New insight into prediction of phase behavior of natural gas hydrate by different cubic equations of state coupled with various mixing rules

Progress in hydrate thermodynamic study necessitates robust and fast models to be incorporated in reservoir simulation softwares. However, numerous models presented in the literature makes selection of the best,proper predictive model a cumbersome task. It is of industrial interest to make use of cubic equations of state(EOS) for modeling hydrate equilibria. In this regard, this study focuses on evaluation of three common EOSs including Peng–Robinson, Soave–Redlich–Kwong and Valderrama–Patel–Teja coupled with van der Waals and Platteeuw theory to predict hydrate P–T equilibrium of a real natural gas sample. Each EOS was accompanied with three mixing rules, including van der Waals(vd W),Avlonitis non-density dependent(ANDD) and general nonquadratic(GNQ). The prediction of cubic EOSs was in sufficient agreement with experimental data and with overall AARD% of less than unity. In addition, PR plus ANDD proved to be the most accurate model in this study for prediction of hydrate equilibria with AARD% of 0.166.It was observed that the accuracy of cubic EOSs studied in this paper depends on mixing rule coupled with them,especially at high-pressure conditions. Lastly, the present study does not include any adjustable parameter to be correlated with hydrate phase equilibrium data.

A compositional model for CO_(2) ooding including CO_(2) equilibria between water and oil using the Peng–Robinson equation of state with the Wong–Sandler mixing rule

This paper presents a three-dimensional, three-phase compositional model considering CO2 phase equilibrium between water and oil. In this model, CO2 is mutually soluble in aqueous and hydrocarbon phases, while other components, except water,exist in hydrocarbon phase. The Peng–Robinson(PR) equation of state and the Wong–Sandler mixing rule with non-random two-liquid parameters are used to calculate CO2 fugacity in the aqueous phase. One-dimensional and three-dimensional CO2 flooding examples show that a significant amount of injected CO2 is dissolved in water. Our simulation shows 7% of injected CO2 can be dissolved in the aqueous phase, which delays oil recovery by 4%. The gas rate predicted by the model is smaller than the conventional model as long as water is undersaturated by CO2, which can be considered as 'lost' in the aqueous phase. The model also predicts that the delayed oil can be recovered after the gas breakthrough, indicating that delayed oil is hard to recover in field applications. A three-dimensional example reveals that a highly stratified reservoir causes uneven displacement and serious CO2 breakthrough. If mobility control measures like water alternating gas are undertaken, the solubility e ects will be more pronounced than this example.

Thermodynamic Consistency Test for Binary Gas ＋ Water Equilibrium Data at Low and High Pressures

Phase equilibrium in binary gas + water mixtures over wide ranges of temperatures and pressures are modeled and tested for thermodynamic consistency. For modeling, the Peng-Robinson equation of state was used and the Wong-Sandler mixing rules were incorporated into the equation of state parameters. In the Wong-Sandler mixing rules the van Laar model for the excess Gibbs energy was applied. In addition, a reasonable and flexible method is applied to test the thermodynamic consistency of pressure-temperature-concentration(P-T-x) data of these binary mixtures.Modeling is found acceptable in all cases, meaning that deviations in correlating the pressure and the gas phase concentration are low. For all cases the thermodynamic consistency method gives a clear conclusion about consistency or inconsistency of a set of experimental P-T-x data.

A Modified Mixing Rule for PSRK Model and Application for the Prediction of Vapor-Liquid Equilibria of Polymer Solutions

To extend the PSRK (predictive Soave-Redlich-Kwong equation of state) model to vapor-liquid equilibria of polymer solutions, a new EOS-gE mixing rule is applied in which the term ∑ xi ln(b/bi) in the PSRK mixing rule for the parameter a, and the combinatorial part in the original universal functional activity coefficient (UNIFAC) model are cancelled. To take into account the free volume contribution to the excess Gibbs energy in polymer solution, a quadratic mixing rule for the cross co-volume bij with an exponent equals to 1/2 is applied[bij1/2= 1/2(bi1/2+bj1/2)]. The literature reported Soave-Redlich-Kwong equation of state (SRK EOS) parameters ofpure polymer are employed. The PSRK model with the modified mixing rule is used to predict the vapor-liquid equilibrium (VLE) of 37 solvent-polymer systems over a large range of temperature and pressure with satisfactory results.

Extension of LCVM-type mixing rule to three-parameter equations of state for vapor-liquid equilibria of mixtures

In this paper, the LCVM mixing rule is extended to the multi-parameter equations of state by combining infi- nite-pressure and zero-pressure mixing rule models. The new LCVM-type mixing rule, coupled with Patel-Teja equation of state (EOS) is applied for vapor-liquid equilibria of different polar and non-polar systems in which the NRTL activity coefficient model is used to calculate the excess Gibbs free energy. The tested results agree well with existing experimental data within a wide range of temperatures and pressures. In comparison with the Van der Waals mixing rule, the new mixing rule gives much better corre- lations for the vapor-liquid equilibria of non-polar and polar systems.

Extension of Huron-Vidal-type Mixing Rule to Three-parameter Harmens-Knapp Cubic Equation of State

In this paper was extended the HV-type mixing rules to Harmens-Knapp cubic equation state(HK CEOS). The new HV-type mixing rule with HK CEOS was tested for Vapor-liquid equilibrium(VLE) of different polar and nonpolar systems. The tested results are in good agreement with existing experimental data within a wide range of temperatures and pressures. In comparison with the VDW mixing rule, the new mixing rule gives much better predictions for the VLE of nonpolar and polar systems.

A New Excess Free Energy Mixing Rule for Representing Vapor-Liquid Equilibria of Mixed Refrigerants

A suitable mixing rule is important for vapor liquid equilibrium(VLE)investigations for mixed refrigerants.In this work,a new excess free energy mixing rule(MRv)was proposed at zero pressure based on the linear relationship between dimensionless parameter 1/(u-1)and a.MRv mixing rule was explicit adopted variable liquid molar volume.The applicable temperature range of MRv could be extended by means of an empirical method to estimate the liquid molar volume for components at high temperatures.Three mixing rules modified Huron-Vidal mixing rule(MHV1),Wong-Sandler mixing rule(WS),and MRv at two reference pressures were used to compare the VLE data in the calculation of 37 mixed refrigerants.Results demonstrated that MRv had a relatively similar accuracy to MHV1 and WS for component and pressure calculation.Moreover,the average excess Gibbs free energy using the MRv mixing rule for the 37 selected mixed refrigerants(0.0013)was much lower than those using the MHV1(0.0078)and WS(0.0809)mixing rules,which was very valuable for the design and optimization of thermodynamic systems using mixed refrigerants.

Presenting decision tree for best mixing rules and Z-factor correlations and introducing novel correlation for binary mixtures

The significance of gas compressibility factor in petroleum engineering encourages the researchers to employ the most accurate and precise methods for estimation of this factor.Commonly,empirical correlations due to their simplicity have been referred more than other approaches for prediction of Z-factor.There is no clear and reliable report to address an appropriate combination of correlation and mixing rule for each type of gas.In the present study,combination of several empirical correlations and mixing rules is examined and a decision tree is constructed to suggest best combination for each gas system.For this reason,2329 experimental data were used for analysis.According to the results,LelandeMueller mixing rule/Sanjari and Lay correlation is the best combination for sour and natural gas.Also,Van NesseAbbot mixing rule/HalleYarborough correlation,StewarteBurkhardteVoo mixing rule/Heidarian correlation and SattereCampbell mixing rule/Papay correlation are the most appropriate combination for gas condensate,binary and ternary mixtures respectively.For binary mixtures,a robust and novel empirical correlation was developed based on Kay mixing rule to estimate Z-factor.The results employed how good the new correlation is in agreement with the experimental data with significant R-squared 0.9843.

Phase Equilibrium Calculation of Mixtures: Comparison of SAFT, Modified SAFT, and BACK EOS for Supercritical CO_2-C_2H_5OH System

Three calculational models, statistical associating fluid theory (SAFT), modified SAFT, and Boublík Alder Chen Kreglewshi (BACK) are compared for supercritical CO 2 C 2H 5OH using a set of van der Waals type mixing rules for both the BACK equation of state (EOS) and the SAFT EOS. Equations are presented for the residual Helmholtz free energy, residual chemical potentials, and compressibilty factor for mixtures. A comparison with experimental vapor liquid equilibrium (VLE) data reveals that the BACK EOS together with the suggested mixing rules provides more accurate prediction of the binary system than the SAFT or the modified SAFT model with no adjustable binary parameters. The correlation results are improved with an adjustable parameter.