Models Redlich-Kwong

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

SRK (Soave-Redlich-Kwong) model, phase equilibria simulation, 446-448 S T (shell-and-tube) heat-exchangers, 545-552. 613 Stabilizing chemicals, adding feeds for,... 

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. 

The present paper deals with one aspect of this problem the calculation of phase separation critical points in reacting mixtures. The model employed is the Soave-Redlich-Kwong equation of state (1 ), which is typical of several equations of state (2, 5) which have relatively recently come into wide use as phase equilibrium models for light gas mixtures, sometimes including water and the acid gases as components (4, . 5, 6). If the critical point contained in the equation of state (perhaps even for the mixture at reaction equilibrium) can be found directly, the result will aid in other equilibrium computations. 

Physical property data for many of the key components used in the simulation for the ethanol-from-lignocellulose process are not available in the standard ASPEN-Plus property databases (11). Indeed, many of the properties necessary to successfully simulate this process are not available in the standard biomass literature. The physical properties required by ASPEN-Plus are calculated from fundamental properties such as liquid, vapor, and solid enthalpies and density. In general, because of the need to distill ethanol and to handle dissolved gases, the standard nonrandom two-liquid (NRTL) or renon route is used. This route, which includes the NRTL liquid activity coefficient model, Henry s law for the dissolved gases, and Redlich-Kwong-Soave equation of state for the vapor phase, is used to calculate properties for components in the liquid and vapor phases. It also uses the ideal gas at 25°C as the standard reference state, thus requiring the heat of formation at these conditions. 

The column was modeled with AspenPlus / using the rigorous radf rac column model, in conjunction with the Redlich-Kwong-Soave equation of state for property estimation. Steady-state calculations indicated a reflux ratio of 87.67. This is a consequence of the difficult separation problem posed by the two closeboiling components. 

Mujtaba (1989) used CMH model to simulate the operations considered by Domenech and Enjalbert (1974). Since the overall stage efficiency in the experimental column was 75%, the number of theoretical plates used by Mujtaba was 3. The column was initialised at its total reflux steady state values. Soave-Redlich-Kwong (SRK) model was used for the VLE property calculations. Vapour phase enthalpies were calculated using ideal gas heat capacity values and the liquid phase enthalpies were calculated by subtracting heat of vaporisation from the... 

In this separation, there are 4 distillation tasks (NT-4), producing 3 main product states MP= D1, D2, Bf) and 2 off-cut states OP= Rl, R2 from a feed mixture EF= FO. There are a total of 9 possible outer decision variables. Of these, the key component purities of the main-cuts and of the final bottom product are set to the values given by Nad and Spiegel (1987). Additional specification of the recovery of component 1 in Task 2 results in a total of 5 decision variables to be optimised in the outer level optimisation problem. The detailed dynamic model (Type IV-CMH) of Mujtaba and Macchietto (1993) was used here with non-ideal thermodynamics described by the Soave-Redlich-Kwong (SRK) equation of state. Two time intervals for the reflux ratio in Tasks 1 and 3 and 1 interval for Tasks 2 and 4 are used. This gives a total of 12 (6 reflux levels and 6 switching times) inner loop optimisation variables to be optimised. The input data, problem specifications and cost coefficients are given in Table 7.1. 

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. 

Firstly, we will examine the VLE of binary mixtures. The Wilson model is selected for liquid activity with Redlich-Kwong EOS for vapor phase. The predictions offered by Aspen Plus [9] are in agreement with experimental data [5], except... 

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. 

The fugacity coefficient is usually obtained by solving an equation of state (e.g., Peng-Robinson Redlich-Kwong). The activity coefficient is obtained from a liquid phase activity model such as Wilson or NRTL (see Walas, 1985). 

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. 

A broad range of cubic equation of state models (EOS) are successfully used today. The EOS range from the standard Soave-Redlich-Kwong and Peng-Robinson, which is widely used in the hydrocarbon processing and related industries (oil gas and petrochemicals), to a new class of models that extend the range of applications to chemicals. " New models are continually being developed and are too numerous to cite. 

Several cubic equations of state such as Redlich-Kwong, Soave-Redlich-Kwong, and Peng-Robinson have been used to calculate vapor liquid equilibria of fatty acid esters in supercritical fluids. Comparisons are made with experimental data on n-butanol, n-octane, methyl oleate, and methyl linoleate in carbon dioxide and methyl oleate in ethane. Two cubic equations of state with a non quadratic mixing rule were successful in modeling the experimental data. 

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 ... 

The UNIFAC model has also been combined with the predictive Soave-Redlich-Kwong (PSRK) equation of state. The procedure is most completely described (with background literature citations) by Horstmann et al. [Fluid Phase Equilibria 227 157-164 (2005)]. 

Mass transfer coefficients and interfacial areas were computed using the model of Bravo et al. (1985) described in Section 12.3.3. K values and enthalpies were estimated using the Soave-Redlich-Kwong equations of state (see, e.g., Walas, 1985). 

Other approaches to the computation of solid-liquid equilibria are shown in Table 11.2-3. The Soave-Redlich-Kwong equation of state evaluates fugacities to calculate solid-liquid equilibria,7 while Wenzel and Schmidt developed a modified van der Waals equation of state forthe representation ofphase equilibria. The Wenzel-Scbmidt approach generates fugacities, from which the authors developed a trial-and-error approach to compute solid-liquid equilibrium. Unno et a .9 recently presented a simplification of the solution of groups model (ASOG) that allows prediction of solution equilibrium from limited vapor-liquid equilibrium data. 

Elevated pressures for a vapor mixture that contains one or more polar and/or associating compounds Use an equation of state, such as the Peng-Robinson or Soave-Redlich-Kwong equation with the excess Gibbs energy-based mixing rules (see Sec. 9.9) and the appropriate activity coefficient model (see Table 9.11-1). 

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