Redlich-Kwong modified equation

A high-pressure circulation-type apparatus was designed and constructed to investigate the vapor-liquid equilibria (VLE) of systems containing limonene, linalool and supercritical carbon dioxide. VLE data of binary and ternary systems of these compounds can be determined in the ranges of pressure and temperature of interest for the deterpenation of cold-pressed orange oil. The preliminary results obtained for the binaries CC -linalool and C02-limonene were compared to data already published with acceptable accuracy and well correlated by a modified Soave-Redlich-Kwong (SRK) equation of state. 

Fuller, G. G., 1976. A modified Redlich-Kwong-Soave equation of state capable of repre.sent-ing the liquid state. Ind. Eng. Chem. Fund, 15 254—257. 

The Redlich-Kwong equation of state was modified further by Soave to give the Redlich-Kwong-Soave equation of state (called RK-Soave in Aspen Plus), which is a common one in process simulators ... 

In this study, the phase equilibrium in the binary mixtures that are expected to be found in the flash distillation was modeled with the Predictive Soave-Redlich-Kwong (PSRK) equation of state [4], using modified molecular parameters r and q. Five binary ethanol + congener mixtures were considered for new yield values for parameters r and q. The congeners considered were acetic acid, acetaldehyde, furfural, methanol, and 1-pentanol. Subsequently, the model was validated with the water + ethanol binary system, and the 1 -pentanol + ethanol + water, 1-propanol + ethanol + water, and furfural + ethanol + water ternary systems. 

I shall refer to Equation 49 as the modified Redlich-Kwong (MRK) equation. As seen from Table 1, the MRK equation yields a very accurate value for zQ. Furthermore, the MRK equation of state of methyl chloride, listed in Table III, is in excellent agreement with experiment. Clearly, using an accurate expression for P0 in place of the (V — Nb) 1 term leads to a dramatic improvement in the equation of state. 

We now consider modifications to the repulsive term in the van der Waals equation. Although the van der Waals hard-sphere term is correct at low densities. Figure 4.13 shows that it quickly becomes erroneous as the density is increased the excluded volume is not constant, but depends on density in some complicated way. Therefore we can improve the equation of state by using the Carnahan-Starling form (4.5.4) for Z/jg. Our modified Redlich-Kwong (mRK) equation of state is then [29]... 

Figure 4.14 Comparison of the van der Waals (vdW), Redlich-Kwong (RK), and modified Redlich-Kwong (mRK) equations for predicting the compressibility factor of carbon dioxide along the supercritical isotherm T = 350 K. For each equation the parameters a and b were computed from expressions in Table 4.4, using Tc = 304.2 K and = 73.82 bar. Points are exp>erimen-tal values taken from Vargaftik [19].

This extension is just a first step, however, because it will not be a good approximation at extremely high pressmes. The Redlich-Kwong equation of state is a modification of van der Waal s equation of state, and then was modified further by Soave to give the Soave-Redlich-Kwong (SRK) equation of state, which is a common one in process simulators. Another variation of Redlich-Kwong equation of state is Peng-Robinson (PR) equation 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 ]). 

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. 

The constants a and b are determined from the critical point data of the gas. The compressibility factor at the critical point is equal to one-third. The equation was developed by Austrian chemist Otto Redlich (1896-1978) and loseph Neng Shun Rwong in 1949. The equation was further developed and modified by Pitzer, Wilson, and Soave to improve the predictability of gas behaviour. See soave-redlich-kwong (srk) equation of state. 

Compilation of binary experimental data reduced with the Wilson equation and, for high pressures, with a modified Redlich-Kwong equation. 

Soave, G. (1972), Equilibrium constants from a modified Redlich-Kwong equation of state . Chem. Eng. Sci., Vol. 27, p. 1197. 

To illustrate this thermodynamic consistency test, Figs. 15, 16, and 17 show plots of the appropriate functions needed to calculate Areas I, II, and III, respectively, for the nitrogen-carbon dioxide system at 0°C the data are taken from Muirbrook (M5). Fugacity coffiecients were calculated with the modified Redlich-Kwong equation (R4). 

Figure A3.3 compares the experimental (corresponding states) results with the predictions from the van der Waals. modified Berthelot, Dieterici, and Redlich-Kwong equations of state.b The comparison is not so direct for the Soave and Peng-Robinson equations of state, since the reduced equation still includes to, the acentric factor. Figure A3.4 compares the corresponding states line, with the prediction from the Soave equation, using four different values of to. The acentric factors chosen are those for H (o> = —0.218), CH4 (to = 0.011),...

Figure A3.3 Comparison of the experimental r (dashed lines) with the c values calculated from the (a) van der Waals, (b) modified Berthelot, (c) Dieterici, and (d) Redlich-Kwong equations of state expressed in reduced form.

Soave (1972) modified the Redlich-Kwong equation to extend its usefulness to the critical region, and for use with liquids. 

There are, however, some published examples of equations of state being applied to associating substances. Heidemann (1) used the Redlich-Kwong equation as modified by Wilson (2j to caTculate aqueous hydrocarbon systems. Similar calculations were done by Peng and Robinson (3) using their own equation of state. In both... 

Kerrick D. M. and Jacobs G. K. (1982). A modified Redlich-Kwong equation for H2O, CO2 and H2O-CO2 mixtures at elevated pressures and temperatures. Amer. Jour Set, 281 735-767. 

Corresponding states have been used in other equations. For example, the Peng-Robinson equation is a modified Redlich-Kwong equation formulated to better correlate vapor—liquid equilibrium (VLE) vapor pressure data. This equation, however, is not useful in reduced form because it is specifically designed to calculate accurate pressure data. Reduced equations generally presuppose knowledge of the pressure. 

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 mass flows and purities obtained by experiments in a pilot plant with a height of 4 m were used as a basis. By applying a modified Redlich-Kwong equation of state (1.21. the heat and mass balances were calculated for the new plant, which contains an extractor with an inner diameter of 7 cm and a height of 6.5 m. 

Soave s Modified Redlich-Kwong Equation of State... 

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