Volume-translated Peng-Robinson Research Articles

Measurement of Critical Temperatures, Critical Pressures and Densities of Acetone–Water Solutions for Simulation

Critical temperature, critical pressure and P–T–ρ–X data of acetone–water solutions with water mole fractions in a range of 0–60% were measured to provide fundamental data for CFD simulations. Critical temperatures were determined via observing critical opalescence in fused quartz capillary tubes. Meanwhile, critical pressures were measured by heating acetone–water solutions to its critical temperature in an autoclave. The standard deviations of critical temperature and critical pressure were 0.55 K and 0.029 MPa, respectively. The results indicate that only one phase exists during mixing of acetone with water. Moreover, P–T–ρ–X data under 15 and 20 MPa in the temperature range of 460–550 K were measured in the autoclave. The relative deviation of density was 0.32%. Volume-translated Peng-Robinson and Soave–Redlich–Kwong state equations were used to illustrate the P–V–T–X relationship of acetone–water solutions, and the Peng–Robinson state equation with an average absolute relative deviation of 1.19% between fitting and experimental densities was found more accurate.

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.

Experimental data and thermodynamic modeling of the CO2 + Acetone + Efavirenz system at high pressures

It is important to understand the fluid phase behavior of the systems containing CO2, acetone, and Efavirenz for processes that use supercritical fluids to produce micro and/or nanoparticles for drug encapsulation. Thus, the purpose of this work is to measure experimentally data on the phase transitions of CO2 + Efavirenz and CO2 + acetone + Efavirenz systems using the visual static synthetic method and a variable-volume cell integrated into the experimental equipment. The experimental settings for the binary system were: pressures up to 16 MPa, temperatures of 333.15, 338.15, and 343.15 K, and the global Efavirenz mole fraction from 4 × 10−5 up to 15 × 10−5. The experimental settings for the ternary system were: pressure up to 10 MPa, temperatures from 303.15 to 333.15 K, and the global CO2 mole fraction from 0.2 up to 0.9. For the binary systems, the observed phase transitions are solid–fluid transitions; for the ternary systems, the observed phase transitions are bubble point (BP) transitions. Thermodynamic simulations using the Group Contribution Volume-Translated Peng-Robinson (GC-VT-PR) and Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) equations of state (EoS) demonstrated a striking correlation with experimental data. The relative deviations from pressure and temperature corroborate the efficiency of the thermodynamic models used in this work.

Combining cubic equations with group contribution methods to predict cycle performances and design working fluids for four different organic Rankine cycles

• The property deviations are obtained and analyzed by PR, VTPR, GCM-PR and GCM-VTPR. • The prediction deviations of models are investigated for four different ORCs. • Novel working fluids are designed for subcritical and transcritical cycles. Selecting high-efficient and environmentally friendly working fluids has always been the research focus of Organic Rankine cycle (ORC). Thus, in this work, based on the group contribution method (GCM) and cubic equation of state (CEOS), relationships between molecular structures and cycle performances are established to design working fluids for subcritical and transcritical cycles. In order to determine the calculation deviation, Peng-Robinson (PR) and volume translated Peng-Robinson (VTPR) models are firstly employed to predict the entropy, enthalpy and density. Meanwhile, the two equations are combined with GCMs to estimate these properties. Thereafter, cycle performances are predicted for four different ORCs, namely subcritical basic/regenerative cycles, transcritical basic/regenerative cycles. The obtained results show that PR and VTPR have satisfied and equivalent accuracy for the calculation of thermodynamic properties and cycle performances. Meanwhile, although the calculation deviations of GCM-CEOS are higher than those of CEOS, the deviations caused by GCM-CEOS are still within acceptable limits. For the subcritical cycle, average absolute relative deviations (AARDs) of net work and cycle efficiency are respectively less than 2.251% and 2.528%. As for the transcritical cycle, the corresponding AARDs are smaller than 9.168% and 8.364%. Based on the GCM-CEOS, working fluid can be designed for the four ORCs. Thus, a design case of working fluid is provided under a given heat source and PR is employed for simplicity. In the design process, when a working fluid is generated by combining groups, the corresponding cycle parameters are optimized with the target of maximizing output work. Thereafter, environmental and safety properties are furtherly considered to determine the optimum fluid. It is discovered that the optimum fluid for subcritical basic and regenerative cycles is R245cb, while R272fa and 1,1,2-trifluoropropane are respectively selected for transcritical basic and regenerative cycles.

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.

A Tangent-Line Approach for Effective Density Used in the Ideal Mixing Rule: Part II—Evaluation of Mixing Characteristics of Oil/Gas Systems and Application Criteria

Summary Although in Part I of this study (Chen and Yang 2020) we developed a tangent-line approach for effective density that is more general, robust, and flexible than the methods proposed by Saryazdi (2012) and Saryazdi et al. (2013), its application is only limited to heavy-oil/bitumen-associated mixtures [i.e., specifically, it has only been applied to bitumen-rich liquid phase (denoted as L2)]. As indicated in Part I, the density of nitrogen (N2)/hydrocarbon mixtures cannot be accurately predicted by using the ideal mixing rule (IM) with either real density or effective density. Not only do we need to explain and evaluate the observed deviations and patterns, but also the density prediction of solvent/Fraction 1 systems [i.e., Fraction 1 of the Athabasca bitumen, which has a molecular weight (MW) of 268.8 g/mol, as reported in Azinfar et al. (2018a, 2018b, 2018c)] needs to be improved for practical use. In this study, we evaluate the mixing characteristics of different molecules in a mixture using the tangent-line approach. By evaluating and comparing performances of the IM with effective density (IM-E) and the IM with real density (IM-R), the observed patterns and deviations together with those calculated from the Westman equation indicate that the oil/gas molecules somewhat behave like solid particles in mixing. Accordingly, we further modify the effective density used in the IM to bridge the gap between the IM-E and the IM-R. The database has been extended to light-oil/gas systems such as black oils, volatile oils, gas condensates, carbon dioxide (CO2) miscible fluids, sour gases, and wet/dry gases. The IM with modified effective density (IM-ME) has also been applied to solvent/Fraction 1 systems and the C2 or C3 or n-C4-extraction L1 phase (bitumen-related mixtures) with better accuracy. Also, we develop new criteria for the uses of the IM-E, IM-ME, and IM-R that can cover the density predictions for almost all types of oil/gas systems in the petroleum industry with high accuracy. The performances of the IM are thoroughly evaluated and compared with the volume-translated (VT) Peng-Robinson equation of state (EOS) (VT PR EOS), from which the deviations provide new insights for accurately quantifying the mixture density in a more robust and reliable manner.

Comparison of different alpha functions, α(Tr), applied in the prediction of supercritical properties of different polar and nonpolar fluids at Boyle temperature

The Boyle temperature is the temperature at which the second virial coefficient becomes zero. In this work, capability of different alpha functions, α(Tr), in prediction of supercritical properties of different polar and nonpolar fluids at Boyle temperature is investigated. In this direction, eight different alpha functions, α(Tr), including Peng – Robinson original form (1976), Coquelet et al. (2004), Haghtalab et al. (2011), Saffari – Zahedi (2013), Soave – Redlich – Kwong original form (1972), Ozokwelu – Erbar (1987), Soave (1993) and Nasrifar – Bolland (2004) are coupled with different cubic equations of states including Peng – Robinson (PR), Soave – Redlich – Kwong (SRK), volume – translated Peng – Robinson (VTPR), volume translated Soave Redlich-Kwong (VTSRK) and Patel ‒ Teja ‒ Valderrama (PTV). The obtained results have been compared with the most popular relations, such as Tsonopoulos and Meng – Duan correlations. To understand better, the second virial coefficient and Zeno line have been also depicted and compared with the available experimental data. In addition, the residual properties (HR, SR, UR, and GR) and the second order thermodynamic derivatives (Cp, Cv, us, μJT) at the Boyle condition have been also investigated. Furthermore, the trend of the inversion temperature (Tinv) versus the Boyle temperature is studied for n-alkanes, n-alkenes, amines and noble gases.

Measurements and modeling of the density of rocket propellant RP-2 at temperatures to 573 K and pressures to 100 MPa

Liquid rocket propellants are subject to wide ranges of temperature and pressure when flowing through high performance liquid rocket engines. For example, as rocket propellant (RP) is used for regenerative cooling, near-wall fluid temperatures can exceed 700 K. The pressure can reach as high as 100 MPa when exiting the fuel pump. Therefore, accurate thermophysical property data, particularly density, are needed to accurately model the flow in rocket engines using computational fluid dynamics (CFD) and other engineering design tools. In this work, we report the density of two RP-2 samples at temperatures to 573 K and pressures to 100 MPa. A high-temperature, high-pressure (HTHP) variable-volume, windowed densimeter is used to determine the density. The experimental density data are satisfactorily correlated by the modified Tait equation that provides a means for interpolating the density within the experimental conditions investigated in this study. The HTHP perturbed-chain statistical associating fluid theory (PC-SAFT), Peng-Robinson (PR), and HTHP volume-translated PR equations of state are used to model RP-2 density over the entire temperature and pressure ranges.

Phase Behavior of Heavy-Oil/Propane Mixtures

Summary The phase behavior of heavy-oil/propane mixtures was mapped from temperatures ranging from 20 to 180°C and pressures up to 10 MPa. Both vapor/liquid (VL1) and liquid/liquid (L1L2) regions were observed. Saturation pressures (VL1 boundary) were measured in a Jefri 100-cm3 pressure/volume/temperature (PVT) -cell and blind-cell apparatus. The propane content at which a light propane-rich phase and a heavy bitumen-rich (or pitch) phase formed (L1/L1L2 boundary) was visually determined with a high-pressure microscope (HPM) while titrating propane into the bitumen. High-pressure and high-temperature yield data were measured using a blind-cell apparatus. Here, yield is defined as the mass of the indicated component(s) in the pitch phase divided by the mass of bitumen in the feed. A procedure was developed and used to measure propane-rich-phase and pitch-phase compositions in a PVT cell. Pressure/temperature and pressure/composition phase diagrams were constructed from the saturation-pressure and pitch-phase-onset data. High-pressure micrographs demonstrated that, at lower temperatures and propane contents, the pitch phase appeared as glassy particles, whereas at higher propane contents and temperatures, it appeared as a liquid phase. Ternary diagrams were also constructed to present phase-composition data. The ability of a volume-translated Peng-Robinson cubic equation of state (CEOS) (Peng and Robinson 1976) to match the experimental measurements was explored. Two sets of binary-interaction parameters were tested: temperature-dependent binary-interaction parameters (SvdW) and composition-dependent binary-interaction parameters (CDvdW). Models derived from both types of binary-interaction parameters matched the saturation pressures and the L1L2 boundaries at one pressure but could not match the pressure dependency of the L1L2 boundary or the measured L1L2 phase compositions. The SvdW model could not match the yield data, whereas the CDvdW model matched yields at temperatures up to 90°C.

Phase Equilibrium Study of the Ternary System CO2 + H2O + Ethanol At Elevated Pressure: Thermodynamic Model Selection. Application to Supercritical Extraction of Polar Compounds

The purpose of this study is to select an appropriate thermodynamic model among the ones available in commercial process simulators for representing the phase behavior of the carbon dioxide + ethanol + water system. The following versions of the Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) cubic equations of state (EoS) were considered: Panagiotopoulos-Reid, modified Panagiotopoulos-Reid, Huron-Vidal-NRTL, Modified Huron-Vidal (MHV2-UNIFAC), Predictive Soave-Redlich-Kwong (PSRK) and Volume-Translated Peng–Robinson (VTPR). The Polar Perturbed-Chain SAFT EoS deriving from the Statistical Associating Fluid Theory (PPC-SAFT) was also selected for the present investigation. This study highlighted that the optimal thermodynamic models for the application of interest have to be chosen among the VTPR, PSRK and MHV2-UNIFAC EoS. Once identified a suitable thermodynamic model for the CO2 + ethanol + water ternary system, it has been possible then to simulate the extraction process of polar compounds from natural products and to discuss how water influences the process efficiency.

Thermodynamic Modeling and Simulation of Biodiesel Systems at Supercritical Conditions

Biodiesel is becoming a promising fuel in many markets in the world for being a renewable energy source and for not requiring significant adaptation in existing diesel engines. It is biodegradable and its polluting gas emissions are less harmful to the environment. Transesterification is used for the biodiesel synthesis at supercritical conditions using triacylglycerols and solvents in a heterogeneous reaction. The Peng–Robinson (PR), the volume-translated Peng–Robinson (VT-PR), and the perturbed chain statistical associating fluid theory (PC-SAFT) equations of state were using to predict the fluid phase behavior of systems containing solvents and components present in the synthesis of biodiesel at supercritical conditions. Two pure component parameters for the VT-PR equation, N and k3, and the five pure component parameters for the PC-SAFT equation, m, σ, and e as well as the associating parameters κAiBj and eAiBj, were predicted based on the vapor pressures and the saturated liquid volumes. Results were...

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.

Prediction of the Boyle temperature, second virial coefficient and Zeno line using the cubic and volume – translated cubic equations of state

In this study, the Boyle temperature of 174 substances are predicted using the cubic and volume – translated cubic equations of state. In this regard, the Peng - Robinson (PR), Soave – Redlich – Kwong (SRK), volume – translated Peng – Robinson (VTPR), volume – translated Soave – Redlich – Kwong (VTSRK) and Patel – Teja – Valderrama (PTV) equations of state are used. The Boyle temperature is calculated for different polar, non – polar and associating substances including alkanes, cycloalkanes, alkenes, aromatics, ethers, esters, ketones, refrigerants, halogens, amines and water. The obtained results are compared with the results of other known correlations published so far, such as Tsonopoulos, Meng – Duan and Estrada – Torres et al. equations. For better understanding, the second virial coefficient and the Zeno line (unit compressibility) are also calculated and compared with the available experimental data. The results show that PR, VTPR and PTV have lower average temperature difference between EoSs and Tsonopoulos or Meng – Duan correlations. The dependency of the reduced Boyle temperature (TB/TC) as functions of the Pitzer's acentric factor (ω), hydrocarbon chain length (NC) and the reduced dipole moment (μR) has been also studied.

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.