Fugacity Coefficients Research Articles

Mutual solubility study for 94.2:5.8 of ethanol to octane with supercritical carbon dioxide solvent

Solubility data of a mixture containing 94.2% ethanol and 5.8% octane was measured in carbon dioxide solvent using a high-pressure type phase equilibrium apparatus at pressures up to 103.5 bar and at temperature of 75 °C. The results showed that considerable separation was not achieved in this ethanol and octane ratio. However, the experimental data were then compared with the theoretical data which were obtained from two models which are regular solution theory and Redlich–Kwong equation of state. Regular solution theory is employed to each phase by applying activity coefficient expressions. Redlich–Kwong equation of state is employed to the vapor phase and then with applying fugacity coefficient, liquid phase data is obtained. The regular solution theory as a novel model approach has been found to be encouraging for the prediction of phase equilibria solubilities. It concluded that the regular solution theory model could predict two phases equilibrium data better than Redlich–Kwong equation of state.

Some useful expressions for deriving component fugacity coefficients from mixture fugacity coefficient

It is proved that the fugacity coefficient ( ϕ) of a mixture and the fugacity coefficient of component i ( ϕ ˆ i ) follow the relation ln ϕ ˆ i = ∂ ( n ln ϕ ) / ∂ n i T , P , n j ( j ≠ i ) , = ∂ ( n ln ϕ ) / ∂ n i T , P , V t , n j ( j ≠ i ) , where n i is the amount-of-substance of component i, and T, P, V t and n are the temperature, pressure, total volume and total amount-of-substance of the system, respectively. This relation is very useful for the derivation of ϕ ˆ i . It allows the ϕ function to contain both P and V, so ϕ can be expressed with various equations of state (either volume-explicit or pressure-explicit). This approach can also use the similarity of the ϕ expressions of pure fluids and mixtures to simplify the derivation of ϕ ˆ i . Besides, ϕ ˆ i can also be directly derived from equation of state through a variation of the approach above. These approaches are much easier than the commonly used ones when the equation of state for fluids is complex.

Experimental and Analytical Studies of Hydrocarbon Yields under Dry, Steam, and Steam-Propane Distillation

This paper presents experimental studies to confirm and understand oil production accelerated when propane is used as additive during steam injection. Distillation experiments were performed using seven-component synthetic oil consisting of equal weights of alkanes. For comparison purposes, three different distillations were investigated: dry, steam, and steam-propane distillation, the latter at a propane-steam mass ratio of 0.05. Based on the experimental results, it is noted that the components appear to boil off at lower temperatures with steam-propane injection than with pure steam injection (with reference to dry distillation). Lowering of hydrocarbon boiling points by steam-propane injection appears to be the fundamental phenomenon that can explain: (1) higher yields during distillation of the synthetic oil, and (2) production acceleration, reduction in produced oil density and viscosity, and improved steam injectivity during steam-propane displacement of crude oils. Also, a thermodynamic description of the hydrocarbon synthetic mixture was done. The activity fugacity coefficient, the specific Gibbs energy, and the vaporization equilibrium ratio were calculated. It was founded that the largest activity fugacity coefficient and the smallest specific Gibbs energy were presented when steam-propane is used in the distillation experiments. The experimental procedure and method of analysis developed in this study will be beneficial to future researches in understanding the effect of propane as steam additive on actual crude oils.

Comparison of two different equations of state for application of carbon dioxide sequestration

We suggest that different equations of state (EOS) algorithms can and frequently will provide very different predictions of CO 2 migration following injection for sequestration. Rather than carry out an exhaustive examination of all EOS algorithms available, we elected to evaluate this general hypothesis by making detailed comparisons of simulation results of two very common EOS algorithms. We simulated and compared CO 2 migration patterns using two fundamentally different EOS algorithms – Modified Redlich-Kwong EOS (MRKEOS) and Span and Wagner EOS (SWEOS). In general, the predictions of thermophysical properties for both algorithms are close, except for a contrast in the predicted fugacity coefficient of CO 2, which subsequently propagates to a contrast in predicted solubility in water/brine. Typically, MRKEOS underestimates solubility of CO 2 compared to both SWEOS and experimental solubility data. In simulations of CO 2 migration, dissolution rates of separate-phase CO 2 predicted from the two EOS algorithms were significantly different, even for small contrasts in predicted fluid properties from EOS algorithms, resulting in markedly different migration patterns. We also examined the potential disparities of simulating integrity of caprock using these two common EOS algorithms. To simplify the analysis and to isolate the roles of specific properties, we limited these simulations to one dimension. Simulation results from both EOS algorithms indicate that the distance that separate-phase CO 2 migrates through an unfractured caprock varies linearly with the amount of injected CO 2, logarithmically with permeability, and inversely with porosity. More general sensitivity analyses were conducted to investigate the roles of individual parameters with respect to various properties, including how brine density, viscosity, and CO 2 solubility in brine, affect CO 2 flow and transport. General results suggest that both brine density and CO 2 solubility are critical factors. The combined results of this study suggest that choice of EOS algorithm is critical, because even small differences in predicted density and solubility can lead to dramatic differences in migration patterns and timing of different processes such as gravity segregation and caprock penetration. We only evaluated two EOS algorithms, but the resulting disparities were great enough that we conclude that other EOS algorithms will also produce variable results in predicted migration and related processes.

Determining sublimation pressures from solubility data of solids in different solvents

Solvent effects in the calculation of the sublimation pressure of pure solids using high pressure solubility data are discussed. Three binary gas–solid systems containing anthracene, napthalene and phenanthrene as solutes and carbon dioxide, ethane, ethylene, fluoroform, chlorotrifluoromethane as solvents are considered in the study. The Peng–Robinson EoS with the mixing rules proposed by Wong and Sandler are used to evaluate the fugacity coefficient φ S included in the classical solubility equation which relates the mole fraction of a dissolved solid in a compressed gas phase. The sublimation pressure P S of the solid is considered as a parameter to be determined by regression analysis of experimental solubility data (TPy), and theoretically it should be independent of the solvent. The results show that the determination of sublimation pressure using high pressure solubility data is reliable and produce unique values of sublimation pressure independent of the solvents in the mixtures.

Comments on “Measurement and Modeling of the Solubility of Water in Supercritical Methane and Ethane from 310 to 477 K and Pressures from 3.4 to 110 MPa”

We describe a new flow cell apparatus for measuring the water content of gases up to 120 MPa at 490 K that uses a combination of gravimetric and electrical resistance techniques to determine the solubility of water in the gaseous phase. The new experimental data for the solubility of water in supercritical methane and ethane were obtained with our apparatus spanning pressures from 3.4 to 110 MPa covering a temperature range from 310 to 477 K. We model the experimental results by combining two equations of state; vapor-phase fugacities and fugacity coefficients are calculated with a modified Peng−Robinson equation of state, and aqueous-phase fugacities are calculated using an equation by Wagner and Pruss (J. Phys. Chem. Ref. Data 2002, 31, 387−535) or by a modification of a correlation developed by Saul and Wagner (J. Phys. Chem. Ref. Data 1987, 16, 893−901). We compare the model results with new and existing experimental data and with commercially available simulators. Our model reproduces the experimenta...

Estimation of thermodynamic properties of the ternary molten salt system, LiF-NaF-BeF2, by the modified Peng-Robinson equation

The molten salt reactor (MSR), which is one of the generation IV reactors, can meet the demand of transmutation and breeding. The thermodynamic properties of the molten salt system like LiF-NaF-BeF2 influence the design and construction of the fuel salt and coolant in the MSR for the new generation. In this paper, the equation of state of the ternary system 15%LiF-58%NaF-27%BeF2, over the temperature range from 873.15 to 1 073.15 K at one atmosphere pressure, is described using a modified Peng-Robinson (PR) equation. The densities of the ternary system and its components are estimated by this equation directly, and compared with the experimental data. Based on the equation of state, the other thermodynamic properties such as the enthalpy, entropy and heat capacity at constant pressure are estimated by the residual function method and the fugacity coefficient method respectively. The densities calculated by PR equation are highly in agreement with the experimental data, and the enthalpy, entropy and heat capacity evaluated by the two different methods are consistent with each other. It can be concluded that the modified PR equation can be applied to evaluate the density of the molten salt system, and it is recommended that it be used as the basis to estimate the enthalpy, entropy and heat capacity of the molten salt system.

Fugacity coefficients for water vapor

The fugacity coefficient of water vapor were calculated along the saturation line at temperatures from 273.16 to 647.14 K and at supercritical temperatures from 673.15 to 1073.15 K and pressures from 5 to 1000 MPa.

Measurement and Modeling of the Solubility of Water in Supercritical Methane and Ethane from 310 to 477 K and Pressures from 3.4 to 110 MPa

We describe a new flow cell apparatus for measuring the water content of gases up to 120 MPa at 490 K that uses a combination of gravimetric and electrical resistance techniques to determine the solubility of water in the gaseous phase. The new experimental data for the solubility of water in supercritical methane and ethane were obtained with our apparatus spanning pressures from 3.4 to 110 MPa covering a temperature range from 310 to 477 K. We model the experimental results by combining two equations of state; vapor-phase fugacities and fugacity coefficients are calculated with a modified Peng−Robinson equation of state, and aqueous-phase fugacities are calculated using an equation by Wagner and Pruss (J. Phys. Chem. Ref. Data 2002, 31, 387−535) or by a modification of a correlation developed by Saul and Wagner (J. Phys. Chem. Ref. Data 1987, 16, 893−901). We compare the model results with new and existing experimental data and with commercially available simulators. Our model reproduces the experimental data within 2−6% using one adjustable parameter, indicating that the predictions of the model are equal to or superior to the commercially available simulators.

Henry's law constants of 1-butene, 2-methylpropene, trans-2-butene, and 1,3-butadiene in methanol at 374–490 K

Henry's law constants of 1-butene, 2-methylpropene, trans-2-butene, and 1,3-butadiene in methanol in the temperature range of 374–490 K are experimentally obtained. A similar method to a gas stripping method is applied to measure the Henry's law constants at high temperatures up to the critical point of methanol. The rigorous formula for evaluating the Henry's law constants from these measurements is applied to the data reduction for these highly volatile mixtures. By using this formula, a volume effect of vapor phase is discussed. The plot of Henry's law constants versus temperature goes through a maximum and approaches an unique point at the critical temperature of methanol. The fugacity coefficient of the solute in the vapor phase at infinite dilution and the infinite dilution activity coefficient of the solute in liquid phase are evaluated from these experimental data.

A quasi-chemical nonrandom lattice fluid model: General derivation and application to pure fluids and mixtures

A quasi-chemical nonrandom lattice fluid model without temperature dependence of the close packed volumes of a mer, segment numbers and energy parameters of pure systems is presented. The explicit nonrandom lattice fluid (NLF) model with quasi-chemical approach was capable of describing properties for complex systems, but this model had strong the temperature dependence of energy parameters and segment numbers of pure systems. In this work, a quasi-chemical nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems is proposed. And the model was extended to mixtures by using consistent method for phase equilibrium calculation with fugacity coefficients derived from the present equation of state. We tested consistently the present model on 17 phase equilibrium data sets of vapor–liquid equilibria and compared with the NLF model and the SAFT model. The present model (three pure parameters for pure component and one binary interaction parameter) showed better results for most systems than the NLF model (six adjustable pure parameters and one binary interaction parameter) and the SAFT model (three pure parameters and one binary interaction parameter).

A multi-fluid nonrandom lattice fluid model: Mixtures

A multi-fluid nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems and its consistent method for phase equilibrium calculation were presented in the previous paper. In this work, the model was extended to mixtures by using consistent method for phase equilibrium calculation with fugacity coefficients derived from the present equation of state and it was applied to vapor-liquid equilibrium. We consistently tested the present model on 17 phase equilibrium data sets of vapor-liquid equilibria and compared it with the MF-NLF model and the SAFT model. The present model (3 pure parameters for pure component and one binary interaction parameter) showed better results for most systems than the MF-NLF model (6 adjustable pure parameters and one binary interaction parameter) and the SAFT model (3 pure parameters and one binary interaction parameter).

An analytical consistent pseudo-component delumping procedure for equations of state with non-zero binary interaction parameters

For mixtures with many components, some or most of the components are grouped into pseudo-components in order to reduce the dimensionality of the problem for phase equilibrium calculations, and therefore the computational effort. However, knowing the detailed fluid phase split may be important for a variety of applications. The detailed phase compositions resulting from a flash calculation performed on a lumped mixture can be predicted using a delumping (inverse lumping) procedure [C.F. Leibovici, E.H. Stenby, K. Knudsen, Fluid Phase Equilibr. 117 (1997) 225–232]. If the mixture parameters of an equation of state (EoS) can be expressed as a linear combination of pure component parameters and the phase mole fractions, then the component fugacity coefficients can also be expressed as a linear combination of pure component parameters with coefficients only depending on mixture properties. As a result, the equilibrium coefficients are related only to component properties and EoS coefficients, independently on phase compositions. In this work, we show using a reduction method how to effectively obtain such an expression of the equilibrium constants even for non-zero binary interaction parameters (BIPs) in the EoS, and based on these results, we propose a totally consistent analytical procedure for the estimation of equilibrium constants of detailed mixtures from lumped information, which is an extension of Leibovici's delumping method. For several examples with non-zero BIPs between hydrocarbon components and classical contaminants, phase mole fractions and the vapor mole fraction of the delumped mixture are in excellent agreement with the exact values obtained by flashing the original mixture. The delumping procedure has multiple applications, mainly for reservoir simulation and distillation problems.

A Unified Single-Event Microkinetic Model for Alkane Hydroconversion in Different Aggregation States on Pt/H−USY-Zeolites

A single-event microkinetic model for the catalytic hydroconversion of hydrocarbons on Pt/H-US-Y bifunctional zeolite catalysts developed for low-pressure vapor phase conditions was extended to cover high-pressure vapor phase and liquid phase conditions. The effect of the density of the bulk hydrocarbon phase on the physisorption as well as on the protonation steps of the reaction network was accounted for explicitly and can be interpreted in terms of "compression" of the hydrocarbon sorbate inside the zeolite pores and "solvation" of the catalyst framework by the dense bulk hydrocarbon phase. The bulk phase density effect on the physisorbed state is described via a single excess free enthalpy of physisorption. A dense bulk hydrocarbon phase destabilizes the sorbate molecules inside the catalyst pores. An expression of the excess free enthalpy of physisorption involving the fugacity coefficient and a zeolite dependent factor allows description of physisorption data. Typical excess free enthalpy values are in the range 1.5-5.1 kJ mol(-1) increasing with carbon number in the series of C5-C16 alkanes. At high-pressure vapor phase and liquid phase conditions, the excess standard protonation enthalpy is estimated at -7.8 kJ mol(-1) leading to relatively more stable carbenium ions at dense bulk phase conditions. As a result of the excess physisorption and protonation properties, the lightest hydrocarbons in mixtures are more competitive at dense phase conditions and their conversion is enhanced compared to low-density conditions.

Prediction of thermodynamic properties of natural gas mixtures using 10 equations of state including a new cubic two-constant equation of state

In this contribution, 10 equations of state (EoSs) are used to predict the thermo-physical properties of natural gas mixtures. One of the EoSs is proposed in this work. This EoS is obtained by matching the critical fugacity coefficient of the EoS to the critical fugacity coefficient of methane. Special attention is given to the supercritical behavior of methane as it is the major component of natural gas mixtures and almost always supercritical at reservoir and surface conditions. As a result, the proposed EoS accurately predicts the supercritical fugacity of methane for wide ranges of temperature and pressure. Using the van der Waals mixing rules with zero binary interaction parameters, the proposed EoS predicts the compressibility factors and speeds of sound data of natural gas mixtures with best accuracy among the other EoSs. The average absolute error was found to be 0.47% for predicting the compressibility factors and 0.70% for the speeds of sound data. The proposed EoS was also used to predict thermal and equilibrium properties. For predicting isobaric heat capacity, Joule–Thomson coefficient, dew points and flash yields of natural gas mixtures, the predictive accuracy of the EoS is comparable to the predictive accuracy of the Redlich–Kwong–Soave (RKS) EoS or one of its variants. For predicting saturated liquid density of LNG mixtures, however, the accuracy of predictions is between the RKS and Peng–Robinson (PR) EoSs.

Henry's law constants of propane, propene, butane, and 2-methylpropane in methanol at 374–490 K

Henry's law constants of propane, propene, butane, and 2-methylpropane in methanol in the temperature range of 374–490 K are experimentally obtained. A similar method to a gas stripping method is applied to measure the Henry's law constants at high temperatures up to the critical point of methanol. The rigorous formula for evaluating the Henry's law constants from these measurements is applied to the data reduction for these highly volatile mixtures. By using this formula, the effect of the vapor space of the cell is discussed. The plot of Henry's law constants versus temperature goes through a maximum and approaches an unique point at the critical temperature of methanol. The fugacity coefficient of the solute in the vapor phase at infinite dilution and the infinite dilution activity coefficient of the solute in liquid phase are evaluated from these experimental data.

Computation of Temperature-Pressure Phase Diagrams of High-Pressure Nitrides

AbstractWe propose an explicit scheme to include the fugacity of nitrogen in computations of phase diagrams of nitride compounds at high-temperature/high-pressure conditions. The assessment is based on available thermochemical data and two kind of extrapolating functions to provide upper and lower boundary for the fugacity coefficient as a funtion of p and T. The procedure is applied to investigate the synthesis of novel nitrides of tantalum, tungsten, and platinum. The combination of first-principle and thermochemical calculations let us predict the synthesis of a new high-pressure phase of Ta3N5 at about 27 GPa. Synthesis of WN2 becomes feasible at about 45 GPa. We furthermore explain why the synthesis of the noble metal subnitride, PtN2, occurs at about 40 GPa, and why PtN is not accessible in high-pressure experiments.

An improved model for the calculation of CO 2 solubility in aqueous solutions containing Na +, K +, Ca 2+, Mg 2+, Cl −, and SO 42−

An improved model is presented for the calculation of the solubility of carbon dioxide in aqueous solutions containing Na +, K +, Ca 2+, Mg 2+, Cl −, and SO 4 2− in a wide temperature–pressure–ionic strength range (from 273 to 533 K, from 0 to 2000 bar, and from 0 to 4.5 molality of salts) with experimental accuracy. The improvements over the previous model [Duan, Z. and Sun, R., 2003. An improved model calculating CO 2 solubility in pure water and aqueous NaCl solutions from 273 to 533K and from 0 to 2000 bar. Chemical Geology, 193: 257–271] include: (1) By developing a non-iterative equation to replace the original equation of state in the calculation of CO 2 fugacity coefficients, the new model is at least twenty times computationally faster and can be easily adapted to numerical reaction-flow simulator for such applications as CO 2 sequestration and (2) By fitting to the new solubility data, the new model improved the accuracy below 288 K from 6% to about 3% of uncertainty but still retains the high accuracy of the original model above 288 K. We comprehensively evaluate all experimental CO 2 solubility data. Compared with these data, this model not only reproduces all the reliable data used for the parameterization but also predicts the data that were not used in the parameterization. In order to facilitate the application to CO 2 sequestration, we also predicted CO 2 solubility in seawater at two-phase coexistence (vapor–liquid or liquid–liquid) and at three-phase coexistence (CO 2 hydrate–liquid water–vapor CO 2 [or liquid CO 2]). The improved model is programmed and can be downloaded from the website http://www.geochem-model.org/programs.htm.

Henry's Law Constants and Infinite Dilution Activity Coefficients of Propane, Propene, Butane, 2-Methylpropane, 1-Butene, 2-Methylpropene, trans-2-Butene, cis-2-Butene, 1,3-Butadiene, Dimethyl Ether, Chloroethane, and 1,1-Difluoroethane in 2-Propen-1-ol

Henry's law constants and infinite dilution activity coefficients of propane, propene, butane, 2-methylpropane, 1-butene, 2-methylpropene, trans-2-butene, cis-2-butene, 1,3-butadiene, dimethyl ether, chloroethane, and 1,1-difluoroethane in 2-propen-1-ol in the temperature range of (250 to 330) K were measured by a gas stripping method. Partial molar excess enthalpies were calculated from the activity coefficients. A rigorous formula for evaluating the Henry's law constants from the gas stripping measurements was used for the data reduction of these highly volatile mixtures. The estimated uncertainties are about 2 % for the Henry's law constants and 3 % for the infinite dilution activity coefficients. In the evaluation of the infinite dilution activity coefficients, the nonideality (fugacity coefficient) of the solute cannot be neglected, especially at higher temperatures. The estimated uncertainty of the infinite dilution activity coefficients includes 1 % for the nonideality. In general, the Henry's law ...

Henry’s law constants and infinite dilution activity coefficients of cis-2-butene, dimethylether, chloroethane, and 1,1-difluoroethane in methanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, isobutanol, tert-butanol, 1-pentanol, 2-pentanol, 3-pentanol, 2-methyl-1-butanol, 3-methyl-1-butanol, and 2-methyl-2-butanol

Henry’s law constants and infinite dilution activity coefficients of cis-2-butene, dimethylether, chloroethane, and 1,1-difluoroethane in methanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, isobutanol, tert-butanol, 1-pentanol, 2-pentanol, 3-pentanol, 2-methyl-1-butanol, 3-methyl-1-butanol, and 2-methyl-2-butanol in the temperature range of 250 K to 330 K were measured by a gas stripping method and partial molar excess enthalpies were calculated from the activity coefficients. A rigorous formula for evaluating the Henry’s law constants from the gas stripping measurements was used for the data reduction of these highly volatile mixtures. The uncertainty is about 2% for the Henry’s law constants and 3% for the estimated infinite dilution activity coefficients. In the evaluation of the infinite dilution activity coefficients, the nonideality of the solute such as the fugacity coefficient and Poynting correction factor cannot be neglected, especially at higher temperatures. The estimated uncertainty of the infinite dilution activity coefficients includes 1% for nonideality.