Peng-Robinson Equation Research Articles

Characterizing Dynamic Contact Angle during Gas-Liquid Imbibition in Microchannels by Lattice Boltzmann Method Modeling.

Spontaneous imbibition in microchannels is a critical phenomenon in various industrial applications, such as enhanced oil recovery and microfluidic systems. One of the key factors influencing the imbibition process is the dynamic wetting effect, which governs the interaction between the liquid and solid surfaces. This paper improves the original pseudopotential model for interfluid forces by coupling it with the Peng-Robinson equation of state. The model's accuracy is verified through thermodynamic consistency checks, simulations of gas-liquid interfacial tensions, and testing of static equilibrium contact angles. Following model validation, we use it to simulate spontaneous gas-liquid imbibition in microchannels and investigate dynamic contact angle evolution during the process. The results demonstrate that (1) as the microchannel width increases, inertia forces become more significant during the initial imbibition stages, leading to a greater difference between the dynamic and static contact angles. (2) A decrease in fluid-solid interaction strength results in a larger gap between dynamic and static contact angles. (3) Higher interfacial tension strengthens the capillary forces, accelerating the imbibition rate and enlarging the difference between the dynamic and static contact angles. Furthermore, the dynamic contact angle data obtained from our simulations can be used to correct the traditional Lucas-Washburn equation. The corrected equation predicts imbibition distances that closely match the simulation results.

Quantification of Mutual Mass Transfer Coupled with Heat Transfer for CO2/C3H8-Heavy Oil Systems Under Reservoir Conditions

Summary Experimental and theoretical methods have been developed to quantitatively assess the heat and bidirectional mass transfer between a hot solvent (i.e., CO2 and C3H8) and heavy oil. Experimentally, we performed diffusion experiments for hot solvent-heavy oil systems at elevated pressures and temperatures using a pressure/volume/temperature (PVT) setup. The dynamic volume change of the oleic phase has been continuously measured and recorded throughout each experiment. At the conclusion of each test, gas chromatography (GC) analysis has been conducted on the collected gas samples. Theoretically, a diffusion model has been integrated with heat transfer to determine the mutual diffusivities for the hot CO2/C3H8-heavy oil systems by incorporating the volume-translated (VT) Peng-Robinson equation of state (PR EOS) together with the modified alpha functions and acentric factor redefined at Tr = 0.6. The mutual diffusivities can be determined once the computed parameters, including oil swelling factors and gas composition, match the measured ones. Due to solvent dissolution, heavy oil is found to swell faster initially as both heat and mass transfer contribute to the oil swelling. After the system temperature is stabilized, the volume of the diluted oil expands slowly as a result of the ongoing mass transfer. The extraction process was evident during the experiments with the presence of oil components in the collected gas samples, and it was found to be stronger at a higher temperature. The diffusivities determined using different alpha functions in the PR EOS are similar, but the newly defined acentric factor with the optimum alpha function minimizes the deviation between the measured and computed parameters. In addition to new experimental data, the bidirectional mass transfer between solvent and heavy oil has been quantified for the first time by coupling heat transfer.

Quantitative assessment of a novel method for fluid thermodynamic test simulation in multicomponent systems

This paper presents a quantitative methodology for simulating fluid thermodynamic tests, including constant composition expansion (CCE), differential liberation (DL), and separator tests, within multicomponent systems. The approach combines equilibrium ratios, flash calculations, and the Peng-Robinson equation of state. Utilizing the PVTp (Pressure - Volume - Temperature) package regression procedure enables the calibration of OmegaA and OmegaB values, enhancing accuracy and minimizing error margins in fluid thermodynamic calculations compared to empirical data. Numerical results demonstrate the effectiveness of this method. Bubble point pressure values from observed, software-generated, and calculated data are 2344, 2339, and 2350.42 psia, respectively. Calculated fluid thermodynamic test results closely align with software predictions and exhibit acceptable error levels compared to the measured data. However, discrepancies in the solution gas - oil ratio during the DL test highlight the need for more comprehensive measured data to improve simulation accuracy and reduce error margins. The comparison between the proposed methodology and collected data confirms the effectiveness of integrating equilibrium ratios, flash calculations, and the Peng-Robinson equation of state for precise fluid thermodynamic calculations. This approach offers a quantitative framework for simulating fluid thermodynamic tests, providing insights while reducing reliance on costly laboratory experiments.

Analysis of Thermodynamic Models for Liquid-Vapor Equilibrium: Evaluating Accuracy and Applicability

This article investigates the liquid-vapor equilibrium of four binary refrigerant systems: R134a + R290, R152a + R1234ze, R152a + R1243zf, and R1243zf + R134a. The study employs three thermodynamic models for accurate predictions: the Peng-Robinson equation with the classical mixture rule of van der Waals (vdW) and the Wilson model, the PC-SAFT equation, and the PR-MC-WS-NRTL model. Activity coefficients are determined using the Peng-Robinson equation with vdW and the Wilson model. The PC-SAFT equation and the PR-MC-WS-NRTL model are also applied to model the data. The calculated results show good agreement with reference data. Favorable agreements exist between the calculated results and the reference data, with relative errors remaining below (0.15 and 0.42) % for the molar fraction and the pressure, respectively. This research provides valuable insights into the accuracy and applicability of different thermodynamic models in predicting liquid-vapor equilibrium within refrigerant systems.

High-pressure phase equilibria in methane + pentadecane system: Experimental measurement and modeling with Peng-Robinson equation of state

High-pressure phase equilibria in methane + pentadecane system: Experimental measurement and modeling with Peng-Robinson equation of state

A New General Correlation for the Influence Parameter in Density Gradient Theory and Peng-Robinson Equation of State for n-Alkanes.

The Density Gradient Theory (DGT) permits obtaining the surface tension by using an equation of state and the so-called influence parameter. Different correlations of the influence parameter versus temperature have been proposed, with the two-coefficient ones from Zuo and Stenby (full temperature range) and Miqueu et al. (valid for the lower temperature range) being widely used. Recently, Cachadiña et al. applied the DGT with the Peng-Robinson Equation of State to esters. They proposed a new two-coefficient correlation that uses a universal exponent related to the critical exponent associated with the dependence of coexistence densities on temperature near the critical point. When applied to n-alkanes, it is shown that the Cachadiña et al. correlation must be modified to improve the lower temperature range behavior. The proposed modification results in a three-coefficient correlation that includes the triple point temperature as an input parameter and incorporates the Zuo and Stenby and Miqueu et al. correlations as particular cases. Firstly, the correlation coefficients for each of the 32 n-alkanes considered are obtained by fitting the selected values for the surface tension obtained from different databases, books, and papers. The results obtained are comparable to other specific correlations reported in the literature. The overall mean absolute percentage deviation (OMAPD) between the selected and calculated data is just 0.79%. Secondly, a general correlation with three adjustable coefficients valid for all the n-alkanes is considered. Despite the OMAPD of 4.38% obtained, this correlation is discarded due to the high deviations found for methane. Finally, it is found that a new six-coefficient general correlation, including the radius of gyration as an input fluid parameter, leads to an OMAPD of 1.78% for the fluid set considered. The use of other fluid properties as an alternative to the radius of gyration is briefly discussed.

Mathematical modelling of essential oil supercritical carbon dioxide extraction from chamomile flowers

AbstractThis study investigates the supercritical extraction process of essential oil from chamomile flowers. Essential oils of chamomile are used extensively for medicinal purposes. Many different chamomile products have been developed, the most popular of which is herbal tea. In this study, a mathematical model is formulated that describes the governing mass transfer phenomena in a solid–fluid environment under supercritical conditions using carbon dioxide. The concept of quasi‐one‐dimensional flow is applied to reduce the number of spatial dimensions. The flow of carbon dioxide is assumed to be uniform across any cross‐section, although the area available for the fluid phase can vary along the extractor. The physical properties of the solvent are estimated based on the Peng–Robinson equation of state. Model parameters, including the partition factor, internal diffusion coefficient, and decaying factor, were determined through maximum likelihood estimation based on experimental data assuming normally distributed errors. The model parameters were combined to obtain a set of correlations. The generalized process model is capable of reproducing the dataset with satisfactory accuracy.

Fundamental properties of the green solvent CO2 expanded ethyl lactate: Peng-Robinson equation of state, molecular dynamics simulation, and density functional theory studies

The industrial application of the eco-friendly switchable solvent CO₂ expanded ethyl lactate (CXEL) requires a comprehensive understanding of its fundamental properties. However, no systematic analysis of its structure or essential properties, such as density and viscosity, has been reported. This inaugural study addresses this gap by examining densities and viscosities using the Peng-Robinson equation of state (PR EoS), classical molecular dynamics (MD) simulations, and density functional theory (DFT) studies. We firstly conducted a detailed structural analysis of CXEL, focusing on key descriptors such as radial distribution function, mean square displacement, and hydrogen bond for CO₂ mole fractions (x1, representing the CO₂ mole fraction) ranging from 0 to 1.0. Additionally, solvation analysis using frontier molecular orbital and the conductor-like screening model for real solvent (COSMO-RS) revealed that CO₂ interactions modulate the solvent's polarity, switching its solvation behavior and compatibility. This study is the first to systematically report detailed densities and viscosities across the entire range of x1 at 308.15 K and 20.0 MPa, revealing significant findings, including a density peak at x1 = 0.6. Densities predicted by PR EoS and ReaxFF MD simulations showed strong agreement with literature data, with average absolute relative deviations of 1.33 % and 10.79 %, respectively. While PR EoS has limitations, MD simulations offer more valuable insights into densities and viscosities prediction and intermolecular interactions investigation. Moreover, ReaxFF was utilized to determine the kinematic viscosities of CXELs across the CO₂ mole fraction range, supporting the development of an extraction kinetic model. These findings enhance our understanding of CXELs, underscoring their potential for diverse eco-friendly industrial applications, particularly in extraction processes.

Maximizing the Hesperidin Extraction Using Supercritical Carbon Dioxide and Ethanol: Theoretical Prediction and Experimental Results

Agroindustrial waste can be valorized towards the obtaining of several products such as pigments, proteins, fibers, and polyphenolic compounds with antioxidant capacity. Orange peel waste is a promising source of polyphenolic compounds such as hesperidin. However, conventional extraction techniques present some environmental limitations such as high solvent consumption and high wastewater generation. Supercritical fluid extraction (SFE) has emerged as a green extraction technique due to the low use of solvent. The aim of this study was to maximize the hesperidin extraction based on theoretical predictions of the operating conditions from empirical thermodynamic models using SFE with carbon dioxide (CO2) as a solvent. The theoretical conditions were validated experimentally on a semi-pilot scale. The extracts were evaluated in terms of hesperidin content, total polyphenol content, and antioxidant capacity. Thermodynamic prediction of the operating conditions showed that the ethanol used as a co-solvent promotes hesperidin extraction. The optimum operating conditions were 25 °C, 80 bar, and a volumetric co-solvent concentration of 10%. The validation of the operating conditions resulted in a final hesperidin concentration of 11.5 ± 0.03 g/kg of orange peel waste. The experimental results were 30.26-times higher using 10% vol of ethanol than the extraction of hesperidin with pure ethanol as a co-solvent. The total polyphenol content and antioxidant capacity resulted in 831.92 ± 40.01 mg Galic acid/100 g orange peel waste, 15.41± 0.91 EC50/mL, and 5.31 ± 0.67 µMolTrox/100 g orange peel. Finally, the prediction of operating conditions from empirical thermodynamic models such as the Peng–Robinson equation of state with some modifications (Stryjek Vera) for solid–gas equilibrium solubility calculations, allows for maximizing the content of the polyphenolic compounds using SFE.

Experimental data and thermodynamic modeling for n-propane + Brazil nut oil at high pressures

This research aimed to uncover essential phase transition data for the pseudo-binary system of n-propane and Brazil nut oil. Over a range of temperatures from 313 to 343 K and pressures up to 3.42 MPa, our study identified various phase equilibria, including liquid-vapor, liquid-liquid, and liquid-liquid-vapor, using the visual synthetic-static variable volume method. The observed phase transitions fall under the type III classification proposed by Scott van Konynenburg. Leveraging the cubic Peng-Robinson equation of state with the van der Waals mixing rule, we were able to construct isopleths for the proposed system. Additionally, we examined the fatty acid profile of Brazil nut oil to accurately quantify its composition and estimate critical properties of the pseudo component in line with Kay's rule. This research provides critical insights into the behavior of phase diagrams for pressurized fluid-based extraction and separation processes, which are crucial for achieving maximum yield and minimizing energy expenditure.

Modeling of adsorption-controlled binary gas transport in ultratight porous media

Organic-rich ultratight porous media such as shales have complicated pore types and sizes, dictating their unique fluid transport and storage mechanisms. This paper introduces a diffusion-based binary gas (CH4 and CO2) transport model in such porous media, incorporating key transport and storage mechanisms. Binary gas mixture within the pore volume is divided into two domains: the free-phase and the sorbed-phase, both of which contribute to gas mass transport. Thermodynamic properties of the free phase are determined using the Peng-Robinson equation of state, while a modified extended Langmuir isotherm describes the sorbed phase. The bulk diffusion, Knudsen diffusion, and viscous diffusion are reconciled to describe binary gas transport in the free phase, while the surface diffusion is considered in the sorbed phase. The mass flux is finally related to the effective diffusion coefficient and the free-phase concentration gradient through coupling all transport mechanisms via the equivalent resister network model. The governing equations are solved numerically using a finite difference approach to simulate co-diffusion and counter-diffusion of a binary gas mixture in two nanoporous media, shale and coal.The results reveal that surface diffusion is more pronounced in coal than in shale due to coal's higher adsorption capacity. In co-diffusion cases, both free-phase and sorbed-phase concentrations decrease over time. However, the decline of sorbed-phase concentrations is slower than that of the free-phase. Moreover, CO2 tends to remain adsorbed within the coal matrix due to its stronger adsorption affinity, unlike CH4, which is more likely to flow out. In counter-diffusion cases, injected CO2 first accumulates near the fracture region and then diffuses further into the matrix. Despite shale's pore volume being twice that of coal, similar amounts of CO2 are injected, which can be attributed to coal's higher CO2 adsorption capacity.

Vapor-liquid equilibria for the CO2 + trimethoxymethylsilane and CO2 + triethoxymethylsilane systems under high-pressure conditions

New binary isotherms are crucial for designing chemical separation processes within supercritical carbon dioxide (CO2) + trialkoxysilane systems. Vapor-liquid equilibria (VLE) were investigated for two-component systems, trimethoxymethylsilane + CO2 and triethoxymethylsilane + CO2, at five temperatures (313.2, 333.2, 353.2, 373.2, and 393.2 K) and pressures up to 14.07 MPa using a synthetic high-pressure phase equilibria apparatus. The pressure-temperature (P-T) plot indicates that the critical mixture curve lies between the critical points of CO2 and the trialkoxysilane compounds. The solubility of trimethoxymethylsilane and triethoxymethylsilane in CO2 increased with increasing temperature at constant pressure, following a type-I phase behavior characteristic. The experimentally observed VLE values of the CO2 + trialkoxysilane systems were correlated using the Peng-Robinson equation of state with binary parameters (kij and ηij) in the conventional mixing rule. The model accuracy was validated by calculating the average relative deviation percentage for the pressure of the binary systems, resulting in values of 4.98% for the trimethoxymethylsilane + CO2 system and 3.64% for the triethoxymethylsilane + CO2 system. The estimated variables fell within reasonable limits and showed no significant differences between the predicted and observed VLE data for both systems.

Assessment of dissociation enthalpies of methane hydrates in the absence and presence of ionic liquids using the Clausius-Clapeyron approach

The Clausius-Clapeyron (CC) equation is generally preferred to obtain dissociation enthalpies (ΔH) of hydrate-forming systems due to its ease of use. The application of other direct and indirect methods becomes more problematic if complex additives such as ionic liquids (ILs) are also present in the system. In this work, around 400 equilibrium data points for methane hydrates in the presence of over 80 ILs were collected from the literature in the temperature and pressure ranges of (272.10 – 306.07) K and (2.48 – 100.34) MPa, respectively. The ΔH of methane hydrates in the absence and presence of ionic liquids (ILs) have been calculated using the CC equation. The compressibility factor (z), required to calculate ΔH at each phase equilibrium condition has been obtained from three different approaches viz., Peng-Robinson (PR) equation of state, Soave-Redlich-Kwong (SRK) equation of state and Pitzer (Pz) correlation. The results were compared to the experimentally reported dissociation enthalpy (54.5 ± 1.5 kJ.mol−1) of methane hydrates. The role of the compressibility factor along with the slope of the equilibrium data set and the temperature/pressure range in determining the outcome of the CC equation has been discussed. The effect of molar mass, molar volume, and hydrate suppression temperature of the ILs on the ΔH of methane hydrates has been explored. The tested ILs do not show a systematic and significant influence on enthalpies, rather they show a large scattering in the ΔH values, which might mask any existing subtle effect of the ILs on the dissociation enthalpies. Therefore, this approach should be dealt with care to obtain molecular-level insights.

Performance Evaluation of CO2 + SiCl4 Binary Mixture in Recompression Brayton Cycle for Warm Climates

This work demonstrates the potential of CO2 + SiCl4 binary mixture as a working fluid for power generation cycle. Recompression Brayton cycle configuration is considered due to its proven record of high performance for medium- to high-temperature sources. The objective of this study is to assess the thermodynamic performance of a recompression Brayton cycle using a CO2 + SiCl4 binary mixture as a working fluid, particularly under warm climate conditions. The cycle is simulated using the Peng–Robinson equation of state in Aspen Hysys (v11) software, and the model is validated by comparing VLE data against experimental data from the literature. The analysis involves the assessment of cycle’s thermal efficiency and exergy efficiency under warm climatic conditions, with a minimum cycle temperature of 40 °C. The results demonstrate a notable improvement in the cycle’s thermodynamic performance with CO2 + SiCl4 binary mixture compared to pure CO2. A small concentration (5%) of SiCl4 in CO2 increases the thermal efficiency of the cycle from 41.7% to 43.4%. Moreover, irreversibility losses in the cooler and the heat recovery unit are significantly lower with the CO2 + SiCl4 binary mixture than with pure CO2. This improvement enhances the overall exergy efficiency of the cycle, increasing it from 62.1% to 70.2%. The primary reason for this enhancement is the substantial reduction in irreversibility losses in both the cooler and the HTR. This study reveals that when using a CO2 + SiCl4 mixture, the concentration must be optimized to avoid condensation in the compressor, which can cause physical damage to the compressor blades and other components, as well as increase power input. This issue arises from the higher glide temperature of the mixture at increased SiCl4 concentrations and the limited heat recovery from the cycle.

A molecular dynamics study on the supercritical evaporation of liquid ammonia under forced convection conditions

Although the behavior of the supercritical transition during the evaporation of liquid fuels in engine combustion chambers has been studied by many researchers, the effects of convection on the phase transition of liquid fuel in supercritical environments have been little studied. Previous studies mainly focused on hydrocarbon fuels for supercritical evaporation, with fewer on the zero-carbon liquid ammonia fuel. Aiming at the above deficiencies, this study used molecular dynamics simulations (MD) to explore the phase transition of liquid ammonia in a nitrogen supercritical environment under forced convection conditions. The Peng-Robinson equation of state (PR-EoS) was used to calculate the vapor–liquid equilibrium of the ammonia–nitrogen system to determine the supercritical transition time of liquid ammonia under forced convection conditions. The effects of forced convection on the heat and mass transfer process and the evolution of the liquid-phase region and the vapor–liquid interface region were analyzed. It was found that forced convection can promote the mass and heat transfer process and accelerate the phase transition of liquid ammonia to some extent. Forced convection may have a greater effect on the single-phase diffusive mixing process compared to the two-phase evaporation process. The increase in the interfacial thickness under forced convection conditions is mainly attributed to the temperature increase promoted by convection. The interfacial temperature dominates the development of its thickness and the thickness is approximately linear with temperature during the diffusive mixing stage. The shear effect induced by convection has an inhibitory effect on the diffusion of ammonia molecules within the interface region along the vertical convection direction. The cases in this study indicate that forced convection may promote the supercritical transition of liquid ammonia. In addition, a dimensionless number κ was proposed to explore the possibility of scaling up the MD results to the engineering scale.

Vapor-liquid equilibria of the ternary system of methane + n-decane + n-octacosane at high pressures

Alkane mixture phase equilibria is required for a range of industrial applications, most particularly for the petroleum industries. Mixtures containing light and heavy normal alkanes are of even further significance due to their non-ideal thermodynamic behavior. In this work, for the first time, the ternary system of C1 + C10 + C28 was investigated experimentally to obtain bubble point pressures at various concentrations and temperatures ranging from 373 up to 445 K. The synthetic method of phase equilibrium measurements was utilized, which is known to have high accuracy. The resulting bubble points for the mixtures ranged in pressure from about 3 MPa up to 6 MPa. The data indicated that methane concentrations had the greatest impact, not only on the magnitude of the bubble point pressure, but also on the slope of its temperature trend. The relative concentrations of n-decane and n-octacosane had far less impact on the bubble point curves. The results were also modelled using the Peng–Robinson equation of state, and it was found that this equation has the capability to predict the data with an AARD% of 5.1 %. When temperature-independent binary interaction parameters were optimized to the data, the AARD% reduced to 2.4 %. Although the components vary greatly in size, perhaps the success of the Peng–Robinson equation of state for this mixture could be attributed to the fact that it was developed for hydrocarbon mixtures, and so, a reason for its popularity in the petroleum industries, alongside its simplicity and ease of use.

Enhanced Solubility and Miscibility of CO2-Oil Mixture in the Presence of Propane under Reservoir Conditions to Improve Recovery Efficiency

The existence of propane (C3H8) in a CO2-oil mixture has great potential for increasing CO2 solubility and decreasing minimum miscibility pressure (MMP). In this study, the enhanced solubility, reduced viscosity, and lowered MMP of CO2-saturated crude oil in the presence of various amounts of C3H8 have been systematically examined at the reservoir conditions. Experimentally, a piston-equipped pressure/volume/temperature (PVT) cell is first validated by accurately reproducing the bubble-point pressures of the pure component of C3H8 at temperatures of 30, 40, and 50 °C with both continuous and stepwise depressurization methods. The validated cell is well utilized to measure the saturation pressures of the CO2-C3H8-oil systems by identifying the turning point on a P-V diagram at a given temperature. Accordingly, the gas solubilities of a CO2, C3H8, and CO2-C3H8 mixture in crude oil at pressures up to 1600 psi and a temperature range of 25–50 °C are measured. In addition, the viscosity of gas-saturated crude oil in a single liquid phase is measured using an in-line viscometer, where the pressure is maintained to be higher than its saturation pressure. Theoretically, a modified Peng–Robinson equation of state (PR EOS) is utilized as the primary thermodynamic model in this work. The crude oil is characterized as both a single and multiple pseudo-component(s). An exponential distribution function, together with a logarithm-type lumping method, is applied to characterize the crude oil. Two linear binary interaction parameters (BIP) correlations have been developed for CO2-oil binaries and C3H8-oil binaries to accurately reproduce the measured saturation pressures. Moreover, the MMPs of the CO2-oil mixture in the presence and absence of C3H8 have been determined with the assistance of the tie-line method. It has been found that the developed mathematical model can accurately calculate the saturation pressures of C3H8 and/or CO2-oil systems with an absolute average relative deviation (AARD) of 2.39% for 12 feed experiments. Compared to CO2, it is demonstrated that C3H8 is more soluble in the crude oil at the given pressure and temperature. The viscosity of gas-saturated crude oil can decrease from 9.50 cP to 1.89 cP and the averaged MMP from 1490 psi to 1160 psi at 50 °C with the addition of an average 16.02 mol% C3H8 in the CO2-oil mixture.

Controlling particle size of levan in powder form with different technologies

Levan is a fructose polysaccharide with multiple applications in different fields, but its obtaining in powdered form with a narrow particle size distribution is a complicated task. Two techniques, electrospraying and supercritical antisolvent (SAS) precipitation, were used to process levan that was first obtained enzymatically. The SAS process was able to micronize the polymer (at experimental conditions far above the mixture critical point of the solvent-antisolvent system) to obtain spherical particles between 0.30 and 0.50 μm with a proper particle size distribution. In this case, the Peng-Robinson equation of state was used to theoretically determine the mixture critical point. Bigger and elongated particles were obtained with electrospraying (0.60 μm). According to solution properties, mainly rheology, solubility and conductivity, the best solvent for levan electrospraying, in order to avoid problems of solvent evaporation and jet formation, was a mixture of water and ethanol with a polymer concentration of 50 mg·cm−3. Indeed, that solution has a viscous behavior (according to the oscillatory analysis), a low degree of pseudo-plasticity (based on the shear flow analysis), and the highest value of conductivity. Therefore, the particle size distribution of levan in powdered form can be tuned depending on the technique used.

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.

Numerical investigation of acoustic cavitation characteristics of a single gas–vapor bubble in soft tissue under dual-frequency ultrasound

The viscoelastic tissue under dual-frequency ultrasound excitation affects the acoustic cavitation of a single gas–vapor bubble. To investigate the effect of the cavitation dynamics, the Gilmore-Akulichev-Zener (GAZ) model is coupled with the Peng-Robinson equation of state (PR EOS). Results indicate that the GAZ-PR EOS model can accurately estimate the bubble dynamics by comparing with the Gilmore PR EOS and GAZ-Van der Waals (VDW) EOS model. Furthermore, the acoustic cavitation effect in different viscoelastic tissues is investigated, including the radial stress at the bubble wall, the temperature, pressure, and the number of water molecules inside the bubble. Results show that the creep recovery and the relaxation of the stress caused by viscoelasticity can affect the acoustic cavitation of the bubble, which could inhibit the bubble’s expansion and reduce the internal temperature and pressure within the bubble. Moreover, the effect of dual-frequency ultrasound on the cavitation of single gas–vapor bubbles is studied. Results suggest that dual-frequency ultrasound could increase the internal temperature of bubbles, the internal pressure of bubbles, and the radial stress at the bubble wall. More importantly, there is a specific optimal combination of frequencies for particular viscoelasticity by exploring the impact of different dual-frequency ultrasound combinations and tissue viscoelasticity on the acoustic cavitation of a single gas–vapor bubble. In conclusion, this study helps to provide theoretical guidance for dual-frequency ultrasound to improve acoustic chemical and mechanical effects, and further optimize its application in acoustic sonochemistry and ultrasound therapy.