Binary Interaction Coefficients Research Articles

Prediction of compressibility factor for gas condensate under a wide range of pressure conditions based on a three-parameter cubic equation of state

The gas compressibility factor as an essential thermodynamic parameter is often used to analyze PVT behavior in natural gas engineering. To accurately predicate it for various gas condensates, a data base containing 916 data sets covering a wide range of experimental conditions is employed to establish and test the prediction model based on a three-parameter cubic equation of state (EoS). The presented model which based on EPT EoS combines with Elliott–Daubert binary interaction coefficients correlation, Ahmed et al. splitting and Hosseinifar–Jamshidi characterization methods is superior to conventional empirical correlations with three mixing rules and two-parameter EoSs as SRK, PR, PRSV and MPR2. Statistical error analysis shows that it outperforms empirical correlations with average absolute relative errors of 1.45% and coefficient of determination of 0.989. At pressure and temperature up to 95.04 MPa and 429.3 K, respectively, the model also outperforms two-parameter EoSs with average absolute relative errors of 1.65% and coefficient of determination of 0.992. The presented model is efficient and practical for predicting the compressibility factor of gas condensate.

Considerations for the dew point calculation in rich natural gas

Hydrocarbon Dew Point (HCDP) in natural gas processing is a key quality parameter and a critical consideration for pipeline operations. In the present paper, a comparison between equations of state approaches is presented by estimating HCDP in rich natural gas using different approaches, i.e. PR, SRK or GERG-2004 EoS. Further, a parameter comparison is performed discussing the impact on the accuracy of estimating HCDP in natural gas using the selected approaches. The following parameters are compared: binary interaction coefficients, C7+ characterization methods, critical properties for single-carbon number groups and mixing rules. A set of considerations is presented in order to guide users to choose the most accurate right method for calculating HCDP in natural gas.

A Parametric Methodology in Tuning the Peng-Robinson (PR) Equation of State for Gas Condensate Systems

A tuned equation of state (EOS) is used in reservoir engineering for the evaluation of gas and condensate reserves, desired production methods, and facilities for field development. Publications show that the two most widely used sets of parameters from the EOS that are tuned are the binary interaction coefficient (BIC) with the critical properties and acentric factor or BIC and the constants called the omegas (Ωs). A volume shift parameter (VSP) can also be used in cubic EOS as a tuning parameter to correct for the prediction of liquid density. However, the open literature does not demonstrate if the VSP could be used with one or both parameter sets. In this study, the Peng-Robinson EOS was tuned and tested to predict constant volume depletion (CVD) data for six gas condensate samples. The two sets of tuning parameters were used with and without the VSP. Our parametric study demonstrated that the VSP should not be applied with the Ωs when tuning the Peng-Robinson EOS. With weight factors of 1 for liquid volume and 10 for gas compressibility, without the VSP, the Ωs give better prediction of CVD data than the critical properties and acentric factor even with the VSP included. This tuning technique with one regression step showed consistency in tuning the Peng-Robinson EOS with the Ωs and could be used for simulation studies of gas condensate systems.

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.

Thermodynamic performance of the NaNO3–NaCl–NaNO2 ternary system

Calculations of phase diagram for additive ternary molten salt system are carried out by the conformal ionic solution theory. The liquidus temperatures of the system NaNO3–NaCl–NaNO2 are determined according to different types of solid–liquid equilibrium and different values of the binary interaction coefficients. For the system NaNO3–NaCl–NaNO2, the calculated and experimental temperatures differ are very small below 673 K, but the oxidation and decomposition of the mixed salts are found when the temperature is higher than 673 K. Meanwhile, the eutectic point is obtained from calculated phase diagram and the eutectic temperature is 507 K. Thermal stability of this eutectic mixture is investigated by thermo-gravimetric analysis device. Experimental results show this kind of molten salt has a lower melting point (501.28 K), similar to solar salt (493 K). It is thermally stable at temperatures up to 819 K, and may be used up to 827 K for short periods.

Reduced flash calculations with temperature dependent binary interaction coefficients

The inherent simplicity of cubic EoS models with classic mixing rules allows phase behavior calculations to be performed much faster compared to alternative thermodynamic models. To ensure reliability as well, it is required that temperature-dependent binary interaction coefficients (BIP) are utilized, which however, prohibit the application of the well-known reduction methods. In this work, a new method is proposed for extending the applicability of the reduced variables framework to this type of EoS models. A sampling and interpolation technique is utilized to provide the eigenvalues and eigenvectors at the desired temperature during the simulation run. It is shown that the PPR78 and PR2SRK EoS/gE models are perfect candidates for this approach due to the inherent deficiency of their BIP matrix. Nevertheless, the method is directly applicable to any cubic EoS model with temperature dependent BIPs.

A simple correlation to predict high pressure solubility of carbon dioxide in 27 commonly used ionic liquids

Engineers often demand the availability of easy correlations without difficult and time-consuming calculations. Up till now, there has been a lack of such correlations for mixtures of CO2+ionic liquids. This work proposes a correlation to predict CO2 solubility in 27 common ionic liquids. The main advantages are its simplicity and minimal input data, namely temperature and pressure. The ionic liquids investigated ranged within a variety of families, having various anions and cations. Compared with the popular engineering models of Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK), the present correlation is much easier to use, yet it is also more accurate (PR, SRK and the proposed model had AARD% values of 43.5%, 44.3% and 4.9%, respectively for a total of 3073 data), even when binary interaction coefficients of PR and SRK are optimized to experimental data (AARD% values of 17.2%, 16.9% and 4.9% for PR, SRK and the proposed model, respectively).

Modeling interfacial tension of (CH4+N2)+H2O and (N2+CO2)+H2O systems using linear gradient theory

The linear gradient theory (LGT) of fluid interfaces in combination with the cubic-plus-association equation of state (CPA EOS) is applied to determine the interfacial tensions of (CH4+N2)+H2O and (N2+CO2)+H2O ternary mixtures from 298–373 K and 10–300 bar. First, the pure component influence parameters of CH4, N2, CO2 and H2O are obtained. Then, temperature-dependent expressions of binary interaction coefficient for (CH4+H2O), (N2+H2O) and (CO2+H2O) are correlated. These empirical correlations of pure component influence parameters and binary interaction coefficients are applied for ternary mixtures. For (CH4+N2)+H2O and (N2+CO2)+H2O mixtures, the predictions show good agreement with experimental data (overall AAD∼1.31%).

Predicting Pyrolysis Products of PE, PP, and PET Using NRTL Activity Coefficient Model

Using thermodynamic models is a desired method for predicting an equilibrium when occurring in a system. If a thermodynamic model can predict an equilibrium condition in a pyrolysis, for a new way will be open for scientists in predicting equilibrium in a reaction without need to kinetic models. In this work, low‐density polyethylene, polypropylene, and polyethylene terephthalate were used instead of feed of pyrolysis process. The process was maintained at 500°C with 5 different temperature raising ratios 6, 8, 10, 12, and 14. Then the process was modeled thermodynamically using NRTL activity coefficient model. Using this model, the binary interaction coefficients were investigated for the system of “char, oil, and gas.” Results showed that polyethylene and polypropylene produced the maximum liquid product. Calculated RMSD objective function was 0.0157; that it is acceptable for this process.

Effect of solute interaction on interfacial segregation and grain boundary embrittlement in binary alloys

The effect of solute interaction on interfacial segregation and intergranular embrittlement is modeled on the basis of the combined Fowler and Rice–Wang approaches in a binary system using the chosen values of standard thermodynamic parameters of interfacial segregation and varied values of the binary interaction coefficients. It is clearly shown that attractive interaction strengthens interfacial segregation and substantially enhances intergranular embrittlement, while repulsive interaction exhibits an opposite effect. This finding is demonstrated in the available literature data.

New volume translated PR equation of state for pure compounds and gas condensate systems

The purpose of this paper is to improve the Peng–Robinson equation of state (PR EOS 1978) prediction of saturated liquid density of pure compounds and gas condensate systems by volume translation method. Thus, a temperature-dependent volume translation factor has been proposed. Also, a new mixing rule for volume translation factor of mixtures has been proposed. The new model requires only adjusted critical compressibility factor for each compound which has been determined and reported for 29 compounds. No binary interaction coefficients kij are used.The average absolute percent deviation (AAPD) of predicted liquid densities has been calculated in the reduced temperature range (0.3–0.99) for the pure compounds of the alkanes (methane to eicosane), ethylene, propylene, carbon dioxide, carbon monoxide, hydrogen sulfide, nitrogen, and ammonia. The AAPD of PR EOS for aforementioned pure compounds is 8.40%. By using the proposed volume translation model, the AAPD reduced to 1.11 and 1.29 for the optimized parameters and the generalized correlations, respectively. Moreover, the AAPD for 62 different systems of binary, ternary, and up to eight-component systems has been calculated. The AAPD of PR EOS for these mixtures is 7.26%; however, using the proposed model reduced this value to 1.17 and 1.19 for the optimized parameters and the generalized correlations, respectively.

Modeling and Experimental Studies on Phase and Chemical Equilibria in High-Pressure Methanol Synthesis

A solution method was developed to calculate the simultaneous phase and chemical equilibria in high-pressure methanol synthesis (P = 20 MPa, 463 <T <553 K). Algorithms were developed that explicitly consider the existence of a condensed phase and include dew point calculations. A modification of the Soave-Redlich-Kwong equation of state was used to correct for nonideal effects. Binary interaction coefficients were derived from literature data on high-pressure binary vapor liquid equilibria. Predicted equilibrium conversions, with and without formation of a liquid phase, were successfully verified with new experimental results on high-pressure methanol synthesis obtained in a packed bed methanol synthesis reactor. Experimental data coincide very well with model predictions for the equilibrium conversion and gas composition. Remarkably, in some situations the model calculations appeared to predict condensation followed by a disappearing liquid phase (retrograde-like behavior) with increasing extent of the methanol synthesis reactions. Finally, at equilibrium only a gas phase remained present.

Simulation of the phase behaviour of Athabasca vacuum residue + n-alkane mixtures

Phase behaviour measurement and prediction for ill-defined hydrocarbons such as vacuum residue + light hydrocarbons present significant challenges, from view-cell design and operation, to thermolysis reactions at high temperature to fluid speciation and phase stability analysis during equilibrium calculations. In a prior contribution, simulated phase behaviour results for Athabasca vacuum residue + n-decane mixtures based on the Peng–Robinson equation of state were presented. In that work, Athabasca vacuum residue pseudo components that were identified exogenously and parameters for the model were computed from these pseudo components using the Marrero and Gani group contribution method. Here, this thermodynamic model is extended to include Athabasca vacuum residue + n-alkanes from n-pentane to n-dodecane. Only binary interaction coefficient values between residue pseudo components and n-alkanes were tuned. Densities of co-existing liquid phases present in the three-phase regions are calculated and compared to the experimental data for AVR + n-decane. The simulations are in qualitative and quantitative agreement with measurements over a broad ranges of temperature, pressure, and composition. The results presented in this contribution illustrate the reliability of the proposed thermodynamic modeling approach and its potential use as a universal heavy oil modeling tool for the simulation of paraffinic deasphalting, separation and refining processes for ill-defined hydrocarbon mixtures.

Phase Behavior of High Pressure and Temperature Gas Reservoirs: Water Solubility and Density Measurement and Modeling from (3.7 to 132) MPa and Temperatures from (422 to 478) K

New water content and gas phase density data were measured for two synthetic light and intermediate gas mixtures from (3.7 to 132) MPa at temperatures of (422 and 478) K. The Cubic-Plus-Association equation of state (CPA EoS) was implemented in this study to reproduce the measured data. Accurate predictions were generated for the compositions of the equilibrium liquid and vapor phases by the CPA equation once the cross-association between molecules of water and light saturated hydrocarbons was considered in the phase equilibrium calculations. The performance of the CPA equation with zero binary interaction coefficients between water and hydrocarbons in reproducing the water content data was satisfactory; however the predicted hydrocarbons solubility data were poor. By coupling the CPA equation with the concept of cross-association no improvement was observed in the gas phase density predictions compared to the predicted results of the CPA equation with zero or tuned binary interaction coefficients.

Supercritical pressure–density–temperature measurements on CO 2–N 2, CO 2–O 2 and CO 2–Ar binary mixtures

This paper presents new supercritical volumetric measurements on three binary mixtures mainly composed of carbon dioxide. The interest in the tested mixtures derives primarily from carbon capture and storage applications. In particular, CO 2-rich streams with low amounts of nitrogen, oxygen and argon are representative of the flows that are treated by the compression units and the purification units employed in the oxy-fuel fired power plants. These flows are then transported from power plants to storage sites in supercritical conditions. For each type of binary mixture, two different molar compositions are here considered. Isothermal pressure–density–temperature measurements are performed for all the mixtures in a temperature range from 303 K to 383 K and in a pressure range from 1 MPa to 20 MPa by way of a vibrating tube densimeter-based apparatus. The experimental data are used subsequently for the regression of new binary interaction coefficients for two types of cubic equations of state, the Peng–Robinson and the Redlich–Kwong–Soave–Peneloux, and a multi-parameter equation, the Benedict–Webb–Rubin–Starling. The absolute deviations with respect to experimental data are in the range 2.10–2.56%, 3.05–4.07% and 1.71–1.97% for the three equations respectively. The results confirm the superiority of the multi-parameter equation of state over the cubic models in the supercritical region.

Thermodynamic modeling of hydrogen sulfide solubility in ionic liquids using modified SAFT-VR and PC-SAFT equations of state

Equations of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) and the perturbed chain statistical associating fluid theory (PC-SAFT) have been used to model the PVT behavior of ionic liquids and the solubility of H 2S in six imidazolium-based ionic liquids. The studied systems included [bmim][PF6], [hmim][PF6], [bmim][BF4], [hmim][BF4], [bmim][NTF2] and [hmim][NTF2] at various temperatures and pressures. For pure components, parameters of the models have been obtained by fitting the models to experimental data on liquid densities; the average relative deviation between the calculated and experimental densities for ionic liquids is less than 2.42% in the PC-SAFT model and 5.44% in the SAFT-VR approach, the latter which incorporates the square-well potential for short-range interactions. In both models an additional term has been added to account for dipole–dipole interactions between solute molecules resulting from the permanent charges on the chain molecules of the solvents. The model parameters have also been correlated as functions of the molecular weight of the solvents. For binary mixtures of ionic liquids and H 2S, the association interactions between H 2S molecules and between the ionic liquids and H 2S molecules have also been taken into account in both approaches, using binary interaction coefficients. The results show an average deviation of less than 5% in the calculation of the mole fraction of H 2S in the ionic liquids. The effect of inclusion of the polar term has been studied for binary systems in both models.

Experimental study of high pressure phase equilibrium of (CO 2 + NO 2/N 2O 4) mixtures

Experimental bubble pressure, as well as liquid density of (CO 2 + NO 2/N 2O 4) mixtures are reported at temperatures ranging from (298 to 328.45) K. Experiments were carried out using a SITEC high-pressure variable volume cell. Transition pressures were obtained by the synthetic method and liquid density was deduced from measurement of the cell volume. Correlation of experimental results was carried out without considering chemical equilibrium of NO 2/N 2O 4 system. (Liquid + vapour) equilibrium was found to be accurately modelled using the Peng–Robinson equation of state with classical quadratic mixing rules and with a binary interaction coefficient k ij equal to zero. Nevertheless, modelling of liquid density values was unsatisfactory with this approach.

Combined chemical and phase equilibrium for the hydration of ethylene to ethanol calculated by means of the Peng–Robinson–Stryjek–Vera equation of state and the Wong–Sandler mixing rules

Due to the economics of the ethylene market and the subsidized production of fermentation-based ethanol in some countries, use of the ethylene hydration process to make ethanol has been steadily declining. The economics of this process might improve by combining the reaction and separation in a reactive distillation column, whose conceptual design requires a study of the combined chemical and phase equilibrium (CPE) of the reacting system. In this work, the Peng–Robinson–Stryjek–Vera equation of state was combined with the UNIQUAC activity coefficient model through the Wong–Sandler (WS) mixing rules in order to correlate the available experimental data for the vapor–liquid equilibria (VLE) of the ethylene–water, ethylene–ethanol, and ethanol–water binary systems at 200 °C. The interaction energies of the UNIQUAC model and the binary interaction coefficient of the WS mixing rules were used as the fitting parameters. From the optimum values of these parameters, both the VLE and the combined CPE of the ethylene–water–ethanol ternary system were predicted at 200 °C and various pressures. At this temperature, the catalytic activity of a H-pentasil zeolite has already been reported to exhibit a maximum for ethylene hydration, and also the experimentally measured two-phase region of the ternary system is sufficiently wide. By means of the reactive flash method, the chemical equilibrium compositions of the liquid and vapor phases were determined for several pressures, and the equilibrium conversion and the vapor fraction were calculated as functions of the ethylene to water feed mole ratio. It turns out that the vapor–liquid mixed-phase hydration of ethylene achieves equilibrium conversions much higher than those computed for a vapor-phase reaction that would hypothetically occur at the same conditions of pressure and feed mole ratio. It was found that the reactive phase diagram of the ternary system exhibits a critical point at 200 °C and 155 atm.

Solubility of light reservoir gasses in water by the modified Peng-Robinson plus association equation of state using experimental critical properties for pure water

Cubic-Plus-Association (CPA) equations of state (EOS) have found special interest in thermodynamic modeling of processes in which the solubility of light gasses in water is important. In this class of EoSs the association contribution of Helmholtz free energy proposed by Wertheim has been added to cubic EoSs such as Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) to extend their application to associating substances. In the development of CPA EoSs it is a common practice to adjust the pure component properties like the critical temperature, the critical pressure and the acentric factor in addition to the association parameters. This work focuses on the extension of a modified version of PR (mPR) EoS to water by addition of the compressibility factor contribution based on Wertheim theory. However, in contrast to other CPA EoSs the critical properties and the acentric factor are not considered as adjustable parameters and their experimental values are used. The temperature dependent parameters of the mPR EoS are modified by introduction of two correction factors which are correlated as functions of reduced temperature. Different association site schemes were examined for water. The results show that the 2-site association scheme produces the best predictions. The average absolute percent deviations of 0.43% and 0.03% for liquid density and vapor pressure in the range of 0.422 < T r < 0.980 were obtained. Then the solubilities of light hydrocarbon gasses (CH 4, C 2H 6, C 3H 8 and n-C 4H 10), and some common industrial non-hydrocarbon gasses (H 2S and CO 2) were calculated over wide ranges of pressure and temperature. Binary interaction coefficients (BIP) were regressed as a function of temperature. Accurate results show that the proposed model is able to produce excellent description of pure water properties as well as the solubilities of light gasses in water.

Salting-Out Effect of NaCl and KCl on the Liquid–Liquid Equilibrium of Water + 2-Methylpropanoic Acid + (1-Methylethyl)-benzene System at Several Temperatures

The salting-out effect of NaCl and KCl on the liquid–liquid equilibrium (LLE) of the ternary system of {water (1) + 2-methylpropanoic acid (2) + (1-methylethyl)-benzene (3)}, a recommended system for liquid–liquid extraction investigations, was studied at temperatures of (288.15, 298.15, and 313.15) K. The generated data for salt-free system have been used to estimate the binary molecular interaction parameters for the nonrandom two-liquid (NRTL) activity coefficient model. Results show that this model reproduces very good tie lines by estimated binary molecular interaction coefficients. The distribution coefficient of 2-methylpropanoic acid between organic/aqueous phases increases with its concentration, both in salt-free and in the presence of salt cases; however, it decreases moderately with temperature, within the range used. Adding a 0.05 mass fraction (based on mass of initial water) NaCl leads to an average enhancement of about 4 4% in distribution coefficient, and hence, it reaches to about 124 % ...