Chorng H. Twu

An internally consistent correlation for predicting the critical properties and molecular weights of petroleum and coal-tar liquids

Twu, C.H., 1984. An internally consistent correlation for predicting the critical properties and molecular weights of petroleum and coal-tar liquids. Fluid Phase Equilibria, 16: 137–150. The objective of this work was to use normal boiling points and specific gravities to develop simple but reliable and accurate methods for predicting the critical properties and molecular weights of petroleum and coal-tar liquids. The normal boiling points of the systems investigated range up to 1778 R and the specific gravities up to 1.436. This virtually covers the entire range of practical interest. The predictions of critical properties based on the above data show significant improvement over published correlations.

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.

A new generalized alpha function for a cubic equation of state Part 1. Peng-Robinson equation

Abstract A generalized temperature and acentric factor dependent function of the attractive term, called the alpha function, of the Peng-Robinson cubic equation of state (PR CEOS) is developed. The approach in this work allows the alpha function to become a linear function of the acentric factor at a constant reduced temperature, not a fourth or sixth order function as suggested by Soave and other researchers. The advantage of a linear function in the acentric factor is obvious in the extrapolation of the alpha function to heavy hydrocarbons, petroleum fractions, and gas condensates. The new generalized alpha function, when used with the PR CEOS, allows the accurate reproduction of the vapor pressure data from the triple point to the critical point for hydrocarbons. The new CEOS provides much more reliable and accurate vapor pressure predictions for light as well as heavy hydrocarbons than the original PR equation.

A new generalized alpha function for a cubic equation of state Part 2. Redlich-Kwong equation

Abstract The approach described in the previous paper (Twu, C.H., Coon, J.E. and Cunningham, J.R., 1994a. A new generalized alpha function for a cubic equation of state. Part 1. Peng-Robinson equation. Fluid Phase Equilibria, 105: 49–59) is applied to the Redlich-Kwong cubic equation of state (RK CEOS) to develop a new generalized alpha function for this equation. The new generalized alpha function for the RK CEOS reproduces the vapor pressure for hydrocarbons from the triple point to the critical point with almost identical accuracy to the generalized alpha function used for the Peng-Robinson CEOS in the previous paper. This indicates that the approach developed should be a general one, applicable to any cubic equation of state. The alpha function has been generalized in terms of the reduced temperature and acentric factor, so it can be used for any hydrocarbons and petroleum fractions, with no additional characterization to the standard methods required (Twu, 1984). The new alpha function is more appropriate for the RK CEOS than Soaves alpha function, which has been widely used in phase behavior calculations in the petroleum production and refinery industries over the last twenty years.

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.

A new cubic equation of state

Abstract Two-parameter cubic equations of state are analyzed and a new three-parameter cubic equation of state is proposed with the critical compressibility factor taken as substance dependent. An apparent critical compressibility factor is determined by optimizing the calculation of saturated liquid densities while the equality of fugacities along the saturation curve is imposed. The new cubic equation of state, combined with a previously proposed α function and mixing rule, proves to be a powerful equation for predicting properties of pure components and mixtures. The new equation not only improves volumetric property calculations relative to earlier efforts, but also achieves high degree of accuracy in the calculation of vapor-liquid equilibria for highly nonideal systems such as polar/nonpolar mixtures. Alcohol/hydrocarbon mixtures are used as an extreme test of the new equation of state.

Prediction of thermodynamic properties of normal paraffins using only normal boiling point

Abstract Twu, C.H., 1983. Prediction of thermodynamic properties of normal paraffins using only normal boiling point. Fluid Phase Equilibria, 11: 65–81. The main objective of this work is to develop a generalized equation of state for normal alkanes from only the normal boiling point. Since the equation of state for normal alkanes is found to be a function only of normal boiling-point temperature, the new correlation should be very useful for correlating departures of other systems from normal-alkane behavior using a normal alkane as a nonspherical reference. The equation of state represents accurately the vapor pressures, densities and enthalpy departures of the vapor, liquid and fluid states as a function only of boiling-point temperature over the entire range of interest for the normal paraffins methane (CH4) through n-hectane (C100H202).

A generalized vapor pressure equation for heavy hydrocarbons

Abstract Twu, C.H., Coon, J.E. and Cunningham, J.R., 1994. A generalized vapor pressure equation for heavy hydrocarbons. Fluid Phase Equilibria, 96: 19-31. Pitzers acentric factor is widely used in physical property estimations; one important area is that of generalized vapor pressure correlations. Since Pitzers acentric factor is defined in terms of the vapor pressure at a reduced temperature equal to 0.7, using this approach to generalize a vapor pressure equation gives excellent accuracy at reduced temperatures between 0.7 and 1.0, but predicts vapor pressures less accurately at lower reduced temperatures. To improve the vapor pressure prediction of hydrocarbons at low reduced temperatures, the definition of the acentric factor is re-examined and a modified acentric factor is proposed. Two sets of generalized vapor pressure equations are presented, with Pitzers acentric factor and the modified acentric factor, respectively, as the third corresponding states parameter. These two equations are applied from the triple point to the critical point. Both correlations give more accurate vapor pressure predictions than the Lee-Kesler (1975) 2 correlation, especially at low reduced temperatures, with the correlation using the modified acentric factor as the third parameter being the most accurate. Additionally, an internally consistent approach is proposed for estimating the normal boiling point, critical temperature and critical pressure of petroleum fractions using a single low temperature vapor pressure data point. The procedure proposed uses either correlation from this work and gives an accurate estimation of the normal boiling point and acentric factor for heavy petroleum fractions for use in equations of state.

A versatile liquid activity model for SRK, PR and a new cubic equation-of-state TST

Abstract The recent development of a new excess Gibbs function GE by Twu, Sim and Tassone allows infinite-pressure cubic of equations of state/AE (CEOS/AE) mixing rules to transition smoothly to the conventional van der Waals one-fluid mixing rules. The incorporation of their proposed GE model into a cubic equation-of-state allows an equation-of-state to describe both van der Waals fluids and highly non-ideal mixtures over a broad range of temperatures and pressures in a consistent and unified framework. We continue our work to develop a versatile excess Gibbs free energy function for zero-pressure CEOS/AE mixing rules, in addition to the infinite-pressure CEOS/AE mixing rules. An optimal two-parameter cubic equation-of-state TST (Twu–Sim–Tassone) has been found to allow better prediction of liquid densities for heavy hydrocarbons and polar components. The alpha function of the TST cubic equation-of-state is generalized here. The generalized alpha function is a linear function of the acentric factor at a constant reduced temperature, not a fourth-order or a sixth-order function as suggested by Soave and other researchers. The advantage of a linear function in the acentric factor is obvious in the extrapolation of the alpha function to heavy hydrocarbons, petroleum fractions, and gas condensates. The new generalized alpha function, when used with the TST, allows very accurate prediction of the vapor pressure from the triple point to the critical point of hydrocarbons. The performance of SRK, PR and TST is examined using the versatile excess Gibbs free energy function in the zero-pressure CEOS/AE mixing rules for the prediction of high pressure and high temperature phase equilibria of highly non-ideal systems.

An equation of state for carboxylic acids

Abstract A cubic equation of state (CEOS) has been extended to treat systems containing carboxylic acids by taking into account association. The incorporation of chemical theory for carboxylic acids into the cubic equation of state is based on the simple and elegant approach for pure components by Heidemann and Prausnitz (1976). Using the approach of Heidemann and Prausnitz, a monomer-dimer chemical equilibrium model is built into the cubic equation of state to take care of association of carboxylic acid molecules. A closed-form equation of state, which is in terms of monomer parameters and the chemical equilibrium constant, is derived. The determination of the pure monomer parameters of an associating component is a crucial step in the application of an equation of state for associated systems. An internally consistent method is proposed to determine the pure monomer parameters for the associated component. The method reproduces the critical point and the saturated vapor pressure of the associated component accurately.