Valderrama Patel Teja Research Articles

Use of Thermodynamically Consistent Phase Equilibrium Data to Obtain a Generalized Padé-Type Model for the Henry’s Constants of Gases in Ionic Liquids

A generalized Padé-type expression is proposed for Henry’s constant of gases in ionic liquids. The constants are determined using an equation of state, and generalized expressions for the Henry’s constants of the gases in the ionic liquids are proposed. The solute gases included in the study were oxygen, hydrogen, and carbon monoxide in three solvent ionic liquids ([MDEA][Cl], [Bmim][PF6], and [Hmim][TF2N]). The Valderrama–Patel–Teja equation of state with the mixing rules of Kwak and Mansoori are employed to correlate the solubility data, to examine the thermodynamic consistency of the experimental data, and to determine the fugacity (fi) for each concentration (xi) of the solute gas in the liquid phase. From these data, the fugacity coefficients (fiL/xi) are determined to obtain Henry´s constant as Hi = lim(fiL/xi) when xi→0. The calculated Henry’s constants are correlated in terms of the temperature and acentric factor of the gases to finally obtain a generalized expression for Henry´s constant, Hi.

A comprehensive thermodynamic modeling of the solubility of sugar alcohols in ionic liquids

Environmental regulations have recently drawn attention from fossil sources to green materials, among which sugar alcohols (SA) have particular importance due to their vast use in the nutrition, pharmaceutical, and chemical industries. Their properties and equilibrium conditions, including the extraction and solubility behavior utilizing novel solvents such as ionic liquids (ILs), are essential for developing further processes and their optimization. On account of this, the present study aims to develop a comprehensive thermodynamic approach based on simple and accurate tools such as activity coefficient models (ACMs) and equations of state (EoSs), which have not been hitherto addressed. To this end, eleven calculation schemes based on these two approaches were applied to the largest databank investigated thus far (13 SAs, 21 ILs, and 653 data points), and the performance of the models was analyzed. NRTL, free-volume Flory-Huggins (FVFH), and Redlich-Kister (RK) ACMs with different schemes, as well as athermal and ideal solution models, were evaluated and compared against well-known cubic EoSs such as Peng-Robinson (PR) and Valderrama-Patel-Teja (VPT). Benefitting from three adjustable parameters and a simple form, the three-parameter RK model yielded the best results with a 0.82 % (2.77 K) deviation in the entire databank. Moreover, employing temperature-dependent interaction parameters with FVFH ACM (3.55 K, 1.05 %), PR EoS (3.60 K, 1.07 %), and VPT EoS (3.66 K, 1.08 %) improved the accuracy of the calculations remarkably. The results of this contribution prove that thermodynamic models based on NRTL, FVFH, and RK ACMs are the best options for calculating solid–liquid conditions equilibrium of SA-IL systems with a simple and precise calculation procedure, and can therefore be employed for the simulation and optimization tools. This study investigates the most extensive SA-IL databank, a large number of models from different routes, and the nature of SA-IL pairs employing the obtained parameters.

Modeling solubility of CO2\u2013N2 gas mixtures in aqueous electrolyte systems using artificial intelligence techniques and equations of state

Determining the solubility of non-hydrocarbon gases such as carbon dioxide (CO2) and nitrogen (N2) in water and brine is one of the most controversial challenges in the oil and chemical industries. Although many researches have been conducted on solubility of gases in brine and water, very few researches investigated the solubility of power plant flue gases (CO2–N2 mixtures) in aqueous solutions. In this study, using six intelligent models, including Random Forest, Decision Tree (DT), Gradient Boosting-Decision Tree (GB-DT), Adaptive Boosting-Decision Tree (AdaBoost-DT), Adaptive Boosting-Support Vector Regression (AdaBoost-SVR), and Gradient Boosting-Support Vector Regression (GB-SVR), the solubility of CO2–N2 mixtures in water and brine solutions was predicted, and the results were compared with four equations of state (EOSs), including Peng–Robinson (PR), Soave–Redlich–Kwong (SRK), Valderrama–Patel–Teja (VPT), and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT). The results indicate that the Random Forest model with an average absolute percent relative error (AAPRE) value of 2.8% has the best predictions. The GB-SVR and DT models also have good precision with AAPRE values of 6.43% and 7.41%, respectively. For solubility of CO2 present in gaseous mixtures in aqueous systems, the PC-SAFT model, and for solubility of N2, the VPT EOS had the best results among the EOSs. Also, the sensitivity analysis of input parameters showed that increasing the mole percent of CO2 in gaseous phase, temperature, pressure, and decreasing the ionic strength increase the solubility of CO2–N2 mixture in water and brine solutions. Another significant issue is that increasing the salinity of brine also has a subtractive effect on the solubility of CO2–N2 mixture. Finally, the Leverage method proved that the actual data are of excellent quality and the Random Forest approach is quite reliable for determining the solubility of the CO2–N2 gas mixtures in aqueous systems.

Toward predicting SO2 solubility in ionic liquids utilizing soft computing approaches and equations of state

BackgroundThe use of novel and green solvents like ionic liquids (ILs) for the capture of air pollutant gases has gained extensive attention in recent years. However, getting reliable and fast predictions of gases solubility in ILs is complex. MethodsFour soft computing methods including deep belief network (DBN), group method of data handling (GMDH), genetic programming (GP), and K-nearest neighbor (KNN) were utilized for estimating the solubility of sulfur dioxide (SO2) in ILs. A total of 374 experimental data points of SO2 solubility in 15 types of ILs were collected and used for model development. Moreover, Valderrama-Patel-Teja (VPT), Zudkevitch-Joffe (ZJ), Peng-Robinson (PR), Redlich-Kwong (RK), and Soave-Redlich-Kwong (SRK) equations of state (EOSs) were applied for the solubility predictions in the SO2 + ILs systems. Significant findingsThe results illustrated that DBN model is the most reliable predictive tool for the SO2 solubility in ILs by having an average absolute percent relative error (AAPRE) of 3.56%. Furthermore, the proposed simple to use GMDH mathematical correlation also provides good estimations with an AAPRE of 8.05%. Despite the weaker performance of the EOSs than the intelligent models, the PR EOS presented better estimations among other EOSs for the SO2 solubility in ILs.

Evaluating cubic equations of state for predictions of solid-fluid equilibrium in liquefied natural gas production

Solid formation and deposition in liquefied natural gas (LNG) production is a process hazard avoidable by careful determination of impurity solubility in the process stream. Accurate freeze-out predictions for LNG require robust thermodynamic models tuned to high-quality experimental data. Cubic equations of state (EoS) can be used to calculate solid–fluid equilibria (SFE) for LNG-relevant binary mixtures with the necessary accuracy, while retaining the computational efficiency ideal for process simulations. A comprehensive literature survey of the available experimental SFE data of LNG-relevant binary mixtures was carried out and used to determine the optimal binary interaction parameters for a range of commonly-used cubic EoS. Overall, the Peng-Robinson (PR) EoS performed best representing the SFE temperatures with a standard uncertainty of less than 2 K for most of the examined mixtures; the Soave-Redlich-Kwong (SRK), Peng-Robinson-Stryjek-Vera (PRSV) and Patel-Teja-Valderrama (PTV) equations produced similar results. The solubility of various impurities in methane was investigated with the optimized EoS across a range of temperatures, and various retrograde behaviors were examined. The EoS models and the best-fit parameters obtained in this work have been incorporated into the ThermoFAST desktop application and a new free online implementation ThermoFAST Web.

Influence of thermodynamically inconsistent data on modeling the solubilities of refrigerants in ionic liquids using an artificial neural network

In this work, a general thermodynamic consistency test is applied to analyze phase equilibrium data (PTx) for binary refrigerant and ionic liquid mixtures. The Valderrama-Patel-Teja (VPT) equation of state and the Kwak and Mansoori (KM) mixing rules are employed to correlate the solubility data of several refrigerants in different ionic liquids, and the Gibbs-Duhem equation is employed to check the thermodynamic consistency of six hundred forty-two experimental data points. The main purpose of this work is to analyze the influence of experimental data that are declared thermodynamically inconsistent on modeling the solubilities of refrigerants in ionic liquids using an artificial neural network. The results obtained via the test are classified into three categories: thermodynamically consistent, not fully consistent and thermodynamically inconsistent. Subsequently, a multilayer perceptron is trained to predict solubility in three cases: i) learning with isotherms that are declared thermodynamically consistent; ii) learning with isotherms, including those that are declared thermodynamically consistent and those that are not fully consistent; and iii) learning with all isotherms, even those that are declared thermodynamically inconsistent. For each case, the architecture, input combination and number of parameters necessary to achieve reasonable predictions are determined. The results show that the use of thermodynamically consistent and not fully consistent data is sufficient for finding an artificial neural network with a reasonable number of parameters.

Experimental and modeling using a generalized Patel-Teja-Valderrama equation of state for computation of mono ethanol amine (MEA) solution density in a CO2 capturing pilot plant

In this work, to obtain optimal process conditions in a CO2 capturing plant, novel equipment modifications are made to achieve the desired product specification in the small and large pilot plants with low and high pressures. For this purpose, results from two different CO2 capturing pilot plants are compared at different process variables, using the different concentration of aqueous MEA (25, 28, 30, 33) wt.% and within the temperature range of 50 ~ 77°C in the absorber and 100 ~120°C in desorber. We used the generalized Patel-Teja-Valderrama (PTV) EoS, Peng-Robinson (PR) EoS, and Soave-Redlich-Kwong (SRK) equation of state through a MATLAB code and Aspen Plus default with the NRTL model. Moreover, critical properties for MEA solutions are estimated based on Valderrama et al. approach. The correlation relation of the PTV EoS was used for the calculation of MEA liquid density data for rich and lean Mono-Ethanol Amine (MEA) solution in the CO2 capturing pilot plants. Comprehensive studies were carried out to investigate the validity of the present predictions provided by the experimental results' implementation. Finally, with proper process modification, the predicted liquid density values by Patel-Teja-Valderrama (PTV) EoS were achieved with an average absolute deviation (AAD %) of about 0.12 ~ 0.23 in different temperature profiles in absorber section and 0.14 ~ 0.26 in desorber section for both pilot plants. In the present work, the results of Patel-Teja-Valderrama EoS in the present simulation model were in good agreement with the experimental data.

A model based on the equality of chemical potentials for describing the liquid-liquid interfaces of water-hydrocarbons up to high pressures

A reliable model was used to describe the interfacial tension, composition, and density of the liquid-liquid interfaces of water-hydrocarbons. The parachor model was combined with the equality of the chemical potential of components at the interface and the bulk liquid. The fugacity coefficient was used for computing chemical potentials. To compute the fugacity coefficients of the components, various types of equations of state (The Valderrama Patel-Teja, cubic plus association, and the simplified Perturbed-Chain Statistical Association Fluid Theory) were utilized. These models were applied to the temperature and the pressure range of (285.65–423) K and (1–3000) bar, respectively. The adjustable parameters of these models were regressed based on the experimental interfacial tensions of (water/hydrocarbon) binary systems at the pressure of 1 bar. These adjustable parameters were used to predict the interfacial tension, composition, and density of (water/hydrocarbon) binary systems at high pressures. It was found that Valderrama Patel-Teja (AAD% = 1.49) and cubic plus association (AAD% = 2.33) equations of state had the best results for ternary and quaternary systems, respectively.

Comparison of different alpha functions, α(Tr), applied in the prediction of supercritical properties of different polar and nonpolar fluids at Boyle temperature

The Boyle temperature is the temperature at which the second virial coefficient becomes zero. In this work, capability of different alpha functions, α(Tr), in prediction of supercritical properties of different polar and nonpolar fluids at Boyle temperature is investigated. In this direction, eight different alpha functions, α(Tr), including Peng – Robinson original form (1976), Coquelet et al. (2004), Haghtalab et al. (2011), Saffari – Zahedi (2013), Soave – Redlich – Kwong original form (1972), Ozokwelu – Erbar (1987), Soave (1993) and Nasrifar – Bolland (2004) are coupled with different cubic equations of states including Peng – Robinson (PR), Soave – Redlich – Kwong (SRK), volume – translated Peng – Robinson (VTPR), volume translated Soave Redlich-Kwong (VTSRK) and Patel ‒ Teja ‒ Valderrama (PTV). The obtained results have been compared with the most popular relations, such as Tsonopoulos and Meng – Duan correlations. To understand better, the second virial coefficient and Zeno line have been also depicted and compared with the available experimental data. In addition, the residual properties (HR, SR, UR, and GR) and the second order thermodynamic derivatives (Cp, Cv, us, μJT) at the Boyle condition have been also investigated. Furthermore, the trend of the inversion temperature (Tinv) versus the Boyle temperature is studied for n-alkanes, n-alkenes, amines and noble gases.

The Antoine equation of state: Rediscovering the potential of an almost forgotten expression for calculating volumetric properties of pure compounds

Antoine is mainly known for the equation usually used for predicting vapor pressure of pure compounds that bears his name. In this article we show a little known equation of state (EoS), as well as its functionality to predict current PvT properties of more than forty compounds including industrial, noble, and organic gases. The Antoine EoS has been parameterized in three regions: Pr<1.2,1.2⩽Pr⩽10 and Pr>10 in order to improve its performance in the widest possible area. The proposed sets of optimized parameters were fitted by minimizing deviations after comparing predicted values with available experimental data in open literature.The volumes predicted with the optimized Antoine EoS have been compared with those calculated with the widely-known Soave-Redlich-Kwong (SRK), Peng-Robinson-Stryjek-Vera (PRSV2) and Valderrama-Patel-Teja (VPT) equations of state. Results obtained by using the optimized Antoine EoS show better accuracy in the zone of high reduced pressures for all compounds and, in a more general way, for most of the compounds in the remaining zones than the other equations of state. The extension to noble gases and other compounds originally not taken into account by Antoine have been successfully achieved.

Prediction of the Boyle temperature, second virial coefficient and Zeno line using the cubic and volume – translated cubic equations of state

In this study, the Boyle temperature of 174 substances are predicted using the cubic and volume – translated cubic equations of state. In this regard, the Peng - Robinson (PR), Soave – Redlich – Kwong (SRK), volume – translated Peng – Robinson (VTPR), volume – translated Soave – Redlich – Kwong (VTSRK) and Patel – Teja – Valderrama (PTV) equations of state are used. The Boyle temperature is calculated for different polar, non – polar and associating substances including alkanes, cycloalkanes, alkenes, aromatics, ethers, esters, ketones, refrigerants, halogens, amines and water. The obtained results are compared with the results of other known correlations published so far, such as Tsonopoulos, Meng – Duan and Estrada – Torres et al. equations. For better understanding, the second virial coefficient and the Zeno line (unit compressibility) are also calculated and compared with the available experimental data. The results show that PR, VTPR and PTV have lower average temperature difference between EoSs and Tsonopoulos or Meng – Duan correlations. The dependency of the reduced Boyle temperature (TB/TC) as functions of the Pitzer's acentric factor (ω), hydrocarbon chain length (NC) and the reduced dipole moment (μR) has been also studied.

The Impact of Vapor/Liquid-Equilibria Calculations on Scale-Prediction Modeling

Summary Vapor/liquid-equilibria (VLE) calculations, particularly involving the phase behavior of carbon dioxide (CO2) and hydrogen sulfide (H2S), are used in scale-prediction modeling. In this work, the impact of VLE calculations for CO2- and H2S-rich gas phases and for acid- and sour-gas mixtures on scale-prediction calculations is evaluated. Three equations of state (EOSs)—Soave-Redlich-Kwong (SRK) (Soave 1972), Peng-Robinson (PR) (Peng and Robinson 1976), and Valderrama-Patel-Teja (VPT) (Valderrama 1990)—are implemented in the Heriot-Watt model and used in VLE calculations. The solubility of single-component CO2 and H2S in water and the solubility of a gas mixture in water were compared with experimental data in terms of the absolute relative deviation (ARD). The solubility data were then used in PHREEQC (USGS 2016) to calculate the impact of using different EOSs on carbonate and sulfide scales, particularly on calcium carbonate (CaCO3) and iron sulfide (FeS). Average ARDs of 6.04, 4.10, and 3.77% between experimental and calculated values for CO2 solubility in water were obtained for the SRK, PR, and VPT EOSs, respectively. Similarly, for H2S solubility in water, average ARDs of 6.49, 6.66, and 6.48% were obtained for each EOS, respectively. For the solubility of sour- and acid-gas mixtures in water, average ARDs of 13.92, 13.25, and 10.78% were obtained, respectively. It has thus been concluded that the VPT EOS performs better than the SRK and PR EOSs in VLE calculations for the analyzed data. The errors introduced in VLE calculations have been found to impact the calculation of the amount of CaCO3 precipitated, with consequences for scale-inhibitor selection. Higher deviations were found in the amount of CaCO3 precipitation for gas mixtures when compared with a single-component, CO2-rich phase. Furthermore, the large errors occurring in VLE calculations for H2S solubility have not been found to impact the calculation of the amount of FeS precipitated when H2S is in excess with respect to Fe2+. In addition to this, a case study that was performed by use of formation-water data from the Brazilian presalt revealed that the choice of EOS can cause errors of 6 kg of precipitate during each day of production. Scale-prediction calculations carried out with PHREEQC demonstrate that VLE calculations can have a high impact on mineral precipitation. Thus, it is recommended that the best VLE model available should always be used for scale-prediction modeling, particularly when mixtures of gases are present.

Evaluation of various types' equations of state for prediction of rate of double gas hydrate formation based on Kashchiev model in flow loop apparatus

This paper compares the effects of using various types of equations of state such as Peng Robinson (PR), Soave Redlich Kwong (SRK), Esmaeilzadeh – Roshanfeker (ER), Patel Teja (PT) and Valderrama–Patel–Teja (VPT) on the rate of hydrate formation based on the Kashchiev model for gaseous mixtures with experimental data points obtained in a mini flow loop apparatus in presence of the kinetic inhibitors (such as modified starch and l-tyrosine) at various pressures (1–4 MPa) and specified temperature (277.15 K). For this purpose, a laboratory mini flow loop apparatus was set up to measure the rate of gas hydrate formation when a hydrate forming mixture is contacted with water in the presence or absence of dissolved inhibitor under suitable temperature and pressure conditions. In each experiment, a water blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of the required gas make-up. The total average absolute deviation was found to be 18.7%, 19.8%, 19.2%, 20.2% and 20.7% of the PR, ER, SRK, VPT and PT equations of state for calculating of gas consumption for gaseous mixtures during gas hydrate formation (in the presence and absence of kinetic gas hydrate inhibitor), respectively. Comparison results between the calculated and experimental data points of gas consumption were obtained in a flow loop indicate that the PR and ER equations of state have lower errors than the SRK, VPT and PT equations of state for this model.

The importance of liquid phase compositions in gas hydrate modeling: Carbon dioxide–methane–water case study

Liquid compositions obtained through vapor+liquid+hydrate equilibrium modeling are often neglected and not reported in literature. This work demonstrates the sensitivity and importance of the liquid phase compositions on selected models and parameters. The equations of state used to model two-phase systems are the Soave–Redlich–Kwong, the Valderrama–Patel–Teja and the Trebble–Bishnoi equations of state. The modeling analysis for three-phase systems is based on the Trebble–Bishnoi equation of state along with the model by van der Waals and Platteeuw. The vapor+liquid equilibrium model predictions at gas hydrate formation conditions were found to be greatly dependant on the liquid phase compositions. At the three-phase equilibrium, small modifications in the equation of state’s interaction parameters significantly affected the liquid composition predictions while leaving the vapor compositions mostly unchanged. Lastly, the interaction parameters were optimized for the two phases separately using vapor+liquid equilibrium data. When optimized only for liquid, vapor and liquid compositions were predicted correctly. However, when optimized only for vapor, liquid compositions failed to fit experimental data.

Assessment of clathrate hydrate phase equilibrium data for CO2 + CH4/N2 + water system

Outlier diagnostic in phase equilibrium data of binary clathrate hydrates containing CO2 is the main aim of the present work. The treated experimental data are concerning the clathrate hydrates of CO2+CH4/N2 in the presence of water. The utilized algorithm applies the basis of a mathematical approach, in which the statistical Hat matrix, Williams plot, and the residuals of two models results bring about the probable outliers detection. The range of applicability of the applied models and quality of the existing experimental data are also investigated. The van der Waals and Platteeuw (vdW–P) solid solution theory is used to model the hydrate phase, and the Valderrama–Patel–Teja equation of state (VPT-EoS) along with the non-density dependent (NDD) mixing rules is applied to deal with the fluid phases in the first model. The compositions of the vapor phase in equilibrium with gas hydrate and liquid water as well as the equilibrium pressures are predicted through the mentioned model. The second model includes a correlation proposed by Adisasmito et al., which is utilized to represent the hydrate dissociation pressures for three-phase equilibrium conditions (liquid water–vapor–hydrate). It is interpreted from the obtained results that the applied models for calculation/estimation of the phase behavior of the investigated binary clathrate hydrate systems have wide ranges of applicability. Consequently, we may, with high confidence level, say that among all data treated, one experimental equilibrium pressure value and four experimental hydrate dissociation values are probable doubtful ones.

Experimental Measurements and Predictions of Gas Hydrate Dissociation Conditions in the Presence of Methanol and Ethane-1,2-diol Aqueous Solutions

In this work, experimental hydrate dissociation conditions of methane in the presence of 0.06, 0.10, and 0.20 mass fractions of methanol and 0.10 and 0.25 mass fractions of ethane-1,2-diol in aqueous solutions are reported. In addition, phase equilibria of a ternary mixture of methane (0.9319 mole fraction) + ethane (0.0481 mole fraction) + propane (0.02 mole fraction) in the presence of 0.25 mass fraction of ethane-1,2-diol aqueous solution is investigated. A high-pressure equilibrium cell is used for measurement of hydrate dissociation conditions in the temperature range of (265.4 to 282.0) K and pressure range of (1.97 to 6.96) MPa. The experimental gas hydrate dissociation conditions are modeled using the van der Waals and Platteeuw (vdW-P) solid solution theory for dealing with the hydrate phase and the Valderrama–Patel–Teja equation of state (VPT-EoS) along with the nondensity dependent (NDD) mixing rules to account for the fluid phases. The obtained experimental data are finally compared with selected experimental data from the literature as well as the model predictions, and acceptable agreements are observed.

Experimental Data Assessment Test for Composition of Vapor Phase in Equilibrium with Gas Hydrate and Liquid Water for Carbon Dioxide + Methane or Nitrogen + Water System

Accurate knowledge of the compositions of the equilibrium phases in the systems containing gas hydrates is essential for many hydrate-based separation processes. Unfortunately, there are limited sets of such experimental data available in the literature partly due to the difficulties in measurements of the compositions of the phases in equilibrium with gas hydrate. Consequently, satisfactory accuracy of the measurements may not be obvious. Therefore, reliability of the corresponding data should be checked prior to their further applications. In this article, we present a thermodynamic assessment test (consistency test) based on the area test approach for the experimental compositional data of vapor phase in equilibrium with gas hydrate + liquid water for the carbon dioxide + methane or nitrogen + water system. The van der Waals and Platteeuw (vdW-P) solid solution theory is used to model the hydrate phase, and the Valderrama–Patel–Teja equation of state (VPT-EoS) along with the nondensity dependent (NDD) mixing rule is applied to deal with the fluid phases. The results show that only one of the studied experimental data sets seems to be thermodynamically consistent, and the rest of the data seem to be either not fully consistent or inconsistent.

Experimental study and thermodynamic modelling of methane clathrate hydrate dissociation conditions in silica gel porous media in the presence of methanol aqueous solution

In this work, the phase equilibria of clathrate hydrates of methane in the presence of pure water and 0.035 mass fraction of methanol aqueous solution in confined silica gel pores with (10 and 15)nm mean diameters are measured and reported. A thermodynamic model is also developed for prediction of the obtained experimental hydrate dissociation data. The Valderrama–Patel–Teja (VPT-EoS) equation of state (EoS) accompanied with the non-density dependent (NDD) mixing rules coupled with a previously developed activity model are applied to evaluate the fugacity of the species present and the activity coefficient of water in methanol aqueous solution. Acceptable agreement between the reported data and the predicted results using the proposed model and an existing method reported in the literature demonstrates the reliability of the presented model.

Applications of cubic equations of state for determination of the solubilities of industrial solid compounds in supercritical carbon dioxide: A comparative study

Representation/predictions of the solubilities of industrial solid compounds in supercritical carbon dioxide have been a challenge since the last two decades. In this communication, the Soave–Redlich–Kwong (SRK), the Peng–Robinson (PR), the Patel–Teja–Valderrama (PTV), the Esmaeilzadeh–Roshanfekr (ER) and the modified Esmaeilzadeh–Roshanfekr (m-ER) equations of state (EoS) accompanied with several mixing rules including the Wong–Sandler (WS), the covolume-dependent (CVD) and the van der Waals one (vdW1) and two (vdW2) fluid mixing rules are applied to calculate/estimate the solubilities of 23 mostly used solid compounds in supercritical carbon dioxide. In addition, the Van-Laar excess Gibbs energy (Gex) activity model is also used in phase equilibrium calculations. The probable global optimal values of the proposed thermodynamic model parameters are evaluated by the differential evolution (DE) optimization strategy. The results indicate that the combination of the m-ER EoS with the WS mixing rule leads to more accurate predictions (AARD=7%) in comparison with other ones. Finally, application of Chrastil semi-empirical correlation for estimation of the solubilities of several compounds in supercritical carbon dioxide is investigated at wide ranges of temperatures.

Effect of various types of equations of state for prediction of simple gas hydrate formation with or without the presence of kinetic inhibitors in a flow mini-loop apparatus

This paper compares the effects of using various types of equations of state (PR, 1 1 Peng–Robinson. SRK, 2 2 Soave–Redlich–Kwong. ER, 3 3 Esmaeilzadeh–Roshanfekr. PT 4 4 Patel–Teja. and VPT 5 5 Valderrama–Patel–Teja. ) on the calculated driving force and rate of gas consumption based on the Kashchiev and Firoozabadi model for simple gas hydrate formation for methane, carbon dioxide, propane and iso-butane with experimental data points obtained in a flow mini-loop apparatus with or without the presence of kinetic inhibitors at various pressures and specified temperatures. For this purpose, a laboratory flow mini-loop apparatus was set up to measure gas consumption rate when a hydrate forming substance (such as C 1, C 3, CO 2 and i-C 4) is contacted with water in the presence or absence of dissolved inhibitor under suitable temperature and pressure conditions. In each experiment, a water blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of the required gas make-up. The total average absolute deviation was found to be 15.4%, 16.3%, 15.8%, 17.8% and 17.4% for the PR, ER, SRK, PT and VPT equations of state for calculating gas consumption in simple gas hydrate formation with or without the presence of kinetic hydrate inhibitors, respectively. Comparison results between the calculated and experimental data points of gas consumption were obtained in flow loop indicate that the PR and ER equations of state have lower errors than the SRK, VPT and PT equations of state for this model.