Association Equation Of State Research Articles

Calculations of mean ionic activity coefficients of copper and manganese salts in aqueous solutions

Accurately predicting the activity coefficients of copper and manganese salts in aqueous solutions is crucial for treating industrial wastewater, and it is of practical interest to calculate the activity coefficients of heavy metals in aqueous solutions using the Equation of State because of its high flexibility and wide range of applicability. This work conducts a modeling study on the mean ionic activity coefficients of copper and manganese salts in aqueous solutions. The thermodynamic framework used in this work is an electrolyte version of the Cubic Plus Association Equation of State (e-CPA). The model's ion-water binary interaction parameters are obtained by regressing the osmotic coefficients and mean ionic activity coefficients in aqueous solutions. The modeling results indicate that the electrolyte Equation of State can satisfactorily correlate the water activity, osmotic coefficients, and mean ionic activity coefficients of copper and manganese salts in aqueous solutions over a wide range of salt concentrations. Among all the systems at 298.15 K, the biggest average relative deviation between calculated and experimental values is within 6.7 % and 2.3 % for the mean ionic activity coefficients and water activity, respectively. Furthermore, this work discusses the impact of ion pairs on the phase equilibrium of aqueous systems from a microscopic mechanism perspective and analyzes and discusses the model's adaptability. The model used in this work can accurately predict the activity coefficients of a variety of copper and manganese salts in aqueous solutions over wide concentration ranges and provides an improved interface for improving the calculation accuracy of the model under high concentration or other complex conditions.

Thermodynamic study of water/solvent, bitumen/solvent, water/bitumen, and water/bitumen/solvent systems: From CPA EoS parametrization towards phase diagram construction

Various fluid phase equilibria happen in solvent-aided steam-assisted gravity drainage (SA-SAGD). An appropriate fluid model is a prerequisite for reservoir simulation, SA-SAGD operation analysis, and the design of various phase behavior experiments. Computational thermodynamics is a powerful tool for phase behavior studies in this application. We used the Cubic Plus Association Equation of State (CPA EoS) to predict equilibrium properties due to the presence of molecules with highly directional attractive forces. Calibration of the thermodynamic model is performed by parametrizing its unknown parameters versus two-phase equilibrium data. The model’s prediction capability of three-phase experimental data is evaluated, and it is used to construct the phase diagram of water/multicomponent solvent and water/multicomponent solvent/bitumen systems. For the water/multicomponent solvent system, the Txy diagram is obtained at 25 bar, and various phase equilibria regions are specified. These phase regions are presented on ternary diagrams for water/multicomponent solvent/bitumen systems at 25 bar and 475 K, 480 K, and 485 K. The steam/solvent coinjection analysis shows that at the same pressure, temperature, and steam/solvent composition, the multicomponent solvent/steam coinjection yields more aqueous phase compared to pure solvent/steam. This results in the transfer of more latent heat to bitumen, significantly contributing to its viscosity reduction. Analysis of the SA-SAGD operating conditions shows that a multicomponent solvent outperforms pure solvents in promoting steam condensation. The results aids in designing experiments, reducing the risk of failure of experiments, and saving time and resources in phase behavior studies.

CO2 solubility in aqueous solution of salts: Experimental study and thermodynamic modelling

AbstractThere are many economic obstacles and complex engineering problems associated with CO2 capture and storage in saline aquifers that need to be addressed. Overcoming such challenges requires precise knowledge on the fluid phase equilibria of CO2‐brine systems. Having accurate CO2 solubility data over a wide range of temperature and pressure can greatly assist in resolving these obstacles by improving the performance and accuracy of the thermodynamic modeling and subsequent CCS engineering success.CO2 solubility in pure water and NaCl solutions has been widely studied in the literature, however, there is a lack of data on CO2 solubility at lower temperatures (below 298 K). Furthermore, limited phase equilibria data are available for CO2 solubility in CaCl2, MgCl2, and KCl solutions at elevated temperatures (i.e., T > 323.15 K).In this work, the phase equilibria of CO2 and brine systems are investigated experimentally and theoretically. In this study, solubilities of CO2 in pure water and various concentrations of NaCl (10, 15, 20, and 22 wt%), KCl (10, 15, and 22 wt%), CaCl2 (7.5, 10, 15.7, and 23.4 wt%), and MgCl2 (6.7, 11, 18, and 29 wt%) aqueous solutions are reported. All CO2 solubilities were measures at 323.15, 373.15, and 423.15 K and over various pressure ranges, while solubilities in 10 and 20 wt% NaCl aqueous solutions were also measured over the temperature range of 263 to 298 K and pressures up to the hydrate dissociation pressure of each system. Equation of state modelling using the PC‐SAFT and the Cubic Plus Association equations of state, is performed in the theoretical part of the study to validate the measured solubility data. © 2024 The Author(s). Greenhouse Gases: Science and Technology published by Society of Chemical Industry and John Wiley & Sons Ltd.

Modeling of CO2/CH4 Solubility in Single- and Mixed-Salt Solutions Using the Association Equation of State

Modeling of CO₂/CH₄ Solubility in Single- and Mixed-Salt Solutions Using the Association Equation of State

Solubility measurement of methane in triethylene glycol aqueous solutions (90,95,98 wt.% triethylene glycol) from 298 to 323 K and 0.17 to 2.5 MPa

Limited phase equilibria data exists for the methane + water + triethylene glycol system. In this work, new phase equilibrium data were measured for this system for a temperature range of 298 to 323 K and a pressure range of 0.17 to 2.5 MPa. These data add to the information that is required in the design of TEG contactor units since they normally operate over a temperature and pressure range of 283 to 329 K, and 2 to 10 MPa respectively. The data were measured using a static synthetic apparatus. The measured data were modelled in Apen Plus V12.1 using the Cubic Plus Association equation of state. The model correlation yielded a satisfactory description of the measured data since the maximum absolute average relative deviation in pressure was 4.30 %.

Quantitative analysis method for absorption mechanism and energy consumption of CO2 capture by amino acid ionic liquids

Amino acid ionic liquids (AAILs) are attractive candidates for CO2 capture due to their high solubility for CO2. Quantitatively analyzing the interaction of amino groups in AAILs with CO2 and evaluating the energy consumption of CO2 capture is critical to the molecular design of ideal AAILs. In this work, a thermodynamic model based on the cubic plus association equation of state was proposed to calculate the contribution from the chemical reactions between various stoichiometric ratios of CO2 and AAIL (Nm:n,m:n is stoichiometric ratio) on CO2 solubility. The results show that the larger contribution to the CO2 solubility in [Glu], [Tyr] and [Gln]-IL with strong polar groups is derived from association scheme N1:2, while the N1:1 association interaction is the dominant contribution of [Gly], [Ala], [Val] and [Pro]-IL with hydrogen atom or short alkyl side chains, and [VBIm]-IL with multiple amino groups. The N2:1 association interaction is primary between CO2 and [Cho][His] or [Cho][Arg]. Besides, the contributions of these association effects are greater than that of dispersion and repulsion to CO2 solubility. Then, the solvent cyclic capacity and regeneration energy of AAILs in the pressure swing and temperature swing CO2 capture system were estimated. More amino groups result in higher regeneration energy consumption and do not necessarily increase solvent cyclic capacity. Among the studied AAILs, [Cho][Gly] which exhibits high cyclic capacity and low energy consumption has great potential in CO2 capture solvent.

Modeling H2S solubility in aqueous MDEA, MEA and DEA solutions by the electrolyte SRK-CPA EOS

In this study, an electrolyte cubic plus association equation of state (e-CPA EOS) has been proposed to predict the vapor–liquid equilibrium of (H2S) in aqueous solutions of monoethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA). This EOS is composed of repulsive forces, short-range interactions, short-range ionic interactions, association term, long-range ionic interactions, and Born term. The Soave– Redlich– Kwong EOS is used as a non-electrolyte part. A new iterative procedure based on the Jacobi method is introduced to obtain the compositions of all species in the liquid phase. The genetic algorithm (GA) is used to find the optimal values of binary interaction coefficients between molecules and ions. Compared with experimental data, the e-CPA EOS model successfully describes the vapor–liquid equilibrium of H2S in the aqueous solutions of MEA, DEA, and MDEA. The average absolute deviations for 313 data of MEA-H2S-H2O, 156 data of DEA-H2S-H2O, and 145 data of MDEA-H2S-H2O systems were obtained as 8.20 %, 8.04 %, and 9.41 %, respectively. In addition, for some similar cases, the capability of the e-CPA EOS was compared with the Clegg–Pitzer, N-Wilson-NRF, e-NRTL, and e-CTS models. The results indicated that the e-CPA EOS has less error than the four other models.

Direct measurement of hydrate equilibrium temperature in CO2 and CO2 rich fluids with low water content

A high-pressure experimental setup was used to obtain experimental data on the hydrate equilibrium (melting) temperature (HET) of hydrates formed from low water content CO2 and CO2 rich mixtures. A novel method was used to measure hydrate formation temperature in addition to melting temperature directly at realistic temperature/pressure conditions encountered in transport by pipelines or ship. The method can be used to evaluate the likelihood of hydrate formation in pipelines/ships transporting pure CO2 and CO2 coming from capture processes as well as from high CO2 content produced gas. The data generated from the measurement can also be used to investigate the kinetics of hydrate formation and dissociation in low water content fluids at pipeline/ship conditions. This paper details the experimental equipment, methods, test fluids and results. Experimental results are compared against predictions of the simplified cubic plus association equation of state (sCPA-EoS) coupled with the van der Waals and Platteeuw solid solution theory.

Phase equilibria calculations of a hydrocarbon system consisting water and asphaltene using association equation of state: A generalized auto-tune procedure

A generalized algorithm is proposed for four-phase flash calculations in hydrocarbon-water systems in which asphaltene has tendency to be precipitated. The systems which are going to be studied in this paper can be either single phase, two-phase, three-phase or four-phase of gas, oil-rich, asphaltene-rich and aqueous phases. The properties of vapor and oil-rich (liquid) phases can be predicted using any EOS while Henry's law is performed for calculating the properties of water-rich (aqueous) phase. In addition, an association equation of state (AEOS) has been used to predict the amount of the precipitated asphaltenes at different conditions. Using the proposed algorithm, one can predict the number and types of phases and also the properties of each phase, as accurate as possible. As tuning of EOS models is tedious and time consuming, a generalized and auto-tune method based on sensitivity and optimization algorithms is also applied in this study so that the best model could be found easily, quickly and automatically. The proposed approach proved to be efficient, and very good agreement between the results of the presented method and experimental data was found for different test problems. This new procedure can be very useful in compositional reservoir simulation of certain enhanced oil recovery methods and in surface facility process simulation.

Vapor-liquid-liquid equilibrium (VLLE), density, and viscosity of the ternary mixtures of normal hexane, water and bitumen at T=185–210°C and at P= 2.5 MPa

This paper presents a study on the vapor-liquid-liquid equilibrium (VLLE) of a ternary system consisting of normal-hexane (n-C6) as a solvent, water (H2O), and Mackay River bitumen. The study was conducted at temperatures ranging from 185 to 210 °C and a pressure of 2.5 MPa. The solvent/steam and solvent/bitumen ratios were varied to understand the effect of solvent (n-C6) on the phase behavior and the thermophysical properties of the associated phases. The co-injected solvent with steam is often reported as the concentration of solvent in the solvent/steam mixture. Two concentrations of n-C6 in n-C6/water mixture, including mole fractions of 0.01 and 0.05 (i.e., 6.85 and 27.70 vol.%), were considered to examine the effect of the co-injected solvent with steam. Also, two different mole fractions of n-C6 in the mixture of bitumen/n-C6 at 0.7 and 0.4 (37.45 and 14.61 vol.%), respectively, were considered to examine the effect of solvent solubility in bitumen. In addition to the VLLE study, the viscosity and density of the two distinct liquid phases, hydrocarbon-rich oleic and water-rich aqueous phases, were measured and reported. The results from the experiment infer that the concentration of n-C6 co-injected with steam does not significantly affect the equilibrium phase concentrations and thermophysical properties. However, the mixture showed liquid-liquid equilibria (LLE) instead of the vapor-liquid-liquid equilibria (VLLE) when the concentration of n-C6 in bitumen/solvent mixture was less than the equilibrium solubility of n-C6 in the hydrocarbon-rich phase at that operating condition. Furthermore, the results suggest that the presence of bitumen in equilibrium with n-C6 and H2O has no significant effect on the concentration of n-C6 in the vapor phase when compared with the n-C6/H2O binary mixture. Thermodynamic modelling of the VLLE data was performed using the cubic plus association equation of state (CPA EoS). The matching parameters were obtained by tuning the two-phase data, and those parameters were used in predicting the VLLE data. The model was also used to construct the phase regions of the solvent/bitumen/water system on the ternary diagram at different temperatures and pressures. Different phase regions were determined by phase stability analysis. The findings provide insight into steam/solvent condensation behavior with applications to the solvent-aided thermal recovery of bitumen from oil sands.

Modification of e-CPA for estimating phase equilibria and development of predictive models for electrical conductivity in aqueous electrolyte solutions

We modify the electrolyte cubic plus association equation of state (e-CPA EoS) and inetgrate it with two electrical conductivity models to estimate the electrical conductivity of 11 monovalent electrolytes solutions in water. The e-CPA EoS is modified by including the ion-ion and ion-solvent association interactions and tuned using experimental data of mean ionic activity coefficient and density of the electrolyte solutions. The modified e-CPA model shows a better performance in estimating the bubble pressure data. The hybridization of two electrical conductivity models with e-CPA results in two predictive models for estimating the electrical conduction of dilute and concentrated electrolyte solutions. Finally, we generalize these predictive models by correlating their model fitting parameters to the electrolyte physical parameters such as mean hard-sphere diameter or to association volume. The two predictive electrical conductivity models estimate electrical conductivity with AARD of 11.15 % and 13.87 % over wide ranges of temperature and electrolyte concentration.

Modelling phase equilibria in the CO2/CH4-H2O-NaCl system using the association equation of state

A new association model, CPA-MHV1, is developed by combining the Soave-Redlich-Kwong (SRK) equation of state (EoS) with the Cubic-Plus-Association (CPA) EoS based on Michelsen's improved Huron-Vidal mixing rule. The model is utilized to investigate the vapor-liquid equilibrium (VLE) of binary mixtures involving methane (CH4), carbon dioxide (CO2), and water (H2O) binary mixtures, as well as ternary mixtures containing sodium chloride (NaCl). CO2 is modeled as a non-associating, non-self-associating (solvation in water) component and as a self-associating component with two, three, or four association sites; furthermore, CH4 is modeled as a non-associating and pseudo-associating component. In the regression of the adjustable parameters, dependence on temperature is considered and the parameters are fitted as functions of temperature. The results demonstrate that the best performance is achieved when solvation between CO2 and H2O is considered, with the average absolute relative deviation (AARD) of 4.50 % in the H2O-rich phase, 5.48 % in the CO2-rich phase, and 3.28 % in NaCl solution. CH4 with pseudo-association scheme has the highest comprehensive prediction performance, and AARD values in H2O-rich phase, CH4-rich phase and NaCl solution are 5.26 %, 5.90 % and 9.19 %, respectively.

Modelling mixtures of ammonium and pyridinium-based ionic liquids and carbon dioxide with the Cubic Plus Association Equation of state

Modelling mixtures of ammonium and pyridinium-based ionic liquids and carbon dioxide with the Cubic Plus Association Equation of state

Vapor-liquid equilibria (VLE) of the binary mixture of normal hexane and water at P = 2.5 MPa and T=(456.85 – 487.85 K)

We report the vapor-liquid equilibria (VLE) of the binary mixture of the n-C6/H2O system at P=2.5 MPa and T=(456.85 – 487.85 K). The result showed an azeotropic behavior with a co-condensation temperature of ∼456.85 K at an n-C6 mole fraction of ∼0.6029. The measured experimental data are modeled with the Cubic Plus Association Equation of State (CPA-EoS) and activity coefficient-based Non-Random Two Liquid (NRTL) model. The infinite dilution activity coefficient of n-C6 and H2O are also estimated over the temperature range of interest. The overall root mean square deviation (RMSD) of the n-C6 mole-fraction in vapor and liquid phases for the CPA EoS and NRTL models are 0.0370 and 0.0765, respectively.

Thermodynamic model for CO2 absorption in imidazolium-based ionic liquids using cubic plus association equation of state

In order to achieve efficient capture of carbon dioxide (CO2) by ionic liquids (ILs), IL with good performance of high CO2 absorption capacity and low energy consumption need to be explored. Density, heat capacity, CO2 solubility and absorption enthalpy are key properties for the performance evaluation of IL solvents. In this work, the cubic plus association equation of state (CPA EoS) was applied for the integrated modelling of above properties in CO2 physical and chemical absorption by 22 imidazolium-based ILs. The results show that the density, heat capacity of pure ILs and CO2 solubility in a broad range of temperature (281–403 K) and pressure (0.1–23 MPa) were accurately calculated with deviations less than 1.27%, 0.54% and 3.73%, respectively. CO2 chemisorption was satisfactorily described by CPA EoS with an error of 0.12% considering interactions for the reactive sites between CO2 and amino groups in IL. Furthermore, the prediction capabilities of CPA EoS were verified with results showing good quantitative agreement with density and solubility data in literature. The effects of structures of ILs studied in this work on the CO2 solubility and absorption enthalpy were analyzed. [NH2emim][BF4], [Omim][Tf2N] and [Emim][eFAP] were found to have better performance of CO2 absorption. This model provides a feasible approach to determine synthetically the key properties of CO2-IL systems for the selection of proper ILs, design and simulation of the CO2 capture process.

Thermodynamic effects of the interaction of multiple solutes and dodecahedral-cage deformation on the semi-clathrate hydrate formation with CH4-CO2

The accurate prediction of thermodynamic equilibrium hydrate formation pressure (Peq) is crucial to the industrial application of hydrate-based gas separation. This study evaluated Peq of CH4-CO2 gas mixtures with different TBAB solutions at different temperatures. Unlike previously reported models, the proposed model accounted for the effects of interaction of multiple solutes and the deformation of dodecahedral (D)-cages on Peq, thereby minimizing deviations in predictions. The effects of the interaction of multiple solutes on Peq can be attributed to gas dissolution and the presence of electrolytes. For accurate prediction, the proposed model incorporated the aforementioned effects based on the electrolyte-cubic plus association equation of state and the parameters for interaction among guest molecules in cages Furthermore, the proposed model can quantitatively describe the effects of gas dissolution, the presence of electrolytes and deformation of D-cages on the Peq values for corresponding systems.

CO2 hydrate formation in NaCl systems and undersaturated aqueous solutions

A high-pressure experimental setup was used to obtain experimental data on the Hydrate Equilibrium (melting) Temperature (HET) of aqueous phases undersaturated with CO2, at different CO2 saturation levels and with different aqueous phase compositions (sodium chloride and sodium chloride/calcium chloride). This paper details the experimental equipment, methods, test fluids, and results. To study the phase equilibria of CO2-brine systems and further validate the results, hydrate dissociation conditions of CO2 in different concentrations of NaCl aqueous solutions were measured in the low-temperature region and over a wide range of pressure. Experimental results were compared against predictions of the simplified Cubic Plus Association Equation of State (sCPA-EoS) coupled with the van der Waals and Platteeuw solid solution theory.

An Overview of the Oil+Brine Two-Phase System in the Presence of Carbon Dioxide, Methane, and Their Mixture

An overview of the molecular simulation studies of the oil+brine two-phase system in the presence of CO2, CH4, and their mixture at geological conditions is presented. The simulation results agreed well with the experimental results and the density gradient theory predictions on the basis of the cubic–plus–association equation of state (CPA EoS) (withDebye–Hückel electrostatic term) and the perturbed chain statistical associating fluid theory (PC-SAFT) EoS. The interfacial tension (IFT) of the alkane+H2O system showed almost a linear increase with an increasing number of carbon atoms in the alkane molecule. These IFTs are approximately equal for linear, branched, and cyclic alkanes. Here, the negative surface excess of the alkanes might explain the increase in the IFTs with an increase in the pressure. The surface excesses of the alkanes increased with decreasing temperature. This may explain the decrease of the slopes in the IFT versus pressure plot with a decrease in the temperature. The IFT behavior of the alkane+water+CH4/CO2 system was found to be similar to that observed for the alkane+water system. The addition of CO2 had a more significant influence on the IFT than the addition of CH4. Here, CH4 and CO2 exhibited a positive surface excess. The negative surface excess of the salt ions probably explains the increase in the IFTs of the alkane+brine system with increasing salt content. The solubilities of CH4 and/or CO2 in the H2O-rich phase of the alkane+brine+CH4/CO2 system increased with decreasing salt content (salting-out effect). The IFT of the aromatic hydrocarbon+H2O system is much lower than that of the alkane+H2O system. The surface excess followed the order o-xylene > ethylbenzene > toluene > benzene for the aromatic hydrocarbon+H2O system. This trend has a direct correlation with the aromatic–aromatic interaction.

A Global Optimization Approach for Parameter Estimation of Cubic Plus Association Equations of State in Asphaltene Modeling: Studying the Temperature, Solvent, and Binary Interactions

A Global Optimization Approach for Parameter Estimation of Cubic Plus Association Equations of State in Asphaltene Modeling: Studying the Temperature, Solvent, and Binary Interactions

Thermodynamic modeling of density, viscosity and critical micelle concentration of aqueous Tween and Span solutions via Cubic plus association equation of state

The Cubic Plus Association (CPA) equation of state (EoS) has been offered to separately compute different thermodynamic properties of the aqueous non-ionic surfactant solutions, including Tween 80, Tween 60, Span 80, and Span 60. These surfactants have been modeled for the first time, and 5 pure components parameters of the CPA EoS have been fitted to the Critical Micelle Concentration (CMC) data at various temperatures. Tweens and Spans surfactant molecules have been modeled as associating constituents via considering 3 × 2B association scheme. Furthermore, applying the adjusted parameters, the liquid mixture density of the noted aqueous solutions has been predicted marvelously at various temperatures. Moreover, the liquid mixture viscosity has been compared reasonably using four different theories at ambient conditions. Besides, the effects of temperature have been investigated in the case of liquid mixture viscosity. Additionally, several new correlated equations have been introduced considering the optimized parameters of non-ionic surfactants.