Isobaric Vapor - Liquid Equilibria of Gasoline Additives Systems At 101.3 kPa

In this study, isobaric vapor-liquid equilibrium of gasoline a dditives for three ternary sys tems: “ MTBE + E thanol + 2-Methyl-2-propanol ” , “ Ethanol + 2-Methyl-2-propanol + Oct ane ” , and “ MTBE + Etha nol + Oct ane ” at 101.3 k Pa are studied. Furthermore t hree bi nary systems: “ ethanol + 2-Methyl-2-propanol ” , “ MTBE + Ethanol ” , and “ MTBE + Octane ” at 101.3 kPa have been studied. T he binary system “ MTBE + Ethanol ” forms minimum boiling a zeotrope. The azeotrope data are x 1 (AZ) =0.955 m ole fraction a nd T(AZ) =327.94 K. The other ternary systems and the other binary systems do not form azeotrope. All the literature data used passed successfully the test for thermodynamic consistency using McDermott-Ellis test method. In this study th e c alculation of VLE K – values is done by usi ng three methods, the first method uses mo dified So ave Redlich and Kw ong (SRK), modified Peng and Robinson (PR) equations of sta te for two phases. The second method uses SRK-EOS for vapor phase with (NR TL, UNIQUAC a nd UNIFAC activity coefficient models) f or liq uid phase and usi ng PR-EOS for vapor phase with (NRTL, UNIQU AC and UNIF AC activity coefficient models) for liquid phase. The third method uses the Wong-Sandler mixing rules and the PRSV-EOS based on GE of (NRTL and UNIQUAC activity coefficient models). The non ideality of both vapor and liquid phases for the literature data for the ternary an d binary systems have been accounted for predicting VLE K – values using the maximum likelihood principle for parameter estimation which provides a mathematical and com putational guarantee of global optimality in pa rameters estimation. The Wong-Sandler mixing rules and the PRSV-EOS based on excess Gibbs free energy G E of NRTL activity c oefficient m odel give more accurat e resul ts for correlation and prediction of the K-values th an other methods for the ternary and binary systems which contain asymmetric and polar compounds.


Introduction
Ethers and alcohols used as gasoline additives have excellent antiknock properties and are environmentally acceptable substances.Gasoline blended with about 7-15 % 2-methoxy-2-methyl propane (MTBE) has been used for high-performance premium gasoline.On the other hand, recommendations for gasoline additives include not only pure MTBE but also mixtures with alcohols for high-octane gasoline [1].
The study of gasoline + alcohol and ether mixtures using the methods of physical-chemical analysis is considered at the present time as a difficult goal as gasoline is an extremely complex mixture of hydrocarbons of varying composition.Accordingly, a more appropriate approach would seem to be to study model hydrocarbon + alcohol and ether mixtures composed of a small number of individual compounds [2].
The reasons for studying mixtures of hydrocarbons and oxygen-containing compounds relating to the use of oxygencontaining compounds in motor fuels [3].
For MTBE + ethanol, one set of isobaric VLE at 101.3 kPa is reported by Arce et al. [4].VLE for the system MTBE + octane at 94 kPa has been measured by Wisniak et al. [5].
For the ethanol + 2-methyl-2-propanol system, one set of isobaric VLE data at 101.3 kPa is reported by Suska et al. [6] and one set of isothermal data at 313.15 K have been measured by Oracz [7].
The literature data were correlated using activity coefficient models for the liquid phase and equation of state (EOS) for the vapor phase and some time with the liquid phase too, and study their abilities to predict vapor-liquid equilibria Kvalues for binary and ternary systems accurately.
Many An important advance in the description of phase equilibria is to combine the strengths of both EOS and activity coefficient approaches by forcing the mixing rule of an EOS to behave with composition dependence like the G E model.These are called G E mixing rules and generally include the direct use of activity coefficient parameters fitted to VLE data [8].

System Selection:
Ethers and alcohols used as gasoline additives have excellent antiknock qualities and are considered environmental protection substances.Gasoline including 2methoxy-2-methylpropane (MTBE) has been used for a high performance premium gasoline.In recent years, mixtures of ethers with alcohols have been considered for blending with gasoline to reduce carbon monoxide that is created during the burning of the fuel.Binary Systems: Three binary systems are used in this study: 1-binary system(I) consists of Ternary Systems : Three ternary systems are used in this study: 1-ternary system(I) consists of

Thermodynamic Consistency Test:
One of the greatest arguments in favor of obtaining redundant data is the ability to assess the validity of the data by means of a thermodynamic consistency test.The consistency of the experimental data was examined to provide information on the thermodynamic plausibility or inconsistency and to recognize any deviations of the measured values.
According to McDermott-Ellis test method [10], two experimental points a and b are thermodynamically consistent if the following condition is fulfilled: The local deviation D is given by In this method, it is recommended using of a fixed value of 0.01 for D max [10], If the accuracy in the measurement of the vapor and the liquid mole fraction is within 0.001.The local maximum deviation, D max , due to experimental errors, is not constant, and is given by The conclusion can be drawn that all the data are thermodynamically consistent.

Improvement of Equation of State and Activity Coefficients Models:
The almost infinite number of possible mixtures and wide range of temperature and pressure encountered in process engineering are such that no single thermodynamic model is ever likely to be applicable in all cases.Consequently, knowledge and judgment are required to select the most appropriate methods by which to estimate the conditions under which two phases will be in equilibrium [11].
The first method was rigorously tested using two various mixing rules for vapor-liquid equilibria calculation [12].The first mixing rules tested for the PR equation of state [13].The second mixing rules tested are for the SRK equation of state [14].
The second method is obtained for properties of vapor liquid equilibria when fugacity of the component in the liquid phase is estimated from an activity coefficient mode.
The activity coefficients are correlated with the UNIQUAC model [15], UNIFAC model [16,17] and NRTL model [18,19].The non random two liquid (NRTL) equation using the α term as either a fitting parameter or a fixed value.In the case of the systems containing an alcohol with a hydrocarbon or an ether, it was acceptable to correlate using the fixed value of 0.47 as the α term [20].
The parameters in the equation were obtained by using maximumlikelihood principle method.The sum of squares of relative deviations in the activity coefficients was minimized during optimization of the parameters [21].
The third method for the vapor liquid equilibrium calculations with the Wong-Sandler mixing rules and the Peng-Robinson Stryjek-Vera PRSV-EOS based on excess Gibbs free energy G E models [22,23].

Phase Equilibrium Calculations (K-values)
The basic conditions for equilibrium between vapor and liquid phases in a system of n components, which are required, equality of temperature and pressure and the fugacity coefficient of both phases.
In terms of fugacity coefficient, these equations become L and Φ i V are liquid and vapor fugacity coefficients.
We have an equation of state from which we may calculate the fugacity coefficients of all components in both phases.
The activity coefficients γ i are calculated with the equation [ In cases where it is preferable to obtain the fugacity of components in the liquid phase from an activity coefficient model, we write Eq.( 4) as The state of the vapor and liquid phases in contact at a given temperature and pressure may be conveniently specified by the vaporization equilibrium ratio . When the two phases are in thermodynamic equilibrium, Ki is given by Or, in term of an activity coefficient model instead of Φ i L , by The concept of ideality in vapor and liquid mixtures is often useful as a means of obtaining an initial approximation to the solution of VLE problem.For an ideal vapor mixture, all fugacity coefficients are unity, while for an ideal liquid mixture, all activity coefficients and poynting factors are unity.Eq.( 6)then reduces to Raoult `s law.
Consequently, the total pressure in an isothermal ideal vaporliquid system is a linear function of the mole fractions in the liquid phase; alternatively, the inverse of the total pressure is a linear function of the mole fraction in vapor phase.
All the required physical property data are available for MTBE to calculate these terms accurately [20].The activity coefficients were therefore calculated on the assumption of an ideal vapor phase.The vapor pressures of the pure components, P i s , were obtained using the Antoine equation.

C T B
Values of the constants A, B and C which appear in this equation are shown in Table (B-1) in Appendix B [11,24].
In order to test accurately the suitability of the G E method [22,23], the three binary and ternary systems that have been chosen encompassing compounds of a wide different molecular weights and mixtures of various types of non ideality (ideal, nearly ideal, highly not ideal) including polar mixture.
The predicted value for the equilibrium constants (K-values) are compared with the literature value and good agreement is obtained for all method used.
It appears from It appears from tables (B2-B15) in Appendix B that the calculated VLE is sensitive to the type of cubic EOS and activity coefficients models used and to the value of the adjustable parameters, particularly when the EOS are coupled with the modified mixing rules.In addition, it can be observed that the type of cubic EOS significantly changes the results when the number of parameter is increased.
With the effect of the number of adjustable parameters (two, three or more) on the VLE calculations, including mixtures with polar compounds as one component or systems containing dissimilar constituents, as more parameters are used the accuracy of calculated results is increased.It is evident that the more constants in an equation of state, the more flexibility in fitting experimental data but it is also clear that to obtain more constants, one requires more experimental information.
The literature and calculated data of VLE for the ethanol +2methyl-2-propanol system is shown graphically in figures (1) and (2).
To measure the Azeotropic point, a method is introduced for graphical determination of the binary Azeotropic point on the basis of experimental binary vaporliquid equilibrium data.Also, a method is evolved for determination of the binary and ternary Azeotropic points by using the extended Redlick -Kister equation applicable to the condition of constant pressure [25].The agreement between prediction and experimental data is good.
The MTBE + ethanol system forms minimum boiling azeotrope.The azeotrope data are x 1 (AZ) =0.955 mole fraction and T(AZ)=327.94K.The literature on VLE for the MTBE + Ethanol system is shown in Figures (3) and (4).
The tendency of a mixture to form an azeotrope depends on two factors [26]: • The difference in the pure component boiling points.
• The degree of non ideality.The closer the boiling points of the pure components and the less ideal mixture, the greater the likelihood of an azeotrope.
The literature and calculated VLE for the binary system MTBE +Octane is shown graphically in Figures (5) and (6).

Conclusions
Based on this study, the following conclusions can be made:

Analysis of Dispersion
To know the applicability and accuracy of any proposed correlation, it is very important to know how this correlation fits the experimental data which is done by comparing the obtained results from the proposed correlation with the experimental data.
The various measurement of dispersion or variation are available, the most common being the Mean Overall Deviation and Average Absolute Deviation.The Mean Overall Deviation "mean D %" is a more tangible element indicating the overall goodness of the fit of the data by the correlation and it reads [27]: 100 %

...( A-2)
Where M is an intensive property and n is the number of data point [27].
These equations are used to calculate Mean Overall Deviation "mean D%" and Average Absolute Deviation "AAD" of literature results of binary and ternary systems.

Maximum-Likelihood Principle
The estimation of parameters in theoretical and semi-empirical mathematical models from experimental data is an important requirement in many fields of science and engineering.In the maximumlikelihood analysis, it is assumed that all measured data are subject to PDF created with pdfFactory Pro trial version www.pdffactory.comFor each experiment, the true values of the measured variables are related by one or more constraints.Because the number of data points exceeds the number of parameters to be estimated, all constraint equations are not exactly satisfied for all experimental measurements.Exact agreement between theory and experiment is not achieved due to random and systematic errors in the data and to "lack of fit" of the model to the data.Optimum parameters and true values corresponding to the experimental measurements must be found by satisfaction of an appropriate statistical criterion.
If this criterion is based on the maximum-likelihood principle, it leads to those parameter values that make the experimental observations appear most likely when taken as a whole.The likelihood function is defined as the joint probability of the observed values of the variables for any set of true values of the variables, model parameters, and error variances.The best estimates of the model parameters and of the true values of the measured variables are those which maximize this likelihood function with a normal distribution assumed for the experimental errors.
The parameter estimation algorithm based on the maximum likelihood principle, converges rapidly for almost any initial estimates of the parameters.The rapid convergence is due in part to the similarity to Gauss-Newton iteration method and in part to the successful application of a steplimiting procedure that assures superior convergence behavior [21].
The maximum likelihood principle method provides a mathematical and computational guarantee of global optimality in parameter estimation that provides the best fit to measured data.The objective function in nonlinear parameter estimation problems is given below: The assumed standard deviations had been based on the results of duplicated analyses of samples, and then this inconsistency could indicate either systematic error in the data or lack of fit of the model to the data.In this case, however, they are a priori estimates, and the results of the parameter estimation procedure serve merely to provide best estimates of the standard deviations [21].

3 )
Where the superscripts c and lit indicate calculated and literature values, respectively, the σ 2 are the estimated variances of the corresponding variables, and the sum is taken over all M literature data, and N is the number of compounds in the mixtures.The standard deviations assumed are:σ P = 0.5 mmHg σ T = 0.1 o C PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal, Vol.28, No. 0.001 mole fraction σ y = 0.005 mole fraction

table (
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Table ( B-4) Optimized interaction parameters for binary systems for modify PR-EOS &SRK-EOS.
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Table ( B-12): Adjustable parameters value when applying WS mixing rule with UNIQUAC model on PRSV-EOS to binary systems at101.3KPa Binary Systems No. of data Temp.(K) k ij C
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276 Table (B-15) Adjustable parameters value when applying WS mixing rule with NRTL model on PRSV-EOS to ternary systems at101.3KPa Ternary systems
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