CPA (Cubic-Plus-Association) is an equation of state that is based on a combination of the Soave-Redlich-Kwong (SRK) equation with the association term of the Wertheim theory. The development of CPA started in 1995 as a research project funded by Shell (Amsterdam), and the model was first published in 1996. Since then, it has been successfully applied to a variety of complex phase equilibria, including mixtures containing alcohols, glycols, organic acids, water, and hydrocarbons. Focus has been placed on cases of industrial importance, e.g., systems with gas-hydrate inhibitors (methanol, glycols), glycol regeneration and gas dehydration units, oxygenate additives in gasoline, alcohol separation, etc. This manuscript, which is the first of a series of two papers, offers a review of previous applications and illustrates current focus areas related to the estimation of pure compound parameters, alcohol-hydrocarbon vapor-liquid equilibria (VLE) and solid-liquid equilibria (SLE), as well as aqueous systems. The capabilities and limitations of CPA are discussed and suggestions for extension of the model to systems not covered in this work are provided.

Two modifications to perturbed-chain statistical associating fluid theory are proposed which simplify the calculation of phase-equilibrium properties for nonassociating and associating systems, polymers, and simple molecules without loss of accuracy. A simple linear extrapolation scheme is proposed to obtain parameters for linear alkanes up to polyethylene. It is shown that computing times are greatly reduced using these modifications and compare favorably with traditional equations of state for nonassociating and associating systems.

In this second article of the review on the applications of the CPA (Cubic-Plus-Association) equation of state, the focus is placed on cross-associating systems. Various such mixtures are investigated, including (i) systems with two self-associating compounds (e.g., water−alcohol systems or glycols, mixtures with organic acids, or two alcohols) but also binaries with only one self-associating substance, where solvation is expected (e.g., CO2 or styrene with water). The method of accounting for cross-association (combining rules) and the association scheme of alcohols are investigated. Finally, the manuscript concludes with a summary of current capabilities and limitations of CPA and a list of future challenges.

A group-contribution (GC) method is coupled with the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) to predict its characteristic pure compound parameters. The estimation of group contributions for the parameters is based on a parameter database of 400 low-molecularweight compounds estimated by fitting experimental vapor pressures and liquid densities. The method has been successfully used for estimating the PC-SAFT parameters for common polymers. Specifically, using the new polymer parameters as calculated from the proposed GC scheme, the simplified PC-SAFT yields rather good predictions of polymer densities and gives promising modeling results of various binary polymer mixtures exhibiting both vaporsliquid and liquidsliquid phase equilibria. In summary, the data required for calculating polymer phase equilibria with the proposed method are the molecular structure of the polymer of interest in terms of functional groups and a single binary interaction parameter for accurate mixture calculations.

Monte Carlo simulation methods for determining fluid- and crystal-phase chemical potentials are used for the first time to calculate liquid water-methane hydrate-methane vapor phase equilibria from knowledge of atomistic interaction potentials alone. The water and methane molecules are modeled using the TIP4P/ice potential and a united-atom Lennard-Jones potential, respectively. The equilibrium calculation method for this system has three components, (i) thermodynamic integration from a supercritical ideal gas to obtain the fluid-phase chemical potentials, (ii) calculation of the chemical potential of the zero-occupancy hydrate system using thermodynamic integration from an Einstein crystal reference state, and (iii) thermodynamic integration to obtain the water and guest molecules' chemical potentials as a function of the hydrate occupancy. The three-phase equilibrium curve is calculated for pressures ranging from 20 to 500 bar and is shown to follow the Clapeyron behavior, in agreement with experiment; coexistence temperatures differ from the latter by 4-16 K in the pressure range studied. The enthalpy of dissociation extracted from the calculated P-T curve is within 2% of the experimental value at corresponding conditions. While computationally intensive, simulations such as these are essential to map the thermodynamically stable conditions for hydrate systems.

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Asphaltene precipitation has been one of the major problems in the oil industry, and its modeling is still believed to be a quite complex issue due to the different characteristics of thousands of heavy components in crude oil. There have been several attempts to model asphaltene precipitation using various equations of state and empirical models. In the past few years, association models based on CPA and SAFT equations of state have been found to be promising models for studies of asphaltene precipitation. In this work, we compare asphaltene precipitation results obtained from different modeling approaches based on CPA, PC-SAFT with association (PC-SAFT (WA)), and PC-SAFT without association (PC-SAFT (WOA)) models. While the modeling approaches for the CPA and PC-SAFT (WOA) have been described before in various literature, the modeling approach for PC-SAFT (WA) is proposed in this work. All three models require the same number of experimental data points (at least three upper onset pressures and one bubble pressure) in order to obtain model parameters. Different types of asphaltene phase behavior for different reservoir fluids, where asphaltene solubility either decreases or increases with temperature, and where asphaltene precipitation occurs during reservoir fluid depressurization, and the effect of gas injection are studied in order to investigate thoroughly the potential and reliability of the models. A total of five reservoir fluids and one model oil are studied with all three models. It is found that the modeling approach with the CPA EoS is more reliable compared to the other two approaches used in this study. The advantage of the association term to describe interactions between asphaltene and other stock tank oil (STO) heavy components is also evident from this study. The sensitivity of SARA data to the modeling approach based on PC-SAFT (WOA) is also analyzed. Finally, the relationship between the binary interaction parameter of the asphaltene–CO 2 pair and crossover temperature, below which asphaltene solubility increases in reservoir fluid, with CO 2 gas injection is also studied.