Modification of Esmaeilzadeh–Roshanfekr equation of state to improve volumetric predictions of gas condensate reservoir

The Peneloux–Rauzy–Freze (PRF) method of improving volumetric predictions by introducing the volume shift into the equation of state, is applied to the Esmaeilzadeh–Roshanfekr equation of state (ER-EOS). The ER-EOS is a new three parameter equation of state that was developed in 2006 aiming to be applied to reservoir fluids. First, this equation of state was developed for pure hydrocarbons and then was extended to mixtures by using mixing rules [M. Bonyadi, F. Esmaeilzadeh, Fluid Phase Equilib. 260 (2007) 326–334]. The modified ER-EOS (mER-EOS) is expected to improve volumetric predictions of gas condensate by applying volume shift for heavy end(s). In this study, three gas condensate fluid samples taken from three wells in a real field in Iran, referred here as SA1, SA4 and SA8, as well as two samples from literature have been used to check the validity of the modified ER-EOS in calculating the PVT properties of gas condensate mixtures. Some experiments such as constant composition expansion (CCE), constant volume depletion (CVD) and dew point pressures are carried out on these samples. Relative volume and condensate drop-out in CCE and CVD tests were predicted by ER-EOS, mER-EOS, PR-EOS and SRK-EOS [D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1), (1976) 59–64; G. Soave, Chem. Eng. Sci. 27 (1972) 1197–1203]. Comparison results between experimental and calculated data indicate that the mER-EOS has smaller error than the ER-EOS, PR-EOS and SRK-EOS. By this modification, the total average absolute deviations of the predicted liquid saturation from CVD experiments and relative volume from CCE experiments are 13.17% and 0.99%, respectively.     

An improved perturbed hard-sphere equation of state

The Carnahan–Starling–Patel–Teja (CSPT) equation of state was revisited to improve the fitting accuracy of vapour–liquid equilibrium data of pure fluid substances. By setting the pseudo-critical compressibility factor and the correction coefficient in the attractive parameter as the temperature-dependent variables, the fitting accuracies of the vapour pressures and the saturated liquid-phase densities from the new CSPT increased significantly compared with the Patel–Teja equation of state (PT) and the Peng–Robinson equation of state (PR) and the original CSPT model. The new CSPT combined with temperature-dependent functions was applied to the vapour–liquid equilibrium data available for 45 pure substances. The results indicate that the new CSPT model can accurately reproduce the experimental vapour–liquid equilibria in the whole temperature and pressure range. The successful calculations of the PVT in the critical region suggest the new CSPT has wide applicability. The new CSPT model is also superior to PR and the original CSPT for calculating the phase behaviour of binary mixtures.     

Measurement and calculation of gas compressibility factor for condensate gas and natural gas under pressure up to 116 MPa

The volumetric properties of two reservoir fluid samples collected from one condensate gas well and one natural gas well were measured under four groups of temperatures, respectively, with pressure up to 116 MPa. For the two samples examined, the experimental results show that the gas compressibility factor increases with the increase of pressure. But the influence of the temperature is related to the range of the experimental pressure. It approximately decreases with the increase of temperature when the pressure is larger than (45 to 50) MPa, while there is the opposite trend when the pressure is lower than (45 to 50) MPa. The dew point pressure was also determined for the condensate gas sample, which decreases with the increase of temperature. The capabilities of four empirical correlations and a thermodynamic model based on equation of state for describing gas compressibility factor of reservoir fluids under high pressure were investigated. The comparison results show that the thermodynamic model recommended is the most suitable for fluids whatever produced from high-pressure reservoirs or conventional mild-pressure reservoirs.     

Pressure–volume–temperature properties and free volume parameters of PEO/PMMA blends

Melt-miscible polymer blends of poly(ethylene oxide)/atactic poly(methyl methacrylate (PEO/a-PMMA)) were prepared by melt-mixing and characterized by pressure–volume–temperature (PVT) dilatometry in the pressure and temperature range of 0 to 200 MPa and 20 to 200°C, respectively. The PVT data were analyzed in terms of two equations of state (EOS). The empirical Tait EOS was applied in the glassy, semicrystalline, and equilibrium melt state, and the Simha-Somcynsky EOS theory was applied in the equilibrium melt and glassy state. The Simha-Somcynsky EOS theory contains a free volume function. The temperature, pressure, and composition dependence of the free volume fraction h calculated from the Simha-Somcynsky EOS theory was studied. As a function of blend composition we observe that the free volume fraction, thermal expansivity, and compressibility all deviate mainly positively from linearity while the specific volume deviates mainly negatively from linearity. These findings are reconciled with composition-dependent free volume parameters, the free volume and cell volume as well as with self- and cross-interaction parameters derived from the Simha-Somcynsky EOS theory as applied to polymer mixtures. Moreover, the pressure dependence of glass and melting transitions as well as crystallization kinetics have been investigated. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1061–1080, 1998     

Predicting the dew point pressure for gas condensate reservoirs: empirical models and equations of state

This paper presents a new empirical model to estimate dew point pressure (DPP) for gas condensate reservoirs as a function of routinely measured gas analysis and reservoir temperature. The proposed model was developed using experimentally measured and collected data of 340 gas condensate samples covering a wide range of gas properties and reservoir temperatures. The new model has an average relative deviation (ARD) of 0.44% and average absolute deviation (AAD) of 7.68% or 346 psia (1 psia=6.894757E−3 mPa). The accuracy of the model has been compared to SRK-EOS, PR-EOS and other correlations. Gas condensate samples from this study as well as from literature have been used to check the validity of the proposed model against EOS simulation. These examples have shown that the model successfully captures the physical trend and that the model is reliable. This model is useful to provide an estimate of the DPP when experimentally measured ones are not available.The current study also shows that predicting the DPP for gas condensates depends on the EOS(s), the number of pseudo-components and the characterization of the plus fraction. For most of the gas condensates used in this study, a 10–12 pseudo-components of the heptane plus (C₇₊) fraction resulted in minimum error in calculation of DPP using PR-EOS with Pedersen et al. characterization of the plus fraction.     

A new three-parameter cubic equation of state for calculation physical properties and vapor–liquid equilibria

A new three-parameter cubic equation of state is presented by combination of a modified attractive term and van der Waals repulsive expression. Also a new alpha function for the attractive parameter of the new EOS is proposed. The new coefficients of alpha function and the other parameters of the attractive term are adjusted using the data of the saturated vapor pressure and liquid density of almost 60 pure compounds including heavy hydrocarbons. The new EOS is adopted for prediction of the various thermophysical properties of pure compounds such as saturated and supercritical volume, enthalpy of vaporization, compressibility factor, heat capacity and sound velocity. Following successful application of the new EOS for the pure components, using vdW one-fluid mixing rules, the new EOSs are applied to prediction of the bubble pressure and vapor mole fraction of the several binary and ternary mixtures. The accuracy of the new EOS for phase equilibrium calculation is demonstrated by comparison of the results of the present EOSs with the PT, PR, GPR and SRK cubic EOSs.     

A three-parameter cubic equation of state for prediction of thermodynamic properties of fluids

A new cubic three-parameter equation of state has been proposed for PVT and VLE calculations of simple, high polar and associating fluids. The parameters are temperature dependent in sub-critical region, but temperature independent in super-critical region. The results for 42 simple and 14 associative pure compounds indicate that the calculated saturation properties and volumetric properties over the whole temperature range, up to high pressures, by the proposed equation of state (EOS), were in better agreement with the experimental data, compared with those obtained by the five well-known EOSs (P–R, P–T, Adachi et al., Yu–Lu, and M4). Two derivative properties, molar enthalpy and heat capacity of water and ammonia have been calculated, and demonstrated the thermodynamic consistency of the EOS parameters. Also VLE calculations have been performed for 41 binary mixtures of different type of fluids, including those of interest in petroleum industry. The results indicated the high capability of the proposed EOS for calculating the thermodynamic properties of pure and fluid mixtures.     

Empirical correction to the Peng–Robinson equation of state for the saturated region

This work presents an empirical correction to improve the Peng–Robinson equation of state (PR EOS) for representing the densities of pure liquids and liquid mixtures in the saturated region using the volume translation method. A temperature-dependent volume correction is employed to improve the original PR EOS so that it can match the true critical point of pure fluids. The volume correction is generalized as a function of the critical parameters and the reduced temperature. The volume translation PR (VTPR) EOS with the generalized volume correction accurately represents the saturated liquid densities for different polar and non-polar fluids, including alkanes, cycloparaffins, halogenated hydrocarbons, olefins, cyclic olefins, aromatics and inorganic molecules. The average relative deviations for 91 pure compounds was 1.37%. The generalized VTPR EOS was also used to predict the saturated liquid density of 53 binary mixtures with a relative deviation of 0.98%. The generalized VTPR EOS can also be extended to other materials. The accuracy of the generalized VTPR EOS compares well with other methods and equations of state.     

Measurements and predictions of density and carbon dioxide solubility in binary mixtures of ethanol and n-decane

The solubility of carbon dioxide (CO₂) in binary mixtures of ethanol and n-decane has been measured using an in-house developed pressure-volume-temperature (PVT) apparatus at pressures up to 6 MPa and two different temperatures (303.2 and 323.2 K). Three different binary mixtures of ethanol and n-decane were prepared, and the densities of the prepared mixtures were measured over the studied pressure and temperature ranges. The experimental data of CO₂ solubility in the prepared mixtures and their saturated liquid densities were then reported at each temperature and pressure. The solubility data indicated that the gas solubility reduced as the ethanol mole fraction in the liquid mixture increased. The dissolution of CO₂ in the liquid mixtures resulted in the increase in the saturated liquid densities. The impact of gas dissolution on the saturated liquid densities was more pronounced at the lower temperature and lower ethanol compositions. The experimental solubility and density data were compared with the results of two cubic equations of state (EOSs), Soave–Redlich–Kwong (SRK) and Peng–Robinson (PR). The modeling results demonstrated that both EOSs could predict the solubility data well, while the saturated liquid densities calculated with the PR EOS were much better than those predicted with the SRK EOS.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

Volumetric profile of polymer melts from the ISM equation of state

Knowledge of the volumetric or pressure–volume–temperature (PVT) profile of molten polymers is important for both engineering and polymer physics. Ihm–Song–Mason (ISM) equation of state (EOS) has been employed to predict the volumetric properties of 12 molten polymers. The significance of the present paper is three temperature-dependent parameters of the ISM EOS to be determined using corresponding states correlations based on the molecular scaling constants, dispersive energy parameters between segments/monomers (ε) and segment diameter (σ) rather than bulk properties, e.g. the liquid density and temperature both at normal boiling point. The ability of the ISM EOS has been evaluated by comparing the results with 1390 literature datapoints for the specific volumes over the temperature range from 293 to 603.5 K and pressure range from 0.1 to 200 MPa. The average absolute deviation (AAD) of the calculated specific volumes from literature data was found to be 0.52%. The isothermal compressibility coefficients, κ_T values of molten polymers have also been predicted using the ISM EOS. From 684 datapoints examined, the AAD of estimated κ_T was equal to 7.55%. Our calculations on the volumetric and thermodynamic properties of studied polymers reproduce the literature data with reasonably good accuracy.     

Molecular simulations on volumetric properties of natural gas

We have employed Monte Carlo simulation in the NPT ensemble to determine the molar volume and the compressibility factor of naturally occurring hydrocarbon gas mixtures. The simulation results were compared to experimental data as well as to predictions based on both the Peng–Robinson and AGA 8 equations of state. The mean error of the simulation results was roughly of the same order as those of the equation of state values. For pressures higher than the retrograde dew point pressure, systematic deviations were found especially if the gases contained a high proportion of heavy components. The quality of the simulation results increased with rising temperature. In the region of retrograde condensation, we used the Gibbs ensemble technique to determine the molar volume as well as the composition of the phases. Both were in agreement with the results of flash calculations combined with the Peng–Robinson equation of state. At pressures far from the retrograde dew point pressure, the simulation results followed the experimental liquid drop out curve.     

A systematic experimental study on the phase behavior of complex fluid mixtures up to near-critical region

The near-critical phase behavior of five synthetic reservoir fluid mixtures has been systematically studied using a ROP (France) high-pressure PVT system. The C₇⁺-content in the prepared samples ranges from 6.67 to 11.15 mol%. Through a series of constant composition expansion experiments performed in the temperature range of 303–433 K, the compressibility factor of compressed fluid (in the single-phase region), partial pressure–temperature (P–T) phase envelope, total molar volume and liquid volume fraction in the two-phase region have been measured for each sample. In addition, the critical point data of three samples were determined.     

A simple non-classical equation of state for fluids and fluid mixtures

A method for improving the behavior of classical equations of state (EOS) in the critical region, originally proposed by Fox [J.R. Fox, Fluid Phase Equilibria 14 (1983) 45–53], has been modified in this work for the Patel–Teja (PT) EOS [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37, 463–473]. The application of the new equation (NPT) for predicting PVT and vapor pressure behavior of pure substances, as well as vapor–liquid equilibrium behavior of binary mixtures, is demonstrated. The NPT equation is simple to use and requires the same input information as the original PT equation. However, it reproduces the correct PVT behavior in the critical region. Limitations of both the PT and NPT equations in calculating the isochoric heat capacity are discussed.     

Prediction of thermodynamic derivative properties of natural condensate gases at high pressure by Monte Carlo simulation

We have employed Monte Carlo simulation in the isobaric–isothermal ensemble to determine thermodynamic derivative properties of naturally occurring hydrocarbon gas mixtures. Thermal expansivity, isothermal compressibility, heat capacity and Joule–Thomson coefficient have been obtained from a fluctuation method detailed in our previous work [Phys. Chem. Chem. Phys. 3 (2001) 4333]. We have investigated two natural gases using an original method to model hydrocarbon distribution in a representative way with a limited number of linear, branched and cyclic hydrocarbon molecules. The composition used in Monte Carlo simulations was represented by 500 molecules of 20 different types with up to 35 carbon atoms. The two condensate gases are composed of rigid and flexible molecules for which intermolecular potentials have been used without fitting any parameters. Predictions are in good agreement with respect to available molar volumes at high pressure. Joule–Thomson coefficients and the other thermodynamic derivative properties have been then predicted at pressures up to 110 MPa at reservoir temperature, showing a consistent behaviour compared with light hydrocarbon gases. Inversion pressure of the Joule–Thomson effect is obtained within 1.2% compared to experimental value from volumetric measurements.     

A new equation of state for studying the thermodynamic properties of real gases

In this study, based on the compressibility effect of gas molecules, a new three-parameter cubic equation of state (EOS) is derived. To validate this EOS, density predictions of methane, ethane, carbon dioxide and oxygen have been studied using the new EOS at the temperature of 373 K and at the pressures up to 100 MPa. The results show a good agreement with reference data and this suggests that the proposed EOS would help to improve the study of thermodynamic properties for real gases.     

Efficient methods for calculations of compressibility,density and viscosity of natural gases

This study presents two new methods for calculating properties of natural gases. The first is an efficient empirical model to calculate compressibility and density of natural gases containing high amount of heptane plus and none-hydrocarbon components. The model is derived from 2400 measurements of compressibility and density of various gases presented in this study. Accuracy of the model is compared to various equations of state (EOS), corresponding state, and empirical methods. The study shows that the new model is simpler and more efficient than EOS. It eliminates the numerous computations involved in EOS calculations. The new method also eliminates the characterization of the heptane plus fraction and estimation of binary interaction parameters needed for EOS calculations. Experimentally measured density of several gases has been used to study the validity of the proposed method. These measurements indicate that the new method successfully capture the physical trend of changing gas density as a function of pressure, temperature, and composition.The second method is a modification of Lee–Gonzalez–Eakin gas viscosity correlation. The new method accounts for the presence of heptane plus, hydrogen sulfide, and carbon dioxide in natural gases. The proposed method is compared to other EOS-based viscosity model, corresponding state methods, and correlations. The comparison indicates the superiority of the new method over the other methods used to calculate viscosity of natural gases.     

Determination of Critical Parameters of Carbon Dioxide ＋ Butyraldehyde System with Different Compositions

Supercritical carbon dioxide（SC-CO2 ） is considered in green chemistry as a substitute for conventional solvents in chemical reactions due to its environmentally benign character. Recently we have reported the homogeneous hydroformylation of propylene in supercritical carbon dioxide（ SC-CO2 ） , which is an example of this kind of application of carbon dioxide. The determination for the critical parameters of carbon dioxide ＋ butyraldehyde mixtures is necessary for this reaction design which is the focus of the present paper. The critical parameters of the binary systems were determined via the static visual method at a constant volume with the molar fraction of butyraldehyde ranging from 1.0% to 2. 2% and the pressure ranging from 5 to 10 MPa. The experimental results show that the critical pressure and temperature increased with increasing the molar fraction of butyraldehyde. The bubble（dew） temperatures and the bubble （dew） pressures for the binary systems were also determined experimentally. The p-T Figures at different compositions of the binary systems were described. In addition, the critical compressibility factors Zc of the binary systems at different concentrations of n-butyraldehyde were calculated. It was found that the critical compressibility factor values of the binary systems decreased with increasing the molar fraction of n-butyraldehyde in the experimental range.