International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-8 Issue-12S2, October 2019 Prediction of Vapour Liquid Equilibria for Binary Azeotropic Systems using Models

Sivaprakash .B, Manojkumar M.S

Abstract—Distillation operations are inevitable in chemical and operation of the distillation equipments are important and petrochemical process industries. Design of distillation from economic and also environmental points of view [5]. equipment requires knowledge of precise vapor-liquid The presence of azeotropic mixture however complicates the equilibrium data. Due to the complexity and expenses incurred to design of ordinary distillation principles [6]. It is impossible obtain the VLE data experimentally for those systems for which the data are not available, solution and phase to conduct the distillation process in the case of azeotropic equilibria serve as an important tool in theoretical VLE composition.Azeotropes or close-boiling mixtures. The prediction. In the current investigation five binary azeotropes molecular interactions when two or more components are namely Acetone-water, Acetone-methanol, Ethanol-water, mixed may cause the mixture to form certain “inseparable” Ethanol-benzene, and Methanol-water are taken for study. The compositions where the vapor and liquid compositions at theoretical prediction of VLE for these systems were computed equilibrium are equal within a given pressure and using activity coefficient models namely NRTL, UNIQUAC, UNIFAC and modified form of Florry - Huggins equations (SRS temperature range. These specific mixture compositions are and TCRS). The parameters for the five systems of four models called azeotropes. The defining condition of an azeotropic viz. NRTL, UNIQUAC, SRS and TCRS were computed using mixture and the physical phenomena leads to nonideality. Newton Raphson technique. UNIFAC model was adopted using Nonideal mixtures exhibit positive (γi> 1) or negative (γi< 1) Analytical solution of group contribution (ASOG) method. The deviations from Raoult’s law [. If these deviations become performance of these models are tested using thermodynamic so large that the vapor pressure exhibits an extremal point at consistency test and validation from experimental VLE from literature. It was seen that the Acetone - Water system follows constant temperature, or, equivalently, an extremal point in TCRS model, Acetone - Methanol and Ethanol - Water and the boiling temperature at constant pressure. Azeotropes Methanol - Water systems follow UNIFAC model, whereas SRS play an important role in vapor-liquid equilibrium separation model suits for the Ethanol - Benzene system with highest processes. For efficient design of distillation equipment or accuracies. any other separation processes which are diffusional in nature requires quantitative understanding of vapour liquid Keywords: Vapour liquid Equilibrium, Azeotrope, Non ideal equilibria. In Vapour liquid equilibrium phases are system, Activity Coefficient model, Thermodynamic consistency expressed through vapour phase coefficients and I. INTRODUCTION the liquid phase activity coefficients. At low or modest pressures fugacity coefficient can be estimated easily for Separation of chemical in to the constituents is an art for very simple mixtures or ideal solutions, but for non-ideal millennia [1]. Chemical Engineers are more concerned with mixtures, estimation of liquid phase activity coefficient is separations process. Separation methods include distillation, quite difficult [7]. In the present work five azeotropic absorption, liquid-liquid extraction, leaching, drying and systems namely acetone-methanol, chloroform-methanol, crystallization etc [2]. Distillation, which is the most widely, acetone-water, ethanol-benzene and methanol-water were used separation technique in the chemical process industries taken for study. Experimental VLE of these systems were [3] accounts for about 3% of the world energy consumption. taken from literature . Applicability of five activity Also it has substantial advantages over the other processes coefficient models to these systems were tested in the study applied in order to separate a mixture, such extraction, viz. NRTL, UNIQUAC, UNIFAC and two forms of crystallization, semi permeable membranes etc. Distillation modified Flory – Huggins equations (SRS and TCRS). Also process is based on the fact that the composition of the thermodynamic consistency test for these models was boiling liquid and that of the vapour over it differ. Thus, if carried out by Redlich-Kister method. the boiling temperature is low (e.g., air separation), it is necessary to use low temperature refrigerants and conduct II.METHODOLOGY &LOW PRESSURE VLE the process at a higher pressure. If it is high (e.g., in DATA REDUCTION separation of heavy oil fractions or metals), high temperature heat carries or fire preheating have to be used There are different methods available for the regression of and the process is run under vacuum [4]. Because of the isothermal and isobaric VLE data. The gamma/phi (γ-ᵩ) high energy demand of these processes the optimal design formulation of VLE or more commonly known as the combined method was used in this work to regress the VLE data [8]. The combined method uses an equation of state to Revised Manuscript Received on September 14, 2019. Sivaprakash .B, Department of , Annamalai University, Annamalai Nagar, Tamilnadu, India Manojkumar M.S, Department of Petrochemical Engineering, Mahendra Institute of Engineering and Technology, Nammakkal, Tamilnadu, India

Published By: Retrieval Number: L101310812S219/2019©BEIESP Blue Eyes Intelligence Engineering DOI: 10.35940/ijitee.L1013.10812S219 67 & Sciences Publication

PREDICTION OF VAPOUR LIQUID EQUILIBRIA FOR BINARY AZEOTROPIC SYSTEMS USING ACTIVITY COEFFICIENT MODELS θ τ calculate the fugacity coefficients that describe the vapour R j ij phase non-idealities, while an activity coefficient model is ln  i  qi [1 - ln ( jθ jτ ji )   j used to calculate the activity coefficients that describe the kθk τkj liquid phase non-idealities. The gamma/phi method relies (9) upon liquid phase activity coefficient models to represent z VLE data, and give accurate result for non li  (ri  qi ) - (ri 1) 2 (10) which is given by i Sat r  Σ v R φi yi P  γi xi Pi (1) i k k k (11) i yi is mole fraction in vapour phase; xi is mole fraction in q  Σ v Q sat i k k k liquid phase; Pi is vapour pressure and P is operating (12) pressure; ᵠi is fugacity coefficient and γi is activity where   segment or volume fraction of the component coefficient. i θi  area fraction of the component Fugacity Coefficient: r  volume parameter of the component At low to moderate pressure (0 to 10 atm), fugacity i coefficient can be calculated by the following equations. q  surface area parameter of the component 0 1 i ln φ  (B  ω B )P /T i r r (2) UNIquac Functional group Activity Coefficient (UNIFAC) method f  φ P i i (3) UNIFAC is based on UNIQUAC model, has a 1.6 combinatorial term that depends on the volume and surface B  0.083 - 0.422/T area of each molecule and a residual term that is the result of 0 r (4) the energies of interaction between the molecules [11]. The 1 4.2 B  0.139 - 0.172/T combinatorial term is evaluated using equation (8) When r (5) using the UNIFAC model one first identifies the functional ϕ is fugacity coefficient; B0& B1 are virial coefficients; ɷ i subgroups present in each molecule. Next the activity is accentric factor; P is reduced pressure; T is reduced r r coefficient for each species is written as temperature. ln   ln  (combinato rial)  ln  (residual) Activity Coefficient Models: i i i (13) NRTL (Non-Random Two Liquid) Model i i ln  (residual)   v [ln   ln Γ ] The non random two liquid (NRTL) equation proposed by i k k k k (14) Renon and Prausnitz, [9] is applicable to partially miscible φm  ψ as well as completely miscible systems. The equations for km ln ΓK  Qk [1  ln (ΣmφmΨmk )  Σm ] the activity coefficients are ΣnφnΨnm 2 (15)   G   G  2   21  12 12  u  u   a   x     exp - mn nn mn 1 2  21 x  x G  2  mn    exp  1 2 21  (x2  x1G12 )  RT  T ln   (16) (6) i where k is residual activity coefficient; a is 2 mn   interaction parameter; umnis interaction energy between 2  G   G   x   12   21 21  group m and n. 2 1 12 2   x  x G  (x  x G )  Simplified Ruckenstein and Shulgin model (SRS)   2 1 12  1 2 21  ln The SRS equation for lni s are [12] given as (7) lnγ1  ln(x1  x2L12)  x2[A12 A21](lnL12 lnL 21) where G12and G21 energy interaction between the molecules.        x  1  x  2 UNIQUAC (UNIversal Quasi-Chemical) model  1 2 2 2 2 1   x1 x1  The UNIQUAC equation was developed by Anderson   (19) and Prausnitz [10] who incorporated the two-liquid model ln γ 2  ln(x 2  x1L 21)  x1[A12  A 21] (lnL 12  lnL 21) and the theory of local composition. The UNIQUAC  1 2  equation consists of two parts a combinatorial part that takes 12  x12  x11  x x into accounts the differences in sizes and shapes of the  1 1  (20) molecules and the residual part that is due to the  Lij  intermolecular forces between the molecules. In the form of A    ij x  x L an equation, this is represented as Where  1 2 ij  (21)  θ C i z i i ln γi  ln  qi ln  li   j x jl j xi 2 i xi (8)

Published By: Retrieval Number: L101310812S219/2019©BEIESP Blue Eyes Intelligence Engineering DOI: 10.35940/ijitee.L1013.10812S219 68 & Sciences Publication International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-8 Issue-12S2, October 2019

Mathematical Computation Vj  λij λii  Lij  exp  The theoretical estimation of VLE using the five activity V  RT  i   (22) coefficient models, NRTL, UNIQUAC, UNIFAC, SRS and x1 TCRS was accomplished using Newton Raphson technique i  with computer programming in Java software of 1.6 version. x1  x 2L ji (23) The output of the programming yielded the parameters of x   2 the models along with the theoretical values of the VLE. j x  x L The relative error percentages between the experimental and 2 1 ji (24) model predicted vapour phase mole fractions are calculated where x and x are mole fraction in liquid phase. A and 1 2 12 using the equation A21 are two adjustable parameters related to pure component molar volume and characteristic energy difference.  and  1 2 y Experiment al - y1 Calculated are segment fraction of the components and χ is an energy 1 REy1  x 100 interaction between molecules of components. y1 Experiment al Theoretically Consistent Ruckenstein and Shulgin model (30) (TCRS) Thermodynamic Consistency test : Like NRTL equation the new equation (TCRS) is also Of all the thermodynamic consistency tests the integral three parameter models. Their expression for lni’s are [12] test proposed by Redlich - Kister given below is employed. 2 ln    ln( x  x L exp( x  ))  x [A  A ]  x x  (A  A )1 (ln L  ln L   (x  x )) 1 1 2 12 1 12 2 ij ji 1 2 12 ij ji γ1 12 21 12 1 2 ln dx1  0 0 γ  1 2  2 (31)    x   x    2x    1 2 2 2 x 2 x 2 1 2 12 If ln γ1/γ2 is plotted against x1, the area above the axis  1 1  (23) should equal to area below it. ln γ  ln(x  x L exp(x δ ))  x [A  A ] x 2x δ (A  A )  (lnL  lnL  δ (x  x )) 2 2 1 21 2 12 1 12 21 1 2 12 12 21 III. RESULTS12 21 AND12 DISCUSSI1 2 ON  1 2  The vapour phase ideality was characterized by fugacity    x   x   x    2x    1 2 1 2 x 1 1 1 1 x 1 1 2 12 coefficient calculation using equations (2-5). From the  1 1  calculations, the fugacity coefficient was found to be closer (24) to unity. Hence it is reasonable to consider that the vapour phase for all the five systems taken in the present study as V j ij  ii  Lij = exp  ideal. The activity coefficient (1) calculated from the Vi  RT  experimental VLE using Equation (1) for the five azeotropic where (25) systems is also incorporated in tables 1-5. Since the 12  21  numerical values of activity coefficient (1) are greater than  12=   unity for all the systems the liquid phase feature strong non  RT    (26) ideality. This is due to the fact that the liquid phase molecules are much closely spaced than in vapor phase due  Lij exp(x112 )    to which attraction / repulsion among the molecules are high. Also all the five azeotropic systems show positive  x1  x2Lij exp(x112 )  Aij= (27) deviation from ideality (minimum boiling azeotropes). This x1 is because the dissimilar molecular structures of five i  azeotropic systems exert repulsive forces other than x  x L exp[x  ] 1 2 ij 1 12 attractive forces. The repulsive forces results in higher (28) x concentration of molecules in vapour phase than in the 2 liquid phase with higher activity coefficient (γ).  j  x2  x1L ji exp[x212 ] (29) Table 1.Estimated NRTL, UNIQUAC, SRC and TCRS parameters of five azeotropic systems NRTL J/mol K UNIQUAC J/mol K SRS J/mol K TCRS J/mol K System 12-11 21-22 u12-u22 u21-u11 12-11 21-22 12-11 21-22 Acetone- - 5326.913 2160.1319 18602.345 1112.3450 3066.913 29.5959 - 2230.4040 water 580.1319 0

Acetone- - - 17460.218 4769.778 19434.015 1646.530 -1633.5299 8046.530 - 8033.5299 methanol 51385.655

Published By: Retrieval Number: L101310812S219/2019©BEIESP Blue Eyes Intelligence Engineering DOI: 10.35940/ijitee.L1013.10812S219 69 & Sciences Publication

PREDICTION OF VAPOUR LIQUID EQUILIBRIA FOR BINARY AZEOTROPIC SYSTEMS USING ACTIVITY COEFFICIENT MODELS

Ethanol- - - - - 1835.131 12920.345 1392.345 3400.00 2780.00 water 860.1319 1232.8499 1852.849

Ethanol- -1920.1319 9922.3450 320.1319 852.3450 167.1500 4800.00 132.8499 4500.00 benzene

Methanol - 12399.86 - 12980.27 water 699.8679 1542.3499 21832.32 - 16828.438 -16430.404 8 11867.654 9

The experimental and correlated x-y diagrams of five azeotropic systems using the five models are given in Figures 1-5.

Figure 3. Experimental and Correlated xy Diagram of Ethanol-water System at 101.325 kPa.

Figure 1. Experimental and Correlated xy Diagram of Acetone-water System at 101.325 kPa.

Figure 4. Experimental and Correlated xy Diagram of Ethanol-benzene System at 101.325 kPa.

Figure 2. Experimental and Correlated xy Diagram of Acetone-methanol System at 101.325 kPa.

Published By: Retrieval Number: L101310812S219/2019©BEIESP Blue Eyes Intelligence Engineering DOI: 10.35940/ijitee.L1013.10812S219 70 & Sciences Publication International Journal of Innovative Technology and Exploring Engineering (IJITEE) ISSN: 2278-3075, Volume-8 Issue-12S2, October 2019

The overall error percentages of the VLE for acetone- water system using five activity coefficient models NRTL, UNIQUAC, UNIFAC, SRS and TCRS are 7.9438, 8.4590, 6.0952, 8.9785, and 4.0380 respectively. It is observed that TCRS model have lesser error percentages than the other four models. Acetone-methanol system shows significant validity for the UNIFAC and UNIQUAC models with the least error percentage of 3.3167 and 4.1357 whereas the other models have more than 5 %. Error occurred in UNIFAC model (5.6071 %) provide good representation of VLE for ethanol-water system when compared to other models. The SRS and NRTL model gave better results for the ethanol-benzene system yielding an error percentage of 3.5758 and 5.6974. Of all the five models chosen, the UNIFAC and UNIQUAC models gives better result for methanol-water system with least error percentage of 2.3301 and 4.5305. Related outcome were observed with the Redlich-Kister method of thermodynamics consistency test (Eq. 31) and reported in Table 2. Figure 5. Experimental and Correlated xy Diagram of Methanol-water System at 101.325 kPa.

Table 2 Thermodynamic Consistency test of five azeotropes system using Redlich - Kister method System Area Under the Curve NRTL UNIQUAC UNIFAC SRS TCRS Acetone-water 0.0791 0.09075 0.01625 0.4445 0.00375 Acetone- 0.1789 0.08512 0.03621 0.2172 0.2005 methanol Ethanol-water 0.0158 0.0221 0.0201 0.1173 0.1067 Ethanol- 0.0165 0.4714 0.4041 0.0054 0.3823 benzene Methanol-water 0.0409 0.0052 0.0041 0.0157 0.0560

It can be seen that value of TCRS model close to zero for acetone-water system. In a similar approach the acetone- IV. CONCLUSION methanol system shows good thermodynamic consistency In case of VLE prediction of azeotropes, NRTL, for UNIFAC and UNIQUAC activity coefficient models UNIQUAC UNIFAC, SRS and TCRS models were tested whereas the ethanol-water own good concurrence with for the systems namely Acetone-water, Acetone-methanol, UNIFAC model. For ethanol-water system SRS and NRTL Ethanol-water, Ethanol-benzene, and Methanol-water. The model gives better result of VLE consistency. experimental VLE findings show that all the five systems Correspondingly UNIFAC and UNIQUAC models show show minimum boiling azeotropes (positive deviation from appreciable thermodynamic consistency for methanol-water ideality). Major finding of the present work is the estimation system. The order of fitness for each system is furnished in of NRTL, UNIQUAC, SRS and TCRS parameters for the Table 3. five systems. These parameters can be utilized for VLE Table 3 Order of fitness for the azeotropes calculation at any temperature and pressure conditions. S. Azeotropic Order of fit No. System REFERENCES 1 Acetone - Water TCRS > UNIFAC > NRTL > UNIQUAC > SRS 1. Seader, J. D., J. Henley, 2006. Separation process Principles, John Wiley and Sons Publication, New 2 Acetone - UNIFAC > UNIQUAC > Jersey. Methanol NTRL > TCRS > SRS 2. Geankoplis, C.J., 2003. Transport Process and Separation 3 Ethanol - Water UNIFAC > UNIQUAC Process, Prentice Hall Publication, New Jersey. >TCRS > NRTL > SRS 3. Vivekjulka, MadhuraChiplunkar, L. O. Young, 2009. 4 Ethanol - SRS > NRTL > TCRS > Selection Entariner for Azeotropic Distillation, Chemical Benzene UNIFAC > UNIQUAC Engineering Progress, 47-53. 5 Methanol - UNIFAC > UNIQUAC > Water SRS > NRTL > TCRS

Published By: Retrieval Number: L101310812S219/2019©BEIESP Blue Eyes Intelligence Engineering DOI: 10.35940/ijitee.L1013.10812S219 71 & Sciences Publication

PREDICTION OF VAPOUR LIQUID EQUILIBRIA FOR BINARY AZEOTROPIC SYSTEMS USING ACTIVITY COEFFICIENT MODELS 4. MohamadAzamudin, I., 2010. Effects of Temperature On Dr. M. S. Manojkumar is Working as an Vapor Liquid Equilibrium OfMtbe-Methanol Mixtures, Assistant professor in Department of Bachelor thesis, University Malaysia Pahang. Petrochemical Engineering, MIET Namakkal. 5. Laszlo, H., 2013. Improvement of Batch Distillation He has teaching experience of five years and Separation of Azeotropic Mixtures, Phd thesis, Budapest six years of research experience. His fields of University of Technology and Economics. interest are Chemical engineering 6. Gadekar, S. V., R. V. Naik, J. D. Bapat, 2004. Acetic Thermodynamics and Distillation .He has published six Acid-Water-Toluene System Batch Distillation research journals and he has attended seven national and Parametersfor Heterogeneous Azeotropic systems, international conferences. Chemical Engineering World, 44. 7. Managobinda, B., 2010. VLE modeling Using Unifac Group Contribution Method and its application in Distillation Column Design and Steady State Simulation, Dissertation for Bachelor thesis, National Institute of Technology, Rourkela. 8. Negema, P. T., 2010. Separation process for high purity ethanol production, Dissertation for the M.S. Degree, Durban University of Technology. 9. Renon, H., J.M. Prausnitz, 1968. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures, Journal of American Institute of Chemical Engineers, 14: 135-144. 10. Anderson, T.F., J.M Prausnitz, 1978. Application of the UNIQUAC equation to calculation of multicomponent phase equilibria, Industrial and Engineering Process Design and Development, 17 (4): 561-567. 11. Fredenslund, A. , J. Gmehling, M.L. Michelson, P. Rasmussen, 1977. Computerized Design of Multicomponent Distillation Columns using the UNIFAC Group Contribution Method, Industrial and Engineering Chemistry Process Design and Development 16 (4): 450-462. 12. Sabarathinam, P.L., B. Sivaprakash, 2002. Theoretically consistent modified Local composition and Flory- huggins equations in VLE data prediction, M. E.Thesis, Annamalai University.

AUTHOR PROFILE

Dr. B. Sivaprakashis working as an Associate Professor in the Department of Chemical Engineering, Annamalai University. He has a teaching experience of 17 years and research experience of 18 years. His fields of interest are Solution Thermodynamics and Bioprocess Modeling. He has guided one doctoral student and 15 post graduate students and has published 23 research papers in journals. He has attended 25 National and International conferences and visited Thailand, Singapore and Malaysia on academic background. He served as the Coordinator of the Students' Chapter of the Indian Institute of Chemical Engineers - Annamalai Regional Centre (July 2006 to June 2017) and received the Pidelite Best Student Chapter award in 2010. Presently he is the Faculty Advisor of the Chemical Engineering Students' Chapter of The Institute of Engineers (India) - Annamalai University Centre. In 2019 he bagged two Tamilnadu State awards Viz. Best Faculty Advisor award and the Best Division award. He is also serving as the NSS and RRC Programme officer in the Department of Chemical Engineering. He has organized one ISTE STTP sponsored by the CSIR, Hyderabad, two National Conferences funded by the UGC, DST - SERB, New Delhi and TNSCST, Tamilnadu, two seminars and one industrial workshop funded by UGC. He is a placement trainer and serving as placement coordinator in the Department of Chemical Engineering for 13 years.

Published By: Retrieval Number: L101310812S219/2019©BEIESP Blue Eyes Intelligence Engineering DOI: 10.35940/ijitee.L1013.10812S219 72 & Sciences Publication