Iraqi Journal of Chemical and Petroleum Engineering Vol.12 No.4 (December 2011) 37-51 ISSN: 1997-4884 Improved Method to Correlate and Predict Isothermal VLE Data of Binary Mixtures Venus Majeed Bakall Bashy Al-Temimi Abstract Accurate predictive tools for VLE calculation are always needed. A new method is introduced for VLE calculation which is very simple to apply with very good results compared with previously used methods. It does not need any physical property except each binary system need tow constants only. Also, this method can be applied to calculate VLE data for any binary system at any polarity or from any group family. But the system binary should not confirm an azeotrope. This new method is expanding in application to cover a range of temperature. This expansion does not need anything except the application of the new proposed form with the system of two constants. This method with its development is applied to 56 binary mixtures with 1120 equilibrium data point with very good accuracy. The developments of this method are applied on 13 binary systems at different temperatures which gives very good accuracy. Keywords: VLE, vapor liquid equilibrium, isothermal data prediction, new thermodynamic relation, VLE of binary mixtures. 1. Introduction: There are so many applications of VLE; therefore, techniques for calculation and experimental determination of this particular type of phase equilibrium are more highly developed than any other thermodynamic types. Therefore, this subject should be the first of the application to be mastered. Besides the complexity of running VLE experiment at constant temperature it is expensive. Hence it would be of great advantage to be able to predict the shape of the VLE curve without the need to run an experiment. [1] Many methods are suggested to predict VLE data which are summarized here. 2. Methods for VLE Calculation: The methods usually used to calculate VLE data can be summarized as follows: a. VLE Data from EOS: EOS and CEOS have a theoretical aspect through the derivation. Many forms are introduced to calculate VLE data based on the required conditions, and the type of systems like RK EOS [2], SRK EOS [3], PR EOS [4], PRSV EOS [5], etc. Besides it is capable to represent vapor and liquid phases, it has many short comes. So, efforts are directed to improve it. VLE calculation by an EOS is difficult to treat unsymmetrical mixtures. Therefore, adjustable parameters are University of Baghdad College of Engineering Iraqi Journal of Chemical and Petroleum Engineering Improved Method to Correlate and Predict Isothermal VLE Data of Binary Mixtures 38 IJCPE Vol.12 No.4 (December 2011) Available online at: www.iasj.net introduced in order to fit the experimental data. [6] All the introduced adjustable parameter or parameters need an experimental data points in order to be evaluated at certain temperature and pressure. Another out-come appears through the calculation of VLE by EOS where for various systems there is a number of equations of states; each is specified to certain temperature and pressure ranges, polarity, or hydrocarbon cut. This is a reason why there are a very large number of equations of state instead of one EOS representing all systems in all conditions. b. Models to Predict VLE Data: These models are much more empirical in nature when compared to the property predicted from EOS which is typically used in the hydrocarbon mixtures. The tuning parameters of any activity models should be fitted against a representative sample of experimental data and their application which should be limited to moderate pressure and usually these constants are subjects to single temperature. Consequently, more caution should be exercised when selecting these models for particular simulation. The individual activity coefficient for any system can be obtained from derived expression for excess Gibbs Duhem equation. [7] The early models (Margules [8], Van Laar [8]) provide an empirical representation of VLE and that limits their application. The newer models such as Wilson [9], NRTL [8], UNIQUAC [8], and UNIFAC [10] utilize the local composition concept and improvement in their general application and reliability. All these models involve the concept of binary interaction parameters and require that they be fitted to experimental data. [7] The activity coefficient models are used as a tool for phase equilibrium calculations. All such models are empirical in nature and represent the activity coefficient of a component in a mixture (and hence its fugacity) in terms of an equation that contains a set of parameters. Two general approaches are employed: i. The parameters of activity coefficient model are determined in a fit to experimental VLE data in a binary mixture; in this sense, these models are only a correlation for the binary systems. Although they may allow extrapolation with respect to temperature or pressure but it is truly predictive for multicomponent systems. Examples of these models are Wilson, TK-Wilson [8], NRTL, and UNIQUAC activity coefficient models. ii. An alternative approach, which requires no experimental data, is one in which the parameters of the activity coefficient model are estimated by group contribution method. Several such schemes have been developed with functional group parameters determined by regression against a very large data base of experimental VLE results. Examples of these approaches are ASOG [11] and UNIFAC [10] models. [12] 3. New Method to Predict isothermal VLE Data: Prediction of VLE data is one of the most important objects of researchers for centuries. Because of the difficulties associated with the experiments and the error might happen during the experiment. So, a predictive tool is needed. This correlation is based on a statistical hypothesis and the flexibility of the proposed function to represent VLE Venus Majeed Bakall Bashy Al-Temimi Available online at: www.iasj.net IJCPE Vol.12 No.4 (December 2011) 39 data for a binary mixture at certain temperature. Since all the previous method and approaches used to calculate or predict VLE data with numerical or physical base need constants in order to eliminate the deviation or error which appears in comprised with the experimental data. This method benefits from the mathematical behavior of exponential function when representing the VLE data of isothermal binary mixtures. This method can calculate VLE data at any vapor composition at certain temperature with the need of two constants values for the binary at that temperature. The proposed function has the following form: P = A exp( B y ) …………………..(1) Where: P= saturation pressure for the selected binary mixture and is taken in mmHg for these constants. A, and B= equation constants for specified mixture at certain temperature y= vapor phase mole fraction For any binary mixture, there are binary constant which are (A and B). These constants remain unchanged for the same binary mixture at certain temperature over the whole system composition; i.e, this simple relation can give P, x, y diagram representation for the binary mixture where x (liquid phase mole fraction) can be calculated by flash calculation. This method is very simple in application with reasonable accuracy if it is compared to previously used methods for VLE calculation. All of the used constants are specified for each system in order to match the experimental data in spite that some of them have a theoretical base. Besides the simplicity of the proposed equation, it can be applied to polar and non polar systems at any conditions and from any group except the mixtures which confirm azeotropes. Because of this limitation the proposed equation behaves as an exponential function. Also, the new form can be applied for all systems temperatures and compositions ranges. The proposed equation is applied on 56 different mixtures at different temperatures that range from different groups or families with 20 data points for each binary mixture at certain temperature; i.e, 1120 data points for all binary mixtures with very reasonable accuracy as shown in Table (1), where R 2 is called a recursion formula. It represents a statistical measure that represents the deviation from the proposed method. When R 2 approaches one, very good representation of equation is obtained. While, if recursion formula approaches zero, a very poor representation is obtained. To see the graphical behavior of the proposed function which has a solid line representation with the experimental data representing figures by shapes for the whole system composition range at different temperatures. The figures are: Fig. 1, n-Heptane + Benzene system 0 2000 4000 6000 8000 10000 0 0.2 0.4 0.6 0.8 1 P re ss u re (m m H g ) Benzene vapor mole fraction T=45 T=60 T=75 T=80 T=110 T=125 T=140 Improved Method to Correlate and Predict Isothermal VLE Data of Binary Mixtures 40 IJCPE Vol.12 No.4 (December 2011) Available online at: www.iasj.net Table 1, new proposed equation constants and its accuracy No. System [13] Temp. o C Equation 1 constants R 2 A B 1 n-heptane + benzene 45 115.7529 0.7278 0.9880 60 213.6991 0.6677 0.9872 75 363.5689 0.6311 0.9891 80 436.0013 0.6071 0.9879 110 1072.1799 0.5597 0.9893 125 1609.5652 0.5102 0.9664 140 2272.9713 0.4920 0.9848 155 3123.5234 0.4659 0.9924 170 4248.2850 0.4402 0.9947 185 5607.0912 0.4258 0.9973 2 n-heptane + Toluene 25 30.3824 0.4636 0.9574 30 38.9761 0.4530 0.9581 40 62.1667 0.4434 0.9547 3 n-heptane + 1-chlorobutane 30 58.45 0.812 0.9970 50 142.3911 0.7317 0.9965 80 431.4 0.6419 0.9966 4 n-butane + 1-butene 37.8 2727.3818 0.1596 0.9179 51.7 3860.5502 0.1777 0.9205 65.6 5512.6930 0.1703 0.9344 5 n-butane + 1,3-butadiene 37.8 2727.3818 0.1596 0.9179 51.7 3926.7768 0.1397 0.9205 65.6 5600.6035 0.1341 0.9344 6 n-octane + benzene 55 42.0097 1.9801 0.9652 65 83.3906 1.626 0.9669 75 120.2414 1.6121 0.9715 7 n-decane + toluene 100.4 48.81 2.2036 0.9177 110.5 75.7478 2.1146 0.9337 120.6 127.9465 1.9380 0.9836 8 carbon tetrachloride + toluene 35 39.9962 1.3598 0.9671 40 51.0098 1.3297 0.9691 45 64.3979 1.2869 0.9707 55 99.8127 1.2233 0.9730 65 149.8724 1.1633 0.9756 9 carbon tetrachloride + 2,4,4 trimethylpentane 35 77.6443 0.8085 0.9964 45 117.4508 0.7869 0.9937 55 175.1214 0.7483 0.9914 65 254.1325 0.7184 0.9905 10 methanol + water 35 35.7739 1.6956 0.9804 39.8 45.0487 1.7007 0.9721 50 78.8519 1.6149 0.9810 60 131.2698 1.5336 0.9856 65 173.1995 1.4649 0.9873 100 728.2713 1.2615 0.9935 140 2651.8723 1.1504 0.9974 11 ethane + propane -145.5 0.0624 4.1169 0.7159 -128.9 0.7112 3.5759 0.7752 -101.1 11.836 2.9892 0.8839 -73.3 96.7761 2.4878 0.8895 -70 191.4197 2.0470 0.9678 12 1,2dichloroethane + isoamylalcohol 50 12.5169 2.7301 0.8899 60 25.0624 2.4697 0.9134 70 45.2774 2.2645 0.9288 80 77.5508 2.0834 0.9422 13 n-heptane + Ethylbenzene 25 7.8495 1.6876 0.9759 40 18.2654 1.5563 0.9796 54.6 38.0839 1.445 0.9759 Venus Majeed Bakall Bashy Al-Temimi Available online at: www.iasj.net IJCPE Vol.12 No.4 (December 2011) 41 Fig. 2, n-Heptane + Toluene system Fig. 3, n-Heptane + 1-chlorobutane system Fig. 4, n-Heptane + Ethylbenzene system Fig. 5, n-Butane + 1-Butene system Fig. 6, n-Butane + 1,3-Butadiene system Fig. 7, n-Octane + Benzene system 0 20 40 60 80 100 120 0 0.2 0.4 0.6 0.8 1 P re ss u re (m m H g ) Toluene vapor mole fraction T=25 T=30 T=40 0 200 400 600 800 1000 0 0.2 0.4 0.6 0.8 1 P re ss u re (m m H g ) 1-Chlorobutane vapor mole fraction T=30 T=50 T=80 0 40 80 120 160 200 0 0.2 0.4 0.6 0.8 1 P re ss u re ( m m H g ) n- Heptane vapor mole fraction T=40 T=54.6 T=25 0 1000 2000 3000 4000 5000 6000 7000 0 0.2 0.4 0.6 0.8 1 P re ss u re (m m H g ) 1-Butene vapor mole fraction T=37.8 T=51.7 T=65.6 0 1000 2000 3000 4000 5000 6000 7000 0 0.2 0.4 0.6 0.8 1 P re ss u re (m m H g ) 1,3-Butadiene vapor mole fraction T=37.8 T=51.7 T=65.6 0 100 200 300 400 500 600 700 0 0.2 0.4 0.6 0.8 1 P re ss u re (m m H g ) Benzene vapor mole fraction T=55 T=65 T=75 Improved Method to Correlate and Predict Isothermal VLE Data of Binary Mixtures 42 IJCPE Vol.12 No.4 (December 2011) Available online at: www.iasj.net Fig. 8, n-Decane + Toluene system Fig. 9, Carbon tetrachloride + Toluene system Fig. 10, Carbon tetrachloride +Trimethylpentane system Fig.11, Methanol + Water system Fig. 12, 1,2 Dichloroethane + isoamylalcohole system Fig.13, ethane + Propane system 0 200 400 600 800 1000 1200 0 0.2 0.4 0.6 0.8 1 P re ss u re (m m H g ) Toluene vapor mole fraction T=100.4 T=110.5 T=120.6 0 100 200 300 400 500 600 0 0.2 0.4 0.6 0.8 1 P re ss u re ( m m H g ) Carbon tetrachloride vapor fraction T=35 T=40 T=45 T=55 T=65 0 100 200 300 400 500 600 0 0.2 0.4 0.6 0.8 1 p re ss u re ( m m H g ) Carbon tetrachloride vapor fraction T=35 T=45 T=55 T=65 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0 0.2 0.4 0.6 0.8 1 P re ss u re ( m m H g ) Water vapor mole fraction T=35 T=39.8 T=50 T=60 T=65 T=100 T=140 0 100 200 300 400 500 600 700 800 0 0.2 0.4 0.6 0.8 1 p re ss u re ( m m H g ) 1,2 dichloroethane vapor fraction T=50 T=60 T=70 T=80 0 300 600 900 1200 1500 1800 2100 0 0.2 0.4 0.6 0.8 1 P re ss u re ( m m H g ) Ethane vapor mole fraction T= (-145.5) T= (-128.9) T= (-101.1) T= (-73.3) T= (-70) Venus Majeed Bakall Bashy Al-Temimi Available online at: www.iasj.net IJCPE Vol.12 No.4 (December 2011) 43 4. Improving the New Proposed Function In order to expand the applicability of the proposed equation, a new method is introduced. The improved method tries to calculate the equation constants at any temperature within a certain temperature range. It is noticed that (A and B) constants are functions of experiment temperature. The A and B proposed function or formulas have the following forms: A = a e bT ….…….…(2) …..………(3) Where: A, B : equation (1) constants values specified for each binary mixture a, b, a * , b * : are new constants for each binary system at certain temperature range. T : the required temperature measured in ( o C) needed to calculate the constants. The shape of the proposed relations and its fitting to the experimental data are given in the following figures: Temperature – A constant relationship Temperature – B constant relationship Fig. 14, n-Heptane + Benzene system for A, and B constants relations Fig. 15, n-Heptane + Toluene for A and B constants relations Fig. 16, n-Heptane + 1,Chlorobutane for A and B constants relations y = 43.958e0.0274x R² = 0.9863 0 2000 4000 6000 8000 0 50 100 150 200 A c o n st a n t va lu e s temperature( OC) y = 0.8403e-0.0038x R² = 0.9920 0.4 0.5 0.6 0.7 0.8 0 50 100 150 200 B c o n st a n t va lu e s temperature( OC) y = 9.2887e0.0476x R² = 0.9997 20 30 40 50 60 70 10 20 30 40 50 A c o n st a n t va lu e s Temperature ( OC) y = 0.4961e-0.0029x R² = 0.9556 0.44 0.445 0.45 0.455 0.46 0.465 20 25 30 35 40 45 B -c o n st a n t va lu e s temperature ( OC) y = 18.3916e0.0397x R² = 0.9973 0 100 200 300 400 500 0 20 40 60 80 100 A c o n st a n t va lu e s Temperature (OC) y = 0.9305e-0.0047x R² = 0.9976 0.4 0.5 0.6 0.7 0.8 0.9 0 20 40 60 80 100 B co n st a n t va lu e s temperature (OC) Improved Method to Correlate and Predict Isothermal VLE Data of Binary Mixtures 44 IJCPE Vol.12 No.4 (December 2011) Available online at: www.iasj.net Fig. 17, n-Heptane + Ethylbenzene for A and B constants relations Fig. 18, n-Butane + 1-Butene for A and B constants relations Fig. 19, n-Butane + 1,3-Butadiene for A and B constants relations Fig. 20, n-Octane + Benzene for A and B constants relations y = 2.0975e0.0534x R² = 1.0000 0 10 20 30 40 50 20 30 40 50 60 A c o n st a n t va lu e s temperature ( OC) y = 1.9178e-0.0052x R² = 1.0000 1.4 1.5 1.6 1.7 0 20 40 60 B c o n st a n t va lu e s temperature ( OC) y = 1,046.0643e0.0253x R² = 0.9999 0 1000 2000 3000 4000 5000 6000 20 40 60 80 A c o n st a n t va lu e s temperature ( OC ) y = 0.1498e0.0023x R² = 0.3597 0.155 0.16 0.165 0.17 0.175 0.18 20 40 60 80 B c o n st a n t va lu e s temperature ( OC ) y = 1,026.9113e0.0259x R² = 0.9999 2000 3000 4000 5000 6000 0 20 40 60 80 A c o n st a n t va lu e s temperature ( OC ) y = 0.1991e-0.0063x R² = 0.9144 0.08 0.12 0.16 0.2 20 40 60 80 B c o n st a n t va lu e s temperature ( OC ) y = 2.4578e0.0526x R² = 0.9701 30 50 70 90 110 130 150 40 50 60 70 80 A c o n st a ts v a lu e s temperature ( OC ) y = 3.3776e-0.0103x R² = 0.7813 1 1.5 2 2.5 50 60 70 80 B c o n st a n t va lu e s temperature ( OC ) Venus Majeed Bakall Bashy Al-Temimi Available online at: www.iasj.net IJCPE Vol.12 No.4 (December 2011) 45 Fig. 21, n-Decane + Toluene for A and B constants relations Fig. 22, Carbon tetrachloride + Toluene for A and B constants relations Fig. 23, Carbon tetrachloride + Trimethyl pentane for A and B constants relations Fig. 24, Methanol + Water for A and B constants relations y = 0.4001e0.0477x R² = 0.9974 0 20 40 60 80 100 120 140 90 100 110 120 130 A c o n st a n t va lu e s temperature ( OC ) y = 4.2044e-0.0064x R² = 0.9590 1.9 2 2.1 2.2 2.3 80 100 120 140 B c o n st a n t va lu e s temperature ( OC ) y = 8.7652e0.0439x R² = 0.9989 0 40 80 120 160 200 0 25 50 75 A -c o n st a n t va lu e s temperature ( OC ) y = 1.6353e-0.0053x R² = 0.9985 1.15 1.2 1.25 1.3 1.35 1.4 20 35 50 65 80 B - co n st a n t va lu e s temperature ( OC ) y = 19.6302e0.0396x R² = 0.9994 0 100 200 300 20 40 60 80 A c o n st a n t va lu e s temperature ( OC ) y = 0.9363e-0.0040x R² = 0.9879 0.68 0.72 0.76 0.8 0.84 20 40 60 80 B c o n st a n t va lu e s temperature ( OC ) y = 9.9564e0.0412x R² = 0.9896 0 1000 2000 3000 4000 0 50 100 150 A c o n st a n t va lu e s temperature ( OC ) y = 1.9446e-0.0040x R² = 0.9735 1 1.2 1.4 1.6 1.8 0 50 100 150 B c o n st a n t va lu e s temperature ( OC ) Improved Method to Correlate and Predict Isothermal VLE Data of Binary Mixtures 46 IJCPE Vol.12 No.4 (December 2011) Available online at: www.iasj.net Fig. 25, Ethane + Propane for A and B constants relations Fig. 26, 1,2-dichloro ethane + isomamyl alcohole for A and B constants relations The improvement of the new method constants extend the application of system constant to a range of temperature depending on a, b, a * , and b * as the calculated range for the heat capacity constants calculation. The new constants calculation method is applied on 13 systems with different temperatures range and from different groups or families as shown in Table (2). Table (2) shows very good applicability for the extend temperature range. Now, if any researchers needs VLE data for a selected system at a selected temperature within the constant temperature range the following steps should be followed: 1. Find constant a, b, a * , and b * from a table for a certain binary mixture. 2. Select the required temperature which should be within the constant range. 3. Substitute the constants a, b and the temperature in eq 2 to calculate A constant. 4. Substitute the constants a * , b * and the temperature in eq 3 to calculate B constant. 5. Substitute the obtained constants A and B in eq. 1 to calculate saturation pressure at any vapor mole fraction. 6. Make flash calculation at this temperature, pressure, and vapor mole fraction to calculate liquid mole fraction. 7. Draw P, x, and y figure and also, x, y figure. This method really lowers the experimental cost and the difficulty associated with the experiment where at high pressure the VLE experiment is very difficult to manage and expensive. y = 214,468.3934e0.1006x R² = 0.9882 0 50 100 150 200 -200 -150 -100 -50 A co n sta n t va lu e s temperature ( OC) y = 1.2677e-0.0081x R² = 0.9497 1 2 3 4 5 -150 -100 -50 0 B co n sta n t va lu e s temperature ( OC) y = 0.6295e0.0606x R² = 0.9966 0 20 40 60 80 100 40 50 60 70 80 90 A c o n st a n t va lu e s temperature ( OC) y = 4.2567e-0.0090x R² = 0.9981 1.8 2 2.2 2.4 2.6 2.8 40 55 70 85 B c o n st a n t va lu e s temperature ( OC) Venus Majeed Bakall Bashy Al-Temimi Available online at: www.iasj.net IJCPE Vol.12 No.4 (December 2011) 47 Table 2, The new improved relation constants 5. Discussion Prediction of VLE data is one of the most important objectives of the researchers for centuries. Because of the difficulties associated with the experiments and because error might happen through the experiment, a predictive tool is needed. Historically EOS is used to predict VLE data and the researchers tried to improve EOS in order to be capable of representing VLE data. Besides the capability of EOS to predict VLE data, it has many short comes. The most important of them is the incapability of EOS to represent all components and component mixtures; in other word the equations of state are classified according to component families or groups (polar, non-polar, ketones, hydrocarbons, heavy hydrocarbons, light hydrocarbons, alcohols …etc.) and also, according to the operation condition; i.e (system temperature and pressure). Till the eighties of the past century, researchers turn to improve EOS approximately stopped and the improvement of EOS mixing rules was adopted. EOS mixing rules has also a short out-comes. Its short comes is that different forms depend on mixing rules. One of the most important short comes is that mixing rules share with it the adjustable parameter introduced in order to eliminate the deviation of each mixture from the ideal mixture which EOS hypothesis based on through its derivation. While, the other methods adopted to calculate VLE data have a number of constants specified for each system; this makes these methods also difficult to work with. This work over comes all the short comings of EOS without any No. system No. of points Temp. range o C Eq. 2 constants R 2 Eq. 3 constants R 2 A B a * b * 1 n-heptane + benzene 100 45_185 43.958 0.0274 0.9863 0.8403 -0.0038 0.992 2 n-heptane + Toluene 30 25_40 9.2887 0.0476 0.9997 0.4961 -0.0029 0.9556 3 n-heptane + 1-chlorobutane 30 30_80 18.3916 0.0397 0.9973 0.9305 -0.0047 0.9976 4 n-butane + 1-butene 30 37.8_65.6 1046.0643 0.0253 0.9999 0.1498 0.0023 0.3597 5 n-butane + 1,3-butadiene 30 37.8_65.6 1026.9113 0.0259 0.9999 0.1991 -0.0063 0.9144 6 n-octane + benzene 30 55_75 2.4578 0.0526 0.9701 3.3776 -0.013 0.7813 7 n-decane + toluene 30 100.4_120.6 0.4001 0.0477 0.9974 4.2044 -0.0064 0.959 8 carbon tetrachloride + toluene 50 35_65 8.7652 0.0439 0.9989 1.6353 -0.0053 0.9985 9 carbon tetrachloride + 2,4,4 trimethylpentane 40 35_65 19.6302 0.0395 0.9994 0.9363 -0.0040 0.9735 10 methanol + water 70 35_140 9.9564 0.0412 0.9896 1.9446 -0.0040 0.9735 11 ethane + propane 50 -145.5_-70 214468.3934 0.1006 0.9882 1.2677 -0.0081 0.9497 12 1,2dichloro ethane + isoamylalcohol. 40 50_80 0.6295 0.0606 0.9966 4.2567 -0.0090 0.9981 13 n-heptane + Ethylbenzene 30 25_54.6 2.0975 0.0534 0.9990 1.9178 -0.0052 0.9993 Improved Method to Correlate and Predict Isothermal VLE Data of Binary Mixtures 48 IJCPE Vol.12 No.4 (December 2011) Available online at: www.iasj.net theoretical base but the need of two constants which represent the binary system mixture under the temperature range which the temperature constants accept it. So, the researchers can obtain very accurate experimental data points for any required temperature within the temperature range of the constants which represent that binary mixture. Besides its capability to represent VLE data with the system vapor pressure at any needed temperature this method is very simple to apply with very good accuracy compared with other used methods as will be seen in Table (3). The improved relation is derived from the observation of the regular transmission behavior of the same mixture from temperature to another at constant pressure. This relation can be applied to all types of binary mixtures at any conditions except the mixtures which confirm azeotropes because the inabilities of the exponantional function to represent the VLE data of azeotropes. Also, from the table results one can observe that systems under very low temperatures or in other word negative experiment condition will give less accurate results compared with positive temperature of the experimental conditions results. Noting that these proposed relations is function to component with higher vapor pressure. The error associated with the experimental data also affected the accuracy of the derived relation and this can be shown clearly when representing the data with poor R 2 factor for different binary mixtures. This method compared with Antoine equation to calculate vapor pressure with the need to three constants. This method needs only these constants at certain temperature. Besides that, this method can be modified to calculate the vapor pressure of any binary mixture at any temperature with the need of four constants at acceptable range temperature. This improvement cannot be achieved by Antoine or any other equation with very good accuracy. Venus Majeed Bakall Bashy Al-Temimi Available online at: www.iasj.net IJCPE Vol.12 No.4 (December 2011) 49 Table 3, Comparison between the accuracy of the systems after and before applying the improving of the proposed correlation system Temp. ( O C) A constant from eq. 2 B constant from eq. 3 ABE% at exact A, and B values eq.1 ABE% at general A, and B values eq. 2&3 n-heptane + benzene 45 150.8426 0.7082 1.7707 2.8782 60 227.5197 0.6690 1.6750 6.5731 75 343.1736 0.6319 1.5005 5.5489 80 393.5613 0.6200 1.5187 9.0305 110 859.3699 0.5532 1.4256 1.6787 125 1350.5091 0.5226 2.2304 1.5458 140 2037.0071 0.4936 1.4271 1.0283 155 3072.4695 0.4663 0.9856 1.7633 170 4634.2836 0.4404 0.8001 9.1080 185 699.0075 0.4160 0.5687 2.3999 Over all ABE% 1.39024 4.15547 n-heptane + Toluene 25 30.53271 0.4614 2.2558 2.2695 30 38.73713 0.4548 2.1803 2.2935 40 62.35218 0.4418 2.2927 2.2831 Over all ABE% 2.2429 2.2820 n-heptane + 1-chlorobutane 30 60.5152 0.8081 0.8944 3.1636 50 133.8733 0.7356 1.0102 6.1097 80 440.4928 0.6389 0.8709 1.8830 Over all ABE% 0.92517 3.7188 n-butane + 1-butene 37.8 2721.854 0.1634 1.1944 1.1945 51.7 3868.951 0.1687 0.2633 0.4284 65.6 5499.479 0.1742 0.0779 0.0977 Over all ABE% 0.51187 0.57353 n-butane + 1,3-butadiene 37.8 2733.48 0.1569 1.1944 1.2178 51.7 3918.017 0.1437 1.0293 1.0251 65.6 5615.865 0.1317 0.8956 0.8785 Over all ABE% 0.70643 1.04047 n-octane + benzene 55 49.5091 1.6523 6.2710 11.8731 65 78.3477 1.4509 6.9992 6.9904 75 123.9846 1.2740 6.0223 9.0550 Over all ABE% 6.43083 9.30617 n-Decane + toluene 100.4 48.0883 2.2113 14.3077 13.4844 110.5 77.85197 2.0729 11.9136 11.8038 120.6 126.0375 1.9431 4.8759 4.5214 Over all ABE% 10.36573 9.93653 carbon tetrachloride + toluene 35 40.7432 1.3584 5.5607 5.0466 40 50.7438 1.3229 5.6526 5.2520 45 63.1991 1.2883 5.2505 5.1291 55 98.0316 1.2218 4.8305 5.2396 65 152.0622 1.1587 4.4040 6.4604 Over all ABE% 5.13966 5.42554 carbon tetrachloride + 2,4,4 trimethylpentane 35 78.4977 0.8085 1.2127 1.5779 45 116.6373 0.7821 1.3823 1.4740 55 173.3078 0.7514 1.6183 1.7135 65 257.5127 0.7219 1.5679 2.4187 Over all ABE% 1.4453 1.79603 methanol + water 35 42.1071 1.6906 4.6667 6.8630 39.8 51.3146 1.6584 5.7752 4.6207 50 78.8519 1.5921 4.3085 4.7792 60 117.9447 1.5297 3.6429 5.3192 Improved Method to Correlate and Predict Isothermal VLE Data of Binary Mixtures 50 IJCPE Vol.12 No.4 (December 2011) Available online at: www.iasj.net 6. Conclusion  The proposed relation can represent VLE data without a need to any other relation except two constants that represent each binary system at the specified temperature like any other constants introduced through historically used relations.  The improving of this relation made it very elastic in representing a very large rang of VLE data of the binary systems.  The derivation of the constants should cover the required calculated VLE temperature.  When the temperature range increases the error slightly increases.  The results of calculation show that constant A has a more effect than B on the accuracy of calculated VLE data.  The obtained error might be from the experimental error causing an error through VLE calculation.  The calculated constants are functions of the component and experimental temperature.  This equation can calculate the systems with higher vapor pressure without the need to run an experiment.  Experiment run under negative temperature will give less accurate results compared with that at positive experimental temperature. Abbreviations References: 1. Harold A. Beaty, and George Calingaert, (1934), "Vapor Liquid Equilibrium of Hydrocarbon Mixtures", Ind. And Eng. Chem., vol. 26, No. 5, PP. (504) 2. Smith, J. M., Van Ness, H.C., Abbott, M. M., (2004), "Introduction to chemical engineering thermodynamics", McGraw-Hill companies. 3. Soave, G., (1972), "Equilibrium constants from a modified RK EOS", chem. Eng. scie., vol. (27), PP. (1197). 4. Ding-yu Peng, and Donald B. Robinson, (1976), " A New two 65 144.9249 1.4994 3.3458 7.1379 100 612.9084 1.3035 2.2133 6.5336 140 3185.025 1.1108 1.2889 8.9827 Over all ABE% 3.6059 6.3195 ethane + propane -145.5 0.0943 4.1196 23.0094 17.3828 -128.9 0.5009 3.6013 17.4166 31.7519 -101.1 8.20922 2.8752 13.6966 33.4154 -73.3 134.5502 2.2955 9.15259 10.4304 -70 187.526 2.2349 6.4944 6.7880 Over all ABE% 13.9539 19.9537 1,2dichloroethane + isoamylalcohol 50 13.0289 2.7142 6.2004 7.3514 60 23.8831 2.4806 3.4433 4.6633 70 43.7797 2.2671 6.2076 2.1002 80 80.2519 2.0720 5.2163 9.5582 Over all ABE% 5.2669 5.9183 n-Heptane + Ethylbenzene 25 7.9705 1.6840 5.2406 3.9192 40 17.7564 1.5577 4.5968 5.1011 54.6 38.7212 1.4438 3.8001 3.9025 Over all ABE% 4.54583 4.3076 All systems over all ABE% 4.3485 5.7487 ABE Average absolute error CEOS Cubic equation of state EOS Equation of state VLE Vapor liquid equilibrium Venus Majeed Bakall Bashy Al-Temimi Available online at: www.iasj.net IJCPE Vol.12 No.4 (December 2011) 51 constants EOS", Ind. Eng. Fandam., vol. 15, no. 1, PP. (59). 5. Stryjek, R., and Vera, J. H., (1986), "PRSV: An Improved PR EOS of pure components and mixtures", the cand. J. of chem. Eng., vol.64, PP. (323). 6. Soave, G., (1993), "20 years of RK EOS", fluid phase equilibrium, vol. 82, PP. (345). 7. Hysys company, (2001), "property Methods and calculation"), ver. 2 manual 8. Smith, J. M., Van Ness, H.C., Abbott, M. M., (1996), "Introduction to chemical engineering thermodynamics", McGraw-Hill companies. 9. Wilson, G. M., (1964), J. Am. Chem. Soc., vol. 86, PP. (127). 10. Gmehling, J., and Rasmussen, P., and Fredenslund, Aa, (1982), "VLE by UNIFAQ group contribution revision and extension 2", IEC. Process Des. Dev., vol. 21, PP. (118). 11. Soave, G., (1993), "Application of EOS and the theory of group solutions to phase equilibrium prediction", fluid phase equilibrium, vol.47, PP. (189). 12. Marc, J. Assael. Martin Trusler, J. P.: Thomas F. Tsolakis, (1996), "thermophysical properties of fluids", published by ICP, London. 13. Shuzo ohe, (1989), "VLE Data", physical data science 37, published by Elsevier, Tokyo, Japan. تطوير طريقة جديدة لربط و استحصال نقاط توازن البخار مع السائل عند درجة حرارة ثابتة للخالئط الثنائية من قبل د. فينوس مجيد بقال باشى التميمي طريقة جديدة لحساب توازن البخار مع السائل ايجاد طريقة لحساب توازن البخار و السائل دائما تحتاج. قدمت وكانت باسلوب سهل جدا" وأعطت نتائج جيدة جدا" مقارنة مع الطرق التي أستخدمت سابقا" بدون الحاجة الى اي خاصية فيزياوية ألي من المركبات . ما عدا الحاجة الى ثابتان اثنان فقط يمثالن ذلك الخليط. باألضافة الى انه ممكن تطبيقها لحساب توازن البخار مع السائل ألي خليط ثنائي بأي قطبية و من أي مجموعة على هذه الطريقة عكس الطرق السابقة. ما عدا الخالئط التي تكون مركبات ايزوتروبية. هذه الطريقة قد طورت لتشمل شكل جديد ين فقط. وقد تم تطبيق بحيث تغطي مدى من درجات الحرارة. هذا المدى اليحتاج خالل التطبيق سوى ثابت وازن مختبرية وكانت النتائج نقطة ت 2211مركب عند درجات حرارة مختلفة لـ 65المعادلة المقترحة على مزيج ثنائي عند درجات حرارة مختلفة واعطت نتائج جيدة جدا". 21جدا". بينما تطوير الطريقة طبق على جيدة