Cubic Plus Association Research Articles

Ten Years with the CPA (Cubic-Plus-Association) Equation of State. Part 1. Pure Compounds and Self-Associating Systems

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. Th...

Ten Years with the CPA (Cubic-Plus-Association) Equation of State. Part 2. Cross-Associating and Multicomponent 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.

Liquid−Liquid Equilibria for Binary and Ternary Systems Containing Glycols, Aromatic Hydrocarbons, and Water: Experimental Measurements and Modeling with the CPA EoS

Liquid−liquid equilibrium data of four binary glycol + aromatic hydrocarbon systems and three ternary systems containing water have been measured at atmospheric pressure. The measured systems are monoethylene glycol (MEG) + benzene or toluene, triethylene glycol (TEG) + benzene or toluene, MEG + water + benzene, MEG + water + toluene, and TEG + water + toluene. The binary systems are correlated with the Cubic-Plus-Association (CPA) equation of state while the ternary systems are predicted from interaction parameters obtained from the binary systems. Very satisfactory liquid−liquid equilibrium correlations are obtained for the binary systems using temperature-independent interaction parameters, while adequate predictions are achieved for multicomponent water + glycol + aromatic hydrocarbons systems when accounting for the solvation between the aromatic hydrocarbons and glycols or water.

Application of the Cubic-Plus-Association Equation of State to Mixtures with Polar Chemicals and High Pressures

The cubic-plus-association (CPA) equation of state has been previously applied to vapor−liquid, liquid−liquid, and solid−liquid equilibria of mixtures containing associating compounds (water, alcohols, glycols, acids, amines). Although some high-pressure applications have been presented, emphasis was given to low pressures and liquid−liquid equilibria. In this work, CPA is applied to two classes of mixtures containing polar chemicals for which high-pressure data are available: acetone-containing systems and dimethyl ether mixtures. They are of both scientific and industrial importance. Moreover, CPA is applied to high-pressure solid−liquid equilibria (SLE) for alcohol−alkane mixtures. In the case of acetone−hydrocarbon mixtures, satisfactory results are achieved if acetone is allowed to self-associate. Satisfactory high-pressure acetone−water vapor−liquid equilibrium (VLE) is obtained, comparable to conventional models such as MHV2. Very good results are also obtained for multicomponent vapor−liquid−liqu...

Application of the Cubic-Plus-Association (CPA) Equation of State to Complex Mixtures with Aromatic Hydrocarbons

The cubic-plus-association (CPA) equation of state is applied to phase equilibria of mixtures containing alcohols, glycols, water, and aromatic or olefinic hydrocarbons. Previously, CPA has been successfully used for mixtures containing various associating compounds (alcohols, glycols, amines, organic acids, and water) and aliphatic hydrocarbons. We show in this work that the model can be satisfactorily extended to complex vapor−liquid−liquid equilibria with aromatic or olefinic hydrocarbons. The solvation between aromatics/olefinics and polar compounds is accounted for. This is particularly important for mixtures containing water and glycols, but less so for mixtures with alcohols. For water/hydrocarbons, a single binary interaction parameter which accounts for the solvation is fitted to the experimental liquid−liquid equilibria (LLE) data. The interaction parameter of the physical term of the model (the Soave-Redlich-Kwong (SRK) equation of state) can be obtained from mixtures with aliphatic hydrocarbon...

Extension of the Cubic-plus-Association (CPA) Equation of State to Amines

The cubic-plus-association (CPA) equation of state has been extended to modeling mixtures containing amines. Special focus was given to primary and secondary amines, which are known to self-associate, thus forming hydrogen bonds in mixtures with alkanes. Pure-compound parameters have been determined from vapor pressure and liquid density data, but phase equilibrium data were also used as guidance for selecting the optimum sets among those which best represent the pure-compound properties. Diethylamine was modeled as a two-site molecule, whereas the two primary amines considered (methylamine, ethylamine) were modeled using both the two-site and three-site schemes. Both schemes perform overall equally well, when care is exercised in the parameter estimation, by giving more weight on the vapor pressures rather than the liquid densities. Thus, only results using the two-site scheme are shown. Excellent binary vapor−liquid equilibria have been obtained for amine + aliphatic hydrocarbons with a low value of the binary interaction parameter. Satisfactory results are obtained also for cross-associating systems with alcohols but less so with water, using, moreover, a rather high value of the interaction parameter.

Application of the Cubic-Plus-Association (CPA) Equation of State to Cross-Associating Systems

The cubic-plus-association (CPA) equation of state (EoS) is applied, using different combining rules, to vapor−liquid equilibria (VLE) and liquid−liquid equilibria (LLE) of alcohol−water systems. It is demonstrated that the Elliott combining rule (ECR) with a common temperature-independent interaction parameter provides very adequate VLE correlations over extended temperature and pressure ranges, yielding also a very satisfactory description of the azeotropic behavior. LLE of heavy alcohol−water systems is best described with the CR-1 combining rule and a single interaction parameter. Satisfactory predictions of multicomponent, multiphase equilibria of water−alcohol−alkane systems at various conditions are achieved using solely one interaction parameter per binary. A study of the dominant binary systems for the prediction of the multicomponent systems demonstrates that both the binary alcohol−water and alcohol−hydrocarbon systems are crucial for the prediction of the partition coefficients of alcohols. Finally, the CPA EoS combined with a model for the solid-complex formation can successfully describe solid−liquid equilibria of glycol/methanol−water systems including the description of the solid-complex phase, which is known to exist at intermediate concentrations.

Accuracy of the theoretical calculation of the Soret coefficient for water–ethanol mixtures in comparison with experimental data

The Soret coefficient of water–ethanol mixtures at one atmosphere and temperatures ranging from 20°C to 40°C has been studied in detail. Comparisons between the experimental data and predictions of existing theoretical models showed satisfactory agreement only for certain conditions. In order to properly model the behavior of water in the mixture, the thermodynamic properties of water–ethanol mixtures were calculated using the Cubic Plus Association (CPA) equation of state. Compared to the theoretical models of Haase, Kempers, Dougherty and Drickamer, the Firoozabadi model was found to perform much better in predicting the thermal diusion phenomena for water–alcohol mixtures.

Recent applications of the cubic-plus-association (CPA) equation of state to industrially important systems

The cubic-plus-association equation of state (CPA EoS) has been extended to phase equilibria of industrially important binary mixtures of alcohol–hydrocarbon, alcohol/glycol–water systems and mixtures with organic acids. The ability of the model to predict different types of equilibria was tested. Very satisfactory VLE and SLE prediction is achieved for alcohol–hydrocarbon systems, while the sensitivity of the LLE to the interaction parameter is demonstrated. It has been shown that CPA can perform VLE/LLE/SLE calculations in the case of alcohol–hydrocarbon binary systems with a single interaction parameter. Satisfactory SLE correlation of alcohol/glycol–water systems is achieved using a single interaction parameter over an extended temperature range. Moreover, satisfactory prediction was achieved for the multiphase equilibria of the mixture acetic acid–water–hexane based solely on binary interaction parameters.

Application of the CPA equation of state to organic acids

The CPA (Cubic-Plus-Association) equation of state has been extended to modeling of organic acids. We will focus in this work on formic, acetic, and propanoic acids due to their importance to the chemical and petrochemical industries. Organic acids, unlike many other associating compounds, have a strong tendency to dimerise in the vapor phase at normal condition resulting in strong non-ideal behavior, even at low pressures. Pure compound parameters have been determined from vapor pressure and liquid density data for the three acids. Among the three tested association schemes (one-site, two-site, and four-site), only the one-site association scheme describes satisfactorily the association in both the gas and the liquid phase. Second virial coefficients are predicted well with the proposed one-site model. Excellent binary VLE and acceptable LLE correlations have been obtained for acid + aliphatic hydrocarbons employing a low value of a binary interaction parameter.

Application of the CPA equation of state to glycol/hydrocarbons liquid–liquid equilibria

The Cubic Plus Association (CPA) equation of state is a thermodynamic model, which combines the well-known cubic SRK (Soave–Redlich–Kwong) equation of state and the association term proposed by Wertheim, typically employed in models like SAFT (statistical associating fluid theory). CPA has been shown in the past to be a successful model for phase equilibria calculations for systems containing water, hydrocarbons and alcohols. In this work, CPA is applied for the first time to liquid–liquid equilibria (LLE) for systems containing glycols and hydrocarbons. It is shown that excellent correlation is achieved with solely a single interaction parameter per binary system. The correlation procedure as well as the nature of the experimental data play a crucial role in the parameter estimation and they are thus extensively discussed.

Extension of the Cubic-Plus-Association Equation of State to Glycol−Water Cross-Associating Systems

The application of the cubic-plus-association (CPA) equation of state has been extended to mixtures containing cross-associating compounds such as glycols and water. In this case, combining rules are required in the association term of CPA for the cross-association energy and volume parameters. Different types of such combining rules have been suggested over the past years for association models such as statistical associating fluid theory. These are tested in this work for CPA in terms of their correlation and prediction capabilities for vapor−liquid equilibria of glycol−water systems. Comparisons with the Soave−Redlich−Kwong equation of state are also provided. It has been found that the arithmetic mean combining rule for the cross-association energy parameter and the geometric mean for the cross-association volume parameter provide overall the best results for cross-associating systems containing glycols and water. Moreover, preliminary results show that the CPA model can be used to predict multicomponent, multiphase equilibria for glycol−water−hydrocarbons based solely on binary interaction parameters.

Water/Hydrocarbon Phase Equilibria Using the Thermodynamic Perturbation Theory

Two equations of state, the cubic plus association (CPA) and the statistical associating fluid theory (SAFT), which account explicitly for the effect of hydrogen bonding on the thermodynamic properties of associating fluids using the perturbation theory of Wertheim (J. Stat. Phys. 1986, 42, 459, 477), are applied to predict the phase equilibrium of pure water, n-alkanes, and 1-alkenes as well as the low- and high-pressure phase equilibrium of water/hydrocarbon mixtures. The pure compound parameters for the two equations are estimated by fitting experimental vapor pressure and saturated liquid density data that cover a very wide temperature range from approximately the triple point to very close to the critical point. One temperature-independent binary interaction parameter is calculated for each of the mixtures examined. The analysis of the results shows that the increased complexity of SAFT over CPA does not offer any improvement in modeling highly nonideal fluid behavior, at least for the systems examined here.

Prediction of Phase Equilibria in Binary Aqueous Systems Containing Alkanes, Cycloalkanes, and Alkenes with the Cubic-plus-Association Equation of State

The cubic-plus-association (CPA) equation of state (EoS) is applied in this study to binary aqueous mixtures containing hydrocarbons. The CPA EoS combines the Soave−Redlich−Kwong (SRK) cubic equation of state for the physical part and perturbation theory for the chemical (association) part. Rigorous expressions for the contribution of the association term to the pressure and to the chemical potential, which do not include any derivatives of the mole fraction of molecules i not bonded at site A (XAi), are presented. Three different association models for water have been considered depending on the number of hydrogen bonding sites per water molecule: the two-, three-, and four-site models. Successful correlation of both vapor pressures and saturated liquid volumes is obtained with all three models. However, satisfactory correlation results of the mutual solubilities of water/aliphatic hydrocarbon systems are obtained only with the four-site model using a single interaction parameter (kij) in the attractive...