A combination of multi-fluid mixture models with COSMO-SAC

A theoretically based departure function for multi-fluid mixture models

Cubic Plus GE (CPGE): Cubic equation of state with simple mixing rule plus excess Gibbs energy that satisfies low-density condition

Van der waals mixing rules for cubic equations of state. Applications for supercritical fluid extraction modelling

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

Equations of state: From the ideas of van der Waals to association theories

Phase equilibria of binary Lennard-Jones mixtures with cubic equations of state

A new concept for the development of mixing rules for cubic equations of state consistent with statistical mechanical theory of the van der Waals mixing rules is introduced. Utility of this concept is illustrated by its application to the Redlich-Kwong (RK) and the Peng-Robinson (PR) equations of state. The resulting mixing rules for the Redlich-Kwong and the Peng-Robinson equations of state are tested through prediction of solubility of heavy solids in supercritical fluids and prediction of phase behavior of binary mixtures of hydrocarbons and nonhydrocarbons.

A new mixing rule developed for cubic equations of state equates the excess Helmholtz free energy at infinite pressure from an equation of state to that from an activity coefficient model. Use of the Helmholtz free energy insures that the second virial coefficient calculated from the equation of state has a quadratic composition dependence, as required by statistical mechanics. Consequently, this mixing rule produces the correct low‐ and high‐density limits without being density‐dependent.As a test, the mixing rule is used for ternary mixtures of cyclohexane + benzene + water, ethanol + benzene + water and carbon dioxide + n‐propane + water, and all the constituent binaries. The new mixing rule and a simple cubic equation of state can be used for the accurate correlation of vapor‐liquid and liquid‐liquid equilibria for binary mixtures. Using the parameters obtained from binary systems, the phase behavior of ternary mixtures can be predicted. Also, unlike previous empirical mixing rules, this theoretically based mixing rule is equally applicable and accurate for simple mixtures containing hydrocarbons and inorganic gases and mixtures containing polar, aromatic and associating species over a wide range of pressures. This mixing rule makes it possible to use a single equation of state model with equal accuracy for mixtures usually described by equations of state and for those traditionally described by activity coefficient models. It is the correct bridge between these two classes of models.

Assessment of the liquid mixture density effect on the prediction of supercritical carbon dioxide volume expansion of organic solvents by Peng-Robinson equation of state

A cubic equation of state with a new alpha function and a new mixing rule

Modeling of solid–supercritical fluid phase equilibria with a cubic equation of state— Gex model

On the mixing rules matter: The VLE predictions for binary systems

Adsorption equilibrium models are essential for optimizing coalbed methane (CBM) production and carbon dioxide (CO2) sequestration processes. Although numerous frameworks are available for describing the adsorption phenomenon, two-dimensional (2-D) equations of state (EOS) offer distinct advantages in modeling supercritical, high-pressure adsorption systems. Current applications of 2-D EOS typically involve regressions of data on individual adsorption isotherms to determine the temperature-dependent EOS parameters (, , k). For the EOS to have maximum utility, generalized correlations for these parameters are needed. Such generalizations would facilitate (1) correlation of adsorption data over a range of operating temperatures and (2) a priori predictions of adsorption behavior. Accordingly, we have focused on developing new correlations for the 2-D EOS parameters that yield precise representations and accurate predictions of supercritical, pure-gas adsorption encountered in CBM recovery and CO2 sequestration. Furthermore, we have extended the 2-D EOS to adsorption from gas mixtures by incorporating mixing rules to describe the composition dependence of the model parameters. In this work, we have used the 2-D Peng-Robinson (PR) EOS to illustrate the proposed method for determining the EOS pure-fluid parameters and to demonstrate the 2-D EOS capability to represent and predict pure-gas adsorption of CBM gases (methane, nitrogen, and CO2) on carbon adsorbents. Experimental adsorption measurements, including both activated carbons and coals (both dry and wet), were used to evaluate the efficacy of this approach. The new correlations for the 2-D EOS parameters appear effective in modeling pure-gas adsorption on carbon matrices at supercritical and near-critical conditions. Using the new parameter correlations, the 2-D PR EOS can represent adsorption on activated carbon and coals within their expected experimental uncertainties. Specifically, the 2-D EOS parameter correlations can represent the pure-gas adsorption over a range of temperatures with an average absolute deviation (AAD) of 2.4% for activated carbons and an AAD of 4.4% for coals. Furthermore, the new generalized parameter correlations, expressed in terms of accessible adsorbate and adsorbent properties, can predict (1) pure-gas adsorption on activated carbons with an AAD of 9% (within three times the expected experimental uncertainties) and (2) binary and ternary gas adsorption within three times the experimental uncertainties, on average.

Two equations from the two classes of thermodynamic functions, in terms of their simplicity and complexity of functional forms, are compared, applying them in prediction of second-order derivative properties such as sound velocity and isobaric and isochoric properties of hydrocarbon fluids. Peng-Robinson (PR) equation of state, from the simple class, and SAFT-BACK equation from the complex family are selected for this purpose and their results are compared in both super and subcritical regions. The results reveal the superiority of the SAFT-BACK equation over the PR equation of state, especially at the liquid region or the high-density conditions. At low pressures (low densities) similar results are observed through both approaches. These results imply the inaccuracy of the cubic equations of state in prediction of second derivative properties, and moreover, suggest the prediction of sound velocity as a consistency test for any cubic equation of state.

Cubic equations of state (EOS), such as the Peng-Robinson EOS, are routinely used by the oil and gas industry for the design of recovery and processing operations of gases at high pressures. Nonetheless, many non-cubic equations of state, derived from statistical thermodynamics and with solid theoretical basis, have been proposed in recent years. Among them, EOS of the SAFT-family are possibly those with widest acceptance. In this work, we compare the performance of the Peng-Robinson and PC-SAFT EOS in the calculation of dew points, bubble points, and critical points of natural gases. Binary interaction parameters in both EOS were set equal to zero in all calculations to test the predictive capability of the models. Calculations were performed for 19 synthetic natural gases for which experimental data are available in literature. For most mixtures, predictions of the PC-SAFT EOS are in better agreement with the experimental data.