Soave-Redlich-Kwong Equation Of State Research Articles

A Cubic Equation of State with a Repulsion Term

A new cubic equation of state (EoS) was proposed to address the lack of repulsion terms in conventional cubic EoSs, with a molar critical compressibility factor Zc = 0.273 and suitable for most molecular fluids. Similar to Soave-Redlich-Kwong (SRK) EoS, its α-function is related to the fluids’ acentric factors by fitting with 44 molecular fluids. Differently, the new EoS can pass the α-consistency test, confirming the robustness across all temperatures. With only three parameters (ac, b, m) to be determined, it is as convenient as the SRK EoS in application. But it is more accurate - tested against experimental data - for both single and multi-component fluids than SRK EoS.

Simulation of multiphase behavior in supercritical CO2–heavy oil–water sludge extraction systems using Cubic-Plus-Association Equation of State

A new methodology was proposed for predicting the multiphase behavior of a supercritical CO2–heavy oil–water–solvent system during supercritical CO2 extraction. The cubic-plus-association equation of state (CPA EoS) was used to model the hydrogen bond association between asphaltene and water and to develop a nine-step characterization method for asphaltene-containing oil. Results showed that the proposed method could represent phase behavior for three equilibrium phases: the vapor phase and high-density and low-density liquid phases. The absolute average relative deviation between the predicted and experimental phase boundary pressures was 3.6–11.8%, smaller than those (7.0–20.8%) calculated using Soave–Redlich–Kwong EoS with Huron–Vidal mixing rules. Moreover, case studies on appropriate extraction conditions showed that the extraction pressure increased with increasing molecular weight and critical pressure of each pseudocomponent. Increasing extraction pressure for H2O-containing systems was beneficial for improving extraction efficiency.

Flash point prediction of binary partially and totally miscible alcohol-water mixtures by various equation of states and experimental validation

In the present article, the experimental flash points (FPs) of partially miscible and non-ideal mixtures including 3-pentanol + water, 2-pentanol + water, and 1-hexanol + water are reported for the first time. The measured FPs were predicted based on the vapor pressure concept and ‎thermodynamic equilibrium. The cubic-plus-association (CPA) equation of state (EoS) along with the CR-1 combining rule and Elliot combining rule (ECR) were used to investigate the non-ideality of investigated systems. In the following, the same method was used with the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) EoSs to evaluate whether simpler EoSs can accurately predict the FPs of non-ideal mixtures. Therefore, in addition to 3-pentanol + water, 2-pentanol + water, and 1-hexanol + water, numerous totally and partially miscible aqueous-organic systems containing 1-pentanol, isobutanol, 2-butanol, 1-‎butanol, isopropanol, propanol, ethanol, and methanol were studied in terms ‎of FP prediction. The findings indicated that SRK is marginally more effective than PR. Moreover, ‎SRK EoS was almost as effective as the CPA EoS with the CR-1 combining rule. The CPA EoS ‎that used ECR, on the other hand, was far superior to the SRK and PR EoSs. To the best of our knowledge, CPA parameters for 2-pentanol, 3-pentanol, and 1-‎hexanol were calculated and reported for the first time.

Validation of Soave–Redlich–Kwong equation of state coupled with a classical mixing rule for sound speed of non-ideal gas mixture of oxygen-hydrogen as liquid rocket propellants

Numerical simulations of inlet jets flow of propellants in the main combustion chamber equipped in a liquid rocket engine have been conducted by compressible CFD technics employing a van der Waals-type equation of state (EOS) and chemical reaction models. Various simulations have been already conducted both for combustion and non-combustion state in the chamber; however, the accuracy of EOS for the mixture of propellant employing a classical mixing rule (CMR), particularly for the sound speed, has not been understood well. Therefore, we have validated the applicability of Soave–Redlich–Kwong (SRK) EOS as one of the van der Waals-type EOSs coupled with the CMR for the sound speed using molecular dynamics (MD) simulations against an imaginary model of oxygen-hydrogen mixture system. We found that SRK EOS coupled with a well-employed CMR can reproduce the sound speed in the MD simulations within a relative error of several percent and that the CMR hardly increases the deviation of the SRK EOS in the single component. The present results suggest that the SRK EOS with the CMR cannot be the main factor to cause critical errors in the CFD based on RANS, which will give reliability to current CFD simulations for internal flows in a combustion chamber of a liquid rocket engine.

Experimental analysis and thermodynamic modelling of lenalidomide solubility in supercritical carbon dioxide

• Lenalidomide (LND) solubility in supercritical CO 2 (sc-CO 2 ) was measured for the first time. • Solubility data were correlated by different density-based models. • Experimental data was also correlated by Modeified Wilson and SRK models. • The accuracy of the models was evaluated by statistical criteria (AARD %), ( Radj ). • Thermodynamic enthalpies of Lenalidomide were estimated. Reduction of the size of pharmaceutical particles to micro/nano scale is an approved strategy to enhance their dissolution rate at decremented side effects. Production of drug micro/nanoparticles via a supercritical carbon dioxide (sc-CO 2 )- based process requires accurate data on the drug solubility in sc-CO 2 . In this study, the solubility of Lenalidomide (LND), an anti-cancer, was experimentally determined in sc-CO 2 at various temperatures (308–338 K) and pressures (120–300 bar). Furthermore, the obtained solubility data were correlated by different theoretical methods. LND solubility, in terms of mole fraction, was obtained in the range of 0.02 × 10 −4 –1.08 × 10 −4 depending on the conditions. The empirical models with different adjustable parameters, Soave–Redlich–Kwong equation of state (SRK-EoS) with two parameters van der Waals (vdW2) mixing rule, and expanded liquid theory (modified Wilson’s model) were applied for experimental data correlation. According to the results, modified Wilson’s model can correlate LND solubility in sc-CO 2 with high accuracy. However, the SRK-EoS did not show acceptable accuracy in the correlation of LND solubility in sc-CO 2 . Among the empirical models, Alwi and Garlapati, Sung and Shim, Ch and Madras, Hozhabr et al. , Garlapati and Madras, Keshmiri et al. , Sparks et al. , Reddy and Garlapati, Bian et al. (2011) and Belghait et al. showed R adj values higher than 0.99 and produced the best correlation with 3,4, 5, 6 and 8 adjustable parameters, respectively. Moreover, the approximate values of total mixing heat ( Δ H total ) as well as vaporization ( Δ H vap ), and solvation ( Δ H sol ) enthalpies were computed.

Interface Mass Transfer in Reactive Bubbly Flow: A Rigorous Phase Equilibrium-Based Approach

In this work, the driving force of interfacial mass transfer is modeled as deviation from the gas–liquid equilibrium, which by assumption is thought to exist at the interface separating the gas and liquid phases. The proposed mass transfer model provides a flexible framework where the phase equilibrium description in the driving force can be substituted without difficulties, allowing the mass transfer modeling of distillation, absorption/stripping, extraction, evaporation, and condensation to be based on a thermodynamically consistent phase equilibrium formulation. Phase equilibrium by the Soave–Redlich–Kwong equation of state (SRK-EoS) is in this work compared to the results of the classical Henry’s law approach. The new model formulation can predict mass transfer of the solvent, which Henry’s law cannot. The mass transfer models were evaluated by simulating a single-cell protein process operated in a bubble column bioreactor, and the solubilities computed from the SRK-EoS and Henry’s law were in qualitative agreement, albeit in quantitative disagreement. At the reactor inlet, the solubility of O2 and CH4 was 150% higher with the SRK-EoS than with Henry’s law. Furthermore, the SRK-EoS was computationally more expensive and spent 10% more time than Henry’s law.

On the Evaluation of Interfacial Tension (IFT) of CO2–Paraffin System for Enhanced Oil Recovery Process: Comparison of Empirical Correlations, Soft Computing Approaches, and Parachor Model

Carbon dioxide-based enhanced oil-recovery (CO2-EOR) processes have gained considerable interest among other EOR methods. In this paper, based on the molecular weight of paraffins (n-alkanes), pressure, and temperature, the magnitude of CO2–n-alkanes interfacial tension (IFT) was determined by utilizing soft computing and mathematical modeling approaches, namely: (i) radial basis function (RBF) neural network (optimized by genetic algorithm (GA), gravitational search algorithm (GSA), imperialist competitive algorithm (ICA), particle swarm optimization (PSO), and ant colony optimization (ACO)), (ii) multilayer perception (MLP) neural network (optimized by Levenberg-Marquardt (LM)), and (iii) group method of data handling (GMDH). To do so, a broad range of laboratory data consisting of 879 data points collected from the literature was employed to develop the models. The proposed RBF-ICA model, with an average absolute percent relative error (AAPRE) of 4.42%, led to the most reliable predictions. Furthermore, the Parachor approach with different scaling exponents (n) in combination with seven equations of state (EOSs) was applied for IFT predictions of the CO2–n-heptane and CO2–n-decane systems. It was found that n = 4 was the optimum value to obtain precise IFT estimations; and combinations of the Parachor model with three-parameter Peng–Robinson and Soave–Redlich–Kwong EOSs could better estimate the IFT of the CO2–n-alkane systems, compared to other used EOSs.

Solubility of Water in Hydrogen at High Pressures: A Molecular Simulation Study

Hydrogen is one of the most popular alternatives for energy storage. Because of its low volumetric energy density, hydrogen should be compressed for practical storage and transportation purposes. Recently, electrochemical hydrogen compressors (EHCs) have been developed that are capable of compressing hydrogen up to P = 1000 bar, and have the potential of reducing compression costs to 3 kWh/kg. As EHC compressed hydrogen is saturated with water, the maximum water content in gaseous hydrogen should meet the fuel requirements issued by the International Organization for Standardization (ISO) when refuelling fuel cell electric vehicles. The ISO 14687-2:2012 standard has limited the water concentration in hydrogen gas to 5 μmol water per mol hydrogen fuel mixture. Knowledge on the vapor liquid equilibrium of H2O-H2 mixtures is crucial for designing a method to remove H2O from compressed H2. To the best of our knowledge, the only experimental high pressure data (P > 300 bar) for the H2O-H2 phase coexistence is from 1927 [J. Am. Chem. Soc., 1927, 49, 65-78]. In this paper, we have used molecular simulation and thermodynamic modeling to study the phase coexistence of the H2O-H2 system for temperatures between T = 283 K and T = 423 K and pressures between P = 10 bar and P = 1000 bar. It is shown that the Peng-Robinson equation of state and the Soave Redlich-Kwong equation of state with van der Waals mixing rules fail to accurately predict the equilibrium coexistence compositions of the liquid and gas phase, with or without fitted binary interaction parameters. We have shown that the solubility of water in compressed hydrogen is adequately predicted using force-field-based molecular simulations. The modeling of phase coexistence of H2O-H2 mixtures will be improved by using polarizable models for water. In the Supporting Information, we present a detailed overview of available experimental vapor-liquid equilibrium and solubility data for the H2O-H2 system at high pressures.

Generalized critical shifts of confined fluids in nanopores with adsorptions

Confined fluids undergo substantial changes in terms of their physicochemical properties when the pore radius reduces to the nanometric scale and be comparable to the molecular size. Adsorptions, which are the corresponding changes in the concentration of a given fluid at the interface compared with the other contacting phase, strongly affect the vapour-liquid equilibrium (VLE), especially in nanopores. No published literature so far has been found to study the critical shifts of confined fluids with adsorptions in nanopores. In this study, first, the van der Waals (vdW) and Soave-Redlich-Kwong (SRK) equations of state (EOSs) are extended to calculate the VLE of confined fluids in nanopores. Second, a new empirical correlation is developed to calculate the fluid adsorption thickness in nanopores. Finally, two generalized analytical formulations, on a basis of the modified vdW and SRK EOSs, are initially proposed to calculate the shifts of critical temperatures and pressures by considering the fluid adsorptions in nanopores. All the extended EOSs, new adsorption correlation, and two generalized formulations have been validated to be accurate by comparing with the experimental or literature data. Overall, the critical properties of the confined fluids are found to shift more with adsorptions in nanopores. Moreover, the compressibility factors of the confined Lennard–Jones fluids are proven to be universal and independent of the pore radius effect.

Modeling the Saturation Pressure of Systems Containing Crude Oils and CO2 Using the SRK Equation of State

This work investigates the saturation pressure of crude oil–CO2 mixtures and how the oil plus-fraction characterization methods affect it. Different distribution functions were tested to split the plus-fraction as well as correlations to calculate the critical parameters and the acentric factor. The Soave–Redlich–Kwong (SRK) equation of state was used to calculate the saturation pressure of the crude oil and its mixtures with pure and impure CO2. The results were compared with experimental data and reveal that the effect of the characterization methods on the modeling of the saturation pressure of reservoir fluids is strong mainly for CO2 molar fraction values higher than 50%.

Prediction of phase equilibrium of methane hydrate below 272.2 K based on different equations of state

By revealing that a key parameter D in Chen-Guo model is related to the temperature T, a new temperature-dependent parameter D(T) trained by the reported experimental data is proposed with Chen-Guo model to improve the prediction accuracy of phase equilibrium conditions of methane hydrate in the range of 145.75 K- 272.2 K. Four equations of state (EOS) such as Redlich-Kwong (RK), Soave- Redlich-Kwong (SRK), Peng-Robinson (PR) and Patel-Teja (PT) are chosen to calculate the gas fugacity respectively and the corresponding prediction accuracy is evaluated by the average absolute deviation percentage (AADP). The process of training D(T) based on the Chen-Guo model employed with SRK EOS is described in detail first, and the prediction results show that the corresponding prediction accuracy is greatly improved, whose AADP decreases from 10.83% to 3.31%. In order to verify that training D(T) is an effective way to improve the prediction accuracy, the same procedure is also used to the Chen-Guo models employed with RK, PR and PT EOS respectively, and the corresponding AADP decreases from ∼11% to ∼3%. In addition, the prediction accuracy according to the proposed D(T) is also evaluated by other temperatures different from the data used for training D(T) to verify its feasibility and effectiveness.

Modeling of the Asphaltene Onset Pressure from Few Experimental Data: A Comparative Evaluation of the Hirschberg Method and the Cubic-Plus-Association Equation of State

Asphaltene onset pressure (AOP) is a key parameter to determine the flow assurance of live oils. In this study, the capabilities of the cubic-plus-association (CPA) equation of state (EoS) and the Hirschberg method of calculating the AOP of five oils are compared to a new approach using few experimental data. Two experimental data points of AOP and only one of the bubble pressure (BP) are required for adequate parametrization of both models. The number of non-zero binary interaction parameters needed for the CPA EoS is reduced to only four binary pairs. In the Hirschberg method, the BP calculations were performed with the Soave–Redlich–Kwong EoS. For all oils, the CPA EoS provided lower deviations for both AOP and BP. To achieve a good correlation, the Hirschberg method requires the use of AOP experimental data to calculate the difference between the liquid-phase solubility parameter and the asphaltene solubility parameter. Similarly, CPA EoS requires the calculation of the cross-associating energy parame...

Thermodynamic modeling of phase equilibria of clathrate hydrates formed from CH4, CO2, C2H6, N2 and C3H8, with different equations of state

Abstract A thermodynamic model to predict three phase (L-H-V and I-H-V) equilibria of gas hydrates is presented. In this model we have employed a fugacity based approach where the hydrate phase is modeled using van der Waals-Platteeuw solid solution theory and the liquid phase activity coefficients are determined from the modified UNIFAC method. For the vapour phase fugacity calculations we have investigated three equations of state (EOS): Peng-Robinson-Stryjek-Vera (PRSV), Patel-Teja (PT) and Soave-Redlich-Kwong (SRK). This model employs only parameters reported in the literature. The coexistence pressures predicted by our model for the sI hydrates of methane, carbon dioxide and ethane are in reasonable agreement with experiments, whereas our model overestimates the coexistence pressures for the sII clathrates of nitrogen and propane. The predicted cage occupancies are found to increase with increasing temperature in the L-H-V equilibria. For I-H-V equilibria the cage occupancy is observed to decrease with temperature. We have also estimated the solubility of each guest in the liquid phase (for L-H-V equilibria) using the Henry’s law. The solubilities predicted using all three EOS are in good agreement for all guest molecules, with the exception of nitrogen where at relatively higher temperatures the estimates from the PRSV EOS are noticeably lower than the corresponding predictions from the PT and SRK EOS.

Optimization of the Reduced Temperature Associated with Peng–Robinson Equation of State and Soave–Redlich–Kwong Equation of State To Improve Vapor Pressure Prediction for Heavy Hydrocarbon Compounds

A pragmatic technique has been developed to optimize the reduced temperature for the acentric factor associated with the Peng–Robinson equation of state (PR-EOS) and the Soave–Redlich–Kwong equation of state (SRK-EOS) by minimizing the deviation between the measured and calculated vapor pressures for nonhydrocarbon compounds and hydrocarbon compounds including heavy alkanes up to n-tritetracontane (n-C43H88) under different conditions. All the compounds are divided into four categories, that is, light-saturated hydrocarbons, heavy-saturated hydrocarbons, aromatic compounds, and other compounds, among which the first three categories are used to examine their effects on the optimum reduced temperature for the entire database. By redefining the reduced temperature, three existing alpha functions together with the newly developed alpha functions for the PR-EOS as well as one existing alpha function and the newly developed alpha functions for the SRK-EOS are then used to evaluate their respective accuracy of ...

Phase behavior and densities of propylene + toluene and ethylene + toluene systems to 580 K and 70 MPa

In this study, we report phase behavior data for propylene + toluene and ethylene + toluene mixtures at temperatures to 580 K and pressures to 8.5 MPa. We also report high-pressure, mixture density data for the two mixtures at temperatures to 555 K and pressures to 70 MPa. Both the phase behavior and density data are simultaneously determined using a windowed variable-volume, high-pressure view cell coupled with a linear variable differential transformer. The phase behavior and mixture density data are modeled with the Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), Modified Sanchez–Lacombe (MSL), and Perturbed–Chain Statistical Associating Fluid Theory (PC-SAFT) equations of state (EoS). The PC-SAFT and MSL EoS provide very good fits of the phase behavior for both the propylene + toluene and ethylene + toluene systems with each binary interaction parameter, kij, set to zero. The PC-SAFT equation also provides the best fit of the high-pressure, mixture density data for the ethylene + toluene system. However, the SRK EoS provides the best fit of the high-pressure, mixture density data for the propylene + toluene system. Although both equations slightly over predict the solution density for the two studied systems, the fit of the densities are insensitive to small variations in kij.

Prediction of thermodynamic behavior of binary mixtures by applying the crossover approach to Soave–Redlich–Kwong equation of state

Thermodynamic analysis of binary mixtures near the critical region is essential for many chemical process designs. In this research, based on isomorphism principle and incorporating general crossover approach the original Soave–Redlich–Kwong (SRK) equation of state (EOS) was developed for the binary mixtures. We have introduced an additional term in the crossover function in order to take into account the difference between the classical critical parameters and the real critical parameters. The applicability of this crossover EOS was verified against methane–ethane mixture to describe their thermodynamic properties over a wide range of thermodynamic states, because of their wide applications. It is shown that based on this approach we can received too much more accuracy for predicting thermodynamic properties in comparison with classical form of SRK EOS.

Uncertainty assessment of equations of state with application to an organic Rankine cycle

ABSTRACTEvaluations of equations of state (EoS) should include uncertainty. This study presents a generic method to analyse EoS from a detailed uncertainty analysis of the mathematical form and the data used to obtain EoS parameter values. The method is illustrated by comparison of Soave–Redlich–Kwong (SRK) cubic EoS with perturbed-chain statistical associating fluid theory (PC-SAFT) EoS for an organic Rankine cycle (ORC) for heat recovery to power from the exhaust gas of a marine diesel engine using cyclopentane as working fluid. Uncertainties of the EoS input parameters including their corresponding correlation structure, are quantified from experimental measurements using a bootstrap method. Variance-based sensitivity analysis is used to compare the uncertainties from the departure function and the ideal-gas contribution. A Monte Carlo procedure propagates fluid parameter input uncertainty onto the model outputs. Uncertainties in the departure function (SRK or PC-SAFT EoS) dominate the total uncertainties of the ORC model output. For this application and working fluid, SRK EoS has less predictive uncertainty in the process model output than does PC-SAFT EoS, though it cannot be determined if this is due to differences in the data for parameter estimation or in the mathematical form of the EoS or both.

A new correlation for vapor pressure prediction of natural gas mixture

ABSTRACTIn this study, the Antoine equation of vapor pressure prediction for pure substances has been extended to predict vapor pressure values of a natural gas mixture at a temperature range of 125–230 K. The correlation was modified by applying the software MATLAB 8.2 R2013b (The MathWorks, Natick, MA). The developed correlation for multicomponent natural gas mixture is predictable with few input data of critical temperature, critical pressure, and the acentric factor. For the examined natural gas mixture, the predicted vapor pressures show comparable values with those obtained by applying well-known and accurate cubical equation of state (EOS) of Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR) for the whole range of studied temperatures. From the results, an average absolute deviation of 1.735% for the developed correlation in this work was obtained from the actual results calculated experimentally, which is lower than that obtained by SRK EOS and close to results of PR EOS.

Prediction of water solubilities in hydrocarbons and oils using F-SAC coupled with SRK–EoS

In the present work, the F-SAC (Functional-Segment Activity Coefficient) model was used to predict the water solubility at high temperatures (and pressures) of defined hydrocarbons and non-defined oil fractions. Since in the F-SAC model no pressure effects are considered, the model was coupled with the Soave-Redlich-Kwong (SRK) equation of state by means of the Self-Consistent Mixing Rule (SCMR) in order to properly compute high-pressure data. The F-SAC parameters for hydrocarbon-water systems were revised using the combined model SRK + SCMR(F-SAC) and a data set with 648 infinite-dilution activity coefficient (IDAC), and 589 liquid-liquid equilibrium (LLE) points, including high temperature and pressure data. For defined hydrocarbon–water systems, calculated absolute average deviation (AAD) in logarithm units for IDAC and LLE were 0.12 and 0.29 respectively. The determination coefficients were close to 1.0, which indicates a strong correlation between the calculations and the experimental data. For the non-defined oil predictions, the F-SAC group fragmentation was simply determined by assuming a linear alkane structure. In spite of this crude approximation, for the studied petroleum fractions, the proposed model was capable of satisfactory represent the experimental water solubility data, with an overall AAD 0.088 for the logarithm of molar fractions.

Comparison of SRK and CPA equations of state for phase equilibrium of binary and ternary systems containing aromatics

In this work, the binary and ternary vapor–liquid and liquid–liquid equilibrium (VLE and LLE) data of different systems including N-formylmorpholine (NFM), alkanes, aromatics are collected from previously published literature and then modeled using two different equations of state including Soave–Redlich–Kwong (SRK) and cubic-plus-association (CPA). Since the main purpose of this work is set on the evaluation of the SRK and CPA EoS's capability for modeling of polar systems and to know the importance of association part of CPA EoS, binary and ternary systems of NFM are considered as the objective function. Besides, this investigation is directed in a way that a single “engineering approach” obtains for applying CPA to NFM–aromatic mixtures. Respect to this, different approaches are used to find the functionality of modeling using CPA EoS. These approaches including 3 association schemes for pure NFM (assuming a non-associating compound or a self-associating fluid with two or four association sites) and different possibilities to model mixtures of NFM+Ethylene Glycol (EG) and aromatics (application of just one interaction parameter kij or assuming cross-association interactions leads to obtain relevant parameters either via a combining rule). At last, based on the obtained results it is concluded that CPA is a powerful model that can be used for predictions of binary and ternary mixture properties even without adjustable interaction parameters. In addition, the results revealed that the functionality of the CPA EoS is higher than the SRK EoS in most of the cases especially for predicting the vapor pressure of NFM solvent.