Modeling Of Phase Behavior Research Articles

Equation of State for Nanopores and Shale: Pore Size–Dependent Acentric Factor

Nanopores pose a challenge to phase-behavior modeling when using the equation of state (EOS), and common methods do not capture their vapor pressure or become difficult to implement because they require additional tuning parameters. This study focuses on improving the vapor-pressure prediction of EOS in nanopores by proposing a pore size–dependent acentric factor (ACF). It determines the ACF from experimental data and implements it in EOS along with critical pressure and temperature. The proposed approach is then applied to the vapor-pressure measurements of nitrogen, argon, oxygen, methane, and ethane in pores ranging from 3.5 nm to 8.1 nm. The results show that the ACF in nanopores increases as the pore size decreases, and the degree of size dependency varies across different pure components. The results also demonstrate that the proposed approach enables EOS predictions to match the measurements with good accuracy. This study quantifies the effects of pore size on the ACF for the first time and presents simple correlations for estimating the ACF when the pore radius is smaller than or equal to 10 nm. The proposed approach simplifies the application of EOS in nanopores and unconventional hydrocarbon reservoirs.

Asphaltene Phase Behavior Modeling Using Peng-Robinson 78A-EOS for a Crude Oil Sample from Buzurgan Oil Field

Asphaltene Phase Behavior Modeling Using Peng-Robinson 78A-EOS for a Crude Oil Sample from Buzurgan Oil Field

An empirical model for predicting saturation pressure of pure hydrocarbons in nanopores

Due to the confinement and strong adsorption to the pore wall in meso‑ and nano pores, fluid phase behavior in the confined media, such as the tight and shale reservoirs, can be significantly different from that in the bulk phase. A large amount of work has been done on the theoretical modeling of the phase behavior of hydrocarbons in the confined media. However, there are still inconsistencies in the theoretical models developed and validations of those models against experimental data are inadequate.In this study, we conducted a comprehensive review of experimental work on the phase behavior of hydrocarbons under confinement and analyzed various theoretical phase-behavior models. Emphasis was given to the modifications to the Peng-Robinson equation of state (PR EoS). Through the comparative analysis, we developed a modified alpha-function in PR EoS for accurate prediction of the saturation pressures of hydrocarbons in porous media. This modified alpha-function accounts for the pore size and was derived based on the regression results through minimizing the deviation between the experimentally measured and numerically calculated saturation pressure data. Meanwhile, the thermodynamic properties of propane were calculated in the bulk phase and in the nanopores. Finally, we validated the newly developed model using the experimental data in synthesized mesoporous materials and real reservoir rocks.By applying the modified PR EoS, a more accurate representation of the experimentally measured saturation pressure data in confined nanopores was achieved. This newly developed model not only enhanced the accuracy of the predictions but also provided valuable insights into the confinement effects on the phase behavior of hydrocarbons in nanopores. Notably, we observed significant changes in the properties of propane within confined nanopores, including suppressed saturation pressure and fugacity, indicating a greater tendency for the gas to remain in the liquid phase. Enthalpy of vaporization was found to increase highlighting increased difficulty in transitioning from liquid to gas phase under confinement. Additionally, the new model predicts an increased gas compressibility factor in the nanopores suggesting a close resemblance of ideal gas due to the counterbalance between the attractive and repulsive forces. To validate the model, new datasets containing saturation pressures of propane and ethane under a wide range of temperatures and pore sizes were employed. The newly developed model was further applied to the experimental data obtained in real rock samples (sandstones, limestones, and shales). Interestingly, it was observed that the phase change in these samples predominantly occurred in the smallest pores. This finding highlights the importance of considering the pore size distribution when studying the phase behavior of hydrocarbons in a capillary medium even if the rock has high permeability.This study provided a simple and easy-to-implement modification to the PR EoS for accurate prediction of the phase behavior of petroleum fluids under confinement. The newly developed model for calculating saturation pressures of hydrocarbons demonstrates improved accuracy in representing experimental data compared to the previous models, while offering a more straightforward and simplified approach.

An efficient polar cubic equation of state for predictive modeling of phase behavior and critical phenomena of mixtures

AbstractA polar cubic equation of state (EOS) is developed by incorporating the dipolar theory of Jog and Chapman into the Soave‐Redlich‐Kwong (SRK) EOS. We propose simplifying assumptions in the dipolar term of Jog and Chapman to reduce the double and triple sums in the theory to single sums. The simplified version of the dipolar theory can significantly improve computational speed and can be used with either Cubic EOS or SAFT‐based EOS. The proposed model, which we call Simplified Polar SRK (SP‐SRK), is parametrized in a similar fashion to classical cubic EOS to exactly reproduce , and will self‐consistently reduce to the base SRK EOS in the absence of polar interactions. Binary VLE data with a non‐polar reference hydrocarbon is used to extract the polarity of the respective functional group. The model shows superior performance in capturing the phase behavior of polar mixtures compared to the base SRK.

Towards rational design of API-poly(D, L-lactide-co-glycolide) based micro- and nanoparticles: The role of API-polymer compatibility prediction

Due to their unique properties, such as controlled drug release and improved bioavailability, polymeric microparticles and nanoparticles (MPs and NPs) have gained considerable interest in the pharmaceutical industry. Nevertheless, the high costs associated with biodegradable polymers and the active pharmaceutical ingredients (APIs) used for treating serious diseases, coupled with the vast number of API-polymer combinations, make the search for effective API-polymer MPs and NPs a costly and time-consuming process. In this work, the correlation between the compatibility of selected model APIs (i.e., ibuprofen, naproxen, paracetamol, and indomethacin) with poly(lactide-co-glycolide) (PLGA) derived from respective binary phase diagrams and characteristics of prepared MPs and NPs, such as the drug loading and solid-state properties, was investigated to probe the possibility of implementing the modeling of API-polymer thermodynamic and kinetic phase behavior as part of rational design of drug delivery systems based on MPs and NPs. API–PLGA-based MPs and NPs were formulated using an emulsion-solvent evaporation technique and were characterized for morphology, mean size, zeta potential, drug loading, and encapsulation efficiency. The solid-state properties of the encapsulated APIs were assessed using differential scanning calorimetry and X-ray powder diffraction. The evaluated compatibility was poor for all considered API–PLGA pairs, which is in alignment with the experimental results showing low drug loading in terms of amorphous API content. At the same time, drug loading of the studied APIs in terms of amorphous content was found to follow the same trend as their solubility in PLGA, indicating a clear correlation between API solubility in PLGA and achievable drug loading. These findings suggest that API-polymer phase behavior modeling and compatibility screening can be employed as an effective preformulation tool to estimate optimum initial API concentration for MP and NP preparation or, from a broader perspective, to tune or select polymeric carriers offering desired drug loading.

Investigation of the Low-Pressure Phase Behavior and SAFT Modeling of 1-Alcohol and n-Alkane Binary Systems

Investigation of the Low-Pressure Phase Behavior and SAFT Modeling of 1-Alcohol and <i>n</i>-Alkane Binary Systems

Modeling and prediction of thermodynamic phase behaviors of oxaprozin and irbesartan in biorelevant media

Modeling and prediction of thermodynamic phase behaviors of oxaprozin and irbesartan in biorelevant media

A Systemic Comparison of Physical Models for Simulating Surfactant–Polymer Flooding

Three different reservoir simulators that utilize both two-phase and three-phase microemulsion phase behavior models are used to model surfactant–polymer flooding to determine and compare their results. Different models are used in each simulator to describe the physical behavior of injected chemicals into the reservoir, which raises the need to benchmark their results. The physical behavior models of polymer and surfactant were constructed and verified on a 1D scale reservoir model and further verified in a 3D model. Finally, simulations were conducted in a field-scale reservoir containing 680,400 grids, where results were compared and analyzed. The 1D and 3D model results suggest an excellent match between the different simulators in modeling surfactant–polymer floods. In the case of the field-scale model, the simulators matched in terms of oil recovery and total volumes produced and injected, while having similar reservoir pressure profiles but with significant discrepancies in terms of injected and produced chemicals. These results indicate that despite the differences in the calculated injected and produced chemicals due to the different models in the simulators, the effect of surfactant–polymer floods on oil recovery, total injected and produced fluids, and average pressure profiles can be comparably modeled in all of the three simulators.

Physical-informed deep learning framework for CO[formula omitted]-injected EOR compositional simulation

CO2 injection for enhanced oil recovery (CO2-EOR) is one of the industry’s most widely applied techniques for CO2 utilization. People use the compositional simulation technique to clearly describe CO2 injection processes for EOR, which is always computational-expensive. The main objective of this study is to utilize deep learning (DL) techniques to describe phase behaviors and accelerate compositional simulations. First, we constructed a new DL-based compositional simulation framework. Instead of solving equations of state for every grid cell, this framework can aggregate millions of phase behavior solvers and determine all mixtures’ phase status in one single round of calculation. This trait can significantly improve the efficiency of solving numerical equations. Next, we illustrated how to develop DL-based phase behavior models to determine phase status accurately. Our newly proposed single-phase identification model can resolve the difficulty in inaccurate single-phase labeling within compositional simulations, greatly benefiting the numerical convergence of simulation. Finally, we tested abundant complicated cases covering near-miscible and miscible gas injection processes and demonstrated the new DL-based method’s strength in accelerating the compositional simulation. Besides, we also presented the DL-based method’s more substantial power in numerical convergences that it could succeed in cases where the standard simulation method fails. This work can contribute to more efficiently and effectively describing complex fluid displacement processes, benefiting CO2 injection EOR and other utilizations like CO2 sequestrations.

Modeling Flow and Transport in Saline Aquifers and Depleted Hydrocarbon Reservoirs for Hydrogen Energy Storage

Summary Hydrogen (H2) is an attractive energy carrier, and its true potential is in decarbonizing industries, such as for providing heat for buildings and being a reliable fuel for trains, buses, and heavy trucks. Industry is already making tremendous progress in cutting costs and improving the efficiency of hydrogen infrastructure. Currently, heating is primarily provided by using natural gas and transportation by gasoline with a large carbon footprint. Hydrogen has a similarly high energy density, but there are technical challenges preventing its large-scale use as an energy carrier. Underground geologic storage of hydrogen in porous media (aquifers and hydrocarbon reservoirs) could offer substantial storage capacity at low cost as well as buffer capacity to meet changing seasonal electricity demands or possible disruptions in power supply. Underground geologic storage must have adequate capacity and ability to inject/extract high volumes with a reliable caprock. A thorough study is essential for a large number of site surveys to locate and fully characterize the subsurface geological storage sites both onshore and offshore. An isothermal compositional reservoir simulator was used to evaluate hydrogen storage and withdrawal from saline aquifers and depleted oil/gas reservoirs. The phase behavior, fluid properties, and petrophysical models were all calibrated against published laboratory data for density, viscosity, relative permeability, and capillary pressure for a given site. History-matched dynamic models of two CO2 injection field projects in saline aquifers and one natural gas storage in a depleted oil reservoir were considered as hypothetical hydrogen seasonal storage sites. A wide range of working gas volume/cushion gas volume ratios was observed, meaning that careful optimization is required for a successful storage project. For the aquifer cases, the range was 0.292 to 1.883 and a range of 1.045 to 4.4 was observed for the depleted hydrocarbon reservoir scenarios. For the saline aquifer cases, a higher injection rate, longer injection/withdrawal (I/W) cycles, and the use of pump wells to control the hydrogen plume spreading were all beneficial for improving the working gas/cushion gas ratio and the working gas volume. Plume control was important for storage in the oil reservoir in which changes in the well length location and orientation showed high sensitivity in the working and cushion gas volumes. Sensitivities to the initial gas saturation in the depleted gas reservoir scenarios suggested that both cushion and working gas volumes increased with the initial gas saturation while the ratio of working to cushion gas volumes decreased with the initial gas saturation. Finally, when comparing the ratios of working to cushion gas volumes, it was the highest for the depleted oil reservoir, followed by the depleted gas reservoir, and the aquifer.

High pressure phase behavior and thermodynamic modeling of the carbon dioxide + chloroform + globalide system

The high-pressure phase behavior of the ternary system constituted by carbon dioxide + globalide + chloroform was studied. Experiments were conducted applying the synthetic-visual method in a variable-volume view cell at a mass ratios of globalide to chloroform of 0.5:1, 1:1, and 2:1, over a temperature range from 313.15 to 343.15 K, and pressures from 5.17 to 20.25 MPa. Phase transitions of vapor–liquid bubble point (VLE-BP), vapor–liquid dew point (VLE-DP), liquid–liquid (LLE), and vapor–liquid-liquid (VLLE) type were observed. Furthermore, through the P-w diagram, the phase behavior of the ternary system in chloroform free-basis was analyzed between 0.4250 to 0.9735 of carbon dioxide mass composition. It has been observed that high quantities of chloroform lead to lower transition pressures. Moreover, PT-diagrams efficiently displayed that higher pressures are necessary to achieve a single phase medium as temperature rises, which characterize LCST behavior. PR-vdW2 model was used to estimate binary interaction parameters. Additionally, the ternary system was compared with binary systems available in the literature. The data presented in this work provides necessary information for the optimization and improvement of poly(globalide) synthesis in supercritical media.

Predictive Modeling of Phase Behavior of Reservoir Fluids under Miscible Gas Injection Using the Peng-Robinson Equation of State and the Aromatic Ring Index.

Improved correlations among critical temperature, critical pressure, and acentric factor are developed for an extensive database of hydrocarbons. The correlations rely on measurements of molecular weight and refractive index at ambient conditions and utilize the concept of the aromatic ring index (ARI) recently developed by Abutaqiya et al. as a distinctive characterization factor for nonpolar hydrocarbons [Abutaqiya M. I. L.Aromatic Ring Index (ARI): A Characterization Factor for Nonpolar Hydrocarbons from Molecular Weight and Refractive Index. Energy Fuels2021, 35( (2), ), 1113-1119.]. The new correlations are then implemented for modeling the phase behavior of a variety of oils under miscible gas injection in a fully predictive manner using the Peng-Robinson equation of state (PR EOS). The results indicate that the proposed modeling framework yield accurate predictions for bubble pressure of oil/gas blends with an average absolute deviation of 6.4% for a wide variety of oils and injection gases including lean, rich, H2S, CO2, and N2. Additionally, an interesting crossover behavior in the phase envelope of live oils under CO2 injection is observed using PR EOS. This behavior has been previously reported in the literature for modeling results using PC-SAFT EOS and seems to be characteristic of CO2.

Modeling of High-Pressure and High-Temperature Microemulsion Experiments using HLD-NAC-Based Equation of State

Summary Surfactant flooding is a promising technique that can reduce interfacial tension (IFT) between oil and water to ultralow values, mobilizing previously trapped oil. For reservoirs at moderate to high pressures, understanding and modeling how pressure affects the phase behavior of a surfactant-brine-oil system is important to the design and implementation of an efficient/cost-effective surfactant flooding project. Typically, however, phase behavior experiments and models of that phase behavior are made only at low pressures. The main objective of this paper is to show how to model experimental data in a unified way for a large range of pressure, temperature, and other parameters, using hydrophilic-lipophilic deviation (HLD) and net-average curvature (NAC)-based equation-of-state (EOS). Pressure and temperature scans show that pressure has a significant effect on the surfactant microemulsion phase behavior, shifting it from an optimal three-phase system at low pressure to a nonoptimal two-phase system at high pressure. Further, multiple scans at different water/oil ratios (WORs) show a shift in the optimum indicating that phase behavior partitioning of the various components is changing with oil saturation. We obtained good fits of all experimental data including all two- and three-phase regions using a single tuned HLD-NAC EOS for a wide range of simultaneous variations in pressure, temperature, salinity, and overall composition. Such a simultaneous match and prediction by a single set of model parameters has never been done before. We also demonstrate the type of data needed for an accurate EOS. When input into a numerical simulator, the tuned EOS improves the predictions of the resulting phase behavior (size and shape of the two-phase lobes and three-phase regions) and IFTs with changing pressure, temperature, salinity, WORs, and surfactant/alcohol concentrations.

Assessment of the applicability of binary mixture hypothesis to modeling the phase behavior of heavy oil/bitumen-solvent systems for EOR applications

Conventional production methods in heavy oil reservoirs are not efficient primarily due to the high viscosity of the oil. Several methods such as VAPEX and ES-SAGD have been developed to overcome production challenges from these reservoirs, which mainly rely on oil viscosity reduction. Solvent injection dilutes the oil and produces a complex asymmetric mixture. It is difficult to study the phase behavior of oil due to the diversity of its components, and it gets more complicated with the addition of solvent. One of the assumptions to simplify the problem is considering heavy oil as a single pseudo component and investigating the thermophysical properties of binary mixtures with diluents. This study collected and evaluated more than 1000 experimental data on various types of heavy oil/bitumen and several hydrocarbon and non-hydrocarbon solvents. The data were divided into two groups, below and above the critical temperature of the solvent, according to experimental temperatures. Modeling of mixture phase behavior as a binary mixture was performed using the advanced Peng-Robinson equation of state (APR-EoS). EoS tuning to match the experimental data was performed by optimizing the binary interaction coefficients (kij). The results showed that the binary mixture assumption could be used as a practical approach to construct pressure-composition phase diagrams. Optimized values of kij were proposed as two empirical correlations according to the dimensionless ratio Tco/Tcs (oil critical temperature to solvent critical temperature). The model constructed using these correlations showed an average deviation of about 16% compared to experimental data. It is necessary to note that the vapor-liquid-liquid three-phase regions may occur in a heavy oil/bitumen and solvent mixture. But according to the Gibbs phase rule, with two components and three phases in the system, the degree of freedom equals one. So, investigating the effects of pressure change on three-phase regions is not possible using this model.

An extension of gases-brine mutual solubility models to include geochemical reactions: Modeling and applications

Accurate and quantitative numerical modeling of phase behavior and speciation of gas-water-rock systems is crucial for fluid and rock evolution analysis, and important in scientific research and engineering applications. In our previous work, mutual solubility models of series gases and brine have been developed for wide temperature, pressure and composition ranges. The gas components included CO2, CH4, H2S, N2 and O2. The existing experimental data can be reproduced accurately. In this paper, the models are extended to include water-rock interactions by means of a full coupling with the open-source software package PHREEQC. With the new coupled model, the solubility of gases and various minerals can be correctly and reliably reproduced. The proposed numerical framework is properly implemented and it can be applied in different scenarios of gas-water-rock interactions. Three practical applications have been investigated: calculation of uranium in situ leaching, CO2 geological storage and natural gas souring are provided in the paper. The application cases have additionally proven the stability and reliability of the proposed model.

A statistical thermodynamics-based equation of state and phase equilibrium calculation for confined hydrocarbons in shale reservoirs

The phase behavior of confined fluid in nanopores of shale reservoirs deviates significantly from that of bulk fluid. Confined fluid refers to fluid whose thermal motion is affected by nanopores, since nanopores have a comparative size to the mean free path of fluid molecules. To describe deviated phase behavior in nanopores, Travalloni et al. proposed PR-C EOS by introducing empirical modifications to the canonical partition function. The modifications consider the two main mechanisms that cause nanopore phase behavior to deviate: the finite volume effect and the fluid-pore wall interaction effect. However, in addition to its weakness on a theoretical basis, PR-C EOS possesses imperfections when applied to predict nanopore phase behaviors. In this work, we propose a new EOS derived from statistical thermodynamics for slit-like nanopores, named PR-X EOS. The PR-X EOS has an extra term to represent the fluid-pore wall interaction effect and a modification to the cubic EOS parameter to represent the finite volume effect. PR-C EOS and PR-X EOS are non-cubic, and each has some new parameters. The new parameters can be determined by fitting adsorption isotherms. When pore size approaches infinity, PR-C EOS and PR-X EOS both degenerate into classic PR EOS. To apply these two non-cubic EOS in reservoir simulators, we improve gas-oil phase equilibrium calculation methods. The improved simulator can model chemical potential equilibrium between the nanopore grid and the bulk grid, with chemical potentials of the two grids calculated using the modified EOS and conventional EOS, respectively, so that bulk grid pressure can be obtained. As a consequence, we can plot the adsorption isotherm or phase diagram under bulk pressure, which is practically measurable pressure. Therefore, we can validate the modified EOS with experimental or molecular simulation data. Validations demonstrate that PR-X EOS can match type I and type IV adsorption isotherms; whereas, PR-C EOS fails to match the type IV adsorption isotherm. Moreover, the phase diagrams calculated using PR-X EOS consistently shrink as pore size decreases, while PR-C EOS cannot guarantee this consistency. These two facts show that PR-X EOS is superior to PR-C EOS in modeling phase behavior of confined hydrocarbons. Furthermore, shale oil reservoir simulation shows that considering the confinement effect would lead to lower GOR.

Ideal Gas Heat Capacity and Critical Properties of HFE-Type Engineering Fluids: Ab Initio Predictions of Cpig, Modeling of Phase Behavior and Thermodynamic Properties Using Peng–Robinson and Volume-Translated Peng–Robinson Equations of State

Ideal Gas Heat Capacity and Critical Properties of HFE-Type Engineering Fluids: Ab Initio Predictions of Cpig, Modeling of Phase Behavior and Thermodynamic Properties Using Peng–Robinson and Volume-Translated Peng–Robinson Equations of State

Modeling phase behavior of nano-confined fluids in shale reservoirs with a modified Soave-Redlich-Kwong equation of state

• A m-SRK EOS for modeling the phase behavior of nano-confined fluids is proposed. • A more accurate empirical formula for critical temperature shift is developed. • Phase transformation of nano-confined fluid is revealed by nano-confined index. • There is a critical pore radius around 2 nm that phase behavior deviates sharply. The conventional cubic equation of state (EOS), as a robust and efficient method for phase behavior prediction of bulk fluids, is no longer applicable for nano-confined fluids because of the fluid phase behavior deviation induced by the confinement effect in shale reservoirs. In this work, a modified Soave-Redlich-Kwong (m-SRK) EOS is proposed for modeling the fluid phase behavior in nanopores. Three parameters, including the fluid distribution coefficient, relative effective molecular volume coefficient, and nano-confined index, are defined to revise the molar volume term in the SRK EOS. Then, the empirical formulas of adsorption layer thickness and critical temperature shift are established by correlating the data points collected from the literature to solve the m-SRK EOS. Finally, two analytical formulas are derived for calculating critical property shifts. Computational accuracy of critical temperature shift in this work is remarkably improved for the dimensionless pore radius more than 0.2 compared with analytic models proposed by other scholars. Besides, the nano-confined index can comprehensively reflect the phase transformation law of nano-confined fluids. Modifying the molar volume term in EOSs is crucial for the phase behavior prediction when the pore radius is less than 100 nm, especially for the pores less than 10 nm. There is a critical pore radius around 2 nm that the molar volume of nano-confined fluids changes sharply. When the pore radius equal 1 nm, the descend range of the bubble point pressure increases sharply as the temperature increases compared with that of bulk fluids.

Design and application of an alkaline–surfactant–polymer (ASP) slug for enhanced oil recovery: a case study for a depleted oil field reservoir

Three chemicals alkali, surfactant, and polymer owing to their unique properties were thoroughly investigated on a laboratory scale to identify an optimal chemical enhanced oil recovery (CEOR) slug for depleted oil field reservoirs. A series of laboratory-scale experiments were conducted on crude oil (CO) and a reservoir rock of Barail formation. CEOR combinations were studied based on interfacial tension (IFT), emulsion stability, thermal stability, phase behavior analysis, rheology study, core flooding, economic evaluation, and modeling and simulation for optimization of CEOR application. Three anionic surfactants black liquor (BL), sodium dodecyl sulfate (SDS), and sodium dodecyl benzene sulfonate (SDBS), three nonionic surfactants Triton X-405 (TX 405), Tergitol 15-s-7 (TG7), and Tergitol 15-s-9 (TG9) were chosen for the study. The addition of co-surfactant propan-2-ol and alkali sodium hydroxide (NaOH) resulted in a much lower IFT of the SA slug up to 0.05 mN/m. Emulsification of a combined SA slug containing SDBS, TG9, propan-2-ol, and NaOH was found to be maximum whereas all the samples were observed to be thermally stable. Laboratory core flooding study of the designed ASP gave an overall recovery efficiency of 33.25% at 12.566 chemical cost ($)/incremental bbl oil whereas simulation run resulted in a recovery of 47%.

Modeling of Phase Behavior of Coacervates

Modeling of Phase Behavior of Coacervates