P & I Desgn Ltd Process Instrumentaton Consultancy & Desgn 2 Reed Street, Gladstone Industral Estate, Thornaby, TS17 7AF, Unted Kngdom. Tel. +44 (0) 1642 617444 Fax. +44 (0) 1642 616447 Web Ste: www.pdesgn.co.uk PROCESS MODELLING SELECTION OF THERMODYNAMIC METHODS by John E. Edwards jee@pdesgn.co.uk MNL031B 10/08 PAGE 1 OF 38
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 www.pdesgn.co.uk
Process Modellng Selecton of Thermodynamc Methods References 1. C.C. Coffn, J.Chem.Educaton 23, 584-588 (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, 1993. 5. 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 1999. 7. J.R.W.Warn, Concse Chemcal Thermodynamcs, van Rostrand Renhold, 1969. 8. Kent, R. L. and Esenberg, Hydrocarbon Processng, Feb. 1976, p. 87-92. 9. F.G. Shnskey, Process Control Systems, McGraw-Hll, 1967. 10. O.Levenspel, Chemcal Reacton Engneerng, Wley, 2 nd Edton, 1972. 11. J.Wlday and J.Etchells, Workbook for Chemcal Reactor Relef Szng, HSE Contract Research Report 136/1998. 12. H.S.Fogler, Elements of Chemcal Reacton Engneerng, 3 rd Edton, Prentce Hall, p122. 13. 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, TX77042 www.chemstatons.com 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 www.pdesgn.co.uk
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 www.dechema.de, DIPPR www.ache.org/dppr/, TÜV NEL Ltd www.ppds.co.uk 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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 100 2241.5 P M P M P M B MB PB PB VB = PBMB 100 2241.5 C MC PC PC VC = PCMC 100 2241.5 Total 100 1 PM 2241.5 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 22.415 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 2241.5 (kg/m3 ) we have: Volumetrc Flow Q = W G O 2241.5 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 273 3 ρ = G kg / m 22.415 Zf Tf where 22.415 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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 108.8 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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 = 1 + 2 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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 1 1 2 γ 2 2 0 2 α = γ γ 1 2 p p 0 1 0 2 = 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 www.pdesgn.co.uk
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 = 8.314 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 www.pdesgn.co.uk
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 = -0.25 and C = 48 kj/mol For endothermc reactons α = -0.75 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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 25.0000* 25.0000 Pres bar 1.0000* 1.0000 Enth MJ/h 52.256-83.906 Enthalpy balance (Str2 Str1) -83.9-52.2 = -136.1 MJ/h Vapor mole fracton 1.0000 1.0000 Total kmol/h 2.0000 1.0000 Total kg/h 30.0698 30.0700 Total std L m3/h 0.1091 0.0845 Total std V m3/h 44.83 22.41 Hydrogen kmol/h 1.0000 0.0000 Ethylene kmol/h 1.0000 0.0000 Ethane kmol/h 0.0000 1.0000 Equp. No. 1 No of Reactons 1 Specfy reacton phase 1 Specfy thermal mode: 2 C 25.0000 MJ/h -136.1326 Temperature Unts: 3 Pressure Unts: 4 Heat of Reacton Unts: 4 Molar Flow Unts: 1 Edt Reacton No. 1 Calc Overall Ht of Rx -136.1330 (MJ/h) Reacton Stochometrcs and Parameters Reacton no. 1 Base component 1 Frac.converson 1.0000 1-1.0000 2-1.0000 3 1.0000 The heat of reacton s -136.13 MJ/h, and the heat duty s also -136.13 MJ/h. The flowrate of 1 kmol/h gves a heat of reacton of -136.13 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 www.pdesgn.co.uk
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 120.0000* 120.0000 Pres bar 1.0000* 1.0000 Enth MJ/h 8.2364-477.95 Enthalpy balance gves heat duty: Str2 Str1 = -477.9-8.2 = -486.1 MJ/h Vapor mole fracton 1.0000 1.0000 Total kmol/h 3.0000 2.0000 Total kg/h 36.0306 36.0300 Total std L m3/h 0.0861 0.0361 Total std V m3/h 67.24 44.83 Hydrogen kmol/h 2.0000 0.0000 Oxygen kmol/h 1.0000 0.0000 Water kmol/h 0.0000 2.0000 Equp. No. 1 No of Reactons 1 Specfy reacton phase 1 Specfy thermal mode: 2 C 120.0000 MJ/h -483.2837 Temperature Unts: 3 Pressure Unts: 4 Heat of Reacton Unts: 4 Molar Flow Unts: 1 Edt Reacton No. 1 Calc Overall Ht of Rx -483.6400 (MJ/h) Reacton Stochometrcs and Parameters for unt no. 1 Reacton no. 1 Base component 1 Frac.converson 1.0000 1-2.0000 2-1.0000 3 2.0000 The heat of reacton s -483.64 MJ/h. The heat duty of the reactor s H = -483.28 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 www.pdesgn.co.uk
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 25.0000* 25.0000 Pres bar 1.0000* 1.0000 Enth MJ/h -0.00459418-572.04 Enthalpy balance gves heat duty: Str2 Str1 = -572.0 MJ/h Vapor mole fracton 1.0000 0.00000 Total kmol/h 3.0000 2.0000 Total kg/h 36.0306 36.0300 Total std L m3/h 0.0861 0.0361 Total std V m3/h 67.24 44.83 Hydrogen kmol/h 2.0000 0.0000 Oxygen kmol/h 1.0000 0.0000 Water kmol/h 0.0000 2.0000 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 25.0000 MJ/h -569.1345 Temperature Unts: 3 Pressure Unts: 4 Heat of Reacton Unts: 4 Molar Flow Unts: 1 Edt Reacton No. 1 Calc Overall Ht of Rx -483.6400 MJ/h Reacton Stochometrcs and Parameters for unt no. 1 Reacton no. 1 Base component 1 Frac.converson 1.0000 1-2.0000 2-1.0000 3 2.0000 The reacton enthalpy balance at 25 C, under deal gas condtons, gves -483.6 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 -569.1 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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 90-200ºC 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 (275-475ºK) 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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
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 = 298.15K 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 = 101.325 M atm k m H 3 [( ) Pa] mol aq aq A commonly used unt s atm where k H k H,Inv = 55. 3 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 0.00063 87000 CO 2 /Water 0.034 1600 1440 H 2 S/Water 0.1 553 CO/Water 0.00091 60700 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 www.pdesgn.co.uk
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 www.pdesgn.co.uk
Process Modellng Selecton of Thermodynamc Methods Appendx VI Post Combuston Carbon Capture Thermodynamcs (8) In the study of post combuston carbon capture the K-Amne and H-Amne CHEMCAD model has been successfully appled n the study of the absorpton and desorpton of CO2 n ethanolamne solutons. Aqueous solutons of ethanolamnes are used for the reactve absorpton of CO 2 at atmospherc pressure. The reacton mechansms are as follows: 2 R-NH 2 + CO 2 R-NH 3 + + R-NH-COO - R-NH 2 + CO 2 + H 2 O R-NH 3 + + HCO 3 - In CHEMCAD Amne model uses the Kent Esenberg method to model the reactons. The followng amnes are ncluded n the Amne model allowng for further nvestgaton as requred. Dethanolamne (DEA) Monoethanolamne (MEA) Methyl dethanolamne (MDEA) The chemcal reactons n the CO 2 -Amne system are descrbed by the followng reactons: where R and R' represent alcohol groups. RR'NH2 + H + + RR'NH RR'NCOO + H2O RR'NH + HCO3 CO2 + H2O HCO3 - + H + HCO3 - CO3 - - + H + H2O H + + OH - The reacton equatons are solved smultaneously to obtan the free concentraton of CO2. The partal pressure of CO2 s calculated by the Henry's constants and free concentraton n the lqud phase. The heat of reacton s also accurately predcted to allow thermal studes to be carred out. In the study of CO 2 Compresson and Transport, due to CO 2 beng close to the super-crtcal state n whch the temperature s greater than the crtcal temperature, makes fugacty calculaton dffcult. The Benedct Webb Ruben Starlng equaton of state has been used because t s the only E-o-S that allows specfc parameters for CO 2, shown below, to be used. PAGE 32 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK www.pdesgn.co.uk
Process Modellng Selecton of Thermodynamc Methods Appendx VII Thermodynamc Gudance Note Water - organc Systems 1. If no data s avalable UNIFAC / UNIFAC LLE s a 'reasonable' model to try. It wll predct results that are consstent and t s not unreasonable to trust UNIFAC to be near the results. The more non-deal the organc the less accurate the results. If usng NRTL / UNIQUAC, for other reasons, regress the behavour of water-organc from UNIFAC. 2. If some data s avalable, try to valdate the UNIFAC results. 3. If some data s avalable and suffcently relable, regress bnary nteracton parameters (BIPs) wthout UNIFAC. 4. If workng n ppm concentraton range regress nfnte dluton actvty coeffcents. Only use UNIFAC f t matched data and there were dffcultes regressng the data nto NRTL or f wantng to use UNIFAC for some other reason. If there are NRTL/UNIQUAC parameters and some data for valdaton, use the data to valdate BIPs. UNIFAC Group Contrbuton Method for Hydrocarbons. The two uses of the group contrbuton method are: 1. To determne pure component propertes (Tb, Tc, Pc) for hydrocarbons, 15% accuracy s typcal for straght branch, C8 and lower hydrocarbons. See Appendx VIII for predctve methods. 2. Determnng non-real bnary behavour due to sze and shape of the two molecules. The UNIFAC groups and ther nteractons are used to calculate the lqud fugacty and to determne the sze and shape of a 'part' of the molecule. Regressng BIPs for UNIFAC makes t more useful. When UNIFAC s nsuffcent for the components you can stll use t for the vapor phase, but t fals on the lqud phase and on TPxy behavour. Interacton parameters between groups dctate the nteracton between groups. The overall behavour s the sum of partal nteractons. If the nteractons between some of the groups for two components are not avalable, t means that the groups are beng gnored. For example acetc acd and xylene have groups that do not have known nteracton parameters, whch means that part of the shape of the two s beng gnored. There s no H2O group. Ths means that water s consdered to be an deal crcle of deal gas law sze when nteractng wth another component. H2O s not a sphere, so the lqud fugacty calculaton s wrong. The lqud fugacty for xylene-water and xylene-acetc acd s assumed to be 'regular soluton,' and the lqud fugacty for xylene-acetc acd s an ncomplete result. UNIQUAC or NRTL wth vapor phase assocaton. UNIFAC s not sutable due to lack of nteracton parameters for the man groups acetc acd and xylene and there s no water subgroup. PAGE 33 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK www.pdesgn.co.uk
Process Modellng Selecton of Thermodynamc Methods Lqud Lqud Extracton Appendx VII Thermodynamc Gudance Note To select a K model that wll support the calculaton of two lqud phases, set the vapor/ lqud/lqud/sold opton on the K value screen. Models NRTL, UNIQUAC, UNIFAC LLE are sutable. It s possble to regress Txy data for a par of components but be sure to set the K flag V/L/L/S opton before regressng, because dfferent regressons are used. Txy data can also be regressed for a ternary system, such as data from a bnodal. For a dscusson on alpha functons nfluence on the calculaton of actvty coeffcents for the two lqud phases reference: Smth and Van Ness, Introducton to Chemcal Engneerng Thermodynamcs. When usng an actvty coeffcent model to determne equlbrum between two lqud phases, the SCDS UntOp can be used to determne separaton and gamma1, gamma2 show separaton regardless of what the two phases are. The calculatons for LLE on a stage are the same that would be used for VLE on a stage. There s a specal UntOp, the extractor (EXTR) whch s nothng more than an SCDS unt modfed to work for two lqud phases rather than one lqud phase and one vapor phase. Whenever your data s expressed as an actvty coeffcent, you could use the gamma regresson. The Flash UntOp wll always brng the vapor and lqud to equlbrum, whch s equvalent to a Murphree Effcency of 1.0. Bnodal plots should be obtaned for verfcaton of parttonng behavour. To do a sngle stage lqud - lqud extracton wth Murphree effcency appled Excel UntOp can be used to desgn a specal UntOp. For such low extractons set 2 stages wth effcences of around 0.2 to 0.3 LLE UntOp needs a mnmum of 2 stages and a sngle flash gves equlbrum. To generate rectangular coordnate(x-solute n raffnate, y-solute n extract) dagram showng the equlbrum and operatng lnes export a bnodal plot and tower profle plot to Excel, then combne the data. Regressng BIPs for NRTL( K flag set for V/L/L/S) for LLE when usng UNIFAC LLE wth water present s acceptable provded the water s formng a second phase, t s always best to check wth data though. General Rules Lqud phase water wth anythng else most tmes use NRTL. You can regress NRTL BIPs for the other components from UNIQUAC or UNIFAC f you don't have NRTL bps. SRK s an equaton of state whch uses the accentrc factor of a component and some 'general curve ft' parameters from lots of lab studes to calculate the fugacty on the bass that both molecules n the bnary mxture are spheres, the only dfference s how bg they are. Agan, water s not a sphere and t's non-deal behavor stems from ts shape as well as ts sze. Peng Robnson and SRK Equatons of State are good for non-water mxtures of gases and excellent for lght gases and refrgerants. However they cannot handle two phase water but are good for two phase hydrocarbons. Great for non-polar, not so good for polar solutons. PAGE 34 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK www.pdesgn.co.uk
Process Modellng Selecton of Thermodynamc Methods Appendx VII Thermodynamc Gudance Note You can regress a BIP for bnary behavour whch s really just a mxng bp (Kj=K/Kj=A+B*T) If usng an EOS wth water there are two methods: 1. Use NRTL and turn on ether Vapor Fugacty Correcton (use SRK for the vapor phase fugacty) 2. Use NRTL wth Henry's component set for near supercrtcal lght gases. Actvty coeffcents are good for polar solutons, f you have actvty coeffcent bps regressed. UNIFAC s good for hydrocarbons, even polar hydrocarbons, f you have subgroups. Not good f there s a lqud phase. Batch Dstllaton For a mult-component organc-water system, wth regressed vapor pressure data, the frst choce would be NRTL. An equaton of state s unsutable unless the accentrc factor s tuned; more detals are avalable n the Help secton. When usng the pseudo bnary method to correlate the behavour of a mxture based on the behavour of pars of components to each other, the stuaton may occur where ths sn't vald (phase parttonng, ternary azeotropes) because the ternary, quaternary system behaves sgnfcantly dfferent than pseudo bnary predcts. When guessng BIPs from UNIFAC ths can be a danger. When uncertan of BIPs t s not wse to make column specfcatons based on composton. VLE data s avalable from DECHEMA. Regresson of User Component Data Enter the User Component screen for the physcal property to be regressed and enter the upper and lower lmt temperatures wth the relevant physcal property data n the correct unts. Note the regresson equaton on ths screen s not set n stone and may be changed. Densty s partcularly dffcult to acheve a regresson and changng the equaton to 100 the straght lne functon may help as densty approxmates to ths over a narrow range. Successful results can be acheved wth two data ponts only, but ensure that data at 0 C s not entered. Key data ponts can be weghted e.g. 10000 to force regresson through the pont. Pseudo component method s for hydrocarbons to calculate Tc and Pc e assumes component s a hydrocarbon. Use pseudo components for hydrocarbons. If t s not a hydrocarbon use Joback or UNIFAC dependng on the compound and do not enter an SG; note ths should have no effect on pure component regressons. If user component below mp at 60ºF do not enter SG. Joback s easer to get halogens nto, more flexble groups, but UNIFAC does a better job characterzng Poly Cyclc compounds. When usng UNIFAC f error message sayng "UNIFAC groups unspecfed for component" there are no groups and the actvty coeffcent for that component s set = 1 e bass wll be taken as deal behavour The most mportant thng s to try t several ways, and understand that these estmaton methods DO NOT replace the need for actual lab data on your compound. Once laboratory data s avalable the ssue s resolved. PAGE 35 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK www.pdesgn.co.uk
Process Modellng Selecton of Thermodynamc Methods APPENDIX VIII Predcton of Physcal Propertes Predctve Procedures CHEMCAD uses ndvdual component DIPPR coeffcents for the common temperature dependent varables such as vapour pressure, lqud densty and vscosty. If DIPPR coeffcents cannot be sourced then alternatve estmatng procedures are resorted to. Two group contrbuton methods, namely Lyderson/Joback and UNIFAC, are avalable for estmatng propertes from functonal groups contaned n the molecule. If the functonal group s not avalable, as s the case wth most organo-phosphorous compounds, these methods cannot be used. To handle functonal groups contanng phosphorus copy a smlar compound and then edt the HoV, VP, et al curves wth real data. However, the Benson method ncludes some data for many compounds and can be used to predct standard state C p, H f, S. Ths nformaton could be extended to nclude components not ncluded usng addtvty rules. S.W.Benson Addtvty Rules for the Estmaton of Thermochemcal Propertes J.Chem.Phys., pp309-310, 29, 546 (1968) The pseudo-component method estmates propertes of hydrocarbons n the form of lumped components usng API methods and can be adapted to model other compounds. Ths method requres M, T b and SG at 60 F and wll estmate the propertes T c, P c, V c, ω, lqud volume constant, IG heat capacty coeffcents and solublty parameter. As ths method s for pure hydrocarbons t s preferable to optmse the method by obtanng as many parameters as possble from alternatve methods/lterature sources e.g. DIPPR and DECHEMA lbrares. Model Parameter Lqud Densty Lqud Vscosty Vapour Vscosty HoV Enthalpy Datum Heat of Reacton EoS K Values Latent Heat Heat Balance Vapour Pressure Intrnsc value requred for CHEMCAD predcton T c P c V c, lqud volume constant, Rackett constant T c P c ω T c P c, Dpole Moment, Molecular dameter T b IG heat of formaton IG heat of formaton, HoV(no DIPPR) T c P c V c ω HoV(no DIPPR) C p T b ω (Notes 1&2) Notes 1. CHEMCAD wll always use DIPPR coeffcents f avalable wth the excepton of the IG heat capacty polynomal equaton whch s the default. 2. Method due to Klncewcz derves crtcal temperature Tc wth an expected error of 2%. Tc = 50.2 0.16M + 1.41T b PAGE 36 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK www.pdesgn.co.uk
Process Modellng Selecton of Thermodynamc Methods Component Propertes for Process Smulaton:- APPENDIX VIII Predcton of Physcal Propertes For modellng reactons n the lqud phase the followng component propertes are requred:- Chemcal formula. Molecular weght M. Lqud heat capacty C p. Two data ponts n operatng range preferred. Less mportant f reacton s sothermal. If the problem component s very dlute the soluton C p can be used snce enthalpy s a partal molar property and f x s small you can assume the soluton C p wll not be sgnfcantly nfluenced. Specfc gravty at 20 C. If the problem component s very dlute the soluton lqud densty ρ f can be used. Ideal Gas (IG) Heat of Formaton or Heat of Reacton. For component flashng process:- Normal bolng pont T b Heat of Vaporsaton (HoV) at normal bolng pont h fg The HoV at other temperatures can be found by correlaton from HoV at T b but ths s not the most accurate predcton. HoV can be estmated from T r and ω Accentrc factor ω Vapour pressure can be estmated usng T b, T c and M usng Gomez Thodos method but regresson from several data ponts s to be preferred. For mxed phase process:- VLE data of the component n the reacton mxture It s doubtful that Ideal wll apply, and UNIFAC VLE wll also not sutable for ths case. For solds formaton:- Solublty data over operatng temperature range PAGE 37 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK www.pdesgn.co.uk
Process Modellng Selecton of Thermodynamc Methods APPENDIX VIII Predcton of Physcal Propertes Useful References for Physcal Property Predctons S. W. Benson, F.R. Cruckskank, D.M. Golden. G.R. Haugon, H.E. O Neal, A.S. Rodgers, R. Shaw, and R. Walsh, Chem. Rev. 69, 279-324 (1969). S. W. Benson, Thermochemcal Knetcs, 2nd Edton, John Wley and Sons, New York (1976). S. W. Benson and J. H. Buss, J. Chem. Phys. 19, 279 (1968). F. N. Frtsch and R. E. Carlson, SIAM J. Numercal Analyss 17, 258-46 (1980). F. N. Frtsch and J. Butland, UCRL-85104, Lawrence Lvermore Laboratory, October, 1980. B. K. Harrson and W. H. Seaton, A soluton to the mssng group problem for estmaton of deal gas heat capactes, Ind. Eng. Chem. Res. 27, 1536-40 (1988). J. E. Hurst, Jr., and B. K. Harrson, Estmaton of lqud and sold heat capactes usng a modfed Kopp s rule, Chem. Eng. Commun, 112, 21-30 (1992). C. D. Ratkey and B. K. Harrson, Predcton of enthalpes of formaton for onc compound, Ind. Eng. Chem. Res. 31 (10), 2362-9 (1992). W. H. Seaton, Group Contrbuton Method for Predctng the Potental of a chemcal composton to cause an exploson, J. Chem. Educ. 66, A137-40 (1989). C. A. Daves, D.J. Frurp, E. Freedman, G.R. Hertel, W.H. Seaton, and D. N. Treweek, CHETAH 4.4: the ASTM chemcal thermodynamc and energy release program, 2nd edton, ASTM Publcaton DS 51A (1990). J. R. Downey, D. J. Frurp, M. S. LaBarge, A. N. Syverud, N. K. Grant, M. D. Marks, B. K. Harrson, W.H. Seaton, D. N. Treweek, and T. B. Selover, CHETAH 7.0 Users Manuals: the ASTM Computer program for chemcal thermodynamc and energy release evaluaton, NIST Specal Database 16, ASTM, ISBN 0-8031-1800-7, Phladelpha, PA (1994). Gustn, J.L., "Thermal Stablty Screenng and Reacton Calormetry. Applcaton to Runaway Reacton Hazard Assessment at Process Safety Management, J. Loss Prev. Process Inc., Vol. 6, No. 5, (1993). Chng-L Huang, Dr. Keth Harrson, Jeffry Madura, and Jan Dolfng, Gbbs Free Energes of Formaton of PCDDS: Evaluaton of Estmaton Methods and Applcaton for Predctng Dehalogenaton Pathways, Envronmental Toxcology and Chemstry, Vo. 15, No. 6, pp. 824-836, 1996. PAGE 38 OF 38 MNL 031B Issued November 2008, Prepared by J.E.Edwards of P & I Desgn Ltd, Teessde, UK www.pdesgn.co.uk
IDEAL SOLUTION Txy DIAGRAM Fgure 1 Raoult s Law p = y P = x p o at system temperature T Dew pt Bubble pt
ENTHALPY ISOBAR Fgure 2 Temperature T Tc Lqud enthalpy h = Cp(Ts-Tr) Wet vapour enthalpy H = h + ql crtcal pont Saturaton enthalpy Hs = h + L Superheat enthalpy Hsup = Hs + Cp(T-Ts) Superheat temp T Lqud lne Dry vapour lne Superheat T-Ts Ts Lqud Vapour- lqud q=1 Superheated vapour Reference Tr=298K h L Hsup Sensble Latent(dryness q) Superheat Heat added Q
THERMODYNAMIC PHASES Fgure 3 Pressure P Pc Crtcal Isotherm Crtcal Pont van der Waals equaton P = RT- a V-b V 2 Ps LLE Zone VLE Zone E-o-S Zone Sngle phase lqud Two phases vapour lqud Sngle phase gas Lqud-gas Coexstence curve Isotherms Volume V
van der Waals EQUATION of STATE Fgure 4 COMPONENT MW BP T C P C V C STATE CONSTANTS kg/kmol degc degk bar cm 3 /gmol a b HYDROGEN 2.0158-252.76 33.12 12.9595 65 2.4685E+05 2.6561E+01 VAN DER WAAL H2 @ Tc van der Waals equaton 20.00 P=(RT/(V-b))-(a/V^2) where we have a=(27/64)(r^2)(tc^2)/pc b=(rtc)/(8pc) R=83.144 (bar.cm^3)/(mol.k) Reference: Red,Prausntz,Polng Propertes Gases Lquds Table 3-5 p42 PRESSURE(bar) PRESSURE(bar) 15.00 10.00 5.00 0.00 0 50 100 150 200 250 VOLUME (cm3/gmol) VAN DER WAAL >Tc(100K) 300.00 250.00 200.00 150.00 100.00 50.00 0.00 0 50 100 150 200 250 VOLUME(cm3/gmol) VAN DER WAAL <Tc(20K) PRESSURE(bar) 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0 50 100 150 200 250 VOLUME(cm3/gmol)
RELATIVE VOLATILITY IN VLE DIAGRAM Fgure 5 α = 2.5 α = 4.0 α = 3.0 α = 10
AZEOTROPE γ VALUE IN VLE DIAGRAM Fgure 6 EtAc bp 77C Azeotrope bp=65c Hexane bp 69C Azeotrope X1=0.62 γ 1 =1.135 γ 2 =1.428 γ 1 =2.62 γ 2 =2.41
VLE DIAGRAM AND CONVERGENCE EFFECTS Fgure 7
CHEMCAD K AND H VALUES WIZARD Fgure 8 SINGLE COMP? MULTI CHEMICAL K=VAP H=LATE SPECIAL METHODS AMINE K=AMINE H=AMINE SOUR K=SOUR H=SRK POLYMER K=UPLM H=LATE HCL/NH3 K=PPAQ H=SRK HTSL? OTHER K=VAP H=SRK NG - CO2 K=BWRS H=BWRS K=ESSO (90 to 200ºC) H=LK < 7 BAR HEAVY HC P CHEM< 10 BAR Data j > 50% NRTL, UNIQUAC WILSON (Not LL) Data j < 50% UNIFAC LLE UNIFAC (Not LL) H=LATE (all) For P > 50 PSI Actvate Poyntng > 7 BAR K=GS (P < 200BAR) H=LK CHEM> 10 BAR? Data j > 50% SRK, PR Data j < 50% SRK, PSRK H=LATE (all) K=SRK H=SRK OTHER > -70ºC T K=PR H=PR < -70ºC
K VALUE MODEL DECISION TREE Fgure 9 GAS PHASE? LIQUID VAP ONLY? NAT GAS or CO2 VLE LIQUID? LLE GAS EQUATION SOAVE REDLICH KWONG(SRK) H=SRK - LATE HYDROCARBON PENG ROBINSON H=PENG ROBINSON BENEDICT WEBB RUBIN STARLING (BWRS) H=BWRS NO NRTL (5 PAR) UNIQUAC (2 PAR) UNIFAC(INCREM) H=LATENT HEAT IDEAL? IDEAL VAPOR H=LATENT HEAT YES AZEOTROPE IDEAL VAP PRESS GAS EQUATION BIP MODEL H=LATENT HEAT NRTL (5 PAR) UNIQUAC (2 PAR) UNIFAC(INCREM) H=LATENT HEAT BIP MODEL LLE BIPS H=LATENT HEAT