David Bluck

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

Twu C.H., Bluck D., Cunningham J.R. and Coon J.E., 1991. A cubic equation of state with a new alpha function and a new mixing rule. Fluid Phase Equilibria, 69: 33-50. A new temperature-dependent function (α) for a cubic equation of state is proposed. The new α function used in the cubic equation of state not only correlates the vapor pressures of pure components, but extrapolates correctly to the supercritical region. The new cubic equation of state has been used to accurately describe the vapor pressure and liquid heat capacity for over 1000 chemical components. The accuracy of reproducing the vapor pressure from the triple point to the critical point is generally within the experimental error. A new mixing rule has also been developed for correlating phase equilibrium data. The mixing rule can reproduce the activity coefficients in the infinite dilution region as well as model phase behavior throughout the finite range of concentration. This mixing rule allows the accurate representation of polar/non-polar systems and can be extended to multicomponent systems. The cubic equation of state with the proposed new α function and the new mixing rule is applicable to important systems encountered in industrial practice.

CEOS/AE mixing rules from infinite pressure to zero pressure and then to no reference pressure

Abstract A CEOS/AE mixing rule with no reference pressure is presented. An approach is developed that shows that the excess Helmholtz free energy at any pressure relative to its value for a van der Waals fluid is equivalent to the same relative value of the excess Gibbs energy at the same pressure. This approach allows the mixing rule to incorporate a GE model at any pressure and temperature without requiring any additional binary interaction parameters or causing any thermodynamic inconsistency. The methodology of developing the no-reference-pressure mixing rule avoids the common assumption of constant excess Helmholtz free energy with respect to pressure that is often made for the infinite pressure approach and extends the range of solution of the liquid volume to the critical point for the zero-pressure approach. The mixing rule is density (temperature) dependent in an explicit form. Because of this density function, the mixing rule reproduces accurately the incorporated GE model.

Equations of state using an extended Twu-Coon mixing rule incorporating UNIFAC for high temperature and high pressure phase equilibrium predictions

A mixing rule recently developed by Twu and Coon [C.H. Twu, J.E. Coon, CEOS/AE mixing rules constrained by the vdw mixing rule and the second virial coefficient, AIChE J. 42 (1996) 3212–3222 is extended to incorporate the UNIFAC group contribution method into an equation of state for the prediction of phase behavior of highly non-ideal systems over wide ranges of temperature and pressure. The mixing rule developed by Twu and Coon reduces to the van der Waals mixing rule. The Helmholtz excess free energy function with respect to a van der Waals fluid at infinite pressure has been related rigorously to the Helmholtz excess free energy at zero pressure. This extension of the Twu-Coon Mixing Rule goes gracefully from the classical van der Waals one-fluid mixing rule for non-polar fluids needed in the refining and gas processing industries to a mixing rule combining excess free energy models at low pressure with equations of state for the strongly polar systems found in the chemical industries. When the UNIFAC group contribution method is incorporated, the mixing rule becomes totally predictive. The completely predictive equation of state is shown to give accurate results for systems for which the UNIFAC model is in agreement with the experimental activity coefficients at low pressure. The UNIFAC-incorporated mixing rule provides a simple way to extend the UNIFAC group contribution method to high temperatures and pressures.

A zero-pressure cubic equation of state mixing rule for predicting high pressure phase equilibria using infinite dilution activity coefficients at low temperature

Abstract The infinite dilution activity coefficients (γi∞) of a solute in a solvent are important data in process separation calculations. These values reflect the degree of non-ideal solution behavior of the solute in the solvent. This paper investigates the use of infinite dilution activity coefficients in cubic equation of state mixing rules for the prediction of phase behavior at high pressures. A mixing rule recently developed by Twu and Coon has been extended from infinite pressure to zero pressure. The methodology for extending the infinite-pressure Twu–Coon mixing rule was developed so that the zero-pressure Twu–Coon mixing rule reproduces the excess Gibbs free energy, as well as liquid activity coefficients of any activity models, with extremely high accuracy without requiring any additional binary interaction parameters. We compare the performance of this new mixing rule with the MHV1 and Wong–Sandler mixing rules for its ability to use γi∞ in the prediction of high pressure phase behavior for strongly non-ideal systems.

A cubic equation of state : relation between binary interaction parameters and infinite dilution activity coefficients

Abstract Twu, C.H., Bluck, D., Cunningham, J.R. and Coon, J.E., 1992. A cubic equation of state: relation between binary interaction parameters and infinite dilution activity coefficients. Fluid Phase Equilibria, 72: 25-39. A modified Redlich-Kwong cubic equation of state (CEOS) is applied to the calculation of phase equilibria for highly non-ideal systems. Owing to the new mixing rule used in the CEOS, the physical meaning of the binary interaction parameters in the CEOS can be explained in terms of infinite dilution activity coefficients. Equations relating the binary interaction parameters in the equation of state to the infinite dilution activity coefficients are presented. A robust technique is proposed for obtaining the interaction parameters without regressing PTxy data. The equation of state with the binary interaction parameters derived from the infinite dilution activity coefficients is suitable for the process design of separation processes, especially for environmental concerns, which require prediction of high purity products. The results of calculations are compared with experimental PTxy data.

Connection between zero-pressure mixing rules and infinite-pressure mixing rules

Abstract Infinite-pressure mixing rules and zero-pressure mixing rules are related by a very simple equation. The zero-pressure models and the infinite-pressure models are interchangeable through this connection. This paper will show how to convert the Huron–Vidal infinite-pressure mixing rule to a zero-pressure mixing rule, or vice versa. The MHV1 zero-pressure mixing rule will be reformulated to satisfy second virial coefficient constraint. The Twu–Coon and Wong–Sandler infinite-pressure mixing rules will be modified to improve their accuracy for reproducing the incorporated G E model. A simplification of the Twu–Coon–Bluck [TCB( r )] zero-pressure mixing rule will be presented. The MHV1 mixing rule will be shown to be a special case of TCB( r ).

Static and dynamic simulation of NOx absorption tower based on a hybrid kinetic-equilibrium reaction model

Abstract The NO x absorption process is very complex with over forty reactions having been identified. The NO x absorption tower is a key operation in the production of nitric acid. In this work, we proposed a simple yet theoretically sound reaction model consisting of only four reactions (one kinetic and three equilibrium). We apply the Soave-Redlich- Kwong equation of state and NRTL activity-coefficient model, respectively, to account for the thermodynamic vapor and liquid non-idealities for the NO x -HNO 3 -O 2 -N 2 -H 2 O system. Based on the reaction model and thermodynamic framework in this work, the NO x absorption tower has been simulated statically by SimSci PRO/II and dynamically by SimSci DYNSIM. The simulation results agree well with the reference data. For the dynamic simulation, the simulation speed is well above the stringent speed requirement by a special dynamic application. In addition, the simulation of the tower azeotropic phenomenon has been discussed.