Ammonia Synthisis Loop

Ammonia Synthesis with Alternate Feedstock

Rob Deobald Jeff Hayes Stefan Sigurdson

Department of Chemical Engineering University of Saskatchewan 2006-2007

Executive Summary Saskferco produces ammonia, urea and nitric acid (to make UAN). One future option considered by the company is producing ammonia from a mixture of hydrogen and nitrogen gas received from a petroleum coke gasification facility. This feed stream would contain fewer impurities than the existing process. Our design team was requested to design an ammonia synthesis loop based on the existing process to accommodate this change in the feedstock. The project would involve determining the increase in the extent of conversion achieved across the reactor catalyst beds, as well as examining the excess heat that would be released from having a more pure feedstock. The excess heat from the reaction would be recovered by steam boilers. This steam would be used to power steam turbines that would compress both the incoming feed stream as well as a carbon dioxide gas stream to be used in Saskferco’s urea plant. Before the steam created can be used by the turbines, it must pass through a natural gas-fired superheater so that is superheated upon its arrival at the turbines. Also generated in the superheater will be a lower-pressure steam stream for the urea plant in order to optimize the heat recovery from the superheater. Over a seven-month period, XDGR Engineering Systems has developed an ammonia synthesis process designed to meet the specifications described above. The following report gives a detailed examination of the design process that was followed and the conclusions that were reached in the synthesis of ammonia with an alternate feedstock.

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Table of Contents Nomenclature……………………………………………………………………………...1 1.0 Project Background……………………………………………………………………7 2.0 Project Definition……………………………………………………………………...8 3.0 Ammonia Conversion………………………………………………………………..10 4.0 Steam Superheater…………………………………………………………………...12 4.1 Overview……………………………………………………………………..12 4.2 Heat Requirements…………………………………………………………...14 4.3 Optimum Steam Passes and Number of Tubes………………………………15 4.4 Radiant Section…………………………………………………………........16 4.5 Shield Bank Section…………………………………………….....................19 4.6 Finned Bank Section…………………………………………………………20 4.7 Emission Stack……………………………………………………………….22 4.8 Construction Material………………………………………………………..24 5.0 Heat Exchangers……………………………………………………………………..26 5.1 Overview……………………………………………………………………..26 5.2 Gas/Gas Heat Exchanger…………………………………………………….26 5.3 Waste Heat Exchangers ……………………………………………………..27 5.4 Heat Exchange Summary…………………………………………………….28 6.0 Compressors and Turbines…………………………………………………………...29 6.1 Compressors………………………………………………………………….29 6.1.1 Synthesis Gas Compressor…………………………………………29 6.1.2 CO2 Compressor…………………………………………………...30 6.2 Steam Turbines………………………………………………………………31 6.3 Compressor and Turbine Summary………………………………………….32 7.0 Economics……………………………………………………………………………34 7.1 Overview……………………………………………………………………..34 7.2 Compressor Pricing………………………………..…………………………35 7.3 Steam Turbine Pricing……………………………………………………….35 7.4 Heat Exchange Equipment Pricing…………………………………………..36 7.5 Feasibility of Firing the Superheater with Hydrogen………………………..37 7.6 Ammonia Convertor Pricing………………………………………………....38 7.7 Stream Cost Analysis………………………………………………………...39 7.8 Economic Summary………………………………………………………….40 8.0 Conclusion…………………………………………………………………………...41 ii

References………………………………………………………………………………..44 Acknowledgements………………………………………………………………………45 Appendix A: Process Flow Diagram…………………………………………………….46 A.1 Process Flow Diagram and Stream Compositions…………………………..47 Appendix B: Ammonia Conversion……………………………………………………...50 B.1 Determining the Feed Requirement to Produce 1900 Tonnes of Ammonia/day…………………………………………………………………….51 B.2 Deriving Equations to Interpret Stream Composition Changes……………..53 B.3 Estimating the Equilibrium Conversion of the Ammonia Synthesis Reaction………………………………………………………………………….56 B.4 Reactor Composition Iterative Procedure for 8R1 and 8R2………………...60 B.5 Energy Balance Iteration Procedure for 8R1 and 8R2………………………70 Appendix C: Steam Superheater…………………………………………………………74 C.1 Calculating the Net Heating Value of the Natural Gas Stream……………...75 C.2 Heating Requirements of the Steam Streams………………………………..77 C.3 Calculations for the Radiant Section………………………………………...79 C.4 Determining the Optimum Number of Superheated Steam Passes………….81 C.5 Determining the Optimum Number of Urea Steam Passes………………….82 C.6 Calculations for the Shield Bank Section……………………………………83 C.7 Finned Bank Section Calculations (Vaporization of Urea Water Stream)…..87 C.8 Finned Bank Section Calculations (Heating of Liquid Urea Stream).………91 C.9 Calculating the Minimum Allowable Tube Wall Thickness………………...95 C.10 Calculating the Required Stack Dimensions……………………………….97 C.11 Determining the Required Number of Tubes in the Radiant Section…….100 C.12 Summary of Superheater Results…………………………………………102 Appendix D: Heat Exchangers………………………………………………………….109 D.1 Heat Exchanger Specifications…………………………………………….110 Appendix E: Compressors and Turbines……………………………………………….111 E.1 Compressor and Turbine Specifications……………………………………112 E.2 Synthesis Gas Compressor Pressure Safety Valve Design…………………113 E.3 CO2 Compressor Pressure Safety Valve Design…………………………...115 Appendix F: Economics………………………………………………………………...117 F.1 Determining the Bare Module Cost of the Required Equipment…………..119 F.2 The Feasibility of Firing the Super Heater using Hydrogen………………..125 F.3 Stream Cost Analysis……………………………………………………….126

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List of Tables Table A.1.1: Ammonia synthesis loop streams………………………………………….47 Table A.1.2: Water and steam system streams…………………………………………..47 Table A.1.3: CO2 compressor streams…………………………………………………...48 Table A.1.4: Superheater fuel and flue gas streams……………………………………...48 Table B.3.1: Conversion of hydrogen as a function of temperature……………………..58 Table B.4.1: Stream 1 concentrations entering 8R1. ……………………………………64 Table B.4.2: Synthesis loop composition at zero conversion. …………………………..65 Table B.4.3: Stream 2 exiting 8R1. ……………………………………………………...66 Table B.4.4: Stream 3 exiting 8R2. ……………………………………………………...67 Table B.4.5: The recycle stream.………………………………………………………...68 Table B.4.6: Summary of final stream compositions and flow rates…………………….69 Table B.5.1: Example stream compositions for an equilibrium temperature of 750 K for reactor 8R1 and an equilibrium temperature of 720K for reactor 8R1…………………………………………………………………………72 Table C.1.1: Calculating the average molecular weight…………………………………75 Table C.1.2: Calculating the average lower heating value………………………………75 Table C.1.3: Calculating the air requirement for combustion…………………………...75 Table D.1.1: Heat exchanger specifications……………………………………………110 Table D.1.2: Heat exchanger inlet and outlet specifications…………………………...110 Table E.1.1: Summary of compressor/turbine information…………………………….112 Table E.1.2: Stream compositions as H/N ratio varies…………………………………112 Table F.1.1: Summary of the cost of each piece of process equipment………………...118 Table F.1.2: Feed stream costs………………………………………………………….118 Table F.1.3: Product stream prices……………………………………………………..118

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List of Figures Figure 3.1: Ammonia synthesis loop…………………………………………………….10 Figure 4.1: Steam superheater schematic………………………………………………...13 Figure 6.1: Synthesis gas compressor and turbine system……………………………….30 Figure 6.2: Carbon dioxide compressor and turbine system……………………………..31 Figure A.1.1: Process flow diagram……………………………………………………..49 Figure B.3.1: Ammonia synthesis equilibrium at various stream compositions………...59 Figure C.12.1: Heat available from the combustion of a 19,700 Btu/lb (LHV) refinery gas.…..……………………..…………………………………………...104 Figure C.12.2: Distribution of radiant heat transfer rate around the tubes, dependent upon coil arrangement and firing mode…………………………………105 Figure C.12.3: Determining the duty-split between radiant and convection sections based on the bridgewall temperature...………………..………………..106 Figure C.12.4: Finding the dimensionless parameter J to determine the heat transfer coefficients on the flue-gas side of serrated fins.…..…………………...107 Figure C.12.5: Determining the fin efficiency based on the convection film coefficient as well as the fin design & thermal conductivity.………..…108

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Nomenclature A

Area (m2)

AC

Cross-sectional area of schedule 40 piping (m2)

AFB,LIQ

Convective heat transfer surface, liquid heating phase (m2)

AFB,VAP

Convective heat transfer surface, vaporization phase (m2)

AFREE

Finned bank free area (m2)

Ai

Inner surface area per tube length (ft2/ft)

Ao

Outer surface area per tube length (ft2/ft)

AR

Required radiant surface area (m2)

ARE

Air requirement for 20% excess air (kg air/kg fuel)

ARm

Air requirement (kg air/100kmol fuel)

ARw

Air requirement (kg air/kg fuel)

ASB

Shield bank surface area (m2)

ASS

Surface area required for the superheated steam (m2)

At

Finned tube surface area per unit tube length (ft2/ft)

AUS

Surface area required for the urea steam (m2)

AVT

Vertical tube radiant surface (m2)

BWT

Bridgewall temperature (ºC)

c

Catalyst cost ($/kg)

CBM

Bare module cost ($)

CP

Average fluid heat capacity (BTU/lb·°F)

CP1

Average heat capacity of synthesis stream in reactor 8R1 (kJ/kmol·K)

CP2

Average heat capacity of synthesis stream in reactor 8R2 (kJ/kmol·K)

CPur

Purchased equipment cost ($)

D

Required diameter of the stack (m)

DG

Draft gain (inH2O)

DGC

Convection section draft gain (inH2O)

DL

Damper loss

do

Outer diameter of each tube (in)

Do

Orifice diameter (m)

DUA

Draft under arch 1

ef

Fin efficiency

ETL

Effective vertical tube length (m)

F

Correction factor specific to the type of tubes used

FAR

Molecular flow rate of argon gas stream (kmol/day)

FBL

Finned bank loss

FBM

Base bare module factor

FBMa

Actual bare module factor

FC

Mass flow rate of fuel consumed (kg/h)

fc/c

Factor for conductive/convective effects (0.85)

FG

Flue gas mass flow rate (kg/h)

FGT

Flue gas temperature exiting the convection section (ºC)

fh

Fin height (in)

FH2

Molecular flow rate of hydrogen gas stream (kmol/day)

FIN

Inlet molar flow rate (kmol/s)

Flwf

Lost work due to friction (W/(kg/s))

FM

Material factor

FNH3

Molecular flow rate of ammonia gas stream (kmol/day)

FP

Pressure factor

FSS

Superheated steam mass flow rate (kg/s)

FSS’’

Superheated steam mass velocity (kg/s⋅m2)

ft

Fin thickness (in)

FUS’’

Urea steam mass velocity (kg/s⋅m2)

FUS

Urea steam mass flow rate (kg/s)

fv

Factor for local variation in heat flux (1.25)

g

Acceleration due to gravity (9.81 m/s2)

G

Fluid mass velocity (kg/s⋅m2)

h

Height above datum (m)

H

Required stack height (m)

%H

Percent heat extraction from the superheater

HA,BWT

Heat made available based on the bridgewall temperature (kJ/kg)

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HA,FGT

Heat available based on the flue gas temperature exiting the convection section (kJ/kg)

HA,SB

Heat made available based on the flue gas temperature leaving the shield bank (kJ/kg).

hC

Convection film heat transfer coefficient (W/m2·K)

hi

In tube heat transfer coefficient (W/m2·K)

ho

Total convection coefficient (W/m2·K)

(ho)eff

Effective total convection heat transfer coefficient (W/m2·K)

ΔHR1

Available heat of reaction per mole of hydrogen reacted in reactor 8R1 (MJ/kmol)

ΔHR2

Available heat of reaction per mole of hydrogen reacted in reactor 8R2 (MJ/kmol)

hRG

Gas radiation heat transfer coefficient (W/m2·K)

HT

Total heat fired by the superheater (GJ/h)

hw

Tube wall heat transfer coefficient (W/m2·K)

I.D.

Inner diameter (m)

J

Dimensionless parameter applied to determine the flue gas heat transfer coefficient for serrated fins

k

Average fluid thermal conductivity (BTU/ft·h·°F)

KM

Tube wall thermal conductivity (BTU·in/ft2·h·°F)

L

Horizontal tube length (ft)

LHV

Lower heating value of the natural gas (kJ/100kmol)

LMTD

Log-mean temperature difference (°C)

LS

Section height (ft)

LVessel

Length/Height of Vessel (m)

m&

Mass flow rate (kg/s)

~ m

Molar flow rate (kmol/s)

mAr

Mass flow rate of argon (tonnes/day)

mH2

Mass flow rate of hydrogen (tonnes/day)

mNH3

Mass flow rate of ammonia (tonnes/day)

mTOTAL

Total mass flow rate(tonnes/day)

3

MW

Molecular weight (kg/kmol)

MWave

Average molecular weight (kg/kmol)

nAr

Molar flow rate of argon (kmol/day)

nH2

Molar flow rate of hydrogen (kmol/day)

nNH3

Molar flow rate of ammonia (kmol/day)

nSS

Number of superheated steam passes

nTOTAL

Total molar flow rate(kmol/day)

nUS

Number of urea steam passes

N

Number of tubes per row

Nf

Number of fins per inch of tube

NHV

Net heating value of the natural gas (kJ/kg)

NR

Number of tube rows

NSE

Net stack effect (inH2O/ft)

NSS

Number of vertically aligned superheated steam tubes in the radiant section

NT

Number of tubes per row

NUS

Number of vertically aligned urea steam tubes in the radiant section

P

Pressure (Pa)

ΔP

Change in pressure (Pa)

Patm

Atmospheric pressure (psia)

PSS

Superheated steam operating pressure (psia)

Q

Volumetric flow rate (m3/s)

QC

Heat transfer in the convective section (GJ/h)

QFB, LIQ

Convection section heat absorption, liquid water heating phase (GJ/h)

QFB, VAP

Convection section heat absorption, vaporization phase (GJ/h)

QMAX’’

Maximum local radiant heat flux (BTU/h·ft2)

QR

Heat transfer in the radiant section (GJ/h)

QR’’

Average radiant heat flux (BTU/h·ft2)

QSB

Heat absorption in the shield bank section (W)

QSS

Heat absorbed by the superheated steam (GJ/h)

QT

Total heat duty for the superheater (GJ/h)

4

QUS

Heat absorbed by the urea steam (GJ/h)

r

Ratio of maximum radiant heat flux to average radiant heat flux (1.93)

%R

Predicted radiant heat losses

Re

Flue gas Reynolds number

Rt

Total heat transfer resistance (m2·K/W)

s

Spacing between tube centers (in)

S

Design stress, 90% of the yield strength for austenitic steel (psia)

SBL

Shield bank loss

SD

Required stack draft (inH2O)

SD’

Stack draft gain per foot of stack (inH2O/ft)

SEL

Stack entrance loss

SFA

Shield-bank free area (m2)

SFL

Stack frictional loss per foot (inH2O/ft)

SOL

Stack outlet loss

t

Tube wall thickness (in)

T

Temperature (K)

ΔT

Temperature Change (K)

Ta

Ambient temperature (°R)

TCD

Tube-circle diameter in the radiant section (m)

TFG

Total flue gas (kg flue gas/kg fuel)

TFG

Temperature of flue gas (°C)

(TFG)AVE

Average flue gas temperature (°F)

(TFG)IN

Inlet flue gas temperature

(TFG)OUT

Outlet flue gas temperature

Tga

Flue gas temperature (°R)

TM

Tube metal temperature (K)

tMARGIN

Margin of tube wall allowance against corrosion and creep (cm)

tMIN

Minimum allowable tube thickness (cm)

TRTW

Radiant tube wall temperature (ºC)

(TSS)OUT

Outlet superheated steam temperature (ºF)

TUS

Temperature of urea steam (°C) 5

(TUS)IN

Inlet urea water temperature (ºF)

(TUS)OUT

Outlet urea steam temperature (ºF)

tw

Tube wall thickness (in)

u

Bulk fluid viscosity (lb/ft·h)

U

Overall heat transfer coefficient (W/m2·K)

V

Velocity (m/s)

V2

Exit velocity (m/s)

Vg

Specific volume of the flue gas at the point in question (ft3/lb)

VH

Velocity head (inH2O)

wS

Shaft power (W)

X

Hydrogen gas conversion across the ammonia reactor

X8R1

Extent of conversion of hydrogen across reactor 8R1

X8R2

Extent of conversion of hydrogen across reactor 8R2

(yAr)F

Mole fraction of argon in the feed stream

(yH2)F

Mole fraction of hydrogen in the feed stream

(yNH3)F

Mole fraction of ammonia in the feed stream

(yAr)P

Mole fraction of argon in the product stream

(yH2)P

Mole fraction of hydrogen in the product stream

(yNH3)P

Mole fraction of ammonia in the product stream

(yAr)R

Mole fraction of argon in the recycle stream

(yH2)R

Mole fraction of hydrogen in the recycle stream

(yNH3)R

Mole fraction of ammonia in the recycle stream

εi

Efficiency (%)

ρ

Density (kg/m3)

ρ~

Molar density (kmol/m3)

ρB

Catalyst bulk density (kg/m3)

ρSS

Density of superheated steam (kg/m3)

ρUS

Density of urea steam (kg/m3)

μ ~ %

Calculated efficiency Mole Percent 6

1.0

Project Background Saskferco is one of the largest producers of nitrogen fertilizers in North America.

Their facility is located in Belle Plaine, Saskatchewan and has been operating since 1992. Originally they produced 1500 tonnes per day of anhydrous ammonia, 77% of which was used to produce 2000 tonnes of granular urea. Their current anhydrous ammonia synthesis process was upgraded in 1997 to increase the production of ammonia to 1900 tonnes per day, which increased production of granular urea to 2900 tonnes per day. They have also added the production of a small nitric acid plant, for the production of urea ammonium nitrate, in both 28% and 32% solutions. The existing feed to their ammonia synthesis loop has a composition of approximately 73.43 mol% hydrogen gas, 24.92 mol% nitrogen gas, 1.26 mol% methane, and 0.39 mol% argon and helium. Hydrogen for this reaction is prepared through the steam reforming of methane. The synthesis gas is compressed to a pressure of 190 bars, and mixed with any unreacted gas that left the two ammonia convertors in the synthesis loop. After compression, the synthesis gas is put through the reactors, and cooled off with large waste heat steam boilers after each reactor. The gas then enters the separation system, where the ammonia is separated from the hydrogen and nitrogen reactants. A fraction of this recycle stream is purged, to keep impurities from building up in the system, and then it is sent back to the compressors to be mixed with the fresh feed gas.

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2.0

Project Definition In the future, it may be possible for Saskferco to purchase synthesis gas for the

production of ammonia from a new petroleum coke gasification facility being built nearby. One option for this new feed that is being considered is constructing a second ammonia synthesis loop, producing an additional 1900 tonnes per day of ammonia. The new feed for the process would consist of 74.25 mol% hydrogen gas, 24.75 mol% nitrogen gas, and only 1 mol% argon. Because many of the inert components in the original feed stream are recycled through the synthesis loop, the feed currently enters the first ammonia convertor, 8R1, containing approximately 11 mol% methane, helium, and argon. These impurities lower the partial pressure of hydrogen, which lowers the overall conversion of the reactor. With the new feed stream, only approximately 3 mol% of inert argon enters the first ammonia convertor, resulting in a higher partial pressure of the reactants, which results in higher conversions and larger temperature rises across the catalytic reactor beds. There are three challenges to redesigning a synthesis loop to use the new feedstock. The first is analyzing the kinetics of the ammonia synthesis reaction and determining the new conversions now that the impurities have been reduced. The second is to design a steam superheater that will convert the waste heat recovered from the ammonia reactors into high pressure steam. The final design challenge is to take the high pressure steam and use it to power the compressors that bring the feed up to the pressure required for the reaction. Determining the behaviour of the ammonia synthesis reaction was accomplished by finding an equation for the conversion of hydrogen as a function of equilibrium temperature based on ammonia synthesis data from literature. Once we had this equation, it was possible to calculate the composition of the streams leaving both reactors

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2.0

Project Definition

8R1, and 8R2; however, to do so we must use two iteration loops. The first assumes the outlet temperatures of the two reactors, and calculates the composition of the product streams, and must be iterated until these compositions no longer change due to changes in the recycle stream. The second iteration is an energy balance over the reactors, and must be iterated until the outlet temperatures calculated are the same as those we assumed when calculating the outlet compositions. To complete these calculations, some assumptions had to be made about the separation system. A detailed design of the ammonia separator units is beyond the scope of our project. We remove heat of reaction from the system through waste heat boilers positioned after each of the reactors. This heat boils water making high pressure (120 bar) saturated steam. To make this steam useful, we must send it to a natural gas-fired superheater that brings the temperature up to 510oC. Excess energy generated by the superheater is also used to generate 23 bar saturated steam at a rate of 25 tonnes/h for use in a Saskferco urea plant. Enough superheated steam is generated by the superheater to power two compressors. The first compressor takes an almost pure stream of carbon dioxide at 5 bar, and brings the pressure up to 150 bar at a rate of 95 tonnes/h. The second compressor brings the synthesis gas feed at 50 bar up to 190 bar, and mixes it with the recycle gas from the reactors. A turbine is associated with each compressor, which takes the 120 bar superheated steam, and exhausts it at a vacuum pressure of 30 kPa.

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3.0

Ammonia Conversion Feed enters the ammonia synthesis loop straight from the synthesis gas

compressor which is discussed in Section 6.1, where it has been mixed with the recycle gas from the ammonia separator and been compressed to 190 bar. The gas then passes through the gas/gas exchanger that heats up the synthesis gas feed with the hot gas leaving the system and heading towards the separator. The feed then enters the first ammonia convertor, 8R1. This reactor has two catalyst beds, and a small internal heat exchanger with a heat exchange area of 239.6 m2. The first bed has an effective catalyst volume of 21.55 m3 and the second having a volume of 29.70 m3. The second convertor, 8R2, has a single catalyst bed with a volume of 46.70 m3. Both reactors use an aluminasupported iron catalyst promoted with alkali and various other metal oxides.

Figure 3.3: Ammonia synthesis loop

The ammonia synthesis reaction, shown as equation B.1.1, is highly exothermic. This leads to a significant temperature rise across both reactors. As is shown in Appendix B, having specified the inlet temperature to 8R1 as 300oC, the conversion, 10

3.0

Ammonia Conversion

outlet temperature and outlet composition was able to be calculated. The conversion of hydrogen was determined to be 32.8%, resulting in an exit temperature of 507.8oC. The gas is cooled in the waste heat boiler, 8E1, directly following the first reactor. This exchanger cools the synthesis gas down to 400oC by creating high pressure saturated steam. It is discussed in detail in Section 5.0, and in Appendix E. Conversion across 8R2 was determined to be an additional 11.8%, resulting in an outlet synthesis gas temperature of 473.0oC. Concentrations in each stream are summarized in Table B.4.6. Data for modeling the ammonia synthesis reaction was found in the publication Catalytic Ammonia Synthesis by J.R. Jennings1. In this publication, equilibrium data was given for a feed stream identical to the new feed stream being implemented. This equilibrium data was converted into the form of total hydrogen conversion at equilibrium as a function of temperature. Because the reaction will not reach equilibrium before leaving each reactor, an approach to equilibrium of 10°C was used to approximate the actual hydrogen conversion achieved. The temperatures of the synthesis gas leaving each reactor were approximated from data given for the current temperature rise across each reactor. Because the same reactors will be used for the new feedstock, a reaction enthalpy was found per hydrogen gas converted and was applied for the new synthesis stream. These heats of reaction estimated in Appendix B.5 to be approximately 36.6 MJ/kmol of hydrogen converted under the conditions present in 8R1, and 38.2 MJ/kmol of hydrogen under the conditions present in 8R2.

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4.0 4.1

Steam Superheater Overview: The purpose of the steam superheater is to heat the saturated steam leaving the

waste heat boilers at an approximate pressure of 120 bar. After heating the waste heat boiler steam, the resulting superheated steam would be split between the synthesis gas turbine and the CO2 turbine to run their corresponding compressors. The temperature of saturated steam at 120 bar was determined from the Peng-Robinson thermodynamic model in the HYSYS program to be 323.7°C. The temperature of the superheated steam was recommended by our supervisor to be 510°C. In order for the superheated steam to generate enough power for the two turbines at 510°C temperature and 120 bar pressure, it was determined that the mass flow rate of the steam must be 90.65×103 kg/h. To heat this amount of steam, a superheater was designed to run off of natural gas. The combustion of this gas would heat the piping of the steam stream and would therefore heat the steam within. In order to reach the desired superheated steam temperature, the waste heat boiler steam would have to be heated in the radiant section of the superheater. In this section, entirely radiant heat transfer is assumed between the steam and the radiant walls of the superheater. The tubes in this section would be bare with no fins would encircle the combustion flame in the radiant section in the form of a vertical radiant coil. Once the flue gas from the radiant section combustion leaves the radiant section, much of its heat will be unrecovered by the superheated steam. However, by this point, the flue gas will not be hot enough to be used by the superheated steam. To take advantage of this available flue gas heat, a second stream of steam could potentially be heated. This stream was decided to be a stream 23 bar saturated steam to be used by Saskferco’s urea plant. The water used to make this steam was specified to reach the

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4.0

Steam Superheater

superheater as a liquid at a pressure of 23 bar and a temperature of 131.8°C. This water would be heated into the form of saturated steam at 23 bar, giving it a temperature of 220.1°C. The water would be heated by convective heat transfer by the flue gas and partially by radiant heat transfer from the radiant section. The water would flow in cross flow with respect to the flue gas flowing up towards the emission stack. The tubes in the finned bank section would be equipped with circular fins to improve the process of convective heat transfer. The urea water stream would flow down the finned bank section before reaching the shield bank section. In this section, the tubes are bare, and the heat transfer in this section is assumed to be a combination of convective and radiant heat transfer. The urea steam would then briefly enter the radiant section in order to optimize the available heat within the section before being sent to the urea plant.

Figure 4.1: Steam superheater schematic

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4.0

Steam Superheater Once the desired heat has been removed, the flue gas exits the superheater to the

atmosphere through an emission stack. The stack should be tall enough to induce a negative draft within the radiant section. This allows for safe observation of the natural gas combustion through a peep door. The stack should also have a large enough diameter so that the flue gas exits at a desired mass velocity. Shown on the previous page is a diagram illustrating the approximate layout and design of the superheater. This type of furnace is classified as being vertical-cylindrical with a cross flow convection section. The superheater was designed based on the published recommendations of Herbert Berman found in the Journal of Chemical Engineering2. The calculations performed for the superheater design can be found in Appendix C. These calculations are placed in Appendix C in the order by which they were performed. The most crucial assumption that was used in the design of the superheater was assuming a negligible drop in the steam pressures. Because many of the equations and correlations given in Berman’s publication were performed in empirical units, the majority of the calculations were performed in these units. All of the significant final results have been converted to SI units and have been communicated as such within this section. A summary of the important results determined from the superheater analysis can be found in section 12 of Appendix C.

4.2

Heating Requirements: The natural gas stream used to fuel the superheater was specified to have the

following molar composition: 92% methane, 5% ethane, and 3% propane. For this gas stream, the net heating value was estimated to be 49.51 MJ/kg. The net heating value

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4.0

Steam Superheater

was found based on the lower heating values of each of the components. This net heating value also assumed complete combustion of the natural gas stream. To ensure enough air would be made available for complete combustion, it was specified 20% excess air by mass would be made available. This was found to result in 21.33 kg of flue gas per kilogram of natural gas combusted. Based on implementing the Peng-Robinson thermodynamic model in the HYSYS program, the heating requirement to produce the urea steam was found to be 57.61 GJ/h. As well, the heating requirement for the superheated steam was found to be 50.64 GJ/h. This results in the total heating duty of the superheater to be 108.25 GJ/h. The flue gas was specified to be leaving the convection section at a temperature of 215.1°C. Based on heat available at this temperature from Figure C1 of Appendix C, the heating efficiency of the superheater was found to be 87.85%. From this, it was determined that 2433 kg/h of natural gas would be required to meet the heating demands of the furnace, and 51.9 tonnes/h of flue gas would be released into the atmosphere. The natural gas stream was assumed to not contain particulates or impurities. Based on this assumption, the flue gas would be comprised entirely of CO2, H2O, N2 and O2 gas. The molar composition of the emitted flue gas was determined to be 72.8% N2, 15.7% H2O, 8.27% CO2 and 3.23% O2. All sample calculations pertaining to the heating requirements of the superheater can be found in sections 1 & 2 of Appendix C.

4.3

Optimum Steam Passes and Number of Tubes: Before the steam streams could be passed through the superheater, the optimum

number of passes for each of the two steam streams had to be determined. As was found

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4.0

Steam Superheater

in Berman’s publication2, the optimum mass velocity for superheated steam in a superheated steam generator should be between 146.5 and 366.2 kg/s·m2. It was also specified that the optimum linear velocity of the steam exiting the superheater should be 10 m/s. For the given exiting density of the steam, the optimum mass velocity of the superheated steam sold to the turbines was found to be 365.8 kg/s·m2. Because schedule 40 piping was used for all of the piping within the superheater, the cross-sectional area could be determined (8.21×10-3 m2). This provided enough information to determine that the optimum number of superheated steam passes would be 8.38 for the superheater. Rounding up, this gave 9 actual superheated steam passes within the furnace. Sample calculations for this part of the analysis can be found in section 4 of Appendix C. The optimum mass velocity for the generating saturated steam was found to be between 488.2 and 732.4 kg/s·m2. Using a mass velocity of 500 kg/s·m2 for the exiting 23 bar saturated steam for the urea plant, and given the cross-sectional area for schedule 40 piping, the optimum number of urea steam passes was found to be 1.69. Because the number of passes of saturated steam through the superheater has to be a whole number, the mass velocity for the urea steam can’t fall within the optimum range for saturated steam. It was decided that it was better to have two steam passes instead of one so that some steam would still be sent to the urea plant in case one of the passes would fail. Sample calculations for this part of the analysis can be found in section 5 of Appendix C.

4.4

Radiant Section: As previously stated, entirely radiant heat transfer is assumed to occur in the

radiant section. As was recommended by Berman2, the temperature of the radiant tube

16

4.0

Steam Superheater

walls was designed to be 75ºF (41.7ºC) hotter than the exit temperature of the superheated steam. This gave a radiant tube temperature of 552ºC. Based on this tubewall temperature, the bridgewall temperature was found from Figure C3 of Appendix C to be 927ºC. By determining the ratio of the heat available at the bridgewall and radiant tube temperatures, the ratio of the heat transfer in the radiant section to the total heat transfer in the superheater should have the same value. From this analysis, the heat transfer in the radiant section was determined to be 63.60 GJ/h. Because the total heat transfer to the steam streams was previously determined to be 108.24 GJ/h, this means the heat transferred in the radiant section would be 44.64 GJ/h. Because this value is less than the total heat requirement for the saturated urea steam (57.61 GJ/h), this means that the urea steam would have to pass through part of the radiant section in order to be completely saturated steam once sent to the urea plant. When determining the required surface area of tubing required for absorbing all of the available heat in the radiant section, he first row of the shield bank section must be acknowledged. This row is assumed to absorb its share of the radiant heat released from the furnace walls due to its vicinity to the radiant section. The total surface area of the bottom row of the shield bank section was found to be 28.0m2. Given an assumed radiant heat flux of 0.125 GJ/h·m2 (average expected heat flux for a steam superheater) throughout the entire radiant section, the required surface area to absorb the total radiant heat transfer was found to be 509.1m2. This means that the total surface area of the vertical tubes within the radiant section must be equal to 481.1 m2. Calculations pertaining to this analysis can be found in section 3 of Appendix C.

17

4.0

Steam Superheater Based on the surface area required in the radiant section, the number of vertical

tubes required for both the superheated steam and the urea steam would have to be determined. Based on the heating requirement of each type of stream, the distribution of the vertical tube surface area in the radiant section was found to be 405.4 m2 for the superheated steam and 75.7 m2 for the saturated urea steam. The number of vertical tubes for each steam stream must then be of the same ratio as the surface areas for each steam stream. Additionally, the number of tubes for each steam stream must be divisible by the number of passes for each stream. In other words, the number of superheated steam vertical tubes must be divisional by 9 and the number of urea steam vertical tubes must be divisible by 2. When 108 vertical tubes for the superheated steam were specified, it was found that approximately 20 vertical tubes for the urea steam were required. This gives a total of 128 vertically aligned bare tubes within the radiant section. Based on the number of superheated steam tubes and the required surface area for the superheated steam, it was determined that the required equivalent tube length for each tube in the coil would be 10.45 m. When this equivalent tube length was applied to the urea steam in the radiant section, it was found that the surface area for the urea steam would be 75.1 m2. This means that the surface area exposed for the urea steam would be 0.6 m2 less than initially determined. This wasn’t considered a problem as this deficit in urea steam surface area would be made up for within the convection section calculations. Given a spacing of 8 inches between the vertical tubes, the approximate diameter of the radiant tube circle was found to be 8.28 m. The ratio between the equivalent tube lengths with respect to the tube circle diameter would then be 1.26. Design calculations outlined within this paragraph can be found in section 11 of Appendix C.

18

4.0 4.5

Steam Superheater Shield Bank Section: In the shield bank of the convection section, it was assumed that heat would be

transferred to the urea steam both by convective heat transfer and by radiant heat transfer. It was decided that the shield bank section would consist of 3 rows, each having 16 bare tubes 4.88 meters in length. To determine the temperature of the flue gas exiting the shield bank of the convection section, an iterative technique was used starting with an initial guess for the outlet temperature. What was known was that the temperature of the urea steam would be constant during this phase (220.1°C). The inlet temperature of the flue gas was known because it would be the same as the bridgewall temperature (926.7°C). The final value of the flue gas outlet temperature was found to be 765.6°C. The log-mean temperature difference between the flue gas and the steam was found to be 622.6°C based on these temperatures. To find the heat transfer coefficient outside of the tubes, empirical equations given by Berman2 were used to find the coefficients of both convective heat transfer and radiant heat transfer. These results were then combined by equation C.6.4 to determine the overall heat transfer coefficient outside of the shield bank tubes. The total convection coefficient outside the tubes was found to be 17.93 W/m2·K. Based on the average thermodynamic properties of the two-phase water within the shield bank section, the convection coefficient within the tube was determined to be 963.2 W/m2·K. Based on the thermal conductivity of the tube wall itself, the tube convection coefficient was found to be 2396 W/m2·K. To determine the overall heat transfer coefficient (U), a summation of the thermal resistances was found, and the reciprocal of the total thermal resistance was taken as U. Using this value, the log-mean

19

4.0

Steam Superheater

temperature difference, and the total surface area exposed in the section, the total amount of heat absorbed in this section was determined to be 3.28 GJ/h. Using equation C.6.11, a ratio of the heat absorbed before and after the shield bank was equated to the ratio of the heat made available before and after the shield bank to determine the heat made available based on the assumed outlet flue gas temperature. The heat made available after the shield bank was determined to be 12,140 BTU/lb. This value was then plotted on Figure C1 to determine the outlet flue gas temperature to see if it was the same as was initially assumed. If this weren’t the case, the steps outline in this paragraph would be repeated until the determined outlet flue gas temperatures converged to be same value. Once this temperature converged, the shield bank calculations were complete. The iterative process used can be found in section 6 of Appendix C.

4.6

Finned Bank Section: The finned bank section was divided into two separate sets of calculations: one

for set the feed water is being heated, the other for when the feed water begins to be vaporized. It was determined using the HYSYS simulation program that 26.21 GJ/h would be absorbed to vaporize water within the finned bank section, and 7.81 GJ/h would be needed to heat the water after it initially enter the furnace. It was decided that rows consisting of 16 finned tubes each 4.88 meters in length would be used in the design. The number of rows required would be determined from the calculation process. The fins that would be used in our design would be circular fins. They would be spaced 3 per inch (1.2 fins per cm), ¾ inches high (1.9 cm), and 0.05 inches thick (0.13 cm). The amount of surface area that these tubes would possess per unit of tube length was found

20

4.0

Steam Superheater

to be 2.23 m2/m, and the total free area across each tube row was found to be 6.49 m2. From this determined free area, the flue gas mass velocity through the finned bank must then be 2.22 kg/m2·s. For the vaporization phase of the finned bank, the corresponding Reynolds number for the flue gas flowing past the tubes would be 7304. From Figure C4, this corresponds to the dimensionless J parameter having a value of 0.01. The parameter J is required when estimating the convection coefficient outside of the tubes. From this parameter, and based on the thermodynamic properties at this stage in the convection section, the outer convection coefficient was determined to be 10.46 W/m2·K. However, this value is misleading as it assumes a fin efficiency of 100%. The efficiency of the fins must be taken from Figure C5 of Appendix C. Once this value is known, the effective outer convection coefficient can be found. This value was determined to be 8.97 W/m2·K based on a fin efficiency of 83%. As for the shield bank, the in-film convection coefficient and the tube wall heat transfer coefficient can be determined based on the properties of the urea steam and the tube. These values were determined to be 1282 W/m2·K and 2396 W/m2·K. A summation of the thermal resistances can then be found, and from this, the overall heat transfer coefficient can be found for the vaporization phase of the finned bank section. This value was found to be 8.34 W/m2·K. Based on the heating requirement of this part of the superheater, as well as the overall heat transfer coefficient and the assumed log-mean temperature difference, the required surface area was then found. For the vaporization phase of the finned bank, it was determined that 947 m2 would be required. From the number and length of the tubes, it was found that 3.48 rows of finned tubes would be needed in this part of the finned bank

21

4.0

Steam Superheater

section. To ensure complete vaporization of the urea steam, the number of tube rows was rounded up to 4 rows. This analysis can be found in section 7 of Appendix C. For the water heating phase of the finned bank section, the same technique was used for finding the number of required finned tube rows. The only changes to be made would be the thermodynamic properties of the flue gas and the water. As for all of the superheater design calculations, the thermodynamic properties of the steam and flue gas streams were found based on the Peng-Robinson thermodynamic model. The value of J was determined to be 0.011. The fin efficiency was determined to be 88% for this phase of the finned bank, giving an effective outer heat transfer coefficient of 9.66 W/m2·K. The overall heat transfer coefficient was determined to be 8.93 W/m2·K, and the required surface area for the water heating phase of the finned bank was found to be 733.3 m2. The number of tube rows was then determined to be 2.69, which was rounded up to 3 rows to ensure the urea steam would be completely in the vapor phase. The analysis for this portion of the finned bank section can be found in section 8 of Appendix C.

4.7

Emission Stack: When designing the emission stack for the superheater, it must have a sufficient

diameter to provide a desired mass flux of flue gas into the atmosphere. The height of the stack must be of sufficient length to induce a draft that provides a slightly negative pressure in the radiant section. The negative radiant section pressure would allow for safe observation of the tubing within the radiant section through the peep doors of the furnace.

22

4.0

Steam Superheater It was recommended from Berman2 that the stack be designed to accommodate a

flue gas mass flux of 0.8 lb/s·ft2, which is equivalent to 3.91 kg/s·m2. It was also recommended that the stack be designed to accommodate for a 25% increase in the mass flow rate of flue gas. Given the flue gas emission rate of 51,905 kg/h, the stack will require a diameter of 2.42 meters. For determining the required stack height, the pressure losses, or velocity head, caused by the flue gas flowing across each section of the superheater must be determined. These velocity head losses were determined based on equation C.10.1 of Appendix C. The head losses were determined for the draft under arch and across the shield bank, finned bank, stack entrance, stack exit, and the dampers. The total velocity head losses were determined to be 0.3962 inH2O. Based on equation C.10.8 of Appendix C, the draft gain across the convection section could be determined. The convection section gain was determined to be 0.0946 inH2O. By subtracting the convection section draft gain from the velocity head losses, the draft gain required by the emission stack can be determined. This required stack draft was determined to be 0.3016 inH2O. Using equation C.10.8, the stack draft gain can be found per unit length of stack height. This value was determined to be 0.005485 inH2O/ft. Before this value can be used to determine the required height of the stack, the frictional energy losses in the flue gas as it passes up the stack must be taken into account. From equation C.10.13, these frictional losses were determined to be 0.0003066 inH2O/ft, making the required net stack draft gain equal to 0.005179 inH2O/ft. This means that the height of the required stack must be 17.75 meters. Calculations performed regarding for the stack design can be found in section 11 of Appendix C.

23

4.0 4.8

Steam Superheater Construction Material: The final calculations performed in the superheater design were determining if the

tube wall thickness would be suffice to withstand the effects of corrosion and creep within the tube walls. Corrosion would be caused along the tube walls by the tube metal losing electrons by reacting with the flowing water streams. Creep is a term used to describe the tendency of a metal to move or deform permanently to relive the stress2. Creep commonly occurs when a metal is put under high temperatures and pressures for long periods of time. To combat creep, the tubes would have to be constructed out of a material capable of withstanding high operating temperatures. Because the operating temperature of the radiant section is 927°C, the tube metal chosen must be capable of withstanding these high operating temperatures. The tubing material chosen was type HK-40 austenitic steel. Austenitic steels are classified as alloys consisting of various combinations of iron, chromium, and nickel. Type HK-40 steel composition by mass is defined as 25% chromium, 20% nickel, and 55% iron. The limiting design metal temperature of HK-40 austenitic steel is approximately 1000°C,2 73°C hotter than the maximum operating temperature. It was determined from equation C.9.1 of Appendix C that the maximum expected heat flux in the radiant section would be 71.15 kW/m2. The in-film convection coefficient at the outlet temperature and thermodynamic properties of the superheated steam was found to be 391.0 W/m2·K. Under these conditions, and given the thermal conductivity of austenitic steel, the tube metal temperature at the superheated steam exit was determined to be 584.7°C. To allow for a margin of safety, the maximum operating

24

4.0

Steam Superheater

tube temperature was set at 650°C, which is well within the constraints of HK-40 austenitic steel. The large buffer between the maximum operating temperature and the limiting design temperature for HK-40 steel ensures that issues of corrosion and creep will not be an issue in the designed superheater. To determine if the tube walls are thick enough to withstand the stress of operating pressures, the minimum allowable tube thickness was determined for HK-40 austenitic steel. Based on the maximum operating pressure (120 bar), the outer diameter of the tubes (11.4 cm), and the design stress (90% of the yield strength) for HK-40 steel under the operating conditions, the minimal allowable tube wall thickness for the HK-40 tubes was determined to be 0.307 cm. Given that schedule 40 piping has a wall thickness of 0.602 cm, this allows for a 0.295 cm margin against the effects of corrosion and creep. Calculations regarding the tube wall material can be found in section 9 of Appendix C.

25

5.0 5.1

Heat Exchangers Overview There are three unique shell-and-tube heat exchangers implemented within the

specified design. These heat exchangers include a gas/gas heat exchanger, and two waste heat boilers. The gas/gas heat exchanger serves two purposes. Its first purpose is to heat the incoming synthesis feed entering the first ammonia convertor to reach a feasible reaction temperature. Its second purpose is to cool the synthesized ammonia stream so that the separation units can remove the product more easily. The waste heat exchangers remove heat from the synthesis streams leaving each of the two ammonia convertors. The steam recovered by the waste heat exchangers is then superheated for use by the steam turbines.

5.2

Gas/Gas Heat Exchanger The purpose of the gas/gas heat exchanger is two fold. It must heat the feed

entering the first ammonia convertor to a reasonable reaction temperature as well as cooling the ammonia product stream so that it is more easily separated in the separation units. The result of the exchanger is the synthesis gas feed stream being heated from 31°C to 300°C by the ammonia product before it enters the first ammonia convertor, while the ammonia product stream is cooled from 340°C to 56°C by the feed stream. In order to achieve this large heat exchange between the gas streams, a large effective surface area of 2420 m2 is required. The heat exchanger designed consists of one shell pass of the feed stream and one tube pass of the product stream. Due to the high temperatures of the gases the exchanger had to be constructed from special materials.

26

5.0

Heat Exchangers

The steels used in the gas/gas exchanger have high quantities of chromium and molybdenum to help prevent creep and corrosion. The shell side is constructed from SA387 Gr.11 Cl.2 stainless steel and also has 24 baffles to help with the heat exchange. The tubes of the exchanger are constructed from a slightly different stainless steel, SA213/T11.

5.3

Waste Heat Exchangers Along with the gas/gas exchanger there are also two waste heat exchangers in the

process. The purpose of the waste heat exchangers is to remove the heat from the product streams leaving the ammonia convertors. To achieve this boiler feed water is used as the coolant and is heated to saturated steam while cooling the product stream from the ammonia convertors. This steam is then superheated so that it can be used by the steam turbines to power the compressors. The boiler feed water enters both exchangers as water at 130°C and exits each exchanger as saturated steam at 324°C and 120 bar pressure. This results in the synthesis stream temperatures being lowered from 508°C to 400°C in the first boiler and from 473 °C to 340°C in the second boiler. The split between the boiler feed water required for each exchanger was 41.03 tonnes/hr for the first boiler and 49.62 tonnes/hr for the second boiler, resulting in 90.65 tonnes/hr being sent to the superheater where the steam is superheated for use by the steam turbines. The flow rates of boiler feed water needed were calculated using a HYSYS simulation. It was known how much steam was required to power the two compressors therefore that was the flow rate of boiler feed water used. The boiler feed water temperature and pressure was also specified. Using these

27

5.0

Heat Exchangers

specifications, the amount of heat transferred was calculated and the inlet and outlet temperature of each stream was calculated. Each of the two heat exchangers consists of one shell pass of feed water and two tube passes of the ammonia product. The shell sides of both exchangers have four baffles, to enhance heat exchange, and are constructed from carbon steel. The tube side of each exchanger is constructed using TP 316 stainless steel. These exchangers have exchange areas of 163 m2 and 220 m2 respectively.

5.4

Heat Exchanger Summary Three different heat exchangers were designed to heat and cool different process

streams. A gas/gas heat exchanger was designed to cool the product stream to aid the separation process while heating the feed stream to the first ammonia convertor to a decent reaction temperature. The gas/gas exchanger has an area of 2420 m2 and has one tube pass and one shell pass. Due to extreme temperatures special chromium/molybdenum stainless steels had to be used. Two waste heat exchangers were also designed to remove the heat from the product streams leaving the ammonia convertors while providing saturated steam for the steam superheater. Each of these two heat exchangers consist of one shell pass of and two tube passes and have exchange areas of 163 m2 and 220 m2 respectively. A summary of the heat exchanger information can be found in Appendix D, Tables D.1.1 and D.1.2.

28

6.0 6.1

Compressors and Turbines Compressors A compressor is a machine that increases the pressure of a gas by mechanically

decreasing its volume. Two compressors had to be designed and modeled for use as part of the new ammonia synthesis loop. One compressor was designed to push the synthesis gas through the synthesis loop so that the ammonia could be made. The other compressor was designed to compresses carbon dioxide from 5 bar to 150 bar so that it can be used in the urea plant to make urea.

6.1.1

Synthesis Gas Compressor The synthesis gas compressor takes the feed for the new process and compresses

it from 50 bar to the required 190 bar where it then enters the process loop. A four staged compressor was designed using the HYSYS program (see Figure 6.1). The first three stages take the feed and compress it to 180 bars with a compression ratio of 1.5. In between these three stages the streams are cooled to 25°C before they enter the next stage. This requires in total of 294.6 tonnes per hour of 25°C cooling water that is heated to 60°C. The feed to the fourth stage contains a mixture of the stage 3 outlet as well as a recycle stream which contains the un-reacted hydrogen and nitrogen, along with some argon and ammonia. This mixture is then compressed to the required 190 bar in the fourth stage. The material chosen for the compressor is made out of carbon steel. It then leaves the compressor and heads into the first ammonia convertor. It was determined that this compressor uses 13,704 kW of the power that is generated by the feed steam turbine.

29

6.0

Compressors and Turbines One issue of safety that had to be taken into consideration was the possibility of

over pressuring the existing synthesis loop. The maximum allowable pressure in the synthesis loop is 210 bar. To ensure that over pressurization of the loop by the synthesis gas compressor could not take place a PSV was designed. The PSV constructed was a simple orifice plate with a diameter of 0.044 m (~2 in, see Appendix E, E.1.1 to E.1.4).

Figure 6.1: Synthesis gas compressor and turbine system

6.1.2 CO2 Compressor The second compressor takes carbon dioxide and compresses it from 5 bar to 150 bar so that it can be used by the urea plant to make urea. This compressor also has four stages and uses 6,855 kW of power which is generated by the carbon dioxide turbine. This compressor is also made of carbon steel. Condensation of the carbon dioxide had to be taken into consideration when deciding the flow rates of the water used in the intercoolers. If the carbon dioxide condensed in the compressor there would be major problems. In between the first two stages the stream is cooled to 30°C before it enters the second stage. The next two stages are only cooled to 41°C and 45°C. This is to ensure that the carbon dioxide does not condense in the third or fourth stage of the compressor under the specified pressure. The cooling system requires a total of 160 tonnes per hour

30

6.0

Compressors and Turbines

of 25°C cooling water that is heated by the compressed gases to 60°C. This compressor and cooling system was also designed using the HYSYS simulation (see Figure 6.2). Like the synthesis gas compressor the CO2 compressor will have to have a PSV to prevent the over pressurization of the existing CO2 loop. The maximum allowable pressure in the synthesis loop is 173 bar. The PSV constructed for this compressor was a similar simple orifice plate with a diameter of 0.019 m (~3/4 in, see Appendix E, E.2.1 to E.2.4).

Figure 6.4: Carbon dioxide compressor and turbine system

6.2

Steam Turbines With each of the two compressors requiring different amounts of power to

compress different gases, two separate steam turbines had to be designed to supply the different amounts of power required by each of the compressors. Steam turbines were used because superheated steam was available from the superheater and steam turbines are able to provide tremendous power using relative small space. The power from a steam turbine is generated using steam, which in this case is provided by the designed superheater, to turn a rotor that in turn produces the power needed for the compressors to compress their specific gases. 31

6.0

Compressors and Turbines The CO2 turbine uses 34% or 30.2 tonnes/h of the 510°C steam generated by the

superheater and puts out the required 6,855 kW needed to operate the CO2 compressor. The synthesis gas turbine uses the remaining 66% or 60.4 tonnes/h of the 510°C steam to produce the required 13,704 kW to power the synthesis gas compressor. Both of the above turbines exhaust to vacuum (30 kPa absolute) to generate the needed power. One safety issue that had to be considered with regards to the turbines is the possibility of liquid water in them. This would be possible if the water level in the waste heat boilers is too high. This would cause more water to enter into the superheater and it is possible that the superheater would not be able to completely vaporise all of it. Therefore liquid water could possibly enter into the turbine. This would cause major damage to the two turbines and cause the shutdown of the whole plant. To prevent the possibility of this occurring, a trip was designed that will shut the compressors off and close off the boiler feed water valves closed to protect the turbines. This would still cause the whole plant to shut down without damaging the turbines.

6.3

Compressors and Turbines Summary Two compressors were designed to compress two different gases. One

compressor was designed to compress the synthesis gas stream from 50 bar to 190 bar before it enters. The second compressor was designed to compress CO2 from 5 bar to 150 bar for use in the urea plant. Both of these compressors were designed using the HYSYS simulation. These compressors each have four stages, are centrifugal and are made from carbon steel. Each compressor has a PSV to prevent over pressurization of the individual loops. Two steam turbines were also designed to supply the power

32

6.0

Compressors and Turbines

required by the compressors. These two turbines use the steam generated by the superheater to produce the required 6,885 kW for the CO2 compressor as well as the 13,704 kW for the synthesis gas compressor. Trips were installed in the waste heat boilers to prevent the possibility of liquid water from entering the turbine. A summary of the compressor and turbine information can be found in Appendix E, Table E.1.1.

33

7.0

Economics

7.1

Overview With the complexity and large scope of the project and the design chosen there

were many things that were considered with regards to the economics. One of the major things included was the cost of the necessary equipment needed to make and power the process. This included such things as ammonia convertors, heater exchangers, a superheater and a couple of compressors and steam turbines. Another thing that was looked at was the amount of money the plant would make. This is important because no matter how good a design is it more than likely will not be implemented if the process loses money. Besides the cost of the equipment needed for the process and the money making prospect of this venture other things were also considered. These things included such things as the feasibility of firing the superheater with the feed stream instead of natural gas and coming up with a reasonable price for the ammonia product. The first thing that was tackled was the costing of the equipment. Note that the following costs do not include installation or maintenance costs. There were ten separate pieces of equipment that needed to be priced. These ten pieces of equipment included two compressors, two turbines, two waste heat exchangers, a gas/gas heat exchanger, two ammonia convertors and lastly a steam superheater. Each unit was priced with the methods specified in Ulrich3 (see Appendix F for detailed calculations). A summary of the bare module costs for each piece of equipment can be found in Table F.1.1 while the stream cost/price analysis is found in Tables F.1.2 and F.1.3.

34

7.0 7.2

Economics Compressor Pricing The two compressors were priced first. The three main factors in determining the

price of the compressors were the power required, their efficiencies and the material of construction. The efficiency of each compressor was assumed to be 75% and the material of construction chosen for the compressors was carbon steel. Next the power needed by the compressor was determined using the HYSYS modeling program. These power requirements were found to be 6,855 kW for the CO2 compressor and 13,704 kW for the synthesis gas compressor. With these powers and efficiencies known the purchase price was looked up in the proper Figure. Once the purchase cost was known it was multiplied by the material factor and the bare module cost of the compressors was determined. It was found that the bare module cost of the CO2 compressor was $17,250,000 while the bare module cost of the synthesis gas compressor was determined to be $6,612,500.

7.3

Steam Turbine Pricing With the cost of the compressors now determined the next step was pricing the

two steam turbines that power them. Unlike the compressors there are only two main factors in determining the cost of a steam turbine, power supplied and material of construction. The material of construction once again was chosen to be carbon steel and the power supplied by each individual turbine is the same as that used by its compressor. Using Figure 5.21 from Ulrich3, it was found that the purchase cost of the turbine that powers the CO2 compressor was $270,000 while the turbine that powers the synthesis compressor had a purchase cost of $300,000. Once again the purchase cost and the

35

7.0

Economics

material factor were multiplied together to give the bare module cost. The bare module cost for the synthesis gas compressor was found to be $1,610,000 while the bare module cost of the CO2 was determined to be slightly lower at $1,086,750.

7.4

Heat Exchange Equipment Pricing Next the cost of the three heat exchangers and the superheater were calculated.

The most important factors when determining the cost of heat exchangers are the exchanger surface area, the material of construction and the pressure under which they operate. The first heat exchangers cost to be calculated was the gas/gas heat exchanger. This unit operates under 190 bar of pressure and has a heat exchanger area of 2420 m2. This unit is made of carbon steel and titanium due to the high temperature of the gases and also their high pressures. Knowing the area for heat exchanger the purchase cost was determined using Figure 5.39 in Ulrich3. Once this was known the bare module factor was found using Figure 5.38. This was then multiplied together with the purchase cost and the bare module cost was determined. The bare module cost for the gas/gas heat exchanger was found to be $5,635,000. With the large and expensive gas/gas heat exchanger out of the way the bare module cost of the two waste heat boilers were determined. The method for obtaining the costs for these two pieces of equipment is almost identical to the way in which the cost of the gas/gas heat exchanger was found. In this case the areas are 220 m2 and 162 m2 respectively. Using the same material as the previous exchanger the bare module costs for these exchangers were calculated to be $483,000 for the first waste heat exchanger and $442,750 for the second waste heat exchanger.

36

7.0

Economics The last heat transfer related piece of equipment for which a cost had to be

determined was the superheater. The most important factor when determining the cost of a superheater is its heating duty. This factor along with the materials of construction and the exiting steam pressure were used to calculate the cost of the superheater. The pressure of the exiting steam is 120 bar and the material of construction chosen was austenitic steel due to the high temperatures used in the superheater. Using the heating duty of the superheater the purchase cost of the superheater was found. This was then multiplied by the pressure factor and the bare module factor, which is directly related to the material of construction, to obtain a bare module cost for the superheater. It was found that the bare module cost of the superheater is $ 4,992,000.

7.5

Feasibility of Firing the Superheater with Hydrogen Another economic issue with regards to the superheater that was taken into

account was the possibility of using the hydrogen gas from the feed stream to fire the superheater instead of natural gas. It was thought that it would be quite feasible to fire the superheater with the feed stream given the rising cost of natural gas and the fact that hydrogen gas has a decent heating value. So with the given price of the feed stream given as $6.50/GJ and knowing that it takes 32 GJ to produce one tonne of ammonia the energy cost of hydrogen gas was determined. The analysis found that the energy cost of hydrogen was $10.22/GJ. This is higher than the current price of natural gas that is currently at around $8.50/GJ. This made it unfeasible to used hydrogen gas from the feed stream to fire the superheater at this point in time. It is possible, however, that if the

37

7.0

Economics

price of natural gas could rise above the threshold price $10.22/GJ in the future, using the feed to fire the superheater might be feasible.

7.6

Ammonia Convertor Pricing The last two pieces of equipment to have their bare module costs calculated were

the two ammonia convertors. Both of these reactors contain catalyst that aid in the efficiency of the reactor but also add to the complexity of their calculations. With that in mind the cost of the catalyst had to be determined as it contributed to the cost of the reactor. Using Figure 5.47 in Ulrich, the cost and bulk density of the catalyst were determined to be $8.00/kg and 800 kg/m3 respectively. With this known the bare module factor was determined using a trusted relationship. Now, knowing the inner diameters of each of the two different convertors the purchase price of the catalyst part of the reactor was found using Figure 5.47. With both the bare module factor and the purchase price of the catalyst known the bare module cost of the catalyst part of the reactor was determined. The bare module cost of both ammonia convertors was found to be $341,333. Now the cost of the actual reaction vessel itself could be calculated. Knowing the operating pressure (190 bar) and the material of both convertors to be carbon steel the bare module factor was found using Figure 5.46. With the height and inner diameter of each reactor known to be almost the same the purchase cost for the vessel was calculated. The vessel purchase cost and the bare module factor were then used to determine the bare module cost of the vessel. Once this was found the bare module cost for the vessel and the bare module cost were summed together to give the total bare module cost for the

38

7.0

Economics

reactor. The total bare module cost for each reactor was found to be $1,312,533 for the first reactor and $1,058,613 for the second reactor.

7.7

Stream Cost Analysis Knowing the expense of all the necessary equipment needed to produce the

ammonia was only part of the financial analysis. The money made by production of the ammonia still needed to be calculated. To do this, a method of stream cost/price analysis was used as not enough information was known to do a complete financial study. There are eight major streams used in the process of producing ammonia. The cost streams include the synthesis gas feed, boiler feed water, cooling water and fuel gas for the superheater. The streams that are worth money are the CO2 produced for the urea plant, the low pressure steam used by the urea plant, the turbine condensate and the ammonia product made. With the mass flow rates of each of the different streams already calculated a price per unit mass was just needed to determine the cost or price of the specific streams. Most of the prices for these streams were set by Saskferco while a reasonable ammonia price had to be calculated. The method used was based on the model conventionally used in industry. The price of ammonia depends heavily upon the natural gas price. Knowing the energy to produce a tonne of ammonia (32 GJ/tonne) and the price of natural gas (~$8.00/GJ) a minimum price was calculated. To this a margin of $75/tonne and a combined utility and chemical cost of $10/tonne were added. This gave the final price of ammonia, at this current cost for natural gas, to be $341/tonne. Multiplying the cost per unit mass by the mass flow rate gave a cost/price per unit time for each of the different streams (see Appendix F, F.3.1 to F.3.10). Overall, it was found

39

7.0

Economics

that the revenue from this process is $11,700/hr. This does not include the utility, maintenance or operating costs that would be incurred by this process.

7.8

Economic Summary With the bare module cost of each piece of equipment in the process calculated as

well as the revenue that would be made from this process it was found that the economics of this project are quite good. The total bare module cost of all the equipment was found to be $41,231,946 while the stream analysis yielded a revenue of $11,700/hr. It was also determined that at this moment firing the superheater using the hydrogen gas from the feed stream was not viable but could possibly be explored again in the future.

40

8.0

Conclusions From our analysis of an ammonia synthesis loop for an alternate feedstock,

several significant conclusions were reached regarding its design. It is the feeling of this design team that the conclusions reached from our analysis were found with a high level of accuracy and credibility. It was found through the process of designing the ammonia synthesis loop that: •

The synthesis gas stream would enter the first ammonia convertor at a molar

flow rate of 8.047 kmol/s with an ammonia mole fraction of 0.0270. The synthesis gas would exit the convertor at a molar flow rate of 7.066 kmol/s with an ammonia mole fraction of 0.1696. The extent of hydrogen gas conversion to ammonia would increase from 5.33% to 29.39%. The temperature of the synthesis gas across the catalyst bed would rise from 300.0°C to 507.8°C. •

The synthesis gas stream would enter the second ammonia convertor at a molar

flow rate of 7.066 kmol/s with an ammonia mole fraction of 0.1696. The stream would exit the second convertor at a molar flow rate of 6.755 kmol/s with an ammonia mole fraction of 0.2234. The extent of hydrogen gas conversion would increase from 29.39% to 37.02%. The temperature of the synthesis gas across the catalyst bed would rise from 400.0°C to 473.0°C. •

After specifying complete recycle of hydrogen and nitrogen gas, the final

product stream from the separation units would have a molar flow rate of 1.318 kmol/s, consisting of 98.02 mol% ammonia and 1.98 mol% argon. •

The first waste heat boiler lowers the temperature of the synthesis gas stream

leaving the first ammonia convertor from 507.8°C to 400.0°C in one shell pass. In two

41

8.0

Conclusions

tube passes, boiler feed water is at 130.0°C is converted to saturated steam at 323.7°C and 120 bar at a rate of 41.03 tonnes/h. •

The second waste heat boiler lowers the temperature of the synthesis gas stream

leaving the first ammonia convertor from 473.0°C to 340.1°C in one shell pass. In two tube passes, boiler feed water is at 130.0°C is converted to saturated steam at 323.7°C and 120 bar at a rate of 49.63 tonnes/h. •

The gas/gas heat exchanger heats the synthesis feed stream from 31.2°C to

300.0°C in one shell pass at a rate of 8.047 kmol/s. In one tube pass, the product stream exiting the second ammonia convertor is cooled from 340.1°C to 55.6°C at a rate of 6.755 kmol/s. •

The steam superheater produces two steam products. Saturated steam at 120 bar

pressure from the waste heat boilers is superheated from 323.7°C to 510°C in the radiant section at a rate of 90.65 tonnes/h. Boiler feed water at 131.8°C and 23 bar is heated in the finned bank section, the shield bank section, and the radiant section to saturated steam at 220.1°C at a rate of 25.00 tonnes/h. The heater is fuelled by natural gas at a rate of 2433 kg/h, resulting in a flue gas emission rate of 51.9 tonnes/h. •

Using 60.42 tonnes/h of the produced superheated steam, the synthesis gas

turbine with 70% adiabatic efficiency is powered to produce 13704 kW for the synthesis gas compressor. •

Using 30.23 tonnes/h of the produced superheated steam, the CO2 turbine with

70% adiabatic efficiency is powered to produce 13704 kW for the CO2 compressor. •

The synthesis feed stream is compressed by a four stage synthesis gas

compressor having a 75% adiabatic efficiency. The recycled hydrogen and nitrogen gas

42

8.0

Conclusions

is reintroduced to the feed stream between the third and fourth compression stage. The feed enters at a pressure of 50 bar, a temperature of 25.0°C, and a mass flow rate of 82.95 tonnes/h. The effluent gas exits at a pressure of 50 bar, a temperature of 31.2°C, and a mass flow rate 265.8 tonnes/h. The synthesis is cooled in the compressor by 3 intercoolers by a combined water flow rate of 295 tonnes/h at 25°C and at atmospheric pressure. •

The synthesis feed stream is compressed by a four stage synthesis gas

compressor having an adiabatic efficiency of 75%. The recycled hydrogen and nitrogen gas is reintroduced to the feed stream between the third and fourth compression stage. The feed enters at a pressure of 50 bar, a temperature of 25.0°C, and a mass flow rate of 82.95 tonnes/h. The effluent gas exits at a pressure of 50 bar, a temperature of 31.2°C, and a mass flow rate 265.8 tonnes/h. The synthesis stream is cooled between the compressor stages by 3 intercoolers at a combined cooling water flow rate of 295 tonnes/h at 25°C and atmospheric pressure. •

The CO2 stream for the urea plant is compressed by a four stage CO2

compressor having an adiabatic efficiency of 75%. The CO2 feed stream enters the compressor at a temperature of 30.0°C, a pressure of 5 bar, and a mass flow rate of 95.03 tonnes/h. The CO2 stream exits at a pressure of 150 bar and a temperature of 126.6°C. The CO2 stream is cooled between the compressor stages by 3 intercoolers at a combined cooling water flow rate of 485 tonnes/h at 25°C and atmospheric pressure. It is of the opinion of this design team that this project has produced results satisfying enough to warrant the implementation of the design by Saskferco. This design team is confident in the reliability and feasibility of the conclusions reached from this project.

43

Works Cited

1.

Jennings J.R. Catalytic Ammonia Synthesis: Fundamentals and Practice. New York: Plenum Press, 1991.

2.

Berman H.L. ‘Fired Heaters: Part I-IV’, Journal of Chemical Engineering. Volume 85, June-September 1978.

3.

Ulrich G.D., Vasudevan P.T. Chemical Engineering Process Design and Economics: a Practical Guide. 2nd Edition, Boca Raton, FL: CRC Press, 2004.

44

Acknowledgments

•

Bob Edmondson, Saskferco Technical Director

•

Gordon Hill, ChE 422 Advisor

•

Hui Wang, ChE 422 Advisor

•

Richard Evitts, Professor, University of Saskatchewan

•

Mehdi Nemati, Professor, University of Saskatchewan

45

Appendix A: Process Flow Diagram

46

Appendix A Process Flow Diagram A.1

Process Flow Diagram and Stream Compositions

Table A.1.1: Ammonia synthesis loop streams

Synthesis Gas Feed Compressor Stage 1 Discharge Compressor Stage 2 Suction Compressor Stage 2 Discharge Compressor Stage 3 Suction Compressor Stage 3 Discharge To Stage 4 Mixer Compressor Stage 4 Suction Compressor Stage 4 Discharge Inlet to 8R1 Outlet from 8R1 Inlet to 8R2 Outlet from 8R2 To Gas/Gas Exchanger To Separation Recycle To Stage 4 Mixer Ammonia Product

101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117

Flow Rate kmol / s 2.6096 2.6096 2.6096 2.6096 2.6096 2.6096 2.6096 8.0468 8.0468 8.0468 7.0660 7.0660 6.7551 6.7551 6.7551 5.4372 1.3178

Temperature o C 25.0 77.8 25.0 77.9 25.0 78.0 25.0 25.0 31.2 300.0 507.8 400.0 473.0 340.1 55.6 25.0 4.3

Pressure bar 5.0 76.6 76.6 117.4 117.4 180.0 180.0 180.0 190.0 189.0 184.8 183.9 183.4 183.1 182.0 180.0 5.0

Table A.1.2: Water and steam system streams

Total Boiler Feed Water BFW to Synthesis Loop BFW to Fired Heater BFW to 8E1 BFW to 8E2 Saturated Steam from 8E1 Saturated Steam from 8E2 Saturated Steam to Superheater Low Pressure Saturated Steam High Pressure Steam to Turbines Steam to CO2 Turbine Steam to Synthesis Gas Turbine CO2 Turbine Condensate Synthesis Gas Turbine Condensate

201 202 203 204 205 206 207 208 209 210 211 212 213 214

Flow Rate kmol / s 1.7833 1.3978 0.3856 0.6325 0.7653 0.6325 0.7653 1.3978 0.3856 1.3978 0.4660 0.9318 0.4660 0.9318

Temperature o C 130.0 130.0 130.0 130.0 130.0 323.7 323.7 323.7 220.1 510.0 510.0 510.0 69.2 69.2

47

Pressure bar 129.0 129.0 129.0 129.0 129.0 120.0 120.0 120.0 23.0 120.0 120.0 120.0 0.3 0.3

yH2 0.7425 0.7425 0.7425 0.7425 0.7425 0.7425 0.7425 0.7195 0.7195 0.7195 0.6112 0.6112 0.5703 0.5703 0.5703 0.7085 0.0000

Composition yN2 yNH3 0.2475 0.0000 0.2475 0.0000 0.2475 0.0000 0.2475 0.0000 0.2475 0.0000 0.2475 0.0000 0.2475 0.0000 0.2398 0.0270 0.2398 0.0270 0.2398 0.0270 0.2037 0.1696 0.2037 0.1696 0.1901 0.2234 0.1901 0.2234 0.1901 0.2234 0.2362 0.0400 0.0000 0.9802

yAr 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0100 0.0136 0.0136 0.0136 0.0155 0.0155 0.0162 0.0162 0.0162 0.0154 0.0198

Appendix A Process Flow Diagram

Table A.1.3: CO2 compressor streams Flow Rate kmol / s Stage 1 Feed 301 0.6111 Stage 1 Discharge 302 0.6111 Stage 2 Suction 303 0.6111 Stage 2 Discharge 304 0.6111 Stage 3 Suction 305 0.6111 Stage 3 Discharge 306 0.6111 Stage 4 Suction 307 0.6111 Stage 4 Discharge 308 0.6111

Temperature o C 30.0 110.8 30.0 111.7 41.0 126.0 45.0 126.6

Table A.1.4: Superheater fuel and flue gas streams Flow Rate Temperature o C kmol / s Natural Gas 401 1.7981 9.0 Combustion Air 402 0.0659 5.0 Premixed Fuel 403 1.8639 8.7 Flue Gas 404 1.9050 202.1

Pressure bar 5.0 11.7 11.7 27.4 27.4 64.1 64.1 150.0

Pressure bar 21.0 21.0 21.0 1.0

CH4 0.0000 0.9200 0.0326 0.0000

48

CO2 0.9500 0.9500 0.9500 0.9500 0.9500 0.9500 0.9500 0.9500

C2H6 0.0000 0.0500 0.0017 0.0000

Composition H2O N2 0.0040 0.0400 0.0040 0.0400 0.0040 0.0400 0.0040 0.0400 0.0040 0.0400 0.0040 0.0400 0.0040 0.0400 0.0040 0.0400

O2 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060 0.0060

Composition C3H8 CO2 O2 0.0000 0.0000 0.2323 0.0300 0.0000 0.0000 0.0011 0.0000 0.2241 0.0000 0.0826 0.0323

N2 0.7647 0.0000 0.7376 0.7282

H20 0.0030 0.0000 0.0029 0.1569

Appendix A Process Flow Diagram

49

Appendix B: Ammonia Conversion

50

Appendix B Ammonia Conversion B.1

Determining the Feed Requirement to Produce 1900 Tonnes of Ammonia/day

3H 2 + N 2 ⇒ 2NH 3

(B.1.1)

n ≡ molar flow rate (kmol/day). m ≡ mass flow rate (tonnes/day). MW ≡ molecular weight (kg/kmol). y ≡ mole fraction in the feed stream.

nNH 3 = nNH 3

mNH 3 MWNH 3

(1900 )(1000 ) = (17.0304 ) kg tonne

tonnes day

(B.1.2)

kg kmol

nNH 3 = 111,565 kmol day

nH 2 = 32 × nNH 3

(

nH 2 = 32 × 111,565 kmol day

)

(B.1.3)

nH 2 = 167,348 kmol day

nN 2 = 12 × nNH 3

(

)

nN 2 = 12 × 111,565 kmol day

(B.1.4)

nN 2 = 55,783 kmol day

mH 2 = nH 2 × MWH 2

(

) (

)× (2.01588 ) kg kmol

(B.1.5)

) (

)× (28.0134 )

(B.1.6)

mH 2 = 167,348 kmol day ×

1tonne 1000 kg

mH 2 = 337.4 tonnes day mN 2 = nN 2 × MWN 2

(

mN 2 = 55,783 kmol day ×

1tonne 1000 kg

kg kmol

mN 2 = 1562.7 tonnes day

51

Appendix B Ammonia Conversion

n Ar =

y Ar nH 2 yH 2

n Ar =

(0.0100) 167,348 kmol day (0.7425)

(

)

(B.1.7)

n Ar = 2254 kmol day

m Ar = n Ar × MWAr

(

)(

)(

kg m Ar = 2254 kmol day × 39.948 kmol ×

1tonne 1000 kg

)

(B.1.8)

m Ar = 90.0 tonnes day

nTOTAL = n Ar + n H 2 + n N 2

nTOTAL = (2254 + 167348 + 55783) kmol day

(B.1.9)

nTOTAL = 225,385 kmol day

mTOTAL = m Ar + mH 2 + mN 2

mTOTAL = (90.0 + 337.4 + 1562.7 ) tonnes day

(B.1.10)

mTOTAL = 1990.1 tonnes day

52

Appendix B Ammonia Conversion B.2

Deriving Equations to Interpret Stream Composition Changes

Subscript 1 ≡ variable from the stream entering the ammonia reactor. Subscript 2 ≡ variable from the stream exiting the ammonia reactor. F ≡ molecular flow rate of a particular gas stream (kmol/day). X ≡ extent of conversion of hydrogen gas across the ammonia reactor. Equation 1: Overall mole balance F2 = F1 − 12 [(FH 2 )1 X + 13 (FH 2 )1 X ]

F2 = F1 − 23 (FH 2 )1 X F2 = 1 − 23 ( y H 2 )1 X F1

(B.2.1)

Equation 2: Ammonia mole balance

(FNH 3 )2 = 23 (FH 2 )1 X + (FNH 3 )1 2 (F ) X + (FNH 3 )1 ( y NH 3 )2 = 3 H 2 1

(B.2.2)

F2

Substitute equation 1 into equation 2 to get equation 3:

(FH 2 )1 X + (FNH 3 )1 F1 − 23 (FH 2 )1 X 2 ( y ) XF + ( y ) F ( y NH 3 )2 = 3 H 2 1 2 1 NH 3 1 1 F1 − 3 ( y H 2 )1 XF1 2 ( y ) X + ( y NH 3 )1 ( y NH 3 )2 = 3 H 2 21 1 − 3 ( y H 2 )1 X 3( y ) + 2( y H 2 )1 X ( y NH 3 )2 = NH 3 1 3 − 2( y H 2 )1 X ( y NH 3 )2 =

2 3

(B.2.3)

Rearranging equation 3 gives equation 4: X =

3[( y NH 3 )2 − ( y NH 3 )1 ] 2( y H 2 )1 [1 + ( y NH 3 )2 ]

(B.2.4)

53

Appendix B Ammonia Conversion

Equation 5: Hydrogen mole balance

(FH 2 )2 = (FH 2 )1 − (FH 2 )1 X (FH 2 )2 = (FH 2 )1 [1 − X ] (F ) [1 − X ] ( y H 2 )2 = H 2 1

(B.2.5)

F2

Substitute equation 1 into equation 5 to get equation 6:

(FH 2 )1 [1 − X ] F1 − 23 (FH 2 )1 X F ( y ) [1 − X ] ( y H 2 )2 = 1 2H 2 1 F1 − 3 F1 ( y H 2 )1 X ( y ) [1 − X ] ( y H 2 )2 = H22 1 1 − 3 ( y H 2 )1 X 3( y ) [1 − X ] ( y H 2 )2 = H 2 1 3 − 2( y H 2 )1 X ( y H 2 )2 =

(B.2.6)

Equation 7: Nitrogen mole balance

(FN 2 )2 = (FN 2 )1 − 13 (FH 2 )1 X (FN 2 )2 = (F )1 [( y N 2 )1 − 13 ( y H 2 )1 X ] (F ) [( y ) − 1 ( y ) X ] ( y N 2 )2 = 1 N 2 1 3 H 2 1

(B.2.7)

F2

Substitute equation 1 into equation 7 to get equation 8:

(F )1 [( y N 2 )1 − 13 ( y H 2 )1 X ] F1 − 23 (FH 2 )1 X (F ) [( y ) − 1 ( y ) X ] ( y N 2 )2 = 1 N 22 1 3 H 2 1 F1 − 3 F1 ( y H 2 )1 X (y ) − 1 (y ) X ( y N 2 )2 = N 2 12 3 H 2 1 1 − 3 ( y H 2 )1 X 3( y ) − ( y ) X ( y N 2 )2 = N 2 1 H 2 1 3 − 2( y H 2 )1 X ( y N 2 )2 =

(B.2.8)

All of the above equations (B.2.1 through B.2.8) are dependent on hydrogen gas being the limiting reagent of the ammonia synthesis reaction.

54

Appendix B Ammonia Conversion

Equation 9: Argon mole balance

(FAr )2 = (FAr )1 F2 ( y Ar )2 = F1 ( y Ar )1 ( y Ar )2 =

(B.2.9)

F1 ( y Ar )1 F2

Substitute equation 1 into equation 9 to get equation 10:

( y Ar )2 =

1−

( y Ar )1 ( y H 2 )1 X

(B.2.10)

2 3

55

Appendix B Ammonia Conversion B.3

Estimating the Equilibrium Conversion of the Ammonia Synthesis Reaction

Data for the mol percent of ammonia at equilibrium for several synthesis gases feed compositions was found in Catalytic Ammonia Synthesis by J.R. Jennings1. Interpolation between the data at 175 bar and 200 bar was used to arrive at a set of data for 190 bar. This data was then converted to mole fraction, and using equation B.2.4, we were able to calculate the conversion of hydrogen as a function of the equilibrium temperature, shown in Table B.3.1. Similar data was collected for the original Saskferco stream compositions. This data is presented in Figure B.3.1 for comparison. We were given that a 10 degree approach to equilibrium is a reasonable approximation for calculating the extent of the reaction. This means the conversion value should be calculated as if the stream were 10 degrees hotter than it actually is. Using the trend line option in MS Excel, an 5th order polynomial equation for the conversion as a function of temperature was fitted, with an R2 value of 1.00.

X H 2 = -1.28433 × 10 -13 (T + 10) 5 + 4.27614 × 10 -10 (T + 10) 4 - 5.15002 × 10 -7 (T + 10) 3 + 3.30093 × 10 - 4 (T + 10) 2 − 9 .63269 × 10 - 2 (T + 10) + 12.0537

56

(B.3.1)

Appendix B Ammonia Conversion

Example: T = 503 .15 K ~ % P =175 bar = 80 .205 ~ % P = 200 bar = 81 .855

P − P175 ~ ~ ~ % P =190bar = (% P = 200bar − % P =175bar ) 190 P200 − P175 190bar − 175bar ~ % P =190bar = (81.855 − 80.205) = 81.159 200bar − 175bar ~ % P =190bar ( y NH 3 ) ) 2 = = 0.81159 100

X H2 =

3[( y NH 3 )2 − ( y NH 3 )1 ] 0.81159 = 1.5 = 0.89984 2( y H 2 )1 [1 + ( y NH 3 )2 ] 0.7425(1 + 0.81159)

57

(B.3.2)

Appendix B Ammonia Conversion Table B.3.1: Conversion of hydrogen as a function of temperature Initial Mole %: H2 - 74.25%, N2 - 24.75%, CH4 - 0%, Ar - 1.00% Mole percent of NH3 at equilibrium T (K) 423.15 433.15 443.15 453.15 463.15 473.15 483.15 493.15 503.15 513.15 523.15 533.15 543.15 553.15 563.15 573.15 583.15 593.15 603.15 613.15 623.15 633.15 643.15 653.15 663.15 673.15 683.15 693.15 703.15 713.15 723.15 733.15 743.15 753.15 763.15 773.15 783.15 793.15 803.15 813.15 823.15

P=175 bar 92.595 91.538 90.347 89.018 87.546 85.929 84.165 82.256 80.205 78.017 75.700 73.262 70.715 68.071 65.347 62.559 59.724 56.860 53.985 51.118 48.276 45.478 42.737 40.070 37.487 35.000 32.618 30.346 28.190 26.153 24.235 22.436 20.754 19.187 17.730 16.379 15.129 13.975 12.911 11.930 11.028

P=200bar 93.244 92.288 91.207 89.995 88.647 87.161 85.533 83.764 81.855 79.810 77.634 75.335 72.921 70.404 67.797 65.115 62.373 59.588 56.777 53.957 51.147 48.363 45.620 42.934 40.318 37.784 35.341 32.998 30.762 28.635 26.623 24.725 22.941 21.269 19.708 18.254 16.902 15.648 14.487 13.413 12.422

P=190bar 92.984 91.988 90.863 89.604 88.207 86.668 84.986 83.161 81.195 79.093 76.860 74.506 72.039 69.471 66.817 64.093 61.313 58.497 55.660 52.821 49.999 47.209 44.467 41.788 39.186 36.670 34.252 31.937 29.733 27.642 25.668 23.809 22.066 20.436 18.917 17.504 16.193 14.979 13.857 12.820 11.864

Mole fraction of NH3 at equilibrium (yNH3)2 P=175 bar 0.92595 0.91538 0.90347 0.89018 0.87546 0.85929 0.84165 0.82256 0.80205 0.78017 0.75700 0.73262 0.70715 0.68071 0.65347 0.62559 0.59724 0.56860 0.53985 0.51118 0.48276 0.45478 0.42737 0.40070 0.37487 0.35000 0.32618 0.30346 0.28190 0.26153 0.24235 0.22436 0.20754 0.19187 0.17730 0.16379 0.15129 0.13975 0.12911 0.11930 0.11028

58

P=200bar 0.93244 0.92288 0.91207 0.89995 0.88647 0.87161 0.85533 0.83764 0.81855 0.79810 0.77634 0.75335 0.72921 0.70404 0.67797 0.65115 0.62373 0.59588 0.56777 0.53957 0.51147 0.48363 0.45620 0.42934 0.40318 0.37784 0.35341 0.32998 0.30762 0.28635 0.26623 0.24725 0.22941 0.21269 0.19708 0.18254 0.16902 0.15648 0.14487 0.13413 0.12422

P=190bar 0.92984 0.91988 0.90863 0.89604 0.88207 0.86668 0.84986 0.83161 0.81195 0.79093 0.76860 0.74506 0.72039 0.69471 0.66817 0.64093 0.61313 0.58497 0.55660 0.52821 0.49999 0.47209 0.44467 0.41788 0.39186 0.36670 0.34252 0.31937 0.29733 0.27642 0.25668 0.23809 0.22066 0.20436 0.18917 0.17504 0.16193 0.14979 0.13857 0.12820 0.11864

Conversion of H2 (XH2) 0.96710 0.96174 0.95562 0.94868 0.94087 0.93213 0.92241 0.91166 0.89984 0.88691 0.87284 0.85760 0.84119 0.82359 0.80483 0.78494 0.76395 0.74191 0.71891 0.69503 0.67038 0.64508 0.61925 0.59305 0.56661 0.54009 0.51365 0.48743 0.46158 0.43622 0.41150 0.38750 0.36431 0.34202 0.32068 0.30034 0.28101 0.26272 0.24546 0.22921 0.21396

Appendix B Ammonia Conversion

Figure B.3.1: Ammonia synthesis equilibrium at various stream compositions

59

Appendix B Ammonia Conversion B.4

Reactor Composition Iterative Procedure for 8R1 and 8R2

This iterative procedure calculates the compositions of the several streams, given the inlet and outlet temperatures of both reactors. •

Stream 1: the stream entering the 8R1. A combination of the feed stream and the recycle stream.

•

Stream 2: the stream exiting 8R1.

•

Stream 3: has concentration identical to stream 2

•

Stream 4: the stream exiting 8R2.

•

Recycle: the stream being returned to the process after the ammonia product has been separated out. The composition of the feed was given as yF,H2=0.7425, yF,N2=0.2475, and

yF,Ar=0.0100, and in section B.1 it was calculated that a rate of 225,385 kmol/day or 2.6096 kmol/s of feed was required to produce 1900 tonnes of ammonia per day. The temperatures for each stream are given as follows: T1=573.15 K, T2=780.90 K, T3=673.15 K, and T4=746.15 K. Using the fifth order polynomial equation that was developed in Appendix B.3 we can calculate the percent of hydrogen as ammonia for a 10oC stream 2 equilibrium approach.

X T2 =780 .90 K = 0.2939 This value is the extent of the conversion of hydrogen gas to ammonia. This is equal to the conversion of hydrogen, if we take state 1 to be the concentrations when any ammonia in the system is converted back to hydrogen and nitrogen (ie. y1,NH3 = 0).

60

Appendix B Ammonia Conversion

Using equations B.2.3, B.2.4, B.2.6, B.2.8 and B.2.10 developed earlier, and the conversion calculated above, we can calculate the resulting concentrations exiting both reactors. To calculate the concentrations for the recycle stream, we first needed to develop a rough model for our separators. An in depth separator design was beyond the scope of our project. We were given that the ammonia in the recycle stream, yR,NH3=0.0400, and that 100% of the hydrogen and nitrogen are recycled. We assumed the amount of argon recycled in the original Saskferco design would be proportional to the amount recycled in our system. Based on this, 76.2% of the argon is recycled. The rest leaves dissolved in the ammonia product stream.

(y )

= 0.04

NH 3 R

FR = F4

( y H 2 ) 4 + ( y N 2 ) 4 + 0.762( y Ar ) 4

= 0.762

(y )

=

(y )

=

N2 R

(B.4.2)

1 − ( y NH 3 ) R

( y Ar )R

H2 R

(B.4.1)

( y Ar )4 F4

(B.4.3)

FR

(y ) F H2 4

4

(B.4.3)

4

(B.4.4)

FR

(y ) F N2 4

FR

61

Appendix B Ammonia Conversion

The final step in the first iteration is to calculate the product stream.

FP = F4 − FR

(y )

=

NH 3 P

( y Ar )P

=

(B.4.5)

(

F4 y NH 3

)

4

(

)

+ FR y NH 3

R

(B.4.6)

FP

F4 ( y Ar )4 + FR ( y Ar )R FP

(B.4.7)

Since 100% of the hydrogen and nitrogen are recycled, yH2,P and yN2,P equal 0.00. Now, to recalculate the concentrations in stream 1:

F 1 n + 1 = F F − F Rn

(y )

n +1

H2 1

(y )

n +1

N2 1

(y )

=

=

n +1

NH 3 1

(y )

n +1 Ar 1

(y )

H2 F

( )

n

FF + y H 2

R

FRn

(B.4.9)

F1n +1

(y )

N2 F

( )

FF + y N 2

n R

FRn

(B.4.10)

F1n +1

=

=

(B.4.8)

(y )

NH 3 F

(

FF + y NH 3

)

n R

FRn

(B.4.11)

F1n +1

( y Ar )F FF + ( y Ar )nR FRn

(B.4.12)

F1n +1

Using equation B.2.4, and the equations listed below we can calculate the concentrations of a fictional stream where all the ammonia has been broken down to hydrogen and nitrogen.

62

Appendix B Ammonia Conversion

(y )

=

H2

(y )

=

N2

* n +1

(F )

* n +1

H2

1

+

3 y NH 3 2

n +1

1

(B.4.13)

n +1 NH 3 1

(y )

( ) 1 + (y ) n +1

* n +1

Ar

( ) 1 + (y ) n+1

* n+1

(y )

(y )

N2

1

+

1 y NH 3 2

n +1

1

(B.4.14)

n +1 NH 3 1

(y )

n +1

=

=

Ar

(

1

1 + y NH3

(B.4.15)

)

n +1

1

F1n+1

(B.4.16)

( ) (y )

2 1 − Z H2 3

n +1

1

n +1

NH 3 1

Now we can go back and calculate the concentrations in the streams exiting both reactors using equations B.2.3, B.2.4, B.2.6, B.2.8 and B.2.10, as we did above, and keep iterating until the concentrations in the final streams no longer change. Please see Tables B.4.1 through B.4.6 for an example of these calculations.

63

Appendix B Ammonia Conversion Table B.4.1: Stream 1 concentrations entering 8R1

n

(X )

H2 1

(y )

(y ) (y ) (y )

0

0.0000

0.7425

0.2475

0.0000

0.0100

2.6096

1 2

0.0316 0.0416

0.7301 0.7259

0.2434 0.2420

0.0159 0.0210

0.0106 0.0111

4.3253 5.4988

3 4 5 6

0.0463 0.0489 0.0504 0.0514

0.7238 0.7225 0.7217 0.7211

0.2413 0.2408 0.2406 0.2404

0.0234 0.0248 0.0256 0.0261

0.0115 0.0119 0.0122 0.0125

6.3015 6.8508 7.2269 7.4844

7 8 9 10

0.0520 0.0525 0.0527 0.0529

0.7207 0.7204 0.7202 0.7200

0.2402 0.2401 0.2401 0.2400

0.0264 0.0266 0.0267 0.0268

0.0127 0.0129 0.0130 0.0131

7.6608 7.7817 7.8646 7.9215

11 12 13 14

0.0531 0.0531 0.0532 0.0532

0.7199 0.7198 0.7197 0.7197

0.2400 0.2399 0.2399 0.2399

0.0269 0.0269 0.0270 0.0270

0.0132 0.0133 0.0134 0.0134

7.9606 7.9874 8.0058 8.0185

15 16 17 18

0.0533 0.0533 0.0533 0.0533

0.7196 0.7196 0.7196 0.7196

0.2399 0.2399 0.2399 0.2399

0.0270 0.0270 0.0270 0.0270

0.0135 0.0135 0.0135 0.0136

8.0273 8.0333 8.0374 8.0403

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533 0.0533

0.7196 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195 0.7195

0.2399 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398 0.2398

0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270 0.0270

0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136 0.0136

8.0423 8.0437 8.0446 8.0453 8.0457 8.0461 8.0463 8.0464 8.0466 8.0466 8.0467 8.0467 8.0468 8.0468 8.0468 8.0468 8.0468 8.0468 8.0468 8.0468 8.0468 8.0468

H2

1

N2

1

NH 3

64

1

Ar

1

F1 (kmol/s)

Appendix B Ammonia Conversion Table B.4.2: Synthesis loop composition at zero conversion

n

(y ) H2

(y ) N2

(y ) Ar

F * (kmol/s)

0

0.7425

0.2475

0.0100

2.6096

1 2

0.7422 0.7418

0.2474 0.2473

0.0105 0.0109

4.3939 5.6143

3 4 5 6

0.7415 0.7413 0.7411 0.7409

0.2472 0.2471 0.2470 0.2470

0.0113 0.0116 0.0119 0.0121

6.4492 7.0205 7.4116 7.6794

7 8 9 10

0.7407 0.7406 0.7405 0.7404

0.2469 0.2469 0.2468 0.2468

0.0124 0.0125 0.0127 0.0128

7.8629 7.9886 8.0748 8.1340

11 12 13 14

0.7403 0.7403 0.7402 0.7402

0.2468 0.2468 0.2467 0.2467

0.0129 0.0130 0.0130 0.0131

8.1746 8.2025 8.2217 8.2349

15 16 17 18

0.7402 0.7401 0.7401 0.7401

0.2467 0.2467 0.2467 0.2467

0.0131 0.0132 0.0132 0.0132

8.2440 8.2502 8.2545 8.2575

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7401 0.7400 0.7400 0.7400 0.7400 0.7400 0.7400

0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467 0.2467

0.0132 0.0132 0.0132 0.0132 0.0132 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133 0.0133

8.2596 8.2610 8.2620 8.2627 8.2632 8.2635 8.2638 8.2639 8.2640 8.2641 8.2642 8.2642 8.2642 8.2643 8.2643 8.2643 8.2643 8.2643 8.2643 8.2643 8.2643 8.2643

*

*

*

65

Appendix B Ammonia Conversion Table B.4.3: Stream 2 exiting 8R1

n

(X )

H2 2

(y )

(y ) (y ) (y )

0

0.2939

0.6135

0.2045

0.1702

0.0117

2.2300

1 2

0.2939 0.2939

0.6132 0.6129

0.2044 0.2043

0.1702 0.1701

0.0122 0.0127

3.7550 4.7983

3 4 5 6

0.2939 0.2939 0.2939 0.2939

0.6126 0.6124 0.6122 0.6120

0.2042 0.2041 0.2041 0.2040

0.1700 0.1699 0.1699 0.1698

0.0132 0.0136 0.0139 0.0142

5.5122 6.0008 6.3354 6.5646

7 8 9 10

0.2939 0.2939 0.2939 0.2939

0.6118 0.6117 0.6116 0.6115

0.2039 0.2039 0.2039 0.2038

0.1698 0.1697 0.1697 0.1697

0.0145 0.0147 0.0148 0.0150

6.7217 6.8294 6.9033 6.9540

11 12 13 14

0.2939 0.2939 0.2939 0.2939

0.6114 0.6114 0.6113 0.6113

0.2038 0.2038 0.2038 0.2038

0.1697 0.1696 0.1696 0.1696

0.0151 0.0152 0.0153 0.0153

6.9888 7.0128 7.0293 7.0406

15 16 17 18

0.2939 0.2939 0.2939 0.2939

0.6113 0.6112 0.6112 0.6112

0.2038 0.2037 0.2037 0.2037

0.1696 0.1696 0.1696 0.1696

0.0154 0.0154 0.0154 0.0154

7.0484 7.0538 7.0575 7.0601

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939 0.2939

0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112 0.6112

0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037 0.2037

0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696 0.1696

0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155 0.0155

7.0619 7.0631 7.0640 7.0646 7.0650 7.0653 7.0655 7.0657 7.0658 7.0658 7.0659 7.0659 7.0659 7.0660 7.0660 7.0660 7.0660 7.0660 7.0660 7.0660 7.0660 7.0660

H2

2

N2

2

NH 3

66

2

Ar

2

F2 (kmol/s)

Appendix B Ammonia Conversion Table B.4.4: Stream 3 exiting 8R2

n

(X )

H2 3

(y )

(y ) (y ) (y )

0

0.3702

0.5726

0.1909

0.2243

0.0122

2.1314

1 2

0.3702 0.3702

0.5722 0.5719

0.1907 0.1906

0.2242 0.2241

0.0128 0.0133

3.5892 4.5866

3 4 5 6

0.3702 0.3702 0.3702 0.3702

0.5717 0.5714 0.5712 0.5711

0.1906 0.1905 0.1904 0.1904

0.2240 0.2239 0.2238 0.2237

0.0138 0.0142 0.0146 0.0149

5.2690 5.7362 6.0562 6.2754

7 8 9 10

0.3702 0.3702 0.3702 0.3702

0.5709 0.5708 0.5707 0.5706

0.1903 0.1903 0.1902 0.1902

0.2237 0.2236 0.2236 0.2236

0.0151 0.0153 0.0155 0.0157

6.4256 6.5286 6.5993 6.6478

11 12 13 14

0.3702 0.3702 0.3702 0.3702

0.5705 0.5705 0.5704 0.5704

0.1902 0.1902 0.1901 0.1901

0.2235 0.2235 0.2235 0.2235

0.0158 0.0159 0.0160 0.0160

6.6812 6.7041 6.7199 6.7307

15 16 17 18

0.3702 0.3702 0.3702 0.3702

0.5704 0.5703 0.5703 0.5703

0.1901 0.1901 0.1901 0.1901

0.2235 0.2235 0.2234 0.2234

0.0161 0.0161 0.0161 0.0162

6.7382 6.7434 6.7470 6.7494

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702 0.3702

0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703 0.5703

0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901 0.1901

0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234 0.2234

0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162 0.0162

6.7511 6.7523 6.7532 6.7537 6.7541 6.7544 6.7546 6.7547 6.7548 6.7549 6.7550 6.7550 6.7550 6.7550 6.7550 6.7551 6.7551 6.7551 6.7551 6.7551 6.7551 6.7551

H2

3

N2

3

NH 3

67

3

Ar

3

F3 (kmol/s)

Appendix B Ammonia Conversion Table B.4.5: The recycle stream

(y ) (y ) (y ) (y )

n

(X )

0

0.0778

0.7113

0.2371

0.0400

0.0116

1.7157

1 2

0.0778 0.0779

0.7109 0.7105

0.2370 0.2368

0.0400 0.0400

0.0121 0.0126

2.8892 3.6919

3 4 5 6

0.0779 0.0779 0.0780 0.0780

0.7102 0.7099 0.7097 0.7094

0.2367 0.2366 0.2366 0.2365

0.0400 0.0400 0.0400 0.0400

0.0131 0.0134 0.0138 0.0141

4.2413 4.6173 4.8748 5.0512

7 8 9 10

0.0780 0.0780 0.0780 0.0780

0.7093 0.7091 0.7090 0.7089

0.2364 0.2364 0.2363 0.2363

0.0400 0.0400 0.0400 0.0400

0.0143 0.0145 0.0147 0.0148

5.1721 5.2550 5.3119 5.3510

11 12 13 14

0.0780 0.0781 0.0781 0.0781

0.7088 0.7087 0.7087 0.7086

0.2363 0.2362 0.2362 0.2362

0.0400 0.0400 0.0400 0.0400

0.0149 0.0150 0.0151 0.0152

5.3778 5.3962 5.4089 5.4177

15 16 17 18

0.0781 0.0781 0.0781 0.0781

0.7086 0.7086 0.7085 0.7085

0.2362 0.2362 0.2362 0.2362

0.0400 0.0400 0.0400 0.0400

0.0152 0.0152 0.0153 0.0153

5.4237 5.4278 5.4307 5.4327

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781 0.0781

0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085 0.7085

0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362 0.2362

0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400 0.0400

0.0153 0.0153 0.0153 0.0153 0.0153 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154 0.0154

5.4341 5.4350 5.4357 5.4361 5.4365 5.4367 5.4369 5.4370 5.4370 5.4371 5.4371 5.4372 5.4372 5.4372 5.4372 5.4372 5.4372 5.4372 5.4372 5.4372 5.4372 5.4372

H2 R

H2

R

N2

R

NH 3

68

R

Ar

R

FR (kmol/s)

Appendix B Ammonia Conversion Table B.4.6: Summary of final stream compositions and flow rates Feed Stream:

(y ) (y ) (y ) (y ) H2

1

N2

1

0.7425 0.2475 Product Stream:

NH 3

1

0.0000

Ar

1

0.0100

(y ) ( y ) ( y ) (y ) H2

P

N2

P

0.0000 0.0000 Recycle Stream:

NH 3

P

0.9802

Ar

P

0.0198

(y ) (y ) (y ) (y ) H2

R

N2

R

0.7085 0.2362 Stream Exiting 8R2:

NH 3

R

0.0400

Ar

R

0.0154

(y ) (y ) (y ) (y ) H2

3

N2

3

0.5703 0.1901 Stream Exiting 8R1:

NH 3

3

0.2234

Ar

3

0.0162

(y ) ( y ) ( y ) (y ) H2

2

N2

2

NH 3

2

0.6112 0.2037 0.1696 Stream Entering 8R1:

Ar

2

0.0155

(y ) ( y ) ( y ) ( y ) H2

1

0.7195

N2

1

0.2398

NH 3

1

0.0270

Ar

1

0.0136

F1 (kmol/s) 2.6096

FP (kmol/s) Ammonia Flow rate Ammonia Flow rate 1.3178

FR (kmol/s) 5.4372

F3 (kmol/s) 6.7551

F2 (kmol/s) 7.0660

F1 (kmol/s) 8.0468

69

(kmol/day) 111607

(tonnes/day) 1900

Appendix B Ammonia Conversion B.5

Energy Balance Iteration Procedure for 8R1 and 8R2

This iterative procedure calculates the temperature of the gas leaving the reactors 8R1 and 8R2. Inlet values for the reactors 8R1 and 8R2 were selected to be 300oC and 400oC respectively. (573.15 K and 673.15 K) Guess a value for the outlet temperatures for 8R1 and 8R2. These will be the temperature at which equilibrium will be reached. Using the iterative procedure for calculating reactor compositions in Appendix B.4, find the outlet composition of the reactors. Using equation B.2.4 developed in Appendix B.2, the conversion across each reactor can be calculated: X 8R1 = 1.5

X 8R2 = 1.5

y2, NH 3 − y1, NH 3

`

y1, H 2 + y1, H 2 y2, NH 3 y4, NH 3 − y2, NH 3

(B.5.1)

(B.5.2)

y2, H 2 + y2,H 2 y4, NH 3

These reactors are well insulated, so at steady state almost all of the heat generated goes to heating the synthesis gas in the system, and very little is lost to the atmosphere. This means we can calculate the outlet temperature of the gas if we know the heat capacity of our synthesis gas, and the heat of reaction.

T2 = T1 +

T4 = T3 +

y1,H 2 X 8 R1ΔH H 2 ,8 R1

(B.5.3)

C P ,8 R1 y2,H 2 X 8 R 2 ΔH H 2 ,8 R 2

(B.5.4)

C P ,8 R 2

70

Appendix B Ammonia Conversion

Use the new values for T2 and T4 as the guessed values, and iterate. Alternately, you can use a program like solver from MS Excel to minimize the differences between the guessed and calculated temperature values. The heat capacity was estimated using the HYSIS simulation program. The average of the heat capacity at the inlet and outlet temperature was used and new values were used in the calculations after each iteration until the values stopped changing. Heat of reaction was estimated for both reactors based on the information about the original Saskferco process that we were provided:

In Reactor 8R1: CP1 ≡ average heat capacity of synthesis stream in reactor 8R1 (kJ/kmol·K). ΔHR1 ≡ available heat of reaction per mole of hydrogen reacted in reactor 8R1(MJ/kmol). X1 ≡ extent of conversion of hydrogen across reactor 8R1. ΔT = TOUT – TIN ≡ temperature change of the synthesis stream across the reactor bed (K). FIN ≡ inlet molar flow rate (kmol/s). FIN C P1 ΔT = ΔH R1 X (FH 2 )IN ΔT =

ΔH R1 XFIN ( y H 2 )IN = TOUT − TIN FIN C P1

(TOUT

− TIN ) =

ΔH R1 = ΔH R1 =

(TOUT

ΔH R1 X ( y H 2 )IN C P1

(B.5.5)

− TIN )C P1 X ( y H 2 )IN

(740 K − 573K )( 32.50+236.59 ) kmolkJ⋅K (0.2576)(0.6116)

ΔH R1 = 36.6 kmolMJ⋅H 2

71

Appendix B Ammonia Conversion

In Reactor 8R2: CP2 ≡ average heat capacity of synthesis stream in reactor 8R2 (kJ/kmol·K). ΔHR2 ≡ available heat of reaction per mole of hydrogen reacted in reactor 8R2(MJ/kmol). X2 ≡ extent of conversion of hydrogen across reactor 8R2. FIN C P 2 ΔT = ΔH R 2 X 2 (FH 2 )IN ΔT =

ΔH R 2 X 2 FIN ( y H 2 )IN = TOUT − TIN FIN C P 2

(TOUT

− TIN ) =

ΔH R 2 = ΔH R 2 =

(TOUT

ΔH R 2 X 2 ( y H 2 )IN CP2

(B.5.6)

− TIN )C P 2 X 2 ( y H 2 )IN

(716 K − 673K )( 35.93+237.15 ) kmolkJ⋅K (0.08115)(0.5073)

ΔH R 2 = 38.2 kmolMJ⋅H 2

Example: Guess T2 and T4 equal to 750 K and 720 K respectively. From the procedure in Appendix B.4 we get the following information about the streams:

Table B.5.1: Example stream compositions for an equilibrium temperature of 750 K for reactor 8R1 and an equilibrium temperature of 720K for reactor 8R1 Stream Entering First Convertor: y1,H2 y1,N2 y1,NH3 y1,Ar 0.7194

0.2398

0.0242

0.0166

Stream Exiting First Convertor: y2,H2 y2,N2 y2,NH3 y2,Ar 0.5733 0.1911 0.2159 0.0197 Stream Exiting Second Convertor: y4,H2 y4,N2 y4,NH3 y4,Ar 0.5295

0.1765

0.2733

0.0206

72

Appendix B Ammonia Conversion X 8R1 = 1.5

X 8R2 = 1.5

T2 = T1 +

T4 = T3 +

y 2, NH 3 − y1, NH 3

= 1.5

y1, H 2 + y1, H 2 y 2, NH 3 y 4, NH 3 − y 2, NH 3 y 2, H 2 + y 2, H 2 y 4, NH 3

y1, H 2 X 8 R1ΔH H 2 ,8 R1 C P ,8 R1 y2, H 2 X 8 R 2 ΔH H 2 ,8 R 2 C P ,8 R 2

.2168 − .0274 = .3288 .7195 + .7195(.2168)

= 1.5

.2733 − .2159 = .1179 .5733 + .5733(.2733)

= 573.15 +

(.7194)(.3288)(36600kJ / kmol ) = 841.9 K 32.21kJ / kmolK

= 673.15 +

(.5733)(.1179)(38200kJ / kmol ) = 747.9 K 34.54kJ / kmolK

T2 − T2* = 841.9 K − 750 K = 91.9 K T4 − T4* = 747.9 K − 720 K = 27.9 K

Iterate again until T2 – T2* and T4 – T4* converge on 0. The final temperature values are T2 = 780.9 K and T4 = 746.1 K.

73

Appendix C: Steam Superheater

74

Appendix C Steam Superheater C.1

Calculating the Net Heating Value of Natural Gas Stream

Table C.1.1: Calculating the average molecular weight

Component CH4 C2H6 C3H8

Molecular Weight 16.042 30.068 44.094

Mole % 92.0 5.0 3.0 Total

kg/100kmol of fuel 1475.864 150.340 132.282 1758.486

Table C.1.2: Calculating the average lower heating value

Component CH4 C2H6 C3H8

Lower Heating Value (kJ/kg) 49,994 47,489 46,371 Total

kJ/100kmol of fuel 73.784×106 7.139×106 6.134×106 87.057×106

Table C.1.3: Calculating the air requirement for combustion

Component CH4 C2H6 C3H8

kg air / kg fuel 17.195 15.899 15.246 Total

kg air / 100kmol of fuel 25,377 2,390 2,017 29,785

MWAVE ≡ average molecular weight (kg/kmol). MW AVE = (MWCH 4 )( y CH 4 ) + (MWC 2 H 6 )( y C 2 H 6 ) + (MWC 3 H 8 )( y C 3 H 8 )

kg MW AVE = [(16.042)(0.920) + (30.068)(0.050) + (44.094 )(0.030 )] kmol

MW AVE = 17.585

kg kmol

= 1758.5

(C.1.1)

kg 100 kmol

NHV ≡ net heating value of the natural gas (kJ/kg). LHV ≡ lower heating value of the natural gas (kJ/100kmol).

NHV =

LHV MW AVE

(87.057 × 10 NHV = (1758.5

6

kJ 100 kmol kg 100 kmol

)

)

(C.1.2)

NHV = 49.51 MJ kg

75

Appendix C Steam Superheater

ARw ≡ air requirement (kg air/kg fuel). ARm ≡ air requirement (kg air/100kmol fuel).

ARw = ARw =

ARm MW AVE

(29,785 (1758.5

kg ⋅air 100 kmol ⋅ fuel kg ⋅ fuel 100 kmol ⋅ fuel

) )

(C.1.3)

air ARw = 16.94 kgkg⋅⋅fuel

ARE ≡ air requirement for 20% excess air (kg air/kg fuel). ARE = (1.20 )ARw

(

air ARE = (1.20 ) 16.94 kgkg⋅⋅fuel

)

(C.1.4)

air ARE = 20.33 kgkg⋅⋅fuel

TFG ≡ total flue gas (kg flue gas/kg fuel). ⋅ gas TFG = (1 + ARE ) kgkg⋅ flue ⋅ fuel ⋅ gas TFG = (1 + 20.33) kgkg⋅ flue ⋅ fuel

(C.1.5)

⋅ gas TFG = 21.33 kgkg⋅ flue ⋅ fuel

76

Appendix C Steam Superheater C.2

Heating Requirements of the Steam Streams

QUS ≡ heat absorbed by the urea steam (GJ/h). QUS = 57.61 GJ/h QSS ≡ heat absorbed by the superheated steam (GJ/h). QSS = 50.64 GJ/h QR” ≡ average heat flux in the radiant section (kJ/h·m2). QR” = 11,000 BTU/h·ft2 = 0.1249 GJ/h·m2 FGT ≡ flue gas temperature exiting the convection section (ºC). (TUS)IN ≡ inlet urea water temperature (ºF). FGT = (TUS )IN + 150 o F

(

)

FGT = 269.2 o F + 150 o F

(C.2.1)

FGT = 419.2 o F = 215.1o C

HA,FGT ≡ heat available based on the flue gas temperature exiting the convection section (kJ/kg). HA,FGT = 17,700 BTU/lb = 41,168 kJ/kg %H ≡ percent heat extraction from the superheater. %H =

H A, FGT H A, MAX

× 100%

(41,168 ) %H = (45,819 ) × 100% kJ kg

(C.2.2)

kJ kg

% H = 89.85%

μ ≡ calculated efficiency. %R ≡ predicted radiant heat losses.

μ = %H − %R μ = 89.85% − 2.00% μ = 87.85%

(C.2.3)

77

Appendix C Steam Superheater

QT ≡ total heat duty for the superheater (GJ/h). QT = QUS + QSS

QT = (57.61 + 50.64 ) GJh

(C.2.4)

QT = 108.25 GJh HT ≡ total heat fired by the superheater (GJ/h). HT = HT =

QT

μ

(108.25 GJh )

(C.2.5)

(0.8785)

H T = 120.5 GJh

FC ≡ mass flow rate of fuel consumed (kg/h). HT NHV 120.5 × 10 6 kJh FC = 49,510 kJ kg FC =

(

(

)

)

(C.2.6)

FC = 2433 kgh FG ≡ mass flow rate of flue gas (kg/h). FG = FC × TFG

(

) (

⋅ gas FG = 2433 kg ⋅hfuel × 21.33 kgkg⋅ flue ⋅ fuel

)

(C.2.7)

FG = 51,900 kgh

78

Appendix C Steam Superheater C.3

Calculations for the Radiant Section

TRTW ≡ radiant tube wall temperature (ºC). (TSS)OUT ≡ outlet superheated steam temperature (ºF). TRTW = (TSS )OUT + 75 o F

(

)

TRTW = 950 o F + 75 o F

(C.3.1)

TRTW = 1025 o F = 552 o C

BWT ≡ bridgewall temperature (ºC). BWT = 1700ºF = 927ºC (from Figure C3) HA,BWT ≡ heat made available based on the bridgewall temperature (kJ/kg). HA,BWT = 10,400 BTU/lb = 24,189 kJ/kg (from Figure C1) QR ≡ heat transfer in the radiant section (GJ/h). H A, BWT H A, FGT

=

QR QT

(24,189 ) Q = (41,168 ) (108.24 ) kJ kg

R

kJ kg

(B.3.2)

GJ h

QR = 63.60 GJh QC ≡ heat transfer in the convective section (GJ/h). QC = QT − QR

QC = (108.24 − 63.60 ) GJh

(C.3.3)

QC = 44.64 GJh SFA ≡ shield-bank free area (m2). N ≡ number of tubes per row. L ≡ horizontal tube length (ft). s ≡ spacing between tube centers (in). do ≡ outer diameter of each tube (in).

SFA = N ⋅ L ⋅ (s − do )

( )

SFA = (16)(16 ft )(8.0in − 4.5in) 121ftin

(C.3.4)

SFA = 74.67 ft = 6.94m 2

2

79

Appendix C Steam Superheater

G ≡ flue gas mass velocity (kg/s⋅m2). G= G=

FG SFA 51,905 kgh

(

)

(C.3.5)

(6.94m )(3600 ) 2

s h

G = 2.08 s⋅kgm 2 ASB ≡ surface area of first shield bank row (m2).

ASB = NLπd o

( )

ASB = (16 )(16 ft )π (4.5in ) 121ftin

(C.3.6)

ASB = 301.6 ft 2 = 28.02m 2 AR ≡ required radiant surface area (m2).

AR = AR =

QR QR

''

(63.60 GJh )

(0.1249 )

(C.3.7)

GJ h⋅m 2

AR = 509.1m 2 AVT ≡ vertical tube radiant surface (m2). AVT = AR − ASB

AVT = (509.1 − 28.02 )m 2 AVT = 481.1m

(C.3.8)

2

80

Appendix C Steam Superheater C.4

Determining the Optimum Number of Superheated Steam Passes

FSS’’ ≡ superheated steam mass velocity (kg/s⋅m2). 146.5 s⋅kgm 2 ≤ FSS ' ' ≤ 366.2 s⋅kgm 2

Optimum Mass Velocity:

ρSS ≡ density of superheated steam (kg/m3).

(ρ SS )IN = 75.70 mkg (ρ SS )OUT = 36.58 mkg 3

(C.4.1)

3

(VSS )OUT

Optimum linear velocity:

= 10 ms

FSS ' ' = (ρ SS )OUT (VSS )OUT

(

)

FSS ' ' = 36.58 mkg3 (10 ms )

(C.4.2)

FSS ' ' = 365.8 s⋅kgm 2

AC ≡ cross-sectional area of schedule 40 piping (m2). t ≡ tube wall thickness (in). ⎛d ⎞ AC = π ⎜ o − t ⎟ ⎝ 2 ⎠

2

⎛ (4.5in ) ⎞ AC = π ⎜ − 0.237in ⎟ ⎝ 2 ⎠ 2 −3 AC = 8.211 × 10 m

2

(

6.45 cm 2 in 2

)(

m2 10 cm 2 4

)

(C.4.3)

nSS ≡ number of superheated steam passes. FSS ≡ superheated steam mass flow rate (kg/s). n SS = n SS =

FSS FSS ' '× AC

(25.1746 ) (365.8 )(0.008211m ) kg s

kg

s ⋅m

(C.4.4)

2

2

n SS = 8.38 ≈ 9 passes

81

Appendix C Steam Superheater C.5

Determining the Optimum Number of Urea Steam Passes

FUS’’ ≡ urea steam mass velocity (kg/s⋅m2). 488.2 s⋅kgm 2 ≤ FUS ' ' ≤ 732.4 s⋅kgm 2

Optimum Mass Velocity:

ρUS ≡ density of urea steam (kg/m3).

(ρUS )IN = 921.4 mkg (ρUS )OUT = 11.20 mkg 3

(C.5.1)

3

nUS ≡ number of urea steam passes. FUS ≡ urea steam mass flow rate (kg/s). Let FUS’’ = 500 kg/s⋅m2 nUS = nUS =

FUS FUS ' '× AC

(500

(6.944 ) )(0.008211m ) kg s

kg

s ⋅m

(C.5.2)

2

2

nUS = 1.69 ≈ 2 passes

82

Appendix C Steam Superheater C.6

Calculations for the Shield Bank Section

TUS ≡ temperature of urea steam (°C). (TUS)IN = (TUS)OUT = 220.1°C (in the process of being vaporized) TFG ≡ temperature of flue gas (°C). (TFG)IN = 926.7°C (TFG)OUT = 765.6°C LMTD ≡ log-mean temperature difference (°C). LMTD =

LMTD =

[(T )

− (TUS )OUT ] − [(TFG )OUT − (TUS )IN ] [(T ) − (TUS )OUT ] ln FG IN [(TFG )OUT − (TUS )IN ]

FG IN

[926.7 C − 220.1 C ] − [765.6 C − 220.1 C ] = [706.6] C − [545.5] C [706.6C ] [926.7 C − 220.1 C ] ln ln [545.5 C ] [765.6 C − 220.1 C ] o

o

o

o

o

o

o

o

o

o

o

LMTD = 622.6 o C hC ≡ convection film heat transfer coefficient (W/m2·K). (TFG)AVE ≡ average flue gas temperature (°F). G ≡ water mass velocity (lb/ft2·s). do ≡ outer tube diameter (in). hC = hC =

2.14 ⋅ G 0.6 ⋅ (TFG ) AVE

(

do

0.28

0.4

2.14 ⋅ 0.4257

) ⋅ (1550 F )

lb 0.6 ft 2 s

o

0.28

(C.6.2)

(4.5in )0.4

hC = 5.913 ftBTU = 10.36 mW2 ⋅K 2 ⋅h⋅o F hRG ≡ gas radiation heat transfer coefficient (W/m2·K). hRG = [0.0025(TFG ) AVE − 0.5] ftBTU 2 ⋅h⋅o F

[

(

)

]

hRG = 0.0025 1550 o F − 0.5 hRG = 3.3875

BTU ft 2 ⋅h⋅o F

(C.6.3)

BTU ft 2 ⋅h⋅o F

= 5.936 mW2 ⋅K

83

(C.6.1)

Appendix C Steam Superheater

ho ≡ total convection coefficient (W/m2·K). ho = (1.1)(hC + hRG )

ho = (1.1)(10.36 + 5.936 ) mW2 ⋅K

(C.6.4)

ho = 17.93 mW2 ⋅K hi ≡ in tube heat transfer coefficient (W/m2·K). G ≡ water mass velocity (lb/ft2·h). do ≡ outer tube diameter (ft). k ≡ average fluid thermal conductivity (BTU/ft·h·°F). cP ≡ average fluid heat capacity (BTU/lb·°F). u ≡ bulk fluid viscosity (lb/ft·h). ⎛ k hi = (0.027 )⎜⎜ ⎝ do

(

0.8

⎞⎡ d o G ⎤ ⎡ c P u ⎤ ⎟⎟ ⎢ ⎥ ⎢ ⎥ ⎠⎣ u ⎦ ⎣ k ⎦

)

0.333

(

)⎤ ⎡⎢ (0.77725 )(0.13281 )⎤⎥ ) ⎥⎥⎦ ⎢⎣ (0.15263 ) ⎥⎦

⎛ 0.15263 ftBTU ⎞ ⎡ (0.375 ft ) 311720 ⋅h⋅o F ⎟ hi = (0.027 )⎜ ⎢ ⎜ (0.375 ft ) ⎟ ⎢ 0.13281 ftlb⋅h ⎝ ⎠⎣ hi = 549.6 ftBTU = 963.2 mW2 ⋅K 2 ⋅h⋅o F

(

lb ft 2 ⋅h

0.8

BTU lb⋅o F

lb ft ⋅h

BTU ft ⋅h⋅o F

(C.6.5) hw ≡ tube wall heat transfer coefficient (W/m2·K). KM ≡ tube wall thermal conductivity (BTU·in/ft2·h·°F). tw ≡ tube wall thickness (in). hw =

KM tw

(324 =

BTU ⋅in ft 2 ⋅h⋅o F

hw = 1367

BTU ft 2 ⋅h⋅o F

hw

(0.237in )

)

(C.6.6) = 2396 mW2 ⋅K

84

0.333

Appendix C Steam Superheater

Rt ≡ total heat transfer resistance (m2·K/W). Ao ≡ outer surface area per tube length (ft2/ft). Ai ≡ inner surface area per tube length (ft2/ft). Rt = Rt

Ao A 1 + o + hi Ai hw Ai ho

(1.178 ) + (1.178 ) + 1 = (963.2 )(1.054 ) (2396 )(1.054 ) (17.93 ) ft 2 ft

ft 2 ft

ft 2 ft

W m2K

ft 2 ft

W m2K

W m2 K

(C.6.7)

Rt = (0.0011603 + 0.0004665 + 0.0557724 ) mWK 2

Rt = 0.0573992 mWK 2

U ≡ overall heat transfer coefficient (W/m2·K). U=

1 Rt

U=

1 2 0.0573992 mWK

(

(C.6.8)

)

U = 17.42 mW2 K ASB ≡ shield bank surface area (m2). NR ≡ number of tube rows. NT ≡ number of tube per row. L ≡ horizontal tube length (ft). ASB = N R ⋅ N T ⋅ L ⋅ Ao

(

ASB = (3) ⋅ (16 ) ⋅ (16 ft ) ⋅ 1.178

ft 2 ft

)

(C.6.9)

ASB = 904.7 ft 2 = 84.05m 2 QSB ≡ heat absorption in the shield bank section (W). QSB = U ⋅ LMTD ⋅ ASB

(

)

(

QSB = 17.42 mW2 K ⋅ (622.6 K ) ⋅ 84.05m 2

)

(C.6.10)

QSB = 911.6kW = 3.282 GJh

85

Appendix C Steam Superheater

Verifying the flue gas temperature leaving the shield bank section: HA,SB ≡ heat made available based on the flue gas temperature leaving the shield bank (kJ/kg). H A, BWT H A, SB

=

QR QR + QSB

(24,189 ) kJ kg

H A, SB

=

(63.60 GJh ) (63.60 + 3.282) GJh

(C.6.11)

BTU H A, SB = 25,437 kJ kg = 12,139 lb

From chart, @ HA,SB =12,139 BTU/lb, (TFG)OUT ≈ 765.6°C (as initially assumed)*. *Note that this procedure was repeated via successive substitution on Microsoft Excel until the outlet flue gas temperature for the shield bank converged.

86

Appendix C Steam Superheater C.7

Finned Bank Section Calculations (Vaporization of Urea Water Stream)

QFB, VAP ≡ convection section heat absorption, vaporization phase (GJ/h). QFB, LIQ ≡ convection section heat absorption, liquid water heating phase (GJ/h). QFB, LIQ = 7.400×106 BTU/h = 7.81 GJ/h. (From HYSYS) QFB ,VAP = QUS − QR ,US − QSB − QFB ,.LIQ QFB ,VAP = (54.6 − 12.285 − 10.078 − 7.400 ) × 10 6 QFB ,VAP = 24.84 × 10 6

BTU h

(C.7.1)

BTU h

= 26.21 GJh

(TUS)IN ≡ inlet urea steam temperature = 428.2°F = 220.1°C (TUS)OUT ≡ outlet urea steam temperature = 428.2°F = 220.1°C (TFG)IN ≡ inlet flue gas temperature = 1410°F = 765.6°C (TFG)OUT ≡ outlet flue gas temperature = 650.8°F = 34.8°C LMTD =

LMTD =

[(T )

FG IN

− (TUS )OUT ] − [(TFG )OUT − (TUS )IN ] [(T ) − (TUS )OUT ] ln FG IN [(TFG )OUT − (TUS )IN ]

[(1410 F ) − (428.2 F )] − [(650.8 F ) − (428.2 F )] [(1410 F ) − (428.2 F )] ln [(650.8 F ) − (428.2 F )] o

o

o

o

o

o

o

o

(C.7.2)

LMTD = 511.6 o F = 284.2 K AFREE ≡ finned bank free area (m2). ft ≡ fin thickness (in). fh ≡ fin height (in). Nf ≡ number of fins per inch of tube. s ≡ spacing between tube centers (in). Nt ≡ number of tubes per row. ⎡ s − do 2 ⋅ ft ⋅ fh ⋅ N f ⎤ − AFREE = N t ⋅ L ⋅ ⎢ ⎥ in 12 inft ⎢⎣ 12 ft ⎥⎦ ⎡ (8.0 − 4.5)in 2 ⋅ (0.05in ) ⋅ (0.75in ) ⋅ (3) ⎤ AFREE = (16 ) ⋅ (16 ft ) ⋅ ⎢ − ⎥ 12 inft 12 inft ⎣⎢ ⎦⎥

( )

( )

( )

( )

AFREE = 69.87 ft 2 = 6.49m 2

87

(C.7.3)

Appendix C Steam Superheater

G ≡ flue gas mass velocity (kg/m2·s). FG ≡ flue gas mass flow rate (lb/h). FG AFREE

G= G=

(114431 lbh )

(C.7.4)

(69.87 ft ) 2

G = 1637.85

lb ft 2 h

= 0.455

lb ft 2 s

= 2.22 mkg2 s

u ≡ flue gas bulk viscosity (lb/ft·h). Re ≡ flue gas Reynolds number. Re = Re =

do ⋅ g u 4.5 ( 12 ft ) ⋅ 1637.85

(

(0.0841 )

lb ft 2 h

)

(C.7.5)

lb ft ⋅h

Re = 7304.3 At this number, dimensionless parameter J = 0.01 (from Figure C4) k ≡ flue gas thermal conductivity (BTU/ft·h·°F). cP ≡ flue gas heat capacity (BTU/lb·°F). ho ≡ total convection heat transfer coefficient (W/m2·K). ho =

ho =

J ⋅ CP ⋅ G 2

⎛ u ⋅ CP ⎞ 3 ⎜ ⎟ ⎝ k ⎠ (0.01) ⋅ 0.2968 lbBTU ⋅ 1637.85 ⋅o F

)(

(

(

)(

⎛ 0.0841 ftlb⋅h ⋅ 0.2968 BTU lb⋅o F ⎜ ⎜ 0.03397 ftBTU ⋅h⋅o F ⎝ ho = 5.97 ftBTU = 10.46 mW2 K 2 ⋅h⋅o F

(

)

)⎞⎟

lb ft 2 h

)

(C.7.6)

2 3

⎟ ⎠

ef ≡ fin efficiency. From Figure C5, ef = 0.83 .

88

Appendix C Steam Superheater

(ho)eff ≡ effective total convection heat transfer coefficient (W/m2·K). At ≡ finned tube surface area per unit tube length (ft2/ft).

(ho )eff (ho )eff (ho )eff

⎡[e f ⋅ ( At − Ao )] + Ao ⎤ = ho ⋅ ⎢ ⎥ At ⎦ ⎣ 2 2 2 ⎡[0.83 ⋅ (7.33 ftft − 1.178 ftft )] + 1.178 ftft ⎤ ⎥ = 5.97 ftBTU ⋅⎢ 2 o 2 ⋅h⋅ F ⎢⎣ ⎥⎦ 7.33 ftft = 5.12 ftBTU = 8.97 mW2 K 2 o ⋅h⋅ F

(

)

(C.7.7)

hi ≡ in-tube film heat transfer coefficient, average water properties used (W/m2·K).

⎛ k hi = (0.027)⎜⎜ ⎝ Do

0.8

⎞⎡ Do ⋅ G ⎤ ⎡ C P ⋅ u ⎤ ⎟⎟⎢ ⎥ ⎢ ⎥ ⎠⎣ u ⎦ ⎣ k ⎦

⎛ 0.3037 ftBTU ⋅h⋅o F hi = (0.027)⎜ ⎜ 0.375 ft ⎝ hi = 731.7

BTU ft 2 ⋅h⋅o F

0.333

(

⎞⎡ 0.375 ft ⋅ 1637.85 ftlb2h ⎟⎢ ⎟⎢ 0.2423 ftlb⋅h ⎠⎣

(

)

)⎤ ⎡⎢ (1.075 )⋅ (0.2423 )⎤⎥ ⎥ 0.8

BTU lb⋅o F

⎥⎦ ⎢⎣

lb ft ⋅h

0.3037 ftBTU ⋅h⋅o F

0.333

⎥⎦

= 1282.2 mW2 K (C.7.8)

Rt ≡ total heat transfer thermal resistance (m2K/W). Rt =

At A 1 + t + hi Ai hw Ai (ho )eff 2

Rt =

(731.66

Rt = 0.210

2

7.33 ftft BTU ft 2 ⋅h⋅o F

)(1.054 ) (1367 ft 2 ft

+

7.33 ftft BTU ft 2 ⋅h⋅o F

)(1.054 ) (5.12 ft 2 ft

+

1 BTU ft 2 ⋅h⋅o F

)

(C.7.9)

ft 2 ⋅h ⋅o F BTU

U ≡ total heat transfer coefficient (W/m2·K). U= U=

1 Rt 1 0.210

U = 4.76

(C.7.10)

ft 2 ⋅h ⋅o F BTU

BTU ft 2 ⋅h⋅o F

= 8.34 mW2 ⋅K

89

Appendix C Steam Superheater

AFB,VAP ≡ convective heat transfer surface, vaporization phase (m2). AFB ,VAP = AFB ,VAP =

QFB ,VAP U ⋅ LMTD 24.84 × 10 6

(4.76

BTU ft 2 ⋅h⋅o F

BTU h

)(511.6 F )

(C.7.11)

o

AFB ,VAP = 10193 ft 2 = 947 m 2

NR ≡ number of required rows. NR = NR =

ACB ,VAP N T ⋅ L ⋅ At 10193 ft 2

(

16 ⋅ (16 ft ) ⋅ 7.33 ftft

2

)

N R = 3.48 ≈ 4

(

AFB ,VAP = N R ⋅ N T ⋅ L ⋅ At = (4 ) ⋅ (16 ) ⋅ (16 ft ) ⋅ 7.33 ftft AFB ,VAP = 11728 ft 2 = 1089.6m 2

90

2

)

(C.7.12)

Appendix C Steam Superheater C.8

Finned Bank Section Calculations (Heating of Liquid Urea Stream)

QFB, LIQ = 7.400×106 BTU/h = 7.81 GJ/h. (From HYSYS) (TUS)IN ≡ inlet urea steam temperature = 269.2°F = 131.8°C (TUS)OUT ≡ outlet urea steam temperature = 428.2°F = 220.1°C (TFG)IN ≡ inlet flue gas temperature = 650.8°F = 343.8°C (TFG)OUT ≡ outlet flue gas temperature = 419.2°F = 215.1°C LMTD =

LMTD =

[(T )

FG IN

− (TUS )OUT ] − [(TFG )OUT − (TUS )IN ] [(T ) − (TUS )OUT ] ln FG IN [(TFG )OUT − (TUS )IN ]

[(650.8 F ) − (428.2 F )] − [(419.2 F ) − (269.2 F )] [(650.8 F ) − (428.2 F )] ln [(419.2 F ) − (269.2 F )] o

o

o

o

o

o

o

o

(C.8.1)

LMTD = 183.9 o F = 102.2 K AFREE ≡ finned bank free area (m2). ft ≡ fin thickness (in). fh ≡ fin height (in). Nf ≡ number of fins per inch of tube. s ≡ spacing between tube centers (in). Nt ≡ number of tubes per row. ⎡ s − do 2 ⋅ ft ⋅ fh ⋅ N f ⎤ AFREE = N t ⋅ L ⋅ ⎢ − ⎥ in 12 inft ⎥⎦ ⎢⎣ 12 ft ⎡ (8.0 − 4.5)in 2 ⋅ (0.05in ) ⋅ (0.75in ) ⋅ (3) ⎤ AFREE = (16) ⋅ (16 ft ) ⋅ ⎢ − ⎥ 12 inft 12 inft ⎢⎣ ⎥⎦ AFREE = 69.87 ft 2 = 6.49m 2

( )

( )

( )

( )

(C.8.2)

G ≡ flue gas mass velocity (kg/m2·s). FG ≡ flue gas mass flow rate (lb/h). G= G=

FG AFREE

(114431 lbh )

(C.8.3)

(69.87 ft )

G = 1637.85

2

lb ft 2 h

= 0.455

lb ft 2 s

= 2.22 mkg2 s

91

Appendix C Steam Superheater

u ≡ flue gas bulk viscosity (lb/ft·h). Re ≡ flue gas Reynolds number. do ⋅ g u 4.5 ( 12 ft ) ⋅ 1637.85

Re =

(

Re =

(0.06365 )

lb ft 2 h

)

(C.8.4)

lb ft ⋅h

Re = 9649.5 At this number, dimensionless parameter J = 0.011 (from Figure C4) k ≡ flue gas thermal conductivity (BTU/ft·h·°F). cP ≡ flue gas heat capacity (BTU/lb·°F). ho ≡ total convection heat transfer coefficient (W/m2·K). ho =

ho =

J ⋅ cP ⋅ G 2

⎛ u ⋅ CP ⎞ 3 ⎜ ⎟ ⎝ k ⎠ (0.011) ⋅ 0.2793 lbBTU ⋅ 1637.85 ⋅o F

)(

(

(

)(

⎛ 0.06365 ⋅ 0.2793 ⎜ ⎜ 0.02389 ftBTU ⋅h⋅o F ⎝ ho = 6.13 ftBTU = 10.74 mW2 K 2 ⋅h⋅o F

(

lb ft ⋅h

)

BTU lb⋅o F

)⎞⎟

lb ft 2 h

)

(C.8.5)

2 3

⎟ ⎠

ef ≡ fin efficiency. From Figure C5, ef = 0.88 . (ho)eff ≡ effective total convection heat transfer coefficient (W/m2·K). At ≡ finned tube surface area per unit tube length (ft2/ft).

(ho )eff (ho )eff (ho )eff

⎡[e f ⋅ ( At − Ao )] + Ao ⎤ = ho ⋅ ⎢ ⎥ At ⎣ ⎦ ⎡ [0.88 ⋅ (7.33 ft − 1.178 ft BTU = 6.13 ft 2 ⋅h⋅o F ⋅ ⎢ 2 ⎢⎣ 7.33 ftft = 5.51 ftBTU = 9.66 mW2 K 2 ⋅h⋅o F

(

)

2

ft 2 ft

92

)] + 1.178

ft 2 ft

⎤ ⎥ ⎥⎦

(C.8.6)

Appendix C Steam Superheater

hi ≡ in-tube film heat transfer coefficient, average water properties used (W/m2·K). ⎛ k hi = (0.027 )⎜⎜ ⎝ Do

0.8

⎞ ⎡ Do ⋅ G ⎤ ⎡ c P ⋅ u ⎤ ⎟⎟ ⎢ ⎥ ⎢ ⎥ ⎠⎣ u ⎦ ⎣ k ⎦

⎛ 0.3920 ftBTU ⋅h⋅o F hi = (0.027 )⎜ ⎜ 0.375 ft ⎝ hi = 722.5

BTU ft 2 ⋅h⋅o F

0.333

(

⎞ ⎡ 0.375 ft ⋅ 1637.85 ⎟⎢ ⎟⎢ 0.3699 ftlb⋅h ⎠⎣

(

)

lb ft 2 h

)⎤ ⎡⎢ (1.123 )⋅ (0.3699 )⎤⎥ ⎥ 0.8

⎥⎦ ⎢⎣

BTU lb⋅o F

lb ft ⋅h

0.3920

BTU ft ⋅h⋅o F

0.333

⎥⎦

= 1266.2 mW2 K

(C.8.7) Rt ≡ total heat transfer thermal resistance (m2K/W). Rt =

At A 1 + t + hi Ai hw Ai (ho )eff 2

Rt =

(722.5

Rt = 0.196

2

7.33 ftft BTU ft 2 ⋅h⋅o F

)(1.054 ) (1367 ft 2 ft

+

7.33 ftft BTU ft 2 ⋅h⋅o F

)(1.054 ) (5.51 ft 2 ft

+

1 BTU ft 2 ⋅h⋅o F

)

(C.8.8)

ft 2 ⋅h ⋅o F BTU

U ≡ total heat transfer coefficient (W/m2·K). U= U=

1 Rt 1 0.196

U = 5.10

(C.8.9)

ft 2 ⋅h ⋅o F BTU

BTU ft 2 ⋅h⋅o F

= 8.93 mW2 ⋅K

AFB,LIQ ≡ convective heat transfer surface, liquid heating phase (m2). QFB , LIQ

AFB , LIQ = AFB , LIQ

U ⋅ LMTD 7.400 × 10 6 BTU h = 5.10 ftBTU 183 . 9o F 2 ⋅h⋅o F

(

)(

(C.8.10)

)

AFB , LIQ = 7893 ft 2 = 733.3m 2

93

Appendix C Steam Superheater

NR ≡ number of required rows. NR = NR =

AFB , LIQ N T ⋅ L ⋅ At 7893 ft 2

(

16 ⋅ (16 ft ) ⋅ 7.33 ftft

2

)

N R = 2.69 ≈ 3

(

AFB , LIQ = N R ⋅ N T ⋅ L ⋅ At = (3) ⋅ (16 ) ⋅ (16 ft ) ⋅ 7.33 ftft AFB , LIQ = 8796 ft 2 = 817.2m 2

94

2

)

(C.8.11)

Appendix C Steam Superheater C.9

Calculating the Minimum Allowable Tube Wall Thickness

QR’’ ≡ average radiant heat flux (BTU/h·ft2). r ≡ ratio of maximum radiant heat flux to average radiant heat flux = 1.93 (obtained from Figure C2) fv ≡ factor for local variation in heat flux = 1.25 (assumed) fc/c ≡ factor for conductive/convective effects = 0.85 (assumed) QMAX’’ ≡ maximum local radiant heat flux (BTU/h·ft2).

QMAX ' ' = QR ' '⋅r ⋅ f v ⋅ f c

(

QMAX ' ' = 11000

BTU h⋅ ft 2

)⋅1.93 ⋅1.25 ⋅ 0.85 c

(C.9.1)

= 71154 mW2 QMAX ' ' = 22557 hBTU ⋅ ft 2 FSS ≡ superheated steam mass flow rate = 199847 lb/h = 90650 kg/h FSS’’ ≡ superheated steam mass velocity per tube = 251177 lb/ft2·h = 1.226×106 kg/m2·h (TSS)OUT ≡ final superheated steam temperature = 950°F = 510°C hi ≡ in-tube film heat transfer coefficient, water properties used @ (TSS)OUT (W/m2·K). ⎛ k hi = (0.027 )⎜⎜ ⎝ Do

0.8

⎞ ⎡ Do ⋅ G ⎤ ⎡ C P ⋅ u ⎤ ⎟⎟ ⎢ ⎥ ⎢ ⎥ ⎠⎣ u ⎦ ⎣ k ⎦

⎛ 0.04692 ftBTU ⋅h⋅o F hi = (0.027 )⎜ ⎜ 0.375 ft ⎝

0.333

(

⎞ ⎡ 0.375 ft ⋅ 251177 ⎟⎢ ⎟⎢ 0.07301 ftlb⋅h ⎠⎣

(

)

lb ft 2 h

)⎤ ⎡⎢ (0.3998 )⋅ (0.07301 )⎤⎥ ⎥ 0.8

⎥⎦ ⎢⎣

BTU lb⋅o F

0.04692

lb ft ⋅h

BTU ft ⋅h⋅o F

⎥⎦

hi = 223.1 ftBTU = 391.0 mW2 K 2 ⋅h⋅o F

(C.9.2) TM ≡ tube metal temperature (K). KM ≡ tube metal thermal conductivity (BTU/h·ft·°F). TM = (TSS )OUT +

(

)

TM = 950 o F +

QMAX ' '⋅d o QMAX ' '⋅d o ⋅ t m + hi ⋅ d i K m ⋅ (d o + t m )

(22557 )⋅ (4.5in) + (22557 )⋅ (4.5in) ⋅ (0.237in) (223.1 )⋅ (4.026in) (264 )⋅ (4.5in + 0.237in) BTU h⋅ ft 2

BTU h⋅ ft 2

BTU ft 2 ⋅h⋅o F

BTU h⋅ ft ⋅o F

TM = 1084.4 o F = 584.7 o C

95

(C.9.3)

0.333

Appendix C Steam Superheater

To allow for a safety margin, the maximum design tube temperature is set at 1200°F ≈ 650°C. PSS ≡ superheated steam operating pressure = 120 bar = 1740 psia tMIN ≡ minimum allowable tube thickness (cm). S ≡ design stress, 90% of the yield strength for austenitic steel (psia). t MIN = t MIN =

PSS ⋅ d o 2S + PSS

(1740 psia ) ⋅ (4.5in ) 2(31500 psia ) + (1740 psia )

(C.9.4)

t MIN = 0.121in = 0.307cm tMARGIN ≡ margin of tube wall allowance against corrosion and creep (cm). t MARGIN = t M − t MIN

t MARGIN = (0.602 − 0.307 )cm

(C.9.5)

t MARGIN = 0.295cm

96

Appendix C Steam Superheater C.10

Calculating the Required Stack Dimensions

VH = N ⋅ f ⋅ (0.0030 ) ⋅ G 2 ⋅ V g

(C.10.1)

VH ≡ velocity head (inH2O). N ≡ number of tubes per row. F ≡ correction factor specific to the type of tubes used. G ≡ flue gas mass velocity at the point in question (lb/s⋅ft2). Vg ≡ specific volume of the flue gas at the point in question (ft3/lb). Finding the total velocity for a 25% increase in the flue gas mass velocity: DUA ≡ draft under arch. VH DUA = 0.50inH 2 O SBL ≡ shield bank loss. VH SBL = N ⋅ f ⋅ (0.0030) ⋅ G 2 ⋅ V g

(

VH SBL = (3)(0.2 )(0.0030) 1.25 × 0.42571 s⋅lbft 2

) (52.74 ) ft 3 lb

(C.10.2)

) (35.98 )

(C.10.3)

2

VH SBL = 0.02688inH 2 O FBL ≡ finned bank loss. VH FBL = N ⋅ f ⋅ (0.0030) ⋅ G 2 ⋅ V g

(

VH FBL = (7 )(1.0 )(0.0030) 1.25 × 0.4550 s⋅lbft 2

ft 3 lb

2

VH FBL = 0.2444inH 2 O SEL ≡ stack entrance loss. VH SEL = f ⋅ (0.0030) ⋅ G 2 ⋅ V g

(

VH SEL = (0.5)(0.0030) 0.8 s⋅lbft 2

) (23.00 ) 2

ft 3 lb

(C.10.4)

VH SEL = 0.02208inH 2 O DL ≡ damper loss. VH DL = f ⋅ (0.0030) ⋅ G 2 ⋅ V g

(

VH DL = (1.5)(0.0030 ) 0.8 s⋅lbft 2

) (23.00 ) 2

ft 3 lb

(C.10.5)

VH DL = 0.06625inH 2 O

97

Appendix C Steam Superheater

SOL ≡ stack outlet loss. VH SOL = f ⋅ (0.0030) ⋅ G 2 ⋅ V g

(

VH SOL = (1.0 )(0.0030 ) 0.8 s⋅lbft 2

) (19.07 ) 2

ft 3 lb

(C.10.6)

VH SOL = 0.03660inH 2 O VH = VH DUA + VH SBL + VH FBL + VH SEL + VH DL + VH SOL

VH = (0.050 + 0.02688 + 0.2444 + 0.02208 + 0.06625 + 0.03660 )inH 2 O

(C.10.7)

VH = 0.3962inH 2 O (stack designed to accommodate a mass velocity of 0.8 lb/s⋅ft2 = 3.9 kg/s⋅m2) ⎛ 1 1 ⎞⎟ DG = (0.52 ) ⋅ LS ⋅ Patm ⋅ ⎜ − ⎜T T ⎟ ga ⎠ ⎝ a

(C.10.8)

DG ≡ draft gain (inH2O). LS ≡ section height (ft). Patm ≡ atmospheric pressure (psia). Ta ≡ ambient temperature (°R). Tga ≡ flue gas temperature (°R). DGC ≡ convection section draft gain (inH2O). ⎛ 1 1 ⎞⎟ DGC = (0.52 ) ⋅ LS ⋅ Patm ⋅ ⎜ − ⎜T T ⎟ ga ⎠ ⎝ a ⎛ 1 1 DGC = (0.52 ) ⋅ (9.5 ft ) ⋅ (14.69 psia ) ⋅ ⎜⎜ − o 1519.27 o R ⎝ 509.67 R DGC = 0.09462inH 2 O

(

) (

)

⎞ ⎟⎟ ⎠

(C.10.9)

SD ≡ required stack draft (inH2O). SD = VH − DGC

SD = (0.3962 − 0.09462)inH 2 O

(C.10.10)

SD = 0.3016inH 2 O

98

Appendix C Steam Superheater

SD’ ≡ stack draft gain per foot of stack (inH2O/ft). ⎛ 1 1 ⎞⎟ SD' = (0.52 ) ⋅ LS ⋅ Patm ⋅ ⎜ − ⎜T T ⎟ ga ⎠ ⎝ a ⎛ 1 1 SD' = (0.52) ⋅ (1.0 ft ) ⋅ (14.69 psia ) ⋅ ⎜⎜ − o 803..27 o R ⎝ 509.67 R

(

) (

)

⎞ ⎟⎟ ⎠

(C.10.11)

SD' = 0.005485 inHft2O

D ≡ required diameter of the stack (m). G=

1.25 ⋅ FG (π4 )D 2

3.905982 s⋅m 2 = kg

(

1.25 ⋅ 51,905 kgh

(π4 )D 2

)( ) 1h 3600 s

(C.10.12)

D = 2.42m = 7.95 ft SFL ≡ stack frictional loss per foot (inH2O/ft). SFL =

G 2 ⋅ Tga

(211000)D

(0.8 ) ⋅ (803.67 R ) SFL = lb 2 s ⋅ ft 2

o

(C.10.13)

(211000)(7.95 ft )

SFL = 0.0003066 inHft2O

NSE ≡ net stack effect (inH2O/ft). NSE = SD'− SFL NSE = (0.005485 − 0.0003066) inHft2O

(C.10.14)

NSE = 0.005179 inHft2O H ≡ required stack height (m). SD NSE (0.3016inH 2 O ) H= 0.005179 inHft2O H=

(

(C.10.15)

)

H = 58.24 ft = 17.75m

99

Appendix C Steam Superheater C.11

Determining the Required Number of Tubes in the Radiant Section

ASS ≡ surface area required for the superheated steam (m2). Ass = Ass =

QSS QR ' '

(50.64 GJh )

(0.1249 )

(C.11.1)

GJ h⋅m 2

Ass = 405.4m 2 AUS ≡ surface area required for the urea steam (m2). AUS = AVT − ASS

AUS = (481.1 − 405.4)m 2

(C.11.2)

AUS = 75.7m 2

NSS ≡ number of vertically aligned superheated steam tubes in the radiant section. NUS ≡ number of vertically aligned urea steam tubes in the radiant section. For each vertical tube to be the same length: ASS A = US N SS N US

( (

) )

N US A 75.7 m 2 = US = N SS ASS 405.4m 2

(C.11.3)

N US = 0.1868 N SS

NSS must be a multiple of 9 (nine steam passes), NUS must be a multiple of 2 (two steam passes). For NSS equal to 108: N US = N SS × 0.1868 N US = (108) × 0.1868

(C.11.4)

N US = 20.17 ≈ 20 NTOTAL = NSS + NUS = 128 vertical tubes

(C.11.5)

100

Appendix C Steam Superheater

ETL ≡ effective vertical tube length (m). ETL = ETL =

ASS N SS ⋅ π ⋅ d o

(4363.64 ft ) 2

(C.11.6)

108 ⋅ π ⋅ ( 412.5 ft )

ETL = 34.30 ft = 10.45m AUS = (ETL )( N US )(π )(d o )

AUS = (34.30 ft )(20 )(π )( 412.5 ft )

(C.11.7)

AUS = 808.08 ft 2 = 75.07 m 2

TCD ≡ tube-circle diameter in the radiant section (m). TCD = TCD =

N TOTAL ⋅ s

π

128 ⋅ (128 ft )

(C.11.8)

π

TCD = 27.16 ft = 8.28m

ETL 10.45m = = 1.26 TCD 8.28m

(C.11.9)

101

Appendix C Steam Superheater C.12

Summary of Superheater Results

Heating requirements: •

Superheated steam absorption: 50.64 GJ/h

•

Saturated urea steam absorption: 57.61 GJ/h

•

Natural gas consumption: 2433 kg/h

Flue gas properties: •

Flue gas emission rate: 51.9 tonnes/h

•

Radiant section operating temperature: 927ºC

•

Exiting flue gas temperature: 132ºC

•

Heat extraction efficiency: 87.9%

Radiant section: •

128 vertically-aligned bare tubes.

•

20 tubes for the saturated urea steam (2 passes, 10 tubes for each pass)

•

108 tubes for the superheated steam (9 passes, 12 tubes for each pass)

•

Effective tube length: 10.45 meters

•

Tube circle diameter: 8.28 meters (20.3 cm tube-center spacing)

•

Ratio of effective tube height to tube circle diameter: 1.26

Shield bank section: •

3 rows, 16 bare tubes per row (20.3 cm tube-center spacing)

•

Effective tube length: 4.88 meters

•

Saturated steam for the urea plant (2 passes)

102

Appendix C Steam Superheater

Finned bank section: •

7 rows, 16 finned tubes per row (20.3 cm tube-center spacing)

•

3 circular fins per inch of tube length (1.2 fins/cm)

•

Circular fins: ¾ inches high × 0.05 inches thick (1.91 cm high × 0.13 cm thick)

•

Surface area: 2.23 m2 per meter of tube length

•

Effective tube length: 4.88 meters

•

Saturated steam for the urea plant (2 passes)

Emission Stack: •

Stack diameter: 2.42 meters

•

Stack height: 17.75 meters

Tubing: •

Schedule 40 piping

•

Outer diameter: 4.5 inches (11.4 cm)

•

Inner diameter: 4.03 inches (10.2 cm)

•

Tube wall thickness: 0.237 inches (0.602 cm)

•

Construction material: type HK-40 austenitic steel.

•

Type HK-40 mass composition: 25% chromium, 20% nickel, 55% iron.

•

Minimum allowable tube wall thickness: 0.307 cm

•

Tube wall thickness margin against corrosion and creep: 0.295 cm

103

Appendix C Steam Superheater

Figure C.12.1: Heat available from the combustion of a 19,700 Btu/lb (LHV) refinery gas

104

Appendix C Steam Superheater

Figure C.12.2: Distribution of radiant heat transfer rate around the tubes, dependent upon coil arrangement and firing mode

105

Appendix C Steam Superheater

Figure C.12.3: Determining the duty-split between radiant and convection sections based on the bridgewall temperature

106

Appendix C Steam Superheater

Figure C.12.4: Finding the dimensionless parameter J to determine the heat transfer coefficients on the flue-gas side of serrated fins

107

Appendix C Steam Superheater

Figure C.12.5: Determining the fin efficiency based on the convection film coefficient as well as the fin design & thermal conductivity

108

Appendix D: Heat Exchangers

109

Appendix D Heat Exchangers D.1

Heat Exchanger Specifications

Table D.1.1: Heat exchanger specifications

Unit Waste Heat Exchanger 1 Waste Heat Exchanger 2 Gas/Gas Heat Exchanger

Duty

Surface Area

Overall Heat Transfer Coefficient

Shell

Tube

(kW)

(m2)

(kW/K)

Passes

Passes

27765

162

124

1

2

36835

220

207

1

2

65855

2420

2083

1

1

Table D.1.2: Heat exchanger inlet and outlet specifications

Shell

Shell

Tube

Tube

Waste Heat Exchanger 2

Inlet boiler feed water 130°C 129 bar boiler feed water 130°C 129 bar

Outlet boiler feed water 323.7°C 120 bar boiler feed water 323.7°C 120 bar

Gas/Gas Heat Exchanger

synthesis gas 31.22°C 190 bar

synthesis gas 300°C 189.9 bar

Inlet synthesis gas 507.8°C 184.8 bar synthesis gas 473.0°C 183.4 bar ammonia product 340.1°C 183.1 bar

Outlet synthesis gas 400°C 183.9 bar synthesis gas 340.1°C 183.1 bar ammonia product 55.64°C 1 182 bar

Unit

Waste Heat Exchanger 1

110

Appendix E: Compressors and Turbines

111

Appendix E Compressors and Turbines

E.1

Compressor and Turbine Specifications

Table E.1.1: Summary of compressor/turbine information

Unit

Synthesis Gas Compressor CO2 Compressor Synthesis Gas Turbine CO2 Turbine

Power Required Or Generated (kW)

Steam Flow Rate (tonnes/hr)

Cooling Water Flow Rate (tonnes/hr)

PSV Size (m)

13 704

N/A

295

0.044

6 855

N/A

160

0.019

13 704

60.4

N/A

N/A

6 855

30.2

N/A

N/A

Table E.1.2: Stream compositions as H/N ratio varies

H/N ratio

[H2]

[N2]

[Ar]

MW

2.5 3

0.7061 0.7425

0.2825 0.2475

0.0114 0.0100

5.1239 4.6145

3.5

0.7709

0.2202

0.0089

4.2173

112

Appendix E Compressors and Turbines

E.2

Synthesis Gas Compressor Pressure Safety Valve Design

Case: The discharge of the compressor is blocked in. This will result in no flow through the compressor. We must determine the largest orifice diameter required for our PSV to vent the system. The maximum allowable pressure inside the compressor is 21x106 Pa. Using the mechanical energy balance equation:

⎛P v 2 ⎞ Ws − Flwf Δ⎜⎜ + gh + ⎟⎟ = & ρ m 2 ⎠ ⎝ Let us define our control volume as the PSV. Entering this volume is the fluid at 21x106 Pa, and leaving the control volume the fluid is venting to an atmospheric pressure of 101 Pa. In this situation, we can make three assumptions: •

No work is being preformed by the system.

•

The change in height across the PSV is negligible.

•

The friction loss across the PSV will also be negligible.

•

The fluid will start from rest, because there will be no flow when the compressor outlet is blocked in.

These assumptions reduce the MEB equation to: ⎛ Δ P v 22 ⎞ ⎜⎜ ⎟=0 − 2 ⎟⎠ ⎝ ρ

The target composition for the synthesis gas stream is a ‘hydrogen to nitrogen’ (H/N) ratio of 3. However, it is conceivable that this ratio might vary in a worst case

113

Appendix E Compressors and Turbines

scenario. As we can see in Table E2, the as the H/N ratio gets smaller, the density and molecular weight of the synthesis gas stream gets larger. This smaller H/N ratio will result in a lower velocity, which will increase the size of the PSV required. As the synthesis gas is being compressed to 21x106 Pa, its temperature will increase to approximately 77oC. As a result, the density of the stream, with a H/N ratio of 2.5 will be 65.43 kg/m3, or 6.681 kmol/m3. Solving the MEB for the resulting velocity:

ΔP

(21 × 10 6 Pa − 101Pa ) v2 = 2 = 2 = 799m / s 65.43kg / m 3 ρ

(E.1.1)

The combined flow entering the fourth stage of the synthesis gas compressor is 8.05 kmol/s. Converting this to a volumetric flow rate:

~ m 8.05kmol / s Q= ~ = = 1.205m3 / s 3 ρ 6.681kmol / m

(E.1.2)

The required diameter for the PSV orifice is then:

A=

D=

π 4

D2 = 4

π

A=

Q 1.205m 3 / s = = 1.51 × 10 −3 m 2 v2 799m / s 4

π

(1.51 × 10−3 m 2 ) = 0.0438m = 1.72in.

(E.1.3)

(E.1.4)

Rounding this value up to 2” allows for some extra capacity, and will be a more readily available size.

114

Appendix E Compressors and Turbines

E.3

CO2 Compressor Pressure Safety Valve Design

Case: The discharge of the compressor is blocked in, resulting in no flow through the compressor. We must determine the largest orifice diameter required for our PSV to vent the system. The maximum allowable pressure in the CO2 compressor was assumed to be 17.25x106 Pa. This is 15% greater than the outlet pressure of 15x106 Pa that the compressor will operate at. Following a similar development as in Appendix E.1, we arrive at the following equation. v2 =

2

ΔP

ρ

Compressed to this pressure, the CO2 would be 141oC, with a density of 274.1 kg/m3, and a molar density of 6.346 kmol/m3.

v2 =

2

ΔP

ρ

=

2

(17 . 25 × 10 6 Pa − 101 Pa ) = 354 m / s 274 . 1 kg / m 3

(E.2.1)

The combined flow entering the fourth stage of the CO2 compressor is 0.611 kmol/s. Converting this to a volumetric flow rate: ~ m 0 . 611 kmol / s Q = ~ = = 0 . 0963 m 3 / s ρ 6 . 346 kmol / m 3

(E.2.2)

The required diameter for the PSV orifice is then: A =

D =

π 4

D

4

π

2

=

A =

Q 0 . 0963 m 3 / s = = 0 . 272 × 10 v2 354 m / s

4

π

( 0 . 272 × 10

−3

−3

m

2

m 2 ) = 0 . 0186 m = 0 . 733 in .

115

(E.2.3)

(E.2.4)

Appendix E Compressors and Turbines

Rounding this orifice diameter up to 3/4” allows for some extra capacity. This will also be a more readily available orifice size.

116

Appendix F: Economics

117

Appendix F Economics Table F.1.1: Summary of the cost of each piece of process equipment

Price ($CDN) $17,250,000 $1,610,000 $6,612,500 $1,086,750 $5,635,000 $483,000 $442,750 $5,740,800 $1,312,533 $1,058,613 $41,231,946

Process Unit Synthesis Gas Compressor Synthesis Gas Turbine CO2 Compressor CO2 Turbine Gas/Gas Heat Exchanger Waste Heat Exchanger 1 Waste Heat Exchanger 2 Superheater Ammonia Convertor 1 Ammonia Convertor 2 Total Equipment Cost Table F.1.2: Feed stream costs

Stream

Synthesis Gas Boiler Feed Water Cooling Water Fuel Gas Combustion Air Low Pressure CO2

Mass Flow Rate (tonne/hr) 79.2 115.9 455.5 2.433 49.46 95.03

Cost ($/tonne) 208 0.95 0.50 400 N/A N/A

Cost ($/hr) 16474 110 228 973 N/A N/A

Total Stream Cost $17,785 Table F.1.3: Product stream prices

Stream

Ammonia Product Low Pressure CO2 Steam (23 bar) Turbine Condensate Flue Gas Used Cooling Water

Mass Flow Rate (tonne/hr) 79.2 95.03

Price ($/tonne) 341 20.00

Price ($/hr) 27007 1901

25 90.83 51.89 455.5

20.00 0.85 N/A N/A

500 77 N/A N/A

Total Stream Cost $29,485

118

Appendix F Economics F.1

Determining the Bare Module Cost of the Required Equipment

NOTE: Equations and data used were found from Ulrich and Vasudevan, 20043. Compressors and Turbines: CO2 (Centrifugal) Compressor:

fluid power = ε i × ws = 0.75 × 6855 kW

(F.1.1)

= 5141 kW From Figure 5.30 of Ulrich3, Cpur = $2,300,000 C BM = C Pur × FBM

= $2,300,000 × 2.5

(F.1.2)

= $5,750,000 Synthesis Gas (Centrifugal) Compressor:

fluid power = ε i × ws

= 0.75 × 13704kW

(F.1.3)

= 10,278 kW From Figure 5.30 of Ulrich3, Cpur = $6,000,000 C BM = C Pur × FBM = $6,000,000 × 2.5

(F.1.4)

= $15,000,000

119

Appendix F Economics CO2 Turbine:

ws = 6 855 kW

FBM = 3.5 for steam turbine

From Figure 5.21 of Ulrich3, Cpur = $270,000 C BM = C Pur × FBM = $270,000 × 3.5

(F.1.5)

= $945,000 Synthesis Gas Turbine:

ws = 13 704 kW

FBM = 3.5 (Steam Turbine)

From Figure 5.21 of Ulrich3, Cpur = $300,000 C BM = C Pur × FBM = $400,000 × 3.5

(F.1.6)

= $1,400,000

Heat Exchangers: Gas/Gas Heat Exchanger:

From Figure 5.38 of Ulrich3, a

FBM = 7 A = 2420 m2 From Figure 5.36 of Ulrich3, C Pur = $700,000 C BM = C Pur × FBM

a

= $700,000 × 7

(F.1.7)

= $4,900,000

120

Appendix F Economics Waste Heat Exchanger 1:

From Figure 5.38 of Ulrich3, a

FBM = 7 A = 220 m2 From Figure 5.36 of Ulrich3, C Pur = $60,000 C BM = C Pur × FBM

a

= $60,000 × 7

(F.1.8)

= $420,000

Waste Heat Exchanger 2:

From Figure 5.38 of Ulrich3, a

FBM = 7 A = 162 m2 From Figure 5.36 of Ulrich3, C Pur = $55,000 C BM = C Pur × FBM

a

= $55,000 × 7

(F.1.9)

= $385,000

121

Appendix F Economics Superheater:

C BM = C Pur × FBM × F p = $1,300,000 × 9.3 × 1.65

(F.1.10)

= $4,992,000 Reactors: Ammonia Convertor 1:

From Figure 5.47 of Ulrich3,

c = $8.00 / kg ρ B = 800kg / m 3 cρ B = $6400 / m 3 FBM =

$6400 / m 3 $3750 / m 3

(F.1.11)

=1.7067 C Pur = $200,000 Catalyst Cost: C BM1 = C Pur × FBM = $200,000 × 1.7067

(F.1.12)

= $341,333 Vessel Cost: I.D. = 2.477m LVessel = 10.94 m

122

Appendix F Economics

From Figure 5.45 of Ulrich3, FP = 7.94 (Operating Pressure = 190 bar) FM = 1.00 (Carbon Steel)

From Figure 5.46 of Ulrich3, a

FBM = 16 From Figure 5.44 of Ulrich3, CPur = $50,000 C BM 2 = C Pur × FBM

a

= $50,000 × 16

(F.1.13)

= $800,000 Total Cost: C BM = C BM1 + C BM 2 = $341,333 + $800,000

(F.1.14)

= $1,141,333 Ammonia Convertor 2:

From Figure 5.47 of Ulrich3,

c = $8.00 / kg ρ B = 800kg / m 3 cρ B = $6400 / m 3 FBM =

$6400 / m 3 $3750 / m 3

(F.1.15)

=1.7067 C Pur = $200,000

123

Appendix F Economics

Catalyst Cost: C BM1 = C Pur × FBM

= $200,000 × 1.7067

(F.1.16)

= $341,333 Vessel Cost: I.D. = 2.794m LVessel = 10.85 m From Figure 5.45 of Ulrich3, FP = 7.94 (Operating Pressure = 190 bar) FM = 1.00 (Carbon Steel)

From Figure 5.46 of Ulrich3, a

FBM = 16 From Figure 5.44 of Ulrich3, CPur = $33,000 C BM 2 = C Pur × FBM

a

= $33,000 × 16

(F.1.17)

= $528,000 Total Cost: C BM = C BM1 + C BM 2

= $392,533 + $528,000

(F.1.18)

= $920,533

124

Appendix F Economics F.2

The Feasibility of Firing the Superheater Using Hydrogen

Synthesis Gas Cost: $6.50/GJ Required Energy to produce Ammonia: 32 GJ/tonne NH3 Cost of Ammonia =

=

$6.50 32 GJ × GJ tonne NH 3

(F.2.1)

$208 $0.094 = tonne NH 3 lb syn − gas

1 lb syn − gas = 0.11325 lbmol syn − gas =

0.7425 molH 2 × 0.11375 lbmol syn − gas lbmol syn − gas

(F.2.2)

= 0.084088 lbmol H 2 = 0.084088 lbmol H 2 ×

2.0158 lb H 2 lbmol H 2

1 lb syn − gas = 0.1695046 lb H 2 Net Heating Value of Hydrogen Gas: 54 492 kJ/ lb H2 Net Heating Value of syn − gas =

0.054459 GJ 0.1695406 lb H 2 × lb H 2 lb syn − gas

(F.2.3)

= 0.009231 GJ / lb syn − gas Energy Cost from H 2 =

$0.094 0.009231 GJ × lb syn − gas lb syn − gas

(F.2.4)

= $10.22 / GJ Energy Cost of Natural Gas = $8.50 / GJ Based on this analysis, natural gas is the more economically viable option for firing the superheater.

125

Appendix F Economics F.3

Stream Cost Analysis

Feed Stream Costs:

Cost of syn − gas feed = flow × cos t =

79.2 tonne $208 × hr tonne

(F.3.1)

= $16500 / hr Cost of boiler feed water = flow × cos t =

115.9 m 3 $0.95 × hr m3

(F.3.2)

= $100 / hr Cost of Cooling water = flow × cos t =

455.5 m 3 $0.50 × hr m3

(F.3.3)

= $200 / hr Cost of fuel gas = flow × cos t =

2.433 tonne $400 × hr tonne

(F.3.4)

= $1000 / hr

126

Appendix F Economics Product Stream Prices:

Calculation of Ammonia Price: ammonia product price = energy cos t + profit m arg in + utility cos t =

32GJ $8.00 $75 $10 × + + tonne GJ tonne tonne

=

$341 tonne

(F.3.5)

Pr ice of ammonia product = flow × price =

79.2 tonne $341 × hr tonne

(F.3.6)

= $27,000 / hr Pr ice of compressed CO2 = flow × price =

90.53 tonne $20 × hr tonne

(F.3.7)

= $1,900 / hr Pr ice of 23bar steam = flow × price =

25 tonne $20 × hr tonne

(F.3.8)

= $500 / hr Pr ice of turbine condensate = flow × price =

90.83 m 3 $0.85 × hr m3

= $75 / hr

127

(F.3.9)

Appendix F Economics Overall Revenue: Overall Re venue = ∑ price − ∑ cos t = ($27000 / hr + $1900 / hr + $500 / hr + $75 / hr ) − ($16500 / hr + $100 / hr + $200 / hr + $1000 / hr )

= $11,700 / hr

128

(F.3.10)