Cubic Plus Association Equation Of State Research Articles

Hydrocarbons – water phase equilibria using the CPA equation of state with a group contribution method

AbstractIt is proposed in this paper to extend the original group contribution method PPR78 to systems containing water, by combining it to the Cubic–Plus–Association (CPA) equation of state (EoS). Applying simple geometric combination rules, the binary interaction parameter kij(T) can be calculated from interaction parameters between hydrocarbon groups and water. This model, called the GC–PR–CPA is applied to predict hydrocarbons – water mutual solubilities over a wide temperature and pressure range, depending on available literature data. Group interaction parameters, here CH4, C2H6, CH3, CH2, CH, C, CHaro, CH2,cyclic, CHcyclic/Ccyclic, C2H4, CH2,alkene/CHalkene with H2O have been defined with solubility data. Predictions of the developed model have been validated against independent solubility data as well as water content in hydrocarbon rich phase. Predictions of the new model are in good agreement for light and medium hydrocarbons; however, some deviations are observed for heavier hydrocarbons.

Practical use of statistical learning theory for modeling freezing point depression of electrolyte solutions: LSSVM model

Electrolyte solutions are mixtures comprising a substance with the capability of forming strong associating bonding interactions between molecules. Hence, the predictions of van der Waals based equations of state for properties of these systems are poor. In these cases, employment of an equation of state (EoS) combined with the association term from the statistical associating fluid theory (SAFT) has been recommended in the literature. In this communication, a robust type of learning method developed based on statistical learning theory namely least squares support vector machine (LSSVM) has been employed for calculating the freezing point depression (FPD) of different electrolyte solutions. The predictions of the developed model are compared to the results of cubic-plus-association (CPA) EoS combined with the Debye–Hückel electrostatic term. It is found that the proposed smart technique gives more accurate estimations than CPA EoS that enjoys SAFT for the association part.

A new CPA equation of state for water and primary alcohols

A new version of CPA (cubic-plus-association) equation of state (EOS) for associating fluids is proposed. This equation takes the Nasrifar–Moshfeghian (NM) cubic EOS as a frame for representing the physical interactions of fluid molecules and also an associating term from the bonding term of statistical associating fluid theory (SAFT). The resulting EOS contains five adjustable parameters, three in physical term and two in association-based term. The parameters are determined using vapour pressures and saturated liquid densities of pure associating fluids. The excellent saturated liquid density is obtained for four pure associating fluids including primary alcohols (methanol, ethanol and 1-butanol) as well as water. The total average absolute deviations of the calculated values of densities from the experimental data are within 1.71%. The present model is compared with the original CPA EOS. Results show that our model agrees well with the original one.

Vapor–liquid equilibria of isopropyl alcohol + propylene at high pressures: Experimental measurement and modeling with the CPA EoS

The high pressure vapor–liquid equilibria of binary mixtures of propylene and isopropyl alcohol were measured experimentally within a temperature range of 315–440K and pressures up to 6MPa, using a synthetic method. The experimental data were modeled using the cubic plus association (CPA) equation of state (EoS) by once considering and once not considering solvation between the inert and polar molecules in the mixture. Results indicated that taking solvation into account did not make a huge improvement in the accuracy of CPA for this particular system. In addition, the Soave–Redlich–Kwong (SRK) EoS, representing the widely-used engineering EoS family, was also compared to the CPA. Results showed that both the CPA and SRK perform well for this system in the pressure and temperature range investigated, however, the values of binary interaction coefficients required by SRK to approach the experimental data are much greater than for CPA.

Methanol treatment in gas condensate reservoirs: A modeling and experimental study

Well productivity in gas condensate reservoirs is reduced by condensate blockage when the bottom-hole pressure drops below dew point pressure. The present experimental study on limestone cores shows that the relative permeability of gas decreases due to liquid blockage; furthermore, methanol has proven effective in the removal of condensate and restoration of gas relative permeability. In this research, the decrease in gas relative permeability caused by condensate banking and the effect of methanol treatment on condensate-blocked rocks was simulated using the cubic-plus-association (CPA) equation of state. The CPA equation of state was applied to the modeling of two-phase flows through cores for methanol–hydrocarbon mixtures due to charge transfer and hydrogen bonding, both of which may strongly affect the thermodynamic properties of such mixtures. Differential equations were solved by means of the orthogonal collocation method, a method particularly attractive for solving nonlinear problems. The modeling results confirm the experimental results, and both methods indicate that significant productivity loss can occur in retrograde gas condensate reservoirs when the flowing bottom-hole pressure falls below dew point pressure. Moreover, the results show that methanol treatment can improve gas relative permeability by a factor of about 1.3–1.6. These results may help reservoir engineers and specialists to restore the lost productivity of gas condensate.

Modeling liquid–liquid and vapor–liquid equilibria for the hydrocarbon+N-formylmorpholine system using the CPA equation of state

In this communication, the capability of the CPA (Cubic-Plus-Association) equation of state (EoS) for modeling vapor–liquid and liquid–liquid equilibria of mixtures containing N-formylmorpholine (NFM), alkanes and aromatics in a wide temperature range is studied. First, the CPA EoS parameters for NFM are obtained using vapor pressure and saturated liquid density data. Then, the liquid–liquid equilibrium of binary mixtures of NFM and alkane and later the vapor–liquid equilibrium for systems containing NFM and aromatics is investigated to determine the best parameters and association scheme. It is shown that the use of 4C association scheme for NFM yields satisfactory results.

Capabilities and Limitations of an Association Theory for Chemicals in Liquid or Supercritical Solvents

The cubic-plus-association (CPA) model is an equation of state (EoS) that combines the Soave–Redlich–Kwong (SRK) equation with the association term from Wertheim’s theory as used in statistical associating fluid theory (SAFT). In the form used here, the CPA EoS does not include separate terms for the polar and quadrupolar contributions. The capabilities and limitations of the CPA model when it is applied to mixtures with nonpolar and polar chemicals, as well as associating (hydrogen-bonding) compounds are illustrated. Three case studies are considered, all of which are of industrial relevance. The capabilities of the model are illustrated in the first two case studies: the phase behavior of mixtures used in the oxidation of 2-octanol in supercritical CO2 and the investigation of systems containing acetone, methanol, water, chloroform, and methyl acetate. In each case, both correlations of vapor–liquid and liquid–liquid equilibria for binary systems and predictions for multicomponent mixtures are presented...

Distribution of MEG and methanol in well-defined hydrocarbon and water systems: Experimental measurement and modeling using the CPA EoS

Liquid–liquid equilibria data for two binary and two ternary systems are reported in the temperature range of 303.15–323.15K at atmospheric pressure. The binary systems measured are n-nonane+MEG and ethylbenzene+MEG and the ternary systems are n-nonane+MEG+water and ethylbenzene+MEG+water. These data are satisfactorily correlated (binaries) and predicted (ternaries) using Cubic Plus Association (CPA) equation of state (EoS). CPA is also applied to binary LLE of aromatic hydrocarbon+water and VLE of methane+methanol. Finally the distribution of water and inhibitors (methanol and MEG) in various phases is modeled using CPA. The hydrocarbon phase consists of mixture-1 (methane, ethane, n-butane) or mixture-2 (methane, ethane, propane, n-butane, n-heptane, toluene and n-decane). CPA can satisfactorily predict the water content in the gas phase of the multicomponent systems containing mixture-1 over a range of temperatures and pressures. Similarly the methanol content in the gas phase of mixture-1+water+methanol systems is predicted satisfactorily with accuracy within experimental uncertainty. For VLLE of mixture-2+water, mixture-2+MEG+water and mixture-2+methanol+water systems, the organic phase compositions are satisfactorily predicted whereas modeling results are relatively less satisfactory for the vapor phase compositions partially due to uncertainties in the experimental data.

Equation of state modelling of systems with ionic liquids: Literature review and application with the Cubic Plus Association (CPA) model

For the last decade ionic liquids have been regarded as compounds of interest by the academic and industrial communities. These compounds present several advantages when compared to other typical solvents. However, because of their novelty, a deep understanding of their phase behaviour and their interactions with other components is still needed. In this work, we made a review of literature studies on modelling systems with ionic liquids using equation of state models. Furthermore, we applied the Cubic Plus Association (CPA) equation of state to describe the phase behaviour of two ionic liquids, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C2mim][NTf2]) and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C4mim][NTf2]). The first step was to study an adequate approach for the determination of pure component parameters for the ionic liquids. The parameters were obtained by fitting the predictions of the model to experimental vapour pressure and liquid density data. The parameters provide a good description of both experimental vapour pressures and liquid density, with maximum percentage deviations of respectively 8.9 and 1.3% for [C2mim][NTf2] and 5.7 and 0.5% for [C4mim][NTf2]. Different sets of pure component parameters for each ionic liquid were considered and their suitability to describe the behaviour of ionic liquids was evaluated by modelling the vapour–liquid equilibria (VLE) of mixtures with CO2 and the liquid–liquid equilibria (LLE) with water. The results for VLE proved to be very good in the range of pressures studied when using one temperature-independent binary interaction parameter, with percentage deviations in pressure between 8 and 13% for [C2mim][NTf2] and around 12% for [C4mim][NTf2]. For the LLE of ionic liquids with water a temperature-independent binary interaction parameter was also used, but the results do not describe the experimental data as well as with the VLE, with percentage deviations ranging from 4 to 100%. However, for some of the sets of pure component parameters a good description of the experimental data is obtained and work is in progress for improving the modelling of LLE with the CPA equation of state.

Prediction of asphaltene phase behavior in live oil with CPA equation of state

Asphaltene deposition mostly occurs when the thermodynamic conditions, like temperature, pressure, and oil composition of crude oil change. Therefore predicting asphaltene phase behavior through thermodynamic modeling may help to control its precipitation and reduce the associated problems. In this work, the Cubic-Plus-Association (CPA) equation of state was used to model asphaltene precipitation in live oil. This equation is based on a combination of a physical part and an association term. Through the past decades, CPA equation of state has been successfully applied to several complex mixtures of water, alcohols, glycols, organic acids, and hydrocarbons. As asphaltene molecules have an associative nature, which leads to form aggregation and finally precipitation, this equation can precisely predict the phase behavior of asphaltene and other heavy components in crude oil. In this work, the results of Cubic-Plus-Association equation of state were compared to experimental data of three live oils and the results of two other models. The results showed that CPA equation of state can predict asphaltene precipitation with good accuracy.

Phase Equilibrium and Calorimetric Properties of Mixtures Using the Mattedi-Tavares-Castier Equation of State

Natural gas and oil processing, among many other applications in the chemical industry, depends on accurate predictions of the thermodynamic and transport properties for their accurate and reliable design. Especially in the energy sector, in which the flow rates of process streams are large and equipment is big, improper design can be costly, both in terms of investment and operating costs. Equations of state (EOS) enable the evaluation of thermodynamic properties over a wide range of temperature and pressures and are routinely used for chemical process design. Many EOS exist but relatively few have become widely used, most notably the Peng-Robinson EOS in the oil and gas industry. However, the Peng-Robinson EOS and most other cubic EOS are unsuitable for predicting the phase behavior of mixtures that contain polar compounds. Such mixtures occur even in industries normally associated with the processing of non-polar substances (e.g., hydrocarbons). For example, natural gas may be contaminated by small amounts of water, carbon dioxide, and hydrogen sulfide, often removed using amines and glycols. Modern models such as the SAFT (statistical associating fluid theory), and its variants, and the CPA (cubic plus association) EOS are suitable alternatives but require solving the association equations before computing any thermodynamic property. The Mattedi-Tavares-Castier (MTC) EOS is an entirely explicit model that avoids this drawback but is capable of predictions of accuracy similar to that of the SAFT and CPA EOS. In this paper, we show results of calculations of phase equilibrium and calorimetric properties with the MTC EOS for systems of interest to gas processing industries.

Modeling Phase Equilibria Relevant to Biodiesel Production: A Comparison of gE Models, Cubic EoS, EoS−gE and Association EoS

Liquid−liquid equilibrium (LLE) and vapor−liquid equilibrium (VLE) data of binary and ternary systems formed at the biodiesel production and purification industrial units were used to evaluate the performance of commonly used excess Gibbs energy (gE) models, cubic equations of state (EoS), equations of state with EoS−gE mixing rules, and association equation of state models. The models used in this study are the UNIFAC, Soave−Redlich−Kwong (SRK) EoS, the SRK-MHV2, the Peng−Robinson (PR) EoS using the MHV2 mixing rule, the predictive Soave−Redlich−Kwong (PSRK) EoS, and the Cubic-Plus-Association (CPA) EoS. All models were used with previously established parameters, and the applicability of each model to the various systems investigated and the quality of the description of the phase equilibria are discussed. The results obtained show that the CPA EoS is the most adequate model to be used for the description of the phase equilibria of importance for the design and optimization of biodiesel production plants.

Water solubility of drug-like molecules with the cubic-plus-association equation of state

Although of extreme importance for evaluating the effective therapeutic action, aqueous solubility data involving drug-like molecules are scarce. Thermodynamic models can be used to estimate these solubilities, and different models, namely activity coefficient models, have been applied for that purpose. Still, these frequently cannot describe with accuracy broad temperature and pressure ranges, various solvent compositions or multifunctional molecules. Despite the success of the cubic-plus-association (CPA) equation of state (EoS) in modeling complex systems, it has never been used for modeling the phase equilibria of drug-like molecules, explicitly accounting for the number and nature of associating sites. In this work, aqueous solubilities of different complex solutes, like acetamide, acetanilide, acetylsalicylic acid, adipic acid, ascorbic acid, bisphenol A, camphor, dibenzofuran, hexachlorobenzene, hydroquinone, ibuprofen, nicotinic acid, paracetamol, piperazine, stearic acid, sorbitol, terephthalic acid and vanillin are estimated in a wide temperature range with the CPA EoS. Generally, the modeling results are within the experimental uncertainties using a single temperature independent binary interaction parameter, or a solvation parameter for some non-associating solutes. Globally, an average absolute deviation of 39% was obtained.

Cubic-Plus-Association Equation of State for Asphaltene Precipitation in Live Oils

We apply a cubic-plus-association equation of state (CPA-EOS) to study the asphaltene precipitation in live oils from temperature, pressure, and composition effects. The live oils are characterized by considering the pure components, the pseudo-hydrocarbon components, and the hydrocarbon residue. The hydrocarbon residue is further divided into the “heavy” component and asphaltenes. The asphaltene precipitation is modeled as liquid−liquid equilibrium between the upper onset and bubble point pressures and as gas−liquid−liquid equilibrium between the bubble point and lower onset pressures. In our work, the self-association between asphaltene molecules and the cross-association between asphaltene and “heavy” molecules are taken into account. The EOS parameters are either directly available, from our recent work, or from fitting the bubble point pressure. The cross-association energy between asphaltene and “heavy” molecules depends upon the temperature but is independent of the pressure. We reproduce the exper...

Modeling phase equilibria for acid gas mixtures using the CPA equation of state. I. Mixtures with H2S

AbstractThe Cubic‐Plus‐Association (CPA) equation of state is applied to a large variety of mixtures containing H2S, which are of interest in the oil and gas industry. Binary H2S mixtures with alkanes, CO2, water, methanol, and glycols are first considered. The interactions of H2S with polar compounds (water, methanol, and glycols) are modeled assuming presence or not of cross‐association interactions. Such interactions are accounted for using either a combining rule or a cross‐solvation energy obtained from spectroscopic data. Using the parameters obtained from the binary systems, one ternary and three quaternary mixtures are considered. It is shown that overall excellent correlation for binary mixtures and satisfactory prediction results for multicomponent systems are obtained. There are significant differences between the various modeling approaches and the best results are obtained when cross association is explicitly accounted for, especially using the cross‐association energy from independent experimental studies rather than from combining rules. © 2010 American Institute of Chemical Engineers AIChE J, 2010

Modeling of Biodiesel Multicomponent Systems with the Cubic-Plus-Association (CPA) Equation of State

To supply biodiesel with the quality levels required by the standards for alternative fuels, the separation and purification units are extremely important in the biodiesel production plants. The correct knowledge and description of the phase equilibria in systems composed by transesterification products is essential for a correct operation and optimization of the purification process. For that purpose, the cubic-plus-association equation of state (CPA EoS) was here applied to model the phase equilibria of multicomponent systems common to biodiesel production and purification processes. It is shown that the CPA EoS can provide a good description of the liquid−liquid equilibria of multicomponent mixtures containing alcohols, glycerol, and fatty acid esters in the temperature range of operation of the separation units in biodiesel plants. As the liquid−liquid phase equilibrium description depends on the EoS parameters, a discussion is also presented about the best set of parameters and the method to estimate...

Phase equilibria of glycerol containing systems and their description with the Cubic-Plus-Association (CPA) Equation of State

Biodiesel is nowadays in Europe the most used biofuel for road transportation. During its production, different separation and purification processes are required for the glycerol rich streams such as the recovery of the unreacted alcohol and the removal of water. The adequate design of the recovery and purification steps requires the knowledge about the vapour–liquid equilibria data for water + glycerol and alcohol + glycerol systems that are surprisingly scarce. To overcome this lack of information, experimental measurements for 5 alcohol + glycerol systems were performed. These data were used to evaluate the capability of the Cubic-Plus-Association Equation of State (CPA EoS) to model systems containing glycerol. To achieve a good description of the experimental data a new association scheme is proposed for the glycerol molecule. It is shown that a very good description of the VLE data with average deviations inferior to 1% for the bubble point temperatures is obtained. Two different cross-associating combining rules were tested with similar results. Furthermore the predictive performance of the model is evaluated for multicomponent systems. Good liquid–liquid equilibria predictions are obtained for the ternary system methanol + glycerol + methyl oleate at four different temperatures.

Phase equilibria for petroleum reservoir fluids containing water and aqueous methanol solutions: Experimental measurements and modelling using the CPA equation of state

Thermodynamic inhibitors, such as methanol, are widely used to reduce the risks associated with gas hydrate formation. The work presented in this communication is the result of a study on the phase equilibria of petroleum reservoir fluids in the presence of aqueous methanol solutions. Experimental hydrate dissociation data, for systems composed of methane/water/methanol and natural gas/water/methanol, in addition to experimental freezing point depression data for aqueous methanol solutions, are reported. A statistical thermodynamic approach, with the cubic-plus-association equation of state (CPA-EoS), is employed to model the phase equilibria. The hydrate-forming conditions are modelled by the solid solution theory of van der Waals and Platteeuw. The thermodynamic model was used to predict the hydrate dissociation conditions of methane and natural gases in the presence of distilled water or methanol aqueous solutions. Predictions of the developed model are validated against independent experimental data and the data generated in this work. A good agreement between predictions and experimental data is observed, supporting the reliability of the developed model.

Modeling Systems Containing Alkanolamines with the CPA Equation of State

An association model, the cubic-plus-association (CPA) equation of state (EoS), is applied for the first time to a class of multifunctional compounds (alkanolamines). Three alkanolamines of practical and scientific significance are considered; monoethanolamine (MEA), diethanolamine (DEA), and methyl diethanolamine (MDEA). Vapor pressures and liquid densities, as well as solvatochromic parameters and mixture liquid−liquid equilibria (LLE) data with alkanes are used to estimate the five pure-compound parameters. Vapor−liquid equilibria (VLE) calculations for cross-associating mixtures, especially those with water, are used in the validation of the parameters. The influence on the results of the association scheme, cross-association combining rules, interaction parameters, and the data available is discussed also, in connection with other aqueous cross-associating mixtures previously studied using the CPA equation of state (alcohols, amines, and glycols).

Prediction of Water Solubility in Biodiesel with the CPA Equation of State

The recent growing interest in biofuels is due to the continuous increase in crude oil prices, limited resources of fossil energies, and environmental concerns. In what concerns road transportation, biodiesel is being considered a good alternative to conventional diesels. It consists of a blend of fatty acid esters, and its production and formulation needs to be optimized to ensure that the fuel quality complies with the legal standards. Although in various aspects biodiesel is superior to conventional diesel, it also poses some problems such as its poor behavior at low temperatures and higher hygroscopicity than conventional diesel. Up to now, little information is available about the water solubility in fatty acid methyl and ethyl esters and commercial biodiesels. To overcome this lack of data, water solubility measurements were carried out for 11 pure esters and 6 biodiesels in the temperature range 288.15−323.15 K. This new experimental data was successfully modeled with the cubic-plus-association (CPA) equation of state with global average deviations inferior to 7% for the ester systems, and predictions with deviations of 16% for commercial biodiesels were achieved.