Soave-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 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. 

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. 

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 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). 

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. 

The Predictive Soave-Redlich-Kwong (PSRK) Equation of State A Proposal for Modeling the Flash Vessel... 

The PSRK model was first proposed by Holderbaum and Gmehling [4] and considers the Soave-Redlich-Kwong equation of state [11] and the UNIFAC model for the excess free energy and the activity coefficient in the mixing rules, as shown below ... 

This work proposed the use of the Predictive Soave-Redlich-Kwong (PSRK) model to describe the phase equilibria in the flash distillation, using modified molecular parameters r and q for ethanol. In this way, the PSRK equation of state becomes more empirical, but keeps the predictive capabilities of the model. Furthermore, the introduction of new molecular parameters r and in the UNIFAC model gives more accurate predictions for the concentration of the congener in the gas phase for binary and ternary systems. 

Both the basin modelling (PetroMod, lES GmbH, Germany) and the PVT simulation software used (PVTsim, Calsep a.s., Denmark) applied Soave-Redlich-Kwong type cubic equations of state where fluid systems were modelled at thermodynamic equilibrium. 

Much later Soave (1972) proposed a new modification, known as Soave-Redlich-Kwong EOS, abbreviated here SRK-EOS, in which the model incorporates another important molecular parameter, the acentric factor co(see later the equation 5.12). The result was that the accuracy of VLE computations improved considerably. In the case of SRK-EOS the alpha function is ... 

A first issue is the thermodynamic modelling. For the high-pressure part including the stabiliser, an equation-of-state model is appropriate, as for example Peng-Robinson or Soave-Redlich-Kwong. A specific model for hydrocarbons, as Chao-Seader or Grayson-Streed, may be used equally for the low-pressure part. 

In practice, the most commonly used EOSs are the Soave-Redlich-Kwong equation and the Peng-Robinson equation. These equations were developed for pure components only. Applying these models to multicomponent systems requires mixing rules for the calculation of the parameters a and b in the mixture. These parameters have to be calculated from the pure component parameters and b. ... 

The conditions for this simulation are shown in Figure 4.21 and sununarized in Exercise 4.2. As mentioned before, representative values are assumed for the flow rates of the species in the gas and toluene recycle streams. Also, typical values are provided for the heat transfer coefficients in both heat exchangers, taking into consideration the phases of the streams involved in heat transfer, as discussed in Section 13.3. Subroutines and models for the heat exchangers and reactor are described in the ASPEN and HYSYS modules on Heat Exchangers and Chemical Reactors on the multimedia CD-ROM that accompanies this text. In ASPEN PLUS and HYSYS.Plant, there are no models for furnaces, and hence it is recommended that you calculate the heat required using the HEATER subroutine and the Heater model, respectively. For estimation of the thermophysical properties, it is recommended that the Soave-Redlich-Kwong equation of state be used. 

A light-hydrocarbon mixture is to be separated by distillation, as shown in Figure 9.29, into ethane-rich and propane-rich fractions. Based on the specifications given and use of the Soave-Redlich-Kwong equation for thermodynamic properties, use ASPEN PLUS with the RADFRAC distillation model to simulate the column operation. Using the results of the simulation, with Tq = 80°F, a condenser refrigerant temperature of 0°F, and a reboiler steam temperature of 250°F, calculate the... 

The cubic form of an equation of state is the simplest form which enables the description of the PvT behavior of gases and liquids and thus the representation of the vapor-liquid equilibrium with only one model. At constant temperature and aL a given pressure this equation has three solutions. These solutions may be - depending on the values of temperature and pressure - all of real type or of mixed real and complex type. Figure 2.14 shows an isotherm in the Pv-diagram, calculated with the Soave-Redlich-Kwong equation for ethanol at 473.15 K. The cho.. en temperature is lower than the critical temperature of ethanol (T = 516.2 K),... 

The separation factors mainly depend on composition and temperature. The correct composition dependence is described with the help of activity coefficients. Following the Clausius-Clapeyron equation presented in Section 2.4.4 the temperature dependence is mainly influenced by the slope of the vapor pressure curves (enthalpy of vaporization) of the components involved. But also the activity coefficients are temperature-dependent following the Gibbs-Helmholtz equation (Eq. (5.26)). This means that besides a correct description of the composition dependence of the activity coefficients also an accurate description of their temperature dependence is required. For distillation processes at moderate pressures, the pressure effect on the activity coefficients (see Example 5.7) can be neglected. To take into account the real vapor phase behavior, equations of state, for example, the virial equation, cubic equations of state, such as the Redlich-Kwong, Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), the association model, and so on, can be applied. 

If no experimental data are available gas solubilities can be predicted today with the help of group contribution equations of state, such as Predictive Soave-Redlich-Kwong (PSRK) [43] or VTPR [44]. These models are introduced in Sections 5.9.4 and 5.9.5. 

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