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COMPUTER AIDED PROPERTY ESTIMATION FOR PROCESS AND PRODUCT DESIGN

COMPUTER-AIDED CHEMICAL ENGINEERING Advisory Editor: R. Gani Volume Volume Volume Volume

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Volume 6: Volume 7: Volume 8: Volume 9: Volume 10: Volume 11: Volume 12: Volume 13: Volume 14: Volume 15: Volume 16: Volume 17: Volume 18: Volume 19:

Distillation Design in Practice (L.M. Rose) The Art of Chemical Process Design (G.L. Wells and L.M. Rose) Computer Programming Examples for Chemical Engineers (G. Ross) Analysis and Synthesis of Chemical Process Systems (K. Hartmann and K. Kaplick) Studies in Computer-Aided Modelling. Design and Operation Part A: Unite Operations (I. Pallai and Z. Fonyó, Editors) Part B: Systems (I. Pallai and G.E. Veress, Editors) Neural Networks for Chemical Engineers (A.B. Bulsari, Editor) Material and Energy Balancing in the Process Industries - From Microscopic Balances to Large Plants (V.V. Veverka and F. Madron) European Symposium on Computer Aided Process Engineering-10 (S. Pierucci, Editor) European Symposium on Computer Aided Process Engineering-11 (R. Gani and S.B. Jørgensen, Editors) European Symposium on Computer Aided Process Engineering-12 (J. Grievink and J.van Schijndel, Editors) Software Architectures and Tools for Computer Aided Process Engineering (B. Braunschweig and R. Gani, Editors) Computer Aided Molecular Design: Theory and Practice (L.E.K. Achenie, R. Gani and V. Venkatasubramanian, Editors) Integrated Design and Simulation of Chemical Processes (A.C. Dimian) European Symposium on Computer Aided Process Engineering-13 (A. Kraslawski and I. Turunen, Editors) Process Systems Engineering 2003 (Bingzhen Chen and A.W. Westerberg, Editors) Dynamic Model Development: Methods, Theory and Applications (S.P. Asprey and S. Macchietto, Editors) The Integration of Process Design and Control (P. Seferlis and M.C. Georgiadis, Editors) European Symposium on Computer-Aided Process Engineering-14 (A. Barbosa-Póvoa and H. Matos, Editors) Computer Aided Property Estimation for Process and Product Design (M. Kontogeorgis and R. Gani, Editors)

COMPUTER-AIDED CHEMICAL ENGINEERING, 19

COMPUTER AIDED PROPERTY ESTIMATION FOR PROCESS AND PRODUCT DESIGN Edited by

Georgios M. Kontogeorgis IVC-SEP, Technical University of Denmark Søltofts Plads Department of Chemical Engineering Building 229, DK-2800 Lyngby, Denmark

Rafiqul Gani CAPEC, Technical University of Denmark Søltofts Plads Department of Chemical Engineering Building 229, DK-2800 Lyngby, Denmark

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V

Preface Properties of pure compounds and/or their mixtures are needed in almost every aspect of process/product design. Whether it is evaluation of a product or design of a process/product or simulation of a process flowsheet or analysis of operability of a process, etc., one or more types of properties would be needed. There are several sources or means to obtain the necessary properties. For example, measure the necessary property data, retrieve the necessary property values from a database, calculate the necessary property values through appropriate models, and last but not least, use of specialized software. Although, the use of experimental data provides the most reliable means of getting the right property values, this option is not always feasible due to the time needed to obtain the experimental data and the associated cost. Therefore, among the most interesting options are often use of databases, use of appropriate property models and/or use of specialized software. Although, a number of databases with collections of experimental data exist, and in some cases, also of estimated data, the problem for many users is to know which database can be used and for what data? The most widely used option for obtaining the needed property values is the use of property models. Some of the problems that the users face here are, which models to use, what is their accuracy or what to do if the model's parameters are not available? The user also faces the same questions when using specialized software. A number of books have been written to help the users to estimate the needed properties, with the most well-known of these being the "Properties of Gases and Liquids" by Poling, Prausnitz, and O'Connell. Other books (written by Sandier, Horvath, Smith et al) also provide useful information for the user. Although the currently available books provide a lot of useful information, they do not exactly address the questions from a user-of-models point of view and they mostly focus on vapor-liquid equilibria. The objective of this book is to highlight the computational aspects of property estimation with special focus on their use in process-product design covering a wide spectrum of properties and phase equilibria types. The book does not merely provide a presentation of the most suitable property models available today but provides, as well, some guidelines on how to select the appropriate property model. A systematic approach to property estimation is proposed. That is, first identify the needed properties, then identify the appropriate property model to be used (if the use of a database is not possible), then estimate the needed properties according to step by step calculation procedures. This information will also help the readers to develop their own computer programs.

VI

This book is organized into 16 chapters, which are divided into 4 parts. The chapters of Part I highlight various aspects of computer aided property estimation and the roles of properties and their models in process and product design. Illustrative examples are also included. Each chapter in Part II covers a class of properties and their models. The objective is not to provide an exhausted list of property models but to discuss a few selected models in detail from a process-product design point of view. Useful information about successful application, limitations, performance analysis, etc., is also provided. The chapters include models for pure component properties! equations of state, GEmodels and their combined forms; advanced equations of state such as the CPA model; models for polymer solutions and electrolyte systems! models for diffusion in multicomponent mixtures! and, modeling of solid-liquid equilibrium and of gas hydrates. The chapters in Part III deal with application (or use) of the property models from Part II. Illustrative examples, many of them related to typical process-product design related calculations, are provided. In addition, a chapter on molecular simulation of phase equilibrium for industrial application is included. Finally, Part IV, contains a single chapter on the "challenges and opportunities" in property modeling. The chapter provides an overview of the future directions, the needs and application of property modeling. A number of experts from academia and industry have been invited to contribute. These have been collected and organized by the editors in a way that readers will find it easy to read about the properties, their needs, and how to apply (estimate) them. We take this opportunity to thank all the contributors for providing excellent material, to Elsevier for accepting to publish this book and to our coworkers who have helped us with the organization of the material. We would like to acknowledge those students and co-workers of ours who have proofread parts of this book and/or provided material for it : Dr. Nicolas von Solms, Dr. Thomas Lindvig, Dr. Samer Derawi, Dr. Hongyuan Cheng, Ph.D student Irene Kouskoumvekaki and Amra Tihic. We would like to thank Prof. Michael Michelsen, and Dr. Giorgio Soave for many useful discussions. Finally, we hope that the readers will find the book useful for research, development, and educational purposes. We hope that the book will generate enough interest and valuable feedback for future editions. We would also like to state that even though we are proposing a computer aided property estimation for process-product design, we do value the importance of experimental data. Model development and validation without experimental data is not possible. Therefore, we do hope that there is also an emphasis on systematic plans for property measurements and collection so that better and more versatile models can be developed. Georgios M. Kontogeorgis and Rafiqul Gani

vii

List of contributors Author Jens Abildskov Joao A.P. Coutinho Philippos Coutsikos Jean-Luc Daridon Peter K. Davis J. L, Duda Ioannis G. Economou

Rafiqul Gani Eric Hendriks Georgios M. Kontogeorgis Jorge Marrero Henk Meijer John P. O'Connell

Address CAPEC, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark Departamento de Quimica, University of Aveiro, 3810193 Aveiro, Portugal Diadikassia s.a, Athens, GreecG Laboratoire des Flu ides Complexes, Universite de Pau et des Pays de l'Adour, 64013 Pau, France Department of Chemical Engineering, The Pennsylvania State University 165 Fenske Laboratory, USA Department of Chemical Engineering, The Pennsylvania State University 165 Fenske Laboratory, USA Molecular Modelling of Materials Laboratory Institute of Physical Chemistry National Research Center for Physical Sciences "Dcmokritos", 153 10, Athens, Greece CAPEC, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark Shell Global Solutions Inter national, Shell Research & Technology Centre, Amsterdam, The Netherlands IVC'SEP, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark CAPEC, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark Shell Global Solutions International, Shell Research & Technology Centre, Amsterdam, The Netherlands Department of Chemical Engineering University of Virginia 102 Engineers' Way P.O. Box 400741 Charlottcsvillc, VA 22904-4741 USA

Vlll

Jerome Pauly Michael L. Pinsky

Alexander Shapiro Kiyoteru Takano

Epaminondas C. Voutsas

Laboratoire des Fluides Complexes, Universite de Pau et des Pays de l'Adour, 64013 Pau, France Firmenich Chemical Manufacturing Center 150 Firmenich Way Port Newark, N. J. 07114 USA IVC-SEP, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark Mitsubishi Chemical Corporation Yokohama Research Center Industrial Engineering Laboratory Kamoshida-cho, Aoba-ku Yokohama 227-8502 Japan Thermodynamics and Transport Phenomena Laboratory, Department of Chemical Engineering, National Technical University of Athens

IX

Contents

Page

Preface

v

List of contributors

vii

PART I. Introduction to Computer Aided Property Estimation

1

1. Computer aided property estimation Georgios M. Kontogeorgis & Rafiqul Gani 2. Role of properties and their models in process and product design Rafiqul Gani & John P. O'Connell

3 27

PART II. Models for Properties

43

3. Pure component property estimation: Models & databases Jorge Marerro & Rafiqul Gani 4. Models for liquid phase activity coefficients-UNIFAC Jens Abildskov, Georgios M. Kontogeorgis & Rafiqul Gani 5. Equations of state with emphasis on excess Gibbs energy mixing rules Epaminondas C. Voutsas, Philippos Coutsikos & Georgios M. Kontogeorgis 6. Association models — The CPA equation of state Georgios M. Kontogeorgis 7. Models for polymer solutions Georgios M. Kontogeorgis 8. Property estimation for electrolyte systems Michael L. Pinsky & Kiyoteru Takano 9. Diffusion in multicomponent mixtures Alexander A. Shapiro, Peter K. Davis, J. L. Duda 10. Modelling phase equilibria in systems with organic solid solutions Joao Coutinho, Jerome Pauly, Jean-LucDaridon 11. An introduction to modeling of gas hydrates Eric Hendriks & Henk Meijer

45 59 75

113 143 181 205 229 251

X

Part III: Application of property models & databases

277

12. Molecular simulation of phase equilibria for industrial applications Ioannis G. Economou 13. Property models in computation of phase equilibria Rafiqul Gani & Georgios M. Kontogeorgis 14. Application of property models in chemical product design Rafiqul Gani, Jens Abildskov & Georgios M. Kontogeorgis 15. Computational algorithms for electrolyte system properties Rafiqul Gani & Kiyoteru Takano

279

PART TV- Challenges & Opportunities 16. Challenges and Opportunities for Property Modelling

309 339 371

405 407

Georgios M. Kontogeorgis & Rafiqul Gani Subject Index

417

Author Index

425

Part I: Introduction to Computer Aided Property Estimation

1. Computer aided property estimation Rafiqul Gani & Georgios M. Kontogeorgis 2. Role of properties and their models in process and product design Rafiqul Gani & John P. O'Connell

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Computer Aided Property Estimation for Process and Product Design G.M. Kontogeorgis and R. Gani (Editors) © 2004 Elsevier B.V. All rights reserved.

3

Chapter 1: Introduction to Computer Aided Property Estimation Georgios M. Kontogeorgis and Rafiqul Gani 1.1 INTRODUCTION Computer aided property estimation implies the use of mathematical models for the calculation of the needed properties. Depending on the type of property, the size-scale factor, the required accuracy, the application, etc., the mathematical models have varying degrees of complexity. For example, they may be very simple polynomial functions (correlations) representing various pure component temperature dependent properties, a non-linear set of algebraic equations representing various cubic equations of state, or, a very large set of differential-algebraic equations representing the behavior of atoms within a specified boundary. In all cases, an appropriate mathematical model is derived or selected and solved with the help of computers to obtain the necessary property values. These mathematical models, representing the behavior of atoms, molecules and/or solutions, often include parameters that have been regressed to match the observed behavior of a set of systems (atoms, molecules and/or solutions). Therefore, computer aided property estimation also includes model development and model parameter estimation in addition to property estimation. The essential steps in computer aided property estimation are to select an appropriate model for the desired property and to solve the corresponding model equations to estimate the property, provided all the necessary model parameters are available. A pre-estimation step is to derive or develop the needed property model, which can be time consuming and expensive. Therefore, the availability of computerized libraries of property models from which the needed model can be selected and/or adopted is commonly practiced. The method of solution of the model equations, of course, depends on the type of the model (that is, the set of equations representing the model). However, for single value property estimations involving simple polynomial functions, hand calculators may be used. For repetitive calculations of the same property and the same system within an iterative loop and/or same property for different systems, use of a computer-based calculation option is more appropriate. On the other side of the scale-size factor, for single value property estimations involving complex mathematical models (such as molecular modeling), the method of solution is computer intensive and availability of powerful computers is an advantage. Parameter estimation is necessary when the available parameters do not give acceptable results or are simply not available. In either case, experimental data must be available to fine-tune or regress the model parameters. In this chapter, we will give an overview of computer aided property estimation in terms of types of properties, types of models and types of solution approaches together with a discussion on methods for model development.

4 1.2 CLASSIFICATION OF PROPERTIES & MODELS Properties are classified in this chapter in terms of the scale-size factor, the function-use factor and the dependence factor according to a defined hierarchy. The scale-size factor is used at the inner-level, where, properties are classified in terms of scale & size into microscopic, mesoscopic and macroscopic. Microscopic properties refer to properties of atoms while macroscopic properties refer to properties of molecules. At each scale-size, the properties are further classified in terms of single atoms/molecules or multiple atoms/molecules of different types. At the next level, each type of property from the inner level is classified in terms of the function-use factor as physical, chemical, transport, environmental and so on. That is, the function and/or use of the property define its class. At the outer level, properties are classified as primary (single value property, which can be determined only from the structural information), secondary (property that cannot be explicitly calculated only from the structural information and is usually a function of other properties) or functional (properties that are dependent on the intensive variables, temperature, pressure and/or composition, in addition to the structural information). Figure 1 illustrates this outer-level classification.

Figure 1: Outer-level classification of properties. A model is needed for estimation of any property from any level and sub-level. The type of model to be used depends on the three classification factors. At the macroscopic level, Eqs. 1-4 highlight examples of primary, secondary and functional property models, respectively. Tc = 231.239*Log (Ik hU + I, A, N, + Zt B,• Mj )

(1)

ZC = (PC*VC)/(83.14*TC)

(2)

P,ap = 10IA

(3)

H!(rc>]

5

Lny, = l-ln

E, - (xi*d,/E, + x/Q/Ej)

(4)

In the above models, Eq. 1 illustrates a 3rd-order group contribution based additive model for a single value primary pure component property (critical temperature - Tc) where each of the summation terms indicates group contribution for the corresponding group-order. The theoretical basis here is that the accuracy of property estimation increases with the increase in the number of additive terms. Equation 2 illustrates a secondary property of a pure component or mixture (critical compressibility factor, Zc, as a function of critical temperature, critical pressure and critical volume). Theoretically, if the primary property expressions are introduced into the expression for the secondary property, the corresponding secondary property can be estimated only from the molecular structural information and the parameters for the additive terms. Note, however, that the parameters are regressed (usually) only with the primary property experimental data. The secondary property is usually derived from observed relationships between properties of a class of systems. Equation 3 represents a temperature dependent correlation for the vapor pressure, Pvap, as a function of temperature, T. This class of properties change as the condition of the state (defined by the intensive properties - temperature, pressure and/or composition) change. Therefore, the behavior of systems under different conditions needs to be modeled. Equation 4 represents mixture property - activity coefficient for component i in a binary liquid mixture. The models are classified in this chapter in terms of theoretical, semi-empirical and empirical (see Figure 2). Most of the commonly used property models belong to the semiempirical type. Molecular modeling approaches belong to the theoretical class while correlation functions belong to the empirical type. The main feature of all property models is that regressed values for a set of model parameters are needed in order to estimate the property from the model equations. If these parameters are available in the form of regressed values, then the estimation can be performed. Otherwise, the unavailable model parameter values will need to be regressed or another property model will need to be selected. In some cases, the property model parameter can be predicted, giving rise to truly predictive property models. Thus, property model development and use consists of a model parameter estimation and/or verification step. The application range of the property model, therefore, depends not only on the theoretical aspects (such as the behavior of the system) but also on the data used for the regression of the model parameters.

1.3 PROPERTY MODEL DEVELOPMENT Development of models in general and property models in particular, is a cyclic process as shown in Figure 3. One starts with a definition of the model requirements and a hypothesis, solves the model equations, checks the calculated values against collected experimental data, and if the comparison is not favorable, changes the theory and/or the model parameters (thereby generating a new model) and repeats the cycle. As with other types of models, decisions need to be made in terms of the type of model to be developed for a specific property, the required accuracy, the application range (in terms of systems, conditions, problems), and the expected users. For many property model developments, these decisions

6 are inter-related. For example, property model development, formulated as, develop a model for the estimation of the average density of polymers defines the type of model, the application range and the expected users. On the other hand, a property model development problem defined simply as "develop a model to predict the activity coefficients of liquid solutions" needs further information in terms of types of systems and conditions for which the model will be applicable. Otherwise, the problem definition implies a model applicable to all types of systems and under all conditions, which is almost impossible to develop with the current knowledge.

Figure 2: Classification of property estimation methods. The verification/validation step of property modeling should also check for thermodynamic consistency, such as the Gibbs-Duhem conditions (see Eqs. 5-7), the relation between the normal boiling point and critical temperature (see Eq. 8) and the condition that some property values have a limiting value at the critical point (see Eq. 9).

Figure 3: Steps in the development of property models.

7 In, (Slny/Stij),;,, = 0 ;j = 1,2, ....N

(5)

In, (an(p/SP)n;r =(Z-

(6)

l)n/P

In, (8y/5T)n, P = - H (T, n)/RT

(7)

Tc(i) / Th(i) > 1

(8)

[Hvap(i)]Tc«> = 0

(9)

Before solving the property model equations, especially for computer-aided applications, it is important to perform a degree of freedom analysis in terms of number of equations, number of unknown variables (ie., to calculate number of variables to specify and number of model parameters (which must be known or regressed apriori). A simple example, for purposes of illustration, is shown below for the Wilson model to estimate the liquid phase activity coefficients in binary mixtures. S,.,= (V,/V,) *exp(-A,.,/T) 8,-2 = (V2/V,) *exp(-A ,-2/T) &-/ = (V,/V2) *exp(-A2.,/T) 82-2= (V2/V2) *exp(-A2-2/T)

(10) (11) (12) (13)

E,= X,*§,., +X2*8,.2

(14)

E2= X,*82-, + X2*82-2

(15)

Lny,= l - ln(E,) - (X,*8,., + X2*d2.l)

(16)

Ln n= 1 - ln(E2) - (X,*S,.2 + X2*52.2)

(17)

From the above equations, it can be seen that this Wilson model for binary systems has 8 equations with 8 unknown variables (yh Eh Sj.j, for /= 1,2; 7-1,2), 3 specified variables (T, xh for z-1,2) and 6 parameters (K,, A^, for z'=l,2; /=1,2). Arranging the above equations in the sequence shown in column 1 of Figure 4, a lower tri-diagonal matrix is obtained, indicating that each equation has only one unknown variable. Therefore, the model equations are very easy to solve and is computationally inexpensive. Figure 4 shows an incidence matrix (for the Wilson model1) where the equations are represented in the rows and the variables are represented in the columns. For a solvable set of model equations, there should be the same number of columns for the "unknown" variables as the number of rows and there should not be any * in the diagonal (for an ordered set of equations in the tri-diagonal form). Also, if all

8 the • appear only in the diagonal, then the model equations can be solved sequentially according to the specified order. If there are more than one • in any row on the upper triangular part, it will indicate a system of equations that would need to be solved simultaneously. With very few exceptions, most property models can be arranged in lower tri-diagonal form (see chapters 4 and 13 for more examples).

Figure 4a: Wilson model equations ordered into a lower tri-diagonal form (Note: * indicates variable is known for the corresponding equation; • indicates the unknown variable calculated from the corresponding equation; since A 1.2 = A 1.2 = 0, they are not shown in the above incidence matrix) A similar model analysis is also shown for a cubic equation of state in Figure 4b. The problem being solved by the property model can be defined as, Given: T, P, x;_Calculate: lntpj, for known parameters, properties & constants: kji, y/A, i/zg, e, a; T c j, P c j, coj; R.

1.4 PROPERTY MODEL USE Two types of property model users may be envisaged. Those who use property models to estimate the desired properties, or, those who incorporate property models as parts of larger models and/or solution schemes in order to solve specific (design) problems. In terms of Figure 5, users of the first type only need the property model equations (also called the constitutive equations) and calculate the properties given the known values of the intensive variables and all other model parameters. Users of the second type may use the constitutive equations together with only the constraint equations (for example, for saturation point calculations) or use the constitutive equations together with the balance equations and the constraint equations (for example, for modeling of phase equilibrium-based separation processes). In this case, the property models belong to larger models and/or solution schemes and are usually represented as constitutive equations from within the process model. In the corresponding solution scheme, the property model equations belong to an iterative solution scheme, where for different values of the intensive variables, the needed properties are calculated (see Figure 5). Depending on the numerical method used in the solution of the

9 process model equations and the type of problem being solved (simulation or optimization), first, second and even third derivatives of the properties (constitutive variables) with respect to the intensive variables may be necessary (see chapter 2 for more details). Therefore, property model users who incorporate property models into process simulation/optimization packages need to ensure that the derivative functions exist and that they are continuous.

z = \',( \:-b) - (a Y),

[RT(\' +e b)( V + sb)]

(i)

ab =^ x , b V "

(iii)

SRK Equation of State

m; = m(o".))

[IV)

5C + 4 Equations

(v)

a-

y

= v VT P " 2

(VI)

2

2 2

(vn) (viii)

a' = yA (R T ci ,p ci )[i + nij el - T n f ]

In , = .' (?; V; ,'RT - 1) dP/P | T s =f(dZ,clP. T. P. a. b, a, b) dZ 'dP = f(T. P. a. b. a. b)

(IX)

10C+11 variables Specify: 5C + 7 variables, C is the number of compounds in the mixture.

SRK EOS model equations (Eqs. i-ix) Eqs.

Variables ni;

E-iv E-vii E-v E-vi E-ii E-iii E-i E-viii E-ix

• *

a;;

a;j

• *

• *

* *

b;

• *

* *

a

b

• * * * *

• * * *

z

dz/dp lncpi

• * *

• *

•

Incidence matrix showing the tridiagonal form for solving the model equations Figure 4b: The SRK equation of state and the analysis of the equations for the estimation of fugacity coefficients In either case, the principal steps involved in computer aided estimation of properties are highlighted in Figure 6. One starts with a definition of the problem (step 1); followed by property model generation/creation/selection (step 2); property model validation, including, model parameter estimation and/or tuning (step 3); and finally, property calculation (step 4). If parameters for the selected property model are available and are known to be reliable, step 3 would not be necessary.

10

Figure 5: Property model (constitutive equations) can be solved separately or as part of another model and a larger set of equations (Note: 9_ includes primary, secondary as well as functional properties; model parameters are not shown). 1.4.1

Property Model Selection

Appropriate selection of property model is very important in process and product design. Often the user of a property model does not have the knowledge and experience to choose "wisely" among the myriad of options. Cordiner2 provides a decision tree for property model selection (see Fig. 7).

Figure 6: Principal steps in computer-aided property calculation. The selection is commonly based on familiarity, hearsay or ease of accessibility. However, consideration of the numerous properties (and models) and comprehension of the

11 complexities of current and future property models can be difficult even for the experienced user. The use of an inappropriate property model and/or model parameters can often go beyond wrong numerical results that cause bottlenecking and over-sizing to even yielding wrong process configurations3'4. A simple example of an incorrect choice of a property model is to predict the vapor-liquid equilibrium for an azeotropic binary mixture with a composition independent model for the liquid and vapor fugacity coefficients. Obviously, the azeotrope will never be found.

Figure 7: Decision tree for property model selection (Cordiner2).

12 Using commercial simulator descriptions, a partial list of chemical mixture types, the phases of possible interest and some property models that can be employed for computations of equilibrium among the phases listed is presented in Table 1 (adapted from Gani & O'Connell5) for purposes of illustration not completeness. The last column indicates the types of model parameters that are usually needed by the property model. Gani and O'Connell5'6 and also Carlsen7 have proposed some guidelines for property model selection. Table 1: Partial list of mixture types and property models appropriate for describing phase equilibria. Mixture Type

Phases

Model Type

Hydrocarbon Hydrocarbon aqueous

L V V L

Polar (nonassociating)

V L

Polar (associating)

V L

Aqueous electrolyte

V L S V L S V L

Cubic EOS Cubic EOS EOS EOS1 Gr. EOS EOS' GE EOS EOS' orG F Ideal or EOS GF Ideal Ideal GE Ideal EOSd EOS3 or GE

S L S L S

Ideal Empirical Ideal Empirical Ideal

Mixed solvent electrolyte Polymer - solvent

Parameters E,kij E, kij E, ky E, R, Q, Xij E, ky E, ky E, R, Q, TH E,k'ii E.k'ij E, R, Q, xij

None or ky R, Q, T\J None None or ky R,Q,TY None E,kJy E, k y or R,Q,T\J

Steroids - solvent Amino acid Solvent

None

e4 None

e4

None

Refers to special mixing rules for equations of state or parameters for GH models. Refers to mixture specific property model parameters. 3 Indicates special equations of state such as CPA8 and S AFT9 equation of state usable for all phases and corresponding model parameters. 4 Indicates property models not presently found in standard versions of process simulators. 2

13 1.4.2

Examples of Property Model Use

Example 1: Estimation of unknown pure component properties Estimate the following properties for Corticosterone to be used for finding a suitable solvent and for design of solvent-based extraction - the normal melting point (Tm), the heat of fusion at 298 K (H/lls), the octanol-water partition coefficient (LogPo-w), the water solubility (LogWs) and the Hildebrand solubility parameter (Sp). Step 1- Problem definition Estimation of pure component properties (primary and secondary) as well as mixture properties are needed. Tm and H/m are pure component primary properties; Sp is by definition a secondary property; LogPo-w and LogWs are by definition, mixture properties.

Figure 7: Molecular structural information of Corticosterone Step 2 - Property model selection For the pure component properties, the Marrero & Gani method10 is selected as it has a wide range of groups, a wide range of properties, is predictive and has good accuracy of prediction. An additional advantage with the selection of this method is that Sp, LogPo-w and LogWs are modeled as special pure component primary properties. With the Marrero & Gani method, the following groups are needed to represent the molecular structure of Corticosterone. A check of the property model parameter tables indicates that all the necessary parameters are available. The group representation details are given in Table 2. Step 3 - Model validation & parameter estimation Not necessary in this problem Step 4 - Property estimation The calculated values for the required properties are given in Table 3. For a very quick estimation, the calculated values are reasonably satisfactory. With these properties, solvents

14 can be identified and estimates of solubility in the solvents can be calculated. Table 2: Groups needed to represent the molecular structure of Corticosterone. Third Order Groups Second Order Groups First Order Groups Times Group Times Group Times Group 3 CH multiring 1 CHcyc-OH 2 CH3 2 C multiring 1 CHcyc-CO 2 OH 1 CH2C0 7 CH2 5 CH 2 C 1 CH=C 1 CO Note: Selected Path within molecular structure: O=...-OH Length = 12 Table 3: Comparison of calculated and known experimental values for Corticosterone. Property Tm (K) Hfm (kJ/mol) SP (MPa'A) LogPo-w LogWs (Log(mg/L))

Calculated 458.3 45.8 24.45 1.79 2.12

Known experimental data 454.1 -

1.94 2.29

Example 2: New group definition & parameter estimation Study the effect of HC1 on a binary mixture of ethanol-ethyl acetate in order to design a vapor-liquid based separation. Step 1 - Problem definition This problem requires the estimation of vapor-liquid equilibrium (VLE) for a ternary mixture at pressure of 1 atm (assumed). That is, for fixed amounts of HC1, the saturation temperatures and the corresponding vapor compositions need to be calculated for a series of (given) liquid compositions. Consequently, property models within a calculation scheme for VLE are needed. Step 2 - Properly model creation/selection Since the mixture is non-ideal, the gamma-phi approach where a GE-model is used for the calculation of the liquid phase activity coefficient and an equation of state for the vapor phase fugacity coefficient is appropriate since the pressure is 1 atm. In addition, the vapor pressure of the pure components as a function of temperature is necessary. Since water is not present, assuming HC1 will not dissociate, a non-electrolyte G1 -model is selected. A local G1 -model however needs to be created (as the necessary model parameters are not available) and for

15

this purpose, the group-contribution based UNIFAC-VLE11 (original) is selected. However, since HCl does not exist in the selected UNIFAC model as a group therefore, a new group needs to be created and the interactions between HCl and the other groups representing ethanol and ethyl acetate need to be estimated. For the vapor phase, the ideal gas law is selected while for the vapor pressure, the Antoine correlation regressed to the vapor pressure data for each pure component is selected. The UNIFAC group representations for the 3 compounds and their corresponding size(R) and volume- (V) parameters are given in Table 4. The Antoine correlation parameters and the group interaction parameters are given in the Appendix. The missing group interactions are for HCl versus the main groups CH2, OH and CCOO. Table 4: UNIFAC group representations for the 3 compounds

Ethanol Ethyl acetate

CH3 1 1

CH2 1 1

OH 1

CH3COO 1

1

HCl

Parameters R (size) Q (volume)

HCL

0.9011 0.848

0.744 0.540

1.0 1.2

1.9031 1.7280

1.056 1.100

Step 3 — Model validation and parameter estimation VLE data has been found only for the binary mixtures ethanol-ethyl acetate. Therefore, as a first estimation, all the missing HCl-related group interactions will be assumed negligible since the appropriate experimental data to estimate them are not available. This means that for HCl, only the combinatorial effect and the vapor pressures will be considered. This is quite reasonable since the normal boiling point of HCl (188.15 K) is quite far from that of ethanol (351.44 K) and ethyl acetate (350.2 K). The experimental ethanol-ethyl acetate data will be used to compare the prediction without any HCl and then to compare the effect of adding HCl. Step 4 — Properly estimation

The calculated VLE for 0% HCL and 5 % HCL in binary mixtures of ethanol-ethyl acetate is highlighted in Figure 8. The effect of adding HCl is to shift the azeotrope to the left (that is, to compositions having less ethanol). Example 3: Extraction of heavy compounds using supercritical gases Background Many extractions of heavy compounds and other applications, such as some enzymecatalyzed reactions, are being performed at high pressures in supercritical fluids, such as supercritical CO2,which take advantage of the positive features of CO2 (non-toxic, nonflammable fluid having low viscosity and high diffusion coefficient). Design of these processes require, among others, knowledge of phase equilibria at high pressures, which

16 could either be gas-liquid or solid-gas, depending on the state of solute at the conditions of the process.

Figure 8: Effect of addition of HCL to ethanol-ethyl acetate mixtures Step 1 - Problem definition Estimation of the phase equilibria of CC^/heavy esters such as methyl palmitate or heavy alcohols e.g. hexadecanol, at high pressures. Ultimately, the purpose is to perform VLE calculations for multicomponent systems. Step 2 - Property model selection Due to the high pressures involved, an equation of state is needed. The SAFT or CPA models could in principle be chosen, however they lack parameters for these heavy esters and/or alcohols, and most importantly, they have not been so far systematically tested for SC systems. An appropriate choice here is a cubic EoS using a suitable UNIFAC-type mixing rule, i.e. an EoS/GE model suitable for asymmetric systems (see chapter 5). Most of these models, such as the PSRK or MHV2 have problems for asymmetric systems, while others such as the Wong-Sandier one do not contain gas-based parameters. The optimum choice in this case is the LCVM mixing rule, which has an extensive parameter table12. Step 3 - Model validation and parameter estimation No parameter estimation is needed, since the required parameters are available in the literature13. The LCVM parameter table includes group-parameters between CO2, alkenes, alcohols, acids, ethers and esters. The following group parameters have been estimated from

17 experimental data: CO2-OH (and CO2-methanol), CO2-COOH, CO2-CH2COO, CO2-CH2O, CO2-COO (for aromatic esters) and CO2-CH=CH. Step 4 - Properly estimation Some sample calculations for the requested systems are shown in Figure 9 and Tables 5 and 6, where comparison with experimental data, when available, is shown. The results are satisfactory, even for the two heavy alcohols which were not included in the parameter estimation of the model. Good results are also obtained for multicomponent VLE, where in most cases the error in pressure is below 10%. The higher error for the ternary system CO2/oleic acid/linoleic acid could be attributed to the inability of the conventional UNIFAC model to account for the cross-association between the two acids. The improved results obtained for the quaternary system are possibly due to the large amount of the non-polar hexane and the possible weakening of hydrogen bonding forces. Example 4: Density estimation for polymers Background Knowledge of the density of polymers as a function of process conditions especially temperature is required in many applications that include polymers. For example, density of polymers is a direct input in free-volume activity coefficient models, typically used for phase equilibrium calculations for systems with polymers. Volumetric information is also employed for estimating the equation of state parameters for polymers (see chapter 7). Step 1 - Problem definition As an illustration, the density / molar volume of two widely used polymers will be estimated: i. of butadiene rubber (polybutadiene) at 25 °C [experimental value : 0.875 g/cm ] ii. of polystyrene, having a number average molecular weight equal to 73800 g/mol, at 150 °C [experimental molar volume : 71305.6 cnrVmol ] Step 2 - Property model selection An apparent choice for obtaining the density values of any polymer is to look first into suitable databases e.g. DIPPR 881 or Rodgers et al.v''. These sources contain density information for many polymers as a function of temperature, typically in the form of the Tait correlation-equation. In those cases when the polymer of interest is not included in these databases, the density has to be estimated. Two useful choices are the methods by van Krevelen (see chapter 7) and the GCVOL by Elbro et al.15. Both these methods are based on the group-contribution approach. The van Krevelen method has different forms depending on the physical state of the polymer: •

For amorphous polymers (T>Tg): Va =F,,,(1.30 + 10- 3 r)

18

Figure 9: Prediction of gas-liquid phase equilibria for the system CCh-methylpalmitate at 343.15 K using the LCVM model.

Table 5: Prediction of gas-liquid equilibrium for some binary CC^-polar systems, which were not used into the parameter estimation of the LCVM model. Both the errors between experimental and calculated pressures and vapor phase mole fractions are shown.

co 2 /

1-hexadecanol 1-octadecanol EPA ethyl ester DHA ethyl ester

NDP 15 15 8 10

T(K) 373-573 373-573 313-333 313-333

P (bar) 10-51 10-51 75-132 90-174

AP (%) 9.4 7.9 19.3 23.9

Ay*103 7.5 4.3 2.9 2.1

Table 6: Prediction of multicomponent gas-liquid phase equilibria for some CO2 containing systems with the LCVM model. Both the errors between experimental and calculated pressures and vapor phase mole fractions are shown.

co2/

Methyl oleate / Methyl linoleate Methyl oleate / Oleic acid oleic acid / linoleic acid 1-dodecanol / lauric acid hexadecane / 1 -dodecanol n-hexane / stearic acid /oleic acid

T(K) 313.15 333.15 313.15 313.15 333.15 393 353.2 375.15

P (bar) 47-210

AP (%) 6.8

Ay*103 5.9

45 - 262 59-287

7.3 29.1

3.5 4.5

100-317 100-223 151-259

7.6 7.0 13.1

4.0 3.2 3.5

19 •

For glassy polymers (T (T)/ XT, P,y)

(8) (9)

K, = r/(T^)ps-(T)/P

(10)

K,=ps'{T)/P

(11)

K, = y/ (T,x')/ri"(T,x")

(12)

Eq. 8 uses an equation of state to obtain the fugacity coefficients, ^>,. p o r both phases while Eqs. 9 - 1 1 involve varies approximations for activity coefficients, y,, and vapor pressures, P '. For liquid-liquid equilibria, Eq. 12 would be used. Figure 1 highlights the work-flow and data-flow with respect to the service role of the properties (and property models). Note that for a TP-flash simulation, first the mass balance Eq. 1 together with the constraint (equilibrium condition) Eq. 3 is solved; for each evaluation of Eqs. 1 & 3, the property models are called. When convergence is achieved, the property models are called one more time for the evaluation of the energy balance. In this case, since T and P are fixed, the energy balance computes Q (the energy added/removed) needed to make the operation possible.

Figure 1: The service role of properties and property models This is a typical simulation problem where the property models (Eqs. 4-12) are used in the service role because every time an evaluation of Eqs. 1-3 needs to be made, there is a request

31 for the properties, for which Eqs. 4-7 are called. Another example of the service role is to ask for the density, either to convert the composition in mole fractions to moles/cm or to calculate the volume of the (separation) tank or the height of the liquid in a tank. In each case, only Eq. 7 will be called. 2.2.2 Service/Advice Role In process design and synthesis, property values are often regarded as explicit or implicit target values for a synthesis/design algorithm to satisfy by finding values for the unknown intensive variables. In section 2.2.1, the problem definition assumed (or specified) that a two phase system would exist at the specified T and P. Consider now that we do not know if a two phase system would exist at the specified T and P and also that we are only interested in removing a chemical through precipitation (crystallization). At any assumed (or specified) T, P, and z, we check if the liquid stream F would be stable at T & P. If not, there would be two phases, at least. Also, if the assumed T is above the melting point of at least one of the chemicals (for example, chemical A) in the system and below the melting point of the others, then there is a good chance that this chemical would precipitate, such as if the assumed T is below the saturation temperature of the feed mixture. The advice role here is to determine if solid-liquid based separation is feasible and also which chemical would be obtained as a solid. The design problem is to determine the temperature T of operation that would match the amount of separation (or recovery) that is desired. Figures 2a and 2b show two examples of this advice role. In each case, a solid-liquid equilibrium based saturation diagram is shown for an aqueous electrolyte system and a non-electrolyte system. It should be noted that the feed composition, z, and temperature, T, indicate which solid chemical would be separated.

Figure 2a: Saturation point compositions of naphthalene in a binary mixture of naphthalene-benzene as a function of temperature (y-axis)

Figure 2b: Saturation point compositions of sodium chloride in an aqueous solution as a function of temperature

32

Another example of the advice role can be found in solvent design, where the properties have explicit target values such as solubility and selectivity for a particular solute at a specific condition of operation. Here, the chemical structure of candidate solvents is manipulated until the solution properties match the target values. The process design problem (defined above) and the chemical product (solvent) design problem may be solved as part of a two-step procedure (irrespective of whether they are solved sequentially or simultaneously): Step I - generate alternatives {e.g., T'or solvent) Step II - determine properties (e.g., number of phases, solubility, or selectivity) and screen/verify alternatives through simulation. In Step I (generation), properties play a service/advice role while in Step II (verification) properties play only a service role. Strategies for the advice role attempt to eliminate infeasible solutions, or at least reduce the size of the search space and/or mathematical problem of a given situation, by providing the necessary insight. For example, an initial list of candidate solvents may be generated by searching for substances having similar solubility parameters as the solute. For each candidate solvent-solute combination, solid solubility diagrams (see Figures 2a-2b) would provide advice for selection of the operating temperature. The list of solvents would be reduced as candidates which do not meet the criteria are identified. For final verification, a simulation is needed (that is, solving Eqs. 1-6 for solidliquid equilibrium systems). Other examples of the advice role can be found in Gani & O'Connell[l]. The service/advice role is highlighted in Figure 3. Based on the problem specification, advice role in the generation step checks for feasible solid-liquid separation. If yes, then the service role is played for the verification (simulation) step. Note that the advice role also helps to design the condition of operation (choice of temperature and amount of solvent to be added or removed). Computer-aided molecular design techniques [2] are an example of properties used in their service/advice role, that employs different versions of the product model are employed.

Figure 3: Service/advice role of properties (property models) Often the advice role for properties is less demanding on the property models than is the service role. For example, sometimes the advice role for different product models can be

33

played with only pure component or infinite dilution properties of the compounds present in the mixture; the service role usually needs properties over the entire composition range. 2.2.3 Integration Role The most comprehensive role for properties in the solution of process-product design problems is that of integration. In process/tools integration and in graphical (visual) design techniques, properties actually can define an integrated solution strategy. Typical examples of this role can be traced back to graphical design techniques for separation processes (see for example, Henley and Seader [3] who describe various types of graphical design techniques) and for heat integration based on pinch technology [4]. In the case of distillation column design, the mass balance equation (Eq. 1) and the constraint equation (Eq.3) are represented in a two-dimensional plot of saturation vapor composition on the y-axis and the corresponding liquid composition in the x-axis. Each data point corresponding to the constraint equation represents a liquid in equilibrium with the vapor at the system pressure (usually constant) and temperature which varies over the column. In the case of heat integration, only Eqs. 2, 5 & 6 are needed. The two variables considered are the cumulative enthalpies for the hot and cold streams and the corresponding temperature. In the case of distillation design, the relation between saturation temperature and composition provides integration while in the case of heat integration, the relation between temperature and enthalpy does the integration. Using the process model defined by Eqs. 1-6, the integration role can be visualized through the following simple problem: • •

Given a contaminated product stream with a flowrate of F kmol/h having a composition fc of contaminant (for example, 0.02 mole fraction of phenol), Design a process through which the product stream becomes essentially free of the contaminant (mole fraction of phenol less than l.OxlO"6).

Through the traditional service or service/advice roles, the problem would be solved as follows - find candidate solvents that will create another liquid (solvent) phase and includes as much as possible of the phenol. For each solvent candidate, simulations are made to establish the process design. Now consider the following alternative solution technique called the reverse approach 1. Use Eq. 1 to calculate the required (or design target) solubility. Since the problem information actually provides both inlet and outlet concentrations of the product stream, this must be feasible. Note that since solubility (property) is actually the known variable, the solution of this separation problem does not require a property model. 2. Use Eqs. 3,11 and appropriate activity coefficient models to estimate solubilities for a solute in candidate solvents at selected temperatures. As long as the solubilities match the desired (target) values from step 1, the mass balance equation does not need to be solved.

34

It is interesting to note that in the traditional solution approach, using the generation and test paradigm, a simulation problem needs to be solved for every alternative. For many alternatives, however, a property model may not be available as part of the process model. If the generate and test steps are performed simultaneously (that is, include the simulation as part of an optimization loop), only one process model can be used, thereby severely restricting the application range since only one property model can also be used (unless multiple optimization problems are solved). With the reverse (integrated) approach, however, any number of property models can be used for step 2 while in step 1, property models are not needed at all. The procedure is to first solve a reverse simulation problem to determine the design target in terms of a set of properties, and then solve a reverse property estimation problem to determine the solvents and the operating conditions (for example, temperature). Multiple solutions are obtained, which only need to be ordered according to a performance index to identify the optimal solution. The property (in this case, solubility) plays the integration role to connect the simulation and design problems. On the other hand, from a point of view of the solution of the model equations, it plays the role of decomposition (separation of the balance and constraint equations from the constitutive equations). More details on this reverse approach can be found in [5, 6]. Figure 4 highlights the principal difference between the traditional or forward approach and the reverse approach (with the integration role for properties). Recently, Bek-Pedersen and Gani [7] have defined a driving force which is also a function of the saturation temperature and the corresponding phase compositions. Using the driving force for integration, Bek-Pedersen and Gani [7] have shown how simultaneous design and simulation can be performed for any two-phase separation process. Here, the property model plays all roles; service, advice and integrated solution of the simulation and design problem. The use of the driving force to integrate simulation and design is highlighted in Figure 5.

Figure 4: Integration role of properties and property models.

35

Note that in Figure 5, once the maximum driving force has been located at Fm and a reflux ratio (RR) is selected, by making the two operating lines to intersect on the D-Dx vertical line, the number of stages and the column profile (T, x & y_) can be back-calculated [7]. This means that the design and simulation of the distillation column correspond to the property target (maximum driving force). By definition, at the maximum driving force, the energy consumption is the minimum because this is the external medium that creates the twophase system. In the above examples, the relations among thermodynamic properties and intensive variables generated the integrated algorithm or solution strategy in addition to providing the solutions. "Intelligent" manipulation of the process and property model equations and variables using physicochemical and mathematical insights identified a small number of intensive variables as the unknown process model variables to represent the essential information about the problem. This tools integration, which is most valuable in applying integrated algorithms for synthesis, design and/or control, can be appreciated by considering the roles of properties in different process-product engineering problems through their independent, intensive variables (Table 1).

2.2 PROPERTY ROLES AND PROPERTY MODEL SELECTION In all three roles of properties, the proper selection of property models is important. Depending on the type of the problem, the consequences of property model choice can differ, even for the same property. The use of an inappropriate property model and/or model parameters may not be limited to only wrong numerical results that cause bottlenecking and over-sizing; even wrong process configurations can be found [8, 9].

Figure 5: Driving force based simulation and design (integrator is the driving force, a function of Py (T, P, x, y_) providing integration.

36 Table 1: Relationship between problems and properties in process-product engineering. Purpose

Problem

Determine

Remarks

Synthesis

Generate feasible process alternatives

Effects of T, P, x on process model

Design

Obtain condition of operation

Values of T, P, x that satisfy constraints

Properties affect process model results and play all roles, depending on the solution approach Properties provide target values and can play all the roles, depending on the solution approach

Control

Design control system

T, P,x sensitivities

Property models provide derivative information via service and advice roles

Energy analysis Environmental impact

Determine energy needs Verify that environmental constraints are satisfied

Enthalpies from T, P, x Component flows in effluent streams

Property models are essential via service and advice roles

Economy

Minimize cost of operation and equipment

Cost as a function of capital and operation

Property models affect process model results via service and advice roles

Property models are needed via service and advice roles

Often the user of a property model does not have the knowledge and experience to choose "wisely" among the myriad of options. The selection is commonly based on familiarity, hearsay or ease of accessibility. However, consideration of the numerous property models and comprehension of the complexities of current and future property models can be difficult even for the experienced user. Issues associated with this aspect are discussed by Gani and O'Connell [10]). 2.3.1 Service Role Since property models provide requested property values for quantitative evaluations of conservation of mass and energy, their quantitative accuracy must be evaluated. Some of the important issues related to the choice of the appropriate property model are the following: problem type, system (mixture) type, availability of property model parameters and computational complexities. Note that the estimation of the secondary and/or functional properties such as fugacity or activity coefficients, mixture densities, mixture enthalpies, etc., generally require pure component single value primary properties along with secondary/functional properties. Also, when the property model is used in the service role for a simulation problem, the derivatives of the properties with respect to the unknown variables (usually also the intensive variables T, P and/or composition) are needed when numerical methods like Newton-Raphson are used. Because of the importance of quantitative accuracy, tuning of the model parameters is an issue, especially since it depends on the availability of experimental data. In this case, a sensitivity analysis, that is, variations of the property of interest with respect to changes in

37

model parameters is valuable to fine-tune a small number of parameters. This is particularly useful when only limited experimental data are available. Such analyses show that pure component vapor pressures make a significant difference in the estimated vapor-liquid equilibrium (VLE) compositions for non-ideal systems, while the pure component critical (primary) properties are important for high pressure VLE calculations. Solid-liquid equilibrium (SLE) calculations are very sensitive to heats of fusion. The ratios of the activity coefficients of each component in the two liquid phases have direct impact on liquid-liquid equilibrium (LLE) compositions. Errors in densities effect the equipment sizing (volume and area) parameters. Since only one property model for each property may be used in process models such as the one represented by Eqs. 1-3, only carefully selected property models with fine-tuned model parameters and continuous derivative properties within a wide range of intensive variable values, should be used. Note that in the service role, only one property model may be used for the necessary properties during any simulation; this can be a disadvantage during simultaneous simulation and optimization of process-product problems since process and product models are solved simultaneously. For simulation problems from section 2.2.1 involving only the mass balance (Eq. 1) and the equilibrium condition (Eq.3), it can be noted that any one of Eqs. 8-12 may be appropriate for the equilibrium constant, Kh depending on the type of the problem, system, etc. Interesting issues with respect to the choice of models for Kt are the computational scale and time. If the fugacity and/or activity coefficients need to use complex relations based on groups at the atomic level (such as the SAFT EOSfll]), the models are usually computationally intensive and expensive. On the other hand, interactions at molecular levels (such as the SRK EOS[12]) are commonly less computationally intensive and relatively inexpensive. Consequently, calculation schemes where repetitive solution of Eqs. 1 & 3 are needed, computationally cheap models are usually preferred while for schemes where only a few calculations of Eqs. 1 & 3 are needed, and quantitative accuracy is important, computationally intensive models may be implemented. One alternative in this case is to use the reference and local models. The properties are generated by a reference model {e.g., SAFT EOS) and then matched with a computationally cheaper local model {e.g., the SRK EOS) to create a local, system-problem specific model. This idea is similar to property model simplification techniques proposed some time ago [13, 14]. The difference is that simplified local models needed to be generated for every iteration of a simulation. Here, system/problem specific local models need to be generated only once and can be used for all types of simulation problems for the same chemical system and properties. 2.3.2 Service/Advice Role In addition to the service role, for properties to play the advice role, the corresponding property model must be qualitatively as well as quantitatively correct. This is because the design problem (where advice is needed) usually involves generation and screening of different alternatives and verification of the feasibility of a desired operation (separation or reaction). Therefore, there is more emphasis on the qualitative accuracy. Of course, when the condition of operation (such as the temperature of operation) is to be found, quantitative accuracy is also essential.

38 In the case of equilibrium based separation processes, the advice role depends on the known (or generated) phase equilibrium (needing the solution of Eqs. 3 and 4 only). While these need to be calculated only once for each case, there can be many different chemical systems. Therefore, the choice of the property models (for Eqs. 8-12) needs to consider the application range not only in terms of intensive variable values but also in terms of chemical systems. This is particularly important for designing molecules with desired properties, where the selected property model needs to be predictive with respect to chemical systems to generate and screen large numbers of feasible alternatives. Unfortunately, if solvent selection is done simultaneously with the optimization of the process performance, only one property model per property can be used, restricting the search space for the problem solution. The best property model selection strategy is to choose a group or atomic contribution method (see chapters 3-4) for the advice role because of both predictive ability and qualitatively correctness for a wide range of chemical systems. Then, when a chemical system has been selected by such a method, measured and/or generated data should be used to regress (or fine tune) the model parameters of a local model with limited predictive capabilities. The last step also validates the property model for use in the service role. 2.3.3 Integration Role An important issue in the integration role of properties is how to bring together the special features of property models for process model-based calculation schemes. That is, it is necessary to identify the appropriate properties and the intensive variables. For a number of separation processes, including all of the 2-phase equilibrium separation processes, a driving force has been identified as the integrator (figure 5 and Section 2.2.3). Then the process model equations can be decoupled for integration of simulation and design. Note that the driving force can be calculated from physical equilibrium constants (as in Eqs. 8-12) and the location of the maximum is a function of the intensive variables for the same physical equilibrium constant values. The chemical identities provide an estimate of the chemical equilibrium constants from which the driving force diagram is calculated. Since the design target of minimum energy consumption (or solvent rate, etc.) can only be achieved if the design is based on the maximum driving force, the choice of property models and their accuracy in representing the variations of properties on the intensive variables is very important. In the context of the reverse approach, any number of property models can be used, so it is possible to select the appropriate property model based on their application range. This means that the design and simulation results based on the location of the maximum driving force and the driving force values would be valid for any number of separation problems (chemical systems).For reactive systems (with or without separation), a similar definition of driving force can also be employed to generate a similar diagram as the one showed in Figure 5. Hildebrandt et al. [15] call this driving force-based diagram the attainable region, which forms the basis for reactor design and simulation. Another useful feature of the reverse approach is that it often allows the use of the property models under the same conditions they have been developed and verified. That is, property models are usually validated by model developers through comparison with measured experimental phase equilibrium data not

39 through process simulation results. The driving force diagram involves precisely the same information.

2.3 DERIVATIVE ANALYSIS: A CONNECTION BETWEEN MODEL GENERATORS AND MODEL USERS One final issue, which enters into all property roles, is the question of the derivatives of properties with respect to the intensive variables which illustrates the differences between developers and users. Consider the problem shown in Figure 6. The numerical solution of this simulation/optimization based design problem requires the following derivatives (where 6 is any property and % is any intensive variable):

Figure 6: Simulation & optimization of a PT-flash operation (minimize the amount of heat to be added/removed, keeping the ratio of V/F constant while manipulating the operating temperature and pressure) If the selected property model, i.e., Eqs. 4, 5, 6, have not been tested for the existence of these derivatives, convergence failures are likely to occur. If the derivatives are inconsistent, the Gibbs-Duhem conditions (see chapter 1) will not be satisfied and so the numerical results will not be thermodynamically consistent, even when all other solution criteria may be

40

satisfied. Model developers (generators and implementers) need to recognize this issue and test derivatives for existence and consistency and to provide this information to users. Because the objectives, organizations and styles of property model generators, implementers and users are not usually the same, their interconnections are typically weak. In particular, generators usually seek generalized models to have as large an application range as possible, while they ignore computational speed and derivative issues . On the other hand, property model users commonly implement models having high computational efficiency and as wide spectrum of applications as possible. But they usually do not provide developers with much information on the limitations of their models. Better communication is needed between property model generators and users to deal with these concerns for the most effective impact of models in process-product design applications.

2.4 CONCLUSIONS Three different roles for properties and their corresponding models have been highlighted. Property models can play a much wider role than the traditional service role, for which they are mostly known (or receive credit for). Using them in the advice role can improve the design, widen the search space and increase the efficiency of the solution method. When property models become difficult to use in forward simulation approaches because of complexity, possibilities of using a reverse approach should be investigated. In most design and/or simulation problems, the "exit" conditions are usually known but not actually used in the simulation; they merely verify the simulation results or the design. By using both the known "inlet" and "exit" conditions, property integration can be identified and target values assigned. Many interesting process-product design problems can be solved more easily through this reverse approach. Finally, for property models to play their roles efficiently and for more advanced models to find applications in process-product design, better communication between property model generators, implementers and users is necessary.

REFERENCES 1. R. Gani, J. P. O'Connell, Computers & Chemical Engineering, 25 (2000) 3. 2. J. P. O'Connell, M. Neurock, "Trends in property estimation for process and product design", in: Proceedings of FOCAPD'99, Breckenridge, USA, 1999. 3. J. D. Seader, E. J. Henley, Separation Process Principles, John Wiley & Sons, Inc., New York, USA, 1998. 4. B. Linhoff, J. R. Flower, AIChE J., 24 (1978) 633-642. 5. R. Gani, E. N. Pistikopoulos, Fluid Phase Equilibria, 194-197 (2002) 43-59. 6. M. R. Eden, S. B. Jorgensen, R. Gani, M. M. El-Halwagi, Chemical Engineering & Processing, 43(2004) 595-608. 7. E. Bek-Pedersen, R. Gani, Chemical Engineering & Processing, 43 (2004) 251-262. 8. Y. Xin, B. W. Whiting, Ind & Eng Chem Res, 39 (2000) 2998.

41 9. E. A. Brignole, R. Gani, J. A. Romagnoli, Ind & Eng Chem Process Des & Develop, 24 (1985) 42-48. 10. R. Gani, J.P. O'Connell, Comp. Chem. Eng., 13, (1989) 397-404. 11. J. Gross, G. Sadowski, Ind & Eng Chem Res, 41 (2002) 1084-1093. 12. G. Soave, Chem Eng Sci., 27 (1972) 1197. 13. S. Macchietto, E. H. Chimowitz, T. F. Andersen, L. F. Stutzman, Ind Eng Chem Process Des Develop, 25 (1986) 674-682. 14. J. Perregaard, E. L. Sorensen, Computers & Chemical Engineering, 16S (1992) 247254. 15. D. Hlidebrandt, D. Glasser, C. Crowe, Ind & Eng Chem Res, 29 (1990), 49.

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Part II: Models for Properties

3. Pure component property estimation^ Models & databases Jorge Marerro & Rafiqul Gani 4. Models for liquid phase activity coefficients-UNIFAC Jens Abildskov, Georgios M. Kontogeorgis & Rafiqul Gani 5. Equations of state with emphasis on excess Gibbs energy mixing rules Epaminondas C. Voutsas, Philippos Coutsikos & Georgios M. Kontogeorgis 6. Association models — The CPA equation of State Georgios M. Kontogeorgis 7. Models for polymer solutions Georgios M. Kontogeorgis 8. Property estimation for electrolyte systems Michael L. Pinsky & Kiyoteru Takano 9. Difussion in multieomponent mixtures Alexander Shapiro, Peter K. Davis, J. L. Duda 10. Modeling of phase equilibria in systems with organic solid solutions Joao Coutinho, Jerome Pauly, Jean-LucDaridon 11. An introduction to modeling of gas hydrates Eric Hendriks & Henk Meijer

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45

Chapter 3: Pure Component Property Estimation: Models & Databases Jorge Marrero and Rafiqul Gani 3.1 INTRODUCTION Pure component properties are needed for many process and product design calculations. They may be needed to study the behavior of the product (such as the solubility of drug in water), behavior of a chemical under the conditions of operation of a process (heat of vaporization of a refrigerant or process fluid in a closed cycle), dimensioning of equipment (density of the chemical in a tank), the physical state of the product (melting point and/or boiling point to identify solid, liquid or vapor state) and many more. For the estimation of mixture properties also, the pure component properties are employed in different mixture property models. For example, the well-known SRK equation of state employs the critical properties while an ideal mixing model for liquid density employ only the pure component liquid densities of each chemical species present in the mixture. The objective of this chapter is to provide the reader with a set of pure component property models for a corresponding set of frequently used properties in process-product design. These models have been tested and evaluated against a wide range of chemical species by the authors. A good collection of pure component property models can also be found in many specialized property estimation books, journal papers, commercial software and databases. It is beyond the scope of this chapter to name all the references as well as methods. The calculation methods outlined in each section of this chapter should provide some guidance in terms of the important steps related to estimation of a pure component property.

3.2 MODELS FOR PRIMARY PROPERTIES As described in Chapter 1, primary properties are classified as those, which can usually be determined only from the molecular structural information and have a single unique value. In this chapter, only a set of primary properties that are needed for a wide range of processproduct design calculations are presented through one property estimation approach. This does not mean that the property models used below are the best or have the highest accuracy. These models are, however, frequently used and their details, including the model parameter tables, are readily available. The property model presented below can be classified as an additive method using a group-contribution+ approach. The property estimation methods will be highlighted through the molecular structure of Glycine (CAS No. 000056-40-6). Only the estimated primary and the secondary properties of

46 Glycine are given. When the estimated value for a secondary property for Glycine is not given, it means that not all the dependent properties are available. When experimental data for the property is available, it is also given. The chemical formula, group assignment and 3D molecular structure is given in Figure 1.

Figure 1: Molecular structural details for Glycine 3.2.1

Primary Property Models

All the properties listed below are only functions of the molecular structural information described in terms of first-order, second-order and third-order groups. Note that all molecules must be completely described by first-order groups and may or may not have second- and third-order groups. The estimation steps are as follows: 1. 2. 3. 4.

Identify the groups (first-, and if necessary, second- and third-order groups) Determine how many groups of each type are needed to represent the molecule Retrieve the parameters from the model parameter tables for the property of interest Sum the contributions and use the corresponding property model function

Properties & Models The following property models have been proposed by Marrero and Gani [1,2]. In each case, the summation terms having the following expression Contribution of first-order groups, Sum.Groups.I = £i ni C; for i = 1, NCi Contribution of second-order groups, Sum.Groups.II = Ej rrij Dj for j = 1, NC2 Contribution of third-order groups. Sum.Groups.Ill = Zk Ok Ek for k = 1, NC3

(1) (2) (3)

In the above equations, n;, rrij, Ok are the number of first-, second- and third-order groups of types i, j and k, respectively. Q, Dj and E^ are the contributions for the selected property for first-, second- and third-order groups of types i, j and k, respectively. NCi, NC2 and NC3 are the total numbers of different types of first-, second- and third-order groups representing the molecule. Critical temperature, K Tc = 231.239*Iog(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III)

(4)

47

Glycine: 1028.0 K (experimental: 1028) Critical pressure, bar Pc = l/(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III + 0.108998)2 + 5.9827

(5)

Glycine: = 67.4 bar (experimental: 67.4) Critical volume, cm3/mol Vc = 7.95 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III

(6)

Glycine: = 234.01 cmVmol (experimental: 234.0) Normal melting point, K T m = 147.450*log(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III)

(7)

Glycine: = 535.63 K (experimental: 535.15) Normal boiling point, K Tb = 222.543*log(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III)

(8)

Glycine: = 710.97 K Standard Gibbs free energy of formation. kJ/mol Gf = -34.967 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III

(9)

Glycine: -300.1 kJ/mol (experimental: -300.1) Standard Enthalpv of formation at 298 K, kJ/mol H r = 5.549 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (10) Glycine: -388.49 kJ/mol (experimental: -392.1) Enthalpv of vaporization at 298 K. kJ/mol Hv = 11.733 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (11) Enthalpv of vaporization at TH, kJ/mol HVb - a + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (12) Glycine: = 43.0 kJ/mol Heatoffusionat298K, kJ/mol HfuS = -2.806 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (13) Glycine: 28.4 kJ/mol (experimental: 28.4)

48 3.3 MODELS FOR SECONDARY PROPERTIES As defined in Chapter 1, secondary properties are those that cannot be explicitly calculated only from structural information and usually require the knowledge of other properties. Most of these models have been derived from the principle of corresponding states, although, a number of empirical correlations also exist. There is available, a wide range of methods for prediction of secondary properties. Many books and handbooks provide methods for calculating these properties. Poling el al. [3] provides a good collection of many of the needed methods. Horvath [4] also provides a large number of methods for primary as well as secondary properties. In this section, a set of pure component properties that have a single value is listed together with a corresponding property estimation method. 3.2.1 Secondary Property Models The following steps may be followed in the estimation of pure component secondary properties. 1. For the secondary property of interest, select an estimation method 2. For the selected estimation method, identify the properties (data) needed to use the model and verify the application range of the method in terms of chemical species (type) 3. Retrieve from a database or predict the necessary properties (to be used as input) 4. Calculate the property through the selected method For the secondary properties listed below, the following properties are needed as input. All these properties are also defined below. For each property, first the generic form of the equation in terms of dependency on other properties/variables is given, followed by the method for calculation, the model equations, and finally, the calculated value for the chemical used as an example. Hfus (kJ/mol). Tb (K), Tc (K), Pc (bar), Vc (cmVmol), SolPar (MPa°5), Ss (MPa°5), nD, Dm (debye), ps(bar), Mw (g/mol), Ws (mg/L) Properties & Models For each property, the name of the property, the representation of the property in terms of its dependence on other properties, the method used and the equations involved are presented. Heat of Vaporization at Th. HVb= f(Tj,, Tc, Pc) Method: Correlation (Equation 7-11.5 in Reid et. al. [5]) tr = Tb/Tc X = 0.37691 - 0.37306*tr+ 0.15075/(Pc*tr2) Y = (0.4343*log(Pc) - 0.69431+ 0.89584*tr)/X

49 Hvb = Tb*0.008314*Y (14) Not recommended for Glycine Pitzer's Acentric Factor, co = f(Tb, Tc, Pc) Method: Lee-Kesler Correlation (2-3.4 in Reid et. al. [5])) / Constantinou & Gani [6] 0 = Tb/Tc a = -log(Pc*0.98692327) - 5.92714 + 6.09648/0 + 1.28862*log(6) - 0.169347*96 P = 15.2518 - 15.6875/9 - 13.4721 *log(9) + 0.43577*96 co = a / p (15) Glycine: 0.747 Lee-Kessler 0.673 Constantinou & Gani [6] Critical Compressibility Factor, Zc = f(Tc, Pc, Vc) Method: Theoretical (Equation) Definition ZC = (PC*VC)/(83.14*TC) (16) Glycine: 0.185 Liquid Volume at Tb, Vb =f(Vc), cm3/mol Method: Tyn and Calus Correlation (3-10.1 in Reid et. al. [5]) Vb = 0.285*Vcli)48 (17) Glycine: 86.5 cm /mol Liquid Volume at 298 K, Vm = f(Tc, Pc, co), cmVmol Method: Rackett Modified Correlation t r =1.0-298.15/T c Zra = 0.29056-0.08775*co W=l+(l-trf28571 Vm = (83.14*T0*Zrallunc)/Pc (18) Refractive Index, no = f(Soli>ar) Method: Correlation [4] nD = (0.48872*SolPar+5.55)/9.55 (19) Glycine: 1.8 Molar Refraction, Rm = f(nn, Vm) Method: Correlation [4] Rm = (((nD)2-l)*Vm*1000)/((nD)2 + 2) (20) Surface Tension at 298 K, a = f(Sol|>ar, Vm), dyne/cm Method: Correlation [4]

50 CT = 0.01707*(Sol Par ) 2 *(V m ) 0333333 (21) Entropy of Fusion. Sfus = f(HfUS, T m ), J/(mol*K) Method: Theoretical (Equation) Definition S rus =1000*H fus /T m

(22)

Glycine: 53.07 J/(mol*K) Closed Flash Temperature. Tfc = f(GCcG, Tb), K Method: Constantinou and Gani [6] Tfc = -2.03*(Sum.Groups.Ic G ) + 0.659*T b + 20.00

(23)

Open Flash Temperature, Tfo = f(GCcG, Tb), K Method: Constantinou and Gani [6] Tf0 = 3.63*(Sum.Groups.Ic G ) + 0.409*T b + 88.43

(24)

Glycine: 414 K Hansen Dispersive Solubility Parameter, 8s - f(GCcG, V m ), MPa 0 5 Method: Constantinou and Gani [6] 8s = (Sum.Groups.IcG)/Vm

(25)

Glycine: 17.74 MPa 0 5 Hansen Polar Solubility Parameter, 8 P = f(GC C o, V m ), MPa 0 ' 5 Method: Constantinou and Gani [6] 8 P = [(Sum.Groups.I C G) 05 ]/V m (26) Glycine: 12.16 MPa 0 5 Hansen Hydrogen Bonding Solubility Parameter, 8 H B = f(GCCG, V m ), MPa 0 5 Method: Constantinou and Gani [6] SUB = [(Sum.Groups.IcG)/V m ]° 5 (27) Glycine: 17.38 MPa 0 5 Dipole Moment. D m = f(8 s , V m ), debye Method: Correlation [4] D m = 0.02670*8 s *(V m )° 5 (28) Dielectric Constant, DH = F(Solpar, no, D m ) Method: Correlation [4] I f n D < 0.001. DK = (n D ) 2

51 Else, DE = (SolPar*0.48871-7.5)/0.22 (29) Henry Constant of a gas in water at 298 K, Hhenr), = (pS(298), Mw, Ws), bar*m3/mol Method: Theoretical (Equation) Definition Hhenry = ps(298)*Mw/Ws

(30)

3.3.1 Secondary Properties modeled as Primary Property For a number of secondary of secondary properties, it is sometimes possible to model them as primary properties. That is, it is possible to predict the property only as a function of the molecular structural information. Recently, Marrero and Gani [2] have developed models for Octanol-water partition coefficients, Solubility of a chemical in water at 298 K, and the Hildebrand solubility parameter. Also, the method of Martin and Young [7] for the measure of toxicity in terms of 50% mortality of Fathead Minnow after 96 hours of exposure has been adapted to the Marrero and Gani method. As in the case of primary properties listed in section 3.2, the prediction of the following properties also follow the same steps Octanol-water partition coefficient (LogKow) LogKow = A + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (31) Glycine: -3.41 (experimental:-3.21) Water Solubility, Ws, Log(mg/L) LogWs = A + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (32) Glycine: 5.41

(experimental: 5.39)

Hildebrand solubility parameter at 298 K, Solpar, M(Pa) Solpar = A + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (33) Glycine: 23.9 MPa03 Acute Toxicity (96-h LC50) to Fathead Minnow, mol/L -Log(LC50) = Sum.Groups.I (34) Glycine: 2.82

3.4 FUNCTIONAL PROPERTIES As defined in Chapter 1, pure component functional properties are those that depend on the specific value of temperature and/or pressure. Most prediction methods employ a suitable equation of state, the principle of corresponding states or a specially fitted correlation. In this

52

section, a set of functional properties and a corresponding property model is presented. Note that as in secondary properties, functional properties may also require other properties as input data. Note also that many temperature dependent functional properties are available in databases where the coefficients for the correlation of each property and chemical are stored. These correlation functions are discussed in section 3.4 of this chapter. The following steps may be employed in the estimation of functional properties. 1. For the property of interest, select an appropriate property model. 2. Verify the applicability of the model in terms of chemical species as well as the temperature (and/or pressure) limit of the method. 3. Retrieve or estimate the necessary properties to be used as input data 4. Calculate the property of interest at the condition (temperature and/or pressure) of interest using the selected method 3.4.1 Properties & Models For each property, the name of the property, the functional dependence, the units of measure, the method and the model equations are presented. Diffusion coefficient of component at infinite dilution in water, Dab = f(Vb, Tb, T) cm2/s Method: Modified Tyn & Calus Correlation (11-9.5 in Reid et. al. [5]) X = exp(-24.71 + 4209/T + 0.04527T - 0.00003376*T2) for 273.15 < T < 643.15 Dab = 0.01955/[(Vb)0433]*(T/X) (34) See also Chapter 9 for other prediction methods. Liquid Density,CTL= f(Tc, Pc, co, T), g/cm3 Method: Modified Rackett correlation (3-11.10 in Reid et. al. [5]) Zra = 0.29056-0.08775*© Tfimc = 1 + (1-T/Tcf285714 for T/Tc < 0.9 a, = (83.14*Tc*(Zra)Tfunc)/Pc (35) Thermal Conductivity, Tcon = f(Tb, Tc, T, Mw) W/m*K Method: Correlation (10-9.5 in Reid et. al. [5]) Tr = T/Tc Tbr = Tb/Tc Tcon = [l.ll/[(Mw) 05 ]*(3 + 20*(l-Tr)06666)]/[(3 + 20*(l-Tbr)06666)] (36) forT r 300 K, a melting point < 250 K and the Hildebrand solubility parameter between 25 and 27 MPa . 3.5.2

References for Databases

In this section, a few of the well-known databases found on the internet are listed below in Table 1, while references where useful data can be found are given in Table 2. Table 1: List of well-known databases Name API TECH Database CambridgeSoft ChemFinder

Address & Comments Pure component, petroleum characterization, etc. http://www.epcon.com Searchable data and hyperlink index for thousands of compounds - the ideal starting point for internet "data-mining" http://chemfinder.cambridgesoft.com/

56 Table 1 continued CRC Handbook of Chemistry and Physics DECHEMA Chemistry Data Series DETHERM DIPPR Electrolytes GPSA Data Book IUPAC-NIST SDS Knoval Science and Engineering Resources PDB PPDS TAPP The NIST Webbook

Library Network Database (http://www.hbcpnetbase.com/) A 15 volume data collection Comprehensive collection of thermophysical and mixture properties data, includes Dortmund DDB and ELDAR DDB http://www.dechema.de/f-infsys-e.htm7englisch/dbMain.htm Critically evaluated thermophysical data http://www.aiche.org/dippr/vision.htm IVC-SEP database for properties of electrolyte systems www. i vc- sep .kt. dtu.dk/databank GPSA Engineering Data Book —section 23 (physical properties) & 24 (thermodynamic properties) http://www.gasprocessors.com Solubility Data Series http://www.unileoben.ac.at/~eschedor Library Network Database (International Critical Tables, Polymers -Property Database, Handbook of Thermodynamic and Physical Properties of Chemical Compounds, etc.) Protein Data Bank — Processing and distribution of 3-D biological and macromolecular structural data http://pdb.ccdc.cam.ac.uk/pdb/ Physical Properties Data Service http://www.tds-tds.com/fs_ppds.htm Thermochemical and Physical Properties Database http://www.chempute.com/tapp.htm An excellent source of physical and chemical data http://webbook.nist.gov

3.6 CONCLUSIONS Pure component properties are needed in the solution of various types of process-product design problems as well as input in many models for estimation of mixture properties. Usually, they are stored (experimental data) in databases, at least, the single value properties and the temperature dependent functional properties. The problem, however, is that even though the database may contain thousands of compounds, not all data is available for all the listed compounds. Also, in process-product design, new chemicals may be synthesized, which would not be present in the database. For this reason, property models for estimation of pure component properties are needed. In this respect, the chapter provides the reader a

57 quick guide in terms of the most commonly used pure component properties and a representative set of property models. Table 2: References for data Biochemistry & Biotechnology Drugs- Phase diagrams Octanol-water partition coefficients Polymer Data Solubility data Solubility data Water infinite dilution activity coefficients

Thermodynamic data for biochemistry and biotechnology, Hans-Jurgen Hinz, Editor, Springer-Verlag, 1986 J. Phys Chem Res Data, 1999, 28(4), 889-930 J. Phys Chem Res Data, 1989, 18(3) 1111-1229 Polymer DIPPR 881 Project High&Danner, 1992 Barton Handbook, CRC Press 1990 J. Marrero & J. Abildskov, Solubility and realted properties of large complex molecules. Part 1, Chemistry Data Series, Vol XV, DECHEMA, 2003 Voutsas & Tassios, Ind Eng Chem Res, 1996, 35, 1438 supporting material

REFERENCES 1. J. Marrero, R. Gani, Fluid Phase Equilibria, 183-184 (2001) 183. 2. J. Marrero, R. Gani, Industrial Engineering & Chemistry Research, 41 (2002) 6623. 3. B. E. Poling, J. M. Prausnitz, J. P. O'Connell, "The Properties of Gases and Liquids", McGraw-Hill, New York, 5th Edition, 2000. 4. A. L. Horvath, "Molecular Design", Elsevier, Amsterdam, The Netherlands, 1992. 5. R. Reid, J. M. Prausnitz, B. E. Poling, "The Properties of Gases and Liquids", McGraw-Hill, New York, 4th Edition, 1987. 6. L. C. Constantinou, R. Gani, AIChE J, 40 (1994) 1697 7. T. M. Martin, D. M. Young, Chem. Res. ToxicoL, 14 (2001), 1378 8. T. L. Nielsen, J. Abildskov, P. M. Harper, I. Papaeconomou, R. Gani, J. Chem Eng Data, 46 (2001) 1041.

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59

Chapter 4: Models for Liquid Phase Activity Coefficients - UNIFAC Jens Abildskov, Georgios M. Kontogeorgis and Rafiqul Gani 4.1 INTRODUCTION Computer-optimized design of the separation processes, e.g. distillation, absorption and extraction, typically encountered in the chemical industry, requires thermodynamic models, which can be applied to a variety of chemicals. The investment (capital costs) for the separation steps is often in the neighborhood of 50-70 % of the total cost, and energy costs for separations can be up to 90 % of the total cost. Measured phase-equilibrium data are typically employed at the later design stages. However, for preliminary design, at the earlier stages and for screening purposes i.e. for testing alternative separation techniques, approximate models, which can be widely applicable, are of interest. Such models can provide rapid estimation of phase equilibria over a wide range of conditions. In addition to the case of the forward property prediction problem (chemical system is known but property values need to be calculated or retrieved), the reverse property prediction problem (property values are known but the chemical system is not known) is also of interest. These are typically problems related to the design of molecules/mixtures/blends such as solvents, process fluids, etc., where the desired properties of the chemical are known but the identity of the chemicals or their mixtures are not. Finding a system with properties close to a specified set also requires rapid predictions of phase equilibria for many mixtures. In this latter case, the use of predicted data is probably the only way in which the problem becomes solvable and forms the basis for computer-aided molecular/mixture design techniques. The need of process-product design techniques for rapid estimation of phase equilibria for a wide variety of systems, conditions and problems has been the driving force behind the development of the UNIFAC and other group contribution models. Statistical thermodynamics has not as yet reached a stage where rigorous solution theories of general applicability are available, although some results of limited practical use have been reported1 (see also chapter 12). Semi-empirical methods are, thus, of interest. Of the most well-known semi-empirical methods useful for predictions of phase equilibria, the group contribution concept is possibly the most widely used. They are usually simple, easy to use and are at least qualitatively correct for many systems where no experimental data is available. Examples of such group contribution methods are the analytical solution of groups, ASOG2 and UNIFAC3, both providing the liquid phase activity coefficients for the compounds present in the solution. Despite their limitations (see section 4.3.3), such group contribution methods have found widespread application in engineering design calculations due to their relative simplicity, their predictive power and analytical form.

60 Several reviews have appeared since the 1980s summarizing the developments of these models4"8. This chapter gives a short overview of the most well-established UNIFAC methods, including the most recent developments and their efficient computer-based use. Table 1: Partial list of different versions of the UNIFAC model. UNIFAC Models UNIFAC-VLE

Special Feature 1 -parameter for group interactions

UNIFAC-LLE

1 -parameter for group interactions

Modified UNIFAC Lyngby

3-parameters for group interactions

Modified Dortmund UNIFAC

3-parameters for group interactions

Linear-UNIFAC

2-parameters for group interactions

Linear Dortmund UNIFAC

2-parameters for group interactions

KT-UNIFAC

lst-order (Linear UNIFAC) & 2ndorder group contribution terms

Remarks - Reference Original version with parameter tables [1977]3'9'" Parameters regressed from LLEdata[1981]'2 Changes in model equations & new parameter tables [1987113 Changes in model equations & new parameter tables [1987]14 Changes in model equations & new parameter tables [1992]15 Changes in model equations & new parameter tables [1992]16 Changes in model equations & new 1 st-order and 2nd-order group parameter tables [2002]10

4.2 THE UNIFAC METHOD Since its development in 19759, a number of different versions of the UNIFAC groupcontribution method for the estimation of liquid phase activity coefficients have been developed. The first UNIFAC method will be called here as the UNIFAC-VLE. One of the latest versions of UNIFAC, the KT-UNIFAC, has been developed by Kang et alw. Table 1 gives a partial list of different versions of UNIFAC that will be discussed in this chapter. The characteristic feature of all UNIFAC methods is that all versions are based on the group contribution approach where the liquid phase activity coefficient of component i in solution with one or more components is calculated as a sum of contributions of all groups representing the mixture (solution). These contributions are divided into two terms - a combinatorial term that accounts for the contributions due to differences in size and shape and are based on the group surface area and volume parameters, and a residual term accounting for the energetic differences, which includes the interaction parameters between the groups. With respect to the intensive variables, the UNIFAC method is dependent only on

61 temperature and composition but not pressure. The combinatorial term is dependent on composition only (in addition to the group surface area and volume parameters) while the residual term depends on the temperature, the composition and the group parameters (surface area, volume and interactions). With the exception of KT-UNIFAC, all UNIFAC methods employ lst-order functional groups to represent the compounds present in the liquid mixture. KT-UNIFAC employs both lst-order and 2nd-order functional groups to represent the compounds present in the liquid mixture. Therefore, the combinatorial and residual contributions have first-order and secondorder terms if 2nd-order groups are present. Two examples of representation of molecules with the UNIFAC groups are given below in Table 2. Note that each group is characterized by a main group, a sub-group, the sub-group surface area (Rf), the sub-group surface volume (Qf) and the main-group/main group interaction parameters anmo, amn,o, amn,o- Each compound therefore is represented by NSG number of sub-groups and a corresponding number of main-groups. A total of NMG maingroups are needed to describe all the compounds in the mixture. Table 2: Representation of molecular structures with different types of groups Ethanol (NSG=3, NMG=2) Sub-Groups: 1 CH3, 1 CH2, 1 OH Main-Groups: CH2, OH 2nd-Order groups: None

2-Butanol (NSG=4, NMG=2, NSOG=1) Sub-Groups: 2CH3, 1 CH2, 1 CH, 1 OH Main-groups: CH2, OH 2nd-Order groups: CHOH

4.2.1 General Model Equations (lst-order) The UNIFAC GC-method for the estimation of the liquid phase activity coefficient of component i in a solution consist of a combinatorial and a residual contribution: lny=lny\+lny":

(1)

The combinatorial term (In y/) includes entropic effects due to molecular size and shape differences while the residual term (In j,R) involves the intermolecular interactions. The different versions of the UNIFAC GC-method differ in their formulation of the combinatorial term and the expression of the temperature dependence of the residual part. Combinatorial Term - In j \ C The combinatorial term is written as17 /«r;;=/-j,+/«j,-^,(/--+/«-! * v Li Li) with

(2)

62 L> = ^ — /_, x,

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Distillation Design in Practice (L.M. Rose) The Art of Chemical Process Design (G.L. Wells and L.M. Rose) Computer Programming Examples for Chemical Engineers (G. Ross) Analysis and Synthesis of Chemical Process Systems (K. Hartmann and K. Kaplick) Studies in Computer-Aided Modelling. Design and Operation Part A: Unite Operations (I. Pallai and Z. Fonyó, Editors) Part B: Systems (I. Pallai and G.E. Veress, Editors) Neural Networks for Chemical Engineers (A.B. Bulsari, Editor) Material and Energy Balancing in the Process Industries - From Microscopic Balances to Large Plants (V.V. Veverka and F. Madron) European Symposium on Computer Aided Process Engineering-10 (S. Pierucci, Editor) European Symposium on Computer Aided Process Engineering-11 (R. Gani and S.B. Jørgensen, Editors) European Symposium on Computer Aided Process Engineering-12 (J. Grievink and J.van Schijndel, Editors) Software Architectures and Tools for Computer Aided Process Engineering (B. Braunschweig and R. Gani, Editors) Computer Aided Molecular Design: Theory and Practice (L.E.K. Achenie, R. Gani and V. Venkatasubramanian, Editors) Integrated Design and Simulation of Chemical Processes (A.C. Dimian) European Symposium on Computer Aided Process Engineering-13 (A. Kraslawski and I. Turunen, Editors) Process Systems Engineering 2003 (Bingzhen Chen and A.W. Westerberg, Editors) Dynamic Model Development: Methods, Theory and Applications (S.P. Asprey and S. Macchietto, Editors) The Integration of Process Design and Control (P. Seferlis and M.C. Georgiadis, Editors) European Symposium on Computer-Aided Process Engineering-14 (A. Barbosa-Póvoa and H. Matos, Editors) Computer Aided Property Estimation for Process and Product Design (M. Kontogeorgis and R. Gani, Editors)

COMPUTER-AIDED CHEMICAL ENGINEERING, 19

COMPUTER AIDED PROPERTY ESTIMATION FOR PROCESS AND PRODUCT DESIGN Edited by

Georgios M. Kontogeorgis IVC-SEP, Technical University of Denmark Søltofts Plads Department of Chemical Engineering Building 229, DK-2800 Lyngby, Denmark

Rafiqul Gani CAPEC, Technical University of Denmark Søltofts Plads Department of Chemical Engineering Building 229, DK-2800 Lyngby, Denmark

ELSEVIER 2004

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ISBN: ISSN:

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he paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.

V

Preface Properties of pure compounds and/or their mixtures are needed in almost every aspect of process/product design. Whether it is evaluation of a product or design of a process/product or simulation of a process flowsheet or analysis of operability of a process, etc., one or more types of properties would be needed. There are several sources or means to obtain the necessary properties. For example, measure the necessary property data, retrieve the necessary property values from a database, calculate the necessary property values through appropriate models, and last but not least, use of specialized software. Although, the use of experimental data provides the most reliable means of getting the right property values, this option is not always feasible due to the time needed to obtain the experimental data and the associated cost. Therefore, among the most interesting options are often use of databases, use of appropriate property models and/or use of specialized software. Although, a number of databases with collections of experimental data exist, and in some cases, also of estimated data, the problem for many users is to know which database can be used and for what data? The most widely used option for obtaining the needed property values is the use of property models. Some of the problems that the users face here are, which models to use, what is their accuracy or what to do if the model's parameters are not available? The user also faces the same questions when using specialized software. A number of books have been written to help the users to estimate the needed properties, with the most well-known of these being the "Properties of Gases and Liquids" by Poling, Prausnitz, and O'Connell. Other books (written by Sandier, Horvath, Smith et al) also provide useful information for the user. Although the currently available books provide a lot of useful information, they do not exactly address the questions from a user-of-models point of view and they mostly focus on vapor-liquid equilibria. The objective of this book is to highlight the computational aspects of property estimation with special focus on their use in process-product design covering a wide spectrum of properties and phase equilibria types. The book does not merely provide a presentation of the most suitable property models available today but provides, as well, some guidelines on how to select the appropriate property model. A systematic approach to property estimation is proposed. That is, first identify the needed properties, then identify the appropriate property model to be used (if the use of a database is not possible), then estimate the needed properties according to step by step calculation procedures. This information will also help the readers to develop their own computer programs.

VI

This book is organized into 16 chapters, which are divided into 4 parts. The chapters of Part I highlight various aspects of computer aided property estimation and the roles of properties and their models in process and product design. Illustrative examples are also included. Each chapter in Part II covers a class of properties and their models. The objective is not to provide an exhausted list of property models but to discuss a few selected models in detail from a process-product design point of view. Useful information about successful application, limitations, performance analysis, etc., is also provided. The chapters include models for pure component properties! equations of state, GEmodels and their combined forms; advanced equations of state such as the CPA model; models for polymer solutions and electrolyte systems! models for diffusion in multicomponent mixtures! and, modeling of solid-liquid equilibrium and of gas hydrates. The chapters in Part III deal with application (or use) of the property models from Part II. Illustrative examples, many of them related to typical process-product design related calculations, are provided. In addition, a chapter on molecular simulation of phase equilibrium for industrial application is included. Finally, Part IV, contains a single chapter on the "challenges and opportunities" in property modeling. The chapter provides an overview of the future directions, the needs and application of property modeling. A number of experts from academia and industry have been invited to contribute. These have been collected and organized by the editors in a way that readers will find it easy to read about the properties, their needs, and how to apply (estimate) them. We take this opportunity to thank all the contributors for providing excellent material, to Elsevier for accepting to publish this book and to our coworkers who have helped us with the organization of the material. We would like to acknowledge those students and co-workers of ours who have proofread parts of this book and/or provided material for it : Dr. Nicolas von Solms, Dr. Thomas Lindvig, Dr. Samer Derawi, Dr. Hongyuan Cheng, Ph.D student Irene Kouskoumvekaki and Amra Tihic. We would like to thank Prof. Michael Michelsen, and Dr. Giorgio Soave for many useful discussions. Finally, we hope that the readers will find the book useful for research, development, and educational purposes. We hope that the book will generate enough interest and valuable feedback for future editions. We would also like to state that even though we are proposing a computer aided property estimation for process-product design, we do value the importance of experimental data. Model development and validation without experimental data is not possible. Therefore, we do hope that there is also an emphasis on systematic plans for property measurements and collection so that better and more versatile models can be developed. Georgios M. Kontogeorgis and Rafiqul Gani

vii

List of contributors Author Jens Abildskov Joao A.P. Coutinho Philippos Coutsikos Jean-Luc Daridon Peter K. Davis J. L, Duda Ioannis G. Economou

Rafiqul Gani Eric Hendriks Georgios M. Kontogeorgis Jorge Marrero Henk Meijer John P. O'Connell

Address CAPEC, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark Departamento de Quimica, University of Aveiro, 3810193 Aveiro, Portugal Diadikassia s.a, Athens, GreecG Laboratoire des Flu ides Complexes, Universite de Pau et des Pays de l'Adour, 64013 Pau, France Department of Chemical Engineering, The Pennsylvania State University 165 Fenske Laboratory, USA Department of Chemical Engineering, The Pennsylvania State University 165 Fenske Laboratory, USA Molecular Modelling of Materials Laboratory Institute of Physical Chemistry National Research Center for Physical Sciences "Dcmokritos", 153 10, Athens, Greece CAPEC, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark Shell Global Solutions Inter national, Shell Research & Technology Centre, Amsterdam, The Netherlands IVC'SEP, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark CAPEC, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark Shell Global Solutions International, Shell Research & Technology Centre, Amsterdam, The Netherlands Department of Chemical Engineering University of Virginia 102 Engineers' Way P.O. Box 400741 Charlottcsvillc, VA 22904-4741 USA

Vlll

Jerome Pauly Michael L. Pinsky

Alexander Shapiro Kiyoteru Takano

Epaminondas C. Voutsas

Laboratoire des Fluides Complexes, Universite de Pau et des Pays de l'Adour, 64013 Pau, France Firmenich Chemical Manufacturing Center 150 Firmenich Way Port Newark, N. J. 07114 USA IVC-SEP, Technical University of Denmark, Department of Chemical Engineering, Building 229, DK-2800 Lyngby, Denmark Mitsubishi Chemical Corporation Yokohama Research Center Industrial Engineering Laboratory Kamoshida-cho, Aoba-ku Yokohama 227-8502 Japan Thermodynamics and Transport Phenomena Laboratory, Department of Chemical Engineering, National Technical University of Athens

IX

Contents

Page

Preface

v

List of contributors

vii

PART I. Introduction to Computer Aided Property Estimation

1

1. Computer aided property estimation Georgios M. Kontogeorgis & Rafiqul Gani 2. Role of properties and their models in process and product design Rafiqul Gani & John P. O'Connell

3 27

PART II. Models for Properties

43

3. Pure component property estimation: Models & databases Jorge Marerro & Rafiqul Gani 4. Models for liquid phase activity coefficients-UNIFAC Jens Abildskov, Georgios M. Kontogeorgis & Rafiqul Gani 5. Equations of state with emphasis on excess Gibbs energy mixing rules Epaminondas C. Voutsas, Philippos Coutsikos & Georgios M. Kontogeorgis 6. Association models — The CPA equation of state Georgios M. Kontogeorgis 7. Models for polymer solutions Georgios M. Kontogeorgis 8. Property estimation for electrolyte systems Michael L. Pinsky & Kiyoteru Takano 9. Diffusion in multicomponent mixtures Alexander A. Shapiro, Peter K. Davis, J. L. Duda 10. Modelling phase equilibria in systems with organic solid solutions Joao Coutinho, Jerome Pauly, Jean-LucDaridon 11. An introduction to modeling of gas hydrates Eric Hendriks & Henk Meijer

45 59 75

113 143 181 205 229 251

X

Part III: Application of property models & databases

277

12. Molecular simulation of phase equilibria for industrial applications Ioannis G. Economou 13. Property models in computation of phase equilibria Rafiqul Gani & Georgios M. Kontogeorgis 14. Application of property models in chemical product design Rafiqul Gani, Jens Abildskov & Georgios M. Kontogeorgis 15. Computational algorithms for electrolyte system properties Rafiqul Gani & Kiyoteru Takano

279

PART TV- Challenges & Opportunities 16. Challenges and Opportunities for Property Modelling

309 339 371

405 407

Georgios M. Kontogeorgis & Rafiqul Gani Subject Index

417

Author Index

425

Part I: Introduction to Computer Aided Property Estimation

1. Computer aided property estimation Rafiqul Gani & Georgios M. Kontogeorgis 2. Role of properties and their models in process and product design Rafiqul Gani & John P. O'Connell

This page is intentionally left blank

Computer Aided Property Estimation for Process and Product Design G.M. Kontogeorgis and R. Gani (Editors) © 2004 Elsevier B.V. All rights reserved.

3

Chapter 1: Introduction to Computer Aided Property Estimation Georgios M. Kontogeorgis and Rafiqul Gani 1.1 INTRODUCTION Computer aided property estimation implies the use of mathematical models for the calculation of the needed properties. Depending on the type of property, the size-scale factor, the required accuracy, the application, etc., the mathematical models have varying degrees of complexity. For example, they may be very simple polynomial functions (correlations) representing various pure component temperature dependent properties, a non-linear set of algebraic equations representing various cubic equations of state, or, a very large set of differential-algebraic equations representing the behavior of atoms within a specified boundary. In all cases, an appropriate mathematical model is derived or selected and solved with the help of computers to obtain the necessary property values. These mathematical models, representing the behavior of atoms, molecules and/or solutions, often include parameters that have been regressed to match the observed behavior of a set of systems (atoms, molecules and/or solutions). Therefore, computer aided property estimation also includes model development and model parameter estimation in addition to property estimation. The essential steps in computer aided property estimation are to select an appropriate model for the desired property and to solve the corresponding model equations to estimate the property, provided all the necessary model parameters are available. A pre-estimation step is to derive or develop the needed property model, which can be time consuming and expensive. Therefore, the availability of computerized libraries of property models from which the needed model can be selected and/or adopted is commonly practiced. The method of solution of the model equations, of course, depends on the type of the model (that is, the set of equations representing the model). However, for single value property estimations involving simple polynomial functions, hand calculators may be used. For repetitive calculations of the same property and the same system within an iterative loop and/or same property for different systems, use of a computer-based calculation option is more appropriate. On the other side of the scale-size factor, for single value property estimations involving complex mathematical models (such as molecular modeling), the method of solution is computer intensive and availability of powerful computers is an advantage. Parameter estimation is necessary when the available parameters do not give acceptable results or are simply not available. In either case, experimental data must be available to fine-tune or regress the model parameters. In this chapter, we will give an overview of computer aided property estimation in terms of types of properties, types of models and types of solution approaches together with a discussion on methods for model development.

4 1.2 CLASSIFICATION OF PROPERTIES & MODELS Properties are classified in this chapter in terms of the scale-size factor, the function-use factor and the dependence factor according to a defined hierarchy. The scale-size factor is used at the inner-level, where, properties are classified in terms of scale & size into microscopic, mesoscopic and macroscopic. Microscopic properties refer to properties of atoms while macroscopic properties refer to properties of molecules. At each scale-size, the properties are further classified in terms of single atoms/molecules or multiple atoms/molecules of different types. At the next level, each type of property from the inner level is classified in terms of the function-use factor as physical, chemical, transport, environmental and so on. That is, the function and/or use of the property define its class. At the outer level, properties are classified as primary (single value property, which can be determined only from the structural information), secondary (property that cannot be explicitly calculated only from the structural information and is usually a function of other properties) or functional (properties that are dependent on the intensive variables, temperature, pressure and/or composition, in addition to the structural information). Figure 1 illustrates this outer-level classification.

Figure 1: Outer-level classification of properties. A model is needed for estimation of any property from any level and sub-level. The type of model to be used depends on the three classification factors. At the macroscopic level, Eqs. 1-4 highlight examples of primary, secondary and functional property models, respectively. Tc = 231.239*Log (Ik hU + I, A, N, + Zt B,• Mj )

(1)

ZC = (PC*VC)/(83.14*TC)

(2)

P,ap = 10IA

(3)

H!(rc>]

5

Lny, = l-ln

E, - (xi*d,/E, + x/Q/Ej)

(4)

In the above models, Eq. 1 illustrates a 3rd-order group contribution based additive model for a single value primary pure component property (critical temperature - Tc) where each of the summation terms indicates group contribution for the corresponding group-order. The theoretical basis here is that the accuracy of property estimation increases with the increase in the number of additive terms. Equation 2 illustrates a secondary property of a pure component or mixture (critical compressibility factor, Zc, as a function of critical temperature, critical pressure and critical volume). Theoretically, if the primary property expressions are introduced into the expression for the secondary property, the corresponding secondary property can be estimated only from the molecular structural information and the parameters for the additive terms. Note, however, that the parameters are regressed (usually) only with the primary property experimental data. The secondary property is usually derived from observed relationships between properties of a class of systems. Equation 3 represents a temperature dependent correlation for the vapor pressure, Pvap, as a function of temperature, T. This class of properties change as the condition of the state (defined by the intensive properties - temperature, pressure and/or composition) change. Therefore, the behavior of systems under different conditions needs to be modeled. Equation 4 represents mixture property - activity coefficient for component i in a binary liquid mixture. The models are classified in this chapter in terms of theoretical, semi-empirical and empirical (see Figure 2). Most of the commonly used property models belong to the semiempirical type. Molecular modeling approaches belong to the theoretical class while correlation functions belong to the empirical type. The main feature of all property models is that regressed values for a set of model parameters are needed in order to estimate the property from the model equations. If these parameters are available in the form of regressed values, then the estimation can be performed. Otherwise, the unavailable model parameter values will need to be regressed or another property model will need to be selected. In some cases, the property model parameter can be predicted, giving rise to truly predictive property models. Thus, property model development and use consists of a model parameter estimation and/or verification step. The application range of the property model, therefore, depends not only on the theoretical aspects (such as the behavior of the system) but also on the data used for the regression of the model parameters.

1.3 PROPERTY MODEL DEVELOPMENT Development of models in general and property models in particular, is a cyclic process as shown in Figure 3. One starts with a definition of the model requirements and a hypothesis, solves the model equations, checks the calculated values against collected experimental data, and if the comparison is not favorable, changes the theory and/or the model parameters (thereby generating a new model) and repeats the cycle. As with other types of models, decisions need to be made in terms of the type of model to be developed for a specific property, the required accuracy, the application range (in terms of systems, conditions, problems), and the expected users. For many property model developments, these decisions

6 are inter-related. For example, property model development, formulated as, develop a model for the estimation of the average density of polymers defines the type of model, the application range and the expected users. On the other hand, a property model development problem defined simply as "develop a model to predict the activity coefficients of liquid solutions" needs further information in terms of types of systems and conditions for which the model will be applicable. Otherwise, the problem definition implies a model applicable to all types of systems and under all conditions, which is almost impossible to develop with the current knowledge.

Figure 2: Classification of property estimation methods. The verification/validation step of property modeling should also check for thermodynamic consistency, such as the Gibbs-Duhem conditions (see Eqs. 5-7), the relation between the normal boiling point and critical temperature (see Eq. 8) and the condition that some property values have a limiting value at the critical point (see Eq. 9).

Figure 3: Steps in the development of property models.

7 In, (Slny/Stij),;,, = 0 ;j = 1,2, ....N

(5)

In, (an(p/SP)n;r =(Z-

(6)

l)n/P

In, (8y/5T)n, P = - H (T, n)/RT

(7)

Tc(i) / Th(i) > 1

(8)

[Hvap(i)]Tc«> = 0

(9)

Before solving the property model equations, especially for computer-aided applications, it is important to perform a degree of freedom analysis in terms of number of equations, number of unknown variables (ie., to calculate number of variables to specify and number of model parameters (which must be known or regressed apriori). A simple example, for purposes of illustration, is shown below for the Wilson model to estimate the liquid phase activity coefficients in binary mixtures. S,.,= (V,/V,) *exp(-A,.,/T) 8,-2 = (V2/V,) *exp(-A ,-2/T) &-/ = (V,/V2) *exp(-A2.,/T) 82-2= (V2/V2) *exp(-A2-2/T)

(10) (11) (12) (13)

E,= X,*§,., +X2*8,.2

(14)

E2= X,*82-, + X2*82-2

(15)

Lny,= l - ln(E,) - (X,*8,., + X2*d2.l)

(16)

Ln n= 1 - ln(E2) - (X,*S,.2 + X2*52.2)

(17)

From the above equations, it can be seen that this Wilson model for binary systems has 8 equations with 8 unknown variables (yh Eh Sj.j, for /= 1,2; 7-1,2), 3 specified variables (T, xh for z-1,2) and 6 parameters (K,, A^, for z'=l,2; /=1,2). Arranging the above equations in the sequence shown in column 1 of Figure 4, a lower tri-diagonal matrix is obtained, indicating that each equation has only one unknown variable. Therefore, the model equations are very easy to solve and is computationally inexpensive. Figure 4 shows an incidence matrix (for the Wilson model1) where the equations are represented in the rows and the variables are represented in the columns. For a solvable set of model equations, there should be the same number of columns for the "unknown" variables as the number of rows and there should not be any * in the diagonal (for an ordered set of equations in the tri-diagonal form). Also, if all

8 the • appear only in the diagonal, then the model equations can be solved sequentially according to the specified order. If there are more than one • in any row on the upper triangular part, it will indicate a system of equations that would need to be solved simultaneously. With very few exceptions, most property models can be arranged in lower tri-diagonal form (see chapters 4 and 13 for more examples).

Figure 4a: Wilson model equations ordered into a lower tri-diagonal form (Note: * indicates variable is known for the corresponding equation; • indicates the unknown variable calculated from the corresponding equation; since A 1.2 = A 1.2 = 0, they are not shown in the above incidence matrix) A similar model analysis is also shown for a cubic equation of state in Figure 4b. The problem being solved by the property model can be defined as, Given: T, P, x;_Calculate: lntpj, for known parameters, properties & constants: kji, y/A, i/zg, e, a; T c j, P c j, coj; R.

1.4 PROPERTY MODEL USE Two types of property model users may be envisaged. Those who use property models to estimate the desired properties, or, those who incorporate property models as parts of larger models and/or solution schemes in order to solve specific (design) problems. In terms of Figure 5, users of the first type only need the property model equations (also called the constitutive equations) and calculate the properties given the known values of the intensive variables and all other model parameters. Users of the second type may use the constitutive equations together with only the constraint equations (for example, for saturation point calculations) or use the constitutive equations together with the balance equations and the constraint equations (for example, for modeling of phase equilibrium-based separation processes). In this case, the property models belong to larger models and/or solution schemes and are usually represented as constitutive equations from within the process model. In the corresponding solution scheme, the property model equations belong to an iterative solution scheme, where for different values of the intensive variables, the needed properties are calculated (see Figure 5). Depending on the numerical method used in the solution of the

9 process model equations and the type of problem being solved (simulation or optimization), first, second and even third derivatives of the properties (constitutive variables) with respect to the intensive variables may be necessary (see chapter 2 for more details). Therefore, property model users who incorporate property models into process simulation/optimization packages need to ensure that the derivative functions exist and that they are continuous.

z = \',( \:-b) - (a Y),

[RT(\' +e b)( V + sb)]

(i)

ab =^ x , b V "

(iii)

SRK Equation of State

m; = m(o".))

[IV)

5C + 4 Equations

(v)

a-

y

= v VT P " 2

(VI)

2

2 2

(vn) (viii)

a' = yA (R T ci ,p ci )[i + nij el - T n f ]

In , = .' (?; V; ,'RT - 1) dP/P | T s =f(dZ,clP. T. P. a. b, a, b) dZ 'dP = f(T. P. a. b. a. b)

(IX)

10C+11 variables Specify: 5C + 7 variables, C is the number of compounds in the mixture.

SRK EOS model equations (Eqs. i-ix) Eqs.

Variables ni;

E-iv E-vii E-v E-vi E-ii E-iii E-i E-viii E-ix

• *

a;;

a;j

• *

• *

* *

b;

• *

* *

a

b

• * * * *

• * * *

z

dz/dp lncpi

• * *

• *

•

Incidence matrix showing the tridiagonal form for solving the model equations Figure 4b: The SRK equation of state and the analysis of the equations for the estimation of fugacity coefficients In either case, the principal steps involved in computer aided estimation of properties are highlighted in Figure 6. One starts with a definition of the problem (step 1); followed by property model generation/creation/selection (step 2); property model validation, including, model parameter estimation and/or tuning (step 3); and finally, property calculation (step 4). If parameters for the selected property model are available and are known to be reliable, step 3 would not be necessary.

10

Figure 5: Property model (constitutive equations) can be solved separately or as part of another model and a larger set of equations (Note: 9_ includes primary, secondary as well as functional properties; model parameters are not shown). 1.4.1

Property Model Selection

Appropriate selection of property model is very important in process and product design. Often the user of a property model does not have the knowledge and experience to choose "wisely" among the myriad of options. Cordiner2 provides a decision tree for property model selection (see Fig. 7).

Figure 6: Principal steps in computer-aided property calculation. The selection is commonly based on familiarity, hearsay or ease of accessibility. However, consideration of the numerous properties (and models) and comprehension of the

11 complexities of current and future property models can be difficult even for the experienced user. The use of an inappropriate property model and/or model parameters can often go beyond wrong numerical results that cause bottlenecking and over-sizing to even yielding wrong process configurations3'4. A simple example of an incorrect choice of a property model is to predict the vapor-liquid equilibrium for an azeotropic binary mixture with a composition independent model for the liquid and vapor fugacity coefficients. Obviously, the azeotrope will never be found.

Figure 7: Decision tree for property model selection (Cordiner2).

12 Using commercial simulator descriptions, a partial list of chemical mixture types, the phases of possible interest and some property models that can be employed for computations of equilibrium among the phases listed is presented in Table 1 (adapted from Gani & O'Connell5) for purposes of illustration not completeness. The last column indicates the types of model parameters that are usually needed by the property model. Gani and O'Connell5'6 and also Carlsen7 have proposed some guidelines for property model selection. Table 1: Partial list of mixture types and property models appropriate for describing phase equilibria. Mixture Type

Phases

Model Type

Hydrocarbon Hydrocarbon aqueous

L V V L

Polar (nonassociating)

V L

Polar (associating)

V L

Aqueous electrolyte

V L S V L S V L

Cubic EOS Cubic EOS EOS EOS1 Gr. EOS EOS' GE EOS EOS' orG F Ideal or EOS GF Ideal Ideal GE Ideal EOSd EOS3 or GE

S L S L S

Ideal Empirical Ideal Empirical Ideal

Mixed solvent electrolyte Polymer - solvent

Parameters E,kij E, kij E, ky E, R, Q, Xij E, ky E, ky E, R, Q, TH E,k'ii E.k'ij E, R, Q, xij

None or ky R, Q, T\J None None or ky R,Q,TY None E,kJy E, k y or R,Q,T\J

Steroids - solvent Amino acid Solvent

None

e4 None

e4

None

Refers to special mixing rules for equations of state or parameters for GH models. Refers to mixture specific property model parameters. 3 Indicates special equations of state such as CPA8 and S AFT9 equation of state usable for all phases and corresponding model parameters. 4 Indicates property models not presently found in standard versions of process simulators. 2

13 1.4.2

Examples of Property Model Use

Example 1: Estimation of unknown pure component properties Estimate the following properties for Corticosterone to be used for finding a suitable solvent and for design of solvent-based extraction - the normal melting point (Tm), the heat of fusion at 298 K (H/lls), the octanol-water partition coefficient (LogPo-w), the water solubility (LogWs) and the Hildebrand solubility parameter (Sp). Step 1- Problem definition Estimation of pure component properties (primary and secondary) as well as mixture properties are needed. Tm and H/m are pure component primary properties; Sp is by definition a secondary property; LogPo-w and LogWs are by definition, mixture properties.

Figure 7: Molecular structural information of Corticosterone Step 2 - Property model selection For the pure component properties, the Marrero & Gani method10 is selected as it has a wide range of groups, a wide range of properties, is predictive and has good accuracy of prediction. An additional advantage with the selection of this method is that Sp, LogPo-w and LogWs are modeled as special pure component primary properties. With the Marrero & Gani method, the following groups are needed to represent the molecular structure of Corticosterone. A check of the property model parameter tables indicates that all the necessary parameters are available. The group representation details are given in Table 2. Step 3 - Model validation & parameter estimation Not necessary in this problem Step 4 - Property estimation The calculated values for the required properties are given in Table 3. For a very quick estimation, the calculated values are reasonably satisfactory. With these properties, solvents

14 can be identified and estimates of solubility in the solvents can be calculated. Table 2: Groups needed to represent the molecular structure of Corticosterone. Third Order Groups Second Order Groups First Order Groups Times Group Times Group Times Group 3 CH multiring 1 CHcyc-OH 2 CH3 2 C multiring 1 CHcyc-CO 2 OH 1 CH2C0 7 CH2 5 CH 2 C 1 CH=C 1 CO Note: Selected Path within molecular structure: O=...-OH Length = 12 Table 3: Comparison of calculated and known experimental values for Corticosterone. Property Tm (K) Hfm (kJ/mol) SP (MPa'A) LogPo-w LogWs (Log(mg/L))

Calculated 458.3 45.8 24.45 1.79 2.12

Known experimental data 454.1 -

1.94 2.29

Example 2: New group definition & parameter estimation Study the effect of HC1 on a binary mixture of ethanol-ethyl acetate in order to design a vapor-liquid based separation. Step 1 - Problem definition This problem requires the estimation of vapor-liquid equilibrium (VLE) for a ternary mixture at pressure of 1 atm (assumed). That is, for fixed amounts of HC1, the saturation temperatures and the corresponding vapor compositions need to be calculated for a series of (given) liquid compositions. Consequently, property models within a calculation scheme for VLE are needed. Step 2 - Properly model creation/selection Since the mixture is non-ideal, the gamma-phi approach where a GE-model is used for the calculation of the liquid phase activity coefficient and an equation of state for the vapor phase fugacity coefficient is appropriate since the pressure is 1 atm. In addition, the vapor pressure of the pure components as a function of temperature is necessary. Since water is not present, assuming HC1 will not dissociate, a non-electrolyte G1 -model is selected. A local G1 -model however needs to be created (as the necessary model parameters are not available) and for

15

this purpose, the group-contribution based UNIFAC-VLE11 (original) is selected. However, since HCl does not exist in the selected UNIFAC model as a group therefore, a new group needs to be created and the interactions between HCl and the other groups representing ethanol and ethyl acetate need to be estimated. For the vapor phase, the ideal gas law is selected while for the vapor pressure, the Antoine correlation regressed to the vapor pressure data for each pure component is selected. The UNIFAC group representations for the 3 compounds and their corresponding size(R) and volume- (V) parameters are given in Table 4. The Antoine correlation parameters and the group interaction parameters are given in the Appendix. The missing group interactions are for HCl versus the main groups CH2, OH and CCOO. Table 4: UNIFAC group representations for the 3 compounds

Ethanol Ethyl acetate

CH3 1 1

CH2 1 1

OH 1

CH3COO 1

1

HCl

Parameters R (size) Q (volume)

HCL

0.9011 0.848

0.744 0.540

1.0 1.2

1.9031 1.7280

1.056 1.100

Step 3 — Model validation and parameter estimation VLE data has been found only for the binary mixtures ethanol-ethyl acetate. Therefore, as a first estimation, all the missing HCl-related group interactions will be assumed negligible since the appropriate experimental data to estimate them are not available. This means that for HCl, only the combinatorial effect and the vapor pressures will be considered. This is quite reasonable since the normal boiling point of HCl (188.15 K) is quite far from that of ethanol (351.44 K) and ethyl acetate (350.2 K). The experimental ethanol-ethyl acetate data will be used to compare the prediction without any HCl and then to compare the effect of adding HCl. Step 4 — Properly estimation

The calculated VLE for 0% HCL and 5 % HCL in binary mixtures of ethanol-ethyl acetate is highlighted in Figure 8. The effect of adding HCl is to shift the azeotrope to the left (that is, to compositions having less ethanol). Example 3: Extraction of heavy compounds using supercritical gases Background Many extractions of heavy compounds and other applications, such as some enzymecatalyzed reactions, are being performed at high pressures in supercritical fluids, such as supercritical CO2,which take advantage of the positive features of CO2 (non-toxic, nonflammable fluid having low viscosity and high diffusion coefficient). Design of these processes require, among others, knowledge of phase equilibria at high pressures, which

16 could either be gas-liquid or solid-gas, depending on the state of solute at the conditions of the process.

Figure 8: Effect of addition of HCL to ethanol-ethyl acetate mixtures Step 1 - Problem definition Estimation of the phase equilibria of CC^/heavy esters such as methyl palmitate or heavy alcohols e.g. hexadecanol, at high pressures. Ultimately, the purpose is to perform VLE calculations for multicomponent systems. Step 2 - Property model selection Due to the high pressures involved, an equation of state is needed. The SAFT or CPA models could in principle be chosen, however they lack parameters for these heavy esters and/or alcohols, and most importantly, they have not been so far systematically tested for SC systems. An appropriate choice here is a cubic EoS using a suitable UNIFAC-type mixing rule, i.e. an EoS/GE model suitable for asymmetric systems (see chapter 5). Most of these models, such as the PSRK or MHV2 have problems for asymmetric systems, while others such as the Wong-Sandier one do not contain gas-based parameters. The optimum choice in this case is the LCVM mixing rule, which has an extensive parameter table12. Step 3 - Model validation and parameter estimation No parameter estimation is needed, since the required parameters are available in the literature13. The LCVM parameter table includes group-parameters between CO2, alkenes, alcohols, acids, ethers and esters. The following group parameters have been estimated from

17 experimental data: CO2-OH (and CO2-methanol), CO2-COOH, CO2-CH2COO, CO2-CH2O, CO2-COO (for aromatic esters) and CO2-CH=CH. Step 4 - Properly estimation Some sample calculations for the requested systems are shown in Figure 9 and Tables 5 and 6, where comparison with experimental data, when available, is shown. The results are satisfactory, even for the two heavy alcohols which were not included in the parameter estimation of the model. Good results are also obtained for multicomponent VLE, where in most cases the error in pressure is below 10%. The higher error for the ternary system CO2/oleic acid/linoleic acid could be attributed to the inability of the conventional UNIFAC model to account for the cross-association between the two acids. The improved results obtained for the quaternary system are possibly due to the large amount of the non-polar hexane and the possible weakening of hydrogen bonding forces. Example 4: Density estimation for polymers Background Knowledge of the density of polymers as a function of process conditions especially temperature is required in many applications that include polymers. For example, density of polymers is a direct input in free-volume activity coefficient models, typically used for phase equilibrium calculations for systems with polymers. Volumetric information is also employed for estimating the equation of state parameters for polymers (see chapter 7). Step 1 - Problem definition As an illustration, the density / molar volume of two widely used polymers will be estimated: i. of butadiene rubber (polybutadiene) at 25 °C [experimental value : 0.875 g/cm ] ii. of polystyrene, having a number average molecular weight equal to 73800 g/mol, at 150 °C [experimental molar volume : 71305.6 cnrVmol ] Step 2 - Property model selection An apparent choice for obtaining the density values of any polymer is to look first into suitable databases e.g. DIPPR 881 or Rodgers et al.v''. These sources contain density information for many polymers as a function of temperature, typically in the form of the Tait correlation-equation. In those cases when the polymer of interest is not included in these databases, the density has to be estimated. Two useful choices are the methods by van Krevelen (see chapter 7) and the GCVOL by Elbro et al.15. Both these methods are based on the group-contribution approach. The van Krevelen method has different forms depending on the physical state of the polymer: •

For amorphous polymers (T>Tg): Va =F,,,(1.30 + 10- 3 r)

18

Figure 9: Prediction of gas-liquid phase equilibria for the system CCh-methylpalmitate at 343.15 K using the LCVM model.

Table 5: Prediction of gas-liquid equilibrium for some binary CC^-polar systems, which were not used into the parameter estimation of the LCVM model. Both the errors between experimental and calculated pressures and vapor phase mole fractions are shown.

co 2 /

1-hexadecanol 1-octadecanol EPA ethyl ester DHA ethyl ester

NDP 15 15 8 10

T(K) 373-573 373-573 313-333 313-333

P (bar) 10-51 10-51 75-132 90-174

AP (%) 9.4 7.9 19.3 23.9

Ay*103 7.5 4.3 2.9 2.1

Table 6: Prediction of multicomponent gas-liquid phase equilibria for some CO2 containing systems with the LCVM model. Both the errors between experimental and calculated pressures and vapor phase mole fractions are shown.

co2/

Methyl oleate / Methyl linoleate Methyl oleate / Oleic acid oleic acid / linoleic acid 1-dodecanol / lauric acid hexadecane / 1 -dodecanol n-hexane / stearic acid /oleic acid

T(K) 313.15 333.15 313.15 313.15 333.15 393 353.2 375.15

P (bar) 47-210

AP (%) 6.8

Ay*103 5.9

45 - 262 59-287

7.3 29.1

3.5 4.5

100-317 100-223 151-259

7.6 7.0 13.1

4.0 3.2 3.5

19 •

For glassy polymers (T (T)/ XT, P,y)

(8) (9)

K, = r/(T^)ps-(T)/P

(10)

K,=ps'{T)/P

(11)

K, = y/ (T,x')/ri"(T,x")

(12)

Eq. 8 uses an equation of state to obtain the fugacity coefficients, ^>,. p o r both phases while Eqs. 9 - 1 1 involve varies approximations for activity coefficients, y,, and vapor pressures, P '. For liquid-liquid equilibria, Eq. 12 would be used. Figure 1 highlights the work-flow and data-flow with respect to the service role of the properties (and property models). Note that for a TP-flash simulation, first the mass balance Eq. 1 together with the constraint (equilibrium condition) Eq. 3 is solved; for each evaluation of Eqs. 1 & 3, the property models are called. When convergence is achieved, the property models are called one more time for the evaluation of the energy balance. In this case, since T and P are fixed, the energy balance computes Q (the energy added/removed) needed to make the operation possible.

Figure 1: The service role of properties and property models This is a typical simulation problem where the property models (Eqs. 4-12) are used in the service role because every time an evaluation of Eqs. 1-3 needs to be made, there is a request

31 for the properties, for which Eqs. 4-7 are called. Another example of the service role is to ask for the density, either to convert the composition in mole fractions to moles/cm or to calculate the volume of the (separation) tank or the height of the liquid in a tank. In each case, only Eq. 7 will be called. 2.2.2 Service/Advice Role In process design and synthesis, property values are often regarded as explicit or implicit target values for a synthesis/design algorithm to satisfy by finding values for the unknown intensive variables. In section 2.2.1, the problem definition assumed (or specified) that a two phase system would exist at the specified T and P. Consider now that we do not know if a two phase system would exist at the specified T and P and also that we are only interested in removing a chemical through precipitation (crystallization). At any assumed (or specified) T, P, and z, we check if the liquid stream F would be stable at T & P. If not, there would be two phases, at least. Also, if the assumed T is above the melting point of at least one of the chemicals (for example, chemical A) in the system and below the melting point of the others, then there is a good chance that this chemical would precipitate, such as if the assumed T is below the saturation temperature of the feed mixture. The advice role here is to determine if solid-liquid based separation is feasible and also which chemical would be obtained as a solid. The design problem is to determine the temperature T of operation that would match the amount of separation (or recovery) that is desired. Figures 2a and 2b show two examples of this advice role. In each case, a solid-liquid equilibrium based saturation diagram is shown for an aqueous electrolyte system and a non-electrolyte system. It should be noted that the feed composition, z, and temperature, T, indicate which solid chemical would be separated.

Figure 2a: Saturation point compositions of naphthalene in a binary mixture of naphthalene-benzene as a function of temperature (y-axis)

Figure 2b: Saturation point compositions of sodium chloride in an aqueous solution as a function of temperature

32

Another example of the advice role can be found in solvent design, where the properties have explicit target values such as solubility and selectivity for a particular solute at a specific condition of operation. Here, the chemical structure of candidate solvents is manipulated until the solution properties match the target values. The process design problem (defined above) and the chemical product (solvent) design problem may be solved as part of a two-step procedure (irrespective of whether they are solved sequentially or simultaneously): Step I - generate alternatives {e.g., T'or solvent) Step II - determine properties (e.g., number of phases, solubility, or selectivity) and screen/verify alternatives through simulation. In Step I (generation), properties play a service/advice role while in Step II (verification) properties play only a service role. Strategies for the advice role attempt to eliminate infeasible solutions, or at least reduce the size of the search space and/or mathematical problem of a given situation, by providing the necessary insight. For example, an initial list of candidate solvents may be generated by searching for substances having similar solubility parameters as the solute. For each candidate solvent-solute combination, solid solubility diagrams (see Figures 2a-2b) would provide advice for selection of the operating temperature. The list of solvents would be reduced as candidates which do not meet the criteria are identified. For final verification, a simulation is needed (that is, solving Eqs. 1-6 for solidliquid equilibrium systems). Other examples of the advice role can be found in Gani & O'Connell[l]. The service/advice role is highlighted in Figure 3. Based on the problem specification, advice role in the generation step checks for feasible solid-liquid separation. If yes, then the service role is played for the verification (simulation) step. Note that the advice role also helps to design the condition of operation (choice of temperature and amount of solvent to be added or removed). Computer-aided molecular design techniques [2] are an example of properties used in their service/advice role, that employs different versions of the product model are employed.

Figure 3: Service/advice role of properties (property models) Often the advice role for properties is less demanding on the property models than is the service role. For example, sometimes the advice role for different product models can be

33

played with only pure component or infinite dilution properties of the compounds present in the mixture; the service role usually needs properties over the entire composition range. 2.2.3 Integration Role The most comprehensive role for properties in the solution of process-product design problems is that of integration. In process/tools integration and in graphical (visual) design techniques, properties actually can define an integrated solution strategy. Typical examples of this role can be traced back to graphical design techniques for separation processes (see for example, Henley and Seader [3] who describe various types of graphical design techniques) and for heat integration based on pinch technology [4]. In the case of distillation column design, the mass balance equation (Eq. 1) and the constraint equation (Eq.3) are represented in a two-dimensional plot of saturation vapor composition on the y-axis and the corresponding liquid composition in the x-axis. Each data point corresponding to the constraint equation represents a liquid in equilibrium with the vapor at the system pressure (usually constant) and temperature which varies over the column. In the case of heat integration, only Eqs. 2, 5 & 6 are needed. The two variables considered are the cumulative enthalpies for the hot and cold streams and the corresponding temperature. In the case of distillation design, the relation between saturation temperature and composition provides integration while in the case of heat integration, the relation between temperature and enthalpy does the integration. Using the process model defined by Eqs. 1-6, the integration role can be visualized through the following simple problem: • •

Given a contaminated product stream with a flowrate of F kmol/h having a composition fc of contaminant (for example, 0.02 mole fraction of phenol), Design a process through which the product stream becomes essentially free of the contaminant (mole fraction of phenol less than l.OxlO"6).

Through the traditional service or service/advice roles, the problem would be solved as follows - find candidate solvents that will create another liquid (solvent) phase and includes as much as possible of the phenol. For each solvent candidate, simulations are made to establish the process design. Now consider the following alternative solution technique called the reverse approach 1. Use Eq. 1 to calculate the required (or design target) solubility. Since the problem information actually provides both inlet and outlet concentrations of the product stream, this must be feasible. Note that since solubility (property) is actually the known variable, the solution of this separation problem does not require a property model. 2. Use Eqs. 3,11 and appropriate activity coefficient models to estimate solubilities for a solute in candidate solvents at selected temperatures. As long as the solubilities match the desired (target) values from step 1, the mass balance equation does not need to be solved.

34

It is interesting to note that in the traditional solution approach, using the generation and test paradigm, a simulation problem needs to be solved for every alternative. For many alternatives, however, a property model may not be available as part of the process model. If the generate and test steps are performed simultaneously (that is, include the simulation as part of an optimization loop), only one process model can be used, thereby severely restricting the application range since only one property model can also be used (unless multiple optimization problems are solved). With the reverse (integrated) approach, however, any number of property models can be used for step 2 while in step 1, property models are not needed at all. The procedure is to first solve a reverse simulation problem to determine the design target in terms of a set of properties, and then solve a reverse property estimation problem to determine the solvents and the operating conditions (for example, temperature). Multiple solutions are obtained, which only need to be ordered according to a performance index to identify the optimal solution. The property (in this case, solubility) plays the integration role to connect the simulation and design problems. On the other hand, from a point of view of the solution of the model equations, it plays the role of decomposition (separation of the balance and constraint equations from the constitutive equations). More details on this reverse approach can be found in [5, 6]. Figure 4 highlights the principal difference between the traditional or forward approach and the reverse approach (with the integration role for properties). Recently, Bek-Pedersen and Gani [7] have defined a driving force which is also a function of the saturation temperature and the corresponding phase compositions. Using the driving force for integration, Bek-Pedersen and Gani [7] have shown how simultaneous design and simulation can be performed for any two-phase separation process. Here, the property model plays all roles; service, advice and integrated solution of the simulation and design problem. The use of the driving force to integrate simulation and design is highlighted in Figure 5.

Figure 4: Integration role of properties and property models.

35

Note that in Figure 5, once the maximum driving force has been located at Fm and a reflux ratio (RR) is selected, by making the two operating lines to intersect on the D-Dx vertical line, the number of stages and the column profile (T, x & y_) can be back-calculated [7]. This means that the design and simulation of the distillation column correspond to the property target (maximum driving force). By definition, at the maximum driving force, the energy consumption is the minimum because this is the external medium that creates the twophase system. In the above examples, the relations among thermodynamic properties and intensive variables generated the integrated algorithm or solution strategy in addition to providing the solutions. "Intelligent" manipulation of the process and property model equations and variables using physicochemical and mathematical insights identified a small number of intensive variables as the unknown process model variables to represent the essential information about the problem. This tools integration, which is most valuable in applying integrated algorithms for synthesis, design and/or control, can be appreciated by considering the roles of properties in different process-product engineering problems through their independent, intensive variables (Table 1).

2.2 PROPERTY ROLES AND PROPERTY MODEL SELECTION In all three roles of properties, the proper selection of property models is important. Depending on the type of the problem, the consequences of property model choice can differ, even for the same property. The use of an inappropriate property model and/or model parameters may not be limited to only wrong numerical results that cause bottlenecking and over-sizing; even wrong process configurations can be found [8, 9].

Figure 5: Driving force based simulation and design (integrator is the driving force, a function of Py (T, P, x, y_) providing integration.

36 Table 1: Relationship between problems and properties in process-product engineering. Purpose

Problem

Determine

Remarks

Synthesis

Generate feasible process alternatives

Effects of T, P, x on process model

Design

Obtain condition of operation

Values of T, P, x that satisfy constraints

Properties affect process model results and play all roles, depending on the solution approach Properties provide target values and can play all the roles, depending on the solution approach

Control

Design control system

T, P,x sensitivities

Property models provide derivative information via service and advice roles

Energy analysis Environmental impact

Determine energy needs Verify that environmental constraints are satisfied

Enthalpies from T, P, x Component flows in effluent streams

Property models are essential via service and advice roles

Economy

Minimize cost of operation and equipment

Cost as a function of capital and operation

Property models affect process model results via service and advice roles

Property models are needed via service and advice roles

Often the user of a property model does not have the knowledge and experience to choose "wisely" among the myriad of options. The selection is commonly based on familiarity, hearsay or ease of accessibility. However, consideration of the numerous property models and comprehension of the complexities of current and future property models can be difficult even for the experienced user. Issues associated with this aspect are discussed by Gani and O'Connell [10]). 2.3.1 Service Role Since property models provide requested property values for quantitative evaluations of conservation of mass and energy, their quantitative accuracy must be evaluated. Some of the important issues related to the choice of the appropriate property model are the following: problem type, system (mixture) type, availability of property model parameters and computational complexities. Note that the estimation of the secondary and/or functional properties such as fugacity or activity coefficients, mixture densities, mixture enthalpies, etc., generally require pure component single value primary properties along with secondary/functional properties. Also, when the property model is used in the service role for a simulation problem, the derivatives of the properties with respect to the unknown variables (usually also the intensive variables T, P and/or composition) are needed when numerical methods like Newton-Raphson are used. Because of the importance of quantitative accuracy, tuning of the model parameters is an issue, especially since it depends on the availability of experimental data. In this case, a sensitivity analysis, that is, variations of the property of interest with respect to changes in

37

model parameters is valuable to fine-tune a small number of parameters. This is particularly useful when only limited experimental data are available. Such analyses show that pure component vapor pressures make a significant difference in the estimated vapor-liquid equilibrium (VLE) compositions for non-ideal systems, while the pure component critical (primary) properties are important for high pressure VLE calculations. Solid-liquid equilibrium (SLE) calculations are very sensitive to heats of fusion. The ratios of the activity coefficients of each component in the two liquid phases have direct impact on liquid-liquid equilibrium (LLE) compositions. Errors in densities effect the equipment sizing (volume and area) parameters. Since only one property model for each property may be used in process models such as the one represented by Eqs. 1-3, only carefully selected property models with fine-tuned model parameters and continuous derivative properties within a wide range of intensive variable values, should be used. Note that in the service role, only one property model may be used for the necessary properties during any simulation; this can be a disadvantage during simultaneous simulation and optimization of process-product problems since process and product models are solved simultaneously. For simulation problems from section 2.2.1 involving only the mass balance (Eq. 1) and the equilibrium condition (Eq.3), it can be noted that any one of Eqs. 8-12 may be appropriate for the equilibrium constant, Kh depending on the type of the problem, system, etc. Interesting issues with respect to the choice of models for Kt are the computational scale and time. If the fugacity and/or activity coefficients need to use complex relations based on groups at the atomic level (such as the SAFT EOSfll]), the models are usually computationally intensive and expensive. On the other hand, interactions at molecular levels (such as the SRK EOS[12]) are commonly less computationally intensive and relatively inexpensive. Consequently, calculation schemes where repetitive solution of Eqs. 1 & 3 are needed, computationally cheap models are usually preferred while for schemes where only a few calculations of Eqs. 1 & 3 are needed, and quantitative accuracy is important, computationally intensive models may be implemented. One alternative in this case is to use the reference and local models. The properties are generated by a reference model {e.g., SAFT EOS) and then matched with a computationally cheaper local model {e.g., the SRK EOS) to create a local, system-problem specific model. This idea is similar to property model simplification techniques proposed some time ago [13, 14]. The difference is that simplified local models needed to be generated for every iteration of a simulation. Here, system/problem specific local models need to be generated only once and can be used for all types of simulation problems for the same chemical system and properties. 2.3.2 Service/Advice Role In addition to the service role, for properties to play the advice role, the corresponding property model must be qualitatively as well as quantitatively correct. This is because the design problem (where advice is needed) usually involves generation and screening of different alternatives and verification of the feasibility of a desired operation (separation or reaction). Therefore, there is more emphasis on the qualitative accuracy. Of course, when the condition of operation (such as the temperature of operation) is to be found, quantitative accuracy is also essential.

38 In the case of equilibrium based separation processes, the advice role depends on the known (or generated) phase equilibrium (needing the solution of Eqs. 3 and 4 only). While these need to be calculated only once for each case, there can be many different chemical systems. Therefore, the choice of the property models (for Eqs. 8-12) needs to consider the application range not only in terms of intensive variable values but also in terms of chemical systems. This is particularly important for designing molecules with desired properties, where the selected property model needs to be predictive with respect to chemical systems to generate and screen large numbers of feasible alternatives. Unfortunately, if solvent selection is done simultaneously with the optimization of the process performance, only one property model per property can be used, restricting the search space for the problem solution. The best property model selection strategy is to choose a group or atomic contribution method (see chapters 3-4) for the advice role because of both predictive ability and qualitatively correctness for a wide range of chemical systems. Then, when a chemical system has been selected by such a method, measured and/or generated data should be used to regress (or fine tune) the model parameters of a local model with limited predictive capabilities. The last step also validates the property model for use in the service role. 2.3.3 Integration Role An important issue in the integration role of properties is how to bring together the special features of property models for process model-based calculation schemes. That is, it is necessary to identify the appropriate properties and the intensive variables. For a number of separation processes, including all of the 2-phase equilibrium separation processes, a driving force has been identified as the integrator (figure 5 and Section 2.2.3). Then the process model equations can be decoupled for integration of simulation and design. Note that the driving force can be calculated from physical equilibrium constants (as in Eqs. 8-12) and the location of the maximum is a function of the intensive variables for the same physical equilibrium constant values. The chemical identities provide an estimate of the chemical equilibrium constants from which the driving force diagram is calculated. Since the design target of minimum energy consumption (or solvent rate, etc.) can only be achieved if the design is based on the maximum driving force, the choice of property models and their accuracy in representing the variations of properties on the intensive variables is very important. In the context of the reverse approach, any number of property models can be used, so it is possible to select the appropriate property model based on their application range. This means that the design and simulation results based on the location of the maximum driving force and the driving force values would be valid for any number of separation problems (chemical systems).For reactive systems (with or without separation), a similar definition of driving force can also be employed to generate a similar diagram as the one showed in Figure 5. Hildebrandt et al. [15] call this driving force-based diagram the attainable region, which forms the basis for reactor design and simulation. Another useful feature of the reverse approach is that it often allows the use of the property models under the same conditions they have been developed and verified. That is, property models are usually validated by model developers through comparison with measured experimental phase equilibrium data not

39 through process simulation results. The driving force diagram involves precisely the same information.

2.3 DERIVATIVE ANALYSIS: A CONNECTION BETWEEN MODEL GENERATORS AND MODEL USERS One final issue, which enters into all property roles, is the question of the derivatives of properties with respect to the intensive variables which illustrates the differences between developers and users. Consider the problem shown in Figure 6. The numerical solution of this simulation/optimization based design problem requires the following derivatives (where 6 is any property and % is any intensive variable):

Figure 6: Simulation & optimization of a PT-flash operation (minimize the amount of heat to be added/removed, keeping the ratio of V/F constant while manipulating the operating temperature and pressure) If the selected property model, i.e., Eqs. 4, 5, 6, have not been tested for the existence of these derivatives, convergence failures are likely to occur. If the derivatives are inconsistent, the Gibbs-Duhem conditions (see chapter 1) will not be satisfied and so the numerical results will not be thermodynamically consistent, even when all other solution criteria may be

40

satisfied. Model developers (generators and implementers) need to recognize this issue and test derivatives for existence and consistency and to provide this information to users. Because the objectives, organizations and styles of property model generators, implementers and users are not usually the same, their interconnections are typically weak. In particular, generators usually seek generalized models to have as large an application range as possible, while they ignore computational speed and derivative issues . On the other hand, property model users commonly implement models having high computational efficiency and as wide spectrum of applications as possible. But they usually do not provide developers with much information on the limitations of their models. Better communication is needed between property model generators and users to deal with these concerns for the most effective impact of models in process-product design applications.

2.4 CONCLUSIONS Three different roles for properties and their corresponding models have been highlighted. Property models can play a much wider role than the traditional service role, for which they are mostly known (or receive credit for). Using them in the advice role can improve the design, widen the search space and increase the efficiency of the solution method. When property models become difficult to use in forward simulation approaches because of complexity, possibilities of using a reverse approach should be investigated. In most design and/or simulation problems, the "exit" conditions are usually known but not actually used in the simulation; they merely verify the simulation results or the design. By using both the known "inlet" and "exit" conditions, property integration can be identified and target values assigned. Many interesting process-product design problems can be solved more easily through this reverse approach. Finally, for property models to play their roles efficiently and for more advanced models to find applications in process-product design, better communication between property model generators, implementers and users is necessary.

REFERENCES 1. R. Gani, J. P. O'Connell, Computers & Chemical Engineering, 25 (2000) 3. 2. J. P. O'Connell, M. Neurock, "Trends in property estimation for process and product design", in: Proceedings of FOCAPD'99, Breckenridge, USA, 1999. 3. J. D. Seader, E. J. Henley, Separation Process Principles, John Wiley & Sons, Inc., New York, USA, 1998. 4. B. Linhoff, J. R. Flower, AIChE J., 24 (1978) 633-642. 5. R. Gani, E. N. Pistikopoulos, Fluid Phase Equilibria, 194-197 (2002) 43-59. 6. M. R. Eden, S. B. Jorgensen, R. Gani, M. M. El-Halwagi, Chemical Engineering & Processing, 43(2004) 595-608. 7. E. Bek-Pedersen, R. Gani, Chemical Engineering & Processing, 43 (2004) 251-262. 8. Y. Xin, B. W. Whiting, Ind & Eng Chem Res, 39 (2000) 2998.

41 9. E. A. Brignole, R. Gani, J. A. Romagnoli, Ind & Eng Chem Process Des & Develop, 24 (1985) 42-48. 10. R. Gani, J.P. O'Connell, Comp. Chem. Eng., 13, (1989) 397-404. 11. J. Gross, G. Sadowski, Ind & Eng Chem Res, 41 (2002) 1084-1093. 12. G. Soave, Chem Eng Sci., 27 (1972) 1197. 13. S. Macchietto, E. H. Chimowitz, T. F. Andersen, L. F. Stutzman, Ind Eng Chem Process Des Develop, 25 (1986) 674-682. 14. J. Perregaard, E. L. Sorensen, Computers & Chemical Engineering, 16S (1992) 247254. 15. D. Hlidebrandt, D. Glasser, C. Crowe, Ind & Eng Chem Res, 29 (1990), 49.

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Part II: Models for Properties

3. Pure component property estimation^ Models & databases Jorge Marerro & Rafiqul Gani 4. Models for liquid phase activity coefficients-UNIFAC Jens Abildskov, Georgios M. Kontogeorgis & Rafiqul Gani 5. Equations of state with emphasis on excess Gibbs energy mixing rules Epaminondas C. Voutsas, Philippos Coutsikos & Georgios M. Kontogeorgis 6. Association models — The CPA equation of State Georgios M. Kontogeorgis 7. Models for polymer solutions Georgios M. Kontogeorgis 8. Property estimation for electrolyte systems Michael L. Pinsky & Kiyoteru Takano 9. Difussion in multieomponent mixtures Alexander Shapiro, Peter K. Davis, J. L. Duda 10. Modeling of phase equilibria in systems with organic solid solutions Joao Coutinho, Jerome Pauly, Jean-LucDaridon 11. An introduction to modeling of gas hydrates Eric Hendriks & Henk Meijer

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45

Chapter 3: Pure Component Property Estimation: Models & Databases Jorge Marrero and Rafiqul Gani 3.1 INTRODUCTION Pure component properties are needed for many process and product design calculations. They may be needed to study the behavior of the product (such as the solubility of drug in water), behavior of a chemical under the conditions of operation of a process (heat of vaporization of a refrigerant or process fluid in a closed cycle), dimensioning of equipment (density of the chemical in a tank), the physical state of the product (melting point and/or boiling point to identify solid, liquid or vapor state) and many more. For the estimation of mixture properties also, the pure component properties are employed in different mixture property models. For example, the well-known SRK equation of state employs the critical properties while an ideal mixing model for liquid density employ only the pure component liquid densities of each chemical species present in the mixture. The objective of this chapter is to provide the reader with a set of pure component property models for a corresponding set of frequently used properties in process-product design. These models have been tested and evaluated against a wide range of chemical species by the authors. A good collection of pure component property models can also be found in many specialized property estimation books, journal papers, commercial software and databases. It is beyond the scope of this chapter to name all the references as well as methods. The calculation methods outlined in each section of this chapter should provide some guidance in terms of the important steps related to estimation of a pure component property.

3.2 MODELS FOR PRIMARY PROPERTIES As described in Chapter 1, primary properties are classified as those, which can usually be determined only from the molecular structural information and have a single unique value. In this chapter, only a set of primary properties that are needed for a wide range of processproduct design calculations are presented through one property estimation approach. This does not mean that the property models used below are the best or have the highest accuracy. These models are, however, frequently used and their details, including the model parameter tables, are readily available. The property model presented below can be classified as an additive method using a group-contribution+ approach. The property estimation methods will be highlighted through the molecular structure of Glycine (CAS No. 000056-40-6). Only the estimated primary and the secondary properties of

46 Glycine are given. When the estimated value for a secondary property for Glycine is not given, it means that not all the dependent properties are available. When experimental data for the property is available, it is also given. The chemical formula, group assignment and 3D molecular structure is given in Figure 1.

Figure 1: Molecular structural details for Glycine 3.2.1

Primary Property Models

All the properties listed below are only functions of the molecular structural information described in terms of first-order, second-order and third-order groups. Note that all molecules must be completely described by first-order groups and may or may not have second- and third-order groups. The estimation steps are as follows: 1. 2. 3. 4.

Identify the groups (first-, and if necessary, second- and third-order groups) Determine how many groups of each type are needed to represent the molecule Retrieve the parameters from the model parameter tables for the property of interest Sum the contributions and use the corresponding property model function

Properties & Models The following property models have been proposed by Marrero and Gani [1,2]. In each case, the summation terms having the following expression Contribution of first-order groups, Sum.Groups.I = £i ni C; for i = 1, NCi Contribution of second-order groups, Sum.Groups.II = Ej rrij Dj for j = 1, NC2 Contribution of third-order groups. Sum.Groups.Ill = Zk Ok Ek for k = 1, NC3

(1) (2) (3)

In the above equations, n;, rrij, Ok are the number of first-, second- and third-order groups of types i, j and k, respectively. Q, Dj and E^ are the contributions for the selected property for first-, second- and third-order groups of types i, j and k, respectively. NCi, NC2 and NC3 are the total numbers of different types of first-, second- and third-order groups representing the molecule. Critical temperature, K Tc = 231.239*Iog(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III)

(4)

47

Glycine: 1028.0 K (experimental: 1028) Critical pressure, bar Pc = l/(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III + 0.108998)2 + 5.9827

(5)

Glycine: = 67.4 bar (experimental: 67.4) Critical volume, cm3/mol Vc = 7.95 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III

(6)

Glycine: = 234.01 cmVmol (experimental: 234.0) Normal melting point, K T m = 147.450*log(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III)

(7)

Glycine: = 535.63 K (experimental: 535.15) Normal boiling point, K Tb = 222.543*log(Sum.Groups.I + Sum.Groups.II + Sum.Groups.III)

(8)

Glycine: = 710.97 K Standard Gibbs free energy of formation. kJ/mol Gf = -34.967 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III

(9)

Glycine: -300.1 kJ/mol (experimental: -300.1) Standard Enthalpv of formation at 298 K, kJ/mol H r = 5.549 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (10) Glycine: -388.49 kJ/mol (experimental: -392.1) Enthalpv of vaporization at 298 K. kJ/mol Hv = 11.733 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (11) Enthalpv of vaporization at TH, kJ/mol HVb - a + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (12) Glycine: = 43.0 kJ/mol Heatoffusionat298K, kJ/mol HfuS = -2.806 + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (13) Glycine: 28.4 kJ/mol (experimental: 28.4)

48 3.3 MODELS FOR SECONDARY PROPERTIES As defined in Chapter 1, secondary properties are those that cannot be explicitly calculated only from structural information and usually require the knowledge of other properties. Most of these models have been derived from the principle of corresponding states, although, a number of empirical correlations also exist. There is available, a wide range of methods for prediction of secondary properties. Many books and handbooks provide methods for calculating these properties. Poling el al. [3] provides a good collection of many of the needed methods. Horvath [4] also provides a large number of methods for primary as well as secondary properties. In this section, a set of pure component properties that have a single value is listed together with a corresponding property estimation method. 3.2.1 Secondary Property Models The following steps may be followed in the estimation of pure component secondary properties. 1. For the secondary property of interest, select an estimation method 2. For the selected estimation method, identify the properties (data) needed to use the model and verify the application range of the method in terms of chemical species (type) 3. Retrieve from a database or predict the necessary properties (to be used as input) 4. Calculate the property through the selected method For the secondary properties listed below, the following properties are needed as input. All these properties are also defined below. For each property, first the generic form of the equation in terms of dependency on other properties/variables is given, followed by the method for calculation, the model equations, and finally, the calculated value for the chemical used as an example. Hfus (kJ/mol). Tb (K), Tc (K), Pc (bar), Vc (cmVmol), SolPar (MPa°5), Ss (MPa°5), nD, Dm (debye), ps(bar), Mw (g/mol), Ws (mg/L) Properties & Models For each property, the name of the property, the representation of the property in terms of its dependence on other properties, the method used and the equations involved are presented. Heat of Vaporization at Th. HVb= f(Tj,, Tc, Pc) Method: Correlation (Equation 7-11.5 in Reid et. al. [5]) tr = Tb/Tc X = 0.37691 - 0.37306*tr+ 0.15075/(Pc*tr2) Y = (0.4343*log(Pc) - 0.69431+ 0.89584*tr)/X

49 Hvb = Tb*0.008314*Y (14) Not recommended for Glycine Pitzer's Acentric Factor, co = f(Tb, Tc, Pc) Method: Lee-Kesler Correlation (2-3.4 in Reid et. al. [5])) / Constantinou & Gani [6] 0 = Tb/Tc a = -log(Pc*0.98692327) - 5.92714 + 6.09648/0 + 1.28862*log(6) - 0.169347*96 P = 15.2518 - 15.6875/9 - 13.4721 *log(9) + 0.43577*96 co = a / p (15) Glycine: 0.747 Lee-Kessler 0.673 Constantinou & Gani [6] Critical Compressibility Factor, Zc = f(Tc, Pc, Vc) Method: Theoretical (Equation) Definition ZC = (PC*VC)/(83.14*TC) (16) Glycine: 0.185 Liquid Volume at Tb, Vb =f(Vc), cm3/mol Method: Tyn and Calus Correlation (3-10.1 in Reid et. al. [5]) Vb = 0.285*Vcli)48 (17) Glycine: 86.5 cm /mol Liquid Volume at 298 K, Vm = f(Tc, Pc, co), cmVmol Method: Rackett Modified Correlation t r =1.0-298.15/T c Zra = 0.29056-0.08775*co W=l+(l-trf28571 Vm = (83.14*T0*Zrallunc)/Pc (18) Refractive Index, no = f(Soli>ar) Method: Correlation [4] nD = (0.48872*SolPar+5.55)/9.55 (19) Glycine: 1.8 Molar Refraction, Rm = f(nn, Vm) Method: Correlation [4] Rm = (((nD)2-l)*Vm*1000)/((nD)2 + 2) (20) Surface Tension at 298 K, a = f(Sol|>ar, Vm), dyne/cm Method: Correlation [4]

50 CT = 0.01707*(Sol Par ) 2 *(V m ) 0333333 (21) Entropy of Fusion. Sfus = f(HfUS, T m ), J/(mol*K) Method: Theoretical (Equation) Definition S rus =1000*H fus /T m

(22)

Glycine: 53.07 J/(mol*K) Closed Flash Temperature. Tfc = f(GCcG, Tb), K Method: Constantinou and Gani [6] Tfc = -2.03*(Sum.Groups.Ic G ) + 0.659*T b + 20.00

(23)

Open Flash Temperature, Tfo = f(GCcG, Tb), K Method: Constantinou and Gani [6] Tf0 = 3.63*(Sum.Groups.Ic G ) + 0.409*T b + 88.43

(24)

Glycine: 414 K Hansen Dispersive Solubility Parameter, 8s - f(GCcG, V m ), MPa 0 5 Method: Constantinou and Gani [6] 8s = (Sum.Groups.IcG)/Vm

(25)

Glycine: 17.74 MPa 0 5 Hansen Polar Solubility Parameter, 8 P = f(GC C o, V m ), MPa 0 ' 5 Method: Constantinou and Gani [6] 8 P = [(Sum.Groups.I C G) 05 ]/V m (26) Glycine: 12.16 MPa 0 5 Hansen Hydrogen Bonding Solubility Parameter, 8 H B = f(GCCG, V m ), MPa 0 5 Method: Constantinou and Gani [6] SUB = [(Sum.Groups.IcG)/V m ]° 5 (27) Glycine: 17.38 MPa 0 5 Dipole Moment. D m = f(8 s , V m ), debye Method: Correlation [4] D m = 0.02670*8 s *(V m )° 5 (28) Dielectric Constant, DH = F(Solpar, no, D m ) Method: Correlation [4] I f n D < 0.001. DK = (n D ) 2

51 Else, DE = (SolPar*0.48871-7.5)/0.22 (29) Henry Constant of a gas in water at 298 K, Hhenr), = (pS(298), Mw, Ws), bar*m3/mol Method: Theoretical (Equation) Definition Hhenry = ps(298)*Mw/Ws

(30)

3.3.1 Secondary Properties modeled as Primary Property For a number of secondary of secondary properties, it is sometimes possible to model them as primary properties. That is, it is possible to predict the property only as a function of the molecular structural information. Recently, Marrero and Gani [2] have developed models for Octanol-water partition coefficients, Solubility of a chemical in water at 298 K, and the Hildebrand solubility parameter. Also, the method of Martin and Young [7] for the measure of toxicity in terms of 50% mortality of Fathead Minnow after 96 hours of exposure has been adapted to the Marrero and Gani method. As in the case of primary properties listed in section 3.2, the prediction of the following properties also follow the same steps Octanol-water partition coefficient (LogKow) LogKow = A + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (31) Glycine: -3.41 (experimental:-3.21) Water Solubility, Ws, Log(mg/L) LogWs = A + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (32) Glycine: 5.41

(experimental: 5.39)

Hildebrand solubility parameter at 298 K, Solpar, M(Pa) Solpar = A + Sum.Groups.I + Sum.Groups.II + Sum.Groups.III (33) Glycine: 23.9 MPa03 Acute Toxicity (96-h LC50) to Fathead Minnow, mol/L -Log(LC50) = Sum.Groups.I (34) Glycine: 2.82

3.4 FUNCTIONAL PROPERTIES As defined in Chapter 1, pure component functional properties are those that depend on the specific value of temperature and/or pressure. Most prediction methods employ a suitable equation of state, the principle of corresponding states or a specially fitted correlation. In this

52

section, a set of functional properties and a corresponding property model is presented. Note that as in secondary properties, functional properties may also require other properties as input data. Note also that many temperature dependent functional properties are available in databases where the coefficients for the correlation of each property and chemical are stored. These correlation functions are discussed in section 3.4 of this chapter. The following steps may be employed in the estimation of functional properties. 1. For the property of interest, select an appropriate property model. 2. Verify the applicability of the model in terms of chemical species as well as the temperature (and/or pressure) limit of the method. 3. Retrieve or estimate the necessary properties to be used as input data 4. Calculate the property of interest at the condition (temperature and/or pressure) of interest using the selected method 3.4.1 Properties & Models For each property, the name of the property, the functional dependence, the units of measure, the method and the model equations are presented. Diffusion coefficient of component at infinite dilution in water, Dab = f(Vb, Tb, T) cm2/s Method: Modified Tyn & Calus Correlation (11-9.5 in Reid et. al. [5]) X = exp(-24.71 + 4209/T + 0.04527T - 0.00003376*T2) for 273.15 < T < 643.15 Dab = 0.01955/[(Vb)0433]*(T/X) (34) See also Chapter 9 for other prediction methods. Liquid Density,CTL= f(Tc, Pc, co, T), g/cm3 Method: Modified Rackett correlation (3-11.10 in Reid et. al. [5]) Zra = 0.29056-0.08775*© Tfimc = 1 + (1-T/Tcf285714 for T/Tc < 0.9 a, = (83.14*Tc*(Zra)Tfunc)/Pc (35) Thermal Conductivity, Tcon = f(Tb, Tc, T, Mw) W/m*K Method: Correlation (10-9.5 in Reid et. al. [5]) Tr = T/Tc Tbr = Tb/Tc Tcon = [l.ll/[(Mw) 05 ]*(3 + 20*(l-Tr)06666)]/[(3 + 20*(l-Tbr)06666)] (36) forT r 300 K, a melting point < 250 K and the Hildebrand solubility parameter between 25 and 27 MPa . 3.5.2

References for Databases

In this section, a few of the well-known databases found on the internet are listed below in Table 1, while references where useful data can be found are given in Table 2. Table 1: List of well-known databases Name API TECH Database CambridgeSoft ChemFinder

Address & Comments Pure component, petroleum characterization, etc. http://www.epcon.com Searchable data and hyperlink index for thousands of compounds - the ideal starting point for internet "data-mining" http://chemfinder.cambridgesoft.com/

56 Table 1 continued CRC Handbook of Chemistry and Physics DECHEMA Chemistry Data Series DETHERM DIPPR Electrolytes GPSA Data Book IUPAC-NIST SDS Knoval Science and Engineering Resources PDB PPDS TAPP The NIST Webbook

Library Network Database (http://www.hbcpnetbase.com/) A 15 volume data collection Comprehensive collection of thermophysical and mixture properties data, includes Dortmund DDB and ELDAR DDB http://www.dechema.de/f-infsys-e.htm7englisch/dbMain.htm Critically evaluated thermophysical data http://www.aiche.org/dippr/vision.htm IVC-SEP database for properties of electrolyte systems www. i vc- sep .kt. dtu.dk/databank GPSA Engineering Data Book —section 23 (physical properties) & 24 (thermodynamic properties) http://www.gasprocessors.com Solubility Data Series http://www.unileoben.ac.at/~eschedor Library Network Database (International Critical Tables, Polymers -Property Database, Handbook of Thermodynamic and Physical Properties of Chemical Compounds, etc.) Protein Data Bank — Processing and distribution of 3-D biological and macromolecular structural data http://pdb.ccdc.cam.ac.uk/pdb/ Physical Properties Data Service http://www.tds-tds.com/fs_ppds.htm Thermochemical and Physical Properties Database http://www.chempute.com/tapp.htm An excellent source of physical and chemical data http://webbook.nist.gov

3.6 CONCLUSIONS Pure component properties are needed in the solution of various types of process-product design problems as well as input in many models for estimation of mixture properties. Usually, they are stored (experimental data) in databases, at least, the single value properties and the temperature dependent functional properties. The problem, however, is that even though the database may contain thousands of compounds, not all data is available for all the listed compounds. Also, in process-product design, new chemicals may be synthesized, which would not be present in the database. For this reason, property models for estimation of pure component properties are needed. In this respect, the chapter provides the reader a

57 quick guide in terms of the most commonly used pure component properties and a representative set of property models. Table 2: References for data Biochemistry & Biotechnology Drugs- Phase diagrams Octanol-water partition coefficients Polymer Data Solubility data Solubility data Water infinite dilution activity coefficients

Thermodynamic data for biochemistry and biotechnology, Hans-Jurgen Hinz, Editor, Springer-Verlag, 1986 J. Phys Chem Res Data, 1999, 28(4), 889-930 J. Phys Chem Res Data, 1989, 18(3) 1111-1229 Polymer DIPPR 881 Project High&Danner, 1992 Barton Handbook, CRC Press 1990 J. Marrero & J. Abildskov, Solubility and realted properties of large complex molecules. Part 1, Chemistry Data Series, Vol XV, DECHEMA, 2003 Voutsas & Tassios, Ind Eng Chem Res, 1996, 35, 1438 supporting material

REFERENCES 1. J. Marrero, R. Gani, Fluid Phase Equilibria, 183-184 (2001) 183. 2. J. Marrero, R. Gani, Industrial Engineering & Chemistry Research, 41 (2002) 6623. 3. B. E. Poling, J. M. Prausnitz, J. P. O'Connell, "The Properties of Gases and Liquids", McGraw-Hill, New York, 5th Edition, 2000. 4. A. L. Horvath, "Molecular Design", Elsevier, Amsterdam, The Netherlands, 1992. 5. R. Reid, J. M. Prausnitz, B. E. Poling, "The Properties of Gases and Liquids", McGraw-Hill, New York, 4th Edition, 1987. 6. L. C. Constantinou, R. Gani, AIChE J, 40 (1994) 1697 7. T. M. Martin, D. M. Young, Chem. Res. ToxicoL, 14 (2001), 1378 8. T. L. Nielsen, J. Abildskov, P. M. Harper, I. Papaeconomou, R. Gani, J. Chem Eng Data, 46 (2001) 1041.

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Computer Aided Property Estimation for Process and Product Design G.M. Kontogeorgis and R. Gani (Editors) © 2004 Elsevier B.V. All rights reserved.

59

Chapter 4: Models for Liquid Phase Activity Coefficients - UNIFAC Jens Abildskov, Georgios M. Kontogeorgis and Rafiqul Gani 4.1 INTRODUCTION Computer-optimized design of the separation processes, e.g. distillation, absorption and extraction, typically encountered in the chemical industry, requires thermodynamic models, which can be applied to a variety of chemicals. The investment (capital costs) for the separation steps is often in the neighborhood of 50-70 % of the total cost, and energy costs for separations can be up to 90 % of the total cost. Measured phase-equilibrium data are typically employed at the later design stages. However, for preliminary design, at the earlier stages and for screening purposes i.e. for testing alternative separation techniques, approximate models, which can be widely applicable, are of interest. Such models can provide rapid estimation of phase equilibria over a wide range of conditions. In addition to the case of the forward property prediction problem (chemical system is known but property values need to be calculated or retrieved), the reverse property prediction problem (property values are known but the chemical system is not known) is also of interest. These are typically problems related to the design of molecules/mixtures/blends such as solvents, process fluids, etc., where the desired properties of the chemical are known but the identity of the chemicals or their mixtures are not. Finding a system with properties close to a specified set also requires rapid predictions of phase equilibria for many mixtures. In this latter case, the use of predicted data is probably the only way in which the problem becomes solvable and forms the basis for computer-aided molecular/mixture design techniques. The need of process-product design techniques for rapid estimation of phase equilibria for a wide variety of systems, conditions and problems has been the driving force behind the development of the UNIFAC and other group contribution models. Statistical thermodynamics has not as yet reached a stage where rigorous solution theories of general applicability are available, although some results of limited practical use have been reported1 (see also chapter 12). Semi-empirical methods are, thus, of interest. Of the most well-known semi-empirical methods useful for predictions of phase equilibria, the group contribution concept is possibly the most widely used. They are usually simple, easy to use and are at least qualitatively correct for many systems where no experimental data is available. Examples of such group contribution methods are the analytical solution of groups, ASOG2 and UNIFAC3, both providing the liquid phase activity coefficients for the compounds present in the solution. Despite their limitations (see section 4.3.3), such group contribution methods have found widespread application in engineering design calculations due to their relative simplicity, their predictive power and analytical form.

60 Several reviews have appeared since the 1980s summarizing the developments of these models4"8. This chapter gives a short overview of the most well-established UNIFAC methods, including the most recent developments and their efficient computer-based use. Table 1: Partial list of different versions of the UNIFAC model. UNIFAC Models UNIFAC-VLE

Special Feature 1 -parameter for group interactions

UNIFAC-LLE

1 -parameter for group interactions

Modified UNIFAC Lyngby

3-parameters for group interactions

Modified Dortmund UNIFAC

3-parameters for group interactions

Linear-UNIFAC

2-parameters for group interactions

Linear Dortmund UNIFAC

2-parameters for group interactions

KT-UNIFAC

lst-order (Linear UNIFAC) & 2ndorder group contribution terms

Remarks - Reference Original version with parameter tables [1977]3'9'" Parameters regressed from LLEdata[1981]'2 Changes in model equations & new parameter tables [1987113 Changes in model equations & new parameter tables [1987]14 Changes in model equations & new parameter tables [1992]15 Changes in model equations & new parameter tables [1992]16 Changes in model equations & new 1 st-order and 2nd-order group parameter tables [2002]10

4.2 THE UNIFAC METHOD Since its development in 19759, a number of different versions of the UNIFAC groupcontribution method for the estimation of liquid phase activity coefficients have been developed. The first UNIFAC method will be called here as the UNIFAC-VLE. One of the latest versions of UNIFAC, the KT-UNIFAC, has been developed by Kang et alw. Table 1 gives a partial list of different versions of UNIFAC that will be discussed in this chapter. The characteristic feature of all UNIFAC methods is that all versions are based on the group contribution approach where the liquid phase activity coefficient of component i in solution with one or more components is calculated as a sum of contributions of all groups representing the mixture (solution). These contributions are divided into two terms - a combinatorial term that accounts for the contributions due to differences in size and shape and are based on the group surface area and volume parameters, and a residual term accounting for the energetic differences, which includes the interaction parameters between the groups. With respect to the intensive variables, the UNIFAC method is dependent only on

61 temperature and composition but not pressure. The combinatorial term is dependent on composition only (in addition to the group surface area and volume parameters) while the residual term depends on the temperature, the composition and the group parameters (surface area, volume and interactions). With the exception of KT-UNIFAC, all UNIFAC methods employ lst-order functional groups to represent the compounds present in the liquid mixture. KT-UNIFAC employs both lst-order and 2nd-order functional groups to represent the compounds present in the liquid mixture. Therefore, the combinatorial and residual contributions have first-order and secondorder terms if 2nd-order groups are present. Two examples of representation of molecules with the UNIFAC groups are given below in Table 2. Note that each group is characterized by a main group, a sub-group, the sub-group surface area (Rf), the sub-group surface volume (Qf) and the main-group/main group interaction parameters anmo, amn,o, amn,o- Each compound therefore is represented by NSG number of sub-groups and a corresponding number of main-groups. A total of NMG maingroups are needed to describe all the compounds in the mixture. Table 2: Representation of molecular structures with different types of groups Ethanol (NSG=3, NMG=2) Sub-Groups: 1 CH3, 1 CH2, 1 OH Main-Groups: CH2, OH 2nd-Order groups: None

2-Butanol (NSG=4, NMG=2, NSOG=1) Sub-Groups: 2CH3, 1 CH2, 1 CH, 1 OH Main-groups: CH2, OH 2nd-Order groups: CHOH

4.2.1 General Model Equations (lst-order) The UNIFAC GC-method for the estimation of the liquid phase activity coefficient of component i in a solution consist of a combinatorial and a residual contribution: lny=lny\+lny":

(1)

The combinatorial term (In y/) includes entropic effects due to molecular size and shape differences while the residual term (In j,R) involves the intermolecular interactions. The different versions of the UNIFAC GC-method differ in their formulation of the combinatorial term and the expression of the temperature dependence of the residual part. Combinatorial Term - In j \ C The combinatorial term is written as17 /«r;;=/-j,+/«j,-^,(/--+/«-! * v Li Li) with

(2)

62 L> = ^ — /_, x,

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