Volume-translated Peng-Robinson Equation Of State Research Articles

Auto-calibration strategy for the equilibration phase of Gibbs ensemble Monte Carlo simulations

ABSTRACT This paper proposes simulation protocols in terms of an auto-calibration strategy for the parameterisation of Gibbs ensemble Monte Carlo simulations for Lennard–Jones fluids. The proposed simulation protocols have been deduced from various approaches proposed in literature and have been tested against pure LJ fluids and their mixtures. These simulation protocols are intended to reduce or avoid time-consuming pre-simulations by adjusting the trial move limits, the number of attempted transfers, or the probability of attempted transfer during the equilibration phase, and can serve as a starting point for simulating more complex molecules, beyond LJ-fluids. This new approach aims to adjust simulation parameters to ensure a sufficient amount of successful trial moves as suggested in literature. It is similar to a previously proposed trial move adjustment and can easily be implemented in existing simulation code. Abbreviations: BWR EoS: Benedict–Webb–Rubin equation of state; CBMC: Configurational-bias Monte Carlo; EoS: Equation of state; GEMC: Gibbs ensemble Monte Carlo; LJ: Lennard–Jones; M1; M2; M3: Abbreviations for the three simulated mixtures; MC: Monte Carlo; PAT: Probability of attempted transfer; TL: Translation within a box (GEMC move); TR: Transfer to the other box (GEMC move); t-PR EoS: Volume-translated Peng-Robinson equation of state

Measurement and modelling of the interfacial tensions of CO2 + decane-iododecane mixtures at high pressures and temperatures

Experimentally determined interfacial tensions (IFTs) of CO2 and decane-iododecane mixtures are reported, with iododecane mass fractions of 0%, 50%, 70%, 90% and 100% over the temperature range of 298 K to 353 K and at pressures from 1 MPa up to the mixture critical point pressure. Measurements were carried out in a thermostatic high-pressure view cell by means of the pendant drop method. It was observed that the volume of a fresh drop of hydrocarbon initially increased, while the IFT decreased, before reaching equilibrium values. These observations correspond to two key mechanisms of CO2 flooding: oil swelling and IFT reduction. The equilibrium IFTs decrease with increasing pressure isothermally until the mixture critical point pressure is reached. The IFTs also increase with increasing mass fraction of iododecane. An empirical model was developed that is able to represent the experimental results with an overall average absolute deviation of 0.2 mN∙m−1.The IFT data were modeled with the square gradient theory coupled with the volume-translated Peng-Robinson equation of state. The temperature-independent influence parameters of decane and iododecane were regressed from their surface tensions, while the influence parameter of CO2 was taken from literature. The theoretical predictions are in good agreement with the experimental results with an average absolute deviation of 0.4 mN∙m−1. Finally, we extend a group-contribution approach for the binary interaction parameters in the Peng-Robinson equation of state to encompass the CH2I functional group, thereby facilitating application of the modelling approach to other systems comprising CO2 or N2 with iodoalkanes.

Determination of the concentration-dependent effective diffusivity of CO2 in unconsolidated porous media saturated with heavy oil by considering the swelling effect

Effective diffusivity of CO2 in the unconsolidated sandpack saturated with a Lloydminster heavy oil was determined in the form of an exponential function of CO2 concentration in the diluted and swollen liquid-phase. For such a purpose, two pressure-decay experiments were executed at different pressure ranges (i.e., 855–817 kPa and 1993–1905 kPa) and a temperature of 299.65 K. First, the sandpack saturated with heavy oil was prepared under an increased temperature of 348.15 K because the reduced heavy oil viscosity was required to saturate the sand column with heavy oil in a diffusion cell. Next, the diffusion cell containing the Lloydminster heavy oil-saturated sand column was integrated into a pressure-decay experimental system with pressure-monitoring devices. Then, pressure-history curves of both the diffusion experiments were continuously recorded to be compared with the theoretically calculated ones. The Fick's 2nd law incorporated with the volume-translated Peng-Robinson equation of state (PR-EOS) was implemented to determine the concentration-dependent effective diffusivity of CO2 in a sandpack saturated with heavy oil considering its swelling effect through minimizing the deviations between the theoretically computed pressure-history curves with the experimentally recorded ones. For the computation of the Fick's 2nd law, the Crank-Nicolson scheme finite difference method (FDM) was applied to take the local oil swelling into account for enhancing the accuracy of such a determined diffusivity. The excellent agreements between the theoretically computed and experimentally measured pressure-history curves at both the pressure ranges signify that such a determined effective diffusivity considering the CO2 concentration is accurate and reliable.

Interfacial tensions of systems comprising N2, 7 mass% KI (aq), decane and iododecane at elevated pressures and temperatures

Interfacial tension (IFT) between reservoir fluids is an important property in enhanced oil recovery (EOR) and carbon geological storage (CGS). Quantitative knowledge of IFT is needed to support and assist the interpretation of multiphase flow and wetting behaviour in porous media and to facilitate numerical reservoir simulation. Iododecane and iodide-containing brines are common contrast agents in visualisation of multiphase flow in porous media by X-ray CT imaging. The effect of the introduced contrast agents on the IFT was studied in this work by means of pendant-drop experiments and modelling with the density-gradient theory. We report experimental IFTs between N2, 7 mass% KI (aq), and decane-iododecane mixtures with various iododecane mass fractions at temperatures from 298 K to 353 K and pressures from 1 MPa to 30 MPa. The IFTs between N2 and the liquid phases decrease with the increase of either pressure or temperature and increase with the increasing KI molality or iododecane mass fraction. The IFTs between H2O and decane-iododecane mixtures decrease with temperature or iododecane mass fraction and increase slightly with increasing pressure. The IFT data were modelled by means of the density-gradient theory coupled with the volume-translated Peng-Robinson equation of state. Empirical equations were also developed to correlate all of the measured data. A workflow was proposed for estimating the IFTs between gas, brine and the doped hydrocarbon systems based on the experimental and modelling work.

Determination of effective diffusivity of each component of a binary gas-mixture in porous media saturated with heavy oil

In this work, the conventional pressure-decay technique has been improved and extended to estimate the effective diffusivity of each component in a binary gas mixture in an unconsolidated porous medium saturated with heavy oil. Experimentally, a workflow has been well devised to prepare a heavy oil-saturated sandpack, making it possible for evaluating the preferential contribution of each gas in a mixture to dissolving into heavy oil. Firstly, temperature is increased to reduce viscosity of a heavy oil sample contained in a diffusion cell to construct the heavy oil-saturated silica sand column above which a void space was created. Then, such a well-prepared diffusion cell is integrated with the pressure-decay system to continuously monitor and record the pressure history throughout the diffusion test. At the beginning and end of the test for a binary gas mixture diffusing into heavy oil, the gas-phase samples were collected to have their compositions analysed so that the amount of each gas component dissolved in heavy oil can be determined. Theoretically, mass transfer models are integrated with the volume-translated Peng-Robinson equation of state (PR EOS) to determine the effective gas diffusivity once the discrepancy between the measured and computed composition of each gas component is minimized as well as the deviation between the experimentally measured and computed pressure-decay profiles. Under 299.65 K, the effective diffusivity of CO2 is estimated to be 2.93×10–10 m2/s at 855–817 kPa for pure CO2–heavy oil systems, and those of CO2 and C3H8 are calculated to be 2.78×10–10 m2/s and 11.41×10–10 m2/s, respectively, at 854–783 kPa for the binary gas mixture-heavy oil systems. Furthermore, the reproduced pressure profiles are found to be generally in decent agreements with the experimentally measured ones. Due to the tortuous paths in porous media, the effective diffusivity of each component in the binary gas mixture is found to be smaller than its corresponding molecular diffusivity in the bulk phase, while the cross-term contribution on the mass transfer can be neglected under certain conditions.

Immiscible/Near-Miscible relative permeability for confined fluids at high-pressure and high-temperature for a fractal reservoir

The complex interaction between fluids and solids in reservoirs includes interface slip, capillary confinement and the diffusion and mass transfer between CO2 and oil and results in intensely nonlinear flow complexity. This study proposes a relative permeability model that accommodates a fractal pore size distribution and honors these complex process interactions. The relative permeability to CO2 flooding, in the near-miscible region, is predicted through interpolation based on the Gibbs free energy (GFE). The thermodynamic phase behavior of the fluids in the nanopores is considered by applying critical shifts in the temperatures and pressures. A volume-translated Peng-Robinson equation of state is used to calculate the CO2 and n-alkane densities to high reservoir pressure. Fluid-based correlation and modified volumetric mixing rules are then used to extend the viscosity calculations to mixtures with heavy hydrocarbon components. Predictions from the proposed model better fit experimental observations relative to previous models similarly incorporating fractal theory. The nanopores are shown to increase the relative permeability of the non-wetting phase by decreasing the viscosity ratio of the two phases. Increasing key parameters that are related to the pore structure, e.g. the fractal dimension, Df, and critical pore radius, rc, increases the relative permeability of the non-wetting phase. The GFE-based interpolation contributes to the smooth and continuous change in the relative permeability parameters local to the critical point of the mixture, with the confined fluid more likely to be miscible at the same pressure than the bulk fluid. This model can be integrated with a compositional simulator to solve field-scale problems but accommodating the micro-scale physics of unconventional reservoirs.

A modified cell-to-cell simulation model to determine the minimum miscibility pressure in tight/shale formations

A new oil–gas Minimum Miscibility Pressure (MMP) calculation algorithm is developed in this work based on the classic cell-to-cell simulation model. The proposed algorithm couples the effects of capillary pressure and confinement in the original cell-to-cell simulation model to predict the oil–gas MMPs in a confined space. Given that the original cell-to-cell algorithm relies on the volume predictions of the reservoir fluids in each cell, a volume-translated Peng-Robinson Equation of State (PR-EOS) is applied in this work for improved accuracy on volume calculations of the reservoir fluids. The robustness of the proposed algorithm is examined by performing the confined MMP calculations for four oil–gas systems. The tie-line length extrapolation method is used to determine the oil–gas MMP in confined space. The oil recovery factor calculated by the proposed MMP calculation algorithm is then used to validate the results. First, to achieve stable modeling results for all four examples, a total cell number of 500 is determined by examining the variations in the oil recovery as a function of cell number. Then, by calculating the oil recovery factor near the MMP region, it is found that the MMP determined by tie-line length method is slightly lower than the inflection point of the oil recovery curve. Through the case studies, the effects of temperature, pore radius, and injection gas impurity on the confined oil–gas MMP calculations are studied in detail. It is found that the oil–gas MMP is reduced in confined space and the degree of this reduction depends on the pore radius. For all the tested pore radii, the confined MMP first increases and then decreases with an increasing temperature. Furthermore, compared to pure carbon dioxide (CO2) injection, the addition of methane (CH4) in the injection gas increases the oil–gas MMP in confined nanopores. Therefore, it is recommended to control the content of CH4in the injection gas in order to achieve a more efficient gas injection design.

Phase-Behavior Modeling of Hydrocarbon Fluids in Nanopores Using PR-EOS Coupled with a Modified Young-Laplace Equation.

The effect of capillary pressure on the vapor–liquid two-phase equilibrium calculation has been extensively studied for the past two decades. However, the calculation accuracy is often weakened by the false assumptions and inherent flaws present in the modeling process. In this work, a modified Young–Laplace equation proposed by Tan and Piri [Tan, S.; Piri, M. Equation-of-State Modeling of Confined-Fluid Phase Equilibria in Nanopores. Fluid Phase Equilibr. 2015,393, 48–63.] is coupled with volume-translated Peng–Robinson equation of state to study the effect of capillary pressure on the two-phase equilibrium calculation in confined nanopores. In order to successfully apply the modified Young–Laplace equation during the vapor–liquid equilibrium calculation process, this study models the tuning parameter λ in the modified Young–Laplace equation (as proposed by Tan and Piri for perturbed-chain statistical associating fluid theory equation of state) for several pure hydrocarbons and their mixtures by matching experimental data collected from the literature. The tuning parameter λ can be expressed as a unique function for each pure substance or mixture. It is found that the tuning parameter λ shows a quadratic polynomial relationship with temperature, and the value of λ is always less than one. The λ can become negative under certain circumstances, which adjusts the capillary pressure to a lower value. It increases with an increasing pore radius; this is different from the results obtained by Tan and Piri which showed that the tuning parameter λ decreases with an increasing pore radius. The above rules apply to the tuning parameter λ obtained for both pure substances and mixtures. Using the two-phase equilibrium calculation coupled with the modified Young–Laplace equation, the calculated vapor pressures for pure substances and two-phase boundaries for mixtures match very well with the experimental data. Implementation of the modified Young–Laplace equation greatly improves the accuracy of the two-phase equilibrium calculation considering the capillarity effect. Such a modeling strategy could be integrated into a reservoir simulator to conduct more accurate flow simulations for tight/shale reservoirs.

Modeling the solubility of Alkyl Ketene Dimer in supercritical carbon dioxide: Peng-Robinson, group contribution methods, and effect of critical density on solubility predictions

Alkyl Ketene Dimer (AKD) is a sizing agent commonly introduced into cellulose substrates during papermaking to improve its hydrophobicity. High-pressure impregnation of this solute with supercritical carbon dioxide (scCO2) into cellulose and other substrates can achieve excellent hydrophobicity of the substrate, and may be used as an alternative technique to traditional coating (sizing) methods. In this study, the solubility of AKD in scCO2 was modelled using Peng-Robinson equation of state (PR-EOS) with van der Waals mixing rules, and volume-translated PR-EOS (VTPR). Given the unavailability of AKD's experimental critical properties and vapor pressure data, group contribution estimation methods (GCEM) were used to determine these physical constants. Available experimental data from another research group, collected using cloud-point and extraction methods, was used to regress binary interaction parameters and compare the resulting model's capability in predicting solubility. The models for each experimental method predicted crossover pressures within a small range, but fitted the cloud-point experimental data much better than the extraction data, showing good agreement at pressures beyond 15 MPa and all temperatures investigated. The VTPR model showed the least agreement with experimental data. A relative standard deviation of 0.26 was obtained between modelled and experimental data for the cloud-point method, and 0.42 for the extraction method data. The models were confirmed with the Chrastil equation, and strongly demonstrated the linear relationships predicted by this expression. The models additionally predicted a change in temperature dependence around the critical density, with a common linear relationship independent of temperature being observed at densities below the critical value. This newly observed behavior, not predicted by the Chrastil equation, sets the groundwork for further fundamental investigations, while the developed models will assist the design of alternative sizing processes involving AKD and scCO2.

Volumetric properties of diisopropyl ether with acetone at temperatures from 283.15 K to 323.15 K: An experimental and theoretical study

Accurate density data of binary mixture of diisopropyl ether (DIPE) with acetone are essential for the engineering design and operation of their separation. Densities of acetone+DIPE binary mixtures have been measured over the entire range of composition and at temperatures from (283.15 to 323.15) K under atmospheric pressure. The volume-translated Peng-Robinson equation of state has been applied to predict the densities of the liquid mixtures with an overall average relative deviation of only 0.095%, yielding a substantial improvement to the untranslated Peng-Robinson equation with an average relative deviation over fifty times lower. Excess volumetric properties of excess molar volumes and excess isobaric expansibility coefficients are derived from the experimental density data and well correlated by the Redlich-Kister type polynomial equation. The resultant positive excess volumetric properties confirm the existence of dispersive interactions and dipolar/orientational order change in the binary mixture during mixing.

Vapor-liquid phase boundaries and swelling factors of C3H8-n-C4H10-CO2-heavy oil systems under reservoir conditions

Techniques have been developed to determine vapor-liquid phase boundaries and swelling factors of CO2-heavy oil systems and C3H8-n-C4H10-CO2-heavy oil systems under reservoir conditions. Experimentally, a pure substance of CO2 and a gas mixture consisting of 27.7 mol% C3H8, 23.9 mol% n-C4H10, and 48.4 mol% CO2 are respectively introduced to dilute the highly viscous heavy oil. A pressure-volume-temperature (PVT) setup is used to measure vapor-liquid phase boundaries (i.e., saturation pressures) and swelling factors at high pressures up to 11.1 MPa and elevated temperatures up to 373.35 K. Theoretically, the volume-translated Peng-Robinson equation of state (PR EOS) coupled with a recently modified alpha function is applied as the primary thermodynamic model to reproduce the experimental measurements. The heavy oil which is a complex mixture with unknown molecular structure is characterized as six pseudocomponents by using an exponential distribution splitting function and a logarithm-type lumping method. The optimal exponents in binary interaction parameter (BIP) correlations are obtained by best matching the measured saturation pressures. Subsequently, the comparisons have been performed between this work and a commercial simulator in terms of the overall prediction accuracy of saturation pressures for the quaternary C3H8-n-C4H10-CO2-heavy oil systems. It is found that the minimum absolute average relative deviation (AARD) of 6.7% is obtained by the methodology developed in this work, compared to the AARD of 35.6% obtained by running the commercial simulator.

Using a New Proposed Influence Parameter of Gradient Theory for CH4/n-alkane Binary Systems: What Advances Can Be Achieved?

The main aim of this modeling investigation is to improve the performance of the gradient theory for binary systems of methane and n-alkane. To achieve this aim, the gradient theory (GT) is combined with the volume-translated Peng-Robinson equation of state (VTPR EOS) for accurate description of phase equilibrium and surface tensions of methane/hydrocarbon systems. To improve the phase equilibrium calculations, the binary interaction parameters of VTPR EOS for methane/hydrocarbon systems have been determined based on the mole fraction of methane in liquid phase. A new correlation of the influence parameter based on the densities of bulk phases has been suggested. To make the present model predictive, the binary interaction parameters of the mixture influence parameter have been set equal to zero. The results of the model show that the predictions of the present model agree well with experimental surface tensions, especially for very low values of surface tensions (near-critical interfaces).

Effective diffusion coefficients of gas mixture in heavy oil under constant-pressure conditions

We develop a method to determine the effective diffusion coefficient for each individual component of a gas mixture in a non-volatile liquid (e.g., heavy oil) at high pressures with compositional analysis. Theoretically, a multi-component one-way diffusion model is coupled with the volume-translated Peng-Robinson equation of state to quantify the mass transfer between gas and liquid (e.g., heavy oil). Experimentally, the diffusion tests have been conducted with a PVT setup for one pure CO2-heavy oil system and one C3H8–CO2-heavy oil system under constant temperature and pressure, respectively. Both the gas-phase volume and liquid-phase swelling effect are simultaneously recorded during the measurement. As for the C3H8–CO2-heavy oil system, the gas chromatography method is employed to measure compositions of the gas phase at the beginning and end of the diffusion measurement, respectively. The effective diffusion coefficients are then determined by minimizing the discrepancy between the measured and calculated gas-phase composition at the end of diffusion measurement. The newly developed technique can quantify the contributions of each component of mixture to the bulk mass transfer from gas into liquid. The effective diffusion coefficient of C3H8 in the C3H8–CO2 mixture at 3945 ± 20 kPa and 293.85 K, i.e., \(18.19 \times 10^{ - 10} {\text{m}}^{ 2} / {\text{s}}\), is found to be much higher than CO2 at 3950 ± 18 kPa and 293.85 K, i.e., \(8.68 \times 10^{ - 10} {\text{m}}^{ 2} / {\text{s}}\). In comparison with pure CO2, the presence of C3H8 in the C3H8–CO2 mixture contributes to a faster diffusion of CO2 from the gas phase into heavy oil and consequently a larger swelling factor of heavy oil.

Heterogeneous reactive extraction for isopropyl alcohol liquid phase synthesis: Microkinetics and equilibria

The reaction kinetics for the liquid phase synthesis of isopropyl alcohol (IPA) from propene (P) and water (W) using a macroporous sulfonic acid ion exchange resin as catalyst were determined experimentally in a multiphase CSTR in the temperature range 398K to 433K at 8MPa. This high pressure is necessary to dissolve propene in the aqueous phase and to ensure a liquid or supercritical state of all components. At typical reaction conditions, the reactants form two immiscible phases; the reaction takes place in the water swollen gel phase of the catalysts microspheres. Due to the large excess of water in the gel phase the compositions in the gel phase, in the macropore fluid, and in the catalyst surrounding aqueous phase are assumed to be identical. For temperatures up to 413K the reaction kinetics for the used catalyst size are not influenced by mass transfer resistances within the catalyst matrix. Two reactions, the formation of IPA and the condensation reaction of two IPA molecules forming the by-product diisopropyl ether (DIPE), are investigated. The experimental results can be described sufficiently by pseudo-homogeneous rate expressions in aqueous phase activities. For the formation of IPA, the forward reaction is first-order in propene and water while the reverse reaction is first-order in IPA. The activation energy of the forward reaction was determined to 115.3kJ/mol. The formation of DIPE is second order with respect to the activity of IPA. The reverse reaction is first order with respect to the activities of DIPE and water. The activation energy was determined to 85.6kJ/mol. Simultaneous chemical and phase equilibria were investigated theoretically using the volume translated Peng-Robinson equation of state (VTPR-EoS) in combination with a gE-mixing rule. Parameters of the used gE-model were adjusted to experimental liquid-liquid equilibrium (LLE) data.

Suggestion of mixing rule for parameters of PRμ model for light liquid hydrocarbon mixtures

Our aim is to improve the predictions for the viscosities of selected light liquid hydrocarbon mixtures by using a reliable model based on Peng-Robinson equation of state (PR EOS). Therefore, a viscosity model on the basis of the similarity between PvT and Tμ(viscosity) P has been applied. Based on the volume-translated Peng-Robinson equation of state (VTPR EOS), a correction has been used for viscosity to improve the results of model. The viscosity model can be extended to mixtures by using an appropriate mixing rule for the parameters of the PR model. For a better description of viscosity and improvement of some calculation results, a mixing rule has been proposed for the parameters of the model. The results of the model show that the agreement between experimental and the calculated viscosities is reasonably good and noticeable improvements can be seen in the results of some calculations.

Volume-translated Peng-Robinson equation of state for liquid densities of diverse binary mixtures

Two-parameter cubic equations of state (CEOS) are widely used in process engineering calculations. However, inaccurate liquid density predictions remain a significant deficiency in these equations. To remedy this problem, a volume translation of the CEOS is frequently employed. In a recent work, we presented a volume-translated Peng-Robinson equation of state (VTPR EOS) that is capable of providing accurate density predictions for both saturated- and single-phase regions of pure fluids at high pressures. In the current work, we present an extension of that approach, employing conventional mixing rules, to predict densities of liquid mixtures over large ranges of pressure and temperature. For this purpose, two databases were compiled for vapor–liquid equilibrium and liquid density measurements of 73 binary systems composed of diverse chemical species. The molecular species in the databases ranged widely in terms of molecular size, shape, asymmetry and polarity and, thus, were well suited to test the efficacy of our approach. Overall, the databases contained more than 5000 data points for vapor–liquid equilibrium measurements and over 13,000 data points for liquid density measurements of mixtures.Results indicate that extension of the VTPR EOS to liquid mixtures is capable of providing reliable density predictions for diverse binary mixtures over large ranges of pressure. The VTPR EOS predictions of mixture liquid densities yield errors that are three to five times lower than the corresponding predictions from the untranslated Peng-Robinson equation of state (PR EOS). Specifically, the overall percentage average absolute deviations (%AAD) from the VTPR EOS varied from 1.5 to 3 for binary mixtures. This represents a substantial improvement relative to the untranslated PR EOS, for which errors ranged from 2 to 15%AAD.

Phase Behaviour of C3H8/n-C4H10/Heavy-Oil Systems at High Pressures and Elevated Temperatures

Summary Phase behaviour of C3H8/n-C4H10/heavy-oil systems at high pressures and elevated temperatures has been experimentally and theoretically investigated. Experimentally, a versatile pressure/volume/temperature (PVT) system is used to determine the liquid/vapour phase boundary (i.e., saturation-pressure lines) and swelling factors of C3H8/n-C4H10/heavy-oil systems with varying compositions at high pressures up to 5030.0 kPa and elevated temperatures up to 396.15 K. During the experiments, heavy oil is added continuously into the solvent and the injection process can be terminated within a short period. No noticeable asphaltene precipitation has been observed throughout the measurements for the four mixtures. The viscosities of the corresponding solvent(s)-saturated heavy-oil systems are measured by using a customized capillary viscometer at 298.85 K. Theoretically, the volume-translated Peng-Robinson equation of state (PR EOS) (Peng and Robinson 1976) with a modified alpha function is used to model the experimental phase behaviour of C3H8/n-C4H10/heavy-oil systems. Two binary-interaction-parameter (BIP) correlations, respectively developed for the C3H8/heavy-oil system and n-C4H10/heavy-oil system, are incorporated into the volume-translated PR EOS model. The two BIP correlations together with the volume-translated PR EOS are found to be capable of predicting the saturation pressures and swelling factors of the C3H8/n-C4H10/heavy-oil systems with a good accuracy, although the prediction accuracy is reduced at temperatures close to the critical temperature of a pure solvent. In addition, comparison of five commonly used mixing rules indicates that the Lobe's mixing rule (Lobe 1973) is more appropriate to predict the viscosity of heavy oil diluted by C3H8 and/or n-C4H10.

Superheated fuel injection modeling: An engineering approach

A liquid fuel undergoes a sudden decrease in pressure during an injection process. If the pressure outside the injector is below the saturation pressure of the fuel, superheated conditions are reached and the fuel undergoes a thermodynamic instability. Flash evaporation might take place inside or outside the injector nozzle, thus the liquid jet behaves following different mechanisms. Flashing conditions greatly influences atomization and vaporization processes as well as the mixture formation and combustion. This work presents a homogeneous one-dimensional model for the prediction of flash evaporation in superheated liquid fuel injections, able to deal with both internal and external flashing, useful for initializing 3D spray calculations in CFD codes. In this model a Volume Translated Peng–Robinson Equation of State (VTPR-EOS) is used to calculate thermodynamic properties of hydrocarbon fuels. A Homogeneous Relaxation Model (HRM) is used to predict the evaporation rate during internal flashing which may lead to effervescent atomization outside the nozzle. Standard thermodynamic analysis of the CJ-point is used instead for the evaluation of the evaporation rate outside the nozzle, when an unbroken meta-stable liquid jet is predicted under superheated conditions. Two different sets of numerical simulations have been carried out and the results have been compared versus experimental data in literature.

Heterogeneous reactive extraction for secondary butyl alcohol liquid phase synthesis: Microkinetics and equilibria

The reaction kinetics for the liquid phase synthesis of a racemic mixture of the secondary butyl alcohols (SBA) from linear butene isomers (1-butene (1B); cis-2-butene ( c2B); trans-2-butene ( t2B)) and water (W) using a macroporous sulfonic acid ion exchange resin as catalyst were determined experimentally in a multiphase CSTR in the temperature range 39–433 K at 6–8 MPa. This range of pressures is necessary to dissolve butenes in the aqueous phase and to ensure a liquid state of all components. For temperatures higher than 423 K the reaction kinetics for the used catalyst size are influenced by mass transfer resistances within the catalyst matrix. The reaction takes place in the water swollen gel phase of the catalysts microspheres. Due to the large excess of water in the gel phase the compositions in the gel phase, in the macropore fluid, and in the catalyst surrounding aqueous phase are assumed to be identical. According to the literature the reaction is rather catalyzed by hydrated acid protons ( specific catalysis) than by polymer-bonded-SO 3H groups ( general catalysis). The experimental results can therefore be described sufficiently by a pseudo-homogeneous 3-parameter rate expression in aqueous phase activities. The forward reaction is first-order in butene. The reverse reaction is first-order in secondary butyl alcohol. The activation energy was determined to be 108 kJ/mol. Practically no pressure dependence could be observed for pressures exceeding 6 MPa. The ever-present isomerization of the linear butenes on acid catalysts was found to be remarkably faster than the hydration of butenes to SBA. Therefore, the isomerization is considered to be always in equilibrium during the olefin hydration. The formation of the possible by-product di- sec-butyl ether (DSBE) was never observed to a measurable extent. Simultaneous chemical and phase equilibria were investigated theoretically using the volume translated Peng–Robinson equation of state (VTPR-EoS) in combination with a g E -mixing rule. Parameters of the used g E -model were adjusted to experimental ternary liquid–liquid equilibrium (LLE) data.

A Unified Model for Representing Densities and Viscosities of Hydrocarbon Liquids and Gases Based on Peng-Robinson Equation of State

This work presents a volume translation for the Peng-Robinson (PR) cubic equation of state (EOS) for a better description of densities. A viscosity model has been developed based on the similarity between PVT and TμP relationship. The viscosity model can also describe the relation of the saturated vapor pressure with temperature. The volume translated PR EOS and the EOS based viscosity model are applicable to both liquid and gas phase and both sub and supercritical regions for pure hydrocarbons.