Liquid balance-steam for methanol mixing-Benzen using the Peng Robinson and Van- Laar models

Azeotrope Activity coefficient Fugacity coefficient VLE This paper is related to the procedure for calculating curves dew point and bubble point of a binary system, consisting of the methanol and benzene mixture to 45°C, using the Peng-Robinson cubic equation to calculate the fugacity coefficient of gas i in the mixture, and Van Laar model to calculate the activity coefficient of component i in the liquid mixture. Then a comparison between the theoretical data with the experimental data and later with the commercial simulator HysysAspen, which applies the model of Wilson. The simulation was validated with experimental data, in addition to comparing the results with a commercial simulator.


Introduction
Studies on the equilibrium of the mixing phase are of considerable importance for the design of thermal separation processes and theoretical understanding of molecular behavior [1]. Oxygenated compounds such as methyl tert-butyl ether (MTBE), ethyl tertbutyl ether (ETBE) and methyl tert-amyl ether (TAME) can be used as gasoline additives due to their good anti-knocking properties, VLE data of these additives with alcohols and hydrocarbons Liquid balance -steam for methanol mixing -Benzen using the Peng Robinson and Van-Laar models Balance de líquidos -vapor para mezcla de metanol -Benzen usando los modelos Peng Robinson y Van-Laar Miguel Fernando Palencia-Muñoz 1 , Natalia Prieto-Jiménez 2 , Germán González-Silva 3* are used to develop calculation models for the reformulation of gasoline Jong-Hyeok et al [2], [3] determined isothermal experimental results of liquid-vapor equilibrium for five binary substances among them the mixture methanol and benzene. In the last decade there has been a growing demand for the use of oxygenated compounds to produce unleaded gasoline [4] - [7]. Gramajo de Doz et al. [8] analyzed the equilibrium phases of the systems containing hydrocarbons (benzene, isooctane, toluene, or cyclohexane) and oxygenated compounds (methanol, ethanol, or methyl tert-butyl ether), due to the physical and chemical properties of methanol, as a candidate for an oxygenated fuel additive. However, methanol has partial miscibility with aliphatic hydrocarbons, but not with aromatic hydrocarbons. Therefore, it is of great importance to study systems composed of methanol and hydrocarbon components representative of gasoline. In 2013 García et al [9], focused on studying the diagrams of hydrocarbon phases such as gasoline and methanol through tertiary and quaternary systems, (heptane + benzene + methanol), (heptane + ethylbenzene + methanol), (heptane + m-xylene + methanol), (heptane + benzene + ethylbenzene + methanol), and (heptane + Benzene + m-xylene + methanol) at temperature of 293.15K and atmospheric pressure, to define the solubility of methanol in gasoline at low temperatures. The mixture of these components is not only used for fuel alcohol additives, it has also been used as a raw material for the synthesis of other chemicals and polymers; accurate data on the phase equilibrium of mixtures of propylene oxide with hydrocarbons (methanol-benzene) are necessary for proper design and optimization of the relevant chemical processes and purification steps [10]. Subsequently, these components have been analyzed with the purpose of making an efficient and adequate selection of a solvent for the separation of azeotropes with methanol, which is why ionic liquids (ILS) have received significant interest in recent years as its application in industrial processes refers [11]. In recent years, new applications have been found for methanol derivatives such as gasoline additives, biofuels, diesel fuels etc., because mixtures of this with other substances have proven to be effective and non-toxic inhibitors of ice formation [12].

Materials and methods
Initially to calculate this curve the study temperature must be defined, for this case it is 45° C, the compositions of the liquid phase are assumed and all Φi is set equal to one, which will be used to calculate an estimated value of the pressure of the system as initial data; the critical properties of each component and acentric factor (v) are determined, which were taken from the book by Reid et al [13] and are summarized in Table 1.
The procedure to calculate the bubble point curve, part of the liquid-vapor equilibrium equation at low pressures:

First step (Bubble Point)
The saturation pressure of each component is calculated at a temperature of 45 ° C using units of pressure are Torr, which is subsequently converted to KPa by multiplying by the factor 0.133322. The Antoine coefficients for each component are found in Table II.

Second step (Bubble Point)
The activity coefficients are calculated using the Van Laar model at the temperature and composition of the given liquid phase, the constants for the Methanol-Benzene mixture at 45°C are A 12 =2.1623 and A 21 =1.7925.

Third step (Bubble Point)
The initial system pressure at temperature and established liquid phase compositions is calculated assuming a Φi equal to one, using the following expression:

Fourth step (Bubble Point)
Steam fractions are calculated by clearing yi from equation number 1, the following expression is obtained from this process:

Fifth step (Bubble Point)
With the vapor fractions, the transience coeffi cients for Methanol and Benzene are calculated using equation number 7 and the cubic state equation of Peng Robinson: Using Peng-Robinson to calculate the transience coeffi cient requires several calculations: Polynomial shape: Mixing rules: Fugue coeffi cients for components in solution: The fugacity coeffi cient equation for pure substances is applied to fi nd the φi ^ sat of each component of the mixture, recalculating equations 11, 12 and 13, with the saturation pressure and using them in the following expression:

Sixth step (Bubble Point)
The system pressure is recalculated with equation number 5 using the calculated Φi of each component in the previous step, this procedure or iteration is performed several times until the difference between the initially defi ned system pressure and the system pressure recalculated with the Φi new, be less than the tolerance ε = 0.01 established.
After the above condition is met, the bubble pressure curve is constructed by plotting P system vs X i .

Calculation of the dew point curve
To fi nd this curve, several of the algebraic expressions written above were used, but the procedure varied somewhat with respect to the process explained in section 2. In the fi rst step, the vapor phase compositions are assumed, the saturation pressure is calculated with the Antoine equation, equation number 2; it is assumed Φ i =1 for the fi rst evaluation of the iterative process and in the same way the γ i =1 (since they cannot be calculated and depend on the composition of the liquid phase). With the data and parameters established above, the initial dew pressure of the system is calculated.

Second step (Dew Point):
With the estimated initial system pressure, the compositions of the liquid phase are determined, rearranging equation number 1.

Sixth step (Dew Point)
With the parameters obtained in steps three, four and fi ve the fractions of the liquid phase are recalculated using equation number 22 and they are normalized.
With the normalized X i the activity coeffi cients are recalculated again γ recalculated for the Van Laar model with equations number 3 and 4.

Seventh step (Dew Point)
The γ i delta is evaluated to be less than the tolerance ε = 0.01. If this is not fulfi lled, the fractions of the liquid phase with the last phase are γ recalculated , the X i are normalized and the activity coeffi cient is recalculated to fi nd the new γ recalcula , this procedure is performed until condition Δγ i <ε is met.

Eighth step (Dew Point)
Finally with the γ recalculated the fi nal system pressure is calculated P Sist3 with equation 21 and it is evaluated that ΔP is less than the tolerance ε = 0.01.
If the previous condition is not satisfi ed, the whole process is performed again but using γ recalculado to determine the system pressure P Sist2 and recalculate all parameters, the iterations will continue until the condition ΔP <ε is met. Then the dew pressure curve is constructed by graphing P Sist3 vs Y i .

Comparison between the peng Robinson-Van Laar model theoretically calculated, experimental data and simulation in hysys-aspen de la mix
The procedures described in numeral 2 and 3 were the basis of the algorithm for programming the Matlab code and obtaining the dew point and bubble point curves using the Peng Robinson -Van Laar model to calculate the transience coeffi cients and the coeffi cients of activity of the binary mixture Methanol-Benzene at 45 ° C, the calculated data can be seen in Figure 1 and Table III. To verify the validity of the theoretically calculated data with the Matlab algorithm, a simulation of the liquid-vapor balance of the mixture was performed using the "Hysys-Aspen" program with the Wilson model to the conditions of the case study, the results are shown in Table 4, a comparison was also made with the experimental data of the Methanol-Benzene mixture that he used as a model of transience, the Redlich-Kwong equation, and for the liquid phase he uses the Wilson activity model the results are summarized in Table 5, both models were selected for their degree of reliability for the analyzed system. The comparative graphs (P-X-Y) of the 45° Methanol Benzene mixture with the three models mentioned are shown in Figures 2, 3 and 4.
The theoretically calculated data were subjected to analysis with the data of the other models used to verify the validity of the algorithm and its results; The standard deviation of the theoretical calculations with respect to the other models were (0.146 theoretical vs. experimental), (theoretical 0.0974 vs. simulation program). Figure 2 shows that the theoretical curve of the bubble and dew points is slightly out of phase with respect to the experimental values, a result that was expected due to the standard deviation previously analyzed between these two curves, however the algorithm used to obtaining these theoretical data can be useful as an approximation to analyze the behavior of these curves at different temperatures.
The data simulated with "Hysys-Aspen" recorded in Table 4, show a similar behavior to the experimental data in Table V, which is why at some points the curves overlap; the standard deviation between these two curves was 0.0654, this behavior infers that the simulator data can be reliable to adjust and calibrate the theoretical model calculated with Peng-Robinson and Van Laar used in the Matlab algorithm.    In Figure 3 a comparison of the experimental and simulated data is made with the theoretical data calculated by the algorithm designed for this article following the procedure explained in numeral 2 and 3; all the aforementioned analyzes are consolidated and the similarity between the experimental data and those simulated by "Hysys-Aspen" in which the standard deviation analyzed was 0.0654 between these two curves is clearly observed.
A similar behavior is observed in Figure 3, the theoretical data are outdated with respect to the results shown by the simulator, but in this case the standard deviation was 0.0974 which is slightly smaller than that observed in the curves of Figure 2.

Conclusions
The