Cubic Plus Association Equation Of State Research Articles

Prediction of solid solute solubility in supercritical CO2 with cosolvents using the CPA EoS

Supercritical carbon dioxide (scCO2) is widely used in separation processes applied to the food, chemistry, pharmaceutical and material industries. The knowledge of the solubility of solid solutes in scCO2, with or without cosolvents, is essential for the design and optimization of extraction, fractionation and purification processes. This work evaluates the accuracy of Cubic Plus Association equation of state (CPA-EoS) to predict the solubility of solutes in ternary and/or quaternary systems from the binary interaction parameters. The solubility of 12 solid solutes in scCO2 in presence of different organic cosolvents was investigated, totalizing 19 systems at pressures between 8 and 40 MPa, temperatures ranging from 308 K to 353 K and concentrations of cosolvent varying from 0.73 to 10 mol%. The overall average logarithmic deviation (ALD) between experimental and calculated data with CPA-EoS was 0.47, which is better than that obtained with PR + COSMOSAC previously reported in the literature. Furthermore, the effects of temperature, pressure and of cosolvent type and concentration on the solubility were well estimated with the CPA-EoS.

Experiment and prediction of water content of sour natural gas with an modified cubic plus association equation of state

Abstract In this work, new experimental value for water content in sour natural gas were reported. In addition, to predict the water content in sour natural gas, a modified cubic plus association equation of state (CPA-EoS) was also proposed. In this model, a new energy parameter a was proposed to make an accurate description of saturated liquid density. Additionally, a temperature dependent binary interaction parameter kij for six binary systems was also obtained. Lastly, a comparison between the prediction results of the modified CPA-EoS and the experimental data was presented, and the results showed that the modified CPA-EoS could predict the water content in sour natural gas with high accuracy, which has an AAD of 3.6722% with experimental data in literatures and an AAD of 1.946% for experimental data reported in this work.

Recent advances with association models for practical applications

ABSTRACTAssociation models like Cubic Plus Association (CPA) equation of state and other Statistical Associating Fluid Theory variants have found widespread use, especially over the recent 30 or so years, and this is not limited anymore to universities and researchers. Industry is beginning slowly to adopt such models for some applications and a few of the association models are now provided by commercial simulators. Association models account explicitly for hydrogen bonding (and other complex) phenomena, and for this reason, they are potentially more useful and more successful than traditional models like cubic equations of state and activity coefficient models. Still, for practical applications, all models are judged by their results and these depend on the availability of experimental data, the number and type of adjustable parameters and the performance of the models for phase equilibria and occasionally also for other properties. We will consider four case studies in this work which, will illustrate some of the capabilities and limitations of these association models in different applications. We will offer a ‘model developer’s’ point of view showing in several cases all stages of model development in order to illustrate what worked, what did not and how it was corrected (when possible). The ‘physics’ and ‘application’ aspects of the models will be in all cases discussed. All results will be shown with the CPA equation of state, although we expect that the overall conclusions will be the same for a wide range of association models.

Thermodynamic modeling of amino acid solutions: A new perspective on CPA EOS

Abstract The Cubic Plus Association (CPA) equation of state is applied to simultaneously calculate various thermodynamic properties of single aqueous solutions containing amino acids. Likewise, with a new perspective on CPA model, the highly dependency of amino acid solubility on the prevailing pH value is investigated bringing up dissociation/association equilibria. Hence, pure component parameters of 24 organic amino acids are fitted to density, solute activity coefficient, and water activity of their aqueous solutions at ambient conditions, and solely one temperature independent binary interaction parameter is used for each system. Also, two new equations are presented according to optimized parameters of amino acids. To prove the proficiency of applied models, solubility of aqueous solutions is predicted in binary systems at different temperatures and pH values taking into account the dissociation/association equilibria. Subsequently, the optimized parameters of CPA model are applied to reproduce the literature data for various thermodynamic properties including density and solute activity coefficient at other temperatures which range till 333 K. In addition, the effect of pressure on liquid density is checked, and the liquid density of mixed aqueous solutions containing two amino acids is evaluated. Eventually, it can be comprehended that not only the water activity and activity coefficients of aqueous amino acid solutions, but also liquid density and solubility of single solutions are reasonably calculated by CPA EOS over a wide range of temperatures and solute concentration applying dissociation/association equilibria.

Calculation of thermodynamic properties of water by the CPA equation of state

An appreciable amount of formation water exists inevitably in the porous media of reservoirs, but the existence of water is often neglected in the usual calculation of phase equilibrium. The commonly used equation of state is simple, but may have large deviations in estimating some thermodynamic properties. The existing equation of state, which has been modified, is not very suitable for the system containing polar substances (e.g. hydrocarbons, water, and alcohols). In this paper, the CPA (Cubic-Plus-Association) equation of state which considers both physical and association interactions between molecules was used to calculate the thermodynamic properties of water under the saturated and unsaturated states. Moreover, the disadvantages of the commonly used equation of state in the calculation were analyzed. The following results were obtained. First, the commonly used equation of state can be used to effectively calculate the saturated vapor pressure of water, but it presents certain differences in calculating water density and enthalpy, and the enthalpy calculation is not affected by volume modification. Second, the average absolute/relative deviations between the thermodynamic properties of water calculated by the CPA equation of state and the experimental data are approximately 1%. For the system containing polar substances, the CPA equation of state is preferred in calculating the thermodynamic properties. The accurate estimation of the thermodynamic properties of water is fundamental in identifying the fluid state in the water-bearing gas reservoirs, and it is of great significance in the development and production of such gas reservoirs.

Comments on “Prediction of the surface tension of binary liquid mixtures of associating compounds using the Cubic Plus Association (CPA) equation of state”

The modeling investigation of Hekayati and Raeissi [J. Mol. Liq. 231 (2017) 451–461] is reanalyzed and the calculations are repeated. It is found that this model contains some of the problems. It is known that the CPA EOS is suitable for water+alcohols. The first and biggest problem associated with this model is the big deviations of phase equilibrium by using CPA EOS. Furthermore, this model is only applicable for the surface tension of some of the liquid mixtures, and it is not reliable for the surface composition. Therefore, this model is not successful for a thermodynamic description of non-ideal mixtures.

Prediction of Gas Injection Effect on Asphaltene Precipitation Onset Using the Cubic and Cubic-Plus-Association Equations of State

Gas injection is a proven enhanced oil recovery technique. The gas injection changes the reservoir oil composition, temperature, and pressure conditions, which may result in asphaltene precipitation. In this work, we have used a modeling approach from the literature in order to predict asphaltene precipitation onset condition during gas injection. The modeling approach is used with the Soave–Redlich–Kwong, Soave–Redlich–Kwong-Plus-Huron–Vidal mixing rule and cubic-plus-association (CPA) equations of state (EoS). Six different reservoir fluids are studied with respect to asphaltene onset precipitation during nitrogen, hydrocarbon gas mixture, and carbon dioxide injection. It is also shown how to extend the modeling approach when the reservoir fluid is split into multiple pseudocomponents. It is observed that the modeling approach using any of the three models can predict the gas injection effect on asphaltene onset conditions. The CPA EoS is more reliable than the other two models, which are sensitive to a...

Modelling interfacial properties of binary and ternary liquid mixtures of tetrahydrofuran, 2-propanol and 2,2,4-trimethylpentane

ABSTRACTThe present modelling study has been dedicated to determining the interfacial properties of binary and ternary liquid mixtures made up of tetrahydrofuran, 2-propanol and 2,2,4-trimethylpentane. The variation of the temperature is from 288 to 308 K. By using both UNIFAC activity model and the fugacity model based on the cubic plus association (CPA) equation of state (EOS), a model based on the equality of chemical potentials in the liquid and the surface layer is utilised to describe the liquid–vapour interface of these liquid mixtures. The surface tension, composition and density are simultaneously predicted. The results of this model show that experimental surface tension data are in a good agreement with the predicted ones. The model using CPA EOS and molar volume has a better performance than the one uses the UNIFAC activity model.

Viscosities of Pure Ionic Liquids Using Combinations of Free Volume Theory or Friction Theory with the Cubic, the Cubic Plus Association, and the Perturbed-Chain Statistical Associating Fluid Theory Equations of State at High Pressures

In this study, the behaviors of viscosities of nine ionic liquids (ILs) over wide ranges of pressures and temperatures were determined. The investigated ILs belonged to the three imidazolium-based families of tetrafluoroborate, hexafluorophosphate, and bis[(trifluoromethyl)sulfonyl]imide. The two well-known cubic equations of state (EoS’s) of Peng–Robinson (PR) and the Soave–Redlich–Kwong (SRK), as well as the two more-sophisticated EoS’s of cubic plus association (CPA), and perturbed-chain statistical associating fluid theory (PC-SAFT), were each coupled with two well-known theoretical viscosity models, namely the friction theory and the free volume theory. Calculated results showed that the free volume model, coupled with PC-SAFT, has superior results in comparison to the free volume model with the CPA EoS. For the viscosity model of free volume, the studied cubic EoS’s did not give accurate results. When the friction model was used, the PC-SAFT EoS once more showed better accuracy than the CPA EoS; however, the CPA results in this model were quite close to that of the PC-SAFT, while the differences were great with the free volume model. One of the remarkable conclusions for the friction theory model was the unexpectedly reliable results that it gave with the cubic EoS’s. This suggests that when highly accurate results are not crucial, this combination can be the best choice because of the significantly greater simplicity of a cubic EoS over an association EoS.

Determination of asphaltene precipitation using a new CPA-based equation of state

ABSTRACTAsphaltene precipitation during natural depletion and miscible gas injection is a common problem in oilfields throughout the world. Therefore, predicting asphaltene phase behavior through thermodynamic modeling may help to control its precipitation and reduce the associated problems. In this work, a new modified cubic-plus-association (CPA) equation of state (EoS) was used to model asphaltene precipitation. This equation is based on a combination of a new physical part and an association term.The new physical part has an evolved cubic equation of state with a new attractive term in this work. The results of the new modification of CPA EoS were compared with the experimental data of two oil samples (oil samples 1 and 2) that belonged to Moradi et al. The results showed that this modified CPA EoS can predict asphaltene precipitation with good accuracy.

Prediction of the surface tension of binary liquid mixtures of associating compounds using the Cubic Plus Association (CPA) equation of state

Abstract Accurate knowledge of the surface tension of liquid mixtures is of considerable importance in the development of chemical processes that involve mass and heat transfer across phase interfaces. Despite the significant progress made in the development of advanced equations of state (EOS) for accurate representation of thermophysical properties, as well as sophisticated models for the thermodynamic equilibrium of highly non-ideal mixtures, they nonetheless have been to a large extent underrepresented in the prediction and correlation of the surface tension of such systems. In the current work, a modified version of the Butler equation is adopted alongside the Cubic Plus Association (CPA) EOS, with the objective of predicting and correlating the surface tension of binary liquid mixtures of associating compounds. In doing so, the experimental data of aqueous and non-aqueous mixtures of alcohols, glycols, acids, and phenol, comprised of 238 data points belonging to 18 binary mixtures are studied. It is shown that by incorporation of an association term based on the Wertheim's first-order thermodynamic perturbation theory, the CPA EOS can satisfactorily predict the values of surface tension with an AARD of only 9.78%, compared with deviations of 73.87% and 28.38% obtained for the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) EOSs, respectively. Also, a major advantage of the proposed model is its inherent capability to simultaneously estimate the composition of the surface phase alongside the mixture surface tension. In addition, with only one adjusted binary parameter, AARDs of 5.29%, 7.09%, and 11.02% are obtained for the correlation of the experimental data using the CPA, SRK, and PR EOSs, respectively.

New Three-Phase Multicomponent Compositional Model for Asphaltene Precipitation during CO2 Injection Using CPA-EOS

Numerical modeling of asphaltene precipitation in petroleum reservoirs is important in relation to possible precipitation around the wellbore in the producing well. Production from some reservoirs results in asphaltene precipitation in the wellbore region, leading to productivity loss and need for cleanup. Fluid injection even when there is asphaltene precipitation may not lead to injectivity loss. There are desirable processes in which precipitation of asphaltenes can lead to “in situ” upgrading of heavy oil recovery. Reservoir compositional models that are currently in use rely on cubic equations of state for asphaltene precipitation. The cubic equations, despite their relative reliability in describing reservoir fluids’ phase behavior, become unreliable in asphaltene-rich phase description. A number of noncubic equations of state have been introduced to overcome the shortcomings of cubic equations. The cubic-plus-association equation of state (CPA-EOS) is perhaps the method of choice in representing as...

The application of CPA-vdWP to the phase equilibrium modeling of methane-rich sour natural gas hydrates

To better application of the Cubic-Plus-Association equation of state (CPA-EoS) and van der Waals–Platteeuw (vdW-P) model to the phase equilibrium modeling of the methane-rich sour natural gas, an improved CPA-EoS (iCAP-EoS) with new correlations was proposed. In terms with the new energy parameter a, the saturated liquid density of pure component would be described accurately. Additionally, instead of the constant binary interaction parameter, a temperature-dependent binary interaction parameter was developed for calculating the corresponding binary system. As the results shown, the compositions of the fluid phase for the binary mixtures could be performed accurately with the help of the temperature-dependent binary interaction parameter. The predicted results of the proposed model, for both ternary systems and quaternary systems, were compared with the experimental data on the gas hydrate equilibrium dissociation pressures in good agreements with an AAD approximately to 2.28%. Additionally the results shown that the iCPA-vdWP model had an superior accuracy than the original CPA-EoS and vdW-P(CPA-vdWP) model. In high-acidic gas system, the presented model is also within the acceptable errors. Besides the potential application for phase equilibrium model in sour-gas hydrate based separation process is also obtained.

Prediction of water solubility in petroleum fractions and heavy crudes using cubic-plus-association equation of state (CPA-EoS)

Knowledge of the solubility of water in hydrocarbon fluids is essential for the design, simulation, and optimization of thermal oil recovery processes. This study proposes the use of cubic-plus-association equation of state (CPA-EoS) to predict the mole fraction of water in hydrocarbon fluids with specific gravity and molecular weight as the correlating parameters. Experimental data for water solubility in petroleum fractions, heavy oils, and bitumens was represented with an absolute average relative deviation (AARD) of less than 6.8%. The binary interaction parameter between the water and hydrocarbons was determined for different crudes. The proposed model can be applied to petroleum fractions, heavy oils, and bitumens with molecular weights between 140 and 678g/mol at temperatures up to 560K, which is the practical range of many industrial applications.

Modelling phase equilibria for acid gas mixtures using the CPA equation of state. Part VI. Multicomponent mixtures with glycols relevant to oil and gas and to liquid or supercritical CO2 transport applications

In this work the Cubic Plus Association (CPA) equation of state is applied to multicomponent mixtures containing CO2 with alkanes, water, and glycols. Various modelling approaches are used i.e. different association schemes for pure CO2 (assuming that it is a non-associating compound, or that it is a self-associating fluid with two, three or four association sites) and different possibilities for modelling mixtures of CO2 with other hydrogen bonding fluids (only use of one interaction parameter kij or assuming cross association interactions and obtaining the relevant parameters either via a combining rule or using an experimental value for the cross association energy). Initially, new binary interaction parameters were estimated for (CO2+glycol) binary mixtures. Having the binary parameters from the binary systems, the model was applied in a predictive way (i.e. no parameters were adjusted to data on ternary and multicomponent mixtures) to model the phase behaviour of ternary and quaternary systems with CO2 and glycols. It is concluded that CPA performs satisfactorily for most multicomponent systems considered. Some differences between the various modelling approaches are observed.This work is the last part of a series of studies, which aim to arrive in a single “engineering approach” for applying CPA to acid gas mixtures, without introducing significant changes to the model. An overall assessment, based also on the obtained results of this series (Tsivintzelis et al., 2010, 2011, 2014, 2015, 2015), which is based on an investigation of about 30 multicomponent systems containing acid gases, water, alcohols, glycols and hydrocarbons, reveals that assuming cross association (solvation) of CO2 with glycols, alcohols and water or alternatively considering CO2 to be a self-associating molecule (with three or four sites) are the better approaches which perform similarly and quite satisfactorily. However, the use of the former one (solvation), using whenever possible experimental values for the cross association energy, in all cases is recommended.

Cubic Plus Association Equation of State for Flow Assurance Projects

Thermodynamic hydrate inhibitors such as methanol, ethanol, (mono) ethylene glycol (MEG), and triethylene glycol (TEG) are widely used in the oil and gas industry. On modeling these compounds, we show here how the CPA equation of state was implemented in an in-house process simulator as an in-built model. To validate the implementation, we show calculations for binary systems containing hydrate inhibitors and water or hydrocarbons using the Cubic Plus Association (CPA) and Soave–Redlich–Kwong (SRK) equation of states, also comparing against experimental data. For streams containing natural gas and water, CPA was applied to calculate the loss of the inhibitor to the vapor phase as a function of temperature and pressure. Simulations of dehydration units using TEG were conducted, and the CPA results were compared with that of two commercial simulators which used their available thermodynamic packages for glycol applications, proving that the CPA calculations are in good agreement with these models and showin...

Modelling phase equilibria for acid gas mixtures using the CPA equation of state. Part V: Multicomponent mixtures containing CO2 and alcohols

The Cubic plus association (CPA) equation of state has been previously applied to a variety of binary systems containing CO2 with alkanes, water, alcohols and glycols as well as a few multicomponent mixtures (with triethylene glycol, water and methane). In this study, we evaluate the performance of CPA for ternary and multicomponent CO2 mixtures containing alcohols (methanol, ethanol or propanol) water and hydrocarbons. This work belongs to a series of studies aiming to arrive in a single “engineering approach” for applying CPA to acid gas mixtures, without introducing significant changes to the model. In this direction, CPA results were obtained using various approaches, i.e. different association schemes for pure CO2 (assuming that it is a non-associating compound, or that it is a self-associating fluid with two, three or four association sites) and different possibilities for modelling mixtures of CO2 with water and alcohols (only use of one interaction parameter kij or assuming cross-association interactions and obtaining the relevant parameters either via a combining rule or using an experimental value for the cross-association energy). It is concluded that CPA is a powerful model that can be used for predictions of multicomponent mixture properties using no adjustable parameters fitted to the multicomponent system data. The results are satisfactory and rather similar with most investigated approaches. However, an overall assessment, also based on the obtained results of this series of studies [Tsivintzelis et al. Fluid Phase Equilib. 306 (2011) 38–56, J. Chem. Eng. Data 59 (2014) 2955–2972, Fluid Phase Equilib. 397 (2015) 1–17], reveals that the best approaches are those where the cross-association (solvation) of CO2 with alcohols and water is explicitly accounted for or alternatively when CO2 is considered to be a self-associating molecule (with three or four sites). Furthermore, it is recommended to use the experimental values of the cross-association energy for CO2–water and CO2–alcohols.

High pressure measurement and CPA equation of state for solubility of carbon dioxide and hydrogen sulfide in 1-butyl-3-methylimidazolium acetate

Removal of acid gases such as CO2 and H2S from natural gas is essential for commercial, safety and environmental protection that demonstrate the importance of gas sweetening process. Ionic liquids (IL) have been highly demanded as a green solvent to remove acid gases from sour natural gas and capturing of CO2 from flue gases. In this work, the solubility of CO2 in 1-butyl-3-methylimidazolium acetate ([bmim][Ac]) is measured at temperatures (303.15, 328.15, 343.15)K and pressure range of (0.1 to 3.9)MPa. Moreover, the experiments are carried out for simultaneous measurements of (CO2+H2S) (70%+30% on a mole basis) solubility in the same ionic liquid at T=(303.15, 323.15, 343.15)K and a pressure range of (0.1 to 2.2)MPa. To model the solubility of acid gases in IL, both physical and chemical equilibria are applied so that the (vapour+liquid) equilibrium calculation is carried out through Cubic-Plus-Association (CPA) EoS. The reaction equilibrium thermodynamic model is used in liquid phase so that the chemical reaction is taking place between IL and acid gasses. The Henry’s and reaction equilibrium constants are obtained though optimization of the solubility data. Using CPA EOS, the pure parameters of [bmim][acetate] are optimised and consequently using these parameters, gas partial pressure calculation is performed for the (CO2+IL) and (CO2+H2S+IL) systems. For the (CO2+IL) system, the percent average absolute deviation (AAD%) of 4.83 is resulted and for the (H2S+CO2+IL) system the values of 18.8 and 13.7 are obtained for H2S and CO2, respectively.

Modeling phase equilibria for acid gas mixtures using the CPA equation of state. Part IV. Applications to mixtures of CO2 with alkanes

The thermodynamic properties of pure gaseous, liquid or supercritical CO2 and CO2 mixtures with hydrocarbons and other compounds such as water, alcohols, and glycols are very important in many processes in the oil and gas industry. Design of such processes requires use of accurate thermodynamic models, capable of predicting the complex phase behavior of multicomponent mixtures as well as their volumetric properties. In this direction, over the last several years, the cubic-plus-association (CPA) thermodynamic model has been successfully used for describing volumetric properties and phase behavior of several mixtures of interest in oil and gas industry.The purpose of this work is to evaluate the performance of CPA for CO2–alkane mixtures. CPA calculations were performed using different association schemes for CO2. Firstly, CO2 was treated as non-associating fluid and, at a second level, CO2 was treated as self associating fluid, using the 2B, 3B and 4C association schemes. A systematic investigation of the CPA performance in correlating the phase behavior of CO2–alkane mixtures has been performed. Mixtures with alkanes up to n-hexatriacontane (n-C36) were investigated and the corresponding binary interaction parameters were estimated with all modeling approaches for CO2. CPA parameters were previously available for alkanes up to n-eicosane (n-C20) and new parameters have been estimated for heavier alkanes based on DIPPR correlations. CPA correlations were compared with literature experimental data for three heavy alkanes and a satisfactory agreement was observed. The CPA performance is discussed including trends of the interaction parameters with chain length and comparison to literature studies.

Prediction of CO2 solubility in bitumen using the cubic-plus-association equation of state (CPA-EoS)

The ability to accurately predict the solubility of CO2 in bitumen is essential to the design of bitumen and heavy oil recovery processes. We applied the cubic-plus-association equation of state (CPA-EoS) to calculate the solubility of CO2 in bitumen and the Soave–Redlich–Kwong (SRK) equation of state was applied to treat the physical molecular interactions. The proposed thermodynamic model was verified against the experimental data for CO2 solubility in bitumen over wide ranges of temperature and pressure for four different bitumens from Alberta reservoirs. The CPA-EoS was able to predict the solubility with less deviation from the experimental data than the regular cubic equations of state and the statistical association fluid theory (SAFT). Our results suggest that the CPA-EoS is an effective method of conducting solubility calculations for solvent assisted bitumen recovery processes.