Peng-Robinson Equation Of State Research Articles

New solubility data of Amoxapine (anti-depressant) drug in supercritical CO2: Application of cubic EoSs

The solubility of the anti-depressant drug, Amoxapine drug, in supercritical carbon dioxide has been studied. The experiments were performed by the simple and static procedure at P = 120-300 bar and T(K) = 311, 323, 333, and 343. The drug solubilities (mole fraction) ranged from 0.44×10-6 to 7.81×10-6. The drug solubilities were modeled, first using two cubic equations of state (Peng-Robinson and Soave-Redlich-Kwong EoSs with van der Waals mixing rule) and additionally by 17 semi-empirical density-based correlations (Stahl et al., Chrastil, Kumar-Johnston, Garlapati-Madras (model I and II), Sung-Shim, del Valle and Aguilera, Adachi-Lu, Ch and Madras, Hezave and Lashkarbolooki, Mendez-Santiago-Teja, Bartle et al., Jafari Nejad et al., Hozhabr et al., Keshmiri et al., Khansary et al. and Sodeifian et al.). The results revealed that cubic EoSs and semi-empirical density-based correlations can be used to obtain satisfactory drug solubility correlations at various temperatures and pressures. Between cubic EoSs, Peng-Robinson EoS (with Akaike Information Criterion is -692.12), and among 17 density-based correlations, the Stahl et al. correlation (with AARD% = 4.16%, corresponding corrected Akaike Information Criterion is -700.98 and Radj = 0.9963) gave much better accuracy with the experimental data. The thermodynamic consistency test based on Gibbs-Durham's theory was performed by using both cubic EoSs and all experimental data were examined. Furthermore, the solvation, vaporization, and total enthalpies of Amoxapine-CO2 were calculated by Chrastil, KJ, and Bartle et al. correlations.

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.

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.

A quantum-corrected Peng‒Robinson equation of state for helium-4 from 3 K to 50 K considering quantum swelling effects through the Feynman‒Hibbs correction of the EXP-6 potential

Accurate and efficient prediction of the properties of helium-4 (He-4) via an equation of state (EOS) is a prerequisite for evaluating liquid helium-4 (LHe-4) storage technology. However, the performance of the Peng–Robinson (PR) EOS in predicting the density of LHe-4 and vapour helium-4 (VHe-4) deteriorates within the thermodynamic ranges of the LHe-4 tank: 3–50 K and 60–600 kPa. To modify the PR EOS, we establish first-order and second-order Feynman–Hibbs (FH)-corrected EXP-6 potentials and propose a reduced effective particle diameter (REPD) correlation with four parameters to consider the quantum swelling effects of LHe-4. On the basis of the rational function form of the REPD correlation, we introduce a quantum-corrected covolume term to develop a regression model for the FH-corrected Peng–Robinson (FH-PR) EOS. Moreover, to improve the effectiveness of regression near the saturation curve, we propose a hypothetical boundary consisting of the saturation curve from 3 K to the critical temperature and a virtual saturation curve from the critical pressure to 600 kPa. The results indicate that the FH − PR EOS shows satisfactory engineering application performance in predicting the density of He-4 within the studied range. Under verification conditions, the average absolute relative deviation (AARD) of the density determined via the FH − PR EOS ranges from 0.72 % to 1.77 %, and the maximum relative deviation (MRD) ranges from 2.17 % to 5.62 %. Under test conditions, the AARD of the density ranged from 1.06 % to 1.71 %, and the MRD ranged from 3.77 % to 7.38 %.

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.

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.

Selectivities of Carbon Dioxide over Ethane in Three Methylimidazolium-Based Ionic Liquids: Experimental Data and Modeling.

This work focused on the solubility of ethane in three promising ionic liquids {1-Hexyl-3-methylimidazolium bis(trifluormethylsulfonyl) imide [HMIM][Tf2N], 1-Butyl-3-methyl-imidazolium dimethyl-phosphate [BMIM][DMP], and 1-Propyl-3-methylimidazolium bis(trifluoromethyl-sulfonyl)-imide [PMIM][Tf2N]}. The solubilities were measured at 303.15 K to 343.15 K and pressures up to 1.4 MPa using a gravimetric microbalance. The overall ranking of ethane solubility in the ionic liquids from highest to lowest is the following: [HMIM][Tf2N] > [PMIM][Tf2N] > [BMIM][DMP]. The Peng-Robinson equation of state was used to model the experimental data using three different mixing rules: van der Waals one, van der Waals two, and Wong-Sandler mixing rules combined with the Non-Random Two-Liquid model. The average absolute deviations for the three mixing rules for the ionic liquids at the three temperatures were 4.39, 2.45, and 2.45%, respectively. Henry's Law constants for ethane in [BMIM] [DMP] were the highest (lowest solubility) amongst other ionic liquids studied in this work. The solubility ranking for the 3 ILs was confirmed by calculating their overall polarity parameter (N) using COSMO-RS. The selectivity of CO2 over C2H6 was estimated at three temperatures, and the overall ranking of the selectivity was in the following order: [PMIM][Tf2N] > [BMIM][DMP] > [HMIM][Tf2N] > Selexol. Selexol is an efficient and widely used physical solvent in gas sweetening. It has lower selectivity than the three ionic liquids studied. [PMIM][Tf2N], a promising solvent, has the highest selectivity among the three ILs studied and would, therefore, be the best choice if, in addition to carbon dioxide capture, ethane co-absorption was to be avoided. The enthalpy and entropy of solvation at infinite dilution were also estimated.

Solubility measurement of Ceftriaxone sodium in SC-CO2 and thermodynamic modeling using PR-KM EoS and vdW mixing rules with semi-empirical models

The complete investigation of the solubility of Ceftriaxone sodium drug has not yet been conducted. This communication investigates the solubility of Ceftriaxone sodium drug in supercritical CO2 (SC-CO2) for the first time. The drug solubility measurements were performed using utilizing UV–vis analysis under different operation conditions (at P (bar) = 120–270 and T (K) = 308–338). The results demonstrated that the solubility of Ceftriaxone sodium ranged from 0.90 × 10−6 to 8.01 × 10−6. The mole fraction solubility of Ceftriaxone sodium increases proportionally with an increase in the pressure, while maintaining a constant temperature. However, a crossover was noted. The solubility behavior of Ceftriaxone sodium drug in SC-CO2 was modeled by Peng-Robinson equation of state (PR EoS) with Kwak-Mansoori and van der Waals mixing rules and seven semi-empirical correlations (Bian et al., Kumar-Johnston, Chrastil, Garlapati-Madras, Bartle et al., Sung-Shim and Sodeifian et al.,). The vaporization, total and solvation enthalpies of the Ceftriaxone sodium/SC-carbon dioxide system were obtained by KJ, Chrastil, and Bartle et al. correlations. The evaluation of two methods was performed by absolute average relative deviation (AARD%). Both models exhibited a satisfactory level of agreement with the experimental data. Finally, PR/KM EoS and the Chrastil models, with AARD% values of 8.70 % and 8.10 % respectively, showed superior precision in accurately fitting the solubility data.

Modeling Solubility Induced Elemental Fractionation of Noble Gases in Oils

This study explores the estimation of solubility-induced elemental fractionation of noble gases in hydrocarbon-based oils through existing empirical and theoretical models, complemented by a novel molecular simulation-based approach. Quantifying such fractionation is essential for a deeper understanding of fluid processes and migration in subsurface geological resources, an area currently lacking in experimental data. To address this, the research introduces a predictive model that employs the Peng-Robinson equation of state and a fugacity-coefficient-based method to assess noble gas elemental fractionation in hydrocarbons, including normal alkanes, cycloalkanes, and aromatics. However, this model struggles with precise quantitative predictions, prompting the introduction of adjusted cross-interaction parameters to enhance its performance. Furthermore, molecular simulations, in conjunction with the refined equation of state, are shown to offer a novel method for calculating noble gas fractionation coefficients across different hydrocarbon solvents. A key finding is the identification of a universal master curve, demonstrating that noble gas solubility fractionation at low pressure in simple hydrocarbon solvents can be quantitatively determined by temperature and density alone, without the need for detailed compositional information. Consequently, a new correlation is proposed for deriving elemental fractionation coefficients based solely on oil temperature and density, offering significant improvements over existing empirical methods for a wide range of temperatures. Although limitations are noted when applying this approach to oils rich in complex heavy components like resins and asphaltenes, it allows to address inconsistencies observed in traditionally used experimental correlations at high temperatures.

Fluid Phase Equilibria Carbon Dioxide + Decane + Hexadecane Ternary System

The interest in understanding reservoir fluids' phase behavior is to increase hydrocarbon production without any flow assurance issues. Due to its opacity, the evident complexity of determining phase equilibrium data revolves around the thermodynamic modeling of model systems. The article presents experimental phase equilibrium data and thermodynamic modeling for the CO2 + decane + hexadecane ternary system at 283.15, 298.15, and 323.15 K and pressures up to 20 MPa. The transitions observed during this study were liquid-liquid (LL), vapor-liquid (VL), and vapor-liquid-liquid (VLL). The Peng-Robinson equation of state was used to model this ternary system for various compositions. The temperature-dependent binary interaction parameters (kij) for the CO2 + n-alkane mixtures were adjusted to the experimental data. Additionally, a binary interaction parameter for the n-C16H34/n-C10H22 pair, independent of temperature, was obtained through the critical volume of the components. The results reveal complex behaviors as the mixture's composition of hexadecane progressively increases. Adding this longer-chain linear hydrocarbon influences the phase behavior, leading to the emergence of liquid-liquid transitions and barotropic inversion in the system. This study contributes valuable data on model systems representing crude oil, highlighting complex behaviors in ternary systems with high carbon dioxide content.

High-pressure phase equilibrium for carbon dioxide solubility with biofuels: Experimental and thermodynamic insights in 2,5-dimethylfuran and methyl levulinate

The solubility of carbon dioxide in two solvents, 2,5-dimethylfuran and methyl levulinate, were measured to high pressure, up to 9.1 MPa, at three different temperatures (283.15, 303.15 and 323.15) K. The new data were measured using both the isothermal synthetic technique and the variable volume synthetic method. Two methods were utilised to provide a level of data validation. The uncertainties in the measured data were critically estimated. The experimental phase equilibrium data were modeled using the Peng-Robinson equation of state and the Wong-Sandler mixing rule with a single set of binary interaction parameters for each system. The data indicated that the solubility of carbon dioxide in both 2,5-dimethylfuran and methyl levulinate at high pressures was relatively low, suggesting a low capacity of these biofuels to dissolve carbon dioxide at high pressure.

Precipitation of advanced nanomedicines (curcumin) using supercritical processing; experimental study, design and optimizing operating conditions

Curcumin is a known herbal medicine with numerous therapeutic effects and low bioavailability. Reducing the particle size of this medicine is a confirmed solution to increase its dissolution rate and bioavailability. To do so, Curcumin nanoparticles were produced in the present work by the supercritical gas anti-solvent (GAS) method. First, the minimum GAS operating pressure (Pmin) required to precipitate fine Curcumin particles from two solvents DMSO and ethanol was estimated using Peng-Robinson equation of state (PR-EoS). Then, Curcumin nanoparticles were precipitated from these two solvents under different operating conditions, specified by the Box–Behnken design method. Given the desired operating variables including pressure (120, 180, and 240 bar), temperature (308, 328, and 348 K), initial concentration (5, 35, and 65 mg/ml), flow rate of the supercritical carbon dioxide (scCO2) (10, 50, and 90 ml/min), and stirring rate (500, 1500, and 2500 rpm), their influence on the particle size of Curcumin was investigated, and optimum conditions were determined. At 240 bar and 328 K, nano Curcumin particles with the size of 230 nm and 81 nm were precipitated from DMSO and ethanol solutions with the initial concentration of 5 mg/ml and stirring rate of 1500 rpm, respectively. Results show that scCO2 flow rate is not a significant parameter.The remarkable reduction in the particle size of Curcumin from 28 ± 10 μm of the original sample to nano-scale confirms GAS efficiency. Also, the dissolution rate of the nanoparticles, produced in the optimal condition is much higher than the original sample, which can be due to their nano-metric size and lower degree of crystallinity.

Equilibrium curves and modeling of binary systems for the carbon di-oxide + benzyl acetoacetate and carbon di-oxide + benzyl acetate mixtures under high pressure

The solution phase behavior of the binary systems of supercritical carbon di-oxide (SU-CO2) + benzyl acetoacetate and SU-CO2 + benzyl acetate was investigated in a synthetic high-pressure apparatus at five temperatures from 313.2 to 393.2 K and pressure up to 33.53 MPa for the industrial benefit of food, pharmaceutical and cosmetics application. The solubility of benzyl acetoacetate and benzyl acetate in the SU-CO2 + benzyl acetoacetate and SU-CO2 + benzyl acetate systems were increased with increasing temperature at constant pressure, respectively. Both system isotherms were exhibited in the simple Type-I category phase behavior. Besides, the Peng-Robinson equation of state has been successfully applied to predict the phase behavior of the SU-CO2 + benzyl ester systems using adjustable molecular interaction parameters (kij and ηij). Neither system shows a three-phase behavior at any point of temperature and pressure. A one-fluid-phase locale was ascertained above and throughout the solubility curve whereas a two-phase locale was exhibited inside the critical curve for both binary systems. The critical mixture curve provides the fingerprint for the phase behavior study of any binary system since it is used to understand and calculate thermodynamic properties effectively. The accuracy of the studied model was tested by evaluating the percentage of root mean square deviation utilizing optimized temperature-dependent mixture parameters. Indeed, this is the first reference point for the prediction of phase transition behavior for benzyl acetoacetate and benzyl acetate in SU-CO2 and the findings make a remarkable impression on industrial applications.

Estimation of the interaction parameters between carbon dioxide and an organic solvent by the Peng–Robinson equation of state via an artificial neural network

The equation of state (EoS) is a tool for estimating the thermodynamic and physical properties of compounds, including mixtures, across a range of temperatures and pressures. When dealing with mixtures, a mixing rule is required to calculate the mixture parameters. Mixing rules may involve interaction parameters, such as kij and lij, that correct for differences between components. However, obtaining this data requires specialized equipment and techniques and significant measurement time, resulting in limited reported EoS parameters. In this study, we introduce an artificial neural network (ANN) to predict interaction parameters in the van der Waals one-fluid mixing rule. These parameters are used to calculate the physical properties of mixtures using the Peng–Robinson (PR) EoS. The interaction parameters are used in two cases, namely the one-parameter and two-parameter mixing rules (OP and TP, respectively), in which only kij and both kij and lij are employed, respectively. The vapor–liquid equilibrium (VLE) data of CO2/organic solvent binary systems are collected and correlated by the PR EoS to construct a database of 1286 and 1292 parameters for the OP and TP, respectively. The molecular weight, critical temperature and pressure, acentric factor of the organic solvent, and temperature are used as input parameters for the ANN. In addition, we optimize the structure of the ANN by changing the activation function, number of neurons, and number of hidden layers. The optimized ANN uses a tanh activation function. Hidden layers are used for both the OP and TP, along with 40 and 50 neurons, respectively. The results confirm that the model can determine the interaction parameters of the PR EoS, which can be used to estimate the VLE. These results are useful for incorporation into process simulators for chemical process design.

Brine Salinity: A Deciding Factor for Carbondioxide Dissolution and Trapping during Geological Sequestration

Adequate geological storage of carbondioxide in saline aquifers is a function of several factors that requires understanding and examination. Previous works have argue that solubility of carbondioxide in brine decreases as the salinity of the brine increases, but it is unclear in the literature the impact of salinity on carbondioxide (CO2) trapping during sequestration. This work adopt a simulation based approach to determine CO2 dissolution and trapping at different salinities. A dataset was written and validated with CMG’s greenhouse gases simulator and the thermodynamics properties calculation carried out with Peng-Robinson equation of state. Four sensitivity analyses was conducted with brines of no salinity (pure water), salinity of 100000ppm, 200000ppm and 300000ppm and model outputs compared for CO2 sequestration. The result shows that CO2 solubilised in water with zero level salinity, and a lower gas cap size was formed at the top of the structure. Later, gas cap size increases as the salinity level increases at the top of the structure. Also, the moles soluble in water decreases as the salinity level increases with the least moles for zero water salinity. Alternatively to the moles solubilised, the number of moles of CO2 trapped increases with the salinity level. CO2 storage in deep saline aquifers is the best storage techniques but its injection into aquifer of high salinity reduced its solubility.

Solubility of oxazepam in supercritical carbon dioxide: Experimental and modeling

This study thoroughly investigates the solubility of oxazepam in supercritical carbon dioxide (SC-CO2) at temperatures of 308, 318, 328, and 338 K and pressures ranging from 12 to 30 MPa. The solubility measurements revealed a mole fraction of oxazepam ranging from 2.50 × 10−6 to 7.13 × 10−5, with the highest solubility observed at 338 K and 30 MPa. The solubility data were effectively modeled using semi-empirical density-based models (Mendez-Santiago and Teja (MST), Chrastil, Bartle et al., Kumar and Johnston (K-J), and Alwi-Garlapati), two equations of state (Peng-Robinson and modified-Pazuki) and regular solution models. The K-J model emerged as the best fit for the experimental data, boasting the lowest Average Absolute Relative Deviation (AARD) value of 7.73 %. The Peng-Robinson equation of state outperformed the modified-Pazuki equation, with AARD values of 15.71 % and 18.15 %, respectively. The study's key finding is the low solubility of oxazepam in SC-CO2, which suggests that supercritical antisolvent techniques could be effectively employed for synthesizing nanoparticles of this pharmaceutical compound. These findings have practical implications as they provide valuable insights for optimizing drug formulation processes and demonstrate the potential of SC-CO2 in pharmaceutical applications.

Numerical modeling of the non-equilibrium condensation in multi-component flows through the high expansion ratio nozzles

Excessive flow expansion in the thruster nozzles reduces the flow temperature and pressure. This provides conditions for the condensation phenomena in the nozzle, which can affect the thrust performance of thrusters. In this paper, the condensation effect of water components in the decomposition products of hydrogen peroxide in a typical thruster nozzle is modeled. To describe the state and properties of the real gas mixture, the Peng-Robinson equation of state is used. Moreover, the effects of H2O2 concentration and nozzle profile on the condensation and nozzle performance parameters are studied. The results show that by more flow expansion and crossing the saturated state of condensable components, the thrust coefficient improves up to 6%. This improvement decreases by increasing the H2O2 concentration in the reaction chamber for a fixed nozzle expansion ratio. Due to the small growth of droplets during the free molecular regime of the droplet growth in the high-speed flow, the non-equilibrium condensation continues until the nozzle outflow. In addition, although all the profiles have the same expansion ratio for nucleation start, increasing the nozzle length results in larger nano-droplets, more liquid mass fraction formation up to 4%, and moving the Wilson point to the further upstream sections in the nozzle.

Unconstrained ETD Methods on the Diffuse-Interface Model with the Peng-Robinson Equation of State

Unconstrained ETD Methods on the Diffuse-Interface Model with the Peng-Robinson Equation of State

Measurements and PR EoS Modeling of Thermophysical Properties at Vapor-Liquid Equilibrium Conditions for Natural Gas Condensate/Live Bitumen Mixtures.

In response to the need for less energy-intensive and greener bitumen recovery techniques, the use of multicomponent diluents through the expanding solvent steam-assisted gravity drainage (ES-SAGD) technique has garnered significant interest in recent years. In this work, we report new comprehensive measurements and Peng-Robinson equation of state (PR EoS) modeling of thermophysical properties (saturation pressure, density, viscosity, and K-values) of multicomponent mixtures of methane-bitumen-solvent. The multicomponent solvent is a natural gas condensate comprised of C3, i-C4, n-C4, i-C5, n-C5, C6, and C7+. Density, viscosity, solubility, and K-values of live bitumen (bitumen with dissolved methane) and various multicomponent mixtures are measured in the pressure range of 1-4 MPa and the temperature range of 313.41-459.10 K. A systematic approach is utilized to model the measured data. The experimental data show that the saturation pressure of the live bitumen can be controlled by selecting an appropriate solvent (condensate) composition. Condensate also has a significant effect on reducing the density and viscosity of the system. The results also show that the K-values of the components are almost independent of the composition of the solvent. The new comprehensive data set and the EoS model parameters reported in this work find applications in reservoir simulation as well as the design and optimization of the ES-SAGD process.