Redlich-Kwong interaction parameters

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

Table 5.11 Binary interaction parameters of the Wilson/Redlich-Kwong model.

The following tables summarize the parameters used for the Peng-Robinson calculations presented in this paper. The pure component properties could also be used for Soave-Redlich-Kwong calculations. Binary interaction parameters are given for both equations. 

Cubic equations of state, such as tire Soave/Redlich/Kwong (SRK) and Peng/Robinson (PR) equations, are usually satisfactory for this kind of calculation. Equation (14.50) for, developed in Sec. 14.2, is applicable here, but with a slightly modified combining rale for interaction parameter a, j used in calculation of Thus, Eq. (14.44) is replaced by ... 

The composition dependence of the parameter Z i3 was calculated for the mixture SC CO2 and SC ethane at T = 350 K and P = 10 MPa. For this purpose, precise PVT data [30] were treated using the Soave-Redlich-Kwong [20] EOS and the classical van der Waals mixing rules. The binary interaction parameter qi2 was calculated by minimizing the sum yi.caic 2 where... 

The optimum binary interaction parameters are shown in Table 111. An example of the results is shown in Figure 1 for the PR-EOS applied to carbon dioxide/methyl oleate at 70 C. Comparing the results of those three simple equations of state, the Redlich-Kwong equation of state gave the poorest prediction. 

FIGURE 1.3-2 Composition dependence of fogacity coefficient of hydrogen sulfide in binary mixtures with ethane at 300 K. Curves labeled V are for superheated vapors at 15 har. those labeled L are for subcooled liquids at 50 bsr, Ail curves are computed from the Soave-Redlich-Kwong equation, with values of interaction parameter kla as shown. 

The value of the binary interaction parameter k(j must be estimated or found by fitting mixture data. Our brief introduction to this approach has been based on the Redlich-Kwong equation, but the procedure can be implemented with any PvTx equation. More generally, the approach discussed here can provide accurate predictions of fluid properties at high T and P using model parameters fit at low T and P. The procedure is now routinely used in process simulation software. 

P4.5 Calculate the excess enthalpy of the system benzene (l)-cyclohexane (2) at =25 CandP = 1 bar for a mole fraction of benzene of xi =0.5 using the Soave-Redlich-Kwong equation of state. The required values can be taken from Appendix A. The binary interaction parameter is ki2 = 0.0246. 

For Soave-Redlich-Kwong, Peng-Robinson and more recent equations of state, eq 4.25, applies to aa., often expressed as a T). Calculations using eqs 4.23 to 4.27 are based only on pure component properties without invoking any information concerning the properties of mixtures. It has been recognized that the use of a binary interaction parameter, ky is required to correct the geometric rule of eq 4.25, so that ... 

The description of hydrocarbon mixture VLB at low and high pressure is of major importance to the oil industry. For such mixtures, any of the modern cubic equations of state (such as Redlich-Kwong, Peng-Robinson or Patel-Teja) provide precise predictions when used with a temperature-independent binary interaction parameter of relatively small value (in most cases in between — 0.1 and 0.1). For the case of non-polar hydrocarbon mixtures of similar size, even kij = Q.Q results in excellent prediction of VLB. 

A more difficult and industrially important test for an equation of state is the ability to predict the VLE of ternary and multicomponent mixtures using interactions parameters fitted to corresponding binary data. Tsonopoulos and co-workers analyzed experimental VLE data for 6 ternary mixtures and showed that Redlich-Kwong-Joffe-Zudkevitch is again slightly more precise than the Soave-Redlich-Kwong and Peng-Robinson equations of state. 

Recently, Nasrifar and Bolland" proposed a modified Soave-Redlich-Kwong cubic equation of state that was shown to be more accurate than both the original Soave-Redlich-Kwong and Peng-Robinson equations of state at predicting the compressibility factor and the speed of sound of natural gas mixtures. Furthermore, the proposed equation" was shown to be able to predict (binary interaction parameters set to zero) values of AT-values for these mixtures that were in excellent agreement with experiment. A representative example is shown in Figure 4.4. 

Chapter 11 provides an analysis of ionic liquids thermodynamic properties. Here, only a representative example is provided. A modified Redlich-Kwong cubic equation of state was used to correlate VLE and predict the VLLE of (fluorocarbon + ionic liquid).Because the ionic liquids have no measurable vapour pressure, the equation of state pure-component parameters were fit to the liquid density data and critical constants.To correlate the experimental VLE data at temperature over the range (283 to 348) K, Shiflett and Yokozeki" used three binary interaction parameters. These parameters were used, without further adjustment, to predict the VLLE of these mixtures. In Eigure 4.8, experimental data and correlation are shown for (1,1,1,2-tetrafluoroethane+ 1-butyl-3-methylimidazolium hexafluorophosphate [bmim ][PF6 ]). 

Table 7.1 Interaction parameters kn used in conjunction with the general Redlich-Kwong equation (7.19) and the mixing rule given by equation (7.36) [64].

Jaubert, J.N. Privat, R. (2010). Relationship between the binary interaction parameters (kij) of the Peng-Robinson and those of the Soave-Redlich-Kwong equations of state. Application to the definition of the PR2SRK model. Eluid Phase Equilib., Vol.295, pp. 

Rather, an equation of state and semiemplrical correlations are used e.g. the Chueh-Prausnltz correlation scheme (10). In this approach the critical pressure of the mixture is obtained indirectly from a modified version of the Redlich-Kwong-Chudi equation of state after Tcm and have been obtained directly from quadratic mixing rules which employ the respective Chueh-Prausnitz Interaction parameters, I12 and V3 2 An example based on this method is given in Figure 5 for the ethane-n-heptane binary mixture. Agreement is rather good except in the immediate vicinity of the maximum critical pressure of the mixture. 

You wish to use the Redlich-Kwong equation of state to describe a mixture of carbon dioxide (1) and toluene (2). To be as accurate as possible with the mixing rules, you want to include the binary interaction parameter, ki2- In the literature, you find reference to an experiment with the following conditions ... 

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