用CPA方程結(jié)合重整化群理論計(jì)算締合流體的熱力學(xué)性質(zhì) 許心皓

1、中國(guó)工程熱物理學(xué)會(huì) 工程熱力學(xué)與能源利用學(xué)術(shù)會(huì)議論文 編號(hào)：091213用CPA方程結(jié)合重整化群理論計(jì)算締合流體的熱力學(xué)性質(zhì)* 基金工程：國(guó)家重點(diǎn)根底研究開(kāi)展方案資助 (2021CB219805)第一 許心皓(1985)，男，江蘇南京人，博士研究生，主要從事熱力學(xué)與流體熱物性研究許心皓 段遠(yuǎn)源(清華大學(xué) 熱科學(xué)與動(dòng)力工程教育部重點(diǎn)實(shí)驗(yàn)室，北京 100084)(Tel:E-mail: )摘要：醇，水，氨等締合流體在工業(yè)上有著廣泛的應(yīng)用，而近年來(lái)，在臨界點(diǎn)附近的物性越來(lái)越受到關(guān)注。本文結(jié)合重整化群理論和適用于締合流體的CPA狀態(tài)方程計(jì)算了甲醇，水和氨的熱力學(xué)性質(zhì)。與原C

2、PA方程相比，這種結(jié)合的方法顯著改善了臨界參數(shù)和近臨界區(qū)的氣液相平衡數(shù)據(jù)的描述情況，在單相區(qū)的預(yù)測(cè)精度也較高。關(guān)鍵詞：重整化群理論；CPA狀態(tài)方程；締合流體 中圖分類(lèi)號(hào)：TK121；TK123Investigation of the thermodynamic properties of associating fluids using CPA EOS + renormalization group theoryXU Xinhao, DUAN Yuanyuan(Key Laboratory for Thermal Science and Power Engineering of Ministr

3、y of Education, Tsinghua University, Beijing 100084, China)Abstract: Associating fluids, such as alcohols, water and ammonia, have wide application in industry. The thermophysical properties near the critical point have received increasing attention in the past years. The thermodynamic properties of

4、 methanol, water and ammonia was investigated by combining the renormalization group theory and the CPA equation of state extended for associating fluids. The results showed significant improvement in the representation of the critical property and the phase equilibrium in the region near critical p

5、oint compared with the original CPA EOS. Good results were also obtained in the single-phase region.Key words: renormalization group theory; CPA EOS; associating fluids0 前言狀態(tài)方程是研究流體物性和相平衡性質(zhì)的重要工具。其中，SRKSoave-Redlich-Kwong方程以其形式簡(jiǎn)單，通用性強(qiáng)，計(jì)算精度較高而得到了廣泛的應(yīng)用。但它在計(jì)算締合流體時(shí)精度較差。CPACubic-Plus-Association狀態(tài)方程 ADDIN

6、 EN.CITE Kontogeorgis1996797917Kontogeorgis, G. M.Voutsas, E. C.Yakoumis, I. V.Tassios, D. P.Natl tech univ athens,dept chem engn,sect 2,gr-15773 athens,greece.An equation of state for associating fluidsIndustrial & Engineering Chemistry ResearchInd. Eng. Chem. Res.Industrial & Engineering Chemistry

7、 ResearchInd. Eng. Chem. Res.Industrial & Engineering Chemistry ResearchInd. Eng. Chem. Res.4310-43183511PHASE-EQUILIBRIAHYDROGEN-FLUORIDEMIXTURESSYSTEMSPREDICTIONMOLECULESMETHANOLMODELWATER1996Nov0888-5885ISI:A1996VR70500057Article:/A1996VR70500057 English1是應(yīng)用微擾理論，將SRK狀態(tài)方程與Wertheim締合項(xiàng)相結(jié)合建立的新型狀態(tài)方程。它

8、不僅保持了SRK方程形式的簡(jiǎn)潔，同時(shí)引入了對(duì)氫鍵締合作用的考慮，目前已成功的應(yīng)用于包含締合流體和非締合流體的體系 ADDIN EN.CITE Kontogeorgis2006808017Kontogeorgis, G. M.Michelsen, M. L.Folas, G. K.Derawi, S.von Solms, N.Stenby, E. H.Tech Univ Denmark, Ctr Phase Equilibria & Separat Proc IVC SEP, Dept Chem Engn, DK-2800 Lyngby, Denmark.Kontogeorgis, GM, Te

9、ch Univ Denmark, Ctr Phase Equilibria & Separat Proc IVC SEP, Dept Chem Engn, DK-2800 Lyngby, Denmark.gkkt.dtu.dkTen years with the CPA (Cubic-Plus-Association) equation of state. Part 1. Pure compounds and self-associating systemsIndustrial & Engineering Chemistry ResearchInd. Eng. Chem. Res.Indust

10、rial & Engineering Chemistry ResearchInd. Eng. Chem. Res.Industrial & Engineering Chemistry ResearchInd. Eng. Chem. Res.4855-48684514VAPOR-LIQUID-EQUILIBRIUMTEMPERATURE MUTUAL SOLUBILITIESPHASE-EQUILIBRIASAFT EQUATIONGENERALIZED EQUATIONPHYSICAL-PROPERTIESPROPANE-METHANOLALKANE MIXTURESBINARY-MIXTUR

11、ESCARBON-DIOXIDE2006Jul0888-5885ISI:000238590400001Review:/000238590400001 10.1021/ie051305vEnglish2。然而，與其它基于平均場(chǎng)理論的經(jīng)典狀態(tài)方程一樣，CPA方程沒(méi)有考慮密度的漲落，因而無(wú)法正確描述流體在臨界點(diǎn)附近的性質(zhì)。重整化群renormalization group，RG理論 ADDIN EN.CITE Wilson1971424217Wilson, K. G.Renormalization Group and Critical PhenomenaPhysical Review BPhysic

12、al Review BPhys. Rev. B3174-3205491971ISI:A1971K734100043Article:/A1971K734100043 English3考慮了臨界點(diǎn)附近強(qiáng)烈的密度漲落，是處理流體的臨界性質(zhì)的有效途徑之一。最初的RG理論只適用于非常接近臨界點(diǎn)的區(qū)域。White等 ADDIN EN.CITE Salvino1992373717Salvino, L. W.White, J. A.American univ,dept phys,washington,dc 20016.Calculation of Density Fluctuation Contributio

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14、900053 EnglishWhite1992363617White, J. A.White, ja, american univ,dept phys,washington,dc 20016.Contribution of Fluctuations to Thermal-Properties of Fluids with Attractive Forces of Limited Range - Theory Compared with P-Rho-T and Cv Data for ArgonFluid Phase EquilibriaFluid Phase Equilib.Fluid Pha

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17、sicsJ. Chem. Phys.J Chem Phys2021-2021993THERMODYNAMIC PROPERTIESEQUATIONPENTANE1993Aug0021-9606ISI:A1993LN78200059Article:/A1993LN78200059 EnglishWhite1995393917White, J. A.Zhang, S.White, ja, american univ,dept phys,washington,dc 20016.Renormalization Theory of Nonuniversal Thermal-Properties of F

18、luidsJournal of Chemical PhysicsJ. Chem. Phys.Journal of Chemical PhysicsJ. Chem. Phys.J Chem PhysJournal of Chemical PhysicsJ. Chem. Phys.J Chem Phys1922-19281035HIERARCHICAL REFERENCE THEORY1995Aug0021-9606ISI:A1995RL76700023Article:/A1995RL76700023 EnglishWhite1998696917White, J. A.Zhang, S.Amer

19、Soc Mech Engineers, Heat Transfer Div Standing Comm ThermophysProperties, Natl Inst StandTechnol, Chem SciTechnol Lab, PhysChem Properties, DivRenormalization group theory for fluids to greater density distances from the critical pointInternational Journal of ThermophysicsInternational Journal of Th

20、ermophysicsInt. J. Thermophys.1019-1027194critical pointdensity fluctuationsnonuniversal thermal behaviorradial distribution functionrenormalization groupvolumetricproperties1998Jun 22-27Boulder, ColoradoSpringer NetherlandsISI:000077286300002:/000077286300002 English4-8開(kāi)展了RG理論，建立了Helmholtz自由能的迭代計(jì)算方

21、法，使RG理論可以用于預(yù)測(cè)實(shí)際流體在臨界點(diǎn)附近和遠(yuǎn)離臨界點(diǎn)的全范圍的熱力學(xué)性質(zhì)。這種方法得到了廣泛的關(guān)注，目前已被應(yīng)用到了立方型狀態(tài)方程 ADDIN EN.CITE Cai2004707017Cai, J.Prausnitz, J. M.Univ Calif Berkeley, Dept Chem Engn, Berkeley, CA 94720 USA. Lawrence Berkeley Lab, Div Chem Sci, Berkeley, CA 94720 USA.Prausnitz, JM, Univ Calif Berkeley, Dept Chem Engn, Berkeley

22、, CA 94720 USA.Thermodynamics for fluid mixtures near to and far from the vapor-liquid critical pointFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase EquilibriaFluid Phase Equilib.Fluid Phase EquilibFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase Equilib205-2172192renormalization group th

23、eorycontinuous thermodynamicscriticalstateequation-of-statepolydisperse mixtureEQUATION-OF-STATERENORMALIZATION-GROUP THEORYLENNARD-JONES FLUIDCRITICAL REGIONPHASE-EQUILIBRIACRITICAL EXPONENTSCROSSOVERBEHAVIORTEMPERATURESSIMULATIONS2004May0378-3812ISI:000221516300012Article:/000221516300012 10.1016/

24、j.fluid.2004.01.033EnglishCai2006717117Cai, J.Qiu, D. L.Zhang, L. N.Hu, Y.E China Univ Sci & Technol, Dept Chem, Shanghai 200237, Peoples R China.Cai, J, E China Univ Sci & Technol, Dept Chem, Shanghai 200237, Peoples R China.tsaijunonline.sh Vapor-liquid critical properties of multi-component fluid

25、 mixtureFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase EquilibriaFluid Phase Equilib.Fluid Phase EquilibFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase Equilib229-2352411-2renormalization groupcriticalmulti-componentfluid mixtureEQUATION-OF-STATEGLOBAL THERMODYNAMIC BEHAVIORRENORMALIZAT

26、ION-GROUPTHEORYLENNARD-JONES FLUIDCRITICAL REGIONCRITICAL-POINTCRITICALEXPONENTSCROSSOVERTEMPERATURESSIMULATIONS2006Mar0378-3812ISI:000236637200024Article:/000236637200024 10.1016/j.fluid.2005.11.003EnglishLlovell2021727217Llovell, F.Vega, L. F.Seiltgens, D.Mejia, A.Segura, H.Llovell, F.; Vega, L. F

27、. CSIC, Inst Ciencia Mat Barcelona, ICMAB, E-08193 Barcelona, Spain. Vega, L. F. MATGAS Res Ctr, Barcelona 08193, Spain. Seiltgens, D.; Mejia, A.; Segura, H. Univ Concepcion, Dept Ingn Quim, Concepcion, Chile.Vega, LF, CSIC, Inst Ciencia Mat Barcelona, ICMAB, Campus UAB, E-08193 Barcelona, Spain.lve

28、gaicmab.esAn accurate direct technique for parametrizing cubic equations of state - Part III. Application of a crossover treatmentFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase EquilibriaFluid Phase Equilib.Fluid Phase EquilibFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase Equilib201-21

29、02641-2cubic equation of statesoft-SAFFcrossovercritical regionn-alkanes1-alkanolscarbon dioxidewaterRENORMALIZATION-GROUP THEORYASSOCIATING FLUID THEORYINCLUDINGCRITICAL REGIONCRITICAL-POINTOF-STATETHERMODYNAMIC PROPERTIESBINARY-MIXTURESPURE FLUIDSSAFTPREDICTION2021Mar0378-3812ISI:000253670200021Ar

30、ticle:/000253670200021 10.1016/j.fluid.2007.11.006English9-11和SAFT狀態(tài)方程 ADDIN EN.CITE Llovell2004737317Llovell, F.Pamies, J. C.Vega, L. F.CSIC, Inst Ciencia Mat Barcelona, E-08193 Barcelona, Spain.Vega, LF, CSIC, Inst Ciencia Mat Barcelona, Campus UAB, E-08193 Barcelona, Spain.lvegaicmab.esThermodyna

31、mic properties of Lennard-Jones chain molecules: Renormalization-group corrections to a modified statistical associating fluid theoryJournal of Chemical PhysicsJ. Chem. Phys.Journal of Chemical PhysicsJ. Chem. Phys.J Chem PhysJournal of Chemical PhysicsJ. Chem. Phys.J Chem Phys10715-1072412121EQUATI

32、ON-OF-STATEDIRECTIONAL ATTRACTIVE FORCESVAPOR-LIQUID-EQUILIBRIAMULTIPLE BONDING SITESSOFT-SAFT EQUATIONHEAVY N-ALKANESCRITICAL REGIONPERTURBATION-THEORYPHASE-EQUILIBRIACRITICAL-POINT2004Dec0021-9606ISI:000225136300050Article:/000225136300050 10.1063/1.1809112EnglishMi2004777717Mi, J. G.Zhong, C. L.L

33、i, Y. G.Chen, J.Beijing Univ Chem Technol, Key Lab Nanomat, Minist Educ, Dept Chem Engn, Beijing 100029, Peoples R China. Tsing Hua Univ, State Key Lab Chem Engn, Beijing 100084, Peoples R China.Zhong, CL, Beijing Univ Chem Technol, Key Lab Nanomat, Minist Educ, Dept Chem Engn, POB 100, Beijing 1000

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35、RE-WELL FLUIDSCROSSOVEREQUATIONTHERMAL-PROPERTIESCRITICAL-BEHAVIORMIXTURESTHERMODYNAMICSSIMULATIONSSAFT2004Oct0301-0104ISI:000224321000004Article:/000224321000004 10.1016/j.chemphys.2004.06.031EnglishMi2005767617Mi, J. G.Zhong, C. L.Li, Y. G.Beijing Univ Chem Technol, Dept Chem Engn, Minist Educ, Ke

36、y Lab Nanomat, Beijing 100029, Peoples R China.Zhong, CL, Beijing Univ Chem Technol, Dept Chem Engn, Minist Educ, Key Lab Nanomat, Beijing 100029, Peoples R C Renormalization group theory for fluids including critical region. II. Binary mixturesChemical PhysicsChem. Phys.Chemical PhysicsChem. Phys.C

37、hem PhysChemical PhysicsChem. Phys.Chem Phys31-383121-3renormalization group theorycritical phenomenaSAFTthermodynamicsEQUATION-OF-STATEDIRECTIONAL ATTRACTIVE FORCESPURE FLUIDSTHERMODYNAMIC BEHAVIORPHASE-EQUILIBRIASAFT EQUATIONPOLAR FLUIDSHARD-SPHERESMOLECULESCROSSOVER2005Jun0301-0104ISI:00022820670

38、0004Article:/000228206700004 10.1016/j.chemphys.2004.11.018EnglishLlovell2006747417Llovell, F.Vega, L. F.CSIC, Inst Ciencia Mat Barcelona, E-08193 Barcelona, Spain.Vega, LF, CSIC, Inst Ciencia Mat Barcelona, Campus UAB, E-08193 Barcelona, Spain.lvegaicmab.esGlobal fluid phase equilibria and critical

39、 phenomena of selected mixtures using the crossover soft-SAFT equationJournal of Physical Chemistry BJ. Phys. Chem. BJournal of Physical Chemistry BJ. Phys. Chem. BJournal of Physical Chemistry BJ. Phys. Chem. B1350-13621103DIRECTIONAL ATTRACTIVE FORCESVAPOR-LIQUID-EQUILIBRIARENORMALIZATION-GROUP CO

40、RRECTIONSLENNARD-JONES CHAINSHEAVYN-ALKANESOF-STATECRITICAL REGIONTHERMODYNAMIC PROPERTIESCRITICAL-POINTBINARY-MIXTURES2006Jan1520-6106ISI:000235046300040Article:/000235046300040 10.1021/jp0551465EnglishBymaster2021787817Bymaster, A.Emborsky, C.Dominik, A.Chapman, W. G.Bymaster, Adam; Emborsky, Chri

41、s; Dominik, Aleksandra; Chapman, Walter G. Rice Univ, Dept Chem & Biomol Engn, Houston, TX 77005 USA.Chapman, WG, Rice Univ, Dept Chem & Biomol Engn, 6100 S Main St, Houston, TX 77005 USA.Renormalization-group corrections to a perturbed-chain statistical associating fluid theory for pure fluids near

42、 to and far from the critical regionIndustrial & Engineering Chemistry ResearchInd. Eng. Chem. Res.Industrial & Engineering Chemistry ResearchInd. Eng. Chem. Res.Industrial & Engineering Chemistry ResearchInd. Eng. Chem. Res.6264-62744716EQUATION-OF-STATEDIRECTIONAL ATTRACTIVE FORCESLENNARD-JONES CH

43、AINSVAPOR-LIQUID-EQUILIBRIAMULTIPLE BONDING SITESPHASE-EQUILIBRIASAFTEQUATIONTHERMODYNAMIC PROPERTIESN-ALKANESTHERMAL-PROPERTIES2021Aug0888-5885ISI:000258400300054Article:/000258400300054 10.1021/ie8001167English12-16上。本文將White開(kāi)展的RG 理論與CPA狀態(tài)方程相結(jié)合, 計(jì)算了甲醇，氨和水這三種具有代表性的締合流體在臨界點(diǎn)附近和遠(yuǎn)離臨界點(diǎn)的熱力學(xué)性質(zhì)。1 CPA狀態(tài)方程CP

44、A方程形式如下：(1)式中：p為壓力，R為通用氣體常數(shù)，T為溫度，v為摩爾體積，為密度；a、b是SRK方程的參數(shù)，XA為分子在A位上沒(méi)有參加締合作用的比例。SRK方程的能量參數(shù)a的表達(dá)式如下：(2)式中：a0、c1是系數(shù)；Tr為比照溫度T / Tc。締合作用項(xiàng)XA可通過(guò)下式得到：(3)A位與B位間的締合強(qiáng)度AB可通過(guò)下式得到(4)式中：AB和AB分別為締合能和相互作用體積，g為徑向分布函數(shù)。Kontogeorgis等 ADDIN EN.CITE Kontogeorgis1999818117Kontogeorgis, Georgios M.V. Yakoumis, IakovosMeijer,

45、HenkHendriks, EricMoorwood, TonyMulticomponent phase equilibrium calculations for water-methanol-alkane mixturesFluid Phase EquilibriaFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase Equilib201-209158-160Equation of stateLiquid-liquid equilibriaAssociationMulticomponentAlcoholWater1999 :/ scien

46、cedirect /science/article/B6TG2-3Y9G7WW-3V/2/c9ff1bbdf1de340eab409275a115880d 17提出了g的近似表達(dá)式，形式如下：(5a)(5b)式中，為硬球流體的比照密度。2 CPA結(jié)合RG的方法根據(jù)White對(duì)RG理論的開(kāi)展，Helmholtz自由能密度的迭代計(jì)算過(guò)程如下：(6)(7)(8)(9) (10) (11)(12)(13)式中：下標(biāo)l 和s 分別表示長(zhǎng)波和短波作用。L 是截?cái)嚅L(zhǎng)度，是密度漲落初始最短波長(zhǎng)的函數(shù)。在本文計(jì)算中，這兩個(gè)參數(shù)均為可調(diào)參數(shù)。針對(duì)CPA方程，本文具體采用了如下一些處理。-2表示平均場(chǎng)Helmhol

47、tz自由能密度的引力局部，它取決于具體的分子勢(shì)能模型。本文采用Cai ADDIN EN.CITE Cai2004707017Cai, J.Prausnitz, J. M.Univ Calif Berkeley, Dept Chem Engn, Berkeley, CA 94720 USA. Lawrence Berkeley Lab, Div Chem Sci, Berkeley, CA 94720 USA.Prausnitz, JM, Univ Calif Berkeley, Dept Chem Engn, Berkeley, CA 94720 USA.Thermodynamics for

48、fluid mixtures near to and far from the vapor-liquid critical pointFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase EquilibriaFluid Phase Equilib.Fluid Phase EquilibFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase Equilib205-2172192renormalization group theorycontinuous thermodynamicscriti

49、calstateequation-of-statepolydisperse mixtureEQUATION-OF-STATERENORMALIZATION-GROUP THEORYLENNARD-JONES FLUIDCRITICAL REGIONPHASE-EQUILIBRIACRITICAL EXPONENTSCROSSOVERBEHAVIORTEMPERATURESSIMULATIONS2004May0378-3812ISI:000221516300012Article:/000221516300012 10.1016/j.fluid.2004.01.033EnglishCai20067

50、17117Cai, J.Qiu, D. L.Zhang, L. N.Hu, Y.E China Univ Sci & Technol, Dept Chem, Shanghai 200237, Peoples R China.Cai, J, E China Univ Sci & Technol, Dept Chem, Shanghai 200237, Peoples R China.tsaijunonline.sh Vapor-liquid critical properties of multi-component fluid mixtureFluid Phase EquilibriaFlui

51、d Phase Equilib.Fluid Phase EquilibriaFluid Phase Equilib.Fluid Phase EquilibFluid Phase EquilibriaFluid Phase Equilib.Fluid Phase Equilib229-2352411-2renormalization groupcriticalmulti-componentfluid mixtureEQUATION-OF-STATEGLOBAL THERMODYNAMIC BEHAVIORRENORMALIZATION-GROUPTHEORYLENNARD-JONES FLUID

52、CRITICAL REGIONCRITICAL-POINTCRITICALEXPONENTSCROSSOVERTEMPERATURESSIMULATIONS2006Mar0378-3812ISI:000236637200024Article:/000236637200024 10.1016/j.fluid.2005.11.003English9, 10使用的簡(jiǎn)化表達(dá)方法，將其與CPA方程中的參數(shù)a相關(guān)聯(lián)：(14)類(lèi)似的，本文將max與CPA方程中的參數(shù)b相關(guān)聯(lián)，為了防止計(jì)算值的發(fā)散，本文取：(15)迭代初始項(xiàng)，推導(dǎo)可得：(16)式中：M為分子上的締合位數(shù)。式10的積分采用梯形法計(jì)算，密度區(qū)域分

53、為1000個(gè)區(qū)間。每一個(gè)迭代步得到的自由能密度用三次樣條將其轉(zhuǎn)化為光滑曲線，并在下一步中使用。當(dāng)?shù)綌?shù)n5時(shí)， ADDIN EN.CITE Llovell2004737317Llovell, F.Pamies, J. C.Vega, L. F.CSIC, Inst Ciencia Mat Barcelona, E-08193 Barcelona, Spain.Vega, LF, CSIC, Inst Ciencia Mat Barcelona, Campus UAB, E-08193 Barcelona, Spain.lvegaicmab.esThermodynamic properties

54、 of Lennard-Jones chain molecules: Renormalization-group corrections to a modified statistical associating fluid theoryJournal of Chemical PhysicsJ. Chem. Phys.Journal of Chemical PhysicsJ. Chem. Phys.J Chem PhysJournal of Chemical PhysicsJ. Chem. Phys.J Chem Phys10715-1072412121EQUATION-OF-STATEDIR

55、ECTIONAL ATTRACTIVE FORCESVAPOR-LIQUID-EQUILIBRIAMULTIPLE BONDING SITESSOFT-SAFT EQUATIONHEAVY N-ALKANESCRITICAL REGIONPERTURBATION-THEORYPHASE-EQUILIBRIACRITICAL-POINT2004Dec0021-9606ISI:000225136300050Article:/000225136300050 10.1063/1.1809112EnglishLlovell2006747417Llovell, F.Vega, L. F.CSIC, Ins

56、t Ciencia Mat Barcelona, E-08193 Barcelona, Spain.Vega, LF, CSIC, Inst Ciencia Mat Barcelona, Campus UAB, E-08193 Barcelona, Spain.lvegaicmab.esGlobal fluid phase equilibria and critical phenomena of selected mixtures using the crossover soft-SAFT equationJournal of Physical Chemistry BJ. Phys. Chem

57、. BJournal of Physical Chemistry BJ. Phys. Chem. BJournal of Physical Chemistry BJ. Phys. Chem. B1350-13621103DIRECTIONAL ATTRACTIVE FORCESVAPOR-LIQUID-EQUILIBRIARENORMALIZATION-GROUP CORRECTIONSLENNARD-JONES CHAINSHEAVYN-ALKANESOF-STATECRITICAL REGIONTHERMODYNAMIC PROPERTIESCRITICAL-POINTBINARY-MIX

58、TURES2006Jan1520-6106ISI:000235046300040Article:/000235046300040 10.1021/jp0551465English12, 15。本文中取n=5時(shí)，迭代結(jié)束。3 結(jié)果與討論結(jié)合了重整化群理論的CPA狀態(tài)方程共有7個(gè)可調(diào)參數(shù)：b，a0，c1，AB，AB，L，。本文將NIST提供的飽和蒸氣壓和飽和液相密度數(shù)據(jù) ADDIN EN.CITE 2021878745NIST Chemistry Webbook2021 :/chemistry :/chemistry18作為基準(zhǔn)值，回歸得到了甲醇，水和氨的相關(guān)參數(shù)，其中甲醇采用2B締合方式，水和氨

59、采用3B締合方式?；貧w結(jié)果如表1所示。表1 CPA+RG方程參數(shù)Table 1 Parameters of CPA+RG (m3 mol-1)a0(Pa m6 mol-2)c1AB(Pa m3 mol-1)AB103 (m)甲醇3.15020.434750.4683523647水1.47230.225980.837881791875.00.74.43氨1.97690.18041.29865579247圖1-3比擬了SRK，CPA，CPA結(jié)合RG理論計(jì)算的氣液相平衡結(jié)果與NIST提供的結(jié)果?？梢钥吹絊RK方程在液相區(qū)有較大偏差，原始的CPA方程雖然成功再現(xiàn)了遠(yuǎn)離臨界區(qū)的數(shù)據(jù)，但在近臨界區(qū)計(jì)算的壓力和溫度都偏高。而采用本文建立CPA結(jié)合RG理論的方法，能夠同時(shí)在接近臨界點(diǎn)和遠(yuǎn)離臨界點(diǎn)的區(qū)域再現(xiàn)NIST的數(shù)據(jù)，精度較高。(a)(b)圖1 甲醇的相平衡 (a) T-圖 (b) p-圖Fig. 1 Vapor-liquid coexistence lines for methanol (a) T- diagram (b) p-diagram圖2 水的相平衡 (a) T-圖 (b) p-圖Fig. 2 Vapor-liquid coexistence lines for water (a) T- diagram (b) p-diagram圖3 氨的相平衡 (a) T-圖 (b)