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For the liq on subcritica SRK is relia gy & Applied Sc Hussain an cal Co Robins carbon Hussain nd Material En Sciences and T d, Pakistan cme.nust.edu. quilibrium a role in industry s an appropri omparison of S R) equations o f a mixture o cal region at mathematical avior of binar analysis o tudy the pres he approach u gence with e Soave Redlich flash calculati NTRODUCTION es play a vit r chemical p n of states (EO robust solutio liquid equilibr ses or heavy l sity more accu ric factor and can be made dependence f n the EOS [7-9 mical industri and thermodyn mpounds conta S prediction ompressibility gen and nitro The equations uid-liquid and quid compoun l and superc able, but wh cience Research d Ahsan: A Nu ompari son Eq ns’ Th ngineering Technology .pk and thermod y. 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The purpos umerical app xperimental d umerical appr ompressibility nput and mole quid and vapo ondition of ra enerate more gorithm. The othermal cond ompared, and 2018, 2422-242 ve Redlich Kwo ve Red State f mic Pr Muhamm f Chemical an University of S Islamabad ahsan@scm n case of pola redictions [17 mpressibility fa nt for all mix is involved in the effective r, the relation ameter and the s [23]. Hydr e/propane and this research nd phase equi containing m sh, the calcu separation of Fig. 1. Isot se of this stu proach used data obtained roach for bot factor, pressu e fraction of e or phases is ob atio between precise K-v e relationship ditions for bo d pressure mo 26 ng and Peng-R dlich K for Pr ropert mad Ahsan nd Material En Sciences and T d, Pakistan me.nust.edu.pk ar and heavy c 7, 18]. In PR actor and the P xture compoun n the estimatio e volume for nship of an ace e effective vo rogen/propane d methane/n-d h. Because in ilibrium of hy mixtures have ulation is do f liquid and va thermal flash pro udy is to com for SRK a d from the th cubic equ ure and tempe every mixture btained as resu liquid and va value than i of pressure oth SRK and ole fraction r 2422 Robinson Equa Kwon edictin ties ngineering Technology compounds, it and SRK calc Pitzer acentric nds [6, 19-22 on of the mea both SRK a entric factor w olume is differ e, methane/n- decane mixtu chemical ind drogen, metha e vital role [2 one at vapo apor phases as ocess mpare the inn and PR EOS literature. I uations of sta erature as algo e component ult under the apor fugacity in the start and volume PR EOSs m relationship o ations … ng ng t cannot culation c factor 2]. This an field and PR with the rent for -butane, ures are dustries, ane and 24]. At r-liquid s shown novative S with In this ates the orithm’s in both applied y which of the e under model is of both Engineering, Technology & Applied Science Research Vol. 8, No. 1, 2018, 2422-2426 2423 www.etasr.com Hussain and Ahsan: A Numerical Comparison of Soave Redlich Kwong and Peng-Robinson Equations … models is compared with experimental data for all given mixtures. The comparison shows that in a mixture containing organic compounds the PR model is more precise in both phases. However, when the mixture contains both organic and inorganic compounds, the SRK model is more precise in the liquid phase compared to PR model. II. MATHEMATICAL MODELING The isothermal flash calculation is carried out for the phase equilibrium by iterating pressure to get the liquid and vapor fraction of the mixture. For satisfying the applied condition, iterating pressure applies the loop whereas the temperature and pressure are independent variables for this system. For K- values, where i i i y k x  (1) In literature, empirical correlations are available for K values. In this case, the empirical correlation used is Wilson equation for K-value which is further used for the calculation of phase fraction. If the K-value approaches equilibrium, the convergence occurs for the solution. 1 exp[5.37(1 )(1 )]i ri i Ri T k p    (2) For the calculation of liquid and vapor mole fraction, the Richford Rice procedure is followed. On (5) for liquid mole fraction, the Newton-Raphson method is used, and the method uses the condition given in (7). (1 ) i i i z x L L k    (3) i i iy k x (4) 0 (1 ) ( ) (1 ) cn i i i i k z F L L L k      (5) ( ) old old new old L F L L L dF dL         (6) 51 10 new old L L       (7) i i i i z y L x y    (8) Equation of state parameters is calculated from given equations: 1 1 ( ) ( )c c n n m i j iji j aa x x aa      (9) ( ) (1 ) ( ) ( )ij ij i jaa k aa aa  (10) 1 cn m i ii b xb    (11) For the suitable VLE behavior of the given mixture, we can solve the SRK and PR EOS to get molar volumes of both phases [25]. Because of the difference in phase’s composition, the two solutions are essential for roots of both cubic EOS. The iterative approach is applied to (12) for cubic roots of SRK EOS and to (13) for cubic roots of PR EOS. ( ) ( ) m m m m m m aaRT p V b V V b     (12) 2 ( ) ( 2 ) m m m m m m m aaRT p V b V V b b      (13) Compressibility factor is calculated by using (14): mL L pV Z RT  (14) The fugacity and pressure relation give a dimensionless number which is the fugacity coefficient. The liquid phase fugacity for all components is calculated from (15) and for vapor phase a change is made in (15) by replacing xi with yi and L subscript with V. = 1 2 exp n 2 ( ) ln ( ) ln ln c mL i mL mL mL mL n j ijj mL mL mL mL i mL mL mL mL mL mL mL mL L i V b p V b V b x aa V RTb V b b aa V b b RTb V V b z x                                        (15) To satisfy the equilibrium, (16) is used to converge the solution at certain liquid and vapor composition [26]. If the equilibrium is not satisfied, (21) is used for new K-value and again iterate the process until the satisfaction of equilibrium. − 1 < 10 (16) ∅ = (17) ∅ = (18) ∅∅ = (19) ∅∅ = (20) k = k (21) The overview of the iterative method is explained in the flow chart shown in Figure 2. The operating parameters for EOS modeling are given in Table I. Engineering, Technology & Applied Science Research Vol. 8, No. 1, 2018, 2422-2426 2424 www.etasr.com Hussain and Ahsan: A Numerical Comparison of Soave Redlich Kwong and Peng-Robinson Equations … TABLE I. OPERATING PARAMETERS Parameters Hydrogen Propane Methane n-butane Hydrogen Propane Methane n-butane Tc (K) 33.2 370 190.82 425.32 Pc (atm) 12.8 41.8 45.8 37.42 ω 0.205 0.153 0.012 0.199 T (K) 310.93 310.93 P (atm) 13 - 433 3.536 - 136 Carbon dioxide propane Methane n-decane Carbon dioxide Propane Methane n-decane Tc (K) 304.2 370 190.82 617.8 Pc (atm) 73 41.8 45.8 21.1 ω 0.268 0.153 0.012 0.49 T (K) 277.56 477.594 P (atm) 5.4 - 37.9 3.536 - 136 Fig. 2. Flow chart of the flash calculation III. RESULTS AND DISCUSSION Numerical analysis approach is applied for both SRK and PR EOS on four sets of binary mixtures: hydrogen/propane, methane/n-butane, carbon dioxide/propane and methane/n- decane with a tolerance level of 10-7. Under isothermal conditions for hydrogen, methane, and carbon dioxide the behavior of pressure with volume is observed. Figures 3-5 show the decrease in pressure by the increasing volume for SRK and PR EOS when the temperature is less than the critical compared to when the temperature is close to critical. After some interval, the point from where there is no remarkable change in pressure is reached. In the case of mixture of hydrogen/propane, wide deviation has been reported. This is caused by the presence of hydrogen in the system. In order to overcome this deviation the binary interaction parameter is used. In vapor phase, the phase behavior shows no difference between SRK and PR EOS model results with experimental data [27] but in the liquid phase, the phase behavior results of SRK model show less deviation compared to the results of PR model. Fig. 3. Isotherms for Hydrogen Fig. 4. Isotherms for Methane Fig. 5. Isotherms of Carbon dioxide Engineering, Technology & Applied Science Research Vol. 8, No. 1, 2018, 2422-2426 2425 www.etasr.com Hussain and Ahsan: A Numerical Comparison of Soave Redlich Kwong and Peng-Robinson Equations … Fig. 6. Mole fraction of hydrogen at various pressures Fig. 7. Mole fraction of methane at various pressures Fig. 8. Mole fraction of carbon dioxide at various pressures Fig. 9. Mole fraction of methane at various pressures However, the graphical trend of SRK and PR model follow the same trend of experimental outcomes as shown in Figure 6. The presence of carbon dioxide in the mixture will generate a deviation in the prediction of phase behavior. Figure 8 shows that in the liquid phase the deviation of PR EOS from experimental results is less than that of SRK model, however in vapor phase the deviation of SRK is less compared to PR model but the trend of phase behavior for both SRK and PR EOS model follows the experimental phase behavior. In a binary mixture of methane/n-butane and methane/n-decane the phase behavior predicated by PR EOS model is more precise with experimental results compared to SRK model in liquid phase but in the vapor phase, both SRK and PR EOS are both accurate as shown in Figures 7, 9. This shows that in critical conditions the prediction of phase behavior can be done in a precise way for hydrocarbon mixtures. However, there is a wide difference in volatilities of methane and n-decane, but the mixing rules of the EOS have applied accurately. IV. CONCLUSIONS In this study, numerical analysis is applied on SRK and PR EOS for pressure relation with mole fraction and volume for binary mixtures of hydrogen/propane, methane/n-butane, carbon dioxide/propane and methane/n-decane. The mole fraction relation with pressure for all binary mixtures is acquired at vapor-liquid equilibrium by making an iteration of pressure in the certain domain under critical conditions. The prediction of phase behavior by SRK and PR EOS models show that both models give an accurate prediction for the system of methane/n-butane and methane/n-decane with experimental results under critical conditions. However, in hydrogen/propane mixture the phase behavior in liquid phase predicted by SRK model show less deviation with experimental data compared to PR model. This is due to the presence of lighter gases such as hydrogen in the mixture and low mixture pressure. VLE is affected by the presence of carbon dioxide in carbon dioxide/propane mixture due to which deviation is reported up to a finite range of pressure. The PR model shows less deviation with experimental data in the liquid phase, but SRK model shows less deviation in the vapor phase. The trend of deviation for both SRK and PR with experimental data decreases with increase in pressure and at high pressures it Engineering, Technology & Applied Science Research Vol. 8, No. 1, 2018, 2422-2426 2426 www.etasr.com Hussain and Ahsan: A Numerical Comparison of Soave Redlich Kwong and Peng-Robinson Equations … become almost insignificant. The isotherm from SRK and PR showed that the pressure initially decreases, after it starts increasing and finally reaches constant behavior. In a mixture containing only organic compounds the approach used for PR EOS is more precise with experimental data of pressure and mole fraction at both phases. However, when the mixture contains inorganic and organic compounds the approach used for SRK EOS results in more precise pressure and mole fraction relationship with experimental data in the liquid phase. 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