Redlich-Kwong methods

Redlich-Kwong method Equation with 2 constants determined by the critical data of a substance, many times extended and improved Redlich, O., and Kwong, J., Chem. Rev. 44 (1949) 223. 

Vapor densities for pure compounds can also be predicted by cubic equations of state. For hydrocarbons, relatively accurate Redlich-Kwong-type equations such as the Soave and Peng-Robinson equations are often used. Both require only T, and (0 as inputs. For organic compounds, the Lee-Erbar-EdmisteF" equation (which requires the same input parameters) has been used with errors essentially equivalent to those determined for the Lydersen method. While analytical equations of state are not often used when only densities are required, values from equations of state are used as inputs to equation of state formulations for thermal and equilibrium properties. 

Since non-ideal gases do not obey the ideal gas law (i.e., PV = nRT), corrections for nonideality must be made using an equation of state such as the Van der Waals or Redlich-Kwong equations. This process involves complex analytical expressions. Another method for a nonideal gas situation is the use of the compressibility factor Z, where Z equals PV/nRT. Of the analytical methods available for calculation of Z, the most compact one is obtained from the Redlich-Kwong equation of state. The working equations are listed below ... 

Other important equations of state which can be related to fugacity and activity have been developed by Redlich-Kwong [56] with Chueh [10], which is an improvement over the original Redlich-Kwong, and Palmer s summary of activity coefficient methods [51]. 

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. 

For the monomers in the polymerization under consideration the fugacity coefficients were estimated by Redlich-Kwong equation of state and were found to be close to unity. The activity coefficients (8) for the monomers were estimated by Scatchard-Hildebrand s method (5) for the most volatile monomer there was a temperature dependence but none for the other monomer. These were later confirmed by applying the UNIFAC method (6). The saturation vapor pressures were calculated by Antoine coefficients (5). 

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 second term on the RHS of eq. 22 is the volume expansivity which can be calculated from a two-parameter, cubic equation of state such as the Redlich-Kwong EOS.(14) We chose the Redlich-Kwong EOS because the "a" term is independent of temperature, which simplifies the procedure of solving for the analytical solution. Using the method of implicit differentiation with the Redlich-Kwong equation of state,... 

Six alternate methods for predicting the thermodynamic properties are included. These are known by the names of the authors of the methods, which are Chao-Seader (2), Grayson-Streed (3), Lee-Erbar-Edmister (4), Soave-Redlich-Kwong (5), Peng-Robinson (6) and Lee-Kesler-Ploecker (7, 12). 

The Chao-Seader and the Grayson-Streed methods are very similar in that they both use the same mathematical models for each phase. For the vapor, the Redlich-Kwong equation of state is used. This two-parameter generalized pressure-volume-temperature (P-V-T) expression is very convenient because only the critical constants of the mixture components are required for applications. For the liquid phase, both methods used the regular solution theory of Scatchard and Hildebrand (26) for the activity coefficient plus an empirical relationship for the reference liquid fugacity coefficient. Chao-Seader and Grayson-Streed derived different constants for these two liquid equations, however. 

The Soave modification of the Redlich-Kwong equation is the basis for the fourth thermodynamic properties method. This equation of state is applied to both liquid and vapor phases. Binary interaction coefficients for these applications are from Reid-Prausnitz-Sherwood (13) and the mathematical derivations used here are from Christiansen-Michelson-Fredenslund (14). Temperature and composition derivatives of the thermodynamic functions are included in the later work. These have applications in multistage calculations. 

Estimating the unknown but required starting values of conditions and compositions is an important and sensitive part of these calculations. The composition of the feed is always known, as is the composition of one of the two phases in bubble and dew point calculations. With the Chao-Seader, Grayson-Streed, and Lee-Erbar-Edmister methods, it is possible to assume that both phases have the composition of the feed for the first trial. This assumption leads to trouble with the Soave-Redlich-Kwong, the Peng-Robinson and the Lee-Kesler-Ploecker... 

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). 

A Find the molar volume (in cm3/g mol) of propane at 375 K and 21 atm. Use the Redlich-Kwong and Peng-Robinson equations, and solve for the molar volume using (1) a nonlinear equation solver, and (2) the compressibility factor method. The acentric factor for propane to use in the Peng-Robinson equation is 0.1487. Also, check your results with the value found in a data base or a handbook. 

Example 5.15 Retrofits of distillation columns by thermodynamic analysis The synthesis of methanol takes place in a tube reactor in section 3 in the methanol plant shown in Figure 5.7. The reactor outlet is flashed at 45°C and 75 bar, and the liquid product (stream 407) containing 73.45 mol% of methanol is fed into the separation section (see Figure 5.8), where the methanol is purified. Stream 407 and the makeup water are the feed streams to the section. Table 5.2 shows the properties and compositions of the streams in section 3. The converged simulations are obtained from the Redlich-Kwong-Soave method to estimate the vapor properties, while the activity coefficient... 

In this paper we present a new characterisation method for porous carbonaceous materials. It is based on a theoretical treatment of adsorption isotherms measured in wide temperature (303 to 383 K) and pressure ranges (0 to 10000 kPa) and for different adsorbates (N2, CH4, Ar, C3H8 and n-C4Hio). The theoretical treatment relies on the Integral Adsorption Equation concept. We developed a local adsorption isotherm model based on the extension of the Redlich-Kwong equation of state to surface phenomena and we improved it to take into account the multilayer formation. The pore size distribution fimction is assumed to be a bi-modal gaussian. By a minimisation procedure, it is possible to determine the bi-modal pore size distribution function witch can be used for purely characterisation purposes or to predict adsorption isotherms. 

In this section we introduce several more complex but more accurate equations of state for single species the virial equation, the van der Waals equation, and the Soave-Redlich-Kwong equation. In Section 5.4 we introduce another approach to nonideal gas analysis that makes use of compressibility factors, and we describe Kay s rule, a method for performing PVT calculations on gas mixtures. 

Distillation columns were simulated and designed with the CHEMCAD-SCDS method using the Soave-Redlich-Kwong equation of state. Reflux ratio for C-601 was set at 1.5 Rmin - For C-602, C-603, C-604, and C-605 it was 1.2 Runn. Cooling water was available with an inlet temperature of 29°C and an outlet temperature of 35°C. Plate efficiency of the valve trays was assumed to be... 

Consider the following mixture that is coming out of a methanol reactor CO, 100 kmol/h H2, 200 kmol/h methanol, 100 kmol/h. The gas is at 100 atm and 300°C. Compute the specific volume using (1) ideal gas law (2) Redlich-Kwong equation of state and (3) Redlich-Kwong-Soave equation of state. The acentric factors for the RK-Soave method are CO, 0.049 H2, -0.22 methanol, 0.559. Where did you get the other data you needed How do the three answers compare Is the gas ideal or not Comment. 

Derive equations to calculate the enthalpy departure using each of the following methods (a) the ideal gas equation, (b) the virial equation of state truncated after the second virial coefficient, (c) the Soave-Redlich-Kwong equation of state. 

The Chao-Seader method uses the Redlich-Kwong equation of state for the calculation of Hildebrand s equation for the calculation of the liquid activity coefficient yf, and an extension of Pitzer s modified form of the principle of corresponding states for the calculation of the liquid fugacity ratio [. 

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