Peng-Robinson phase

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. 

For both the Soave and Peng-Robinson equations, the fit is best for uj — 0. The Soave equation, which essentially reduces to the Redlich-Kwong equation when ui — 0, does a better job of predicting than does the Peng-Robinson equation. The acentric factors become important when phase changes occur, and it is likely that the Soave and Peng-Robinson equations would prove to be more useful when 77 < 1. 

Volumetric equations of state (EoS) are employed for the calculation offluid phase equilibrium and thermo-physical properties required in the design of processes involving non-ideal fluid mixtures in the oil, gas and chemical industries. Mathematically, a volumetric EoS expresses the relationship among pressure, volume, temperature, and composition for a fluid mixture. The next equation gives the Peng-Robinson equation of state, which is perhaps the most widely used EoS in industrial practice (Peng and Robinson, 1976). 

Leu and Robinson (1992) reported data for this binary system. The data were obtained at temperatures of 0.0, 50.0, 100.0, 125.0, 133.0 and 150.0 °C. At each temperature the vapor and liquid phase mole fractions of isobutane were measured at different pressures. The data at 133.0 and 150.0 are given in Tables 14.9 and 14.10 respectively. The reader should test if the Peng-Robinson and the Trebble-Bishnoi equations of state are capable of describing the observed phase behaviour. First, each isothermal data set should be examined separately. 

Example 6.5 Repeat the calculations from Example 6.4 taking into account vapor-phase nonideality. Fugacity coefficients can be calculated from the Peng-Robinson Equation of State (see Poling, Prausnitz and O Connell6 and Chapter 4). 

Table 13.10 Phase separation calculated using the Peng-Robinson Equation of State.

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. 

In an earlier paper Q ), the authors presented an efficient procedure for predicting the phase behavior of systems exhibiting a water - rich liquid phase, a hydrocarbon - rich liquid phase, and a vapor phase. The Peng-Robinson equation of state (2) was used to reDresent the behavior of all three phases. It has the following form ... 

The vapor-phase mole fractions of water of Olds et al. (19) can be represented very well using the Peng-Robinson equation of state in conjunction with a constant interaction parameter over the temperature range from 100°F to 460°F. The same interaction parameter can be used to reproduce the data of Sultanov et al. 

As mentioned earlier, we have chosen to model the high-pressure phase behavior using the Peng-Robinson equation (Peng and Robinson, 1976) with standard van der Waals mixing rules ... 

For the epoxidation of /nmv-2-hexen-1-ol to (2R,3R)-( + )-3-propyloxirane-methanol, we have measured the high-pressure phase behavior of each of the reactants, products, and catalysts in C02 and modeled them quite well with the Peng-Robinson equation, even in the cases where we observed vapor/ liquid/liquid equilibria (Stradi et al., 1998). 

Fig. 2. Phase diagram of pure CO2 (Peng-Robinson s model [6]).

The expression for the fugacity coefficient 4> depends on the equation of state that is used and is the same for the vapor and liquid phases. In calculating the mixture properties with the Peng-Robinson equation of state we have used the following combining rule ... 

Figure 2. Phase equilibrium behavior for the binary system carbon dioxide - acetone. Experimental, 313 K (A) experimental, 333 K ( ) literature, 313 K (x) modified Peng-Robinson equation of state (—). Literature data are from reference (10).

A model based on a modified mixing rule for the Peng-Robinson equation of state was able to reproduce quantitatively all features of the observed phase equilibrium behavior, with model parameters determined from binary data only. The use of such models may substantially facilitate the task of process design and optimization for separations that utilize supercritical fluids. 

The first three methods use one set of equations for the vapor phase and another for the liquid, in a similar technique. These methods are identified as Chao-Seader (2), Grayson-Streed (3), and Lee-Erbar-Edmister (4). The other three methods employ the same equations for both vapor and liquid phases. They are identified as Soave-Redlich-Kwong (5), Peng-Robinson (6), and Lee-Kesler-Ploecker (7, 12). At this writing, the present... 

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... 

Due to restriction for space the results on modeling the high-pressure phase behaviour of the system carbon dioxide-water-1 -propanol are presented only briefly. The model used in this work was the Peng-Robinson EOS [8] with an temperature dependent attractive term due to Melhelm et al. [9], Although several mixing rules have been tested, the discussion will be restricted to the two-parameter mixing rule of Panagiotopoulos and Reid [10],... 

Figure 4. Three-phase equilibrium LtL2V in the system carbon dioxide-water-1-propanol at 333 K and 13.1 MPa exp., this work — Calculated with Peng-Robinson EOS using Panagiotopoulos and Reid mixing rule, left side prediction from pure component and binary data alone, right side interaction parameters fitted to ternary three-phase equilibria at temperatures between 303 and 333 K...

Although equations of state based on statistical mechanics, like the Perturbed Hard Chain and Chain of Rotators equations of state are good at predicting phase equilibria at conditions far from the critical point of mixtures, a critical evaluation of six of these type of equations of state showed that they are rather inaccurate in the mixture critical region[3]. Satisfactory correlation of the data is obtained with a Peng Robinson equation of state using two interaction parameters per binary as proposed by Shibata and Sandler[4], The correlations of Huang[5] were used for the pure component parameters. 

The experimental data are correlated with equation of state models. The calculation of binary phase equilibrium data for FAEE is commonly based on the Peng-Robinson-equation-of-state, Yu et al. (1994). Up to now only the solubility of the oil components in the solvent has been subject of various studies. No attention was paid to a correlation of ternary data. The computation of ternary or multicomponent phase equilibrium is the basis to analyse and optimise the separation experiments. 

In a first step the ternary phase equilibrium is calculated using the Peng-Robinson-equation-of-state, Table 2. All components with a volatility higher or equal C18 are lumped into one pseudo component, HVC, while all components that tend to enrich in the liquid phase form the Low-Volatile... 

Related Calculations. As computer-based computation has become routine, a growing trend in the determination of K values has been the use of of cubic equations of state, such as the Peng-Robinson, for calculating the fugacities of the components in each phase. Such calculations are mathematically complex and involve iteration. 

The converged simulation was done using the thermodynamic method of RKS to estimate the properties. The Peng-Robinson equation of state was used for predicting the equilibrium and liquid properties, and the vapor phase was assumed to be ideal. 

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). 

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