A Proxy Peng-Robinson EOS for Efficient Modeling of Phase Behavior

Equation-of-state (EOS) compositional simulation is commonly used to model the interplay between phase behavior and fluid flow for various reservoir and surface processes. Because of its computational cost, however, there is a critical need for efficient phase-behavior calculations using an EOS. The objective of this research was to develop a proxy model for fugacity coefficient based on the Peng-Robinson EOS for rapid multiphase flash in compositional flow simulation. The proxy model as implemented in this research is to bypass the calculations of fugacity coefficients when the Peng-Robinson EOS has only one root, which is often the case at reservoir conditions. The proxy fugacity model was trained by artificial neural networks (ANN) with over 30 million fugacity coefficients based on the Peng-Robinson EOS. It accurately predicts the Peng- Robinson fugacity coefficient by using four parameters: Am, Bm, Bi, and ΣxiAij. Since these scalar parameters are general, not specific to particular compositions, pressures, and temperatures, the proxy model is applicable to petroleum engineering applications as equally as the original Peng-Robinson EOS. The proxy model is applied to multiphase flash calculations (phase-split and stability), where the cubic equation solutions and fugacity coefficient calculations are bypassed when the Peng-Robinson EOS has one root. The original fugacity coefficient is analytically calculated when the EOS has more than one root, but this occurs only occasionally at reservoir conditions. A case study shows the proxy fugacity model gave a speed-up factor of 3.4% in comparison to the conventional EOS calculation. Case studies also demonstrate accurate multiphase flash results (stability and phase split) and interchangeable proxy models for different fluid cases with different (numbers of) components. This is possible because it predicts the Peng-Robinson fugacity in the variable space that is not specific to composition, temperature, and pressure. For the same reason, non-zero binary iteration parameters do not impair the applicability, accuracy, robustness, and efficiency of the model. As the proxy models are specific to individual components, a combination of proxy models can be used to model for any mixture of components. Tuning of training hyperparameters and training data sampling method helped reduce the mean absolute percent error to less than 0.1% in the ANN modeling. To the best of our knowledge, this is the first generalized proxy model of the Peng-Robinson fugacity that is applicable to any mixture. The proposed model retains the conventional flash iteration, the convergence robustness, and the option of manual parameter tuning for fluid characterization.

Modeling the solubility of carbon dioxide in the MDEA + AEEA aqueous solution using the SAFT-HR equation of state and extended UNIQUAC model

In this study, a thermodynamic model has been used to determine the solubility of carbon dioxide in an aqueous solution which is the combination of methyldiethanolamine (MDEA) and aminoethylethanolamine (AEEA). The physical equilibriums have been considered between the liquid and vapor phases and chemical equilibrium in the liquid phase. The SAFT-HR equation of state has been used to specify the fugacity coefficients of the components in the vapor phase. The liquid phase is considered as an electrolyte solution besides; the extended UNIQUAC has been applied to figure out the activity coefficients. The bubble point calculation has been used in this research. This method includes two main loops. Calculations related to chemical equilibrium are performed in the interior loop and the ones associated with phase equilibrium are done in the exterior loop. The solubility of carbon dioxide has been predicted by the optimized parameters of the model in the temperature range of 308.2–368.2 K. It has been calculated that the absolute average relative deviations of the model are 16.65, 19.33, 28.91 and 19.99 in the calculation of partial pressure of carbon dioxide in various loadings at the temperatures of 308.2, 328.2, 343.2 and 368.2 K.

Numerical Modeling of CO2, Water, Sodium Chloride, and Magnesium Carbonates Equilibrium to High Temperature and Pressure

In this work, a thermodynamic model of CO2-H2O-NaCl-MgCO3 systems is developed. The new model is applicable for 0–200 °C, 1–1000 bar and halite concentration up to saturation. The Pitzer model is used to calculate aqueous species activity coefficients and the Peng–Robinson model is used to calculate fugacity coefficients of gaseous phase species. Non-linear equations of chemical potentials, mass conservation, and charge conservation are solved by successive substitution method to achieve phase existence, species molality, pH of water, etc., at equilibrium conditions. From the calculated results of CO2-H2O-NaCl-MgCO3 systems with the new model, it can be concluded that (1) temperature effects are different for different MgCO3 minerals; landfordite solubility increases with temperature; with temperature increasing, nesquehonite solubility decreases first and then increases at given pressure; (2) CO2 dissolution in water can significantly enhance the dissolution of MgCO3 minerals, while MgCO3 influences on CO2 solubility can be ignored; (3) MgCO3 dissolution in water will buffer the pH reduction due to CO2 dissolution.

Binary Mutual Diffusion Coefficients of Polymer/Solvent Systems Using Compressible Regular Solutions Theory and Free Volume Theory

The free volume theory has found practical application for prediction of diffusional behavior of polymer/solvent systems. In this paper, reviewing free volume theory, binary mutual diffusion coefficients in some polymer/solvent systems have been systematically presented through chemical thermodynamic modeling in terms of both activity coefficients and fugacity coefficients models. Here chemical thermodynamic model of compressible regular solution (CRS) was used for evaluation of diffusion coefficients calculations as the pure component properties would be required only. Four binary polymeric solutions of cyclohexane/polyisobutylene,

Effect of Nonideal Solution Behavior on Desalination of a Sodium Chloride Solution and Comparison to Seawater

Proper evaluation of the Gibbs free energy and other properties of seawater and other aqueous solutions is essential in the analysis of desalination systems. Standard seawater has been studied extensively and property data are readily accessible. However, many aqueous solutions requiring desalination have significantly different compositions from seawater and seawater data are generally not accurate for these solutions. Experimental data for a given aqueous solution may be unavailable under the conditions of interest. Therefore, there is a need to model relevant physical properties from chemical thermodynamic principles. In particular, for solutions that are not ideal, the activity and fugacity coefficients must be considered. In this paper, the effect of nonidealities in sodium chloride (NaCl) solutions is considered through a parametric study of the least work of separation for a desalination system. This study is used to determine the conditions under which the ideal solution approximation is valid and also to determine when an NaCl solution is a good approximation to standard seawater. It is found that the ideal solution approximation is reasonable within ranges of salinities and recovery ratios typical of those found in the seawater desalination industry because many of the nonidealities cancel out, but not because the solution behaves ideally. Additionally, it is found that NaCl solutions closely approximate natural seawater only at salinities typically found in seawater and not for salinities found in typical brackish waters.

Effect of Nonideal Solution Behavior on Desalination of a Sodium Chloride (NaCl) Solution and Comparison to Seawater

Proper evaluation of the Gibbs free energy and other properties of seawater and other aqueous solutions is essential in the analysis of desalination systems. Standard seawater has been studied extensively and property data are readily accessible. However, many aqueous solutions requiring desalination have significantly different composition from seawater and seawater data is generally not accurate for these solutions. Experimental data for a given aqueous solution may be unavailable under the conditions of interest. Therefore, there is a need to model relevant physical properties from chemical thermodynamic principles. In particular, for solutions that are not ideal, the activity and fugacity coefficients must be considered. In this paper, the effect of nonidealities in sodium chloride (NaCl) solutions is considered through a parametric study of the least work of separation for a desalination system. This study is used to determine the conditions under which the ideal solution approximation is valid and also to determine when an NaCl solution is a good approximation to standard seawater. It is found that the ideal solution approximation is reasonable within ranges of salinities and recovery ratios typical of those found in the seawater desalination industry because many of the nonidealities cancel out, but not because the solution behaves ideally. Additionally, it is found that NaCl solutions closely approximate natural seawater only at salinities typically found in seawater and not for salinities found in typical brackish waters.