P & I Design Ltd Process Instrumentation Consultancy & Design

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1 P & I Desgn Ltd Process Instrumentaton Consultancy & Desgn 2 Reed Street, Gladstone Industral Estate, Thornaby, TS17 7AF, Unted Kngdom. Tel. +44 (0) Fax. +44 (0) Web Ste: PROCESS MODELLING SELECTION OF THERMODYNAMIC METHODS by John E. Edwards jee@pdesgn.co.uk MNL031B 10/08 PAGE 1 OF 38

2 Process Modellng Selecton of Thermodynamc Methods 1.0 Introducton Contents 2.0 Thermodynamc Fundamentals 2.1 Thermodynamc Energes 2.2 Gbbs Phase Rule 2.3 Enthalpy 2.4 Thermodynamcs of Real Processes 3.0 System Phases 3.1 Sngle Phase Gas 3.2 Lqud Phase 3.3 Vapour lqud equlbrum 4.0 Chemcal Reactons 4.1 Reacton Chemstry 4.2 Reacton Chemstry Appled 5.0 Summary Appendces I II III IV V VI VII VIII Enthalpy Calculatons n CHEMCAD Thermodynamc Model Synopss Vapor Lqud Equlbrum Thermodynamc Model Selecton Applcaton Tables K Model Henry s Law Revew Inert Gases and Infntely Dlute Solutons Post Combuston Carbon Capture Thermodynamcs Thermodynamc Gudance Note Predcton of Physcal Propertes Fgures 1 Ideal Soluton Txy Dagram 2 Enthalpy Isobar 3 Thermodynamc Phases 4 van der Waals Equaton of State 5 Relatve Volatlty n VLE Dagram 6 Azeotrope γ Value n VLE Dagram 7 VLE Dagram and Convergence Effects 8 CHEMCAD K and H Values Wzard 9 Thermodynamc Model Decson Tree 10 K Value and Enthalpy Models Selecton Bass PAGE 2 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

3 Process Modellng Selecton of Thermodynamc Methods References 1. C.C. Coffn, J.Chem.Educaton 23, (1946), A Presentaton of the Thermodynamc Functons. 2. R.M. Felder and R.W. Rousseau, Elementary Prncples of Chemcal Processes, 2 nd Edton, John Wley and Sons. 3. R.C. Red, J.M. Prausntz, B.E. Polng, The Propertes of Gases and Lquds, 4 th Edton, McGraw Hll. 4. I. Smallwood, Solvent Recovery Handbook, Edward Arnold, R.H.Perry, Chemcal Engneers Handbook, McGraw Hll. 6. R.Sander, Complaton of Henry s Law Constants for Inorganc and Organc Speces of Potental Importance n Envronmental Chemstry, Max-Planck Insttute, Verson 3, Aprl J.R.W.Warn, Concse Chemcal Thermodynamcs, van Rostrand Renhold, Kent, R. L. and Esenberg, Hydrocarbon Processng, Feb. 1976, p F.G. Shnskey, Process Control Systems, McGraw-Hll, O.Levenspel, Chemcal Reacton Engneerng, Wley, 2 nd Edton, J.Wlday and J.Etchells, Workbook for Chemcal Reactor Relef Szng, HSE Contract Research Report 136/ H.S.Fogler, Elements of Chemcal Reacton Engneerng, 3 rd Edton, Prentce Hall, p K.J.Ladler, Theores of Chemcal Reacton Rates, New York, R.E.Kreger, 1979, p38. Acknowledgements Ths paper has been developed from experence ganed whlst workng n the smulaton feld. Ths work has been supported throughout by Chemstatons, Houston, Texas, TX and the author s partcularly ndebted to Aaron Herrck and Davd Hll for ther contnued and unstntng help. PAGE 3 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

4 Process Modellng Selecton of Thermodynamc Methods 1.0 INTRODUCTION The selecton of a sutable thermodynamc model for the predcton of the enthalpy-h and the phase equlbrum-k s fundamental to process modellng. An napproprate model selecton wll result n convergence problems and erroneous results. Smulatons are only vald when the approprate thermodynamc model s beng used. The selecton process s based on a detaled knowledge of thermodynamcs and practcal experence. Most smulators are provded wth Wzards to ad selecton whch should be used wth cauton. The selecton process s guded by consderng the followng:- Process speces and compostons. Pressure and temperature operatng ranges. System phases nvolved. Nature of the fluds. Avalablty of data. There are four categores of thermodynamc models:- Equatons-of-State (E-o-S) Actvty coeffcent (γ) Emprcal Specal system specfc Ths paper s not ntended to be a rgorous analyss of the methods avalable or n ther selecton but s offered as an ade memore to the practcng engneer who s lookng for rapd, realstc results from hs process models. The study of complex systems nvarably nvolves extensve research and consderable nvestment n manpower effort by specalsts. There are extensve sources of physcal property data avalable from organsatons such as DECHEMA DIPPR TÜV NEL Ltd amongst others. Ths paper presents selecton methods developed n dscussons wth engneers n the feld. The valdty of the thermodynamc models beng used should be tested aganst known data whenever possble. PAGE 4 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

5 Process Modellng Selecton of Thermodynamc Methods 2.0 THERMODYNAMIC FUNDAMENTALS 2.1 Thermodynamc Energes (1) The thermodynamc fundamentals of flud states n relaton to energes and phase behavour needs to be thoroughly understood. Four thermodynamc varables determne sx thermodynamc energes: Intensve varables Extensve varables (capacty) Pressure (P) Volume (V) Temperature (T) Entropy (S) We defne thermodynamc energy as follows: Energy = Intensve varable x Extensve varable P or T V or S TS represents nternal bound energy sothermally unavalable. PV represents external free energy. Helmholtz Free Energy (F) s the Internal Energy avalable for work and s part of the Internal Energy (U) We have the followng energy relatonshps: Internal Energy Gbbs Free Energy Enthalpy U = T S + F G = F + P V H = T S + F + P H = U + P V V When consderng chemcal reactons we have Chemcal Energy = Chemcal Potental Factor x Capacty Factor du = 0 ( µ ) dn µ Where For equlbrum µ dn 0 dn s change n speces moles µ s chemcal potental speces du = T ds P dv + µ dn = Other equlbrum condtons df = 0 ( constv & T) dg = 0 ( constp & T) du = 0 ( consts & V) ( consts & P) dh = 0 It can be shown that G = µ n PAGE 5 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

6 Process Modellng Selecton of Thermodynamc Methods 2.2 Gbbs Phase Rule (2) The varables that defne a process condton are n two categores Extensve varables Intensve varables moles, mass, volume temperature, pressure, densty, specfc volume, mass and mole fractons of components. The number of ntensve varables that can be ndependently specfed for a system at equlbrum s called the number of degrees of freedom F and s gven by the Gbbs Phase Rule. In a system nvolvng no reactons ths s gven by: F = 2 + m p Where m = no of chemcal speces p = number of system phases Wth r ndependent reactons at equlbrum F = 2 + m r p When defnng a stream condton n the model the phase rule apples. Consder a sngle component lqud n equlbrum wth ts vapour and an nert. Gvng m = 2 p = 2 F = 2 Two varables P and T or Vapour fracton (v) wth T or P wll defne the stream. For a bnary lqud system one degree of freedom s consumed by the composton leavng ether P or T to be specfed. In a VLE system t s preferable to specfy P whch then allows system analyss usng Txy plots. When settng up a Flash UntOp applyng the phase rule wll ensure that the relevant flash condtons are beng set. The stream flash calculaton can be used to determne the bolng pont and dew pont of mxtures wth and wthout nerts present by applyng the followng: The bubble pont of a lqud at the gven pressure s determned by a flash calculaton at a vapour fracton of 0. The dew pont of a vapour at the gven pressure s determned by a flash calculaton at a vapour fracton of 1. Note that for a pure component the bubble pont and the dew pont are dentcal so a flash calculaton at a vapour fracton of 0 or 1 wll yeld the same result Fgure 1 shows the Txy dagram for Benzene/Toluene, a near deal mxture. The bubble pont for a gven composton s read drectly from the lqud curve and the dew pont s read drectly from the vapour curve. PAGE 6 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

7 Process Modellng Selecton of Thermodynamc Methods 2.2 Gbbs Phase Rule (2) (Cont) The bubble pont of a mxture s determned by tral and error from value of T bp that satsfes: P = x p * ( ) T The dewpont of a mxture s determned by tral and error from value of T dp that satsfes: bp y P = 1 * p ( Tdp) The followng table s presented as an ade memore to show the relatonshps between volumes, moles, and mass. Table Presentng Molar and Mass Relatonshps for Mxture wth Speces Volume n Mass n 1 Molar MW % Component 1 m 3 m 3 Mass Flow % w/w Flow v/v kg/kmol m 3 /m 3 kg/m 3 kg/h kmol/h PA A MA PA VA = PAM A 100 PA MA W PA MA W PA P M P M P M B MB PB PB VB = PBMB C MC PC PC VC = PCMC Total PM Acknowledgements to the late Doug Lndsley for ths format. 100 P M P M 100 P B P M C M B C W P B M P M W P C P M 100 W M B C W P P M W P B P M C 100 W P M % mol PA PB PC 100 We have defned: 1 g-mole of any gas occupes ltre(dm 3 ) at 0ºC and 1 atmosphere. Therefore we can say that the same g-mole of any gas wll occupy the same volume gvng: Mole % = Volume % For a Total Flow of W (kg/h) and a mxture densty of ρ G 0 = M (kg/m3 ) we have: Volumetrc Flow Q = W G O W = P M (Nm 3 /h) where average mw P M M = (kg/kmol) 100 To correctng for temperature and pressure gas densty calculatons are calculated from: MW Pf ρ = G kg / m Zf Tf where s n unts of ltre(dm 3 )/g-mole or m 3 /kg-mole of any gas at NTP(0ºC,1atm), M w s molecular weght g/mol or kg/kmol. PAGE 7 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

8 Process Modellng Selecton of Thermodynamc Methods 2.3 Enthalpy Enthalpy s the sum of the nternal energy (U) and the external free energy (PV) where: The heat suppled s gven by: H = U + P V dq = du + P dv The sgn conventon should be noted and s + for heat added and du gan n nternal energy du = C v dt The specfc heat at constant pressure C p s related to heat nput: dq = C p dt The adabatc ndex or specfc rato γ s defned: Cp γ = Cv It can be shown that the followng relatonshp holds Cp Cv = R The heatng of a lqud at constant pressure e.g. water s consdered n Fgure 2. Ths shows the relatonshps between the enthalpes n the dfferent phases namely the sensble heat n the lqud phase, the latent heat of vaporsaton durng the vapour lqud equlbrum phase and the superheat n the gas phase. Enthalpy s calculated usng Latent Heat (LATE) n the lqud and vle phases and E-o-S (SRK) n the superheated or gas phase. Appendx I revews the calculaton methods adopted n CHEMCAD. A standard reference state of 298ºK for the lqud heat of formaton s used provdng the advantage that the pressure has no nfluence on the lqud C p. The enthalpy method used wll depend on the K-value method selected as detaled n Appendx II. CHEMCAD forces the followng H-values from K-value selected. Equlbrum-K Peng Robnson (PR) Grayson-Streed-Choa-Seeder(GS) ESSO Benedct-Webb-Rubn-Starlng (BWRS) AMINE Enthalpy-H PR Lee Kessler (LK) LK BWRS AMINE Specal methods are used for: Enthalpy of water steam tables (emprcal) Acd gas absorpton by DEA and MEA Sold components PAGE 8 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

9 Process Modellng Selecton of Thermodynamc Methods 2.4 Thermodynamcs of Real Processes (7) To establsh f a real process s possble we need to consder: G = H T S The values for H are determned from the heats of formaton of the components and for S from thermodynamc property tables. Superscrpt 0 ndcates materals present n standard state at 298ºK. For sothermal processes at low temperature the H term s domnant. At absolute zero S and T are zero so G = H. The relatonshp shows S becomng of ncreasng mportance as the temperature ncreases. Adsorpton Processes The enthalpy change s H = G + T S wth G beng necessarly negatve. All adsorptons wth negatve entropy change, whch comprse all physcal and the great majorty of chemcal adsorptons, are exothermc. Evaporaton Processes When a lqud bols the vapour pressure s equal to the atmospherc pressure and the vapour s n equlbrum wth the lqud. If there s no superheat the process s reversble and G = 0 and the entropy change can be calculated: H vaporsaton S = TB Entropes of vaporsaton, at these condtons, have values near 88 J/molºK, and substtuton n the above gves Trouton s rule. However n the case of water, due to sgnfcant hydrogen bondng, the entropy change on evaporaton s larger at J/molºK. Endothermc Chemcal Processes The lnk between Gbbs free energy and the reacton equlbrum constant K s represented by the equaton G = -RT log K A reacton wll proceed provded G s negatve. The reacton temperature can alter the sgn and therefore the process feasblty. Chemcal Equlbrum For a reacton at equlbrum (all reactons can be consdered equlbrum snce no reacton goes to completon) there s no net reacton n ether drecton and we have: G = 0 In CHEMCAD the Gbbs reactor s based on the prncpal that at chemcal equlbrum the total Gbbs free energy of the system s at ts mnmum value. The Gbbs reactor can be used n the study of combuston processes ncludng adjustment of ar to fuel ratos and calculaton of the heats of reacton. PAGE 9 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

10 Process Modellng Selecton of Thermodynamc Methods 3.0 SYSTEM PHASES There are three phase states namely sold, lqud and gas. Processes comprse ether sngle phase or multphase systems wth separaton processes nvolvng at least two phases. Processes nvolvng solds such as fltraton and crystallsaton, sold lqud systems and dryng, sold gas system are specal cases and receve no further consderaton here. The prmary area of nterest for thermodynamc model selecton nvolve two phases. Lqud lqud systems, such as extracton and extractve dstllaton, where lqud lqud equlbrum (LLE) s consdered and vapour lqud systems, such as dstllaton, strppng and absorpton, where vapour lqud equlbrum (VLE) s consdered. Fgure 3 shows the nter-relatonshps between the system phases for a seres of sotherms based on the Equaton of State (E-o-S) due to van-der-waal. Ths fgure provdes the frst ndcaton of the valdty of makng a thermodynamc model selecton for the K-value on the bass of the system phases namely sngle phase gas by E-o-S and VLE by actvty coeffcent. 3.1 Sngle Phase Gas (2) An E-o-S relates the quantty and volume of gas to the temperature and pressure. The deal gas law s the smplest E-o-S P V = n R T Where P = absolute pressure of gas V = volume or volume of rate of flow n = number of moles or molar flowrate R = gas constant n consstent unts T = absolute temperature In an deal gas mxture the ndvdual components and the mxture as a whole behave n an deal manner whch yelds for component the followng relatonshps P V n R T p n = = y where y s mole fracton of n gas P n p = y P p P where P s the total system pressure = = 0 = µ + 0 µ R T ln p Note that when p = 1 we have µ = µ the reference condton As the system temperature decreases and the pressure ncreases devatons from the deal gas E-o-S result. There are many equaton of state (3) avalable for predctng non-deal gas behavour and another method ncorporates a compressblty factor nto the deal gas law. PAGE 10 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

11 Process Modellng Selecton of Thermodynamc Methods 3.1 Sngle Phase Gas (2) (Cont) To predct the behavour of real gases the concept of fugacty f s ntroduced gvng: µ 0 = µ + R T ln Fugacty and pressure become dentcal at zero pressure, where lmt f P 0 1 P Fugacty s not the actual pressure. It has to account for the actual behavour of real gases and to overcome the assumpton of perfect behavour beng stll part of the basc equaton. Fugacty s of mportance when consderng processes exhbtng hghly non-deal behavour nvolvng vapour lqud equlbrum. Vral Equaton of State s gven by the followng: f ( T ) C ( T ) + + P V B = R T V V Where B(T) s the second vral coeffcent C(T) s the thrd vral coeffcent Note f B = C = 0 the equaton reduces to the deal gas law. Benedct Webb Rubn (BWR) Equaton of State Ths E-o-S s n the same form as the above equaton extended to a ffth vral coeffcent. BWR s accurate for gases contanng a sngle speces or a gas mxture wth a domnant component e.g. natural gas, and provdes consderable precson. Cubc Equatons of State Ths represents an E-o-S lnear n pressure and cubc n volume and s equvalent to the vral equaton truncated at the thrd vral coeffcent. One of the frst E-o-S was that due to van der Waals (Unversty of Leden), developed n 1873, whch s shown n Fgure 4. Ths was based on two effects 1. The volume of the molecules reduces the amount of free volume n the flud, (V-b) 2. Molecular attracton produces addtonal pressure. The flud pressure s corrected by a term related to the attracton parameter a of the molecules, (P+a/V 2 ) The resultng equaton s: From the relatonshp: = R T a ( V b ) V ( ) P 2 d ln f V = R T t can be shown for van der Waals equaton: dp ln f = ln R T + b V 2 a R T ( V b ) ( ) V b PAGE 11 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

12 Process Modellng Selecton of Thermodynamc Methods 3.1 Sngle Phase Gas (2) (Cont) The most wdely used cubc E-o-S s the Soave modfcatons of the Redlch-Kwong (SRK) equaton whch s a modfcaton to van der Waals orgnal equaton. P = R V ( ) ( + ) V T b α V a b Where α, a and b are system parameters. Parameters a and b are determned from the crtcal temperature T c and crtcal Pressure P c. Parameter α s determned from a correlaton based on expermental data whch uses a constant called the Ptzer Accentrc Factor (3). At the crtcal pont the two phases (gas and lqud) have exactly the same densty (techncally one phase). If T > T c no phase change occurs. Refer to Fgure 2. Appendx VIII revews the predcton of physcal propertes n further detal. Compressblty Factor Equaton of State The Compressblty Factor E-o-S retans the smplcty of the deal gas law but s applcable over a much wder range of condtons. P V = z n R T where z s the compressblty factor. The compressblty factor, dependent on the gas temperature and pressure, vares for dfferent gases and s determned from reference data (5). If data s not avalable for the specfc gas generalsed compressblty charts can be used whch requre the crtcal temperature and crtcal pressure of the gas For sngle phase gas systems the followng gudelnes for thermodynamc model selecton are proposed: Process Applcaton Equlbrum-K Enthalpy-H Hydrocarbon systems Pressure > 1 bar Soave-Redlch-Kwong (SRK) SRK or LATE Non-polar hydrocarbons Pressure < 200 bar Temperature - Grayson-Streed-Choa-Seeder(GS) Lee Kessler (LK) 18ºC to 430ºC Hydrocarbon systems Pressure > 10 bar Peng Robnson (PR) PR Good for cryogenc systems Sngle speces gas system Gas compresson Benedct-Webb-Rubn-Starlng (BWRS) BWRS PAGE 12 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

13 Process Modellng Selecton of Thermodynamc Methods 3.2 Lqud Phase On systems nvolvng lqud phases the thermodynamc K-value selecton s drven by the nature of the soluton. Appendx II provdes a summary of thermodynamc selecton crtera consdered n ths secton. The followng fve categores are consdered: Ideal soluton These solutons are non-polar and typcally nvolve hydrocarbons n the same homologous seres. Non-deal soluton regular These solutons exhbt mldly non deal behavour and are usually non-polar n nature. Polar solutons non-electrolyte These exhbt hghly non-deal behavour and wll use actvty coeffcent or specal K-value models. Polar solutons electrolyte Electrolytes are not consdered n detal here. However, t should be noted that n modellng they can be treated as true speces (molecules and ons) or apparent speces (molecules only) There are two methods MNRTL uses K-value NRTL and H LATE Ptzer method has no restrctons Bnary nteracton parameters (BIPs) are requred by both methods for accurate modellng. Specal Specal models have been developed for specfc systems. In non-polar applcatons, such as hydrocarbon processng and refnng, due to the complex nature of the mxtures and the large number of speces pseudo components are created based on average bolng pont, specfc gravty and molecular weght. The alternatve s to specfy all speces by molecular formula.e. real components. PAGE 13 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

14 Process Modellng Selecton of Thermodynamc Methods 3.2 Lqud Phase (Cont.) Ideal Solutons (3) In an deal soluton the chemcal potental μ for speces s of the form: µ 0 = µ + R T ln ( ) x where µ 0 s the chemcal potental of pure component If an deal soluton s consdered n equlbrum wth a perfect gas the phase rule demonstrates that the two phases at a gven T and P are not ndependent. Raoult s Law descrbes the dstrbuton of speces between the gas and the lqud phases 0 p = y P x p at temperature T = Raoult s Law s vald when x s close to 1 as n the case of a sngle component lqud and over the entre composton range for mxtures wth components of smlar molecular structure, sze and chemcal nature. The members of homologous seres tend to form deal mxtures n whch the actvty coeffcent γ s close to 1 throughout the concentraton range. The followng systems can be consdered sutable for Raoult s Law. 1 Alphatc hydrocarbons Paraffns C n H 2n+2 n-hexane (C6H14) n-heptane (C7H16) Olefnes C n H 2n Alcohols C n H 2n+1 OH methanol (CH3 OH) ethanol (C2H5 OH) 2 Aromatc hydrocarbons benzene (C6H6) toluene (C6H5 CH3) For deal lqud systems the followng gudelnes for thermodynamc model selecton are proposed Equlbrum-K Ideal Vapour Pressure(VAP) Enthalpy-H SRK In dlute solutons when x s close to 0 and wth no dssocaton, onsaton or reacton n the lqud phase Henry s law apples where: p = y P x H at temperature T = Henry s law constants H for speces n gven solvents are avalable. Typcal applcatons nclude slghtly soluble gases n aqueous systems. Refer Appendx IV for further detals. PAGE 14 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

15 Process Modellng Selecton of Thermodynamc Methods 3.2 Lqud Phase (Cont.) Non-deal solutons (3) In a non deal soluton the chemcal potental μ for speces s of the form:- µ = µ 0 ( γ x ) + R T ln Where γ s the actvty coeffcent and component actvty a = γ x Consder a non-deal soluton n equlbrum wth a perfect gas we can derve an equaton of the form: p = k γ x 0 p Raoult s law when γ 1 and x 1 k = p gvng γ = = 1 0 p x Henry s law when γ 1 and x 0 gvng k H For vapour lqud equlbrum at temperature T and pressure P the condton of thermodynamc equlbrum for every component n a mxture s gven by: f v = f l Where the fugacty coeffcent f v φ = note φ 1 y P = for deal gases = The fugacty of component n the lqud phase s related to the composton of that phase by the actvty coeffcent γ as follows: a f l γ = = 0 x x f The standard state fugacty f 0 s at some arbtrarly chosen P and T and n non-electrolyte systems s the fugacty of the pure component at system T and P. Regular solutons Regular solutons exhbt mldly non-deal behavour and occur n non-polar systems where the component molecular sze, structure and chemcal nature do not dffer greatly. These systems can be modelled usng an E-o-S. K-values are calculated from the followng relatonshps usng fugacty coeffcents y φl K = = where fugacty coeffcents x φ φ f v v = P and φ f l l = x P v Process Applcaton Equlbrum-K Enthalpy-H General hydrocarbon (same homologous seres) System pressure > 10 bar PR PR Branch chaned hydrocarbon System pressure > 1 bar SRK SRK Heavy end hydrocarbons System pressure < 7 bar Temperature 90C to430c ESSO LK Branch-chaned and halogenated hydrocarbon Some polar compounds MSRK SRK PAGE 15 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

16 Process Modellng Selecton of Thermodynamc Methods 3.2 Lqud Phase (Cont.) Polar non-electrolyte solutons These are systems where the lqud phase non-dealtes arse predomnantly from molecular assocatons. These systems must be modelled usng actvty coeffcent methods whch wll requre bnary nteracton parameters for accuracy. The vapor phase s taken to be a regular soluton gvng 0 y φl γ f l K = = = x φ φ P Where f 0 l standard fugacty comp φ v fugacty coeffcent vapour comp γ actvty coeffcent Models covered by the actvty coeffcent method nclude NRTL, UNIQUAC, Wlson, UNIFAC, HRNM, Van Laar, Margules and GMAC. In makng a selecton the followng should be consdered Wlson, NRTL, and UNIQUAC When suffcent data s avalable (>50%) UNIFAC When data s ncomplete (<50%) v v PAGE 16 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

17 Process Modellng Selecton of Thermodynamc Methods 3.3 Vapour Lqud Equlbrum (4) VLE dagrams provde a very useful source of nformaton n relaton to the sutablty of the K-value selected and the problems presented for the proposed separaton. Havng selected a K-value method test the TPxy and VLE dagrams aganst known data for the pure components and azeotropes f present. Fgure 5 n the attachments shows the VLE dagrams for N-Hexane systems. N-Hexane(1)/N-Heptane(2) can be consdered close to representng deal behavour whch s ndcated by the curve symmetry (γ 1).The dfferent bnary systems presented n Fgure 5 demonstrate the effect of an ncreasng α and ts nfluence on ease of separaton. We can nvestgate the effect of γ on α by consderng the followng p 0 1 = x p and p = x p 1 γ γ α = γ γ 1 2 p p = α 0 γ γ 1 2 where α 0 s the deal mxture value Snce γ > 1 s the usual stuaton, except n molecules of a very dfferent sze, the actual relatve volatlty s very often much less than the deal relatve volatlty partcularly at the column top. Values of γ can be calculated throughout the concentraton range usng van Laar s equaton ln 2 1 γ1 = A12 where A 12 = ln γ1 wth representng nfnte dluton 1 + A12x1 A21x2 An extensve data bank provdng values of parameter A xy are avalable from DECHEMA. Values of γ can also be calculated at an azeotrope whch can be very useful due to the extensve azeotropc data avalable n the lterature. At an azeotrope we have x1 = y1 gvng y1p = x1 γ1p1 resultng n p Fgure 6 n the attachments shows the VLE dagrams for N-Hexane(1)/Ethyl Acetate(2) system. CHEMCAD Wzard selected K-value NRTL and H Latent Heat and t can be seen that the model s reasonably accurate aganst known data. The γ values are shown and ther nfluence seen at the column bottom and top. Fgure 7 n the attachments shows the VLE dagrams for Ethanol(1)/Water(2) usng K-value method NRTL and SRK whch clearly demonstrates the mportance of model selecton. To acheve convergence for hgh purty near the azeotropc composton t s recommended to start the smulaton wth slack parameters whch can be loaded as ntal column profle (set flag) and then tghten the specfcaton teratvely. 0 γ 1 = P 0 1 PAGE 17 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

18 Process Modellng Selecton of Thermodynamc Methods 4.0 CHEMICAL REACTIONS 4.1 Reacton Chemstry The molecularty of a reacton s the number of molecules of reactant(s) whch partcpate n a smple reacton consstng of one elementary step. Un-molecular One molecule decomposes nto two or more atoms/molecules A B+C One molecule somerzes nto a molecule wth a dfferent structure A B Bmolecular Two molecules can assocate A+B AB Two molecules can exchange A+B C+D The reacton rate (9) depends on the reacton order. Frst order reacton converson vares wth tme and second order reacton converson vares wth square of the reactant concentratons. Frst order reactons have the hghest rate where the converson s least,.e. tme zero. The knetcs of a reacton s determned from the Arrhenus rate law whch states that the rate of a chemcal reacton ncreases exponentally wth absolute temperature and s gven by: Ea k = A exp R T where R = unversal gas constant = J / K mol E a = actvaton energy J / mol A = frequency factor or pre-exponental factor consstent unts The values of E a and A for a reacton can be determned expermentally by measurng the rate of reacton k at several temperatures and plottng ln k vs 1/T. Applyng ln we have: ln k = ln A E R a 1 T E a s determned from the slope E a /R and A from ln A the ntercept of 1/T. In many applcatons the reacton knetcs wll not be known. In these cases the overall heat of reacton H r and frequency factor f are requred to establsh reactor thermal desgn and stablty. If the heat of reacton s not known t can be estmated from the standard heats of formaton, Hf 0 (5), the stochometrc coeffcents ν of the reactant and product speces nvolved, usng Hess s Law (2, page 428) as follows: H r = ν Pr oducts ( 0) ( 0 ν ) H f Reactan ts In applyng Hess s Law t s mportant to correctly apply the heats of formaton for the reacton phases nvolved. Appendx I revews the CHEMCAD handlng of the enthalpy of reactons n some detal. H f PAGE 18 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

19 Process Modellng Selecton of Thermodynamc Methods 4.1 Reacton Chemstry The actvaton energy E a cannot be derved logcally from the heat of reacton H r but can be estmated usng a thermodynamcs analogy (10, pages 21-34), where we have: For lquds and solds: For gases: Ea = Hr R T E a = H r (molecularty-1) RT The Polany-Semenov equaton can also be used: E a = C α (- H r ), α and C are constants. For exothermc reactons α = and C = 48 kj/mol For endothermc reactons α = and C = 48 kj/mol. The values can vary wth reacton type (12, 13) and should be valdated from reference sources. The unts for E a and A are used n varous forms so cauton s requred n ther use. E a s usually n the form energy/(mol reactant speces) and A n mol/s referenced to reactant volume, dependng on the unts of k. In a reacton, where the total moles of reactant N r s converted n reacton tme θ, the converson rate r gven by: = N r r mol/s θ Total heat of reacton H s gven by: H = N H r r The frequency factor f n unts of mol/m 3 s s derved from the reactant mx volume V r r f = mol/m 3 s Vr The mean heat output from the reacton s gven by: Q = r H 4.2 Reacton Chemstry Appled Endothermc reactons exhbt a marked degree of self regulaton n regards to thermal stablty and do not requre further consderaton. Exothermc reactons requre a detaled understandng of the reacton knetcs to determne reacton rate and heat of reacton usng screenng tests usng the approprate calormeter (11) or from references. For exothermc reactons to be carred out safely, the heat removal capablty Q of the reacton system must exceed the maxmum predcted heat output Q r by an acceptable margn. A thermal runaway (ncreasng reacton temperature ncreases rate of reacton) wll occur f the heat cannot be removed fast enough, further accelerated by a reducton n heat transfer area due to a decrease n reactor contents. It may not always be possble to desgn for stablty where not enough heat transfer area s avalable for the desgn temperature dfference. However, stablty wll be assured f heat s removed by bolng one or more of the components snce ths tends to make the system sothermal. For a system U and desgn set T m there s an equlbrum heat transfer area where heat removal capablty equals reacton heat output. Ths consderaton determnes an acceptable reactor sze to ensure adequate heat transfer area under all reacton condtons. r r PAGE 19 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

20 Process Modellng Selecton of Thermodynamc Methods 5.0 SUMMARY CHEMCAD provdes a Wzard to assst n thermodynamc model selecton. The selecton s essentally based on the component lst and operatng temperature and pressure ranges. The Wzard decdes on the model to use from E-o-S, actvty coeffcent, emprcal and specal. If nadequate BIP data s avalable for the actvty coeffcent method the Wzard defaults to UNIFAC. The key decson paths n the method are shown n Fgure 8 n the attachments. When usng the Wzard, ntally exclude utlty streams from the component lst as the presence of water for example wll probably lead to an ncorrect selecton. The followng addtonal ponts should to be consdered when settng the K-Value Vapour phase assocaton Vapour fugacty correcton Water/hydrocarbon solublty Salt typcal systems acetc acd, formc acd, acrylc acd set when usng an actvty coeffcent method P > 1bar mmscblty vald only for non actvty coeffcent methods for whch water s assumed to be mscble consders effect of dssolved salts when usng the Wlson method A thermodynamc model decson tree based on system phases s shown n Fgure 9. A synopss on Thermodynamc Model Selecton s presented n Appendx II and Tables for Thermodynamc Model Selecton based on applcaton are shown n Appendx III. PAGE 20 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

21 Process Modellng Selecton of Thermodynamc Methods Stream Enthalpy by Latent Heat Model Appendx I Enthalpy Calculatons n CHEMCAD CHEMCAD calculates the stream enthalpy begnnng at the deal gas heat of formaton referenced at 25 C, 1 atm, gas [A], subtracts the heat of vaporzaton at 25 C and 1 atm [HoV] to gve the deal lqud heat of formaton at 25 C, 1 atm, lqud [B]. Usng Cp lqud, the lqud enthalpy from 25 C to the desred temperature s calculated. Ths temperature can be the stream temperature and f the stream s a lqud the enthalpy calculaton s complete. If the stream s vapor, the calculaton of lqud enthalpy contnues untl the bolng pont at Tb [C] and the heat of vaporzaton at ths temperature [HoV] s added to come to the gas state [D]. From here Cp deal gas s used to come to the stream temperature [C], f ths s hgher than the bolng pont as shown n the dagram. Enthalpy Dagram of Stream Enthalpy Calculaton Usng the lqud heat of formaton as a startng pont, nstead of the gas heat of formaton, gves the advantage that the pressure has no nfluence on Cp lqud. If the stream s lqud ths gves the optmum soluton. If the stream s a gas, there wll stll be a small problem f the stream pressure s hgh, because Cp gas s measured for deal gas only and there s no pressure correcton avalable. PAGE 21 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

22 Process Modellng Selecton of Thermodynamc Methods Stream Enthalpy by Equaton of State Model Appendx I The gas enthalpy can also be calculated usng an Equaton of State. CHEMCAD begns n that case wth the deal gas heat of formaton. Ths has the advantage for the gas phase that the pressure s part of the enthalpy. The gas models are SRK, PR, Lee Kessler, BWRS and others. In the lqud phase these models are not as good as the Cp lqud calculaton usng the latent heat model. In the case the lqud s hghly non-deal the user should select the Latent Heat model and not an Equaton of State for the enthalpy calculaton. Ths s the reason why the thermodynamc Wzard selects NRTL, or UNIQUAC or UNIFAC together only wth Latent Heat as the best enthalpy model Calculatng the stream enthalpy at 25 C, 1 atm whch means the user goes from A to B to C to D to A. ths should gve the deal gas heat of formaton at 25 C, 1 atm. Theoretcally the thermodynamc rules says that, but because of errors n the measured physcal propertes, whch are used here, there wll be a small devaton n comparson to the data of the databank f the model s latent heat. PAGE 22 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

23 Process Modellng Selecton of Thermodynamc Methods Enthalpy of Reactons Appendx I The calculaton of enthalpy n CHEMCAD reactors s now dscussed. Consder the followng gas phase reacton to check the enthalpy balance. Refer Job Fle EREA2. C2H4 + H2 = C2H6 at 25 C and 1 atm Stream No. 1 2 Temp C * Pres bar * Enth MJ/h Enthalpy balance (Str2 Str1) = MJ/h Vapor mole fracton Total kmol/h Total kg/h Total std L m3/h Total std V m3/h Hydrogen kmol/h Ethylene kmol/h Ethane kmol/h Equp. No. 1 No of Reactons 1 Specfy reacton phase 1 Specfy thermal mode: 2 C MJ/h Temperature Unts: 3 Pressure Unts: 4 Heat of Reacton Unts: 4 Molar Flow Unts: 1 Edt Reacton No. 1 Calc Overall Ht of Rx (MJ/h) Reacton Stochometrcs and Parameters Reacton no. 1 Base component 1 Frac.converson The heat of reacton s MJ/h, and the heat duty s also MJ/h. The flowrate of 1 kmol/h gves a heat of reacton of kj/kmol. Ths result can be checked usng the heat of formaton n the databank. PAGE 23 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

24 Process Modellng Selecton of Thermodynamc Methods Enthalpy of Reactons(Cont) Appendx I Consder the followng vapor phase reacton at 120 C. We can gnore the heat of condensaton. Refer Job Fle: EREA3 2H2 + O2 = 2 H2O at 120 C Stream No. 1 2 Stream Name Temp C * Pres bar * Enth MJ/h Enthalpy balance gves heat duty: Str2 Str1 = = MJ/h Vapor mole fracton Total kmol/h Total kg/h Total std L m3/h Total std V m3/h Hydrogen kmol/h Oxygen kmol/h Water kmol/h Equp. No. 1 No of Reactons 1 Specfy reacton phase 1 Specfy thermal mode: 2 C MJ/h Temperature Unts: 3 Pressure Unts: 4 Heat of Reacton Unts: 4 Molar Flow Unts: 1 Edt Reacton No. 1 Calc Overall Ht of Rx (MJ/h) Reacton Stochometrcs and Parameters for unt no. 1 Reacton no. 1 Base component 1 Frac.converson The heat of reacton s MJ/h. The heat duty of the reactor s H = MJ/h. There s a small dfference between the reactor heat duty and the heat duty calculated as the enthalpy dfference of the two streams calculated manually. PAGE 24 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

25 Process Modellng Selecton of Thermodynamc Methods Enthalpy of Reactons(Cont) Appendx I Consder the followng reacton n whch the product stream s lqud. Refer Job Fle: EREA3 2 H2 + O2 = 2 H2O at 25 C Stream No. 1 2 Temp C * Pres bar * Enth MJ/h Enthalpy balance gves heat duty: Str2 Str1 = MJ/h Vapor mole fracton Total kmol/h Total kg/h Total std L m3/h Total std V m3/h Hydrogen kmol/h Oxygen kmol/h Water kmol/h Water s under 25 C lqud, so the enthalpy of condensaton must be ncluded. The heat of condensaton 40.6 MJ/kmol at 1 bar. Equp. No. 1 No of Reactons 1 Specfy reacton phase 1 Specfy thermal mode: 2 C MJ/h Temperature Unts: 3 Pressure Unts: 4 Heat of Reacton Unts: 4 Molar Flow Unts: 1 Edt Reacton No. 1 Calc Overall Ht of Rx MJ/h Reacton Stochometrcs and Parameters for unt no. 1 Reacton no. 1 Base component 1 Frac.converson The reacton enthalpy balance at 25 C, under deal gas condtons, gves MJ/h, beng equal to the deal gas heat of reacton as before. Because the heat of condensaton s ncluded the heat duty s now MJ/h, whch s close to the enthalpy dfference of the output and nput streams (572 MJ/h). PAGE 25 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

26 Process Modellng Selecton of Thermodynamc Methods Enthalpy of Reactons(Cont) Appendx I There may be a small dscrepancy between the manual calculaton of heat duty, whch s the enthalpy dfference between the output and nput streams and the heat duty calculated by the reactor. Ths s because the reactor calculates the heat duty dfferently. Under the rules of thermodynamcs there should never be any dfference between enthalpy calculatons because the method has no nfluence on the result as long as the ntal and fnal condtons are dentcal. To understand the enthalpy calculaton whch the reactor uses the followng graphc shows the manual calculaton of the heat duty for the reactor. Enthalpy Dagram of an Isothermal Reacton The reactor calculates the heat duty assumng the nput and output streams are gas. 1. Adjust the nput composton, temperature and pressure (A) to 25 C gas and 1 atm (B), beng the condtons of the deal gas heat of formaton. 2. Add the heat of reacton at 25 C at 1 atm (R) 3. Modfy output composton from 25 C and 1 atm to output temperature and pressure (C). So we go from Intal state A to Fnal state C va B and R. The heat duty result s C - A. In ths case the output stream vaporzed so CHEMCAD has to calculate the heat of vaporzaton as shown. The heat of reacton s determned from: Heat of formaton of all products(output) - heat of formaton of all reactants (nput) at 25 C, 1 atm. ( 0) ( 0 Hr = ν H ν H ) Pr oducts f Reactan ts Manual check Heat duty = enthalpy of the output stream (C)- enthalpy of the nput stream (A) Ths heat duty should be the same as the reactor heat duty, because n both cases we calculate C - A. When one stream s gas, one stream s lqud and one stream vaporzed the heat of vaporzaton must be calculated. Ths heat of vaporzaton can be calculated at the normal bolng pont or at the stream temperature or at 25 C. The temperature chosen wll gve 3 dfferent results due to errors n the measured data. f PAGE 26 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

27 Process Modellng Selecton of Thermodynamc Methods Appendx II Thermodynamc Model Synopss Vapor Lqud Equlbrum The prmary consderaton when selectng a thermodynamc model s to consder the lqud phase. Lqud solutons are defned from fve categores: 1. Ideal 2. Regular 3. Polar Non-electrolyte 4. Electrolytes 5. Specal 1 Ideal Solutons are systems where the vapor phase behaves essentally as an deal gas. Pressure wll be low (<1bar), all the molecules n the lqud phase vrtually the same sze and no ntermolecular forces exst. VAP model for K-value and SRK for enthalpy are proposed. Vapor-lqud equlbrum s accordng to Raoult's law: 0 y p K = = where p 0 s pure component vapour pressure x P 2 Regular Solutons are systems where the non-dealtes stem from moderate physcal nteractons due to the dfferences n the sze and shape of the molecules wth mnmal ntermolecular assocatons. The vapor and the lqud phases are assumed to form regular solutons that are mldly non-deal. The followng table should be consdered: K-VALUE METHOD APPLICATION NOTES PR and SRK All non-polar hydrocarbon systems for pressures >10 bar GS Certan wde bolng range hydrocarbon processes 18ºC to 430ºC ESSO Processes wth heavy end hydrocarbons at pressures < 7bar Temperatures n the range 90ºC to 200ºC MSRK Chemcals such as branch-chaned hydrocarbons, halogenated hydrocarbons and some polar compounds K-values are calculated from the followng relatonshps by applyng fugacty coeffcents y φl K = = where fugacty coeffcents x φ φ f v v = P and φ f l l = x P v 3 Polar Non-electrolyte solutons are systems where the lqud phase non-dealtes arse predomnantly from molecular assocatons. These systems must be modelled usng actvty coeffcent methods, whch generally requre BIPs for mproved accuracy. The vapor phase s taken to be a regular soluton gvng: 0 y φl γ f l K = = = where x φ φ P f 0 l standard fugacty comp, φ v fugacty coeff. vapour comp, γ v v actvty coeff. lqud comp. Models covered by actvty coeffcent methods nclude NRTL, UNIFAC, UNIQUAC, Wlson, T.K.Wlson, Van Laar, Margules and GMAC. Use Wlson, NRTL, and UNIQUAC when suffcent data s avalable (>50%) and UNIFAC when data s ncomplete (<50%) 4 Electrolytes are not ncluded n ths paper. 5 Specal Systems are provded for the smulaton of applcaton specfc processes. Henry s Law, see Appendx IV. K-Amne and H-Amne model s of topcal nterest due to ts applcaton to the study of post combuston carbon capture systems. See Appendx VI. PAGE 27 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

28 Process Modellng Selecton of Thermodynamc Methods Appendx III Thermodynamc Model Selecton Applcaton Tables HYDROCARBONS K-VALUE METHOD APPLICATION H-ENTHALPY Soave-Redlch-Kwong Pressure >1bar (SRK) (1) General hydrocarbon SRK API SRK (1) Pressure >1bar General hydrocarbon SRK Peng-Robnson (PR) (1) Pressure >10 bar Cryogencs < -70ºC PR Benedct-Webb-Ruben-Starlng Pressure>1bar (BWRS) (1) Sngle speces BWRS Grayson-Streed (GS) (1) Moderate P >7bar <200bar Temperature 18C to 430C Lee-Kessler (LK) Heavy end hydrocarbons ESSO (3) Pressure < 7bar Temperature ºC Lee-Kessler (LK) Heavy end hydrocarbons Ellott, Suresh, Donohue (ESD) (1) Hydrocarbon water Hydrocarbon-gases SRK SAFT (1) Hydrocarbon water Hydrocarbon-gases SRK Modfed SRK (MSRK) (1) Halogenated alphatcs SRK CHEMICALS K-VALUE METHOD APPLICATION H-ENTHALPY Vapor Pressure (VAP) (3) Ideal solutons SRK P (0-4atm) T ( ºK) UNIFAC (2) Non-deal - two lqud phases Heterogeneous azeotrope LATE Group Contrbuton Predctve Wlson (2) Non-deal soluton wth dssolved solds Homogeneous azeotrope LATE NRTL (2) Hghly non-deal - two lqud phases Heterogeneous azeotrope LATE UNIQUAC (2) Hghly non-deal - two lqud phases Heterogeneous azeotrope LATE Margules (2) Hghly non-deal - two lqud phases Homogeneous azeotrope LATE T.K.Wlson (2) Hghly non-deal - two lqud phases Homogeneous azeotrope LATE Hranuma (HRNM) (2) Hghly non-deal - two lqud phases LATE Regular Soluton (2) Moderately non-deal (Predctve) SRK Van Laar (2) Moderately non-deal LATE Homogeneous azeotrope Modfed SRK (MSRK) (1) 4 parameter Predctve SRK (PSRK) (1) (1) Equaton of State Model (2) Actvty Coeffcent Model (3) Emprcal Method Polar compounds n regular solutons Polar compounds n non-deal solutons Better than UNIFAC at hgh pressures Note: SRK sometmes referred to as Redlch-Kwong-Soave (RKS) SRK LATE PAGE 28 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

29 Process Modellng Selecton of Thermodynamc Methods Appendx III Thermodynamc Model Selecton Applcaton Tables SPECIAL MODELS K-VALUE METHOD APPLICATION H-ENTHALPY Henry s Gas Law (3) Gases dssolved n water LATE Amne (AMINE) Gas sweetenng H2S-MEA-DEA Carbon capture CO2 absorpton Amne Sour Water (SOUR) H2S-CO2- NH3 dssolved n H2O SRK Extended SRK (TSRK) (1) Methanol systems wth lght gases SRK Partal Pressures of Aqueous Mxtures (PPAQ) and/or water Ionc compounds whch dssolve n water and dsassocate e.g. HCl, NH3, HNO3. User specfed K-value. SRK or LATE Tr-ethylene Glycol / Water Dehydraton (TEG) Dehydraton of hydrocarbon systems SRK Flory-Huggns (FLOR) Polymer solutons LATE UNIFAC for Polymers (UPLM) (2) Polymer solutons LATE Ellott-Suresh-Donohue Hydrogen bondng, also at hgh (ESD) (1) pressure SRK SAFT (1) Hydrogen bondng, also at hgh pressure SRK ACTX User specfed actvty coeffcents LATE K Tables User specfed K - value SRK or LATE Polynomal User specfed K - value SRK or LATE User Specfed Subroutne User specfed K value SRK or LATE (1) Equaton of State Model (2) Actvty Coeffcent Model (3) Emprcal Method PAGE 29 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

30 Process Modellng Selecton of Thermodynamc Methods Appendx IV K Model - Henry s Law Revew A good source for Henry s Law constants s publshed by the Max-Planck Insttute (6). Henry s law constant k H can be defned as: where kh = Ca pg C a s concentraton of speces n the aqueous phase p g s the partal pressure of that speces n the gas phase k H s at standard condtons where kh θ s at T = K The common unts for k H are M atm molaq dm = atm 3 aq The offcal SI unts for k H are M Pa molaq m = Pa 3 aq To convert between above unt k H = M atm k m H 3 [( ) Pa] mol aq aq A commonly used unt s atm where k H k H,Inv = a constant for water. M atm atm For the carbon capture CO2 Genosorb system we have: px k p H,Inv g ρflud = = = 3.67 atm xa mwflud An alternatve defnton for Henry s Law s gven by: pg H = where p y P x = g g a Ths relates x a the equlbrum mole fracton of the speces n the lqud phase to ts partal pressure p g n the gas phase. Mole fracton of that speces n the gas phase s y g where P s the total system pressure. In ths last case unts for H are Pa / mole fracton lqud. The Henry s Law constant s a functon of temperature and ndependent of total pressure at low pressures. It can be seen that the H 2 S/Water and CO 2 /Water systems are sgnfcantly more soluble than the N 2 /Water and CO/Water systems. System px Henry s Constant Data at 25ºC Max-Planck Insttute Raschg M/atm bar bar N 2 /Water CO 2 /Water H 2 S/Water CO/Water In CHEMCAD Henry s Law data s gven for CO 2 solublty n water under Parameterc Data. Ths data s presented as coeffcents usng the temperature dependent correlaton below: A p g H = Exp B ln T C T D where H = n unts psa/mol fracton and T s n ºR. T xa Henry s Law temperature dependence can also be determned from the followng correlaton: θ so ln H 1 1 k H = k Hexp θ where T θ =298ºK R T T PAGE 30 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK

31 Process Modellng Selecton of Thermodynamc Methods Appendx V Inert Gases and Infntely Dlute Solutons When nert gases, such as CO2, N2, H2 etc., are present wth non-deal chemcals, they present some computatonal dffcultes when usng actvty models. The K-value s calculated usng: ν V p K = P The problem wth ths method, as far as nert gases are concerned, s that the system s very often operatng above the crtcal pont of the pure nert gas. The standard vapor pressure correlaton cannot be accurately extrapolated nto ths regon. It s necessary, for the nert gas only, to swtch to the Henry's Gas Law method for vapor pressure representaton whenever the system temperature s above the crtcal temperature of a gven compound. Each tme the vapor pressure s calculated, CHEMCAD compares the crtcal temperature of each compound to the system temperature. If the system temperature s greater than the crtcal temperature of one or more of the compounds, then the program wll check to see f the Henry's constants are present for the components n queston. If the Henry's constants are present, then, for the "nert" compounds only, CHEMCAD wll represent the vapor pressure usng the Henry's method. All other components wll use the regular vapor pressure equaton. If the Henry's constants are not present, then the program remans wth the regular default vapor pressure method. In certan unusual cases, ths approach can cause some numercal dffcultes. If the system happens to be operatng rght n the vcnty of the crtcal pont of one of the components, then t s possble that on one teraton the calculaton wll be above the crtcal temperature and on the next t wll be below the crtcal temperature. Ths wll cause the program to swtch back and forth between vapor pressure methods, causng numercal dscontnutes and non-convergence. Ths problem can be overcome by tellng the program to use the Henry's method globally for certan components. Ths s done on the K-value screen. Infntely Dlute Solutons The thermodynamc propertes of nfntely dlute solutons s acknowledged as beng very dffcult to predct and systems nvolvng these condtons should always have the results from process smulaton work valdated by expermental data. The Predctve Soave-Redlch-Kwong (PSRK) equaton s a group contrbuton equaton-of-state whch combnes the SRK and UNIFAC models. Ths concept makes use of recent developments and has the man advantage that vapour-lqud-equlbrum (VLE) can be predcted for a large number of systems wthout ntroducng new model parameters that must be ftted to expermental VLE data. The PSRK equaton of state can be used for VLE predctons over a much larger temperature and pressure range than the UNIFAC approach and s easly extended to mxtures contanng supercrtcal compounds. Addtonal PSRK parameters, ncludng lght gases, allows the calculaton of gas/gas and gas/ alkane phase equlbrum. The modfed UNIFAC model (Dortmund) ntroduces temperature dependent nteracton parameters. Ths allows a more relable descrpton of phase behavour as a functon of temperature. The modfed UNIFAC (Dortmund) method also uses van der Waals (Q and R) propertes whch are slghtly dfferent than those used n the orgnal UNIFAC method. The man advantages of the modfed UNIFAC method are a better descrpton of the temperature dependence and the real behavour n the dlute regon and that t can be appled more relably for systems nvolvng molecules very dfferent n sze. PAGE 31 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK