Redlich-Kwong system

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

There are many other specific techniques applicable to particular situations, and these should often be investigated to select the method for developing the vapor-liquid relationships most reliable for the system. These are often expressed in calculation terms as the effective K for the components, i, of a system. Frequently used methods are Chao-Seader, Peng-Robinson, Renon, Redlich-Kwong, Soave Redlich-Kwong, Wilson. 

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). 

The need for methods of accurately describing the thermodynamic behavior of natural and synthetic gas systems has been well established. Of the numerous equations of state available, three--the Soave-Redlich-Kwong (SRK) (19), the Peng-Robinson (PR) (18) and the Starling version of the Benedict-Webb-Rubin (BWRS) (13, 20)--have satisfied this need for many hydrocarbon systems. These equations can be readily extended to describe the behavior of synthetic gas systems. At least two of the equations (SRK and PR) have been further extended to describe the thermodynamic properties of water-light hydrocarbon systems. 

The basic equations used to predict the thermodynamic properties of systems for the SRK and PFGC-MES are given in Tables I and II, respectively. As can be seen, the PFGC-MES equation of state relies only on group contributions--critical properties etc., are not required. Conversely, the SRK, as all Redlich-Kwong based equations of states, relies on using the critical properties to estimate the parameters required for solution. 

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... 

CHEMKIN REAL-GAS A Fortran Package for Analysis of Thermodynamic Properties and Chemical Kinetics in Nonideal Systems, Schmitt, R. G., Butler, P. B. and French, N. B. The University of Iowa, Iowa City, IA. Report UIME PBB 93-006,1993. A Fortran program (rglib.f and rgin-terp.f) used in connection with CHEMKIN-II that incorporates several real-gas equations of state into kinetic and thermodynamic calculations. The real-gas equations of state provided include the van der Waals, Redlich-Kwong, Soave, Peng-Robinson, Becker-Kistiakowsky-Wilson, and Nobel-Abel. 

Christiansen et al. (54) applied the Naphtali-Sandholm method to natural gas mixtures. They replaced the equilibrium relationships and component vapor rates with the bubble-point equation and total liquid rate to get practically half the number of functions and variables [to iV(C + 2)]. By exclusively using the Soave-Redlich-Kwong equation of state, they were able to use analytical derivatives of revalues and enthalpies with respect to composition and temperature. To improve stability in the calculation, they limited the changes in the independent variables between trials to where each change did not exceed a preset maximum. There is a Naphtali-Sandholm method in the FraChem program of OLI Systems, Florham Park, New Jersey CHEMCAD of Coade Inc, of Houston, Texas PRO/II of Simulation Sciences of Fullerton, California and Distil-R of TECS Software, Houston, Texas. Variations of the Naphtali-Sandholm method are used in other methods such as the homotopy methods (Sec. 4,2.12) and the nonequilibrium methods (Sec. 4.2.13). 

Partitioning of carbohydrates in the vapor-liquid-liquid regions of the acetone+water+car-bon dioxide system and the 2-propanol+water+carbon dioxide system has been investigated experimentally between 313 and 343 K and between 4 and 13 MPa. Both series yielded the same qualitative results. Partitioning of the carbohydrates between the two liquid phases of the vapor-liquid-liquid equilibria (VLLE) shows the dependencies of the carbohydrate K-factors on pressure and temperature. The Soave-Redlich-Kwong equation of state is suitable to reproduce carbohydrate partitioning in the glucose+acetone+water+carbon dioxide system. 

Figure 3. Glucose K-factors (xL2/xL1) from VLLE measurements in the glucose+acetone+ water+carbon dioxide system against system temperature and pressure. ( = experimental data, grid = calculation results with Soave-Redlich-Kwong EOS, see text)...

Phase compositions of VLLE in the systems glucose + acetone + water + carbon dioxide and carbohydrates + 2-propanol + water + carbon dioxide have been determined experimentally. Like for VLE of related systems from literature, the carbohydrate solubility in a phase rises when the phase becomes more similar to the water-rich lower liquid phase. At the same time separation of different carbohydrates becomes more difficult because selectivity decreases. Theoretically based models can help to find an optimum of capacity and selectivity and to minimize the number of necessary experiments. A simple model based on the Soave-Redlich-Kwong EOS which can reproduce glucose partitioning between the two liquid phases in VLLE in the glucose + acetone + water + carbon dioxide system is presented. 2-Propanol is shown to be a better modifier for these systems than acetone, but denaturation of carbohydrates in the carbohydrate + 2-propanol + water + carbon dioxide system limits industrial applications. 

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. 

Reid, Prausnitz, and Poling (see footnote 1) discuss other important cubic equations of state including the Redlich-Kwong, Soave-Redlich-Kwong (SRK). and Peng-Robinson equations. These equations are empirical but have proved remarkably robust in describing a wide variety of systems. Here we will use the SRK expression to illustrate the general characteristics of cubic equations of state. 

Cubic equations of state (EOS) such as the Redlich-Kwong (RK), Soave-Redlich-Kwong and Peng>Robinson equations of state have become important tools in the area of phase equilibrium modeling, especially for systems at pressures close to or above the critical pressure of one or more of these system components. The functional form of the Soave-Redlich-Kwong and Peng-Robinson equations of state can be represented in a general manner as shown in Equation 2 ... 

What are the units of a and b in the SI system for the Redlich-Kwong equation ... 

FIGURE 1.7-2 VLE for tha hydrogen suliide-waier system at 171 C, Circles are data. Curves are computed via the Soave-Redlich-Kwong equation with c,2 = 0.08 and kl2 = 0.163 (Evelein et al,1),... 

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