Modified Peng-Robinson Equation Research Articles

Mathematical modeling of mass transfer in CO2 injection for confined fluids at near-miscible condition

Complex interaction between fluid and solid in tight formations leads to capillary confinement and interface slip. Mass transfer between oil and CO2 in CO2 flooding is essential to understand the flow complexity. Therefore, the objective of this work is to propose a comprehensive model to analyze the mass transfer during CO2 injection in the confined fluids. The modified Peng-Robinson equation of state considering the fluid-wall interaction and adsorption was established to calculate the properties of hydrocarbons and CO2. Relative permeability for the near-miscible state was then estimated using the new relative permeability model with corner flow effect. Predicted results agree well with the experimental observations. Afterwards, it was integrated with a one-dimension mathematical model to analyze the physical mechanisms of CO2 flooding in tight reservoirs. Results indicate that nanoconfinement increases the relative permeability at near-miscible condition, and confined fluid is more likely to be miscible than the bulk fluid. Additionally, nanoconfinement can reduce the velocity of CO2 front and increase the breakthrough time of CO2, which is favorable to improve the efficiency of CO2 flooding. This model provides a deep understanding of mass transfer between CO2 and hydrocarbons, and it can be integrated with compositional simulators to solve the field-scale cases including the microscale mechanism of tight reservoirs.

Adaptive thermodynamic consistency control via interface thickness in pseudopotential lattice Boltzmann method across wide temperature ranges

Multiphase flow phenomena are ubiquitous in real-life applications, and the pseudopotential-based lattice Boltzmann multiphase simulation method has gained extensive usage in fields such as fuel cells, energy storage materials, and boiling heat transfer. Over the past two decades, significant improvements have been made to the pseudopotential model. These advancements have greatly enhanced its accuracy in simulating various processes. In this paper, we employ a numerical stability-based unit conversion scheme to ensure an accurate representation of real-world material properties. Additionally, we introduce a more precise non-ideal two-parameter gas state equation Modified Peng-Robinson (MPR) that closely aligns with experimental data, surpassing the commonly used single-parameter Peng-Robinson state equations. Furthermore, we compare the accuracy of the two-state equations for polar and non-polar substances, finding improved accuracy for non-polar substances and a higher degree of fidelity for polar substances when using the MPR equation. We analyze the constant correction coefficients chosen for thermodynamic consistency regulation from the perspectives of vapor-liquid interface thickness and numerical stability, both when held constant and when employing a dynamic correction approach that balances vapor-liquid interface width, numerical stability, and thermodynamic consistency. Finally, we validate to ensure its practical applicability.

A multi-mechanism numerical simulation model for CO2-EOR and storage in fractured shale oil reservoirs

Under the policy background and advocacy of carbon capture, utilization, and storage (CCUS), CO2-EOR has become a promising direction in the shale oil reservoir industry. The multi-scale pore structure distribution and fracture structure lead to complex multiphase flow, comprehensively considering multiple mechanisms is crucial for development and CO2 storage in fractured shale reservoirs. In this paper, a multi-mechanism coupled model is developed by MATLAB. Compared to the traditional Eclipse 300 and MATLAB Reservoir Simulation Toolbox (MRST), this model considers the impact of pore structure on fluid phase behavior by the modified Peng–Robinson equation of state (PR-EOS), and the effect simultaneously radiate to Maxwell–Stefan (M–S) diffusion, stress sensitivity, the nano-confinement (N-C) effect. Moreover, a modified embedded discrete fracture model (EDFM) is used to model the complex fractures, which optimizes connection types and half-transmissibility calculation approaches between non-neighboring connections (NNCs). The full implicit equation adopts the finite volume method (FVM) and Newton–Raphson iteration for discretization and solution. The model verification with the Eclipse 300 and MRST is satisfactory. The results show that the interaction between the mechanisms significantly affects the production performance and storage characteristics. The effect of molecular diffusion may be overestimated in oil-dominated (liquid-dominated) shale reservoirs. The well spacing and injection gas rate are the most crucial factors affecting the production by sensitivity analysis. Moreover, the potential gas invasion risk is mentioned. This model provides a reliable theoretical basis for CO2-EOR and sequestration in shale oil reservoirs.

Adsorption effects on CO2-oil minimum miscibility pressure in tight reservoirs

CO2 miscible injection holds immense potential for enhancing tight oil recovery, where achieving the minimum miscibility pressure (MMP) is pivotal. Adsorption of CO2 and oil in pores affects the CO2-oil MMP in tight reservoirs, necessitating precise nanoscale MMP calculations and understanding influencing factors. Here, we applied a modified Peng-Robinson equation of state (PR-EOS) for nanoscale MMP calculations, incorporating adsorption layers and effective molar volume to describe adsorption effects. Validation against molecular simulations and nanofluidic experiments shows a maximum deviation of 4.6 %. We found that in nanopores, achieving miscibility demands less CO2 than in bulk. The CO2-oil MMP reduces as pore size decreasing, influenced by adsorption, critical point shift and capillarity. At 5 nm, the MMP is 11.12 MPa, 27.8 % lower than the bulk value (15.4 MPa). Adsorption intensifies this reduction by curtailing free molecules and effective pore radius, and becomes more pronounced for lighter hydrocarbon mixtures. However, the nanoscale CO2-oil MMP is equal to the bulk value when rp ≥ 350 nm. Furthermore, a maximum MMP and the corresponding transition temperature exist for each pore size, and increase as pore size increasing. This method provides a valuable tool for optimizing CO2 miscible injection and carbon storage in challenging nanoscale-pore reservoirs.

Measurement and Modeling the Properties and Equilibrium of Fluid Systems Involving Carbon Dioxide and Hydrocarbons

On the basis of molecular dynamics modeling (MD modeling) and experimental data pVTx, a study was made of the dynamic and thermodynamic properties of a binary system based on light gases containing heavy oil (A-B). The solvent (A) used was carbon dioxide and n-alkanes (methane, ethane, and propane) in the supercritical fluid (SCF) state. Measurements of the pVTx properties were carried out in the temperature, density, and pressure ranges near the critical parameters of the light gas-heavy oil systems. Based on pVTx data and MD modeling in the A-B system, the diffusion coefficient (D) was determined near the critical parameters of the solvent. The values of D in the binary system SCF carbon dioxide or alkanes containing (methane, ethane and propane) heavy oil from the Siyazan field of Azerbaijan are calculated. The D SCF value of methane and ethane in the A-B system is higher than in a system containing SCF propane at given concentrations (c or x) of heavy oil and temperature. The value of D SCF of light gases in the A-B system increases with an increase in the concentration of heavy oil up to x = 2.5 wt. %. Diffusing molecules of SCF gases reduce the viscosity of heavy oil in the A-B system. Dependence D = f(c) tends to have an asymptotic value with increasing oil concentration. In the A-B system, the dependence of D SCF gases on pressure has a non-monotonic form. To calculate mixtures of light gases, the modified Peng-Robinson equation of state (PR EOS) was used. The isothermal dependence P-x of the carbon dioxide-methane binary system is approximated. The calculated P-x curves are consistent with the experimental ones in the temperature range 277-345 K.

Determination of Concentration-Dependent Effective Diffusivity of Each Gas Component of a Binary Mixture in Porous Media Saturated with Heavy Oil under Reservoir Conditions

Summary One frequently used enhanced heavy oil recovery technique is gas injection, during which heavy oil viscosity is reduced due to diffusion of gaseous components and heavy oil swelling in porous media. Effective diffusivities of gas components are generally assumed to be constants, while no attempts have been made to determine both the concentration-dependent effective diffusivity in porous media saturated with heavy oil and the preferential contribution of each component in a binary/ternary gas mixture. In this study, a pragmatic and robust technique has been proposed to determine the concentration-dependent effective diffusivity of each gas component by reproducing the experimental measurements during pressure decay tests for CO2-C3H8-heavy oil systems in porous media. Experimentally, CO2 and C3H8 are utilized to diffuse into sandpacks fully saturated with heavy oil. Under a constant temperature within a thermostatic chamber, the pressures of the aforementioned gas(es)-heavy oil systems are consistently tracked and saved while gas samples are taken at the start and end of the diffusion tests for gas chromatography analyses. Theoretically, a mass transfer model is formulated to determine effective gas diffusivity in heavy oil as a concentration-dependent function by incorporating Fick’s second law and the modified Peng-Robinson equation of state (PR EOS). The concentration-dependent effective diffusivity for each gas component is ascertained when the measured pressure profiles and gas compositions are matched well to their correspondingly calculated values with minimum deviations. Compared to either a constant assumption or a linear concentration-dependent relation with respect to diffusivity, an exponential concentration-dependent relation leads to more accurately reproducing the measured pressure profiles. Compared with pure CO2, its effective diffusivity in a binary (i.e., CO2 and C3H8) gas system is found to be larger, indicating that C3H8 accelerates the CO2 mass transfer into heavy oil under the same circumstances. Furthermore, this study confirms that a larger tortuosity of a porous medium leads to a longer diffusion path with less contact between gas and liquid phases and that a lower concentration of a gaseous component yields a lower effective diffusivity.

An insight into the analogy between solute-solvent binding energy and solubility of acid gases in ionic liquids: Thermodynamic modeling versus molecular dynamic simulation

Ionic Liquids (ILs) have emerged as a promising generation of solvents for the absorption of acid gases (e.g., CO2 and H2S) due to their unparalleled physiochemical properties. This study focuses on thermodynamic modeling and molecular dynamic simulation approaches to estimate the solubility and interaction energies of CO2 and H2S gases in/with different frequently-used ILs. For thermodynamic modeling, the GE/EOS method was employed. This method allows for combining activity-coefficient models in the structure of the cubic equation of states. In the GE/EOS method, the modified Peng-Robinson equation of state (MPR2) together with the LCVM mixing rules was used. Excess Gibbs free energy models of Wilson, NRTL, and UNIQUAC were also applied for combination with the GE/EOS models. The prediction results of the combined models were compared with the experimental solubility data. The results demonstrated the capability of these models to predict the thermodynamic behavior of the acid gas-ILs systems. The results uncovered that the MPR2-LCVM-Wilson model can tabulate the highest correlation with the experimental data compared to the other model combinations. Results of the sensitivity analysis on the principal operational variables (temperature and pressure), showed superior effect of pressure on the gas solubility. In addition, the results of the molecular dynamic (MD) simulation disclosed an agreement between the trends of the solubility of acid gases in ILs with those of the released interaction energies of acid gases absorbed by the ILs. MD results also confirmed that the solubility of acid gases in ILs increases with an increase in the binding energy of the molecules with the ILs.

LLE, VLE and dynamic viscosity for the furfural + nonane mixture at low pressure: Measurements and modeling

This work reports new experimental data for the furfural + nonane mixture for the temperature range between 303.25 K and 441.55 K at low pressure. Vapor-liquid equilibria (VLE), liquid–liquid equilibria (LLE), and dynamic viscosity (µ) are reported and modeled under isobaric condition. Experimental data measurement is done using the same validated equipment applied in authors previous work. The expanded uncertainties for boiling temperature, viscosity- temperature, liquid–liquid temperature and dynamic viscosity are around 0.21 K, 0.12 K, 0.42 K and 0.0881 mPa∙s (0.95 level of confidence). After data is collected, phase equilibria are modeled using a modified Peng-Robinson equation of state coupled with the Huron Vidal and NRTL mixing rules. Also, dynamic viscosity is modeled using a generalized logistic function type in order to describe all the composition domains. The average absolute relative deviation using the models LLE, VLE, and viscosity is around of 0.01 %, 2.39 %, and 2.93 %. The results indicate that the new data can be modeled using the selected models.

Thermodynamic modeling of adsorption of dimethyl sulfide on raw and modified activated carbon by simplified local density model

The simplified local density (SLD) model was employed to analyze the experimental results of the adsorption of dimethyl sulfide (DMS) from a model fuel (n-hexane) on raw and modified walnut shell activated carbon (WSAC) with different impregnated amounts of silver ions (Ag-2, 4, 6, 8, and 10 mass percent). Modified Peng–Robinson equation of state was used in the liquid phase and the 6-12 Lenard Jones (LJ) potential function was implemented to represent the solid-fluid interactions. The LJ parameters for pure DMS and n-hexane were obtained from the Tsonopoulos correlation for the Second Virial coefficient data. Published experimental results of DMS and n-hexane adsorption were used for the physical properties and the molecular parameters needed in SLD model. Excess adsorption amounts of DMS were then calculated and compared with the experimental data. The average absolute deviations (AAD) between the experimental data and calculated results were 0.0072, 0.0727, 0.0377, 0.0601, 0.0605, and 0.0634 mmol/gr adsorbent for WSAC, WSAC-Ag-2, WSAC-Ag-4, WSAC-Ag-6, WSAC-Ag-8, and WSAC-Ag-10, respectively. For the same adsorbents the percent average absolute relative deviation (AARD%) were 14.11, 15.50, 7.70, 15.48, 16.16, and 29.09, respectively. The applicability of the SLD model in liquid-phase adsorption is validated.

An effective characterization procedure for petroleum reservoir fluids using molecular type methods and cubic equations of state

AbstractTwo eminent molecular type composition methods (paraffins, naphthenes, and aromatics [PNA] and saturates, aromatics, and polynuclear aromatics [SAP]) are employed to construct new characterization procedures for predicting the phase behaviour of petroleum fluids using a modified Peng–Robinson equation of state. The PNA and SAP methods divide a petroleum fraction into (PNA) and (SAP) homologous groups, respectively. Two generalized models are developed to predict the physical properties () and equation of state (EOS) parameters () for both PNA and SAP sub‐fractions. Each generalized model covers 18 different correlations in a single mathematical form that enables the model to return 18 outputs for PNA and SAP sub‐fraction parameters. A new lumping method is also developed to convert triple PNA or SAP pseudo‐components into single characterized fractions. Accordingly, seven different characterization procedures are introduced and compared with one another. The first two procedures are completely constructed based on the proposed models, and the other procedures encompass the models already developed. The results obtained from the simulation of the differential liberation test for 12 diverse reservoir fluids and bubble pressure prediction for 40 oil samples revealed that the first two methods (1 and 2) could enhance the abilities of the traditional characterization procedures for reservoir fluid modelling. The mean value of average absolute relative deviations (AARDs) over a total of 52 oil samples is about 6.5% for the proposed methods and is about 13.2% for the best previously existing methods. Moreover, an efficient workflow is provided for the parameter tuning process, which is notably capable of reducing the level of prediction errors using only three adjustable parameters.

Predictions of thermodynamic properties of pure fluids, refrigerants, and binary mixtures using modified Peng-Robinson equation of state

Predictions of thermodynamic properties of pure fluids, refrigerants, and binary mixtures using modified Peng-Robinson equation of state

Prediction of phase equilibria, density, speed of sound and viscosity of 2-alkoxyethanols mixtures: A comparison study between SAFT type EoSs and a modified PR EoS

In this work, a modified Peng-Robinson equation of state with the Huron-Vidal-NRTL mixing rule was used to describe complex polar phase equilibria, density, speed of sound and viscosity at low pressure of alkoxyethanols/alkane, alkoxyethanols/isoalkanes and 2-butoxyethanol/water mixtures. The experimental data is gathered from the literature of a selected alkoxyethanols/alkanes series with the aim of developed generalized expressions for the binary interaction parameters required in the mixing rule model as a function of the RTc/Pc ratio of alkanes. In total 19 mixtures were analyzed (6 used in correlation and 13 mixtures used in prediction processes). For each type of mixture, the generalized expressions were obtained by fitting experimental liquid-liquid equilibria (LLE) data of 3 different mixtures at 100 kPa and to validate them, LLE and vapor-liquid equilibria (VLE) predictions were performed. Adequate results were obtained in all cases. Also, the predictive capabilities of the generalized EoS model have been tested using density, and speed of sound estimations. The overall deviation is below 1.10% for density and 6.84% for speed of sound. Also, the viscosity is correlated and predicted using a simple mixing rule coupled with the generalized EoS model and the absolute deviation is below 3.86%. Finally, two cases of study have been implemented to analyze the possibility of the generalized model to predict other branched-chain alkanes and water systems. The overall results indicated a good agreement with experimental data and proved that the EoS coupled with the Huron-Vidal mixing rule can describe high polar systems and their properties with acceptable and low deviations in comparison to other EoS such as SAFT types or CPA approaches.

Phase Behavior and Physical Properties of Dimethyl Ether/CO2/Water/Heavy Oil Systems under Reservoir Conditions

Summary In this paper, techniques have been developed to quantify phase behavior and physical properties including phase boundaries, swelling factors (SFs), and phase volumes for reservoir fluids containing polar components from both experimental and theoretical aspects. Experimentally, a total of seven pressure-volume-temperature (PVT) experiments, including one set of dimethyl ether (DME)/heavy oil system, one set of DME/water/heavy oil system, three sets of DME/CO2/heavy oil systems, and two sets of DME/CO2/water/heavy oil systems, have been carried out to measure saturation pressures, phase volumes, and SFs by using a versatile PVT setup. Theoretically, the modified Peng-Robinson equation of state (PR EOS) incorporated with the Huron-Vidal (HV) mixing rule and the Péneloux volume-translation strategy is used as the thermodynamic model to perform phase equilibrium calculations. Once validated with the measured phase compositions of DME/water mixtures collected from the literature, the theoretical model developed in this work is used to reproduce the experimental measurements for the aforementioned reservoir fluids. It is observed that the saturation pressures of DME/CO2/water/heavy oil mixtures are higher than those of DME/CO2/heavy oil mixtures at the same temperature and same molar ratio of solvents and heavy oil, owing to the fact that more water molecules can be evaporated into the vapor phase. The binary interaction parameters (BIPs) between DME/heavy oil and CO2/DME pair, which are obtained by matching the measured saturation pressures of DME/CO2/heavy oil mixtures, work well for DME/CO2/heavy oil mixtures in the absence and presence of water. In addition, the swelling effect of heavy oil can be enhanced by adding the DME and CO2 mixtures compared with only DME or CO2. The new model developed in this work is capable of accurately reproducing the experimentally measured multiphase boundaries, SFs, and phase volumes with root-mean-squared relative errors (RMSREs) of 4.68, 0.71, and 9.35%, respectively, indicating that it can accurately provide fundamental data for simulating, designing, and optimizing the hybrid steam-solvent recovery processes for heavy oil reservoirs.

Continuum-Scale Gas Transport Modeling in Organic Nanoporous Media Based on Pore-Scale Density Distributions

SummaryWe present a continuum-scale mass transport model informed by pore-scale density distribution for gas diffusion through organic nanoporous media. A diffusion model and a sorption model are developed by considering multiple transport and storage mechanisms, including bulk diffusion and Knudsen diffusion for free phase, and surface diffusion and multilayer adsorption for sorbed phase. The continuum-scale diffusion equation is derived based on the free-phase concentration for the overall mass conservation of free and sorbed phases, carrying a newly defined effective diffusion coefficient and capacity factor to account for multilayer adsorption. Diffusion in free and sorbed phases is coupled with the sorption model, which provides pore-scale multilayer adsorption properties by utilizing a pore-scale simplified local density (SLD) method combined with the modified Peng-Robinson equation of state (PR-EOS) for confinement effect. The model was first implemented to analyze adsorption data from a krypton (Kr) adsorption experiment on graphite. Then, we applied the developed diffusion model to conduct the sensitivity analysis of the effects of pore size on gas transport for Kr-graphite and methane-coal systems. The model was finally used to study Kr diffusion profiles through a coal matrix obtained by using X-ray micro-computed tomography (microCT) imaging. The results show that the sorbed phase occupies most of the pore space in organic nanopores with less than 10 nm due to multilayer adsorption, and surface diffusion contributes significantly to the total mass flux. Therefore, neglecting the volume of sorbed phase and surface diffusion in organic nanoporous rocks may result in considerable errors in the prediction of hydrocarbon production. We also compared Brunauer-Emmett-Teller (BET) and Langmuir models by analyzing adsorption data for the wide pressure range up to the saturation pressure. The comparison between BET and Langmuir models shows that the Langmuir model can only match the adsorption isotherm at low pressure and yield lower effective surface diffusion coefficients. Therefore, implementing a Langmuir model may be erroneous for organic nanoporous media with strong adsorption capacity, particularly when pore pressure is high.

Suitable Binary and Ternary Thermodynamic Conditions for Hydrate Mixtures of CH4, CO2, and C3H8 for Gas Hydrate-Based Applications.

The selection of suitable hydrate formers and their respective gas composition for high hydrate formation, driving force is critical to achieve high water recovery and metal removal efficiency in the hydrate-based desalination process. This study presents a feasibility analysis on the possible driving force and subcooling temperatures for the binary and ternary mixtures of methane, carbon dioxide, and propane for hydrates-based desalination process. The driving force and subcooling for the gas systems was evaluated by predicting their hydrate formation phase boundary conditions in 2 wt % NaCl systems at pressure ranges from 2.0–4.0 MPa and temperatures of 1–4 °C using modified Peng–Robinson equation of state in the PVTSim software package. The results suggest that the driving force of CH4 + C3H8 and CO2 + C3H8 binary systems are similar to their ternary systems. Thus, the use of binary systems is preferable and simpler than the ternary systems. For binary gas composition, CO2 + C3H8 (70:30) exhibited a higher subcooling temperature of 8.07 °C and driving force of 1.49 MPa in the presence of 2 wt % aqueous solution. In the case of the ternary system, CH4–C3H8–CO2 gas composition of 10:80:10 provided a good subcooling temperature of 12.86 °C and driving force of 1.657 MPa for hydrate formation. The results favor CO2–C3H8 as a preferred hydrate former for hydrate-based desalination. This is attributed to the formation of sII structure and it constitutes 136 water molecules which signifies a huge potential of producing more quantities of treated water.

Extension of a Group Contribution Method to Predict Viscosity Based on Momentum Transport Theory Using a Modified Peng–Robinson EoS

In this work, a semitheoretical model based on the momentum transport theory is generalized through the development of a group contribution method. Viscosity data for temperatures between 13.95 and 950 K and pressures from 1.00 × 10–3 bar up to 1.00 × 104 bar were used to develop and to validate the model. To perform viscosity calculations, the model requires density and residual enthalpy that were obtained from a modified Peng–Robinson equation of state. Also, the model has one adjustable parameter that can be estimated form the group contribution method. Viscosity was calculated for 256 substances including 95 non-polar and 161 polar compounds. In total, 23 organic families were considered. Average deviations below 6.67% were calculated. The performance of the model was compared with those of other models reported in the literature. Calculations were carried out to include the saturation and single-phase regions. In general, it can be considered that the proposed model describes viscosity adequately using only one adjustable parameter.

Modelling of the Phase-Partitioning Behaviors for CO2-Brine System at Geological Conditions

Abstract An improved phase-partitioning model is proposed for the prediction of the mutual solubility in the CO2-brine system containing Na+, K+, Ca2+, Mg2+, Cl-, and SO42-. The correlations are computationally efficient and reliable, and they are primarily designed for incorporation into a multiphase flow simulator for geology- and energy-related applications including CO2 sequestration, CO2-enhanced geothermal systems, and CO2-enhanced oil recovery. The model relies on the fugacity coefficient in the CO2-rich phase and the activity coefficient in the aqueous phase to estimate the phase-partitioning properties. In the model, (i) the fugacity coefficients are simulated by a modified Peng-Robinson equation of state which incorporates a new alpha function and binary interaction parameter (BIP) correlation; (ii) the activity coefficient is estimated by a unified equilibrium constant model and a modified Margules expression; and (iii) the simultaneous effects of salting-out on the compositions of the CO2-rich phase and the aqueous phase are corrected by a Pizter interaction model. Validation of the model calculations against literature experimental data and traditional models indicates that the proposed model is capable of predicting the phase-partitioning behaviors in the CO2-brine system with a higher accuracy at temperatures of up to 623.15 K and pressures of up to 350 MPa. Using the proposed model, the phase diagram of the CO2+H2O system is generated. An abrupt change in phase compositions is revealed during the transfer of the CO2-rich phase from vapor to liquid or supercritical. Furthermore, the preliminary simulation shows that the salting-out effect can considerably decrease the water content in the CO2-rich phase, which has not been well experimentally studied so far.

Measurement of the vapour–liquid equilibrium properties of binary mixtures of the low-GWP refrigerants R1123 and R1234yf

The vapour–liquid equilibrium properties of binary mixtures of R1123 and R1234yf, which are key components of the next generation of refrigerant mixtures, were measured using a recirculation-type vapour–liquid equilibrium property measurement apparatus. Two sets of measurements were conducted by two different technicians (co-authors Nishida and Saito) using the same apparatus and sample. The first set of measurements were conducted at temperatures that were close to the integer values in absolute temperature, whereas the second set of measurements was taken at temperatures that were close to the integer values in terms of degrees Celsius. Both sets of measurements were based on the ITS-90 temperature scale and were found to be in good agreement at the measurement temperatures (300 and 330 K). These data were compared with the predictions of a Helmholtz-type equation of state, and a systematic deviation of approximately 8% was observed at low temperatures. A regression analysis using the binary interaction parameter kij of the modified Peng–Robinson equation of state more accurately reproduced the experimental measurements.

Phase Behavior and Physical Properties of Dimethyl Ether/Water/Heavy-Oil Systems Under Reservoir Conditions

SummaryPhase behavior and physical properties including saturation pressures, swelling factors (SFs), phase volumes, dimethyl ether (DME) partition coefficients, and DME solubility for heavy-oil mixtures containing polar substances have been experimentally and theoretically determined. Experimentally, novel phase behavior experiments of DME/water/heavy-oil mixtures spanning a wide range of pressures and temperatures have been conducted. More specifically, a total of five pressure/volume/temperature (PVT) experiments consisting of two tests of DME/heavy-oil mixtures and three tests of DME/water/heavy-oil mixtures have been performed to measure saturation pressures, phase volumes, and SFs. Theoretically, the modified Peng-Robinson equation of state (EOS) (PR EOS) together with the Huron-Vidal mixing rule, as well as the Péneloux et al. (1982) volume-translation strategy, is adopted to perform phase-equilibrium calculations. The binary-interaction parameter (BIP) between the DME/heavy-oil pair, which is obtained by matching the measured saturation pressures of DME/heavy-oil mixtures, works well for DME/heavy-oil mixtures in the presence and absence of water. The new model developed in this work is capable of accurately reproducing the experimentally measured multiphase boundaries, phase volumes, and SFs for the aforementioned mixtures with the root-mean-squared relative error (RMSRE) of 3.92, 9.40, and 0.92%, respectively, while it can also be used to determine DME partition coefficients and DME solubility for DME/water/heavy-oil systems.

Modified Peng-Robinson equation of state for CO2/hydrocarbon systems within nanopores

Phase behavior of confined fluid demonstrates significant deviation from that of bulk fluid because of the strong molecule-wall interaction and geometric constraint in confined space, resulting in the inapplicability of the classical cubic equation of state (EOS). The objective of this work is to modify the Peng-Robinson EOS (PR EOS) with respect to both the attractive parameter and the covolume term to reflect the impact of molecule-wall interaction and geometric constraint, respectively. The modified PR EOS is applied to compute the phase diagrams of CO2+n-C4H10 and CO2+n-C10H22 binary mixtures, CO2+n-C4H10+n-C10H22 ternary mixture, and CO2+Eagle Ford condensate in nanopores. In this work, correlations of both critical temperature and critical pressure shift with nanopore sizes are proposed to compute the confined attractive parameter and the confined covolume in the modified PR EOS. The proposed EOS model is validated by both the critical temperature and the critical pressure shift data collected from literature. Results demonstrate that confinement effect in nanopores impose an overall shrinkage to the two-phase diagrams of all the CO2-hydrocarbon systems. The upper dew-point pressure of the Eagle Ford condensate sample is calculated to be 2972.6 psi, with a suppression of 27.56% compared to the bulk value of 4103.6 psi. Moreover, the size of the two-phase region in the ternary diagram and the minimum miscibility pressure also decrease in confined space, which is in favor of the miscible gas injection enhanced oil recovery with a higher possibility of achieving first contact miscibility.