Plus Association Equation Of State Research Articles

Modeling of the Mixture Critical Locus with a Modified Cubic Plus Association Equation of State: Water, Alkanols, Amines, and Alkanes

In a phase envelope, an adequate description of the critical point is of high importance. It identifies the conditions where the bubble and dew curves meet, and where the nature of the single phase region outside the phase envelope changes. The knowledge of the mixture critical point is relevant to preventing production and transport problems, as well as to optimizing near-critical and supercritical processes. A modified cubic plus association (CPA) model was recently shown to accurately describe the vapor–liquid equilibrium (VLE) critical temperatures and pressures of pure compounds. The model is usually fitted to pure component data between 0.45Tr and 0.85Tr, while forcing the correct description of both Tc and Pc. Here, the performance of the model is evaluated for mixtures. Interaction parameters are regressed from VLE/liquid–liquid equilibrium (LLE) data at lower temperatures. Accurate results, for binary and ternary mixtures, were obtained. These results concern mainly mixtures containing, water, al...

Solubility of caffeic acid in CO2 + ethanol: Experimental and predicted data using Cubic Plus Association Equation of State

This work evaluated the solubility of caffeic acid (CA) in mixtures of supercritical carbon dioxide (scCO2) and ethanol at different temperatures (313, 323 and 333 K), pressures (20, 30 and 40 MPa) and concentrations of ethanol (2.2, 5.4 and 10.2 mol%). The Soave-Redlich-Kwong and Cubic Plus Association (CPA) equations of state were used to correlate the binary mixture data and to predict the ternary system data. CA solubility in ethanol is approximately 106 times higher than its solubility in pure scCO2. By using 10.2 mol% ethanol in scCO2, CA solubility increased 30,000 times at 313 K and 20 MPa. Both models provided reasonable descriptions of the experimental data for the binary systems. However, CPA-EoS can better describe the strong interactions between acid molecules and ethanol, and can predict that the addition of small amounts of ethanol to scCO2 provides a large increase in CA solubility.

Improved Prediction of Water Properties and Phase Equilibria with a Modified Cubic Plus Association Equation of State

One of the major challenges of an equation of state lies in the description of water and aqueous systems. Its abundance and unique properties turn water into one of the most important molecules in the industry. However, because of these peculiar characteristics, its modeling is far more complex than for any other common solvent. In this work, a modified cubic plus association (CPA) model, which includes the correct description of the pure component critical temperature and critical pressure, is expanded to water and its systems. A brief analysis of the predicted water purity properties is conducted, comparing those to a previous version of the model. Results for a group of binary systems, including liquid–liquid equilibria with alkanes and alcohols, highlighting their minima in aqueous solubility, and gas solubility in water/water solubility in gas, are also presented. Finally, ternary and multicomponent systems of water + hydrocarbons and water + polar compound + hydrocarbons are also modeled and discussed.

Modeling vapor-liquid equilibria of mixtures of SO2 and deep eutectic solvents using the CPA-NRTL and CPA-UNIQUAC models

In this study, the thermodynamic modeling of SO2 solubilities in 14 Deep Eutectic Solvents (DESs) of different nature was investigated for the first time in literature. This is a challenging mixture to model. The thermodynamic modeling approach of γ−ϕ for vapor-liquid equilibria was used. The Cubic Plus Association Equation of State (CPA EoS) was used to represent the vapor phase and the NRTL and UNIQUAC models were both investigated for the liquid phase. The DESs were considered as pseudo-components and their physical properties calculated. Both the CPA-UNIQUAC and CPA-NRTL models showed good agreement with experimental values, with total AARD% of 2.9% and 3.1%, respectively. CPA-UNIQUAC shows slightly better results, while CPA-NRTL is a simpler model. In addition to the γ−ϕ approach, the ϕ−ϕ approach was investigated for all of the systems. However, the results were not reliable, even when incorporating binary interaction parameters as adjustable parameters in the model.

Modeling the Phase Behavior of Carbon Dioxide Solubility in Deep Eutectic Solvents with the Cubic Plus Association Equation of State

The thermodynamic modeling of a new generation of solvents, deep eutectic solvents (DESs) is investigated. Because hydrogen bonding is a dominant molecular interaction, the cubic plus association (CPA) equation of state (EoS) was chosen for modeling. This is the first study to model DES density and carbon dioxide solubility using CPA. Fifteen different DESs were chosen which have density data, as well as CO2 solubility data, available in the literature over wide temperature and pressure ranges. To date, this is the most extended and global databank of DESs which has been employed in relation to a complex EoS. The density data were used to optimize the CPA parameters. The CPA EoS proved to be capable of accurately modeling pure DES densities. The validity of the optimized CPA parameters was further validated with literature density data of mixtures of DES + water, which were estimated successfully by a purely predictive procedure. To calculate CO2 solubility in DES, all the possible association schemes of ...

Modeling of Asphaltene Precipitation from Crude Oil with the Cubic Plus Association Equation of State

In this study, different modeling approaches using the Cubic Plus Association (CPA) equation of state (EoS) are developed to calculate the asphaltene precipitation onset condition and asphaltene yield from degassed crude oil during the addition of n-paraffin. A single model parameter is fitted to calculate the asphaltene onset condition during the addition of different n-paraffin precipitants (n-pentane to n-hexadecane). Three parameters per precipitant are fitted to calculate the asphaltene yield during the addition of the precipitant. The results obtained from the model are compared with the experimental data for eight different crude oils. Results were also obtained for seven crudes using the Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) EoS based approach described in the literature. The CPA EoS based approaches treat the asphaltene fraction as an associating component whereas the PC-SAFT EoS based approach does not. A comparison between the approaches shows that the CPA EoS based app...

Modified quadrupole Cubic Plus Association Equation of State (mqCPA EoS) for thermodynamic modeling of polymer-supercritical CO2 systems

In this work, a modified quadrupole Cubic Plus Association Equation of State (mqCPA EoS) is used to model the cloud point pressure of polymers-supercritical carbon dioxide (scCO2) systems. The residual Helmholtz free energy is expressed as sum of SRK and Quadrupole terms. We used the experimental data of the cloud point pressure for the different copolymer-scCO2 systems to investigate the capability of the present model through liquid-liquid equilibrium calculations. Using mqCPA EoS, the cloud point pressures of the polymer-scCO2 systems for the three types of poly(lactic acid) (PLA), the three types of poly(1-O-(vinyloxy) ethyl-2,3,4,6-tetra-O-acetyl-β-d-glucopyranoside) (P(AcGlcVE) and seven types of poly(vinyl acetate-alt-dibutyl maleate) (PVAc-alt-PDBM) were calculated. These copolymers have different molecular structures, end groups and molar masses. Moreover, we applied both PC-SAFT and PCP-SAFT equations of state for the same polymer-scCO2 systems and their results were compared to those obtained by mqCPA EoS that showed in overall the both PCP-SAFT and mqCPA EoSs give better results with very good accuracy.

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...

Support vector machine and CPA EoS for the prediction of high-pressure liquid densities of normal alkanols

The already numerous industrial applications of alcohols is continuously growing to even higher significance. Accurate estimations of the physical properties of various alcohols within wide ranges of pressures and temperatures are necessary in the design and optimum operation of such processes. In this study, high-pressure liquid densities of the first six members of the normal alkanol family were predicted as a function of temperature and pressure. This was done using two different approaches: The computer method of support vector machine (SVM) and the thermodynamic model of Cubic Plus Association Equation of State (CPA EoS). A total of 2979 experimental data on alcohol density, also covering high pressure and high temperature conditions, were obtained from literature. The results of the calculations show that the value of AARD% for all of the 2979 data was 0.06% for the SVM computer model and 1.36% for the thermodynamic CPA model.

Phase equilibria of CO2+N2 and CO2+CH4 clathrate hydrates: Experimental measurements and thermodynamic modelling

Experimental dissociation conditions for clathrate hydrates of carbon dioxide+nitrogen are reported in the (278.1 to 285.3) K and (3.24 to 29.92) MPa ranges, which were measured using an isochoric pressure search method. The relative molar composition of carbon dioxide and nitrogen in the feed gas, varying between (0.271 and 0.812), were measured by gas chromatography technique. A thermodynamic model based on the Cubic Plus Association equation of state for fluid phases combined with the van der Waals and Platteeuw solid solution theory for the hydrate phase is presented herein. The dissociation data generated in this work along with the experimental data reported in the literature for carbon dioxide+nitrogen and carbon dioxide+methane hydrates are compared with the results of this model and also with the predictions of two other thermodynamic models, namely HWHYD and CSMGem. A discussion is made about the deviations observed between experimental and predictions.

Modeling CO2 Solubility in Aqueous N-methyldiethanolamine Solution by Electrolyte Modified Peng–Robinson Plus Association Equation of State

In the present work, the electrolyte equation of state proposed by Huttenhuis et al. [Fluid Phase Equilibria2008, 264, 99–112] is improved to describe the solubility of carbon dioxide in aqueous solutions of N-methyldiethanolamine (MDEA) in wide ranges of concentration, pressure, temperature, and acid gas loading. The molecular part of the equation is based on the modified Peng–Robinson Plus Association equation of state (mPR-CPA EoS) proposed by Zoghi et al. [J. Pet. Sci. Eng.2011, 78, 109–118]. To account for the presence of ions, three contributions are added to the mPR-CPA EoS to describe short-range interactions, long-range interactions, and the Born term. The same EoS is used for both vapor and liquid phases. A consistent database including 567 experimental data points is utilized in this study. In the first step of modeling the parameters of the EoS have been tuned by regression to the vapor pressure and saturated liquid density experimental data for associating pure components (i.e., water and MDEA). In the next step, the vapor–liquid equilibrium calculations were carried out for adjusting the molecular binary interaction parameters. These parameters are optimized for binary subsystems including H2O–CO2, CO2–MDEA, and H2O–MDEA. Finally, the binary interaction parameters between ionic and molecular species are tuned via the simultaneous vapor–liquid and chemical reaction equilibrium calculations. The results show that the proposed model is able to improve the precision of prediction of the solubility of CO2 in aqueous MDEA solution by more than 6.7% in comparison with that of Huttenhuis et al. [Fluid Phase Equilibria2008, 264, 99–112] in a wide range of pressures, temperatures, acid gas loadings, and aqueous MDEA concentrations.

High-pressure solubilities of carbon dioxide in ionic liquids based on bis(trifluoromethylsulfonyl)imide and chloride

In this work, the solubility of carbon dioxide (CO2) in seven different ionic liquids (ILs) was measured using a high-pressure sapphire cell, in the pressure range of 8–22MPa and at two temperatures, 313.2K and 323.2K. In order to discuss the influence of the cation, ILs based on bis(trifluoromethylsulfonyl)imide, [NTf2] were chosen. They were coupled with 1-butyl-3-methylimidazolium, [C4mim]+, 1-decyl-3-methylimidazolium, [C10mim]+, 1-butyl-1-methylpyrrolidinium, [Pyrr4,1]+, butyltrimethylammonium, [N4,1,1,1]+, methyltrioctylammonium, [N1,8,8,8]+ and trihexyltetradecylphosphonium, [P6,6,6,14]+cation. The phosphonium based cation was also combined with chloride, [Cl]−, giving an opportunity to discuss the influence of an anion as well. The solubility data obtained in this work were used to evaluate the importance of explicitly including association for describing such systems. For that purpose, we compared the solubility modelling results from two cubic equations of state (Peng–Robinson and Soave–Redlich–Kwong) with those from the Cubic Plus Association Equation of State (CPA EoS) using different association schemes for the ionic liquids. We found that for such systems there is no major advantage in considering ILs as associating components.

Measurements of Hydrate Dissociation Temperature of Methane, Ethane, and CO2 in the Absence of Any Aqueous Phase and Prediction with the Cubic Plus Association Equation of State

Gas hydrate formation is undesired in processing and gas distribution. Therefore, it is important to have a thermodynamic model that predicts correctly gas hydrate formation. Hydrate formation is very well studied in the literature in the presence of liquid water, and hydrate thermodynamic models predict correctly its formation. However, only very little information can be found concerning gas hydrate formation without an aqueous phase. A new experimental procedure combining an equilibrium cell with a water measurement by a Karl Fischer coulometer was developed. The water content of the vapor phase is measured as a function of the temperature, and the hydrate dissociation temperature is determined by the slope change of the curve. In the first step, the dissociation temperatures of methane hydrate, ethane hydrate, and carbon dioxide hydrate were determined at different pressures and for different water amounts. In the second step, the obtained results were compared with the literature data and with the calculated values using the classical Platteeuw and van der Waals model associated with the Soave−Redlich−Kwong and the cubic plus association equations of state to calculate the water fugacity in the vapor phase.

Thermodynamic modeling of the vapor–liquid equilibrium of the water/ethanol/CO 2 system

The Cubic Plus Association Equation of State (CPA EoS) developed in this laboratory is applied here in the correlation of the binary vapor–liquid equilibrium (VLE) and in the prediction of the ternary VLE of the water/ethanol/carbon dioxide system at various temperatures and pressures. Carbon dioxide is treated in three different ways: (a) as a non-associating molecule, (b) as an only cross-associating molecule (not self-associating), and (c) as a both self- and cross-associating molecule. The results obtained from the CPA EoS are in good agreement with the experimental data for the binary and ternary systems, when carbon dioxide is considered either as a self-associating or only a cross-associating molecule with the first approach to give better results. Furthermore, the comparison with the results obtained from SAFT EoS indicates that CPA performs overall better than SAFT.

Prediction of phase equilibria in water/alcohol/alkane systems

The Cubic Plus Association Equation of State (CPA EoS) is applied to the prediction of Vapor–Liquid Equilibrium (VLE) and Liquid–Liquid Equilibrium (LLE) in ternary associating mixtures containing water, alcohols and alkanes. The appropriate set of combining rules for the cross-association energy and volume parameters of the EoS is identified by evaluating the performance of four such sets in the correlation of VLE and LLE for water/alcohol mixtures. Using only one interaction parameter per binary mixture, in the physical part of the EoS, CPA gives very satisfactory predictions of ternary VLE and LLE.

Correlation of liquid-liquid equilibria for [formula omitted] mixtures using the CPA equation of state

A recently developed equation of state, which combines the physical term of the classical SRK EoS with the association term based on the perturbation theory of Wertheim, called the Cubic Plus Association Equation of State (CPA EoS) (Kontogeorgis et al. [1]), is applied to liquid-liquid equilibrium (LLE) calculations in alcohol hydrocarbon mixtures. The CPA EoS performs very well in all cases using the conventional van der Waals one-fluid mixing rules in the parameters of the physical term and a temperature-independent interaction parameter. The performance of the CPA EoS is compared to that of the conventional SRK EoS and UNIFAC models, and with another association model, the ESD EoS of Suresh and Elliott [2]. The CPA EoS gives much better results than the two conventional models and results comparable to those obtained with the ESD model.