Redlich Kwong mixing rules

In their original paper, Redlich and Kwong also used the mixing rules given by Eqs. (17) and (18) in addition, however, they made the important simplification a,j = (OjOj)112. This simplification may introduce appreciable error (C3b, J2), and we do not use it here. Instead, we first rewrite Eq. (15) in the form... 

Redlich-Kwong Equation of State — Peng-Robinson Equation of State—Mixing Rules... 

With the use of these guidelines, we now derive the van der Waals mixing rules for the Redlich-Kwong and the Peng-Robinson equations of state. Similar procedure can be used for deriving the van der Waals mixing rules for other equations of state. 

Mixing Rules for the Redlich-Kwonq Equation of State. The Redlich-Kwong equation of state, Equation 6, can be written in the following form ... 

These mixing rules, when joined with the Redlich-Kwong equation of state, will constitute the Redlich-Kwong equation of state for mixtures that is consistent with the statistical mechanical basis of the van der Waals mixing rules. 

The application of cubic equations of state to mixtures requires expression of the equation-of-state parameters as functions of composition. No exact theory like that for the virial coefficients prescribes this composition dependence, and empirical mixing rules provide approximate relationships. The mixing rules that have found general favor for the Redlich/Kwong equation are ... 

The densities of CO2 and ethane were calculated using multi-parameter EOS [17,18], which are accurate near the critical point. The parameters 22 and 33 were obtained from solubility data in binary mixtures (solid/SC fluid and solid/SC entrainer). The Soave-Redlich-Kwong [20] EOS was employed in combination with the classical van der Waals mixing rules as in our previous paper [5]. 

The composition dependence of the parameter Z i3 was calculated for the mixture SC CO2 and SC ethane at T = 350 K and P = 10 MPa. For this purpose, precise PVT data [30] were treated using the Soave-Redlich-Kwong [20] EOS and the classical van der Waals mixing rules. The binary interaction parameter qi2 was calculated by minimizing the sum yi.caic 2 where... 

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. 

Calculate the enthalpy departure of the mixture in Example 1.14 at the same conditions using the Redlich-Kwong equation, but with the mixing rules of Equation 1.15 instead of Kay s rules. Assume = 0. 

The equation performs as well as or better than the Soave-Redlich-Kwong in all cases tested and shows its greatest advantages in the prediction of liquid phase densities.47 The constants, mixing rules, and the expressions for the fugacities and enthalpies for this equation of state are given in Table 14-7. 

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). 

Liquid mixture at elevated pressure that contains only hydrocarbons, nitrogen, o.xy-gen, carbon dioxide, and/or other inorganic gases (but not HF) Use equation of state, such as Peng-Robinson or Soave-Redlich-Kwong with van der Waals one-fiuid mixing rules (see Sec. 9.4). 

Derive the expression for the fugacity coefficient of the Soave-Redlich-Kwong equation of state (Eq. 4.4-lb) with the van der Waals one-fluid mixing and combining rules of Eqs. 9.4-8 and 9.4-9. 

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 ... 

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. ... 

A better approach is to start from a particular model for g (T, P, x) A ), such as the Porter, Margules, or Wilson models introduced in 5.6. Here the A) are the model parameters, whose values are usually obtained by fits to phase-equilibrium data. We then select a PvTx model often a cubic is used. In this discussion, we consider the Redlich-Kwong equation ( 4.5.8). This model contains parameters a, b that depend on composition via some mixing rules ( 4.5.12). Our strategy is to find those mixing rules by matching the model to given by the PvTx equation. 

One of the first implementations of the above procedure was that by Huron and Vidal [8]. They retained the simple mixing rule for the Redlich-Kwong parameter b,... 

Under different assumptions, Wong and Sandler [9] used the Redlich-Kwong equation with the mixing rule (6.5.4) to obtain a quadratic rule,... 

To address this issue, we use the Redlich-Kwong equation of state (8.2.1) with the simple mixing rules from 4.5.12,... 

Use the Redlich-Kwong equation and the mixing rules given in 8.4.4 to compute the spinodal and line of incipient mechanical instability for equimolar mixtures of carbon dioxide and n-butane. Plot your curves on a Pv diagram. (You do not have to compute the saturation curves, since methods for doing so are not presented until Chapter 10.)... 

Write a computer program that determines the stability of a one-phase binary mixture at a proposed T, P, and Xj. Use the Redlich-Kwong equation of state with the simple mixing rules given in 8.4.4. Test your program by applying it to the situation described in 8.4.4. 

The conditions (9.3.23) and (9.3.24) represent two algebraic equations that can be solved for two of the three unknowns (T., P, and where is mole fraction of methane). The equations are nonlinear in all three unknowns and must be solved simultaneously by trial. We found the critical lines by setting a value for T., then solving (9.3.23) and (9.3.24) for and x . The calculations were performed using pure-component critical properties characteristic of methane (T. = 190.6 K, P = 46 bar) and ammonia (T = 405.6 K, P = 112.8 bar). Mixtures of methane and ammonia are known to be members of class D however, we caution that the critical lines provided by the Redlich-Kwong equation with our simple mixing rules are only semiqualitative. But since our intent is only to show qualitative behavior, this simple model is adequate. 

Write a computer program that implements the bubble-P algorithm developed in Problem 11.1. Use the Redlich-Kwong equation with mixing rules from 8.4.4. To compute phase volumes, the cubic is best solved analytically via Cardan s method (Appendix C). 

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