas Adsorption: Radial Dispersion Term This term is only active if you chose vertical bed and two-dimensional spatial discretization:
− ε i E rk
1 ∂ ∂c k r r ∂r ∂r
Gas Adsorption: Convection Term The convection term is:
∂ (v g c k ) ∂z
Gas Adsorption: Gas Phase Accumulation Term The accumulation term is:
εB
∂ck ∂t 1 Gas Adsorption Processes
85
Gas Adsorption: Rate of Flux to Solid Surface The rate of flux to the solid surface is given by:
J = −ρS
∂w ∂t
Gas Adsorption: Rate of Adsorption The rate of adsorption is represented as an accumulation term in the gas phase mass balance. The linear driving force solid-film model is:
J ∂wk = MTCs k (wk − wk* ) = ads ,k ∂t ρs There are analogous expressions for gas films and quadratic driving forces. If a particle material balance was considered,
∂wk is taken to be the integral ∂t
uptake of the particle as determined by the flux through the boundary layer. (See Also Particle MB.) Note: Procedure-defined expressions need adjusting accordingly.
Gas Adsorption: Reaction Term The reaction term accounts for the removal or formation of components in the gas phase, due to reaction on the solid catalyst's surface. It is represented as:
J cat ,reac ,k + ε i J gas ,reac ,k Where:
J cat ,reac ,k
=
rate of consumption or production of k by heterogeneous (catalytic) reactions
J gas ,reac ,k
=
rate of consumption or production of k by homogeneous (gas phase) reactions.
J gas ,reac ,k = −
n reacgas
∑
ν gas , j ,k R gas , j
j =1
J cat ,reac ,k = − ρ s,cat
n reaccat
∑
ν cat , j ,k Rcat , j
j =1
1 Gas Adsorption Processes
86
You must define the rates of reaction in a user procedure, as a function of temperature, and one of partial pressure or component concentration. The total rate of flux to the surface per unit volume is then:
J k = J ads ,k + J cat ,reac ,k + ε i J gas ,reac ,k Jk = ρs
∂ wk + J cat ,reac ,k + ε i J gas ,reac ,k ∂t
Gas Adsorption: Defining the Mass Balance for Additional Solid Phases During the catalytic reaction, solid phases such as coke deposit sometimes form, or a metal oxide catalyst is oxidized and/or reduced. The concentration of each solid component i is calculated from its rate of formation:
∂c sol ,i ∂t
− Rsol ,i = 0
You must define the reaction rate of the solid components in a Fortran subroutine, as a function of temperature, pressure, and solid component concentrations. Aspen Adsim interfaces this subroutine through the procedure pUser_g_Cat_RX_Rate_Pp_Sol.
Gas Adsorption: Summary of Factors that affect the Energy Balance This section lists the factors that affect the energy balance equations in the: •
Gas phase energy balance.
•
Solid phase energy balance.
•
Wall energy balance.
Gas Adsorption: Defining the Energy Balance in the Gas Phase This section lists the factors that affect the energy balance equations in the gas phase.
Gas Adsorption: Effect of Compression The reversible rate of internal energy increase per unit volume by compression is:
P
∂v g ∂z
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87
Gas Adsorption: Convective Term The gas convective term is always included in the gas phase energy balance:
C vg v g ρ g
∂T g ∂z
Gas Adsorption: Accumulation in Gas Phase The enthalpy accumulation in the gas phase is represented as:
ε i C vg ρ g
∂T g ∂t
Gas Adsorption: Axial Thermal Conduction in Gas Phase The axial gas thermal conduction (axial thermal dispersion) term is given by:
− ε i k gz
∂ 2Tg ∂z 2
Where k gz is evaluated based on your choices in: •
Energy Balance tab for 1-dimesional models.
•
Material/Momentum Balance tab for two dimensional models.
Gas Adsorption: Radial Thermal Conduction in Gas Phase The radial gas thermal conduction term (radial thermal dispersion) is represented as:
− ε i k gr
1 ∂ ∂Tg r r ∂r ∂r
Where k gr is evaluated according to the options selected in the material and momentum balance tab for two-dimensional models.
Gas Adsorption: Gas-Solid Heat Transfer Aspen Adsim uses a film resistance model to represent heat transfer between gases and solids: Rate of heat transferred per unit volume = HTCa p (Tg − Ts ) with:
a p = (1 − ε i )
3 rp
This is for adsorption only. You set a p for adsorption and reaction.
1 Gas Adsorption Processes
88
Gas Adsorption: Heat Exchange between Gas and Internal Wall For one-dimensional vertical and horizontal bed models:
4
Hw (Tg − To) DB
Where:
To = Tamb for adiabatic/thin walls and To = Tw for thick walls For other geometries, this term is missing because: •
Radial bed models are always considered to be adiabatic.
•
For two dimensional vertical bed models, the heat transfer to the column wall is one of the thermal boundary conditions for the radial direction.
Gas Adsorption: Rate of Heat Generation by Reaction The rate of heat generation by reaction is the sum of the contributions from individual reactions:
H R = εi
nreac , gas
∑H k =1
Rgas , k
R gas ,k + ρ s ,cat
nreac ,cat
∑H l =1
Rcat ,l
Rcat ,l
Where: k
=
index for the set of homogenous reactions
l
=
index for the set of heterogeneous reactions
H Rgas ,k , H Rcat ,l =
molar heats of reactions k and l, typically in MJ/kmol
Rgas ,k
=
rate of homogenous reaction k, typically in kmol/(m3 s)
Rcat ,l
=
rate of heterogeneous reaction l, typically in kmol/(kg s)
ρ s,cat
=
catalyst bulk density
You must define the rates of reaction in a user procedure, as a function of temperature, and one of partial pressure or concentration. The heat of reaction must also be defined as a function of temperature and mole fraction. See the following procedures, described in the Adsim Library Reference guide: •
pUser_g_Cat_RX_Rate_Pp_Sol
•
pUser_g_Cat_RX_Rate_C_Sol
•
pUser_g_Cat_RX_Rate_Pp
•
pUser_g_Cat_RX_Rate_C
•
pUser_g_Gas_RX_Rate_Pp
•
pUser_g_Gas_RX_Rate_C
•
pUser_g_Cat_RX_Heat
•
pUser_g_Gas_RX_Heat
1 Gas Adsorption Processes
89
Gas Adsorption: Heat Exchange between Gas and Internal Heat Exchanger The heat exchange between the gas phase and a heat exchanger (either as jacket around the packed bed or via tubes surrounded by adsorbents) is given by:
a Hx QHx Where a Hx is the specific heat exchange area per unit bed volume and Q Hx the energy flux exchanged, given by:
QHx = U Hx (Tg − THx )
for single phase exchange media, and
QHx = U Hx ,Cw (Tg − TCw ) + U Hx ,St (Tg − TSt )
for two phase exchange media. See also Configure Form (gas) earlier in this chapter.
Gas Adsorption: Defining the Energy Balance for the Solid Phase This section lists the factors that affect the energy balance equations in the solid phase.
Gas Adsorption: Accumulation in Solid Phase The solid phase enthalpy accumulation is always included in the solid phase energy balance:
ρ s C ps
∂Ts ∂t
Gas Adsorption: Axial Thermal Conductivity in Solid Phase The solid thermal conduction term is:
− k sz
∂ 2Ts ∂z 2
Gas Adsorption: Radial Thermal Conductivity in Solid Phase This term is active only for vertical beds and two-dimensional spatial discretization:
− k sr
1 ∂ ∂Ts r r ∂r ∂r
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90
Gas Adsorption: Heat of Adsorption The rate of heat generation by adsorption of each component i, per unit mass of solid, is a function of the local rate of mass transfer:
HTi = ∆H i
∂wi ∂t
These rates are held in vectors HTi and summed for all components to give the total rate of heat generation by adsorption per unit volume of solid:
ρ s ∑ (− HTi ) i
Gas Adsorption: Heat of Adsorbed Phase The term for each component is a function of the loading and the temperature in the solid phase:
H i = ρ s C pai wi
∂Ts ∂t
The total contribution comes from the sum for all components:
∑ (H ) i
i
You supply C pai (heat capacity of adsorbed component i) as either a fixed value for each component, or through a user procedure or submodel. Try these guidelines when deciding what specific heat capacity to use (Tien, 1994): For T Tc use C pai for compressed gas
Gas Adsorption: Gas-Solid Heat Transfer The gas-solid heat transfer term is the same as for the gas phase, but with the sign reversed:
HTC a p (Tg − Ts )
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91
Gas Adsorption: Defining Energy Balance for the Wall This is applicable only if you selected a rigorous model for the heat transfer to the environment. The following effects are considered: •
Heat exchange between gas and wall.
•
Between wall and environment.
•
Axial thermal conductivity along wall.
•
Heat content of wall.
Gas Adsorption: Heat Exchange between Gas and Wall When the rigorous wall energy balance is selected, Aspen Adsim includes, in the wall energy balance, the heat exchange between the gas in the bed and the inner surface of the wall. The term is represented as:
Hw
4 DB
(DB + WT )2 − DB2
(T
g
− Tw )
Where
DB
=
Internal diameter of layer
WT
=
Width of column wall
The supply of H w is defined by the Form of Gas-Wall Heat Transfer Coefficient option. It is either constant or estimated from a correlation. The heat exchange between gas and wall is also included in the gas phase energy balance. Note that the equation has a slightly different form, since the basis of the equation is per unit volume of gas phase:
4
Hw (Tg − Tw ) DB
Gas Adsorption: Heat Exchange between Wall and Environment When you include a rigorous wall energy balance, the corresponding term in the wall energy balance gives the heat transfer between the outer wall and the environment:
4 Hamb (D B + WT )
(D B + WT )2 − DB2
(Tw − Tamb)
Gas Adsorption: Axial Thermal Conductivity along Wall The axial thermal conduction along the wall is always part of the wall energy balance. The term is represented as:
1 Gas Adsorption Processes
92
∂ 2Tw − kw ∂z 2 You must specify the value of the wall thermal conductivity k w in the Specify table for the layer.
Gas Adsorption: Heat Content of Wall The Heat Content of Wall term is always included in the wall energy balance:
ρ w C pw
∂Tw ∂t
You must specify the value of the wall density
ρw
and the specific heat
capacity of the wall C pw in the Specify table for the layer.
Gas Adsorption: Explanation of Equation Symbols Symbol
Explanation
Aspen Adsim base units
a
Specific particle surface.
m2/m3
aHx
Specific heat exchanger surface.
m2(HX area)/m3(Bed)
aP
Specific particle surface per unit volume bed.
m2(Particle area)/m3(Bed)
A
Area.
m2
AA
Placeholder variable used for DubininAstakhov isotherm evaluation.
b
Kinetic Langmuir factor.
1/bar
cbk
Bulk gas phase concentration.
kmol/m3
ck
Molar concentration of component k.
kmol/m3
cmsk
Macropore gas phase concentration.
kmol/m3
csol
Concentration of solid phase reactant.
kmol/kg
c pai
Specific heat capacity of adsorbed phase.
MJ/kmol/K
c p ,cat
Specific heat capacity of catalyst.
MJ/kg/K
c pg
Specific gas phase heat capacity at constant pressure.
MJ/kmol/K
c ps
Specific heat capacity of adsorbent.
MJ/kmol/K
c pW
Specific heat capacity of column wall.
MJ/kg/K
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93
cvg
Specific gas phase heat capacity at constant volume.
MJ/kmol/K
DB
Bed diameter.
m
Defc
Effective micropore diffusion coefficient.
m2/s
DefP
Effective macropore diffusion coefficient.
m2/s
Dek
Effective adsorbed phase diffusivity of component k.
m2/s
Dki
Knudsen diffusion coefficient of component i.
m2/s
Dmk
Mean molecular diffusion coefficient of component k.
m2/s
Eact ,k
Activation energy for Arrhenius relationship.
MJ/kmol
Eik
Radial dispersion coefficient of component k.
m2/s
E zk
Axial dispersion coefficient of component k.
m2/s
f
Function.
-
f eq
Equilibrium (isotherm) relationship.
-
H amb
Wall-ambient heat transfer coefficient.
MW/m2/K
HB
Height of adsorbent layer.
m
Hi
Rate of change of heat of adsorbed phase.
MJ/m3/s
HR
Combined heats of homogenous and heterogeneous reactions.
MJ/m3 (Bed)/s
H Rcat
Heat of catalytic reaction.
MJ/kmol
H Rgas
Gas phase heat of reaction.
MJ/kmol
H Ti
Heat of adsorption contribution to solid phase energy balance.
MJ/m3/s
Hw
Gas-wall heat transfer coefficient.
MJ/m2/s
∆H i
Heat of adsorption of component i.
MJ/kmol
HTC
Gas-solid heat transfer coefficient.
MJ/m2/s
IP
Isotherm parameter, units depend on isotherm.
j
Colburn j-factor for heat or mass transfer.
-
J ads ,k
Mass transfer rate of component k owing to adsorption.
kmol/m3 (Bed)/s
J cat ,reac ,k
Mass transfer rate of component k owing to heterogeneous catalytic reactions.
kmol/m3 (Bed)/s
1 Gas Adsorption Processes
94
J gas ,reac
Mass transfer rate of component k owing to homogenous, gas phase reactions.
kmol/m3 (Void)/s
Jk
Mass transfer rate of component k to/from adsorbent.
kmol/m3 (Bed)/s
k0 k
Pre-exponential factor for Arrhenius relationship.
m/s
k 0 Pk
Pre-exponential factor for pressure dependent Arrhenius relationship.
m/s
k fk
Film mass transfer coefficient of component k.
m/s
kg
Gas phase thermal conductivity.
MW/m/K
k gr
Effective radial gas phase thermal conductivity.
MW/m/K
k grdyn
Dynamic contribution to
k grstat
Static contribution to
ki
Effective, lumped mass transfer coefficient of component i.
1/s
ks
Solid thermal conductivity.
MW/m/K
k gz
Effective axial gas phase thermal conductivity.
MW/m/K
k sr
Effective radial solid phase thermal conductivity.
MW/m/K
k srstat
Static contribution to
k sz
Effective axial solid phase thermal conductivity.
MW/m/K
kW
Thermal conductivity of column wall.
MW/m/K
K Ki
Isotherm slope of component i (Henry’s coefficient).
m3/kg
K Ki
Dimensionless isotherm slope of component i (Henry’s coefficient).
-
K mac
Macropore mass transfer coefficient.
1/s
K mic
Micropore mass transfer coefficient.
1/s
Kp
Darcy’s constant.
bar s/m2
K Pi
Macropore diffusion coefficient.
m2/s
L
Length of horizontal bed.
m
M
Molecular weight.
kg/kmol
MTC g
Gas film mass transfer coefficient.
1/s
MTCs
Solid film mass transfer coefficient.
1/s
k gr .
k sr .
k gr .
MW/m/K MW/m/K
MW/m/K
1 Gas Adsorption Processes
95
p
Emissivity in calculation of effective thermal conductivities.
P
Pressure.
bar
Pi 0
IAS vapor pressure.
bar
Psat
Saturation pressure.
bar
QHx
Heat transfer rate to internal heat exchanger.
MJ/m2/s
r
Radial co-ordinate (in packed bed or particle).
m
rc
Microparticle (crystal) radius.
m
rp
Particle radius.
m
R
Universal gas constant.
bar m3/kmol/K
Rcat
Catalytic reaction rate.
kmol/kg/s
Rgas
Gas phase reaction rate.
kmol/m3/s
Rsol
Solid phase reaction rate.
kmol/kg/s
t
Time.
s
tcycle
Adsorption cycle time.
s
T
Temperature.
K
T0
Equal to
Tamb
or
TW , depending on
K
context used.
Tamb
Ambient temperature.
K
Tc
Critical temperature.
K
TCW
Cooling water temperature.
K
Ts
Solid phase temperature.
K
Tg
Gas phase temperature.
K
THx
Heat exchange medium temperature.
K
TSt
Steam temperature.
K
TW
Wall temperature.
K
Tort
Adsorbent tortuosity.
-
U Hx
Overall heat transfer coefficient: gas to heat exchange medium.
MW/m2/K
U Hx ,cw
Overall heat transfer coefficient: gas to cooling water.
MW/m2/K
1 Gas Adsorption Processes
96
U Hx , St
Overall heat transfer coefficient: gas to steam.
MW/m2/K
vg
Gas phase superficial velocity.
m/s
wk
Loading.
kmol/kg
wk0
Pure component loading of component k.
kmol/kg
W
Width of horizontal bed.
m
WT
Width of column wall.
m
xchar
Characteristic length.
m
xk
Mole fraction of component k in the adsorbed phase.
-
yk
Mole fraction of component k in the gas phase.
-
z
Axial co-ordinate.
m
Z
Gas compressibility factor.
-
Symbol
Explanation
Aspen Adsim base units
α rg
Radiation contribution to
k grstat .
α rs
Radiation contribution to
k srstat .
β
Factor used in
∆r
Radial discretization distance.
m
εB
Total bed voidage.
m3 (Void+Pore)/m3 (Bed)
εi
Interparticle voidage.
m3 (Void)/m3 (Bed)
εP
Intraparticle voidage.
m3 (Pore)/m3 (Particle)
φ
Function of packing density, used in
k grstat calculation.
k srstat
calculation. φ
Relative pressure:
γ
Factor used in
γi
Activity coefficient of component i.
-
µ
Dynamic viscosity.
N s/m2
µ ads,i
Chemical potential of component i in the adsorbed phase.
MJ/kmol
µ gas,i
Chemical potential of component i in the gas phase.
MJ/kmol
ν jk
Stoichiometric coefficient of component k in reaction j.
-
Pk / Psat ,k .
-
k srstat calculation.
1 Gas Adsorption Processes
97
Π i0
Spreading pressure of component i.
bar m
θ
Time constant for adsorption cycle.
-
ρg
Gas phase molar density.
kmol/m3
ρs
Adsorbent bulk density.
kg/m3
ρ s,cat
Catalyst bulk density.
kg/m3
ρW
Wall density.
kg/m3
Ω
Parameter in Glueckauf expression.
-
Ψ
Particle shape factor.
-
Dimensionless number
Defining expression
Description
NuW
H w xchar kg
Nusselt number for gas wall heat transfer.
PeH
xchar vg ρ g MC pg
Gas-wall heat transfer Peclet number.
PeK
vgH b Ez
Component Peclet number for mass transfer.
Pr
µ C pg
Prandl number.
kg
kg M
Sck
µ Dmi ρ g M
Component Schmidt number.
Shk
k fi 2rp
Component Sherwood number.
Re
2rp M ρ g vg
Dmi Particle Reynolds number.
µ
1 Gas Adsorption Processes
98
2 Gas Cyclic Steady State Modeling
Introduction Aspen Adsim 2004.1 presents an innovative new modeling approach to maximize profitability in the design, simulation, and optimization of periodic adsorption processes for gas separation, processes, such as Pressure Swing Adsorption (PSA), Thermal Swing Adsorption (TSA), Vacuum Swing Adsorption (VSA), etc. Direct determination of the cyclic steady state, without carrying out a dynamic simulation over a large number of cycles, is now available using Aspen Adsim 2004.1. This powerful tool - Cyclic Steady State (CSS) modeling (the result of complete discretization of both time and space) presents a periodic adsorption process as a steady state problem. The Aspen Adsim 2004.1 CSS models offer an extremely efficient design tool that can be more readily used as an optimization package to determine optimal design and operating conditions for an adsorption process. The following sections outline CSS modeling tasks and include instructions on using CSS models for your engineering business: •
What is CSS Modeling…?
•
Discretization Techniques for Time and Space
•
Connectivity Between CSS Models
•
Bed Model Details
•
Material Balance
•
Momentum Balance
•
Kinetic Model
•
Energy Balance
•
Adsorption Equilibrium Models
•
User Guidelines
2 Gas Cyclic Steady State Modeling
99
•
How to Create a CSS Simulation Flowsheet
•
How to Create a Dynamic Simulation Flowsheet using CSS Models
•
How to Convert a CSS Flowsheet to a Dynamic Flowsheet
•
How to a Convert Dynamic Flowsheet to a CSS Flowsheet
•
Developer’s Tips to Get Better Convergence Property in CSS Simulation
What is CSS Modeling…? A periodic adsorption process operates on sequential steps (for example, continuously repeated steps of Feed, Purge, Pressure equalization, Blow down, Production, etc.) with multiple adsorbers packed with single or multiple adsorbent layers. Although the operation of each bed is batchwise, the whole system is continuous because of the use of multi-beds that are ultimately operated in a cyclic steady state within a confined cycle time. Cyclic Steady State (CSS), which is the nature of periodic adsorption processes, implies a steady state in which the conditions at the end of each cycle are identical to those at the beginning. The traditional approach for CSS determination is to carry out a dynamic simulation of the system, beginning with a specified set of initial condition, over a large number of cycles until a CSS is eventually confirmed from a defined criteria, e.g., the cycle initial state at t0 must be identical to the cycle end state at tN, as illustrated in Figure 1. n dynamic simulatio
Cycle end state(t
N)
tN N ep St
cle Cy
tN-1
in ) (t 0 te ta ls itia
Spatial Domain
p Ste
p1 Ste
2
t2 Time Domain
t1
t0
Figure 1 Illustration for traditional dynamic simulation of a periodic adsorption process
2 Gas Cyclic Steady State Modeling
100
Time domain (t)
ia Spat
t2
l dom
t1
x) ain (
tN-1
tN t0
Periodic Boundary State(tN) = State(t0) i.e. Cyclic Steady State
Figure 2 Illustration for the concept of CSS modeling system in Aspen Adsim From a mathematical point of view, the criterion for CSS is considered a unique characteristic of a periodic adsorption process, and has brought ideas to explore a better numerical method toward CSS in terms of cost-effective process simulation. The existence of periodic time boundary inspires to replace the initial condition by a periodicity condition requiring that the system state at the end of each cycle is identical to that at its beginning. As illustrated in Figure 2, the forced reformulation also constrains the system within a specified time domain length, from the starting point (t0) to the ending point (tN). This suggests a steady state simulation is feasible by complete discretization of space and time within a confined time length (i.e., cycle time). Based on the above concept, the CSS models in Aspen Adsim 2004.1 have been developed to determine CSS from purely steady state simulation. Direct determination of CSS will effectively save the costs for the optimization of periodic adsorption process since the technique could offer an extremely efficient design tool that can be more readily used as an optimization package to determine optimal design and operating conditions. Further benefits come from the fact that the graphic user interface of the freshly released CSS models from Aspen Adsim 2004.1 is the same as those of existing Aspen Adsim dynamic models. Therefore, existing Adsim users should find it easy to use this new feature. The high-level functionalities of CSS bed model (gCSS_Adsorber) in Aspen Adsim 2004.1 are listed in Table 1, compared with the original Aspen Adsim dynamic bed model (gas_bed).
2 Gas Cyclic Steady State Modeling
101
Table 1. Functional comparison of CSS and dynamic bed models in Aspen Adsim 2004.1
2 Gas Cyclic Steady State Modeling
102
Discretization Techniques for Time and Space Spatial derivatives of CSS bed model (gCSS_Adsorber) are discretized by one of the following numerical methods: •
CFD4 – 4th Order Central Finite Difference, equivalent to CDS2 in gas_bed
•
OCFE2 – 2nd Order Orthogonal Collocation on Finite Elements
•
OCFE4 – 4 th Order Orthogonal Collocation on Finite Elements
Time derivatives of CSS models are explained using 1st Order Backward Finite Difference approximation:
∂u (tn , x j ) ∂t
≈
u (tn , x j ) − u (tn −1 , x j ) ∆t
Connectivity between CSS Models CSS models contain at least an input and an output port (gCSS_Port). Each port has associated variables that correspond to the material connection stream (gCSS_Material_Connection) that allows reversible flow. These are the available connections for CSS models:
2 Gas Cyclic Steady State Modeling
103
Bed Model Details Material Balance The CSS bed model (gCSS_Adsorber) uses the following material balance for the bulk gas adsorption:
− DLi ε b
∂ 2Ci ∂ (v g Ci ) ∂Ci ∂Qi + + εt + ρb =0 2 ∂x ∂x ∂t ∂t
The physical meanings of each term are:
∂ 2 Ci − DLi ε b Axial dispersion contribution1 2 ∂x ∂ (v g Ci ) ∂x
εt
∂Ci ∂t
ρb
∂Qi ∂t
Convection Gas phase accumulation2 Adsorbed phase accumulation3
The following continuity equation is required to complete the material balance around the system,:
∑C
i
= ρg
i
Notation
Ci
Gas phase concentration for component i, kmol/m3
DLi
Axial dispersion coefficient for component i, m2/s
t
Time, s
Qi
Amount adsorbed for component i, kmol/kg-adsorbent
vg
Superficial gas velocity, m/s
x
Axial distance coordinate, m
εb
Bed (interparticle) voidage
εp
Intraparticle voidage
εt
Total voidage
2 Gas Cyclic Steady State Modeling
104
ρg
Gas density, kmol/m3
ρb
Bed packing density, kg/m3
ρp
Particle density (solid density, true density), kg/m3
References 1
If a concentration gradient exists in a packed bed, a diffusive mass flux will occur. In addition, eddy (turbulent) diffusion due to the flow also contributes to the mass flux. The resultant flux is referred to as mass dispersion, which may be expressed mathematically in terms of Fick’s law, where the proportionality constant is called dispersion coefficient. Dispersion occurs in both radial and axial directions in the bed. The axial dispersed mixing often occurs when a fluid flows through a packed bed and may cause unfavorable separation efficiency as the separation factor is becoming smaller. In general, flow through a packed bed may be adequately represented with inclusion of the axial dispersed plug flow consideration.
2
Here, ε t is the total bed voidage, which is the combined interparticle and intraparticle voidages calculated from
ε t = ε b + ε p (1 − ε b ) . 3
Here,
ρb
is the bed (packing) density calculated from
ρ b = ρ p (1 − ε b ) .
Momentum Balance Gas flow through a packed bed can be described by a relevant pressure drop correlation. Within the CSS adsorber model (gCSS_Adsorber), one of the following pressure drop correlations may be chosen as the one. Note that there is no other option to assume an ideal flow regime, such as Constant Pressure and Velocity and Constant Pressure with Variable Velocity since the CSS models has been developed fundamentally for cyclic process for gas separation. (1) Darcy’s Law:
∂P = − K p vg ∂x (2) Blake-Kozeny: −5 ∂P − 150 × 10 µ g (1 − ε b ) vg = ∂x (2rpψ )2 ε b3 2
2 Gas Cyclic Steady State Modeling
105
(3) Burke-Plummer: −5 ∂P − 1.75 × 10 M w ρ g (1 − ε b ) 2 = vg (2rpψ )ε b3 ∂x
(4) Ergun Equation:
150 × 10 −5 µ g (1 − ε b )2 1.75 × 10 −5 M w ρ g (1 − ε b ) 2 ∂P v vg = − + g 2 3 3 ( ) r 2 ψ ε ∂x ( ) r 2 ψ ε p b p b Notation
Kp
Darcy Coefficient, bar.s/m2
Mw
Molecular weight of gaseous mixture, kg/kmol
P
Gas pressure, bar
rp
Particle radius, m
vg
Superficial gas velocity, m/s
x
Axial distance coordinate, m
εb
Bed voidage (void fraction)
µg
Gas mixture viscosity, cP
ρg
Gas density, kmol/m3
ψ
Particle shape factor
Kinetic Model Rigorous simulation of an adsorption process requires a reliable representation of the adsorption kinetics for the adsorbent used. In adsorption, the mass transfer mechanism consists of four steps: •
Fluid film transfer
•
Pore diffusion
•
Adhesion on surface
•
Surface diffusion
Because the surface adhesion rate approximates the order of the collision frequency of the gas molecule on the solid surface, (which is much greater than for the transport processes) the equilibrium is assumed instantaneously at the interfaces. Adsorptives initially transfer from the bulk gas phase through an external film to the external surface of the particles. The molecules are diffused into the
2 Gas Cyclic Steady State Modeling
106
pores of the particle, adsorbed on the active sites and then diffused along the surface. While fluid film transfer and pore diffusion are treated as sequential steps, pore diffusion and surface diffusion generally occur in parallel. Any combination of the three steps can constitute the rate-controlling mechanism. This mechanism definitely depends on the adsorption system and can vary with the operating conditions of the process. Typically, a film adjacent to the surface confines the mass transfer rate between solid and fluid phases and this external film mass transfer resistance may be determined by the hydrodynamic condition. It is in fact more convenient to depict film transfer rate in terms of an effective transfer coefficient or a lumped resistance coefficient rather than to use a diffusion equation to represent adsorption kinetics in a rigorous manner. The CSS adsorber model (gCSS_Adsorber) within Aspen Adsim 2004.1 limits two types of lumped kinetic models for application. They are: Linear Driving Force Approximation and Quadratic Driving Force Approximation. Both approximations have a lumped resistance coefficient that may be determined at either fluid or solid film where the mass transfer occurs: (1) Linear Driving Force Approximation (LDFA):
ρb
∂Qi = k Fi Ci − Ci* ∂t
(
∂Qi = k Si Qi* − Qi ∂t
(
)
at fluid film
)
at solid film
(2) Quadratic Driving Force Approximation (QDFA):
( )
(C ) − Ci* ∂Q ρ b i = k Fi i ∂t 2Ci 2
( )
∂Qi Q * − (Qi ) = k Si i ∂t 2Qi 2
2
at fluid film
2
at solid film
The lumped mass transfer coefficient, k Fi or k Si , can be determined by a constant or by a certain relationship according to the dynamic conditions of adsorption system. The CSS adsorber model (gCSS_Adsorber) provides the following choices in determining the lumped mass transfer coefficient from the empirical assessment by Aspen Adsim users: •
Constant
•
Arrhenius
ki = k LDFi E k i = k 0i exp − i RTs
2 Gas Cyclic Steady State Modeling
107
•
Effective Diffusivity
ki =
ki = •
π 2 Dei rp2
Linear Driving Force Approximation Quadratic Driving Force Approximation
Pressure Dependent
ki = •
15 Dei rp2
k Pi P
Pressure Dependent Arrhenius
ki =
E k 0 Pi exp − i P RTs
Notation
Ci
Gas phase concentration for component i, kmol/m3
Ci*
Equilibrium gas phase concentration for component i,
Dei
Effective diffusivity for component i, m2/s
Ei
Activation energy for component i, MJ/kmol
ki
Mass transfer coefficient (fluid or solid) for
kmol/m3
component i, 1/s
k LDFi
Mass transfer coefficient as a constant for component i, 1/s
k Pi
Pressure dependent mass transfer coefficient for component i, bar/s
k 0i
Pre-exponent for component i, 1/s
k 0 Pi
Pre-exponent for component i, bar/s
k Fi
Fluid film mass transfer coefficient for component i, 1/s
k Si
Solid film mass transfer coefficient for component i, 1/s
P
Gas pressure, bar
Qi
Amount adsorbed for component i, kmol/kg-adsorbent
Qi*
Equilibrium amount adsorbed for component i, kmol/kg-adsorbent
rp
Particle radius, m
2 Gas Cyclic Steady State Modeling
108
t
Time, s
Ts
Solid temperature, K
R
Gas constant (8.31451e-3), MJ/kmol/K
ρb
Bed packing density, kg/m3
Energy Balance The CSS adsorber model (gCSS_Adsorber) uses the following energy balances to represent the heat transportations of non-isothermal system with compressible flow: (1) In Fluid Phase:
− kgε b
− kgε b
∂ 2Tg ∂x
+ CVg v g ρ g
∂ 2Tg ∂x 2
CVg v g ρ g P
2
∂Tg ∂x
∂v g
+P
∂v g
+ CVg ρ g ε t
∂Tg
∂t A + H s a p (Tg − Ts ) + H w Hi (Tg − Tw ) = 0 VHi
∂x
∂x
Axial thermal conduction
Convection
P-V work compression
∂x
CVg ρ g ε t
∂Tg
∂Tg ∂t
H s a p (Tg − Ts )
Thermal accumulation in gas phase Heat transfer between gas and solid (adsorbent particle)
Hw
AHi (Tg − Tw ) VHi
Heat transfer between gas and the internal wall of adsorber
2 Gas Cyclic Steady State Modeling
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(2) In Solid Phase:
∂ 2Ts ∂T ∂Qi − ks + C Ps ρ b s + ρ p ∑ ∆H i − H s a p (Tg − Ts ) = 0 2 ∂t ∂t ∂x i
∂ 2Ts ∂x 2
− ks
∂Ts ∂t
C Ps ρ b
ρ p ∑ ∆H i i
Axial thermal conduction Thermal accumulation in solid phase
∂Qi ∂t
H s a p (Tg − Ts )
Thermal accumulation by the enthalpy of adsorption Heat transfer between gas and solid
(3) In Wall phase:
− kw
A A ∂ 2Tw ∂T + C Pw ρ w w − H w Hi (Tg − Tw ) + H amb Ho (Tw − Tamb ) = 0 2 VHo VHo ∂x ∂t
− kw
∂ 2Tw ∂x 2
C Pw ρ w
Hw
∂Tw ∂t
A Hi (Tg − Tw ) VHo
H amb
Axial thermal conduction along the wall Thermal accumulation in the wall material Heat transfer between gas and wall
AHo (Tw − Tamb ) Heat transfer between wall and VHo environment
Notation
ap
Particle external surface area to particle volume ratio (=3/rp), m
AHi
Internal wall heat transfer area, m
AHo
External wall heat transfer area, m
CVg
Gas mixture heat capacity, MJ/kmol/K
C Ps
Solid (=adsorbent particle) heat capacity, MJ/kg/K
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C Pw
Adsorber material (e.g., stainless steel) specific heat capacity, MJ/kg/K
Hs
Fluid/solid heat transfer coefficient, MW/m2/K
Hw
Fluid/wall heat transfer coefficient, MW/m2/K
H amb Wall/environment heat transfer coefficient, MW/m2/K kg
Gas mixture thermal conductivity, MW/m/K
ks
Solid phase thermal conductivity, MW/m/K
kw
Wall phase thermal conductivity, MW/m/K
P
Gas pressure, bar
Qi
Amount adsorbed for component i, kmol/kg-adsorbent
t
Time, s
Tg
Gas temperature, K
Ts
Solid temperature, K
Tw
Wall temperature, K
vg
Superficial gas velocity, m/s
VHi
Internal wall element volume for heat transfer, m2
VHo
External wall element volume for heat transfer, m2
x
Axial distance coordinate, m
∆H i
Enthalpy of adsorption for component i (i.e., heat of adsorption), MJ/kmol
εb
Bed voidage (void fraction)
εt
Total voidage
ρg
Gas density, kmol/m3
ρb
Bed packing density, kg/m3
ρw
Wall material density, kg/m3
2 Gas Cyclic Steady State Modeling
111
Adsorption Equilibrium Models Introduction Adsorption equilibrium established after the adsorptive has been in with the adsorbed surface for a long time, and can be represented in general form:
f (Qi , ρ i , T ) = 0
(Eqn 1)
In this equation, Qi is the concentration for component i on adsorbed phase, i.e., amount adsorbed, ρι is the density for component i in fluid phase, and T is the temperature. For an isothermal condition, the Eqn1 can be represented by the adsorption isotherm:
Qi = f ( ρ i ) T and ρ i = f (Qi ) T
(Eqn 2)
Eqn 2, which is commonly referred to as adsorption equilibrium isotherm, is most frequently used in researches including adsorption process simulation. For pure component adsorption, an equilibrium relationship could simply be represented by mathematical equation such as the Langmuir, the Freundlich, the Sips, the Toth, and so on. Eqn 1 can also take the following form and is called the adsorption isostere (see Ref. 1):
ρi = f (T )Q
i
(Eqn 3)
However, the adsorption isostere cannot be measured directly because it is impractical to hold Qi constant. For multi-component system, the explanation of adsorption equilibrium relationship often causes considerable attention due to a unique and complex mixing rule that governing an adsorption system of interest. For many decades, numerous researchers have considered multi-component adsorption equilibria from thermodynamic perspective and developed a number of theories or models based on various assumptions concerning the nature of adsorbed phase. The CSS model in Aspen Adsim offers the following types of adsorption equilibrium models for multi-component system. Please note all equilibrium models only require pure equilibrium information in order to predict mixture equilibrium: References 1
D. M. Young and A. D. Crowell, Physical Adsorption of Gases, Butterworths, London (1962).
2 Gas Cyclic Steady State Modeling
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Mathematical Equation Form for Extended Langmuir 1 Qi =
IP1i IP2i Py i 1 + ∑ {IP2 k Py k } k
(Pressure dependent equilibrium)
Qi =
IP1i IP2i C i 1 + ∑ {IP2 k C k } k
(Concentration dependent equilibrium)
IP1i , IP2i
Isotherm parameters for component i
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
Mathematical Equation Form for Extended Langmuir 2 Qi =
IP1i (IP2i exp[IP3i Ts ])Py i 1 + ∑ {(IP2 k exp[IP3k Ts ])Py k } k
(Pressure dependent equilibrium)
Qi =
IP1i (IP2i exp[IP3i Ts ])C i 1 + ∑ {(IP2 k exp[IP3k Ts ])C k } k
(Concentration dependent equilibrium)
IP1i , IP2i , IP3i Isotherm parameters for component i Ts
Adsorbent particle temperature in Kelvin
P
Total gas pressure
2 Gas Cyclic Steady State Modeling
113
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
Mathematical Equation Form for Extended Langmuir 3 Qi =
(IP1i + IP2iTs ) (IP3i exp[IP4i Ts ])Pyi 1 + ∑ {(IP3k exp[IP4 k Ts ])Py k } k
(Pressure dependent equilibrium)
Qi =
(IP1i + IP2iTs ) (IP3i exp[IP4i Ts ])Ci 1 + ∑ {(IP3k exp[IP4 k Ts ])C k } k
(Concentration dependent equilibrium)
IP1i , IP2i , IP3i , IP4i
Isotherm parameters for component i
Ts
Adsorbent particle temperature in Kelvin
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
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114
Mathematical Equation Form for Extended Langmuir 4 Qi
(IP =
)
TsIP2 i (IP3i exp[IP4i Ts ])Py i 1 + ∑ {(IP3k exp[IP4 k Ts ])Py k } 1i
k
(Pressure dependent equilibrium)
Qi =
(IP
)
TsIP2 i (IP3i exp[IP4i Ts ])C i 1 + ∑ {(IP3k exp[IP4 k Ts ])C k } 1i
k
(Concentration dependent equilibrium)
IP1i , IP2i , IP3i , IP4i
Isotherm parameters for component i
Ts
Adsorbent particle temperature in Kelvin
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
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115
Mathematical Equation Form for Extended Langmuir 5 Qi =
(IP1i exp[IP2i Ts ]) (IP3i exp[IP4i Ts ])Pyi 1 + ∑ {(IP3k exp[IP4 k Ts ])Py k } k
(Pressure dependent equilibrium)
Qi =
(IP1i exp[IP2i Ts ]) (IP3i exp[IP4i Ts ])Ci 1 + ∑ {(IP3k exp[IP4 k Ts ])C k } k
(Concentration dependent equilibrium)
IP1i , IP2i , IP3i , IP4i
Isotherm parameters for component i
Ts
Adsorbent particle temperature in Kelvin
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
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116
Mathematical Equation Form for Loading Ratio Correlation 1 IP1i IP2i (Pyi ) 3i Qi = IP 1 + ∑ IP2 k (Pyk ) 3 k IP
{
}
k
(Pressure dependent equilibrium) IP
Qi =
IP1i IP2i Ci 3i IP 1 + ∑ IP2 k Ck 3 k
{
}
k
(Concentration dependent equilibrium)
IP? i
Isotherm parameters for component i
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
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Mathematical Equation Form for Loading Ratio Correlation 2 IP1i (IP2i exp[IP3i Ts ])(Pyi ) 4 i 5 i s Qi = IP + IP 1 + ∑ (IP2 k exp[IP3k Ts ])(Pyk ) 4 k 5 k IP + IP
T
{
Ts
}
k
(Pressure dependent equilibrium)
IP1i (IP2i exp[IP3i Ts ])Ci 4 i 5 i s Qi = IP + IP 1 + ∑ (IP2 k exp[IP3k Ts ])Ck 4 k 5 k IP + IP
{
T
Ts
}
k
(Concentration dependent equilibrium)
IP? i
Isotherm parameters for component i
Ts
Adsorbent particle temperature in Kelvin
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
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Mathematical Equation Form for Loading Ratio Correlation 3 IP + IP T ( IP1i + IP2iTs )(IP3i exp[IP4i Ts ])(Pyi ) Qi = IP + IP T } 1 + ∑ {(IP3k exp[IP4 k Ts ])(Pyk ) 5i
5k
6k
6i
s
s
k
(Pressure dependent equilibrium) IP + IP T ( IP1i + IP2iTs )(IP3i exp[IP4i Ts ])Ci Qi = IP + IP T } 1 + ∑ {(IP3k exp[IP4 k Ts ])Ci 5i
5k
6k
6i
s
s
k
(Concentration dependent equilibrium)
IP? i
Isotherm parameters for component i
Ts
Adsorbent particle temperature in Kelvin
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
2 Gas Cyclic Steady State Modeling
119
Mathematical Equation Form for Loading Ratio Correlation 4
(IP Q = i
)
TsIP2 i (IP3i exp[IP4i Ts ])(Pyi ) 5 i 6 i IP + IP T 1 + ∑ (IP3k exp[IP4 k Ts ])(Pyk ) 5 k 6 k s
{
1i
IP + IP
Ts
}
k
(Pressure dependent equilibrium)
Qi =
(IP
)
TsIP2 i (IP3i exp[IP4i Ts ])Ci 5 i 6 i IP + IP T 1 + ∑ (IP3k exp[IP4 k Ts ])Ci 5 k 6 k s
{
1i
IP + IP
Ts
}
k
(Concentration dependent equilibrium)
IP? i
Isotherm parameters for component i
Ts
Adsorbent particle temperature in Kelvin
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
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120
Mathematical Equation Form for Loading Ratio Correlation 5 IP + IP ( IP1i exp[IP2i Ts ])(IP3i exp[IP4i Ts ])(Pyi ) Qi = IP + IP T } 1 + ∑ {(IP3k exp[IP4 k Ts ])(Pyk ) 5i
5k
6k
6i
Ts
s
k
(Pressure dependent equilibrium)
Qi =
(IP1i exp[IP2i Ts ])(IP3i exp[IP4i Ts ])Ci IP + IP IP + IP T } 1 + ∑ {(IP3k exp[IP4 k Ts ])Ci 5i
5k
6k
6i
Ts
s
k
(Concentration dependent equilibrium)
IP? i
Isotherm parameters for component i
Ts
Adsorbent particle temperature in Kelvin
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
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121
Mathematical Equation Form for Extended Dual-Site Langmuir 1 Qi =
IP1i IP2i Py i IP3i IP4i Py i + 1 + ∑ {IP2 k Py k } 1 + ∑ {IP4 k Py k } k
k
(Pressure dependent equilibrium)
Qi =
IP1i IP2i C i IP3i IP4i C i + 1 + ∑ {IP2 k C k } 1 + ∑ {IP4 k C k } k
k
(Concentration dependent equilibrium)
IP? i
Isotherm parameters for component i
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
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122
Mathematical Equation Form for Extended Dual-Site Langmuir 2 Qi =
IP1i (IP2i exp[IP3i Ts ]) Py i IP4i (IP5i exp[IP6i Ts ]) Py i + 1 + ∑ {(IP2 k exp[IP3k Ts ]) Py k } 1 + ∑ {(IP5 k exp[IP6 k Ts ]) Py k } k
k
(Pressure dependent equilibrium)
Qi =
IP1i (IP2i exp[IP3i Ts ])C i IP4i (IP5i exp[IP6i Ts ])C i + 1 + ∑ {(IP2 k exp[IP3k Ts ])C k } 1 + ∑ {(IP5 k exp[IP6 k Ts ])C k } k
k
(Concentration dependent equilibrium)
IP? i
Isotherm parameters for component i
Ts
Adsorbent particle temperature in Kelvin
P
Total gas pressure
yi
Gas phase mole fraction for component i
Ci
Fluid phase concentration for component i
Qi
Adsorbed phase concentration (i.e., amount adsorbed) for component I
I.A.S.T. (Ideal Adsorbed Solution Theory) The IAST1 is a widely used engineering thermodynamic method, analogues to Raoult’s law in vapor-liquid equilibrium. The inputs to the IAST calculation are the pure-component adsorption isotherms at the temperature of interest, and the output is a prediction of mixture equilibrium. It has been known that the deviations from IAST might result from the chemical dissimilarity of the adsorptive species (as for deviations from Raoult’s law in vapor-liquid equilibrium) or from the heterogeneity of the adsorbent. Adsorbent heterogeneity might be present in one of following forms2: chemical or structural heterogeneity of the adsorbent surface3, variation of pore size and shape (either along the axis of individual pores or among the pores), or due to connectivity effects4,5. Nonideal adsorption can be accommodated in the general framework of adsorbed solution theory by real adsorbed solution theory (RAST1) , in which nonideal interactions between the adsorbates on the adsorbent surface are accounted for by activity coefficients, and by heterogeneous ideal adsorbed
2 Gas Cyclic Steady State Modeling
123
solution theory (HIAST6), in which the energetic heterogeneity of the adsorbent is taken into account. Subject to the assumption of an ideal adsorbed phase, equality of chemical potential in the bulk gas and adsorbed phases implies:
f i = xi f i 0
(Eqn 1)
where f i is the fugacity of component i in the bulk gas phase and xi is the mole fraction of component i in the adsorbed phase; f i
0
is the standard-
state fugacity, that is, the fugacity of pure component i at the mixture spreading pressure, π ,when the adsorbed and bulk gas phases are in equilibrium. Please note, Eqn 1 describes the ideal adsorbed phase contacting with real (i.e., nonideal) gas phase, which is accounted by introducing gas fugacity instead of gas pressure. When an assumption of ideal gas phase is invoked, then the basic equation of IAST can be written by:
y i P = xi Pi 0
(Eqn 1)
where P is total gas pressure, y i is the gas mole fraction for component i 0
and xi is the mole fraction of component i in the adsorbed phase; Pi is the standard-state pressure, that is, the pressure of pure component i at the mixture spreading pressure, π ,when the adsorbed and bulk gas phases are in equilibrium. The spreading pressure is obtained from the experimental adsorption isotherm, i.e., Qi (Pi ) or Qi (C i ) , via the Gibbs adsorption isotherm:
πA RT
πA RT
f i0
= ∫ Qi d ln f i 0
Pi0
= ∫ Qi d ln Pi 0
(nonideal gas phase assumption)
(Eqn 3)
(ideal gas phase assumption)
(Eqn 4)
where A is the surface area of the adsorbent (which is not required in practice, as the product πA need not be separated in the calculation), R is the gas constant, T is the temperature, f i and Pi are the fugacity and the pressure for pure component i . The complete description of the IAST as a predictive tool for multicomponent adsorption equilibria requires an expression for total amount adsorbed, QT :
x 1 = ∑ i0 QT i Qi
(Eqn 5)
and the stoichiometric constraint:
∑x
i
=1
(Eqn 6)
i
0
In Eqn 5, Qi is the amount component i adsorbed at the standard-state pressure.
2 Gas Cyclic Steady State Modeling
124
The CSS model in Aspen Adsim supports a comprehensive tool in applying the IAST. The main benefits from the IAST application within the CSS model are: •
Capability to account gas phase nonideality by considering the gas fugacity that may be evaluated by either Aspen Properties or User Procedure.
•
No restriction for the type of pure component isotherm in the IAST calculation (namely, isotherm type free IAST). For example, it is now available to assign the best-fit isotherm equation to each component (e.g., the Langmuir isotherm for 1st component, the Freundlich isotherm for 2nd component, the Sips isotherm for 3rd component, so on.), instead of using a specific type isotherm for all adsorbates. The available pure isotherm equations for the IAST within CSS model may be found at:
List of Pure Isotherms Available in IAST Calculation of CSS model References 1
Myers, A. L.; Prausnitz, J. M. AIChE J. 1965, 11, 121.
2
Yun, J.-H.; Düren, T.; Keil, F. J.; Seaton, N. A. Langmuir 2002, 18, in print.
3
Rudzinski, W.; Everett, D. M. Adsorption of Gases on Heterogeneous Surfaces; Academic Press: New York, 1992.
4
López-Ramon, M. V.; Jagiello, J.; Bandosz, T. J.; Seaton, N. A. Langmuir 1997, 13, 4435.
5
Davies, G. M.; Seaton, N. A. Langmuir 1999, 15, 6263.
6
Valenzuela, D.; Myers, A. L.; Talu, O.; Zwiebel, I. AIChE J. 1988, 34, 397.
Pure Isotherm List for the IAST Calculation of CSS The following are the pure isotherm equations available in the IAST calculation by CSS bed model (gCSS_Adsorber) from Aspen Adsim 2004.1. In the application, any combination of the pure isotherm equations will be acceptable in representing mixture adsorption equilibria by means of IAST, as predictive equilibrium theory. Langmuir 1
- 2 parameters / isothermal assumption
Langmuir 2
- 3 parameters / temperature correlation
Langmuir 3
- 4 parameters / temperature correlation
Langmuir 4
- 4 parameters / temperature correlation
Langmuir 5
- 4 parameters / temperature correlation
Dual Site Langmuir 1
- 4 parameters / isothermal assumption
Dual Site Langmuir 2
- 6 parameters / temperature correlation
Sips (Langmuir-Freundlich) 1 - 3 parameters / isothermal assumption
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125
Sips (Langmuir-Freundlich) 2 - 5 parameters / temperature correlation Sips (Langmuir-Freundlich) 3 - 6 parameters / temperature correlation Sips (Langmuir-Freundlich) 4 - 6 parameters / temperature correlation Sips (Langmuir-Freundlich) 5 - 6 parameters / temperature correlation Henry 1
- 1 parameters / isothermal assumption
Henry 2
- 2 parameters / temperature correlation
Henry 3
- 2 parameters / temperature correlation
Henry 4
- 2 parameters / temperature correlation
Freundlich 1
- 2 parameters / isothermal assumption
Toth 1
- 3 parameters / isothermal assumption
BET 1
- 1 parameters /
Langmuir 1 Pressure dependent
Qi =
IP1i IP2i Pi 1 + IP2i Pi
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [bar]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
Concentration dependent
Qi =
IP1i IP2i C i 1 + IP2i C i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/m3]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
Langmuir 2 Pressure dependent
2 Gas Cyclic Steady State Modeling
126
Qi =
IP1i (IP2i exp[IP3i T ])Pi 1 + (IP2i exp[IP3i T ])Pi
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [bar]
IP3i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
Qi =
IP1i (IP2i exp[IP3i T ])C i 1 + (IP2i exp[IP3i T ])C i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/m3]
IP3i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Langmuir 3 Pressure dependent
Qi =
(IP1i + IP2iT ) (IP3i exp[IP4i T ])Pi 1 + (IP3i exp[IP4i T ])Pi
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/kg/ K]
IP3i
Isotherm parameter of comp i [bar]
IP4i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
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127
Concentration dependent
Qi =
(IP1i + IP2iT ) (IP3i exp[IP4i T ])Ci 1 + (IP3i exp[IP4i T ])C i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/kg/K]
IP3i
Isotherm parameter of comp i [kmol/m3]
IP4i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Langmuir 4 Pressure dependent
Qi
(IP =
IP1i
1i
T IP2 i
) (IP
3i
exp[IP4i T ])Pi
1 + (IP3i exp[IP4i T ])Pi
Isotherm parameter of comp i [kmol.K/kgadsorbent]
IP2i
Isotherm parameter of comp i [-]
IP3i
Isotherm parameter of comp i [bar]
IP4i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kgadsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
Qi =
(IP
1i
T IP2 i
) (IP
3i
exp[IP4i T ])C i
1 + (IP3i exp[IP4i T ])C i
IP1i
Isotherm parameter of comp i [kmol.K/kg-adsorbent]
IP2i
Isotherm parameter of comp i [-]
2 Gas Cyclic Steady State Modeling
128
IP3i
Isotherm parameter of comp i [kmol/m3]
IP4i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kgadsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Langmuir 5 Pressure dependent
Qi =
(IP1i exp[IP2i T ]) (IP3i exp[IP4i T ])Pi 1 + (IP3i exp[IP4i T ])Pi
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [K]
IP3i
Isotherm parameter of comp i [bar]
IP4i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
Qi =
(IP1i exp[IP2i T ])(IP3i exp[IP4i T ])Ci 1 + (IP3i exp[IP4i T ])C i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [K]
IP3i
Isotherm parameter of comp i [kmol/m3]
IP4i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
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129
Dual-Site Langmuir 1 Pressure dependent
Qi =
IP1i IP2i Pi IP3i IP4i Pi + 1 + IP2i Pi 1 + IP4i Pi
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [bar]
IP3i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP4i
Isotherm parameter of comp i [bar]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
Concentration dependent
Qi =
IP1i IP2i C i IP3i IP4i C i + 1 + IP2i C i 1 + IP4i C i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/m3]
IP3i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP4i
Isotherm parameter of comp i [kmol/m3]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
Dual-Site Langmuir 2 Pressure dependent
Qi =
IP1i (IP2i exp[IP3i T ]) Pi IP4i (IP5i exp[IP6i T ]) Pi + 1 + (IP2i exp[IP3i T ]) Pi 1 + (IP5i exp[IP6i T ]) Pi
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [bar]
IP3i
Isotherm parameter of comp i [K]
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130
IP4i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP5i
Isotherm parameter of comp i [bar]
IP6i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
Qi =
IP1i (IP2i exp[IP3i T ])C i IP4i (IP5i exp[IP6i T ])C i + 1 + (IP2i exp[IP3i T ])C i 1 + (IP5i exp[IP6i T ])C i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/m3]
IP3i
Isotherm parameter of comp i [K]
IP4i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP5i
Isotherm parameter of comp i [kmol/m3]
IP6i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Sips (Langmuir-Freundlich) 1 Pressure dependent
Qi =
IP1i IP2i Pi
IP3 i
1 + IP2i Pi
IP3 i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [bar]
IP3i
Isotherm parameter of comp i [-]
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Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
Concentration dependent
Qi =
IP1i IP2i C i
IP3 i
1 + IP2i C i
IP3 i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/m3]
IP3i
Isotherm parameter of comp i [-]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
Sips (Langmuir-Freundlich) 2 Pressure dependent
IP (IP exp[IP3i T ]) Pi 4 i 5 i Qi = 1i 2i IP + IP T 1 + (IP2i exp[IP3i T ]) Pi 4 i 5 i
IP + IP T
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [bar]
IP3i
Isotherm parameter of comp i [K]
IP4i
Isotherm parameter of comp i [-]
IP5i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
IP (IP exp[IP3i T ])Ci 4 i 5 i Qi = 1i 2i IP + IP 1 + (IP2i exp[IP3i T ])Ci 4 i 5 i IP + IP
T T
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IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/m3]
IP3i
Isotherm parameter of comp i [K]
IP4i
Isotherm parameter of comp i [-]
IP5i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Sips (Langmuir-Freundlich) 3 Pressure dependent IP + IP ( IP1i + IP2iT )(IP3i exp[IP4i T ]) Pi Qi = IP + IP T 1 + (IP3i exp[IP4i T ]) Pi 5i
5i
6i
T
6i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/kg/K]
IP3i
Isotherm parameter of comp i [bar]
IP4i
Isotherm parameter of comp i [K]
IP5i
Isotherm parameter of comp i [-]
IP6i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
Qi = IP1i
(IP1i + IP2iT )(IP3i exp[IP4i T ])Ci IP + IP IP + IP T 1 + (IP3i exp[IP4i T ])Ci 5i
5i
6i
T
6i
Isotherm parameter of comp i [kmol/kg-adsorbent]
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IP2i
Isotherm parameter of comp i [kmol/kg/K]
IP3i
Isotherm parameter of comp i [kmol/m3]
IP4i
Isotherm parameter of comp i [K]
IP5i
Isotherm parameter of comp i [-]
IP6i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Sips (Langmuir-Freundlich) 4 Pressure dependent
(IP Q =
1i
i
)
T IP2 i (IP3i exp[IP4i T ]) Pi
1 + (IP3i exp[IP4i T ]) Pi
IP5 i + IP6 i T
IP5 i + IP6 i T
IP1i
Isotherm parameter of comp i [kmol.K/kg-adsorbent]
IP2i
Isotherm parameter of comp i [-]
IP3i
Isotherm parameter of comp i [bar]
IP4i
Isotherm parameter of comp i [K]
IP5i
Isotherm parameter of comp i [-]
IP6i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
(IP Q =
1i
i
)
T IP2 i (IP3i exp[IP4i T ])Ci
1 + (IP3i exp[IP4i T ])Ci
IP5 i + IP6 i T
IP5 i + IP6 i T
IP1i
Isotherm parameter of comp i [kmol.K/kg-adsorbent]
IP2i
Isotherm parameter of comp i [-]
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IP3i
Isotherm parameter of comp i [kmol/m3]
IP4i
Isotherm parameter of comp i [K]
IP5i
Isotherm parameter of comp i [-]
IP6i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Sips (Langmuir-Freundlich) 5 Pressure dependent
Qi =
(IP1i exp[IP2i T ])(IP3i exp[IP4i T ]) Pi IP IP + IP T 1 + (IP3i exp[IP4i T ]) Pi
5i
5i
+ IP6 i T
6i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [K]
IP3i
Isotherm parameter of comp i [bar]
IP4i
Isotherm parameter of comp i [K]
IP5i
Isotherm parameter of comp i [-]
IP6i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
Qi =
(IP1i exp[IP2i T ])(IP3i exp[IP4i T ])Ci IP IP + IP T 1 + (IP3i exp[IP4i T ])Ci
5i
5i
+ IP6 i T
6i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [K]
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IP3i
Isotherm parameter of comp i [kmol/m3]
IP4i
Isotherm parameter of comp i [K]
IP5i
Isotherm parameter of comp i [-]
IP6i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Henry 1 Pressure dependent
Qi = IP1i Pi IP1i
Isotherm parameter of comp i [kmol/bar/kg-adsorbent]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
Concentration dependent
Qi = IP1iCi IP1i
Isotherm parameter of comp i [m3/kg-adsorbent]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
Henry 2 Pressure dependent
Qi = (IP1i + IP2iT ) Pi IP1i
Isotherm parameter of comp i [kmol/bar/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/bar/K/kg-adsorbent]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
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T
Temperature [K]
Concentration dependent
Qi = (IP1i + IP2iT )Ci IP1i
Isotherm parameter of comp i [m3/kg-adsorbent]
IP2i
Isotherm parameter of comp i [m3/K/kg-adsorbent]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Henry 3 Pressure dependent
(
)
Qi = IP1i T IP2 i Pi
IP1i
Isotherm parameter of comp i [kmol.K/bar/kg-adsorbent]
IP2i
Isotherm parameter of comp i [-]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
(
)
Qi = IP1i T IP2 i Ci
IP1i
Isotherm parameter of comp i [K.m3/kg-adsorbent]
IP2i
Isotherm parameter of comp i [-]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Henry 4 Pressure dependent
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Qi = (IP1i exp[IP2i T ]) Pi IP1i
Isotherm parameter of comp i [kmol/bar/kg-adsorbent]
IP2i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
T
Temperature [K]
Concentration dependent
Qi = (IP1i exp[IP2i T ])Ci IP1i
Isotherm parameter of comp i [m3/kg-adsorbent]
IP2i
Isotherm parameter of comp i [K]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
T
Temperature [K]
Freundlich 1 Pressure dependent
Qi = IP1i Pi IP2 i IP1i
Isotherm parameter of comp i [kmol/bar/kg-adsorbent]
IP2i
Isotherm parameter of comp i [-]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
Concentration dependent
Qi = IP1iCiIP2 i IP1i
Isotherm parameter of comp i [m3/kg-adsorbent]
IP2i
Isotherm parameter of comp i [-]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
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Ci
Equilibrium concentration of comp i [kmol/m3]
Toth 1 Pressure dependent
Qi =
(IP
2i
IP1i Pi + Pi IP3i
)
1 IP3 i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [bar]
IP3i
Isotherm parameter of comp i [-]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
Concentration dependent
Qi =
(IP
2i
IP1iCi + CiIP3i
)
1 IP3 i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [kmol/m3]
IP3i
Isotherm parameter of comp i [-]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
BET 1 Pressure dependent
IP1i IP2i Qi =
P 1 − is P i
Pi Pi s
P P 1 − is + IP2i is P Pi i
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [-]
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Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Pi
Equilibrium pressure of comp i [bar]
Pi s
Saturated vapour pressure of comp i [bar]
Concentration dependent
IP1i IP2i Qi =
Ci Pi s RT
C C C 1 − s i 1 − s i + IP2i s i Pi RT Pi RT Pi RT
IP1i
Isotherm parameter of comp i [kmol/kg-adsorbent]
IP2i
Isotherm parameter of comp i [-]
Qi
Equilibrium loading of comp i [kmol/kg-adsorbent]
Ci
Equilibrium concentration of comp i [kmol/m3]
Pi s
Saturated vapour pressure of comp i [bar]
R
Gas constant, 8.31433e-2 [bar.m3/kmol/K]
T
Temperature [K]
User Guidelines How to Create a CSS Simulation Flowsheet Preconditions: The user must hold the licenses for Aspen Adsim 2004.1 and Aspen Properties 2004.1 (or Aspen Plus 2004.1). The property file, named air.appdf, is used for component properties definition. 1
Start Aspen Adsim 2004.1.
2
Initialize component properties by loading a property definition.
2 Gas Cyclic Steady State Modeling
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3
Choose target components from the component list. (Example. A user chooses N2 and O2 as the components for a simulation.)
4
Select CSS_Info from Structure Types folder by either pressing [Ctrl + I] or clicking the right mouse button and choosing Create Instance.
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5
A dialog box is displayed for the name of the structure instance, and user enters a name. (Example. Enter CSSInfo as the name of the structure instance.)
6
Aspen Adsim shows the instance in a folder of the same name below Flowsheet\Structures folder.
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7
Select the global non-isothermal/isothermal option by choosing TRUE or FALSE the logical parameter, NonIsothermal, from the Specify Table of the instanced structure. (Example. Switch the global NonIsothermal parameter to TRUE from the Specify Table of the instance structure CSSInfo.)
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8
Construct a simulation flowsheet using models from the CSS folder of Aspen Adsim Gas Library. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.)
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9
The connect models using the stream, gCSS_Material_Connection, from the Stream Types folder of Aspen Adsim Library and rename each model, as shown in the picture. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.)
10 Specify models by putting assumptions and parameter values that are required for process simulation. The following are typical items for the N2PSACSS example. i
Bed1 (gCSS_Adsorber): Click the right mouse button and select Specify table from the Forms menu and specify the CSS bed model B1. Leave all items as default, except the following: Layer(1).xNodes
10
Layer(1).NonAdiabatic
True
Layer(1).RigorousWallBalance
True
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ii
Bed1 (gCSS_Adsorber): Use right mouse button and select Specify_ table from Forms and specify the CSS bed model B1. Leave all items as default, except the following: Layer(1).Hs
1e-007
Layer(1).Ta
298.15
Layer(1).IP("N2",1)
0.00267288
Layer(1).IP("N2",2)
0.136
Layer(1).IP("O2",1)
0.00267287
Layer(1).IP("O2",2)
0.1413
Layer(1).ksLDF("N2")
0.00760501
Layer(1).ksLDF("O2")
0.04476
Table - Specify
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Table - Specify_
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iii TD1 and TD2 (gCSS_TankVoid): these two tank/void models have the same specification. The following items should be changed: Ta
298.15
NonAdiabaticTankVoid
True
Hamb
1.e-005
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Hw
6.e-005
TD1
TD2
iv. VP1 (gCSS_Valve): change CheckValve option to True VP1
11 Select the Cycle Organizer from the Tools menu. Aspen Adsim displays the icon, Cycle_Organizer, on the simulation flowsheet, with a dialog box from Cycle Organizer.
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12 Cyclic Steady State simulation mode can be chosen by selecting Cycle Options from the Cycle menu. To define a CSS simulation flowsheet, check the check box out, Cyclic Steady-State mode.
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13 Define process cycle/step information within the Step menu. For this example, N2PSACSS, we have four process steps, and the interaction and control details are as follows:
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STEP1
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STEP2
STEP3
STEP4
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14 Define the variable to be manipulated and the values within the Cycle Organizer. STEP1
STEP2
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STEP3
STEP4
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15 Generate a Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. Aspen Adsim displays a green check-shape icon on the status bar, indicating a Cycle Task has been created correctly. BEFORE
AFTER
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16 Close the Cycle Organizer, then confirm Aspen Adsim shows a green square on the simulation status bar and that the simulation mode is now set Steady State. If so, the simulation is ready to be run in CSS mode.
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How to Create a Dynamic Simulation Flowsheet using CSS Models Preconditions: The user must be a the licensed user of Aspen Adsim 2004.1 and Aspen Properties 2004.1 (or Aspen Plus 2004.1). The property file, named air.appdf, is used for component properties definition. 1
Start Aspen Adsim 2004.1.
2
Initialize component properties by loading a property definition.
3
Choose target components from the component list. (Example. Choose N2 and O2 as the components for a simulation.)
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4
Select CSS_Info from the Structure Types folder by either pressing [Ctrl + I] or clicking right mouse button and choosing Create Instance.
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5
A dialog box is displayed to enter the name of the structure instance, and the user enters a name. (Example. Enter CSSInfo as the name of the structure instance.)
6
Aspen Adsim displays the instance in a folder of the same name below the Flowsheet\Structures folder.
2 Gas Cyclic Steady State Modeling
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7
Select the global non-isothermal/isothermal option by choosing TRUE or FALSE the logical parameter, NonIsothermal, from the Specify Table of the instanced structure. (Example. Switch the global NonIsothermal parameter to TRUE from the Specify Table of the instance structure CSSInfo.)
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8
Construct a simulation flowsheet using models from the CSS folder of Aspen Adsim Gas Library. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.)
9
Next, connect models using the stream, gCSS_Material_Connection, from the Stream Types folder of Aspen Adsim Library and rename each model, as shown in the picture. (Example. Re-construct N2PSACSS - supplied as one of Aspen Adsim 2004.1 demonstrations.)
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10 Specify models by putting assumptions and parameter values required for the process simulation. – the following are typical items for the N2PSACSS example. v. Bed1 (gCSS_Adsorber): Click the right mouse button and select Specify table from Forms menu, then specify the CSS bed model B1. – leave all items as default, except the following: Layer(1).xNodes
10
Layer(1).NonAdiabatic
True
Layer(1).RigorousWallBalance
True
vi. Bed1 (gCSS_Adsorber): Click the right mouse button and select Specify_ table from Forms and specify the CSS bed model B1 - leave all items as default, except the following: Layer(1).Hs
1e-007
Layer(1).Ta
298.15
Layer(1).IP("N2",1)
0.00267288
Layer(1).IP("N2",2)
0.136
Layer(1).IP("O2",1)
.
00267287
Layer(1).IP("O2",2)
0.1413
Layer(1).ksLDF("N2")
0.00760501
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Layer(1).ksLDF("O2")
0.04476
Table - Specify
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Table - Specify_
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vii. TD1 and TD2 (gCSS_TankVoid): these two tank/void models have the same specification. The following items should be changed: Ta
298.15
NonAdiabaticTankVoid
True
Hamb
1.e-005
Hw
6.e-005
TD1
TD2
viii.
VP1 (gCSS_Valve): change CheckValve option to True.
VP1
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11 Select Cycle Organizer from the Tools menu; Aspen Adsim displays the icon Cycle_Organizer, on the simulation flowsheet and the Cycle Organizer dialog box.
12 Non Cyclic Steady State simulation mode can be chosen from the Cycle Options in the Cycle menu. To define a dynamic simulation flowsheet, uncheck Cyclic Steady-State mode check box and enter the value of Maximum cycle for dynamic simulation. 13 Define process cycle/step information within the Step menu. For this example, N2PSACSS, we have four process steps, and the interaction and control details are as follows:
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STEP1
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STEP2
STEP3
STEP4
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14 Define the variable to be manipulated and the values within Cycle Organizer. STEP1
STEP2
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STEP3
STEP4
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15 Generate a Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. Aspen Adsim displays a green check-shape icon on the status bar, indicating the Cycle Task has been created correctly. BEFORE
AFTER
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16 Close Cycle Organizer and confirm that Aspen Adsim displays a green square on the simulation status bar and that simulation mode is now set Dynamic. If so, the simulation is ready to be run in dynamic mode.
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How to Convert a CSS Flowsheet to a Dynamic Flowsheet Preconditions: There is an existing Aspen Adsim 2004.1 data file defined in CSS mode to convert the simulation mode from CSS to dynamic. If you are not sure which Aspen Adsim data file is defined in CSS mode, please refer to How to Create a CSS Simulation Flowsheet. 1
Open the existing Aspen Adsim flowsheet (defined in CSS simulation mode).
2
Activate the Cycle Organizer by double-clicking the icon and locate the Cyclic Steady-State mode check box on the Cyclic Options Tab.
3
Uncheck the check box to convert the flowsheet from CSS to dynamic. The Cyclic Organizer displays a dialog box to ask the Maximum Variable Steps option (recommended answer is Yes).
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4
Enter the maximum cycles value (e.g., 20) in the Cycle Options Tab and generate the Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer. Aspen Adsim displays a green check-shape icon on the status bar, indicating the Cycle Task has been created correctly.
BEFORE
AFTER
2 Gas Cyclic Steady State Modeling
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5
Close the Cycle Organizer and then confirm Aspen Adsim displays a green square on the simulation status bar and if simulation mode is now set Dynamic. If so, the simulation is ready to be run in dynamic mode.
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How to Convert a Dynamic Flowsheet into a CSS Flowsheet Preconditions: There is an existing Aspen Adsim 2004.1 dynamic flowsheet created using CSS models and the user wishes to convert the simulation mode from dynamic to CSS. If you are not sure which Aspen Adsim data file is defined in dynamic mode using CSS models, please refer to How to Create a Dynamic Simulation Flowsheet using CSS Models. 1
Open an existing Aspen Adsim flowsheet (defined in dynamic simulation mode).
2
Activate the Cycle Organizer by double-clicking the icon and locate the Cyclic Steady-State mode check box on the Cyclic Options Tab. Check the check box to re-define the simulation as CSS flowsheet.
BEFORE
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AFTER
2 Gas Cyclic Steady State Modeling
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3
After confirming (from the status bar of Cycle Organizer) the Cycle Task is active, close the Cycle Organizer. If the Task is not active, generate a Cycle Task either by executing Generate Task from Cycle menu or by clicking Generate Cycle from the status bar of Cycle Organizer.
4
Aspen Adsim displays a green square on the simulation status bar and the simulation mode is now set to Steady State. If so, the simulation is ready to be run in CSS mode.
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Developer’s Tips to Get Better Convergence Property in CSS Simulation 1
Careful consideration in setting Solver Property options is required to ensure convergence of CSS models. In the Non Linear Solver Tab, we recommend selecting the Newton Method for CSS simulation whilst the Fast Newton is normally recommendable in a dynamic simulation.
2
Convergence criterion is recommended to set Residual and Variable.
3
Max. step reductions value should be maximized as 20.
4
Recommended Max. iterations value is 5000.
5
The value of Maximum variable step is highly sensitive for the convergence property. For CSS simulation, a recommended default value is 200, and this may be adjusted (normally increase as problem is complex) but should not exceed 500. Note that the value of the Maximum variable step must be reduced if the flowsheet follows dynamic (not exceed 50).
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Recommended Non Linear Solver Property
6
A new check box, ‘Use transpose’, has been added to the Solver Properties dialog Linear Solver Tab. The recommended selection for this option is CSS simulation.
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7
The following dialog shows the recommended tolerance table for CSS simulation.
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183
3 Ion-Exchange Processes
This chapter contains for information on: •
About Ion-Exchange Processes
•
Bed Model Assumptions for Ion-Exchange Processes
•
Configure Form for Ion-Exchange Processes
•
Configure Layer Form for Ion-Exchange Processes
•
General Tab
•
Material/Momentum Balance Tab
•
About Axial Dispersion in Ion-Exchange Processes
•
Kinetic Model Tab
•
Isotherm Tab
•
Summary of Mass Balance Equations for Ion-Exchange Processes
About Ion-Exchange Processes In ion-exchange processes, a fluid phase (such as an aqueous solution) containing cations and anions, is contacted with an ion-exchange resin. Typically, the ion-exchange resin is inside a packed bed adsorption column. The resin contains bound groups carrying a positive or negative ionic charge, which are accompanied by displaceable ions of opposite charge (counterions). The displaceable ions have the same charge as the ions of interest in the fluid phase: since the ions in the fluid phase have a greater affinity for the bound groups than those originally present, the latter are displaced by the former. Generally, the resin has a fixed total charge capacity, so one ionic solute is exchanged for another while maintaining charge neutrality. Ion-exchange processes have become an important separation technique for aqueous electrolyte solutions and are used in these applications: •
Water softening, where monovalent cations replace multivalent cations.
•
Water purification, where hydrogen or hydroxide ions replace cations (usually monovalent).
•
Multi-component separation of ionic mixtures of different type and charge.
Ion-exchange may be written as a reversible reaction involving charge equivalent quantities. For example, in a water-softening process, the cationexchange process is written as:
Ca 2 + + 2 NaR ⇔ CaR2 + 2 Na +
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where R is a stationary, univalent, anionic group in the poly-electrolyte network of the exchange phase.
Bed Model Assumptions for IonExchange The bed model assumptions for ion-exchange are: •
Overall and component material balances apply for the liquid phase.
•
Isothermal conditions apply.
•
Plug flow or plug flow with axial dispersion applies.
•
The liquid stream pressure is constant (no frictional pressure drop).
•
The superficial velocity and thus volumetric flow rate remain constant. (The ion components are dilute so the effect of adsorption on the overall mass balance is negligible.)
•
Ideal mixing occurs in the aqueous phase. Since the ionic components are very dilute, overall molar volume remains constant.
•
Changes in molar volume between distinct, sequentially fed fluids are allowed.
•
The total exchange capacity of the bed Q is constant.
•
A lumped mass-transfer rate applies, with a liquid- or solid-film resistance. This resistance is either linear, quadratic, or user-defined.
•
The mass-action equilibrium is one alternative model for ion-exchange behavior. Others include the extended Langmuir and extended LangmuirFreundlich models.
Configure Form (ionx) In the Configure Form of the Ion-exchange process bed model: •
Enter the number of layers within the bed (1 or more).
•
Click in the Description box for each layer and type in a brief name or description.
•
Click Configure to open the Configure Layer dialog box.
•
Click Specify to open the specify form for the layer model.
Configure Layer Form (ionx) Use the options in the Configure Layer form to specify the set of equations within each layer of the bed. For more information on choosing the options for your ion-exchange process, see these sections: •
General tab
•
Material/Momentum Balance tab
•
Kinetic Model tab
•
Isotherm tab
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General Tab (ionx) Use the General tab to specify these options for your ion-exchange process: •
Discretization method
•
Number of nodes
General Tab (ionx): Discretization Method to be Used These discretization methods are available for ion-exchange processes: •
UDS1
•
UDS2
•
CDS1
•
LDS
•
QDS
•
MIXED
•
BUDS
General Tab (ionx): Number of Nodes In the Number of Nodes box, choose an appropriate number of nodes for your chosen discretization method.
Material/Momentum Balance Tab (ionx) Use the Material/Momentum Balance tab to specify the basic assumptions about material dispersion in the liquid phase for ion-exchange processes.
Material/Momentum Balance Tab (ionx): Material Balance Assumption In the Material Balance Assumption box, choose from one of the following options: •
Convection Only
•
Convection with Constant Dispersion
•
Convection with Estimated Dispersion
•
Convection with User Procedure Dispersion
•
Convection with User Submodel Dispersion
Material Balance Assumption (ionx): Convection Only This option omits the dispersion term from the material balance, so the model represents plug flow with a zero dispersion coefficient (infinite Peclet number).
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Because the dispersion term is omitted, you do not need to supply the dispersion coefficient.
Material Balance Assumption (ionx): Convection with Constant Dispersion The Convection with Constant Dispersion option includes the dispersion term in the material balance for the bed. You must then supply a fixed value for the dispersion coefficient, E z . With this option, the dispersion coefficient is constant for all components throughout the bed.
Material Balance Assumption (ionx): Convection with Estimated Dispersion The Convection with Estimated dispersion option includes the dispersion term in the material balance for the bed. Here, the dispersion coefficient varies along the length of the bed. Aspen Adsim estimates the components' dispersion coefficients in an ion-exchange bed using this correlation (Slater, 1991):
Re vl d P = 0.2 + 0.011 Ez εi
0.48
where:
Ez
=
Axial dispersion coefficient
vl
=
Liquid Velocity
εi
=
Interparticle voidage
dp
=
Particle diameter
=
Reynolds number
µ
=
Liquid viscosity
ρl
=
Liquid molar density
Ml
=
Liquid molecular weight
Re =
ρ l M l d P vl µ
Material Balance Assumption (ionx): Convection with User Procedure Dispersion The Convection with User Procedure Dispersion option includes the dispersion term in the material balance for the bed. The dispersion coefficient varies with axial position according to a usersupplied Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_i_Dispersion.
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Material Balance Assumption (ionx): Convection with User Submodel Dispersion The Convection with User Submodel Dispersion option includes the dispersion term in the material balance for the bed. The dispersion coefficient varies with axial position according to the usersupplied submodel iUserDispersion.
About Axial Dispersion in IonExchange Processes As a fluid flows through a packed column such as an ion-exchange bed, axial dispersion (mixing) tends to occur, which reduces the efficiency of separation. Axial dispersion should be minimized in bed design, but, if it occurs, then Aspen Adsim must account for its effects. There are several sources of axial dispersion in ion-exchange processes (Ruthven, 1984): •
Channeling caused by non-uniform packing, for example where different sections of the packing have different voidages.
•
Dispersion from wall effects due to non-uniform packing at the wall. This can be avoided by packing the bed well, and having a sufficiently large ratio of bed-to-particle diameters.
•
Hold-up of liquid in the laminar boundary layer surrounding the particles combined with small random fluctuations in the flow.
•
Splitting and recombining of the flow around the particles.
The molecular diffusivities of liquids are too small to contribute significantly to axial dispersion. In general, the mixing effects are additive and can be lumped together into a single effective dispersion coefficient, E z . The dispersion term in the material balance is usually expressed as:
∂ 2 ck − ε i Ez ∂z 2 The type of flow determines whether this term is omitted or included in the material balance.
Deciding When to Use Axial Dispersion in Ion-Exchange Processes In deciding whether to include axial dispersion in the bed model, it is useful to work out the Peclet number, given an effective dispersion coefficient ( E z ), a liquid superficial velocity ( vl ), and a bed height ( H b ):
Pe =
vl H b Ez
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The Peclet number quantifies the degree of dispersion introduced into the system. It is dimensionless so is more convenient than the dispersion coefficient for this purpose. The following table shows the effect of different values of Peclet number: If the Peclet number is
The effect of axial dispersion on bed performance is
0
Infinite: the bulk liquid is perfectly mixed., so the liquid composition is homogeneous throughout the entire bed.
< 30
Significant.
> 100
Very slight: The bed operates under near plug flow conditions.
∞
Zero: The bed operates under plug flow conditions.
Numerical methods used to discretize the spatial derivatives in the general equations can also introduce an artificial form of dispersion.
Kinetic Model Tab (ionx) The overall mass transfer of ionic components between the bulk liquid phase and the adsorbed phase must overcome two resistances: •
Mass transfer resistance located in the boundary layer surrounding the particle.
•
Mass transfer resistance inside the resin particle.
Typically, the second resistance determines the overall mass transfer rate. Aspen Adsim lumps the overall resistance to mass transfer into a single overall factor. You select the type of resistance from: •
Film Model Assumption
•
Kinetic Model Assumption
•
Form of Lumped Resistance
•
Form of Mass Transfer Coefficient
Kinetic Model Tab (ionx): Film Model Assumption In the Film Model Assumption box, choose from: •
Solid — The mass transfer driving force is expressed as a function of the solid phase loading (solid film).
•
Fluid — The mass transfer driving force is expressed as a function of the liquid phase concentration (liquid film).
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Kinetic Model Tab (ionx): Kinetic Model Assumption In the Kinetic Model Assumption box, choose from: •
Lumped Resistance
•
User Procedure
•
User Submodel
Kinetic Model Assumption (ionx): Lumped Resistance Here, the mass transfer driving force for component k is expressed as a function of the liquid phase concentration (liquid film), or solid phase loading (solid film). This function is either linear or quadratic. See Form of Lumped Resistance, later.
Kinetic Model Assumption (ionx): User Procedure With this option, the component rates of mass transfer are related to local conditions in the bed through a relationship you supply in a Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_i_Kinetic.
Kinetic Model Assumption (ionx): User Submodel With User Submodel selected, the component rates of mass transfer are related to local conditions in the bed through the user submodel iUserKinetic.
Kinetic Model Tab (ionx): Form of Lumped Resistance This option is active only if you selected Lumped Resistance as your Kinetic Model assumption. The following options are available: •
Linear
•
Quadratic
Form of Lumped Resistance (ionx): Linear The mass transfer driving force for component k is expressed as a linear function of the liquid phase concentration or solid phase loading.
∂wk = MTCl k (c k − c k* ) ∂t
(fluid film)
∂wk = MTCs k ( wk* − wk ) ∂t
(solid film)
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Form of Lumped Resistance (ionx): Quadratic The mass transfer driving force is expressed as a quadratic function of the liquid phase concentration (fluid film) or solid phase loading (solid film).
(c 2 − (c k* ) 2 ) ∂wk = MTCl k k ∂t 2c k
(fluid film)
(( wk* ) 2 − wk2 ) ∂wk = MTCs k ∂t 2 wk
(solid film)
Kinetic Model Tab (ionx): Form of Mass Transfer Coefficient Use this option to specify how to define the mass transfer coefficients. Choose from: •
Constant
•
User Procedure
•
User Submodel
Form of Mass Transfer Coefficient (ionx): Constant With this option, the mass transfer coefficient for each component is constant throughout the bed. You must supply a constant value of mass transfer coefficient for each component in the Specify table of the layer.
Form of Mass Transfer Coefficient (ionx): User Procedure Here, the mass transfer coefficients are functions of local bed conditions. The function is implemented in a Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_i_MTC.
Form of Mass Transfer Coefficient (ionx): User Submodel With User Submodel selected, the mass transfer coefficients are functions of local bed conditions, and are returned through the user submodel iUserMTC.
Isotherm Tab (ionx) Use the Isotherm tab to specify the adsorption isotherms for use in your ionexchange process.
About Adsorption Isotherms for IonExchange Processes The driving force behind an ion-exchange separation process is the departure from adsorption equilibrium between the aqueous and adsorbed phases. Consequently, adsorption isotherms (also known as ion-exchange equilibria) are important data in the design of ion-exchangers. Aspen Adsim has a list of commonly used, standard multi-component adsorption isotherms.
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Important: The equations presented are for equilibrium conditions. Depending on the mass transfer rate model you choose, they are used to compute either: •
w*, the loading that would be at equilibrium with the actual liquid phase composition -or-
•
c*, the liquid phase composition that would be at equilibrium with the actual loading.
This choice is automatically handled by Aspen Adsim depending on your selection of kinetic model. The equilibrium variable arrays (of size number of nodes × number of components) are named either Ws or Cs. In bed models, these variables are distributed, so they have a qualifier 1, 2, … n (=number of nodes), depending on the bed location.
Isotherm Tab (ionx): Isotherm Assumed for Layer In the Isotherm Assumed for Layer box, choose from: •
Mass Action Equilibrium
•
Extended Langmuir
•
Extended Langmuir-Freundlich
•
User Procedure
•
User Submodel
Isotherm Assumed for Layer (ionx): Mass Action Equilibrium
++
A B R
+
B B B
+ + A
+ R
R
R
The exchange reaction in the ion-exchange process is typically takes the form:
A + mBR ⇔ ARm + mB where m is a stoichiometric coefficient. •
m is an integer or a fraction. It is given by the valence ratio of A and B.
•
A refers to an ionic component in solution.
•
B refers to a counter-ion on the ion-exchanger surface.
•
R refers to a bound group (of opposite sign to B).
The associated equilibrium relationship can be written as:
y x 1 = A B K AB x A y B
m
Q c0
m −1
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where:
K AB
=
Equilibrium constant or selectivity coefficient.
x
=
Equivalent mole fraction in the adsorbed phase.
y
=
Equivalent mole fraction in the aqueous phase.
c0
=
Total ionic concentration.
Q
=
Ion-exchange resin capacity.
In Aspen Adsim, the parameter IP1 equals K AB , and the parameter m equals
IP2 . The equation now becomes:
y x IP1 A A B x A y B
IP2 A
Q c0
IP2 A −1
= 1.0
Isotherm Assumed for Layer (ionx): Extended Langmuir The extended Langmuir isotherm was found to represent some experimental data satisfactorily:
wi =
IP1i ci 1 + ∑ (IP2 k c k ) + IP2b cb k
where b refers to the (original) counter-ion.
Isotherm Assumed for Layer (ionx): Extended LangmuirFreundlich This isotherm is based on the Langmuir isotherm and expressed as:
wi =
1+ ∑
IP1i ciIP2 i IP3k c kIP4 k + IP3b cbIP4 b
(
)
k
where b refers to the (original) counter-ion.
Isotherm Assumed for Layer (ionx): User Procedure You can supply your own, proprietary isotherm relationships through a Fortran subroutine, which Aspen Adsim interfaces using one of two procedures: •
pUser_i_Isotherm_C for solid film kinetic model
•
pUser_i_Isotherm_W for liquid film kinetic model
Isotherm Assumed for Layer (ionx): User Submodel With User Submodel selected, you supply the isotherm relationship through the user submodel iUserIsotherm.
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Summary of Mass Balance Equations for Ion-Exchange Processes This section summarizes the mass balance equations used by Aspen Adsim to simulate ion-exchange processes. The overall material balance is expressed as:
vl
∂ρ l ∂ρ + εi l = 0 ∂t ∂z
This equation accounts for the fact that, during an ion-exchange cycle, solvents of different densities are being used in the different production, purge and regeneration stages. Density remains unchanged as a result of the ion-exchange process itself. Each ionic species in the liquid phase, fed into the ion-exchange column, is governed by the following material balance equation:
− ε i Ez
∂ 2 ck ∂c ∂c + vl k + ε i k + J k = 0 2 ∂z ∂z ∂t
The mass transfer rate J k between the bulk liquid and the resin is given by:
J k = (1 − ε i )
∂wk ∂t
where the uptake rate
∂wk can, for example, be determined by a solid film ∂t
linear driving force relationship, such as:
∂wk = MTC sk wk* − wk ∂t
(
)
The number of counter ions being released from the resin and entering the liquid phase is determined from the number of ions exchanged from the liquid phase — the total charge of both liquid and resin must remain neutral: nc
Jb = ∑ Jk k =1 k ≠b
Hence the behavior of the exchanged counter ion in the liquid phase can be described by:
− ε i Ez
∂ 2 cb ∂ cb ∂cb nc ε + v + − ∑ Jk = 0 l i ∂z 2 ∂z ∂t k =1 k ≠b
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Explanation of Equation Symbols for Ion-Exchange Processes The tables explain the equation symbols used in Aspen Adsim's ion-exchange mass balance equations. Symbol
Explanation
Aspen Adsim base units
cb
Counter ion concentration in liquid phase.
eq/m3
ck
Ion concentration in liquid phase.
eq/m3
c k*
Liquid phase ion concentration in equilibrium with resin phase.
eq/m3
c0
Total liquid phase ion concentration.
eq/m3
dp
Resin particle diameter.
m
Ez
Axial dispersion coefficient.
m2/s
HB
Bed height.
m
IP
Isotherm parameter.
Jb
Counter ion material transfer rate.
eq/m3/s
Jk
Ion material transfer rate.
eq/m3/s
K AB
Mass action equilibrium constant.
m
Stoichiometric coefficient used in mass action equilibrium.
Ml
Solvent molecular weight.
kg/kmol
MTCl
Liquid film mass transfer coefficient.
1/s
MTCs
Solid film mass transfer coefficient.
1/s
Q
Total resin ion capacity.
eq/m3
t
Time.
s
wk
Ion loading on resin.
eq/m3
wk*
Ion loading in equilibrium with liquid phase ion concentration.
eq/m3
xk
Ion mole fraction in adsorbed (resin) phase.
yk
Ion mole fraction in liquid phase.
z
Axial co-ordinate.
m
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εi
Bed voidage.
µ
Solvent viscosity.
N/m2/s
Solvent molar density.
kmol/m3
ρi
Dimensionless number
Defining expression
Description
Pe
vl H B Ez
Peclet number
Re
M l ρ l d P vl
Reynolds number
µ
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4 Liquid Adsorption Processes
This chapter contains information on liquid adsorption processes and how they are simulated in Aspen Adsim. For more information, see the following topics: •
About Liquid Adsorption Processes
•
Bed Model Assumptions for Liquid Adsorption
•
Configure Form
•
Configure Layer Form
•
General Tab
•
Material/Momentum Balance Tab
•
Kinetic Model Tab
•
About Adsorption Isotherms for Liquid Adsorption
•
Guidelines for Choosing Aspen Adsim Isotherm Models
•
Energy Balance Tab
•
Procedures Tab
•
Summary of Mass and Energy Balance
•
Explanation of Equation Symbols
About Liquid Adsorption Processes Liquid phase adsorption has long been used to remove contaminants present at low concentrations in process streams, such as organics from waste water. When contaminants are not well defined, liquid phase adsorption can improve feed quality, defined by color, taste, odor, and storage stability. Unlike trace impurity removal, using liquid phase adsorption for bulk separation on a commercial scale is a relatively recent development. The first commercial operation was in the 1960s, in hydrocarbon processing. Since then, bulk adsorptive separation of liquids has been used to solve a broad range of problems, including individual isomer separations and class separations. The commercial availability of synthetic molecular sieves and ion-exchange resins, and the development of novel process concepts have been the two significant factors in the success of these processes.
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Bed Model Assumptions for Liquid Adsorption For liquid adsorption, the bed model assumes: •
Plug flow, or plug flow with axial dispersion.
•
The liquid phase pressure is either constant or varies according to a laminar-flow momentum balance (with the pressure drop assumed proportional to the flow velocity).
•
The superficial velocity is constant, or varies due to adsorption and according to total mass balance.
•
Molar concentrations are calculated from molar volumes. Ideal mixing is assumed to occur in the liquid phase, so molar volume is a linear function of composition.
•
A lumped mass-transfer rate applies, with a liquid or solid-film resistance. This resistance is either linear, quadratic or user-defined.
•
Mass transfer coefficients are either constant or user defined.
•
The adsorption isotherm is chosen from Aspen Adsim defined isotherms, or specified by you.
•
Isothermal or non-isothermal conditions apply. The energy balance includes terms for: − Thermal conductivity of gas and solid. − Liquid-solid heat transfer. − Heat of adsorption. − Enthalpy of adsorbed phase. − Heat exchange with environment. − Wall energy terms.
Configure Form (liq) This section contains information on the Configure form for a liquid process bed model. The following options are available: •
Enter the number of layers within the bed (one or more).
•
Type a brief name or description in the Description box.
•
Click the Configure button to open the Configure Layer dialog box.
•
Click the Specify button to open the Specify form for the layer model.
Configure Layer Form (liq) Use the options in the Configure Layer form to define the set of equations for each layer of the adsorption bed. For information on choosing the options for your liquid adsorption process, see the following sections: •
General Tab
•
Material/Momentum Balance Tab
•
Kinetic Model Tab
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•
Isotherm Tab
•
Energy Balance Tab
•
Procedures Tab
General Tab (liq) Use the General tab to specify the numerical options for your liquid adsorption process.
General Tab (liq): Discretization Method to be Used These discretization methods are available for liquid adsorption processes: •
UDS1
•
UDS2
•
CDS1
•
LDS
•
QDS
•
MIXED
•
BUDS
General Tab (liq): Number of Nodes In the Number of Nodes box, choose an appropriate number of nodes for your discretization method.
Material/Momentum Balance (liq) Use the Material/Momentum Balance tab to: •
Make basic assumptions about axial dispersion in the liquid phase.
•
Determine how to treat the pressure drop in the adsorption bed model.
•
Specify whether the velocity is constant or varies along the column.
Material/Momentum Balance Tab (liq): Material Balance Assumption In the Material Balance Assumption box, choose the material balance option for your liquid adsorption process. Choose from: •
Convection Only
•
Convection with Constant Dispersion
•
Convection with Estimated Dispersion
•
Convection with User Procedure Dispersion
•
Convection with User Submodel Dispersion
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Material Balance Assumption (liq): Convection Only The Convection Only option leaves out the dispersion term from the material balance for the bed. The model now represents plug flow with a zero dispersion coefficient (infinite Peclet number). Because the dispersion term is omitted, you need not supply the dispersion coefficient.
Material Balance Assumption (liq): Convection with Constant Dispersion The Convection with Constant Dispersion option includes the dispersion term in the material balance for the bed. You need to supply a constant value for the dispersion coefficient, E z . With this option, the dispersion coefficient is constant for all components throughout the bed.
Material Balance Assumption (liq): Convection with Estimated Dispersion The Convection with Estimated Dispersion option includes the dispersion term in the material balance for the bed. With this option, the dispersion coefficient varies along the length of the bed. Aspen Adsim estimates the values during the simulation, for each component, using this correlation (Slater, 1991):
vl rP 0.2 0.011 Re = + ε i Ez ε i ε i ε i
0.48
Where:
Ez
=
Axial dispersion coefficient
vl
=
Liquid Velocity
εi
=
Interparticle voidage
rp
=
Particle radius
Re
=
Reynolds number
Material Balance Assumption (liq): Convection with User Procedure Dispersion The Convection with User Procedure Dispersion option includes the dispersion term in the material balance for the bed. With this option, the dispersion coefficient varies according to a user supplied Fortran subroutine, which Aspen Adsim interfaces through the procedure type pUser_l_dispersion.
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Material Balance Assumption (liq): Convection with User Submodel Dispersion The Convection with User Submodel Dispersion option includes the dispersion term in the material balance for the bed. With this option, the dispersion coefficient varies according to the submodel lUserDispersion.
Material/Momentum Balance Tab (liq): Pressure Drop Assumption Use the Pressure Drop Assumption box to specify how Aspen Adsim treats the pressure drop in the adsorption bed model. You should base your choice on your knowledge of the actual operating conditions in the plant. This option corresponds to how internal superficial velocities are related to local pressure gradients. It applies to laminar flow. You must choose an appropriate material balance model with a particular pressure-drop option. In the Pressure Drop Assumption box, choose from these options: •
None
•
Darcy's Law
•
Karman-Kozeny
Pressure Drop Assumption (liq): None With None selected, there is no pressure drop across the bed.
Pressure Drop Assumption (liq): Darcy's Law Select the Darcy's Law option to apply a linear relationship between the liquid superficial velocity and the pressure gradient at a particular point in a bed. Darcy's law states that the pressure drop is directly proportional to flow rate:
∂p = − K P vl ∂z Where:
Kp
=
Proportionality constant
Pressure Drop Assumption (liq): Karman-Kozeny Select the Karman-Kozeny option to relate velocity to pressure drop: 3 − 1.5 × 10 −3 µ (1 − ε i ) ∂p 2rpψε i = ∂z vl (1 − ε i ) 2rpψ
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Material/Momentum Balance Tab (liq): Velocity Assumption In the Velocity Assumption box, choose from: •
Constant Velocity
•
Varying Velocity
Velocity Assumption (liq): Constant Velocity With Constant Velocity selected, the liquid velocity is constant along the bed, so adsorption from the liquid phase has a negligible effect on the material balance. These assumptions are valid only when modeling the removal of trace components from a bulk liquid.
Velocity Assumption (liq): Varying Velocity With Varying Velocity selected, the superficial velocity varies along the bed according to the rate at which the liquid components are adsorbed onto the solid, or desorbed. The rate is determined from material balance. This option is applicable to bulk separation applications. If you select this option: •
The velocity profile is determined through the total material balance, by the effect of the rate of adsorption.
•
The velocity profile is stored in the discrete variables Vl_in(1)…Vl_in(n), where n is the number of nodes used in the numerical method.
Material/Momentum Balance Tab (liq): Overall Material Balance Assumption In the Overall Material Balance Assumption box, choose from: •
Constant Density
•
Dynamic Density
Overall Material Balance Assumption (liq): Constant Density With the Constant Density option, the mass density is constant along the bed. The velocity alone changes, and that according to the overall mass balance.
Overall Material Balance Assumption (liq): Dynamic Density With Dynamic Density selected, mass density varies according to the material balance. Both mass density and velocity vary according to the overall mass balance.
Kinetic Model Tab (liq) When a species is adsorbed from the bulk liquid phase onto an active surface site of the adsorbents, it typically experiences the following mass transfer resistances:
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•
The resistance between the bulk liquid and the external adsorbents surface.
•
The resistance exerted by the adsorbents pore structure. For bi-disperse adsorbents (such as zeolites), this resistance can be further divided into: − Macropore resistance. − Micropore resistance.
These resistances are typically lumped into a single, overall mass transfer coefficient. The following options are available from the Kinetic Model tab: •
Film Model Assumption
•
Kinetic Model Assumption
•
Form of Mass Transfer Coefficient
Kinetic Model Tab (liq): Film Model Assumption In the Film Model Assumption box, choose from: •
Solid the mass transfer driving force is expressed as a function of the solid phase loading.
•
Fluid the mass transfer driving force is expressed as a function of the liquid phase concentration.
Kinetic Model Tab (liq): Kinetic Model Assumption In the Kinetic Model Assumption box, choose from: •
Linear lumped resistance.
•
Quadratic lumped resistance.
•
Micro and macropore.
•
User procedure.
•
User submodel.
Kinetic Model Assumption (liq): Linear Lumped Resistance With Linear Lumped Resistance selected, the mass transfer driving force for component i is expressed as a linear function of the liquid phase concentration or solid phase loading.
ρS
∂wi = MTCli (ci − ci* ) ∂t
∂wi = MTC si (wi* − wi ) ∂t
(fluid) (solid)
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Kinetic Model Assumption (liq): Quadratic Lumped Resistance With Quadratic Lumped Resistance selected, the mass transfer driving force is expressed as a quadratic function of the liquid phase concentration or solid phase loading.
(
∂wi MTCli ci2 − (ci* ) ρS = ∂t 2c i
(
2
( ∂wi wi* ) − wi2 = MTC si ∂t 2 wi 2
)
)
(fluid)
(solid)
Kinetic Model Assumption (liq): Micro and Macropore Model Two concentration gradients greatly affect the diffusion rate: •
Within the pores of the solid.
•
Within the void spaces between the particles, that is, within the crystallines.
Under practical conditions in gas separation, pore diffusion limits the overall mass transfer rate between the bulk flow and the internal surface of a particle, so it is an important factor in the dynamics of adsorbers. For more information, see Micro and Macro Pore Effects in Chapter 1.
Kinetic Model Assumption (liq): User Procedure The User Procedure option relates the component rates of mass transfer to the local bed conditions through a user-supplied Fortran subroutine, which Aspen Adsim interfaces through the procedure type pUser_l_Kinetic.
Kinetic Model Assumption (liq): User Submodel With User Submodel selected, the bed model calls the submodel lUserKinetic. This submodel needs the relationship between the component rates of mass transfer and the local bed conditions.
Kinetic Model Tab (liq): Form of Mass Transfer Coefficient In the Form of Mass Transfer Coefficient box, you choose how mass transfer coefficients are defined. Choose from: •
Constant
•
User Procedure
•
User Submodel
Form of Mass Transfer Coefficient (liq): Constant With Constant selected, the mass transfer coefficient for each component is constant through the bed. You must supply a constant value of mass transfer coefficient for each component.
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Form of Mass Transfer Coefficient (liq): User Procedure If you choose User Procedure, the mass transfer coefficients are returned by a Fortran subroutine you supply, which Aspen Adsim interfaces through the procedure pUser_l_MTC.
Form of Mass Transfer Coefficient (liq): User Submodel With User Submodel selected, the mass transfer coefficients are defined in the user submodel lUserMTC.
About Adsorption Isotherms for Liquid Adsorption The driving force behind all adsorptive liquid separation processes is the departure from adsorption equilibrium, so adsorption isotherms are important data in adsorber design. If you know the adsorption isotherms for the components of the feed, you can create a bed model to predict the performance of the adsorber bed for the specified operating conditions. Aspen Adsim has a comprehensive list of multicomponent adsorption isotherms.
Guidelines for Choosing Aspen Adsim Isotherm Models Make sure you choose a model that is appropriate for the process you are investigating. The equilibrium specified by the isotherm model affects the driving force for mass transfer. Consequently, you can obtain significantly different simulation results when using different models, even if the model parameters come from the same set of data. The expressions in this section are equilibrium equations. Depending on the mass transfer rate model you choose (See also Kinetic Model Tab (liq) on page 4-202), the expressions are used to compute either: •
w* The loading that would be at equilibrium with the actual liquid phase composition -or-
•
c* The liquid phase composition that would be at equilibrium with the actual loading.
This choice is automatically handled by Aspen Adsim. The equilibrium variable arrays (of size n) are named either Ws or Cs. In bed models, these variables are distributed, so they have a qualifier 1, 2, ... n, to denote their location in the bed.
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The Ideal Adsorbed Solution Theory (IAS) Recently, the Ideal Adsorbed Solution Theory (IAS) has become popular for multicomponent mixtures. The method lets you predict adsorption equilibria for components in a mixture. It needs data only for the pure-component adsorption equilibria at the same temperature, and on the same adsorbent. The model treats the mixed adsorbate phase as an ideal solution in equilibrium with the liquid phase. The model follows the formal, thermodynamic approach for vapor-liquid equilibria, in which the fundamental equations of thermodynamic equilibrium are developed, and applies this to the liquid-adsorbed phase equilibria. At first sight, ideal behavior in the adsorbed phase seems improbable. However, many systems have shown strong correlation between experimental data and predictions by IAS theory, including binary and ternary mixtures on activated carbons and zeolites. IAS is available in Aspen Adsim. To use it, choose the appropriate isotherm on the Isotherm tab of the Configure Layer form. For a full description of the IAS approach, see Chapter 4 of Ruthven (1984) or Chapter 3 of Kast (1988) (German language).
Isotherm Tab (liq): Isotherm Assumed for Layer Use the Isotherm tab to choose which adsorption isotherms are used in your liquid adsorption process. Choose from: •
Langmuir models (1,2)
•
Dual-Site Langmuir models (1,2
•
Extended Langmuir models (1,2)
•
Freundlich models (1,2)
•
Langmuir-Freundlich models (1,2)
•
Extended Langmuir-Freundlich models (1,2)
•
Stoichiometric Equilibrium models (1,2)
•
IAS Langmuir models (1,2)
•
IAS Freundlich models (1,2)
•
IAS Langmuir-Freundlich models (1,2)
•
User Multicomponent Procedure
•
User Multicomponent Submodel
•
User Multicomponent Procedure with IAS
•
User Multicomponent Submodel with IAS
Isotherm Assumed for Layer (liq): Langmuir Models (1,2) There are two types of Langmuir model available in Aspen Adsim: •
Langmuir 1, which is temperature independent.
•
Langmuir 2, which is temperature dependent.
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Langmuir 1 This isotherm is expressed as:
wi =
IP1i IP2i ci 1 + IP2i ci
Langmuir 2 This isotherm is expressed as:
IP IP1i IP2i exp 3i ci Ts wi = IP 1 + IP2i exp 3i ci Ts Isotherm Assumed for Layer (liq): Dual-Site Langmuir Models (1,2) There are two types of Dual-Site Langmuir model available in Aspen Adsim: •
Dual-Site Langmuir 1, which is temperature independent.
•
Dual-Site Langmuir 2, which is temperature dependent.
Dual-Site Langmuir 1 This isotherm is expressed as:
wi =
IP1i IP2i ci nc
1 + ∑ IP2 k ck k =1
+
IP3i IP4i ci nc
1 + ∑ IP4 k ck k =1
Dual-Site Langmuir 2 This isotherm is expressed as:
IP IP IP1i IP2i exp 3i ci IP4i IP5i exp 6i ci Ts Ts + wi = nc nc IP IP 1 + ∑ IP2 k exp 3k ck 1 + ∑ IP5 k exp 6 k ck k =1 k =1 Ts Ts Isotherm Assumed for Layer (liq): Extended Langmuir Models (1,2) Aspen Adsim has two types of Extended Langmuir model: •
Extended Langmuir 1, which is temperature independent.
•
Extended Langmuir 2, which is temperature dependent.
Extended Langmuir 1 This isotherm is expressed as:
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wi =
IP1i IP2i ci nc
1 + ∑ IP2 k ck k =1
Extended Langmuir 2 This isotherm is expressed as:
IP IP1i IP2i exp 3i ci Ts wi = nc IP 1 + ∑ IP2 k exp 3k ck k =1 Ts Isotherm Assumed for Layer (liq): Freundlich Models (1,2) There are two types of Freundlich model available in Aspen Adsim: •
Freundlich 1, which is temperature independent.
•
Freundlich 2, which is temperature dependent.
Freundlich 1 This isotherm is expressed as:
wi = IP1i ciIP2 i Freundlich 2 This isotherm is expressed as:
IP wi = IP1i ciIP2 i exp 3i Ts
Isotherm Assumed for Layer (liq): Langmuir-Freundlich Models (1,2) There are two types of Langmuir-Freundlich model available in Aspen Adsim: •
Langmuir-Freundlich 1, which is temperature independent.
•
Langmuir-Freundlich 2, which is temperature dependent.
Langmuir-Freundlich 1 This isotherm is expressed as:
wi =
IP1i IP2i ciIP3i 1 + IP2i ciIP3i
Langmuir-Freundlich 2 This isotherm is expressed as:
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IP IP1i IP2i ciIP3i exp 4i Ts wi = IP 1 + IP2i ciIP3i exp 4i Ts Isotherm Assumed for Layer (liq): Extended LangmuirFreundlich Models (1,2) There are two types of Extended Langmuir-Freundlich model available in Aspen Adsim: •
Extended Langmuir-Freundlich 1, which is temperature independent.
•
Extended Langmuir-Freundlich 2, which is temperature dependent.
Extended Langmuir-Freundlich 1 This isotherm is expressed as:
wi =
IP1i IP2i ciIP3i n
(
1 + ∑ IP2 j c j 3 j j =1
IP
)
Extended Langmuir-Freundlich 2 This isotherm is expressed as:
IP IP1i IP2i ciIP3i exp 4i Ts wi = n IP IP 1 + ∑ IP2 j c j 3 j exp 4 j j =1 Ts Isotherm Assumed for Layer (liq): Stoichiometric Equilibrium Models (1,2) Aspen Adsim has two types of Stoichiometric Equilibrium model: •
Stoichiometric Equilibrium 1, which is temperature independent.
•
Stoichiometric Equilibrium 2, which is temperature dependent.
Stoichiometric Equilibrium 1 This isotherm is expressed as:
wi =
IP1i IP2i ci nc
∑ IP k =1
c
2k k
Stoichiometric Equilibrium 2 This isotherm is expressed as:
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IP IP1i IP2i exp 3i ci Ts wi = nc IP IP2 k exp 3k ck ∑ k =1 Ts Isotherm Assumed for Layer (liq): IAS Langmuir Models (1,2) With IAS Langmuir Models selected, the multicomponent adsorption behavior is expressed using Ideal Adsorbed Solution theory in combination with pure component isotherms. Aspen Adsim has two versions of the pure component Langmuir model: •
IAS Langmuir 1, which is temperature independent.
•
IAS Langmuir 2, which is temperature dependent.
IAS Langmuir 1 This isotherm is expressed as:
wi =
IP1i IP2i ci 1 + IP2i ci
IAS Langmuir 2 This isotherm is expressed as:
IP IP1i IP2i exp 3i ci Ts wi = IP 1 + IP2i exp 3i ci Ts Isotherm Assumed for Layer (liq): IAS Freundlich Models (1,2) With IAS Freundlich Models selected, the multicomponent adsorption behavior is expressed using the Ideal Adsorbed Solution Theory in combination with pure component isotherms. Aspen Adsim has two versions of the pure component Freundlich model: •
IAS Freundlich 1, which is temperature independent.
•
IAS Freundlich 2, which is temperature dependent.
IAS Freundlich 1 This isotherm is expressed as:
wi = IP1i ciIP2 i IAS Freundlich 2 This isotherm is expressed as:
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IP wi = IP1i ciIP2 i exp 3i Ts
Isotherm Assumed for Layer (liq): IAS Langmuir-Freundlich Models (1,2) With IAS Langmuir-Freundlich selected, the multicomponent adsorption behavior is expressed using the Ideal Adsorbed Solution Theory in combination with pure component isotherms. Aspen Adsim has two versions of the pure component Langmuir-Freundlich model: •
IAS Langmuir-Freundlich 1, which is temperature independent.
•
IAS Langmuir-Freundlich 2, which is temperature dependent.
IAS Langmuir-Freundlich 1 This isotherm is expressed as:
wi =
IP1i IP2i ciIP3i 1+ IP2i ciIP3i
IAS Langmuir-Freundlich 2 This isotherm is expressed as:
IP IP1i IP2i ciIP3i exp 4i Ts wi = IP 1 + IP2i ciIP3i exp 4i Ts Isotherm Assumed for Layer (liq): User Multicomponent Procedure You can supply your own, proprietary isotherm relationships through a Fortran subroutine, which Aspen Adsim interfaces using one of two procedures: •
pUser_l_Isotherm_C for solid film kinetic model
•
pUser_l_Isotherm_W for liquid film kinetic model
The functional relationship is:
wi = f eq (T , c1 ...cnc , IP ) Isotherm Assumed for Layer (liq): User Multicomponent Submodel You can supply your own, proprietary isotherm relationships using the submodel lUserIsotherm. The functional relationship is:
wi = f eq (T , c1 ...cnc , IP )
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Isotherm Assumed for Layer (liq): User Purecomponent Procedure with IAS Select the User Purecomponent Procedure with IAS option to supply pure component, user-specified isotherms, which may be used as multicomponent isotherms. In this case, two Fortran subroutines are needed: The first subroutine is interfaced by the procedure type pUser_l_Isotherm_W. 0
This relates the fictitious pure component concentration ci (resulting in the same spread pressure as the mixture at total concentration ctot ), to the 0
loading wi , using the pure component isotherm:
(
wi0 = f eq T , ci0 , IP
)
The second Fortran subroutine evaluates the integral of the Gibbs isotherm to give the spread pressure. It is interfaced by the procedure type pUser_l_Gibbs. The relationship to be evaluated is:
AΠ i0 = g T , ci0 , IP with g = RT
(
)
ci0
∫ 0
f eq (T , c, IP ) c
dc
Isotherm Assumed for Layer (liq): User Purecomponent Submodel with IAS Select this option to supply pure component, user-specified isotherms, which may be used as multicomponent isotherms. In this case, you must supply two submodels: The first submodel is lUserIsotherm. This relates the fictitious pure 0
component concentration ci (resulting in the same spread pressure as the 0
mixture at total concentration ctot ), to the loading wi , using a pure component isotherm:
(
wi0 = f eq T , ci0 , IP
)
The second submodel, lUserGibbs, evaluates the integral of the Gibbs isotherm to give the spread pressure. The relationship to be evaluated is:
AΠ i0 = g T , ci0 , IP with g = RT
(
)
ci0
∫ 0
f eq (T , c, IP ) c
dc
Energy Balance Tab (liq) Use the Energy Balance tab to specify how the energy balance is incorporated into the model.
Energy Balance Tab (liq): Energy Balance Assumption In the Energy Balance Assumption box, choose from the following options: 4 Liquid Adsorption Processes
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•
Isothermal
•
Non-Isothermal with no Conduction
•
Non-Isothermal with Fluid Conduction
•
Non-Isothermal with Solid Conduction
•
Non-Isothermal with Fluid and Solid Conduction
Energy Balance Assumption (liq): Isothermal The Isothermal option ignores the energy balance. Fluid and solid temperatures are set to the same, constant value.
Energy Balance Assumption (liq): Non-Isothermal with No Conduction The Non-Isothermal with No Conduction option ignores the axial thermal conduction for the fluid and solid phases within the energy balance.
Energy Balance Assumption (liq): Non-Isothermal with Fluid Conduction The Non-Isothermal with Fluid Conduction option includes the thermal conduction (axial thermal dispersion) term in the fluid energy balance. This term is represented as:
− kl
∂ 2T ∂z 2
l
The liquid phase thermal conductivity can be supplied in different ways as specified in the section Form of Fluid Thermal Conductivity.
Energy Balance Assumption (liq): Non-Isothermal with Solid Conduction The Non-Isothermal with Solid Conduction option includes the thermal conduction term in the solid energy balance. The solid thermal conduction term is represented as:
∂ 2TS − kS ∂z 2 You must supply a value for k s .
Energy Balance Assumption (liq): Non-Isothermal with Fluid and Solid Conduction The Non-Isothermal with Fluid and Solid Conduction option includes the thermal conduction term for both fluid and solid phases. The liquid phase thermal conductivity can be supplied in different ways, as specified in the section Form of Fluid Thermal Conductivity field.
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Energy Balance Tab (liq): Consider Heat of Adsorbed Phase Aspen Adsim models enable you to include the heat capacity of the adsorbed phase in the solid-phase energy balance. The Heat of Adsorbed Phase term is optional. In the Consider Heat of Adsorbed Phase box, select from No or Yes: •
No — Choose this option to ignore the enthalpy of the adsorbed phase term in the solid phase energy balance.
•
Yes — Choose this option if the enthalpy content of the adsorbed phase is significant for your process, and you want to include it in the overall energy balance. The term for each component is a function of the loading and the temperature in the solid phase:
H ads ,i = ρ p C Pi wi
∂TS ∂t nc
The total contribution is the sum for all components:
∑H i =1
ads ,i
Energy Balance Tab (liq): Heat of Adsorption Assumption If the solid-phase energy balance is significant for the process, you must include the heat of adsorption within the balance. The rate of heat generation by adsorption of each component i, per unit mass of solid, is a function of the local rate of mass transfer and the heat of adsorption:
HTi =
∂wi ∆H i ∂t
These rates are held in vectors and summed for all components to obtain the total rate of heat generation, by adsorption, per unit volume of solid: nc
ρ p ∑ (HTi ) i =1
In the Heat of Adsorption Assumption box, choose from: •
None
•
Constant
•
User Procedure
•
User Submodel
Heat of Adsorption Assumption (liq): None The heat generation by adsorption term is omitted from the energy balance.
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Heat of Adsorption Assumption (liq): Constant The Constant option assumes the heat of adsorption is constant for each component i. Choose this option to set the heat of adsorption to constant values. These are held in a vector called DH. You must provide the values of the elements of DH.
Heat of Adsorption Assumption (liq): User Procedure With User Procedure selected, the heat of adsorption comes from a usersupplied Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_l_DH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms:
∆H = f (Ts , P, w) Heat of Adsorption Assumption (liq): User Submodel With User Submodel selected, the heat of adsorption comes from the user submodel lUserDH. You can vary the heat of adsorption and make it a function of, for example, local loading, temperature, and pressure. In general terms:
∆H = f (Ts , P, w)
Energy Balance Tab (liq): Form of Heat Transfer Coefficient If you request a non-isothermal energy balance, Aspen Adsim generates the solid and fluid phase energy balances, using a film resistance due to heat transfer between the solid and the fluid. Heat transfer is assumed to occur between the two phases according to: Rate of heat transferred per unit volume of bed = a P (1 − ε i )HTC (Tl − TS ) If there is no heat transfer resistance between the solid and fluid, the temperature of the fluid and solid are equal (“lumped”). To obtain this condition, set the heat transfer coefficient to a very large value (such as 1MW/m2/K). In the Form of Heat Transfer Coefficient box, choose from: •
Constant
•
Estimated
•
User Procedure
•
User Submodel
Form of Heat Transfer Coefficient (liq): Constant Choose Constant to ensure the heat transfer coefficient has a single value, which is held in a variable called HTC.
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Form of Heat Transfer Coefficient (liq): Estimated The heat transfer coefficient is estimated as follows: 1
Calculate the Reynolds number:
Re =
2 rp M ρ l vl
µ
If the calculated value falls below 1E-10, reset it to this value. 2
Calculate the Prandl number:
Pr =
µ C pl kl M
If the calculated value falls below 1E-10, reset it to this value. 3
Calculate the j-factor: If Re < 190 then j = 1.66 Re
4
−0.51
otherwise j = 0.983Re
−0.41
Calculate the heat transfer coefficient:
HTC = jC pl vl ρ l Pr
−2
3
If the calculated value falls below 1E-10, reset it to a value of 1.
Form of Heat Transfer Coefficient (liq): User Procedure With the User Procedure option, the user procedure pUser_l_HTC relates the local heat transfer coefficient to the state of the bed at a particular point in the bed. This means you can interface your own Fortran code to calculate the coefficients. In general terms:
HTC = f (Tl , P, C , vl ) Form of Heat Transfer Coefficient (liq): User Submodel With User Submodel selected, the local heat transfer coefficient is defined through the user submodel lUserHTC.
Energy Balance Tab (liq): Form of Fluid Thermal Conductivity If you selected Non-isothermal with Fluid and/or Solid Conduction, you need to choose the form of fluid thermal conductivity . In the Form of Fluid Thermal Conductivity box, choose from: •
Constant
•
Based on Axial Dispersion
•
User Procedure
•
User Submodel
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Form of Fluid Thermal Conductivity (liq): Constant The thermal conductivity has a constant value, which you set.
Form of Fluid Thermal Conductivity (liq): Based on Axial Dispersion With Based on Axial Dispersion selected, the thermal conductivity coefficient is calculated as the product of the molar heat capacity of the fluid, the axial dispersion coefficient and the molar density of the fluid:
k l = C Pl E z ρ l This method applies the analogy between heat and mass transfer.
Form of Fluid Thermal Conductivity (liq): User Procedure With User Procedure selected, thermal conductivity varies axially along the bed and is defined in a user-defined Fortran subroutine, which Aspen Adsim interfaces using the procedure pUser_l_Kl.
Form of Fluid Thermal Conductivity (liq): User Submodel With User Submodel selected, thermal conductivity varies axially along the bed and is defined in the user submodel lUserKl.
Energy Balance Tab (liq): Heat Transfer to Environment In the Heat Transfer to Environment box, choose from: •
Adiabatic
•
Thin Wall
•
Rigorous Model
•
Heat Exchange between Fluid and Wall
•
Heat Exchange between Wall and Environment
•
Axial Conductivity along the Wall
•
Heat Content of Wall
Heat Transfer to Environment (liq): Adiabatic With Adiabatic selected, there is no heat transfer between the bed and the wall.
Heat Transfer to Environment (liq): Thin Wall With the Thin Wall option, the fluid phase energy balance includes the heat exchange between the fluid in the bed and the environment:
4H w (Tl − Tamb ) DB
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Heat Transfer to Environment (liq): Rigorous Model With Rigorous Model selected, the bed model applies a wall energy balance equation that contains the following terms: •
Heat transfer from the fluid in the bed to the inner wall.
•
Heat transfer from the outer wall to the environment.
•
Axial thermal conduction along the wall.
•
Heat accumulation within the wall material.
The wall is assumed to be thin and conductive enough for the inner and outer wall temperatures to be equal. The adiabatic option (that is, ignoring the wall energy balance) is valid only when the wall is non-conductive, or there is an infinite heat transfer resistance between the liquid and the wall surface.
Heat Transfer to Environment (liq): Heat Exchange Between Fluid and Wall When the rigorous wall energy balance is selected, the heat exchange between the fluid in the bed and the inner surface of the wall is included in the wall energy balance. The term is represented as:
Hw
4 Dwi (Tl − Tw ) D − Dwi2 2 wo
You must define the value of the liquid-to-wall heat transfer coefficient, H w . The heat exchange between fluid and wall is also included in the fluid phase energy balance. Note that the equation has a slightly different form, owing to the different cross-sectional areas of the balances:
Hw
4 (Tl − Tw ) Dwi
Heat Transfer to Environment (liq): Heat Exchange Between Wall and Environment When a rigorous wall energy balance is included, the heat transfer between the outer wall and the environment is expressed as:
H amb
4 Dwo (Tw − Tamb ) D − Dwi2 2 wo
You must define the value of the heat transfer coefficient to the environment H amb and the temperature of the environment, Tamb . To ignore the effect of heat exchange with the environment in the energy balance, set the value of the heat transfer coefficient to zero.
Heat Transfer to Environment (liq): Axial Thermal Conductivity Along Wall The axial thermal conduction along the wall is always included in the wall energy balance. The term is:
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∂ 2Tw − kw ∂z 2 You must specify the thermal conductivity of the wall material, k w .
Heat Transfer to Environment (liq): Heat Content of Wall The heat accumulation of the wall is always included in the wall energy balance. The term is:
ρ wC pw
∂Tw ∂t
You must specify the value of the wall density,
ρ w , and the specific heat
capacity of the wall, C pw .
Procedures Tab (liq) Use the Procedures tab to view a list of the user procedures being used within the current adsorption layer model.
Liquid Adsorption: Summary of Mass and Energy Balance For information on the equations used in Aspen Adsim for mass and energy balances in liquid adsorption processes, see: •
Liquid Adsorption: Mass Balance
•
Liquid Adsorption: Solid Phase Energy Balance
•
Liquid Adsorption: Fluid Phase Energy Balance
•
Liquid Adsorption: Wall Energy Balance
Liquid Adsorption: Mass Balance The overall mass balance for a multi-component liquid phase contains terms for: •
Convection of material.
•
Accumulation of material in the liquid phase.
•
Mass transfer from the liquid to the solid phase.
The governing partial differential equation is: nc ∂ρ Ml ∂ ∂w ( ) εi vl ρ Ml + ρ s ∑ M i i = 0 + ∂t ∂z ∂t i =1
Each component in the liquid phase is governed by a material balance:
− ε i Ez
∂c ∂w ∂ 2 ci ∂ + (vl ci ) + ε i i + ρ s i = 0 2 ∂z ∂z ∂t ∂t
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Liquid Adsorption: Solid Phase Energy Balance The solid phase energy balance includes terms for: •
Thermal conduction.
•
Accumulation of heat.
•
Accumulation of heat in the adsorbed phase.
•
Heat of adsorption.
•
Gas-solid heat transfer (expressed in terms of a film resistance where the heat transfer area is proportional to the area of the adsorbent particles).
The solid phase energy balance is given as:
− ks
∂ 2Ts ∂T ∂T + ρ p C ps s + ρ p s 2 ∂z ∂t ∂t
∑ (C nc
i =1
nc ∂wi ) ρ w + − a HTC (Tl − Ts ) = 0 p ∑ ∆H i pli i ∂t p i =1
Liquid Adsorption: Fluid Phase Energy Balance The fluid phase energy balance includes terms for: •
Thermal conduction.
•
Convection of energy.
•
Accumulation of heat, heat transfer from fluid to solid.
•
Heat transfer from fluid to the internal wall.
The governing partial differential equation is:
− kl ε i
∂ 2Tl ∂T ∂T 4H w (Tl − Tw ) = 0 + C pl ρ l vl l + ε i C pl ρ l l + a p (1 − ε i )HTC (Tl − Ts ) + 2 ∂z ∂z ∂t Dwi
Liquid Adsorption: Wall Energy Balance The wall energy balance includes terms for: •
Axial thermal conduction along the wall.
•
Heat accumulation within the wall material.
•
Heat transfer from the bed to the inner wall.
•
Heat transfer from the outer wall to the environment.
The governing partial differential equation is:
− kw
∂ 2Tw ∂T 4D 4D + ρ wC pw w − H w 2 wi 2 (Tl − Tw ) + H amb 2 wo 2 (Tw − Tamb ) = 0 2 ∂z ∂t Dwo − Dwi Dwo − Dwi
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Liquid Adsorption: Explanation of Equation Symbols Symbol
Explanation
Aspen Adsim base units
ap
Specific particle surface.
m2/m3
A
Area.
m2
ck
Molar concentration of component k.
kmol/m3
ci0
IAS pure component concentration.
kmol/m3
C pl
Specific liquid phase heat capacity.
MJ/kmol/K
C ps
Specific heat capacity of adsorbent.
MJ/kmol/K
C pW
Specific heat capacity of column wall.
MJ/kg/K
DB
Bed diameter.
m
Dwi
Inner bed diameter.
m
Dwo
Outer bed diameter.
m
Ez
Axial dispersion coefficient.
m2/s
f eq
Equilibrium (isotherm) relationship.
-
g
Function.
-
H ads ,i
Heat of component i in adsorbed phase.
MJ/m3/s
H amb
Wall-ambient heat transfer coefficient.
MW/m2/K
HB
Height of adsorbent layer.
m
HTi
Heat of adsorption contribution to solid phase energy balance.
MJ/m3/s
Hw
Gas-wall heat transfer coefficient.
MJ/m2/s
∆H i
Heat of adsorption of component i.
MJ/kmol
HTC
Liquid-solid heat transfer coefficient.
MJ/m2/s
IP
Isotherm parameter, units depend on isotherm.
j
Colburn j-factor for heat or mass transfer.
-
kl
Liquid phase thermal conductivity.
MW/m/K
ks
Solid thermal conductivity.
MW/m/K
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KP
Darcy’s constant.
bar s/m2
M
Molecular weight.
kg/kmol
MTCl
Liquid film mass transfer coefficient.
1/s
MTCs
Solid film mass transfer coefficient.
1/s
p
Pressure.
bar
rp
Particle radius.
m
R
Universal gas constant.
bar m3/kmol/K
t
Time.
s
T
Temperature.
K
Tamb
Ambient temperature.
K
Ts
Solid phase temperature.
K
Tl
Liquid phase temperature.
K
TW
Wall temperature.
K
vl
Liquid phase superficial velocity.
m/s
wk
Loading.
kmol/kg
wk0
Pure component loading of component k.
kmol/kg
W
Width of horizontal bed.
m
WT
Width of column wall.
m
z
Axial co-ordinate.
m
Symbol
Explanation
Aspen Adsim base units
εi
Interparticle voidage.
m3 (Void)/m3 (Bed)
µ
Dynamic viscosity.
N s/m2
Π i0
Spreading pressure of component i.
bar m
ρ M, I
Liquid phase mass density.
kg/m3
ρl
Liquid phase molar density.
kmol/m3
ρp
Adsorbent apparent density.
kg/m3
ρs
Adsorbent bulk density.
kg/m3
ρW
Wall density.
kg/m3
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Ψ
Particle shape factor.
Dimensionless number
-
Defining expression
Description
Pe
vl H b Ez
Peclet number for mass transfer.
Pr
µ C pl
Prandl number.
kl M Re
2 r p ρ M ,l v l
Particle Reynolds number.
µ
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5 Numerical Methods
This chapter describes the numerical methods available in Aspen Adsim to solve its partial differential equations. See these topics for more information: •
About Numerical Methods
•
Choosing the Discretization Method
•
About the Discretization Methods
About Numerical Methods Aspen Adsim uses a set of partial differential equations (PDEs), ordinary differential equations (ODEs) and algebraic equations, together with the appropriate initial and boundary conditions, to fully describe the adsorption or ion-exchange column. Spatial derivatives are discretized using algebraic approximations, and a set of ordinary differential equations and algebraic equations (DAEs) results. The spatial derivative terms within the partial differential equations are firstor second-order derivatives of some distributed variable, such as concentration, temperature or molar flux. The approximations are defined over a fixed, uniform grid of points (nodes); the distributed variables are defined for each node by means of variable sets. The resulting system of differential and algebraic equations must be solved simultaneously since they are coupled. In a sense, the dependent variables at each node ‘march in time’ along parallel lines perpendicular to the spatial axis, which explains the commonly-used name for this solution technique: the numerical method of lines. The first-order spatial derivatives present the greatest challenge in providing numerically accurate and stable approximations, particularly when the system of equations is highly nonlinear a common occurrence in adsorption process simulation. A typical problem is the propagation of steep discontinuities known as fronts or shocks. The failure of approximations to adequately represent the first order derivatives is manifested by two unwanted and spurious effects: •
Numerical diffusion leading to excessive ‘smearing’ of the solution.
•
Numerical oscillations, leading to non-physical solutions and the violation of physical bounds.
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This chapter describes the methods available in Aspen Adsim to approximate first-order spatial derivatives, showing where the methods come from and how they are evaluated.
Choosing the Discretization Method Your choice of discretization method depends chiefly on the type of process you are simulating, and the level of accuracy, stability and speed you are looking for. Each of the numerical methods differ in: •
Method of approximation of spatial derivatives.
•
Number of points.
•
Accuracy (including any tendency towards oscillatory behavior).
•
Stability.
•
Simulation time required.
The three best standard methods, in terms of accuracy, stability, and simulation time are: •
Upwind Differencing Scheme 1.
•
Quadratic Upwind Differencing Scheme.
•
Mixed Differencing Scheme.
The Biased Upwind Differencing Scheme and the Flux Limiter are recommended in cases where the system is highly nonlinear and breakthrough curves are very steep features associated with highly nonlinear adsorption isotherms and near-equilibrium behavior. The Flux Limiter technique gives the accuracy of a higher order technique, but with no oscillations at small node counts. Note that all second-order derivatives are approximated by a second-order accurate central difference scheme, which is known to be accurate, stable, and fast for all cases of interest. For details on the integration of the resulting system of differential equations with time, see the Aspen Custom Modeler Solver Options help.
About the Discretization Methods To specify a discretization method: •
On the General tab, in the Discretization Method to Be Used box, select the method you require.
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Choose from these options: •
Upwind Differencing Scheme 1 (UDS1, first order)
•
Upwind Differencing Scheme 2 (UDS2, second order)
•
Central Differencing Scheme 1 (CDS1, second order)
•
Central Differencing Scheme 2 (CDS2, fourth order)
•
Leonard Differencing Scheme (LDS, third order)
•
Quadratic Upwind Differencing Scheme (QDS, third order)
•
Mixed Differencing Scheme (MDS, ~third order)
•
Biased Upwind Differencing Scheme (BUDS, fourth order)
•
Fromms’ scheme (FROMM, third order)
•
Flux limited discretization scheme (Flux limiter)
If you choose the Flux limited discretization scheme, you need to select one of these suboptions: •
OSPRE
•
SMART
•
van Leer
With schemes of higher order than UDS1 (first order), the bounds for some variable types need modifying. This is because higher order methods that are not flux limited tend to oscillate, so may return negative values for variables types with a lower bound of zero. The typical changes required are: Variable type
Action normally required
g_Conc_Mol l_Conc_Mol i_Conc_Eq
Set the lower bound to minus the upper bound.
g_Loading l_Loading
Set the lower bound to minus the upper bound.
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i_Loading_Eq Molefraction
Widen the upper bound to 2, and set the lower bound to minus the new upper bound.
Fraction
Widen the upper bound to 2, and set the lower bound to minus the new upper bound.
Upwind Differencing Scheme 1 Upwind Differencing Scheme 1 (UDS1) is the preferred option because it is: •
Good all-round performer.
•
Unconditionally non-oscillatory.
•
Unconditionally stable.
•
Cheapest user of simulation time.
•
Reasonably accurate.
You increase accuracy by increasing the number of nodes. If you need greater accuracy with a minimal increase in simulation time, use the Quadratic Upwind Differencing Scheme. For Upwind Differencing Scheme 1 to achieve the same level of accuracy, the number of nodes has to be increased by a factor of two through four, leading to a similar increase in simulation time. In most cases, use Upwind Differencing Scheme 1 first.
Derivation of Upwind Differencing Scheme 1 Upwind Differencing Scheme 1 is a first-order upwind differencing scheme, based on a first-order Taylor expansion. First-order (convection) term:
∂Γ i Γ i − Γ i −1 = ∂z ∆z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Upwind Differencing Scheme 1 Upwind Differencing Scheme 1 has the following advantages (+) and disadvantages (–): +
Unconditionally stable (that is, it does not produce oscillations in the solution).
+
Least simulation time.
–
Only first-order accurate.
–
Gives a large amount of so-called “false” or numerical diffusion. (However, this problem decreases as the number of nodes is increased.)
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Upwind Differencing Scheme 2 The Upwind Differencing Scheme 2 (UDS2) option predicts sharper fronts than Upwind Differencing Scheme 1, but the solution tends to oscillate.
Derivation of Upwind Differencing Scheme 2 Upwind Differencing Scheme 2 is a second-order upwind differencing scheme. The first-order (convection) term:
∂Γ i 3Γ i − 4Γ i −1 + Γ i − 2 = 2∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Upwind Differencing Scheme 2 Upwind Differencing Scheme 2 has the following advantages (+)and disadvantages (–): +
Second-order accuracy (because it includes a higher order derivative than first-order upwind schemes).
–
May produce some numerical oscillations.
Central Differencing Scheme 1 Central Differencing Schemes 1 and 2 (CDS1 and 2) may be used if you choose to include axial dispersion in the problem. They give good accuracy with a reasonable CPU time requirement. In a series of test problems, Central Differencing Scheme 1 used less CPU time than Central Differencing Scheme 2, but produced greater oscillations.
Derivation of Central Differencing Scheme 1 Central Differencing Scheme 1 is a second-order central differencing scheme and takes the form: First-order convective term:
∂Γ Γi +1 − Γi −1 = 2 ∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2
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Evaluation of Central Differencing Scheme 1 Central Differencing Scheme 1 has the following advantages (+) and disadvantages (–): +
Second-order accurate.
–
Numerical instabilities.
To overcome these instabilities, include axial dispersion in the bed model. This may cause errors in simulation if there is little axial dispersion in the beds, but these errors are no more inconvenient than the false diffusion associated with upwind differencing. Using Central Differencing Scheme 1 with axial dispersion may reduce the number of nodes in the grid, allowing smaller simulation times.
Central Differencing Scheme 2 Central Differencing Schemes 1 and 2 (CDS1 and 2) are useful if you choose to include axial dispersion in the problem. They can give good accuracy with a reasonable CPU time requirement. In a series of test problems, Central Differencing Scheme 2 produced smaller oscillations than Central Differencing Scheme 1, but used more CPU time.
Derivation of Central Differencing Scheme 2 Central Differencing Scheme 2 is a second-order central differencing scheme and takes the form: First-order derivative:
∂Γ i − Γ i + 2 + 8Γ i +1 − 8Γ i −1 + Γ i −1 = 12∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Central Differencing Scheme 2 Central Differencing Scheme 2 has the following advantages (+)and disadvantages (–): +
Third-order accurate.
–
Requires increased CPU time.
Leonard Differencing Scheme The Leonard Differencing Scheme (LDS) is comparable with the Quadratic Upwind Differencing Scheme: •
Gives the same instability problems.
•
Less accurate.
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•
Requires less CPU time.
Derivation of Leonard Differencing Scheme The Leonard Differencing Scheme is a linear combination of the Central Differencing Scheme 1 scheme and a second-order, four point finite differencing scheme. This combination yields: First-order derivative:
∂Γ 2Γ i +1 + 3Γ i − 6Γ i −1 + Γ i − 2 = 6∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Leonard Differencing Scheme The Leonard Differencing Scheme has the following advantages (+) and disadvantages (–): +
Accurate.
–
Known to produce oscillations under convective conditions.
Quadratic Upwind Differencing Scheme If you need greater accuracy than the Leonard Differencing Scheme, with a minimal increase in simulation time, use the Quadratic Upwind Differencing Scheme (QDS). The Quadratic Upwind Differencing Scheme is the most accurate of all the methods for the same number of points.
Derivation of Quadratic Upwind Differencing Scheme The Quadratic Upwind Differencing Scheme is based on quadratic interpolation, as opposed to the linear interpolation typical of many other schemes. First-order derivative:
∂Γ i 3Γ i +1 + 3Γ i − 7Γ i −1 + Γ i −2 = 8∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 The scheme is also referred to as QUICK (Quadratic Upstream Interpolation for Convective Kinematics).
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Evaluation of Quadratic Upwind Differencing Scheme The Quadratic Upwind Differencing Scheme has the following advantages (+) and disadvantages (–): +
Very accurate.
+
Little numerical dispersion.
+
Well suited to explicit (time) integration.
–
Oscillates under highly convective conditions.
Advantages of Quadratic Differencing Scheme: Example Both the Quadratic Upwind Differencing Scheme and the Mixed Differencing Scheme are more accurate than Upwind Differencing Scheme 1. They both use about the same simulation time, which is typically about 25% more than Upwind Differencing Scheme 1. For Upwind Differencing Scheme 1 to achieve the same level of accuracy, you must increase the number of nodes for Upwind Differencing Scheme 1 by a factor of two through four, leading to an equivalent increase in simulation time.
Aspen Adsim Breakthrough Plot
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In this breakthrough plot, both the Quadratic Upwind Differencing Scheme and the Mixed Differencing Scheme have 20 nodes. Initially, Upwind Differencing Scheme 1 also had 20 nodes, which caused high numerical diffusion. The number of nodes in Upwind Differencing Scheme 1 is increased first to 50 and then to 100, to reduce this diffusion. The cost of this is increased simulation time for Upwind Differencing Scheme 1.
Mixed Differencing Scheme The Mixed Differencing Scheme is more stable than the Quadratic Upwind Differencing Scheme, so may be the answer if the Quadratic scheme is unstable.
Derivation of Mixed Differencing Scheme The Mixed Differencing Scheme is a combination of the Quadratic Upwind Differencing Scheme and the Upwind Differencing Scheme 1. First-order derivative:
∂Γ 3Γ i +1 + 7Γ i − 11Γ i −1 + Γ i − 2 = 12∆z ∂z Second-order (dispersion) term is approximated with a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Mixed Differencing Scheme The Mixed Differencing Scheme has the following advantages (+)and disadvantages (–): +
Accurate.
Advantages of Mixed Differencing Scheme: Example The Mixed Differencing Scheme is a compromise between accuracy and stability. It uses slightly less simulation time than the Quadratic Upwind Differencing Scheme.
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Axial Profile Plot This graph shows that Upwind Differencing Scheme 1 and Mixed Differencing Scheme are the most stable of all the methods, while Central Differencing Scheme 1 is the least stable. Note that, in cases with initially clean beds, problems can sometimes be more difficult to initialize with Mixed Differencing Scheme than with Upwind Differencing Scheme 1.
Biased Upwind Differencing Scheme It is known that: •
High-order central difference approximations tend to produce excessive oscillations upwind from a discontinuity.
•
Upwind difference schemes tend to produce excessive oscillations downwind of a discontinuity.
Carver and Schiesser (1980) suggest that a correct combination of the two largely cancels out these upwind and downwind oscillations. From this, they developed a five-point biased upwind differencing scheme consisting of one point downwind and three grid points upwind. The approximation is a
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combination of central and upwind difference approximations. Results suggest that the biased scheme performs better than classical approximations. Use Biased Upwind Differencing Scheme (BUDS) when the system is highly nonlinear, and where the presence of sharp fronts requires accurate solution. Because of its fourth-order accuracy, BUDS provides good accuracy for a smaller number of nodes than other lower-order approximations, while the extra CPU time is small. A potential drawback with BUDS is that, under certain circumstances, it also produces oscillatory behavior. If this happens, then all the other linear differencing schemes are also likely to suffer this problem, with the exception of UDS1.
Derivation of Biased Upwind Differencing Scheme The fourth-order Biased Upwind Differencing Scheme is based on a fifth-order Taylor expansion. First order (convection) term:
∂Γ i − Γ i −3 + 6Γ i − 2 − 18Γ i −1 + 10Γ i + 3Γ i +1 = ∆z ∂z Second order (dispersion) term is based on a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2 Evaluation of Biased Upwind Differencing Scheme The Biased Upwind Differencing Scheme has the following advantages (+) and disadvantages (–): +
Fourth-order accurate, so gives good accuracy for small node counts (so is especially suited to sharp fronts).
+
Simulation time only slightly larger than third-order schemes.
+
Good stability, and less likely to produce oscillations than other higherorder linear discretization techniques.
–
May produce oscillations under extreme conditions.
Fromms’ scheme Fromms’ scheme is the sum of a first order and a second order scheme. It may produce instabilities for large ratios of time to spatial discretization step.
Derivation of Fromms' Scheme First order (convection) term:
∂Γ i (Γ i − Γ i −1 ) + 0.25({Γ i +1 − Γ i } − {Γ i −1 − Γ i − 2 }) = ∆z ∂z
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Second order (dispersion) term is based on a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2
Flux Limited Discretization Scheme Flux limited schemes combine the accuracy of higher order finite differencing schemes with the stability of the first order upwind differencing scheme (UDS1).
Derivation of the Flux Limited Discretization Scheme The flux limited differencing scheme is:
∂Γ i Γ i − Γ i −1 1 Γ − Γ i −1 1 Γ − Γ i −2 = + Ψ (ri ) i − Ψ (ri −1 ) i −1 ∂z 2 2 ∆z ∆z ∆z Here Ψ is the flux-limiter function and r the gradient ratio, calculated as:
ri =
Γ i +1 − Γ i Γ i − Γ i −1
There are three versions of the flux-limiter function Ψ to choose from: •
van Leer
•
OSPRE
•
SMART
Second order (dispersion) term is based on a second-order accurate central differencing scheme:
∂ 2 Γ i Γ i +1 − 2Γ i + Γ i −1 = ∂z 2 ∆z 2
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6 Estimation with Aspen Adsim
The chapter contains the following information about the Estimation Module: •
Two Estimation Tools in Aspen Adsim 2004.1
•
About the Estimation Module
•
Defining Estimated Variables in the Estimation Module
•
Steady State Estimation Using the Estimation Module
•
Dynamic Estimation Using the Estimation Module
•
Performing Estimation Using the Estimation Module
•
Converting Estimation Module Data
•
Recommendations when Using the Estimation Module
Two Estimation Tools in Aspen Adsim 2004.1 Aspen Adsim 2004.1 has two estimation tools; one internal, and one external: •
Estimation Module, which is the existing, internal estimation tool that has been available since Aspen Adsim 10.0 This chapter describes how to use the Estimation Module.
•
Estimation features built into Aspen Custom Modeler, which are now accessible from Aspen Adsim 2004.1: − Simulation engine data tables. − Automation (via any COM-compliant application). This new development links Aspen Adsim more tightly to the overall system. For more information, consult the Aspen Custom Modeler help files. To do this, first open the Aspen Adsim 2004.1 help file, navigate to the topic 'Two Estimation Tools in Aspen Adsim 2004.1', then use the available links.
About the Estimation Module The Estimation Module has been in existence since Aspen Adsim 10.0, It provides an alternate estimation method to automation. The interface simplifies the entry of: •
Estimated variables.
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•
Measured data.
•
Estimation solver options.
The Estimation Module provides two main types of estimation: •
Steady-state (fitting constant parameters to static data).
•
Dynamic (fitting constant parameters to time-dependent data).
To access the Estimation Module: •
On the Tools menu, click Estimation Module.
This places an Estimation Module block on the flowsheet, provided one is not already there. The block opens to display the Estimation Module form. An indication is given if either previously defined data or results are available.
The Estimation Module form contains: •
Buttons for commonly performed tasks (these are on the right-hand side).
•
Tabs for different data types.
This table lists the buttons on the Estimation Module form: Button name
Description
Store
Store entered information in flowsheet block.
Clear
Clear all current data in the Estimation Module.
Load
Replace current data with data stored in flowsheet block.
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Open
Open version 10.0 estimation files.
Run
Execute estimation run.
Help
Open help page.
Copy Table
Copy currently visible table onto the clipboard.
This table lists the tabs on the Estimation Module form: Tab name
Description
Estimated Variables
Currently selected Fixed variables to be estimated and their results (if available).
Experimental Data
Measured experimental data.
Estimation Solver Options
Solver options associated with estimation.
Defining Estimated Variables in the Estimation Module Use the Estimated Variables tab to define the variables that need to be fitted against experimental data. A list shows those variables that have a Fixed specification (assumed constant during the simulation), to a maximum of three levels of submodel hierarchy. The list shows only the valid variables that were available on opening.
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To select a variable for estimation, select the adjacent box. All selected variables are added to the table. In the table, you can: •
Modify the initial value (guess).
•
Change the units of measurement of the initial value.
•
View the result after a successful estimation run, along with other statistical information.
Steady-State Estimation Using the Estimation Module Aspen Adsim typically uses steady-state estimation to fit isotherm parameters to static experimental data. For this purpose, the static_isotherm model is provided, which gives access to both the standard inbuilt isotherms and user defined isotherms. The standard flowsheet for static isotherm fitting contains only a static_isotherm block. You can add any number of experiments. Each experiment: •
Can be included in the estimation run.
•
Has an individual experimental weighting (the default value being 1).
Dynamic experimental data cannot used or entered.
Manually Entering Steady-State Experimental Data To add steady-state experimental data: 1
In the Experimental Data tab, click the Add button. The New Experiment dialog box appears, where you select Steady-State experiment type.
The dialog box looks different if experiments already exist in the Estimation Module. These must be of one type: steady-state or dynamic. So as an example, if you are adding to a set of steady-state experiments, then the dialog box only has the steady-state option. 2
Click OK to return to the Experimental Data tab.
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This now has a list of the data sets, as well as extra tabs for adding experimental conditions and measurements. You can weight each experiment individually, the default being 1. 3
Define the experimental conditions using the variables added to the Fixed Variables list, for example the temperature, pressure and mixture composition. Only variables that are Fixed, and which are chosen for estimation, can be selected. The value of the Fixed variables can be modified.
4
Add measured data to the Measured Variables list. The following tips are useful: − − − −
You can add any Free, Initial or RateInitial variable to the list. The units of measurement are those currently active. Each experimental point can have an individual weighting applied, the default weighting being 1. When additional experiments are added, the same variables can be copied from the currently active experiment.
Steady-State Experimental Data from the Clipboard To import steady-state experimental data, for example from Microsoft® Excel: 1
Create a new steady-state experiment, as described in Manually Entering Steady-State Experimental Data on page 6-239. The experimental name is used as the prefix for any copied experiment.
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2
When creation is complete, you are prompted with a dialog box asking if you want to copy data from Microsoft® Excel. Click the Yes button.
3
The Obtain Steady State Experiments From Clipboard dialog box appears, which requires copied data to function. Leave this dialog box untouched for now.
4
Open Microsoft® Excel and copy the data set to the clipboard. The Estimation Module assumes that copied data takes this format: − −
Each row is a single experiment. Columns represent experimental variables (normally, you list the manipulated variables first, followed by the measured variables).
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5
Return to the Obtain Steady State Experiments From Clipboard dialog box, and click the Paste button. A populated table now appears in the dialog box.
6
For each column of data, mark whether it is a varied (manipulated) or measured variable. To do this, select the column and click either the Varied or Measured buttons. A list appears, from which you select the appropriate variable for the column.
7
Transfer the pasted data to the Estimation Module, either by clicking the Close button or the Process button. − −
The experiments created on processing the data are added to any other existing experiments in the Estimation Module. If any bounds are exceeded, a further dialog box opens in which you can automatically readjust the bounds for all variables of a similar type in the simulation.
Dynamic Estimation Using the Estimation Module Use dynamic estimation whenever the experimental data is time-dependent, for example the measured outlet composition over time. Aspen Adsim does not assume a specific flowsheet layout, or the use of specialized models. You can use a standard process flowsheet that includes any operational task.
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Manually Entering Dynamic Experimental Data To add dynamic experimental data: 1
In the Experimental Data tab, click the Add button. The New Experiment dialog box appears, where you select the Dynamic experiment type.
The New Experiment dialog box looks different if experiments already exist in the Estimation Module. These must be of one type: steady-state or dynamic. So as an example, if you are adding to a set of dynamic experiments, then the dialog box has only the dynamic option. 2
Click OK to return to the Experimental Data tab.
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The Experimental Data tab now has a list of the data sets, as well as extra tabs for adding experimental conditions and measurements. You can weight each experiment individually, the default weighting being 1. 3
Define the experimental conditions using the variables added to the Fixed Variables and Initial Variables list, for example the temperature, pressure and mixture composition. Only variables that are Fixed, and which are chosen for estimation, can be selected. The value of the Fixed and Initial variables can be modified.
4
Add measured data to the Measured Variables list. − − − − −
You can add any Free, Initial or RateInitial variable to the list. A new tab is created for each measured variable, through which you define the time dependency. When new variables are added to an experiment, it is possible to copy the same time points from the currently selected variable. The units of measurement for any variable are those currently active. Each experimental point can have an individual weighting applied (the default value is 1).
Dynamic Experimental Data from the Clipboard To import dynamic experimental data, for example from Microsoft® Excel: 1
Create a new dynamic experiment. When this is completed, the Paste Data button is enabled:
2
The Obtain Dynamic Measurements for Experiment DynExpt From Clipboard dialog box appears, which needs copied data to function. Leave this dialog box untouched for now.
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3
Open Microsoft® Excel and copy the data set to the clipboard. The Estimation Module assumes that copied data takes this format: − −
4
Each row represents a time point. Columns represent experimental variables.
Return to the Obtain Dynamic Measurements for Experiment DynExpt from Clipboard dialog box and click the Paste button. A populated table now appears in the dialog box.
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5
For each column of data, mark whether it is the time of measurement, or the measured variable. To do this, select the column and click either the Time or Measured buttons. For measured variables, a list appears, from which you select the appropriate variable for the column.
6
Transfer the pasted data to the Estimation Module, either by closing the dialog box, or by clicking the Process button. − −
The experiments created on processing the data are added to any other existing experiments in the Estimation Module. If any bounds are exceeded, a further dialog box opens in which you can automatically readjust the bounds for all variables of a similar type in the simulation.
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Performing Estimation Using the Estimation Module To perform an estimation using the Estimation Module, click the Run button and leave the module open during the run. You cannot interact with the module during a run. After a successful estimation run, the module retrieves the results and stores them in the Estimation Module block on the flowsheet. The following results are available: •
Final estimated value
•
Standard deviations
•
Correlation matrix
•
Covariance matrix
Converting Estimation Module Data To convert from using the (old) Estimation Module to the (new) estimation tools available in Aspen Custom Modeler, use the script Convert_EstMod located in the Aspen Adsim library Script folder. To use the script: 1
Open the input file you want to convert.
2
Double-click the script in the library. After the script has converted the data, the Estimation Module block disappears from the flowsheet. To view the experimental data, from the Tools menu click Estimation, which accesses the new estimation system.
3
Save the input file.
Recommendations When Using the Estimation Module The following tips will help you get the best out of the Estimation Module: •
To check that the initial values used for the variables to be estimated give a converged solution, complete these two steps: − Execute a steady-state run for steady-state estimation. − Execute an initialization run for steady-state estimation. These two steps are important as they ensure that the first iteration of the estimation solver will succeed.
•
Use estimation solver tolerances that are greater than the general solver options.
•
If simulation convergence gives rise to multiple solutions, try a different initial guess.
•
Try to measure variables that are sensitive to the estimated variables. Singular convergence normally indicates an insensitive measured variable.
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•
Check the bounds of the estimated variables. For example, ensure the lower bound of a strictly positive isotherm parameter is zero.
•
The fit is only as accurate as the range of data presented by the experiments, so include more than one set of experimental data. For example, with a single data set, the estimated value is useful only for the operating range of the data.
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7 Cyclic Operation
Many adsorption processes operate in a cyclic manner. Each cycle is described by a series of single or multiple sequential steps or discrete events. When simulating a cyclic process, you must be able to specify when certain events are going to occur. Aspen Adsim contains a Cycle Organizer for you to define cyclic operations. This chapter contains information on the following topics: •
Cyclic Operations in Aspen Adsim 2004.1
•
About the Cycle Organizer
•
Opening the Cycle Organizer
•
Cycle Organizer Window
•
Step Control
•
Step Variables
•
Interaction Control
•
Additional Cycle Controls
•
Additional Step Controls
•
Generating Cyclic Tasks
•
Activating and Deactivating Tasks
•
Cyclic Reports
Cyclic Operations in Aspen Adsim 2004.1 In Aspen Adsim 2004.1, the Configure form has been extensively modified to allow for many new features. Input files created in previous releases are still compatible. When you open the Cycle Organizer, the old cycle definitions are automatically converted to match the new system, and the old cyclic task is automatically deleted. You then need to regenerate the cyclic task.
About the Cycle Organizer The Cycle Organizer lets you rapidly create the steps that define a cyclic process. Use it to: •
Create any number of steps.
•
Define the step termination event.
•
Manipulate flowsheet variables for a given step.
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•
Generate a cyclic task based on the Task Language.
•
Distribute cycle information to other flowsheet blocks through global variables.
•
Store multiple cycle definitions.
•
Control variable recording and automated snapshots.
•
Execute V(isual)B(asic) scripts for additional calculations and control.
Here is some more information about the Cycle Organizer: •
The main Configure form gives the status of the system and the active state of the cyclic task.
•
All entered data is stored in the block on the flowsheet. This allows the data to be saved with the flowsheet input file.
•
Only one Cycle Organizer block is allowed on the flowsheet.
•
When you configure the flowsheet for cyclic operation, it is advisable to configure it as if it is about to execute the first step of the cycle.
•
On adding a new step, you are asked two questions: − Is the new step to be placed before or after the currently selected step? − Is the information to be copied from the currently selected step into the newly created one (to act as a template).
Opening the Cycle Organizer To access the Cycle Organizer: •
From the Tools menu, click Cycle Organizer.
If a Cycle Organizer block does not exist on the flowsheet, one is automatically placed on the flowsheet and the Cycle Organizer window appears. The block looks like this:
To open Cycle Organizer block present on the flowsheet, use either the Tools menu or double-click the flowsheet block.
Cycle Organizer Window The Cycle Organizer window looks like this:
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The Cycle Organizer toolbar gives access to the various fields and controls needed to define and generate a cyclic task. The table lists the main buttons on the toolbar, their purpose, and the options available on their drop-down menus. (The Print and Online button are not described.) Toolbar button
Purpose
Options
Cycle
Cycle controls, such as creating and activating cycles.
Cycle Options New Cycle Generate Task Activate Cycle Delete Cycle
Step
Step controls, such as modifying and inserting steps.
Control Manipulated Interactions Other Add/Insert Step Delete Step
Variable (available only if you selected Manipulated from the Step menu)
Adding or Deleting variables.
Add Variable/s Delete Variable/s
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Step Control There are three ways to define the termination of a given step: •
Explicit time, where termination is linked to elapsed time.
•
Discrete event, where termination is linked to an event, such as when a vessel has reached a given pressure.
•
Dependent on another step.
If the step is the second half of an interaction, the step is controlled by the elapsed time for the interaction’s first half. This ensures step symmetry within the cycle. To access the step control panel: •
In the Cycle Organizer window, click the Step toolbar button; or from the neighboring drop-down menu, click Control.
Time Driven Step Time Driven Step is the most common step control method. Here, the step control is a fixed elapsed time; for example, the step is set to terminate after 60 seconds. The step time remains constant from cycle to cycle. To select a time-driven step control: •
Enable the Time Driven radio button and give the step time in the specified units:
When the cyclic task is generated, the value is automatically converted to the base time units assumed by the models. Likewise, should the time unit of measurement change, any variable that is ramped in the current step, and any dependent or interacting step, automatically have their times and time units modified.
Discrete Event Driven Step Event-driven step controls are implicit events, for which the time of occurrence is unknown. For example, "the step will terminate when a vessel has reached a given pressure". To define the event, enable one of these three radio buttons:
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•
Value a comparison between a Free variable and a value defines the event.
•
Variable a comparison between a Free variable and another variable defines the event.
•
Expression a complex expression defines the event.
Discrete Event Driven Step: Variable/ValueComparison With Value as your choice of step control, a comparison between a Free variable and a value defines the event.
To define the event: 1
Enable the Value radio button.
2
Specify the monitored variable, either by selecting it from a list of variables, or by typing the exact name.
3
Select a comparison operator from: == Equal to Not equal to = Greater than or equal to
4
Give the value for comparison, in the unit of measurement of the monitored variable. The unit of measurement can be modified.
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Discrete Event Driven Step: Variable/Variable Comparison With Variable as your choice of step control, a comparison between two variables defines the event.
The procedure for this is similar to the Value option, described in the previous subsection, except that you must specify two variables: •
Monitored variable.
•
Variable to make the comparison with.
Discrete Event Driven Step: Complex Expression With Expression selected, a complex expression that is built up from logical operators defines the event. This is useful when the step termination depends on a true or false condition.
To define the expression: 1
Enable the Expression radio button.
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2
Double-click in the Expression text box. The Expression Builder dialog box appears, where you create expressions:
3
Insert typical operations for the comparisons, using the buttons provided. A searchable list is provided to ensure that you insert only valid variables into the expression.
Note: No error checking is provided for the expression entered, so take care to enter values that are within the valid bounds and in the compared variable's base unit of measurement.
Discrete Event Driven Step: Step Dependent The final method of step control is to make the step dependent on a previous step.
To use this option: 1
Enable the Step dependent radio button.
2
In the neighboring drop-down menu, specify the dependent step. Only steps that occur before the current step can be selected. Likewise, this option is not available for the first step in any given cycle.
If the step for which a dependency is being defined, is the start of a chain of step interactions, all interacting steps assume the elapsed time and time unit
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of measurement of the dependent step. Likewise, all ramp times will be checked and converted to the new time unit of measurement.
Step Variables Within each step of a cycle, different variables may be modified. These variables may control, for example: •
Feed condition
•
Valve opening
•
Heater duty
The variable change may be stepped or a gradual/ramped change. To access the list of manipulated variables: •
From the Step button's drop-down list, click Manipulated.
Adding Step Variables To add a new manipulated step variable: 1
Click the Variable button on the toolbar; or from its drop-down list, click Add Variable/s. The Variable Selector dialog box appears, which lists the available fixed and initial variables that have not already been selected in the current step.
2
Select a variable using one of these actions: − − − −
Double-click on the variable in the list. Type the name of the variable in the text box at the top of the dialog box (a dynamic search takes place during typing). Select multiple variables, using either the SHIFT or CTRL key. Use wildcards in the text box to reduce the list size and then select. Valid wildcards are: * for any character combination. ? for a single character place holder.
Note the following points: •
There is no limit to the number of variables that can be manipulated in a given step.
•
You can access all variables in the flowsheet, except global variables.
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•
Selected variables are listed alphabetically in the table.
Removing Step Variables You remove step variables directly from the Cycle Organizer window. To remove a single manipulated variable: 1
Select the row of the required variable.
2
From the Variable button's drop-down menu, click Delete Variable/s.
To remove a series of variables in contiguous rows, select the rows to be deleted.
Changing Step Variable Values
For each defined manipulated variable, the following fields are given: Field
Description
Value
Value of the variable for the current step. A check is made to ensure the value is within the bounds for the variable in the current unit of measurement. If a bound is violated, you can automatically adjust bounds for all variables of the same type.
Units
Unit of measurement. To modify this, double-click the field and a drop-down menu appears. On changing the unit of measurement, any values provided for the Value and Target fields are automatically recalculated.
Spec
Specification of the variable. This cannot be modified.
Ramped
Variable to be ramped. Double-clicking this field displays a drop-down menu, where you choose between no ramping, linear ramping or S-shaped ramping.
Target
Target value of the ramp. This is visible only for ramped variables. For ramped variables, the number in the Value column is used as the initial starting point of the ramp.
Time
Elapsed time of a ramp. This is visible only for ramped variables. For time-driven steps, the value entered here cannot be greater than the step time.
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With discrete event-driven steps; if the event occurs before the ramp has completed, the step terminates when the ramp has completed.
There is no limit to the number of variables that can be ramped in a given step.
Interaction Control If the flowsheet contains interaction units (see Single Bed Approach in Chapter 7), the Step toolbar's drop-down menu contains an Interactions option: This option accesses the Interaction Control table, which lists the interaction units and the currently defined step interactions.
Defining a Step Interaction To define a step interaction: •
Double-click on the step containing the source material, and from the drop-down list, select the step in which the material is returned.
Note the following points about step interactions: •
Once you select an interacting step, the target cell updates automatically.
•
The last row also shows the root defining step for any interactions. This step defines the elapsed time for all associated interacting steps.
•
Interaction numbers are: − Positive for forward interactions, where material is accepted early in the cycle and returned later in the same cycle. − Negative for reverse interactions.
•
A single interaction unit is not restricted to a single set of interacting steps; it can be reused for any number of interacting step sets. However, only a single quantity of material can be accepted or returned for a given step. For this reason, if you want to transfer multiple amounts of material in a step, you must use more than one interaction.
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Deleting Interaction Steps To delete an interaction: •
From the drop-down list, click None.
Adding Extra Interaction Steps If you insert additional steps before or between existing interacting steps, the interaction numbers are renumbered automatically. For example, if you insert a step between the interacting steps 1 and 3 for unit D1, the new interacting steps are now 1 and 4.
Interacting Steps and Time Controls Once you have defined an interacting pair of steps, the second half of the pair is forced to be time controlled. This ensures time symmetry and maintenance of the material balance between interacting steps.
The time control is based on: •
Fixed time for a time driven step.
•
Elapsed time for an event driven step.
The Cycle Organizer continually checks the root defining steps of all interactions, to ensure time controls are in place.
Explanation of Why Time Controls Are Imposed A single step cannot receive material from both a time driven step, and one that is event driven; nor from two similarly controlled steps that use different times or events. This is because the duration of an event driven step may change from cycle to cycle, so the elapsed time can vary. For example, in a five-step process using three interaction units, step 1 is time driven, and step 2 event driven. Interaction unit D1 has interactions 1→ 3 and 5→ 4; interaction unit D2 has a single interaction 2→ 4; interaction unit D3 has a single interaction, 3→ 5.
The table suggests that step 3 is time driven, and step 4 is time driven based on the elapsed time of the event in step 2. In step 5, however, we have two
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interactions: one with step 4 (assumed event driven) and the other with step 3 (assumed time driven). In this instance, the step that occurs first is assumed as the root defining step. Thus steps 2 through 5 are all dependent on the elapsed time of step 1.
Additional Cycle Controls To access additional cycle controls: •
Click the Cycle toolbar button, or from the button’s drop-down menu, click Cycle Options.
The additional controls provided for the overall cycle include: •
Number of cycles to execute.
•
Record frequency.
•
End of cycle snapshots.
•
Cycle steady-state testing.
Maximum Cycles Box Use the Maximum Cycles box to specify the maximum number of cycles to execute in a given run. It is coupled to the Record Initial and Record Frequency options. Assuming you have set the run options for indefinite running, the simulation automatically pauses once the given number of cycles has been performed. Click the Play button again to execute a further batch of cycles.
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Record Initial and Record Frequency Boxes Use the Record Initial box to specify the number of cycles at the start of the simulation for which the record attribute remains on. This applies only to variables that have it set to true and time equals zero. Use the Record Frequency box to specify the cycle at which the record attributes are switched off and then back on for a single cycle. •
If you set these two options to 1, the variables are recorded for all cycles.
•
If you set Record Initial to 5, Record Frequency to 10, and the Maximum Cycles to 25, variables are recorded only for cycles 1, 2, 3, 4, 5, 15 and 25. This significantly reduces the size of the plot data file.
When using these options, the maximum number of cycles is always automatically modified to ensure the last cycle executed is recorded.
Take Snapshot Box To automatically take a snapshot at the end of every cycle (or cycles based on the settings for Record Initial and Record Frequency): •
Select the Take Snapshot at End of Cycle box.
Taking a snapshot at the end of each cycle is useful if you want a material balance at points during the run. The simulator uses the snapshots to rewind to a time point in history.
Cyclic Steady State Testing Box Select the Cyclic Steady State Testing box to test when the dynamic cyclic simulation has reached a periodic, cyclic, steady state. You need to set a tolerance for this option to work. During the simulation, the total loading and total solid temperature at the end of a cycle are compared to the value of the previous cycle.
When their relative difference is below the test tolerance, the simulation pauses.
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If the Record Initial and Record Frequency are not equal to 1, the simulation automatically pauses after the next recorded cycle.
Additional Step Controls To access the additional step controls: •
Click the Step toolbar button, or from the button’s drop-down menu, click Other.
The additional controls provided for the overall cycle include: •
Execution of a named script.
•
End of step snapshots.
Execute End of Step Script Box Select this box to run a flowsheet level script at the end of a step, for every cycle. This is useful for executing external calculations or runtime logging. Specify the script in the Script Name box. If the script does not exist during cyclic task generation, a template script with the name provided is automatically created.
Take Snapshot at End of Step Box To automatically take a snapshot at the end of step for every cycle (or cycles based on your settings for Record Initial and Record Frequency settings): •
Select the Take a Snapshot at End of Step box.
Taking a snapshot at the end of each cycle is useful if you want a material balance at points during the run. The simulator uses the snapshots to rewind back to a time point in history.
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Generating Cyclic Tasks Once a new cycle has been defined, or changes made to an existing definition, the cyclic task needs generating before the simulation can be run. This is indicated in the Cycle Organizer status bar, as follows:
To generate the cyclic task: •
From the Cycle button's drop-down menu, click Generate Task.
View the Cycle Organizer status bar to see how the generation is progressing: •
•
You see when the cyclic task has been successfully generated (should there be any errors, these will be given in the simulation messages window). You see
when there is another inactive cycle.
Note the following points: •
If any variable in a step is ramped, additional tasks are generated. The "callable" task contains a single ramp statement. The names of these additional tasks are prefixed by the main task name, followed by an index indicating the step and the manipulated variable.
•
Generated cyclic tasks are created using the Task Language. You can open and edit tasks using this language, but any changes you make are lost if you regenerate the task using the Cycle Organizer.
•
Only a single cycle definition can be active. If there is more than one cycle description stored within the Cycle Organizer, whenever it is opened it will always display the currently active cycle (or the first cycle definition should no cycle be active).
Activating and Deactivating Cyclic Tasks Use the Cycle Organizer to activate and deactivate cyclic tasks. If cyclic tasks have been generated for all cycle definitions stored within the Cycle Organizer, you must not activate and deactivate the task by doubleclicking the task in the Flowsheet section of Simulation Explorer. To activate a cycle: •
With the cycle currently inactive down menu, click Activate Cycle.
, from the Cycle drop-
To deactivate a cycle:
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•
With the cycle currently active , from the Cycle dropdown menu click Deactivate Cycle. This also deactivates any other currently active cycle definition.
Cyclic Reports Cyclic reports are now available that provide information on the quantity and quality of material passing along a stream during any step, and any cycle. In overview, you are picking out information about particular steps and cycles, from the larger Block and Stream reports. Cyclic reports therefore require: •
A Cycle Organizer on the flowsheet.
•
Block and Stream reporting enabled.
There are two types of Cyclic report: •
Cyclic Stream reports
•
Cyclic Recovery reports
Preparing Aspen Adsim for Cyclic Reporting Before you start your simulation, you need to enable Block and Stream reporting, and specify when to stop recording information for the Cyclic report. To prepare for cyclic reporting: 1
From the Tools menu, point to Report and then click Reporting. The Flowsheet Reporting dialog box appears:
2
Select the Enable blocks/streams reports box, and underneath, state the number of recorded cycle histories.
3
Click OK.
When you now run the simulation, step-by-step and cycle-by-cycle information is recorded, until the number of cycle histories is reached (this is 11 cycles in our example).
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Cyclic Stream Reports
The Cyclic Stream report gives the following information, based on either a total cycle or on an individual step, for each direction of every Aspen Adsim stream on the flowsheet: •
Total material passed.
•
Cycle or step averaged flowrate.
•
Total of component passed.
•
Cycle or step averaged component composition.
•
Total energy passed.
•
Cycle or step averaged enthalpy.
It also gives the start time, end time and the elapsed time of the selected cycle or step.
Creating Cyclic Stream Reports You create Cyclic Stream reports for either a cycle or a step. To create a Cyclic Stream report:
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1
From the Aspen Adsim Tools menu, point to Report and click Stream Report. The Cyclic Report dialog box opens.
You now build the report to view it. 2
Enable either the Cycle radio button or Step radio button.
3
In the Cycle number list, select a cycle number. For a step report, you also need to select a step.
4
Click the Build button, or from its drop-down menu click Stream Report. This builds and then displays the Cyclic Stream report.
Cyclic Stream reports can be: •
Copied to the clipboard, where additional information is added, such as the date and time, and input file name.
•
Printed to the default printer, which prints only the currently visible columns of the report. The report can be resized.
Cyclic Recovery Reports
The Cyclic Recovery Report gives the following recovery information for every product stream with respect to every feed stream: •
Total material
•
Individual component
•
Total energy
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Creating Cyclic Recovery Reports You create Cyclic Recovery reports for either a cycle or a step. To create a Cyclic Recovery report: 1
From the Aspen Adsim Tools menu, point to Report and click Stream Report. The Cyclic Report dialog box opens.
You now build the report to view it. 2
Enable either the Cycle radio button or Step radio button.
3
In the Cycle number list, select a cycle number. For a step report, you also need to select a step.
4
From the Build button's drop-down menu, click Recovery Report. This builds and then displays the Cyclic Recovery report.
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8 Flowsheeting
This chapter contains information on: •
About model types
•
General model types
•
Reversibility
•
About flowsheets in Aspen Adsim
•
Types of Flowsheet in Aspen Adsim
•
Single bed approach
•
Pressure interaction diagram
•
Interactions
•
Specifications for flowsheets
•
Physical properties
•
Connecting to Aspen Dynamics flowsheets
About Model Types For reversible flow within an Aspen Adsim flowsheet, you need to make some modeling assumptions that define the type of flowsheet interactivity. These assumptions are broadly similar between gas, ion-exchange and liquid systems. The models in the Aspen Adsim library support these flow regimes:
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General Model Types The general model types available in Aspen Adsim are: Model type
Used in
Description
Typical models
Non-Reversible
Gas
Assumes that there is no flow reversal in the model. Material flow is from Process_In to Process_Out.
All models (except for adsorbent/resin beds) can be configured in this way.
Ion-Exchange Liquid
Reversible Flow Setter
Gas
Relates pressure drop across the model to the flowrate through the model. Able to specify the flowrate directly. The model does not contain any material holdup, but may contain a momentum balance.
Reversible Pressure Setter
Gas
Accumulates material and energy (adsorbent beds are an exception). The pressure at each port is equated directly to the internal pressure. Able to specify the pressure directly.
Non-Reversible Delay
Gas
Used as part of an interaction train. Stores stream information or passes downstream/upstream pressure information.
Reversible
Ion-Exchange Liquid
Feed or product train to allow for reversible flow.
Typical models: gas_bed, gas_valve, gas_ramp.
. gas_tank_void, gas_buffer_intera ction, gas_feed, gas_product. gas_valve, gas_ramp, gas_interaction.
Feeds, products, valves, tanks, distributors.
Reversibility You get reversibility within the flowsheet by categorizing the models into certain types. Consider the gas phase system as a typical example: The usual modeling approach is to equate the outlet condition to either the internal condition (a tank for example) or inlet condition (a valve for example).
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Tank1
Y1 T1 P1 H1
Ys1,in = Ys1,out Ts1,in = Ts1,out Ps1,in = Ps1,out Hs1,in = Hs1,out
Valve
S1
Ys1,in = Y1 Ts1,in = T1 Ps1,in = P1 Hs1,in = H1
Tank2
Ys2,in = Ys2,out Ts2,in = Ts2,out Ps2,in = Ps2,out Hs2,in = Hs2,out
Y2 T2 P2 H2
S2
F = ƒ(Ps1,out,Ps2,in) Ys1,out = Ys2,in Ts1,out = Ts2,in Hs1,out = Hs2,in
This approach works if the pressure in tank 1 is greater than, or equal to the pressure in tank 2. To allow for a reversed pressure profile, the stream condition must not be directly related to the tank condition, otherwise the model becomes singular. This is where the model type is introduced. To allow for reverse flow between tanks 1 and 2, the stream condition needs to be determined not by the tanks, but by the unit in-between, the valve unit. The valve uses the following information to ensure the appropriate flow condition is selected: •
Internal composition of the tanks, from the tank units.
•
Pressure difference across the valve itself.
We now introduce the concept of flow setter models and pressure setter models: •
As the valve model sets the stream conditions and determines the flow, the underlying model is described as a “flow setter”.
•
The tanks accumulate only material and energy, and relate their pressure to this accumulation, so the underlying model is described as a “pressure setter”.
To finally accomplish this task, the streams must carry information, such as the internal condition of the pressure setters (the tanks), as well as the actual stream condition.
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Tank1
Y1 T1 P1 H1
Ys1,in = Ys1,out Ys1,in,r = Ys1,out,r Ts1,in = Ts1,out Ts1,in,r = Ts1,out,r Ps1,in = Ps1,out Hs1,in = Hs1,out Hs1,in,r = Hs1,out,r
Valve
Ys2,in = Ys2,out Ys2,in,r = Ys2,out,r Ts2,in = Ts2,out Ts2,in,r = Ts2,out,r Ps2,in = Ps2,out Hs2,in = Hs2,out Hs2,in,r = Hs2,out,r
S1
Ys1,in,r = Y1 Ts1,in,r = T1 Ps1,in = P1 Hs1,in,r = H1
Tank2
S2
F = ƒ(Ps1,out,Ps2,in) Ys1,out = Ys2,in Ts1,out = Ts2,in Hs1,out = Hs2,in
Ys2,out,r = Y2 Ts2,out,r = T2 Ps2,out = P2 Hs2,out,r = H2
Y2 T2 P2 H2
If Ps1,out >= Ps2,in Then Ys1,out = Ys1,out,r Else Ys2,in = Ys2,in,r If Ps1,out >= Ps2,in Then Ts1,out = Ts1,out,r Else Ts2,in = Ts2,in,r If Ps1,out >= Ps2,in Then Hs1,out = Hs1,out,r Else Hs2,in = Hs2,in,r By using an alternating sequence of pressure and flow setters, you can model process trains where reversibility may occur, without causing singularities. For adsorbent and resin beds, it is important that the discretization scheme used to solve the partial differential equations can cope with flow reversal at either the inlet and outlet boundaries, or internally.
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Forward Direction
1
Process In
1
Inlet Boundaries
2
1
1
2
n-1
n-1
Discretization Nodes
2
1
Process In
Outlet Boundaries
2
2
Process Out
n
n-1
Outlet Boundaries
Inlet Boundaries
n
n
n-1
n-1
n
Process Out
n
Reverse Direction The scheme used within the adsorbent and resin models assumes a constant discretization mesh, with the boundaries evaluated at each local node with respect to the flow and/or pressure gradient. This approach allows for the chosen discretization method to automatically switch between forward and backward differencing.
About Flowsheets in Aspen Adsim You create Aspen Adsim flowsheets either interactively through the graphical user interface, or from a prepared template. The available models are classified into three main phases or types: •
Gas
•
Ion-exchange
•
Liquid
You can mix these phase types on a flowsheet, subject to these restrictions: •
Use a common global component list.
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•
Interconnect model blocks using only the appropriate stream type for the phase or model type. The only exception is a gas phase model block, which can contain a liquid outlet to remove any condensed material.
The flowsheeting environment is very flexible, allowing you to create any process flowsheet subject to these restrictions: •
Overall model size versus simulation speed.
•
Available models/process operation descriptions.
•
Hardware limitations.
The flowsheet scope should ideally cover only the adsorbent columns and any immediate equipment required to operate the process. When creating new problems, it is good practice to start with a simple flowsheet to ensure the column model assumptions are correct. Once validated, you can then add further complexity, such as column deadspaces, interaction units, other columns and cyclic behavior.
Connectivity on Flowsheets You must use the correct material connection (stream) when connecting model blocks on the flowsheet: Model prefix
Stream type
gas_
gas_Material_connection
ionx_
ionx_Material_Connection
liq_
liq_Material_Connection
Create the connections by dragging and dropping from the library to the flowsheet. Connectivity is enforced by the port types used by each library model and material connection: Model prefix
Port type
gas_
g_Material_Port
ionx_
i_Material_Port
liq_
liq_Material_Port
So, a model with the prefix 'gas_' accepts only connections made with a gas_Material_Connection. The ports and material connections pass the following information between model blocks (depending on phase or type): •
Molar/Volumetric flowrate
•
Molefraction composition/Component concentration
•
Molar density
•
Absolute temperature
•
Pressure
•
Specific enthalpy
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Controllers are not connected using material connections; they use a special stream type called ControlSignal instead. ControlSignal connects a single exposed variable from one model block to another single exposed variable in the same or another model block.
Templates Predefined process templates are available through the Template Organizer. To access this: •
From the File menu, click Templates. The Template Organizer appears:
The available templates feature: •
Recommended solver options.
•
Runtime options set to the appropriate time units.
•
Default component list configured for use with Fortran-based physical properties and populated with dummy components.
•
Flowsheet layouts based on standard descriptions.
Before copying a template to the current working directory, a name is requested, which is then used for both the input file and the directory that houses all the files for the new problem.
Demonstrations All of the examples in the Aspen Adsim casebook come as part of the standard installation. These casebook examples are a further source of process templates.
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To access the example files: •
From the File menu, click Demonstration Organizer. The Demonstration Organizer appears:
To open a casebook example: •
Select the problem of interest and click Open.
You are told if a set of files will be copied, or if a copy of the example already exists.
Types of Flowsheet in Aspen Adsim There are three types of flowsheet in Aspen Adsim: •
Simple flowsheet
•
Intermediate flowsheet
•
Full flowsheet
Types of Flowsheet: Simple Flowsheet The simple flowsheet is the smallest workable flowsheet to operate an adsorbent/resin bed. It is a recommended starting point for new simulations. Use it to: •
Ensure the absorbent/resin bed works effectively.
•
Simplify testing of key parameters and configuration assumptions.
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•
Feed boundary unit.
•
Adsorbent/resin bed (can contain any number of layers).
•
Product boundary unit.
Product Boundary
Adsorbent or Resin Bed
Feed Boundary
Intermediate Flowsheet The intermediate flowsheet is useful for simulating non-interacting adsorption cycles. It builds upon the simple flowsheet by including (except for ionexchange): •
Adsorbent bed deadspaces or voids.
•
Feed and product valves.
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Product Valve Product Boundary Top Deadspace (Tank)
Adsorbent Bed
Bottom Deadspace (Tank)
Feed Boundary Feed Valve Use the intermediate flowsheet to simulate: •
Co-current or counter-current adsorption.
•
Repressurization and depressurization.
•
Purge using streams of different compositions.
Full Flowsheet The full flowsheet is the final step in flowsheet complexity. It builds on either the simple or intermediate flowsheet by including: •
Interactions with other adsorbent/resin beds.
•
Additional feed or product trains.
•
Intermediate buffer tanks or pressure receivers.
•
Feed and product pumps.
To simulate interacting beds, there are two levels of overall model complexity:
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•
Single bed approach — this uses a single bed to simulate processes containing more than one bed.
•
Rigorous multi-bed — this simulates all adsorbent/resin beds with interconnecting units.
Single Bed Approach An inherent problem when modeling an adsorption system is the number of equations to be solved, the majority of which are discretizations of the partial differential equations. One way of modeling adsorption systems that comprise multiple adsorbent/resin beds, is to use the single bed approach. For the method to be valid: •
Each adsorbent/resin bed (or series bed train) must be identical.
•
Each adsorbent/resin bed must undergo the same steps in a given cycle.
If these assumptions are met, then you can rigorously model a single “real” adsorbent/resin bed and store any information (material) that would normally be sent to an interacting bed. This stored information can then be replayed back to the real bed later in the cycle. The single bed approach retains the accuracy of the final results (see the spreadsheet included within the installation): •
Same average purity.
•
Same number of cycles to achieve cyclic steady-state.
Simulation speed is also improved: •
Fewer equations (due to fewer beds).
•
Less data to be communicated between the client (GUI) and the server (simulation engine).
Pressure Interaction Diagram Before creating a flowsheet, it is important to sketch out the pressure interaction diagram for your process. This diagram is a graph of pressure versus time, with material interactions overlaid. In the following example, a simple three step Oxygen VSA process is examined. The process uses three identical adsorbent beds, each undergoing the following steps in a cycle: •
Production at high pressure with some product that counter-currently repressurizes another bed.
•
Evacuate to low pressure. The material is sent to waste.
•
Repressurize using product material.
The Pressure-Interaction diagram for the process looks similar to this:
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P
Bed 1
Bed 2
Bed 3
60
120
180
If the single bed approach is applied, using Bed 1 as the real bed, the interactions would look like this:
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t
Flowsheet Scope Record
Replay
P
Bed 1
Bed 2
Bed 3
60
120
180
t
Material profile information from step 1 can be stored and then replayed back to Bed 1 during step 3. The final pressure-interaction diagram for the new single bed process looks like this:
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P
Bed 1
60
120
180
t
Interactions When material from a step is used by another step, this is called an interaction. Aspen Adsim handles any number of interactions in an adsorption process cycle. Using the Oxygen VSA example, the pressure-interaction diagram was as follows:
P
Bed 1
60
120
180
The three, 60 second duration steps were: •
Step 1 — 0 through 60 seconds — there was production with some material used to repressurize another bed.
•
Step 2 — 60 through 120 seconds — there was counter-current evacuation to waste.
•
Step 3 — 120 through 180 seconds — there was counter-current repressurization with product material.
In this example there is only one interaction, a top-to-top interaction between steps 1 and 3. To create this interaction when using the single bed approach, you must use an interaction model to simulate the bed that the real modeled bed is interacting with. In gas systems, for example, it is named gas_interaction. The interaction model records one or more of the following profiles (dependent on the phase of the system): •
Flowrate
•
Composition or concentration
•
Density
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t
•
Temperature
•
Pressure
•
Specific enthalpy
To use the gas_interaction model, for example: •
The inlet stream must always be connected to a valve (configured as a non-reversible delay) whose inlet is connected to point on the flowsheet where material is withdrawn. The valve passes the interaction unit information about the upstream (or relative bed) pressure. Typically, the valve inlet is connected to a gas_tank_void model that is being used to simulate an adsorbent bed deadspace or void.
•
The outlet stream defines where material is returned to the flowsheet. No valve is required on the outlet stream.
Valve Present In Scope Real Bed Scope
Store Profile
Store
Valve Not Present In Scope
Replay
Real Bed Scope
Replay Profile
Use the withdrawal and return point for material, to define whether the interaction is: •
Top-to-top
•
Top-to-bottom
•
Bottom-to-bottom
•
Bottom-to-top
So, for the Oxygen VSA example, the following additions are needed to create a top-to-top interaction off the real adsorbent bed’s top void.
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Valve
To product
Tank
Interaction
From bed
Notes: o
The interaction units use the Delay function.
o
The accuracy of the delay function is dependent on the communication interval, not the integration step size. It is recommended that you have at least four communication points within the shortest step.
o
If the simulation is closed or a snapshot re-used, the delay buffer is emptied and all historical profile information is lost.
o
The snapshot does not store delay information.
Specifications for Flowsheets This section gives information on: •
Solver Options
•
Run Time Options
•
Model Specification
•
Consistency and Model Definition Checks
Solver Options If you create a flowsheet that is not based on a template, the following solver options are recommended as good initial starting points:
General Tab: Solver Options The recommended solver options are:
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Option
Value
Absolute Variable Tolerance
1e-5
Relative Variable Tolerance
1e-5
Absolute Equation Tolerance
1e-7
Variable Change Tolerance
1e-5
Numerical Derivative Absolute Tolerance
1e-6
Numerical Derivative Relative Tolerance
1e-6
Solver Scaling
Disabled
Eliminate Equivalence Equations
Enabled, Standard
Integrator Tab: Solver Options The recommended solver options are: Option
Value
Integrator
Variable Step Implicit Euler
Initial Integration Step
1
Minimum Integration Step
1
Maximum Integration Step
5
Step Reduction Factor
0.5
Maximum Step Increment Factor
1.5
Absolute Integration Error Tolerance
1e-5
Tear Integration Tolerance
1
Maximum Corrector Iterations
500
Show Highest Integration Errors
0
Use Interpolation
Enabled
Reconverge Torn Variables
Disbaled
Note: When running rapid cycles, the integration steps may need reducing.
Linear Solver Tab: Solver Options The recommended solver options are: Option
Value
Name
MA48
Drop Tolerance
0
Pivot Tolerance
0
Re-analyse Threshold
2
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Re-analyze FLOPS Window Size
0
Re-pivot every
0
Solver searches
3
Non-Linear Solver Tab: Solver Options The recommended solver options are: Options
Value
Mode
General
Method
Fast Newton
Convergence Criterion
Residual
Maximum Divergent Steps
20
Maximum Step Reductions
20
Maximum Iterations
500
Maximum Fast Newton Steps
8
Dogleg Method
Disabled
Run Time Options To set the runtime options for Aspen Adsim: •
From the Run menu, click Run Options.
The following settings are recommended: Options
Value
Comments
Solution Time Units
Seconds
Time unit assumed by library models.
Display Update
2
Interval when data is communicated between client and server.
Communication
Problem dependent
Resolution at which plot data and delay information is saved. Small values make the plot data file grow more rapidly. When using interactions, ensure this value is set to provide at least five communication points in the shortest interaction step. When studying rapid transients, set this to a small value.
Pause at
Problem dependent
Uncheck when using the Cycle Organizer (run time controlled by maximum number of cycles). Check and provide a desired end time for other simulations. This value can also be modified using the Run menu Pause At option.
Pause after
Unchecked
Number of communication intervals to execute.
Real time synchronization
Unchecked
Real time to simulation time factor. A value of zero indicates run as fast as possible.
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Model Specification Aspen Adsim library models may require one or more of the following types of specification: •
Definition of model assumptions.
•
Specification of constant variables.
•
Initial and preset conditions.
The normal approach is to first configure the model, then specify the constant variables exposed and finally, if required, specify the model initial condition.
Defining Model Configurations The model configuration is the selectable assumptions a model may have. For example, with an adsorbent layer, you have the option to: •
Include a dispersive term in the component material balance.
•
Specify whether the layer is isothermal or non-isothermal.
You set these options in the model Configure form, which opens when you double-click a flowsheet model block. This form displays selection boxes for any available adjustable assumptions. On changing an assumption, the model automatically reconfigures, so there may be slight pause depending on the overall complexity of the change.
Specification of Constant Variables All models in the Aspen Adsim library contain recommended fixed variables. This ensures that the overall degrees of freedom of a complete problem are always met. Therefore, there is no need to determine which values are required to be specified. Each model in the Aspen Adsim model library contains a Specify table. You access the Specify table in one of these three ways: •
Using the Configure form for the model.
•
From the Flowsheet menu, clicking Forms options.
•
Using the model’s context sensitive menu (selecting and right-clicking a flowsheet model block).
The recommended columns made visible in the Specify table are: •
Value
•
Units
•
Derivative
•
Specification
•
Description
Presets and Initialization If a model contains state variables (variables that are differentiated with respect to time), initial values are required. Adsorbent layer and tank models typically fall into this category. To define the preset and initial variables, click the button on the Configure form to open the Initials table, which shows the recommended variables to preset and initial.
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For an adsorbent/resin bed: •
Provide values for a single discretization node within a given layer. To propagate this value through the rest of the layer, either click the Initialize button on the model’s configure form, or select Check & Initial from the Flowsheet menu.
•
To specify a layer that is at saturated equilibrium with a given bulk phase composition, initialize the bulk phase values (molefraction or concentration) and for the loading, set the derivatives to zero with a specification of Rateinitial.
•
For a gas adsorbent layer that includes a pressure drop correlation (momentum balance), the standard specification is to initialize the superficial velocity and initial ncomps-1 bulk phase molefractions.
For a gas phase tank or void: •
Preset (provide free specified values for) the internal composition.
•
Preset (provide a free specified value for) the internal pressure.
•
Provide an initial value of the temperature.
•
From the above and using the internal volume, the initialize method calculates the material molar holdup.
•
A valid alternative specification is to initialize the temperature, pressure and ncomps-1 internal molefractions, and to free the internal molar holdup.
If you modify initial or preset values solely in the Initials table (and not elsewhere), the Check & Initial option in the Flowsheet menu always ensures that the problem contains the correct number of initial variables. The recommended columns to made visible in the Initials table are: •
Value
•
Units
•
Derivative
•
Specification
•
Description
Consistency and Problem Definition Checks When creating and specifying a flowsheet, it is recommended that you make these checks: •
For cyclic processes, configure the flowsheet with first step conditions.
•
Check the initial and preset pressure conditions throughout the flowsheet. Ensure the pressure gradient is correct for the direction of material travel, for example feed to product.
•
Allow cross-valve pressure drops of at least 1 mbar.
•
For gas adsorbent beds, for robust initialization assume a small initial superficial velocity, for example 3.55e-4 m/s.
•
Pay particular attention to the deadspaces connected to a gas adsorbent. Ensure the pressure profile between the two units are reasonable and in the correct direction, and that the deadspaces have been correctly
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initialized. Unreasonable initial conditions for deadspace are the principal cause of full flowsheet convergence problems at the start of the simulation. •
Make use of the Flowsheet menu Check & Initial option. It indicates unconnected and invalid streams, corrects interaction unit configurations, runs any model-based initialization methods, and correctly configures material stream source and destination unit types.
•
If the model has too many initial variables, use Variable Finder to find all Initial and Rateinitial variables. Set the specification of any found variables to Free and then use the Check & Initial option from the Flowsheet menu. The default initial condition is reconstructed.
•
Make use of the recommended Fixed variables. If any are set to a specification of Free, another variable needs to be Fixed and vice-versa. For example, using a simple gas flowsheet, the default specification is for it to be pressure driven. If forced feed is required, set the feed unit flowrate specification to Fixed and the product unit specification to Free.
•
The library models contain default specifications. Should the problem become over or underspecified, use either the specification analysis tool; or using Variable Finder, find all variables and from the properties page, set the specification to default values.
•
For flowsheets with interaction units, ensure the run time communication interval allows at least five communication points within the shortest interacting steps.
•
For processes that operate under rapid cyclic conditions, ensure the integrator step sizes are suitable. For example, when using the Variable Step Implicit Euler integrator, try setting the maximum integrator step to half the shortest step time, and the initial and minimum steps sizes to 1/5 through 1/10 of the maximum integrator step.
•
The default solution bounds for variables defined in the library are suitable for most problems. However, when operating with large pressure or temperature swings, or very rapid cycles, the default bounds may need readjusting. Use the Variable Finder for this.
•
If you receive messages stating that empty arrays are being passed to procedures, this usually indicates that the current component list is not defined. When flowsheeting, it is usual to first create the component list and then start placing models on the flowsheet.
•
If a spanner/wrench appears in the specification window when flowsheeting, ensure that a component list is defined and that all connections are in place.
Physical Properties Various physical properties are required by the Aspen Adsim models. Typical properties required are: •
Molecular weight
•
Viscosity
•
Density
•
Enthalpy
Aspen Adsim supports two ways of supplying this physical property data:
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•
User Fortran subroutines.
•
External physical property application (Properties Plus, Aspen Properties).
The component list created for the problem governs the method in which physical properties are called. •
If you use a template, the default component list assumes that user Fortran subroutines are being used.
•
When starting a new problem (without a template), the default component list is configured for use with an external properties application. To modify it for use with user-Fortran, you must first convert it to a component set (to do this, right-click the list and select convert).
•
If a new component list is created, by default it is assumed an external properties application will be used. If you want the user Fortran option, select the Is ComponentSet box is on creation.
Use of User Fortran Historically, Aspen Adsim assumed that any physical property calculations or data were supplied through user Fortran subroutines. The advantages of using user Fortran based calculations are: •
Simulation speed.
•
When distributing a problem, only need to additionally supply the library.
Disadvantages of using the user Fortran method are: •
Inflexibility when changing component names. Arrays indexed by component name are passed to procedures in ASCII order, hence subroutines may need modifying in response to changing component order.
•
Addition and removal of components from the simulation. The user subroutines either need reworking after each change or a collection of different versions of subroutines (each assuming different numbers of components) will be required.
When creating a component list: The interface between the subroutine and model is defined by the Procedure type. The procedure definition defines the calling arguments, subroutine name and library name. The subroutines created then need to be compiled into a library so that they link to the simulation during runtime. It is important that the compiled library is placed in the simulator engine’s working directory. The working directory has the same name as the current simulation, and is one level down from the default working directory. For example, if the name of the current problem is N2PSA.ada and the default working folder has been defined as C:\MySims, the simulation engine’s working folder for this problem is C:\MySims\N2PSA. This applies to both local PC and remote server implementations.
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Using a Physical Properties Application The simplest way of incorporating physical property calculations and data, is to use an external physical properties application such as Properties Plus or Aspen Properties. The advantages of using an external physical properties application are: •
Ability to create a single definition file containing all the components and physical property methods of interest, and only those required in the current problem.
•
Large collection of rigorous physical property methods.
•
Extensive component database.
The disadvantages are: •
Speed penalties.
•
Requires application on same machine.
When using Properties Plus or Aspen Properties, for example, the steps required before using either application are: 1
Create an .appdf file.
2
In Aspen Adsim, within the Explorer window, right-click Component Lists and select Properties. Define where the .appdf is located.
3
Create or convert a component list and select the components required.
Switching Between Methods To switch between using user Fortran and an external properties application for the supply of physical property calculations and data: 1
If converting from user Fortran to an external application, ensure the link to an .appdf file is already defined. (To do this, right-click the ComponentLists object in Explorer and browse for a previously created .appdf file.)
2
Select the currently active component list.
3
Right-click the list and select Convert. The component list switches to the other method it’s currently using. When switching from Fortran to application based properties, if the component names originally defined are present in the .appdf file, the same components will be present, otherwise mismatches will be discarded.
4
Open the Configure form for any library model of the flowsheet. The global variable that switches the two methods is automatically updated.
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Connecting to Aspen Dynamics Flowsheets You can now connect Aspen Adsim flowsheet sections to Aspen Dynamics flowsheet sections (except for ion-exchange flowsheets). There are two new utilities models for this purpose: •
Dynamics_Inlet_Connect
•
Dynamics_Outlet_Connect
These models are in the Utilities folder of the Aspen Adsim library. The model link must be done from within Aspen Adsim; the link cannot be set up from Aspen Dynamics. Tip: If you are creating an Aspen Adsim flowsheet for connection with an Aspen Dynamics flowsheet, it is good practice to name the active component list as 'Type 1'. This simplifies later conversion.
Typical Workflows When you want to connect Aspen Dynamics models to Aspen Adsim models, there are two possible situations: •
Attach individual Aspen Dynamics models to an existing Aspen Adsim simulation.
•
Attach a complete Aspen Dynamics simulation to an existing Aspen Adsim simulation.
Attaching Individual Aspen Dynamics Models To attach an individual Aspen Dynamics model (for example, a rigorous compressor model) to an existing Aspen Adsim simulation: 1
In Aspen Adsim, open the Aspen Adsim simulation.
2
Open the Aspen Dynamics library. To do this: From the File menu, click Open Library and navigate to the Lib folder of the AMSystem 2004.1 installation.
3
Place the required Aspen Dynamics model onto the Aspen Adsim flowsheet.
4
Attach the new Aspen Dynamics flowsheet block to an existing Aspen Adsim flowsheet block, as follows: Attach an Aspen Adsim material stream to the Aspen Adsim flowsheet block, and an Aspen Dynamics material stream to the newly placed Aspen Dynamics flowsheet block. Now connect these two streamsusing either a Dynamics_Inlet_Connect or Dynamics_Outlet_Connect model from the Utility folder of the Aspen Adsim library. Your choice depends on whether the Aspen Dynamics model is on the inlet or outlet side of the Aspen Adsim mode.
5
Repeat steps 3 and 4 until the flowsheet is complete.
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6
7
Check and modify the global variables relating to Aspen Dynamics flow schemes. You do this in the Global variables table, or from the Configure form of a Dynamics_Inlet_Connect or Dynamics_Outlet_Connect block: Global variable
Brief description
Notes
GlobalPDriven
Is the flowsheet pressure driven?
For gas systems, set to True.
GlobalPropMode
Property mode
Default is Local. If property convergence is difficult, set to Rigorous. (Aspen Adsim uses only rigorous property calls.)
GlobalRFlow
Reverse flow?
Set to True if the model is expected to operate reversibly.
Specify, and provide initial values for, the new Aspen Dynamics blocks.
Attaching Complete Aspen Dynamics Flowsheet To attach a complete Aspen Dynamics simulation to an existing Aspen Adsim simulation (for example, an Aspen Dynamics based cryogenic distillation train to an Aspen Adsim TSA system for air dehumidification): 1
In Aspen Adsim, open the Aspen Adsim simulation.
2
Check the component lists being used: −
− − 3
The type of Aspen Dynamics flowsheet that can be imported depends on the type of Aspen Adsim flowsheet: − −
−
4
Ensure matching component list names between the Aspen Adsim and Aspen Dynamics simulations. Typically, the Aspen Dynamics version is called “Type1”. If necessary, you must rename the Aspen Adsim component list name to match. If the Aspen Adsim component list name is Default, you cannot rename it through the GUI. Instead, open the input file (.ada extension) within a text editor and search and replace the original component name, to the new component name. Ensure the same components are actively in use. Ensure the same properties definition file, .appdf, is in use.
For gas-based Adsim flowsheets, imported Aspen Dynamics flowsheets must be pressure driven. See Valid Flowsheet Combinations, later. For liquid-based Aspen Adsim flowsheets, imported Aspen Dynamics flowsheets may be either pressure driven or flow driven. See Valid Flowsheet Combinations, later. You must check the Globals table in Aspen Adsim and set the global parameters GlobalPDriven and GlobalRFlow to match those in the Aspen Dynamics flowsheet to be imported.
From the File menu, click Import Flowsheet. This imports the Aspen Dynamics simulation into Aspen Adsim. Note these points: −
Aspen Adsim does not support flowsheet hierarchy, so all Aspen Adsim based blocks and streams must exist on the main flowsheet.
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−
− − −
Repeated blocks, streams, plots, tables and tasks names are flagged during the flowsheet import. You can rename or delete these repetitions, or import the flowsheet into a hierarchy block. Aspen Adsim automatically opens the Aspen Dynamics model library during the import. The Aspen Adsim simulation flowsheet is updated with the imported Aspen Dynamics simulation flowsheet. For common global variables, Aspen Adsim retains the original settings from before the flowsheet was imported.
5
Repeat steps 2 through 4 until all the required flowsheet sections are present within Aspen Adsim.
6
Between each flowsheet section, connect the appropriate Aspen Adsim or Aspen Dynamics feed and product streams: −
For an existing Aspen Adsim feed or product stream, remove the boundary termination block (unlike Aspen Dynamics, Aspen Adsim has no concept of using open ended streams to indicate flowsheet boundaries). Now connect these open-ended Aspen Adsim streams with their Aspen Dynamics counterparts, using either a Dynamics_Inlet_Connect or a Dynamics_Outlet_Connect from the Utilities folder of the Aspen Adsim library. (Your choice depends on whether the Aspen Dynamics model is on the inlet or outlet side of the Aspen Adsim flowsheet.)
7
Repeat step 6 until the flowsheet is complete.
8
In the Cycle Organizer, modify the cycle description to account for any cyclic operation of imported Aspen Dynamics blocks, then regenerate the cyclic task.
Valid Flowsheet Combinations The valid combinations of Aspen Adsim and Aspen Dynamics flowsheets are: •
Connect gas-based Aspen Adsim flowsheets to pressure driven Aspen Dynamics flowsheet sections.
•
Connect liquid-based Aspen Adsim flowsheets to flow driven Aspen Dynamics flowsheet sections.
Further valid combinations are also possible, and these are listed in the following table. Some combinations have constraints: in the table, bracketed numbers mark where this happens and you should refer to the notes underneath for more details. Inlet side section (Aspen Dynamics)
Outlet side section (Aspen Dynamics)
Gas (Aspen Adsim)
Liquid (Aspen Adsim)
Pressure driven
Pressure driven
Supported (1)
Not Supported
Pressure driven
Not present
Supported (2)
Supported (3)
Not present
Pressure driven
Supported (4)
Supported (5)
Flow driven
Flow driven
Partial support (6)
Supported
Flow driven
Not present
Partial support (7)
Supported
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Not present
Flow driven
Partial support (8)
Supported
Reversible
Reversible
Supported (9)
Not supported
(pressure driven)
(pressure driven)
Reversible
Not present
Supported (10)
Supported
Reversible
Supported (11)
Supported
(pressure driven) Not present
(pressure driven)
You cannot mix flow assumptions, for example a pressure driven inlet and a flow driven outlet. This is because a single set of global variables is used to control the Aspen Dynamics flowsheet assumption. The following notes relate to the bracketed numbers (denoting constraints) in the previous table: 1
Connect the Aspen Dynamics flowsheet sections on both the inlet and outlet sides to a pressure node (a gas_tank_void for example).
2
Connect the Aspen Dynamics flowsheet section on the inlet side to a pressure node (a gas_tank_void for example).
3
Fix a pressure at the Aspen Adsim flowsheet outlet.
4
Connect the Aspen Dynamics flowsheet sections on the outlet side to a pressure node (a gas_tank_void, for example).
5
Fix a pressure at the Aspen Adsim flowsheet inlet.
6
Connect both Aspen Dynamics flowsheet sections only to a gas_bed model.
7
Connect the Aspen Dynamics flowsheet only to an Aspen Adsim gas_bed inlet.
8
Connect the Aspen Dynamics flowsheet only to an Aspen Adsim gas_bed outlet.
9
Connect the Aspen Dynamics flowsheet sections on both the inlet and outlet sides to a pressure node (a gas_tank_void for example). The single bed approach is not recommended; use a full rigorous Aspen Adsim flowsheet instead.
10 Connect the Aspen Dynamics flowsheet section on the inlet side to a pressure node (a gas_tank_void for example). The single bed approach is not recommended; use a full rigorous Aspen Adsim flowsheet instead. 11 Connect the Aspen Dynamics flowsheet section on the outlet side to a pressure node (a gas_tank_void, for example). The single bed approach is not recommended; use a full rigorous Aspen Adsim flowsheet instead.
Global Variables A number of global variables control the operation of both Aspen Adsim and Aspen Dynamics models. These variables can be found in the Globals table within the Simulation object in the Simulation Explorer. You can also access many of these global variables through the Configure form of the Dynamics_Inlet_Connect and Dynamics_Outlet_Connect model blocks.
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The global variables used are as follows: Global variable
Default value
Description
GlobalPropMode
Local
The global property mode. Aspen Dynamics models use GlobalPropMode to select between local or rigorous physical properties calculations: The Local option uses simplified functions whose parameters are updated from an external physical property package. This improves the simulation time. The rigorous option uses methods contained within the external physical properties package. Note: All Aspen Adsim models use rigorous property calls.
GlobalPdriven
False
Is the simulation pressure driven? Aspen Dynamics models use GlobalPdriven to switch the overall flowsheet scheme between pressure-driven flow and flow-driven flow. In general, for Aspen Dynamics models used in conjunction with Aspen Adsim models: When the system is gas, set to True. When the system is liquid, set to False. Note: If you anticipate flow reversibility within Aspen Dynamics models, the flowsheet must be pressure driven (so set the parameter to True).
GlobalRFlow
False
Does the simulation support reverse flow? Aspen Dynamics uses GlabalRFlow to switch between uni-directional and bi-directional flow. For bi-directional flow, you must also set GlobalPdriven to True, otherwise the Aspen Dynamics models will default to unidirectional, flow-driven flow.
GlobalTimeScaler
1
Seconds per model time unit. Aspen Dynamics models assume time units of hours, whereas Aspen Adsim models assume seconds. When models from both products exist on the same flowsheet, a common time unit needs to be adopted to successfully calculate time derivatives and delay times. Aspen Dynamics uses GlobalTimeScaler to rescale time derivatives and calculated delay times, from hours to seconds.
IsSingleBed
False
Is the single bed approach being used? IsSingleBed indicates to Aspen Adsim’s Dynamics_Inlet_Connect and Dynamics_Outlet_Connect models, whether the Aspen Adsim flowsheet is using the Single-Bed approach to simulate a multi-bed flowsheet using a single column. When set to True, a set of equations is enabled that generate pseudo continuous flow from an inherently discontinuous flow.
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Connecting to a Single Bed Approach Flowsheet The single bed approach to modeling a cyclic adsorption process is an abstract representation of the real process, so it suffers from the inherent behavior of discontinuous flow at the flowsheet boundaries. For example, a product stream from an Aspen Adsim flowsheet may be active (producing material) only during one step in the cycle.
Flowrate
Cycle time This behavior can disrupt Aspen Dynamics flowsheets that are connected to this same outlet boundary, as they may be expecting to continuously receive material. For example, a discontinuous supply of material may cause adverse effects to downstream units such as distillation columns or compressors. To counter this problem, the Dynamics_Inlet_Connect and Dynamics_Outlet_Connect models have been developed, which contain a series of expressions to generate a pseudo continuous flow of material. They use a similar set of expressions to the gas_interaction model. The flow, composition, temperature, pressure and enthalpy profiles are recorded during the flow of actual material, whilst a delay function is used to reproduce the same profile, periodically throughout the rest of the cycle.
Flowrate Delayed Profiles 4 x DT 3 x DT 2 x DT DT Cycle time The two models use a variable that switches/toggles to indicate when flow of real material occurs. When set to 1 (that is On, for real flow), the inlet and outlet port variables are mapped together and the time at which the switch
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-5
B1.Toggle 1 2 3 4 5 6 7 8 9 10
0
5
B1.DelayTime 10 15 20 25 30
was set to 1 is recorded. When no real flow is occurring, the variable switches to 0 (that is Off, for pseudo flow); and the time at which the switch occurred is recorded, and a delay time is calculated. The Aspen Dynamics port variables are then mapped to the appropriate Aspen Adsim port variables, but through the delay function. When the elapsed time from the switch off exceeds the calculated delay time, the delay time is incremented by the original delay time.
0
DelayTime
10 20 30 40 50 60 70 80 90 100 Time Seconds
1
2
B1.RealOutput 0 0.5
B1.CalcOutput 1 1.5 0.5
-1
-0.5
The result of this procedure is a continuously variable delay time that produces a profile with a repeating pattern.
0
Output_Values
10 20 30 40 50 60 70 80 90 100 Time Seconds
This method is applicable only if the assumption that the flow profile expected at the inlet and/or outlet side of the Aspen Adsim flowsheet is consistent within a given cycle. The delay function is used to replicate flow profiles. This, coupled with the fact that it uses interpolation of historical data, explains why you may see a slight degradation in the overall material balance.
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9 Reference List for Adsorption Processes
Bird, R.B., Stewart, W.E., Lightfoot, E.N., Transport Phenomena, John Wiley and Sons, New York, 1960. Carberry, J.J., Chemical and Catalytic Reaction Engineering, McGraw-Hill, New York, 1976. Carver, M.B., Scheisser, W.E., American Institute of Chemical Engineers, Annual Meeting, November 16-18, 1980. Costa, E., Sotelo, J.L., Calleja, G., Marron, C., Adsorption of Binary and Ternary Hydrocarbon Gas Mixtures on Activated Carbon: Experimental Determination and Theoretical Prediction of the Ternary Equilibrium Data, AIChE Journal, Vol. 27, No. 1, 1981. Froment, G.F. and Bischoff, K.B., Chemical Reactor Analysis and Design, John Wiley and Sons, New York, 1990. Kast, W., Adsorption aus der Gasphase, VCH, Weinheim, 1988. Nakao, S.I., Suzuki, M.U., Mass Transfer Coefficient in Cyclic Adsorption and Desorption, Journal of Chem. Eng. of Japan, Vol 16, No 2, 1983. Reid, C.R., Prausnitz, J.M., Sherwood, T.K., The Properties of Gases and Liquids, McGraw-Hill, New York, 1977. Ruthven, D.M., Principles of Adsorption and Adsorptive Processes, John Wiley and Sons, 1984. Slater, M.J., The Principles of Ion Exchange Technology, Butterworth, Heinemann, Boston, 1991. Tien, Chi, Adsorption Calculations and Modeling, Butterworth-Heinemann, 1994. Wakoo, N., Chem Eng Sci, 31, pp 11-15, 1976. Yang, R.T., Gas Separation by Adsorption Processes, Butterworth, 1987.
9 Reference List for Adsorption Processes
298
Index
Complex expression step control 248
A
Compressiblity (gas) 21
Activating cyclic tasks 257
Conduction (gas) 65
Adsorbed solution theory (gas) 64
Conduction (liq) 207, 210
Adsorption isotherms (gas)
Configure form (gas)
about 51
about 15
choosing 52
bed types 16
list 55
internal heat exchanger 19
multicomponent mixture isotherms 52
spatial dimensions of beds 18
Aspen Custom Modeler™ 230
Configure form (ionx) 179
Aspen Properties™ 284
Configure form (liq) 192
available 299
Configure form tabs (gas)
Axial dispersion (gas) 22
Energy Balance 64
Axial dispersion (ionx) 182
General 20
Axial dispersion (use for differencing schemes) 223
Isotherm 51
B B.E.T isotherm (gas) 58 B.E.T. Multilayer isotherm (gas) 58
Kinetic Model 31 Material/Momentum Balance 22 Procedures 76 Reaction 73 Configure form tabs (ionx)
Bed model assumptions (gas) 11, 13
General 180
Bed model assumptions (ionx) 179
Isotherm 185
Bed model assumptions (liq) 192
Kinetic Model 183
Bed model ports (gas) 14
Material/Momentum Balance 180
Bed models (gas) 14
Configure form tabs (liq)
Biased Upwind Differencing Scheme 227
Energy Balance 206
Brunaur, Emmet and Teller See B.E.T
General 193
Burke-Plummer equation (gas) 26
Isotherm 200
C Central differencing schemes 222, 223
Kinetic Model 196 Material/Momentum Balance 193 Procedures 213
Index
299
preparing 258
Configure Layer form (gas) 20 Configure Layer form (ionx) 179
Cyclic Stream report 259
Configure Layer form (liq) 192
Cyclic tasks 257
Connecting controllers 268 Connectivity in flowsheets 267
D
Consistency checks for flowsheets 281
Darcy's Law (gas) 26
Constant variables (specifying) 280
Darcy's law (liq) 195
Controllers 268
Deactivating cyclic tasks 257
ControlSignal stream 268
Demonstration Organizer 269
Convection (gas) 23
Demonstrations 268
Convection (ionx) 180
Density (liq) 196
Convection (liq) 193
Discretization methods
Convert_EstMod script 241
about 218
Cycle controls 254
choosing 219
Cycle Organizer
list 219
about 243
recommended 219
cycle controls 254
Discretization methods (gas) 20
Cycle Organizer window 244
Discretization methods (ionx) 180
cyclic reports 258
Discretization methods (liq) 193
cyclic tasks 257
Dispersion (gas) 23
interaction control 252
Dispersion (ionx) 180, 182
opening 244
Dispersion (liq) 193
step controls 246, 256
Dispersion coefficient (ionx) 180
step variables 250
Dispersion coefficient (liq) 193
Cycle Organizer block 244
Dispersive properties (gas) 27
Cycle Organizer window 244
documentation 297
cycle controls 254
Dual Layer B.E.T isotherm (gas) 62
cyclic reports 258
Dual-Site Langmuir isotherm (gas) 61
cyclic tasks 257
Dual-Site Langmuir isotherms (liq) 201
interaction controls 252
Dubinin-Astakov isotherm (gas) 59
step controls 256
Dynamic estimation
step variables 250
about 236
Cycle snapshots 255
entering data manually 237
Cyclic corrections (gas) 49
importing data from clipboard 238
Cyclic operations 243 Cyclic Recovery report 260
E
Cyclic reports 258
Effective diffusivity (gas) 36, 39, 50
Cyclic Recovery reports 260
Energy balance assumption (gas) 64
Cyclic Stream reports 259
Energy balance assumption (liq) 206
Index
300
Energy balance equations (gas)
Extended Langmuir isotherm (ionx) 187
factors affecting equations 81
Extended Langmuir isotherms (gas) 60
gas phase 78, 81
Extended Langmuir isotherms (liq) 201
solid phase 78, 84
Extended Langmuir-Freundlich isotherm (gas) 61
wall 79, 86 Energy balance equations (liq) 213 Energy Balance tab (gas) 64 Energy Balance tab (liq) 206 Enthalpy (gas) 65 Enthalpy (liq) 208
Extended Langmuir-Freundlich isotherm (ionx) 187 Extended Langmuir-Freundlich isotherms (liq) 203
F
Equation symbols (gas) 87
Film model assumption (gas) 31
Equation symbols (ionx) 189
Film model assumption (ionx) 183
Ergun equation (gas) 27
Film model assumption (liq) 197
Estimated mass transfer coefficient (gas) 50
Flow reversibility 263
Estimated Variables tab 232
Flowsheet specifications See Specifying flowsheets
Estimation converting Estimation Module data 241 dynamic 236 estimated variables 232 Estimation Module 230 methods available 230 performing using Estimation Module 241 recommendations 241 steady-state 233 Estimation methods 241 Estimation Module about 230 converting to Aspen Custom Modeler™ methods 241
Flowsheet types 269 full 271 intermediate 270 simple 269 Flowsheets about 266 Connectivity 267 Cycle Organizer block 244 demonstrations 268 interactions 275 model types 263 physical property calculations 282 Pressure Interaction diagram 272
defining estimated variables 232
reversibility of flow 263
dynamic estimation 236
single bed approach 272
recommendations 241
specifications 277
steady-state estimation 233
templates 268
using 241
types 269
Estimation Module block 231
Fluid phase energy balance (liq) 214
Estimation Module form 231
Fluid thermal conductivity (liq) 210
Event-driven step controls 246
Flux Limited Differencing Scheme 229
Experimental Data tab 233, 237
Flux Limiter method? (gas) 21
Expression Builder dialog box 249
Freundlich isotherms (gas) 56
Index
301
Freundlich isotherms (liq) 202
Heat transfer coefficient (gas) 67
Fromm's Scheme 228
Heat transfer coefficient (liq) 209
Full flowsheet 271
Heat transfer to environment (gas) 70
G
Heat transfer to environment (liq) 211 Henry isotherms (gas) 57
g_Material_Port 267
Henry's coefficient (gas) 47
Gas adsorption processes (overview) 11, 12
Heterogeneous rate dependency (gas) 75
Gas model assumption (gas) 21
Heterogeneous reactions (gas) 74
Gas thermal conductivity (gas) 69
Homogeneous rate dependency (gas) 74
gas_Material_connection 267
Homogeneous reactions (gas) 74
Gas-Wall heat transfer coefficient (gas) 72
Horizontal beds (gas) 16
General tab (gas) 20 General tab (ionx) 180
I
General tab (liq) 193
i_Material_Port 267
Generating cyclic tasks 257
IAS (gas) 53, 64
Glueckauf approximation (gas) 49
IAS (liq)
gUserCompressibility submodel 22
about 200
gUserCpa submodel 66
IAS Freundlich isotherms 204
gUserDH submodel 67
IAS Langmuir isotherms 204
gUserDispersion submodel 24
IAS Langmuir-Freundlich isotherms 205
gUserEffDiff submodel 37, 41, 50
Purecomponent procedure with IAS isotherm 206
gUserGibbs submodel 63 gUserHTC submodel 68 gUserIsothermC submodel 63 gUserIsothermPoi submodel 63 gUserIsothermPp submodel 63 gUserKg submodel 69 gUserKinetic submodel 35 gUserKineticModel submodel 43 gUserMTC submodel 49
H
Purecomponent submodel with IAS isotherm 206 IAS Freundlich isotherms (liq) 204 IAS isotherm (gas) 63 IAS Langmuir isotherms (liq) 204 IAS Langmuir-Freundlich isotherms (liq) 205 Ideal Adsorbed Solution theory See IAS Ideal gas (gas) 21 Importing data from Microsoft® Excel dynamic 239 steady-state 235
Heat capacity (gas) 66
Initialization for models 280
Heat capacity (liq) 208
Interaction control 252
Heat exchanger (gas) 19
Interactions 252
Heat of adsorbed phase (gas) 65
Interactions between steps 275
Heat of adsorbed phase (liq) 208
Interactions example 275
Heat of adsorption (gas) 66
Intermediate flowsheet 270
Heat of adsorption (liq) 208
Index
302
Internal heat exchanger (gas) 19
Langmuir isotherms (liq) 200
Ion-exchange adsorption processes (overview) 178
Langmuir-Freundlich isotherm (gas) 57
Ion-exchange equilibria 185 Ion-exchange resins 178 ionx_Material_connection 267 Isotherm assumed for layer (gas) 55 Isotherm assumed for layer (ionx) 186 Isotherm assumed for layer (liq) 200 Isotherm dependency (gas) 64 Isotherm list (gas) 55 Isotherm list (ionx) 186 Isotherm list (liq) 200 Isotherm tab (gas) 51 Isotherm tab (ionx) 185 Isotherm tab (liq) 200 Isothermal conditions (gas) 65 Isothermal conditions (liq) 207 Isotherms (gas) 55 Isotherms (ionx) 185 Isotherms (liq) 199 iUserDispersion submodel 182 iUserIsotherm submodel 187 iUserKinetic submodel 184 iUserMTC submodel 185
K Karman-Kozeny equation (gas) 26 Karman-Kozeny equation (liq) 195 Kinetic model assumption (gas) 31 Kinetic model assumption (ionx) 184 Kinetic model assumption (liq) 197 Kinetic Model tab (gas) 31 Kinetic Model tab (ionx) 183 Kinetic Model tab (liq) 196 Knudson diffusion coefficient (gas) 48
L Langmuir isotherms (gas) 55
Langmuir-Freundlich isotherms (liq) 202 Leonard Differencing Scheme 223 Linear isotherm (gas) 59 liq_Material_connection 267 liq_Material_Port 267 Liquid adsorption processes (overview) 191 Lumped resistance (gas) 32, 44, 46 Lumped resistance (ionx) 184 Lumped resistance (liq) 197 lUserDH submodel 209 lUserDispersion submodel 195 lUserGibbs submodel 206 lUserHTC submodel 210 lUserIsotherm submodel 205, 206 lUserKinetic submodel 198 lUserKl submodel 211 lUserMTC submodel 199
M Mass action equilibrium isotherm (ionx) 186 Mass balance equations (gas) additional solid phase 77, 81 factors affecting equations 79 gas phase 77 Mass balance equations (ionx) 188 Mass balance equations (liq) 213 Mass transfer (gas) about 31 lumped resistance 32, 44 micro and macropore effects 32 molecular diffusivities 45 particle material balance 36, 39 procedures 43 submodels 43 Mass transfer (ionx) 183 Mass transfer (liq) 196 Mass transfer coefficient (gas) 46, 50
Index
303
Mass transfer coefficient (ionx) 185
Non-isothermal conditions (liq) 209, 210
Mass transfer coefficient (liq) 198
Non-Isothermal conditions (liq) 207
Mass transfer driving force (gas) 31
Nonlinearity and numerical methods 218
Mass transfer driving force (ionx) 183
Non-Reversible Delay models 263
Mass transfer driving force (liq) 197
Non-Reversible models 263
Material balance assumption (gas) 23
Number of heterogeneous reactions (gas) 75
Material balance assumption (ionx) 180
Number of homogeneous reactions (gas) 75
Material balance assumption (liq) 193
Number of nodes (gas) 21
Material/Momentum Balance tab (gas) 22
Number of nodes (ionx) 180
Material/Momentum Balance tab (ionx) 180
Number of nodes (liq) 193
Material/Momentum Balance tab (liq) 193
Numerical methods
Maximum number of cycles 254
about 218
Micro and macropore effects (gas) 32, 34, 46
Biased Upwind Differencing Scheme 227
Micro and macropore effects (liq) 198
Central Differencing Schemes 222, 223
Microsoft® Excel 235, 239
Flux Limited Differencing Scheme 229
Mixed Differencing Scheme 226
Fromm's Scheme 228
Model configuration (defining) 280
Leonard Differencing Scheme 223
Model specifications 280
Mixed Differencing Scheme 226
Model types 262
Quadratic Upwind Differencing Scheme 224
Models
recommended 219
list of types 263
selecting 219
reversibility 263
Upwind differencing schemes 221
types 262
Upwind Differencing Schemes 222
Molecular diffusivities (gas) 45 Molecular diffusivity (ionx) 182 Momentum balance assumption (gas) about 25 constant pressure options 25 pressure driven options 26 Multicomponent mixture isotherms (gas) 52
O Obtain Dynamic Measurements for Experiment DynExpt From Clipboard dialog box 238 Obtain Steady State Experiments From Clipboard dialog box 235 Overall material balance assumption (liq) 196
Myers isotherm (gas) 60
P
N
Particle material balance See Particle MB options
New Experiment dialog box
Particle MB 2 option (gas) 39, 50
dynamic 237
Particle MB option (gas) 36, 50
steady-state 233
Particle resistance coefficients (gas) 34
Nodes (gas) 21
PDE differencing schemes
Non-ideal gas (gas) 21
Biased Upwind 227
Non-isothermal conditions (gas) 65
Central 222, 223
Index
304
Flux Limited 229
Properties Plus™ 284
Fromm's 228
pUser_Act_Coeff procedure 64
Leonard 223
pUser_g_Cat_Rx_Heat procedure 83
Mixed 226
pUser_g_Cat_Rx_Rate_C procedure 75, 83
Quadratic Upwind 224
pUser_g_Cat_Rx_Rate_C_Sol procedure 75, 83
Upwind 221, 222
pUser_g_Cat_Rx_Rate_Pp procedure 75, 76, 83
Peclet number (gas) 23 Peclet number (ionx) 183 Physical property calculations about 282 external applications 284 switching between methods 284 user Fortran 283 Port types 267 Prandl number (gas) 68 Prandl number (liq) 210 Presets for models 280 Pressure (gas) 25 Pressure (liq) 195 Pressure drop assumption (liq) 195 Pressure drop options (gas) 27 Pressure Interaction diagram 272 Pressure Interaction diagram example 272 Problem definition checks for flowsheets 281 Procedures (used in) effective diffusivity 50 fluid thermal conductivity 211 gas thermal conductivity 69 heat of adsorbed phase 66 heat of adsorption 67, 209 heat transfer coefficient 68, 210 isotherms 62, 187, 205 kinetic model 43, 184, 198 mass transfer coefficient 49, 185, 199 material balance 24, 181, 194 molecular diffusivities 46 purecomponent isotherms 206 Procedures tab (gas) 76
pUser_g_Cat_Rx_Rate_Pp_Sol procedure 75, 76, 81, 83 pUser_g_Compressibility procedure 22 pUser_g_Cpa procedure 66 pUser_g_De procedure 37, 41, 50 pUser_g_DH procedure 67 pUser_g_Diffusivity procedure 46 pUser_g_Dispersion procedure 24 pUser_g_Gas_Rx_Heat procedure 83 pUser_g_Gas_Rx_Rate_C procedure 74, 83 pUser_g_Gas_Rx_Rate_Pp procedure 74, 83 pUser_g_Gibbs procedure 62 pUser_g_HTC procedure 68 pUser_g_Isotherm_C procedure 62 pUser_g_Isotherm_P procedure 62 pUser_g_Isotherm_Poi procedure 62 pUser_g_Kg procedure 69 pUser_g_Kinetic procedure 35, 43 pUser_g_MTC procedure 49 pUser_i_Dispersion procedure 181 pUser_i_Isotherm_C procedure 187 pUser_i_Isotherm_W procedure 187 pUser_i_Kinetic procedure 184 pUser_i_MTC procedure 185 pUser_l_DH procedure 209 pUser_l_Dispersion procedure 194 pUser_l_Gibbs procedure 206 pUser_l_HTC procedure 210 pUser_l_Isotherm_C procedure 205 pUser_l_Isotherm_W procedure 205, 206 pUser_l_Kinetic procedure 198 pUser_l_Kl procedure 211
Procedures tab (liq) 213
Index
305
pUser_l_MTC procedure 199
Q
Spatial dimensions of beds (gas) 18 Specifying flowsheets checks 281 list of options 277
Quadratic Upwind Differencing Scheme 224
model specification 280
R
run time options 279 solver options 277
Radial beds (gas) 18 Radial nodes (gas) 21
Static_isotherm model 233
Rate dependency (gas) 74, 75
Steady state testing (cyclic) 255
Reaction processes (gas) 73
Steady-state estimation
Reaction tab (gas) 73
about 233
Reactions present? (gas) 74
entering data manually 233
Reactions type (gas) 74
importing data from clipboard 234
Real Adsorbed Solution theory (gas) 64
Step controls 256
Real Adsorbed Solution Theory (gas) 54
Step dependent step control 249
Recommended numerical methods 219
Step interaction control 252
Recording cycle information 255
Step interactions 252, 275
Reference list 292
Step variables 250
Reversibility example 264
Stoichiometric Equilibrium isotherms (liq) 203
Reversibility of flow 263
Submodels (used in)
Reversible Flow Setter models 263
component isotherms 206
Reversible models 263
effective diffusivity 50
Reversible Pressure Setter models 263
fluid thermal conductivity 211
Rigorous multiple bed approach 272
gas thermal conductivity 69
Run time options (specifying) 279
heat of adsorbed phase 66
Running end-of-step scripts 256
heat of adsorption 67, 209 heat transfer coefficient 68, 210
S
isotherms 63, 187, 205
Sherwood number (gas) 47
kinetic model 43, 184, 198
Simple flowsheet 269
mass transfer coefficient 49, 185, 199
Simulation Messages window 254, 255
material balance 24, 182, 195
Single bed approach 252, 272 Single Layer B.E.T isotherm (gas) 61
T
Snapshots 255, 256
Task Language 257
Solid phase energy balance (liq) 214
Template Organizer 268
Solid reactant list (gas) 76
Templates 268
Solid reactants present? (gas) 76
Time controls (reason for) 253
Solver options (specifying) 277
Time-driven step controls 246 Toth isotherm (gas) 57
Index
306
U Upwind differencing schemes 221, 222 User Multicomponent Procedure isotherm (liq) 205 User Multicomponent Submodel isotherm (liq) 205 User Purecomponent Procedure with IAS isotherm (liq) 206 User Purecomponent Submodel with IAS isotherm (liq) 206
V Variable fields 251 Variable Selector dialog box 250 Velocity (gas) 25 Velocity assumption (liq) 196 Vertical beds (gas) 16, 18, 27 Volmer isotherm (gas) 59
W Wall energy balance (liq) 214 Water softening and purification (ionx) 178
Index
307
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