Fugacity Coefficients Research Articles

Modeling the solubility of CO2 and H2S in DEA–MDEA alkanolamine solutions using the electrolyte–UNIQUAC model

A thermodynamic model was developed to represent the solubility of CO2 and H2S in single and blend of aqueous solutions of DEA and MDEA. The model accounts for chemical equilibria in the liquid phase and physical equilibria between the liquid and vapor phases. The Soave–Redlich–Kwong (SRK) equation was used to represent the fugacity coefficient in the vapor phase. The liquid phase was treated as an electrolyte solution and activity coefficients were represented by the electrolyte–UNIQUAC equation. The electrolyte–UNIQUAC equation is composed of two parts, one to account for long range interactions and the other to account for short interactions. Contribution from long range ion–ion interactions were represented by a Debye–Huckel formula suitable for mixed solvent, water and alkanolamines. Adjustable parameters of the electrolyte–UNIQUAC equation, representing short range interactions, were determined by orthogonal distance regression technique using a large and wide range of experimental VLE data. Earlier extensions of UNIQUAC to handle electrolyte solutions are ion-specific. In this work, the adjustable parameters were setup to use the ion-pair interaction approach and satisfy both the principle of like-ion repulsion and local electroneutrality. Eight different systems were considered in this work. The model predictions were in excellent agreement with the experimental measurements and the speciation results are useful to be used in mass transfer models to represent the CO2 and H2S absorption process using alkanolamine solutions.

Solubility of carbon dioxide in aqueous fluids and mineral suspensions at 294K and subcritical pressures

Abstract An experimental investigation has been carried on the solubility of CO2 in water and 1 M NaCl between 0.3 and 4 MPa, in order to test the validity of the results given by various modelling codes. In addition to experiments with pure fluids, the effect of a range of likely reservoir minerals on CO2–water interactions, including K-feldspar, kaolinite, calcite, Ca-montmorillonite and Na-montmorillonite were also investigated. In addition to measurements of CO2 solubility, the pH of the CO2-saturated suspensions was also measured directly at pressures of up to 1 MPa. The results demonstrate that predictions of CO2 solubility made with PHREEQC and Geochemist’s Workbench agree to within 20% with the experimental value, provided corrections are first made off-line for the fugacity coefficient of CO2, while predictions from standalone models are slightly more accurate. In the presence of mineral suspensions, PHREEQC and Geochemist’s Workbench give good results for calcite and kaolinite but underestimate the pH of montmorillonite-bearing assemblages while slightly overestimating the pH of K-feldspar suspensions. These results are significant because they indicate that CO2-charged fluids reacted with clays may be less acidic than indicated by the models, which will impact predictions of the potential for dissolution of reservoir and cap rock minerals, as well as the potential for leaching of toxic metals.

On multiphase negative flash for ideal solutions

There is a recent interest to solve multiphase negative flash problems where the phase amounts can be negative for normal positive feed composition. Solving such a negative flash problem using successive substitution needs an inner loop for phase distribution calculation at constant fugacity coefficients. It is shown that this inner loop, named here as multiphase negative flash for ideal solutions, can be solved either by Michelsen's algorithm for multiphase normal flash, or by its variation which uses F−1 phase amounts as independent variables. In either case, the resulting algorithm is actually simpler than the corresponding normal flash algorithm. Unlike normal flash, multiphase negative flash for ideal solutions can diverge if the feasible domain for phase amounts is not closed. This can be judged readily during the iteration process. The algorithm can also be extended to the partial negative flash situation where several phase amounts must be non-negative and at least one phase amount can be negative.

Geochemical modeling of CO2 sequestration in deep, saline, dolomitic-limestone aquifers: Critical evaluation of thermodynamic sub-models

Geochemical modeling is a common tool to estimate the potential for storing supercritical CO2 in deep saline aquifers, and to predict the effects thereof. Geochemical models necessarily rely on thermodynamic relationships or “sub-models” to estimate quantities such as chemical solubility, activity, and fugacity. In this paper, we compare three proposed models for the fugacity of supercritical CO2, four proposed models for the activity coefficient of dissolved (aqueous) CO2, and four proposed models for the solubility of CO2 in aquifer brine. We examine the conditions under which estimates from these different proposed thermodynamic sub-models agree or disagree. Also, we develop a geochemical model that predicts the effects of injecting CO2 into a deep, saline, dolomitic-limestone aquifer; specifically, we predict the change in brine pH, the mineral precipitation/dissolution, and the potential solubility trapping of injected CO2 in response to the CO2 injection. We test nine different versions of the model, utilizing different combinations of the thermodynamic sub-models listed above. This allows us to quantify how key geochemical predictions depend upon the selection of thermodynamic sub-models. We find that different combinations of thermodynamic sub-models yield similar estimates for equilibrium pH and for quantities of mineral precipitation/dissolution, but that agreement is worse when predicting the equilibrium CO2 concentration in brine and/or the solubility trapping of CO2. These results indicate that the predicted equilibrium pH and mineral precipitation/dissolution are not very sensitive to the underlying thermodynamic sub-models, whereas estimates for the CO2 concentration in brine and potential solubility trapping are. Overall, the geochemical predictions are least sensitive to the choice of CO2 activity coefficient sub-model, are moderately sensitive to the choice of CO2 solubility sub-model, and are most sensitive to the choice of CO2 fugacity coefficient sub-model.

Particle swarm modeling of vapor-liquid equilibrium data of binary systems containing CO2 + imidazolium ionic liquids based on bis[(trifluoromethyl)sulfonyl]imide anion

Based on particle swarm optimization (PSO), a thermodynamic modeling for the vapor-liquid equilibrium of binary mixtures of carbon dioxide with ionic liquids is presented. The Peng-Robinson equation of state with the Wong-Sandler mixing rules is used to evaluate the fugacity coefficient of the systems. Simulations are carried out in five systems containing 1-alkyl-3-methylimidazolium ionic liquids based on bis[(trifluoromethyl)sulfonyl]imide anion. Then, PSO algorithm was used to minimize the difference between calculated and experimental bubble pressure, and calculate the interaction parameters and the excess Gibbs free energy for all systems used. The results show that the bubble pressures were correlated with low deviations between experimental and calculated values. These deviations show that the PSO algorithm is the preferable method to optimize the interaction parameters of the phase equilibria of binary systems of supercritical carbon dioxide with ionic liquids, and can be used for other similar systems.

Investigation on Isobaric Vapor–Liquid Equilibrium for 1-Butanol + Ethylbenzene + o-Xylene + m-Xylene + p-Xylene

Isobaric binary vapor–liquid equilibrium (VLE) data for 1-butanol + ethylbenzene, or o-, or m-, or p-xylene and isobaric quinary VLE data for 1-butanol + ethylbenzene + o-xylene + m-xylene + p-xylene are measured at 101.33 kPa using a modified Rose cell with circulation of both phases. The four binary systems of 1-butanol + ethylbenzene, or o-, or m-, or p-xylene exhibit minimum boiling azeotropes, and the composition of the azeotropes are reported. The VLE data for the four binary systems are checked to meet rigorous thermodynamic consistency by Herington method and the point-to-point test of the Fredenslund method. The nonideality in vapor phase of the measured binary systems is analyzed through calculating fugacity coefficients. Combined with the Hayden–O'Connell (HOC) equation, the VLE data for 1-butanol + ethylbenzene, or o-, or m-, or p-xylene are well-correlated by the nonrandom two-liquid (NRTL), universal quasichemical activity coefficient (UNIQUAC), and Wilson equations. The NRTL model parameter...

Thermodynamics of Si(OH)4 in the vapor phase of water: Henry’s and vapor–liquid distribution constants, fugacity and cross virial coefficients

The fugacity coefficients of Si(OH)4 are evaluated from solubilities of solid phases of SiO2 in the vapor phase of water. The virial equation of state, truncated at the third virial coefficient, is employed to describe the fugacity coefficients of Si(OH)4. The temperature dependencies of the second, B12, and the third, C112, cross virial coefficients for H2O–Si(OH)4 interactions are approximated by empirical relations. It is found that silica–water interactions in the vapor phase are significantly more non-ideal compared to water–water interactions. Knowledge of B12 and C112 allows calculation of solubilities of quartz (Q) and amorphous silica (AS) in steam up to the density of 200kgm−3 in satisfactory agreement with available data, and should provide reasonable solubility values at temperatures where no experimental results exist. The calculated values of the solubility of Q and AS in saturated vapor up to the critical temperature of water, Tc, are tabulated.The partial molar properties of dilute solutes close to the critical point of water are governed by the Krichevskii parameter, the value of which for Si(OH)4 is evaluated from available data (mainly vapor–liquid distribution constants for silica) to be equal to −187±10MPa. The knowledge of the thermodynamic properties of Si(OH)4 in the ideal gas state and in the state of the standard solution in liquid water allows calculating Henry’s constant, kH, for Si(OH)4 up to 623.15K at water saturation pressure P1∗. The theoretically-based equation, containing the Krichevskii parameter, allows extrapolating kH values all the way toward the critical temperature of water. This, in turn, makes possible calculation of the solubility of quartz and amorphous silica in liquid water at P1∗ at all temperatures up to Tc. The presented results should be useful for modeling solid–liquid–vapor, solid–vapor and liquid–vapor equilibria in the H2O–SiO2 system at steam densities up to 200kgm−3.

SolEx: A model for mixed COHSCl-volatile solubilities and exsolved gas compositions in basalt

We present a software application, SolEx, to calculate basaltic melt and coexisting vapour compositions in the system C–O–H–S–Cl. Such a model has great utility in interpreting emitted gas and melt inclusion compositions, especially through the incorporation of sulphur and chlorine, the most commonly measured volcanic gas species. We assume that the behaviour of the fluid phase is controlled by the volumetrically dominant volatile species, H2Oand CO2, whereas sulphur and chlorine partition between the melt and fluid phases. Melt–fluid partition coefficients for S and Cl were parameterised from measurements by Lesne et al. (2011a, p. 1737). The model of Churakov and Gottschalk (2003a, p. 2415) was applied to calculate fugacity coefficients and the equilibrium constants for the reaction imelt→ifluid were thereby deduced. SO2dominates at oxidation states of ΔNNO>0.5 (Jugo et al., 2010, p. 5926), where this model is applicable.In the forward model, total volatile inventories and melt composition are specified by the user. The parameterisation of Dixon (1997, p. 368) is used to predict the partitioning of CO2and H2Obetween vapour and melt phases. An iterative procedure is employed to predict the partitioning of S and Cl components between fluid and melt phases. Melt and gas compositions and gas volume fraction are thereby modelled over pressures in the range 5–4000bar. This approach satisfactorily reproduces independent literature data on S and Cl behaviour in basalt. SolEx is a user-friendly software package available for OS X and Windows, facilitating modelling of closed- and open-system C–O–H–S–Cl degassing in basalts.

Glycol Loss in a Gaseous System: Thermodynamic Assessment Test of Experimental Solubility Data

Triethylene glycol (TEG) is generally used to adjust the water dew point in natural gas processes. Unfortunately, only very few sets of experimental data regarding solubilities of these humidity absorbents in supercritical natural gas components have been reported in the literature partly due to the difficulties in such very low concentration measurements. Therefore, a satisfactory accuracy of measurements is not obvious, and the reliability of the corresponding data must be checked prior to their application. In this study, we focus on presenting the results of a thermodynamic assessment test (consistency test) for experimental solubility data of triethylene glycol in supercritical methane and carbon dioxide. The Gibbs–Duhem equation in terms of pressure, fugacity coefficients, solubilities of triethylene glycol in gas phase, and compressibility factor of gas phase is applied for the consistency test. The Soave–Redlich–Kwong (SRK) equation of state (EoS) along with the van der Waals (vdW2) mixing rules i...

A multi-scale framework for multi-phase equilibrium flash

A general multi-scale framework for multi-component, multi-phase equilibrium flash calculations, which uses information at the molecular and bulk fluid length scales, is described. The multi-scale Gibbs–Helmholtz constrained (GHC) EOS approach of Lucia (2010) is extended to include the use of (1) coarse grained NTP Monte Carlo simulations to gather pure component internal energies of departure, (2) a new linear mixing rule for internal energies of departure for mixtures, (3) a novel expression for partial fugacity coefficients for the GHC EOS, and (4) a novel flash algorithm that uses complex-valued compressibility factors and densities to assist in phase existence determination. Many numerical results for mixtures of CO 2–water, NaCl–water, and CO 2–NaCl–water are used to show that the GHC EOS flash approach is superior to all other approaches currently available. Many geometric illustrations are presented to elucidate key concepts and many experimental validations are used to substantiate claims of superiority.

A semi-empirical Henry's law expression for carbon dioxide dissolution in ionic liquids

A simple model was developed to predict the solubility of carbon dioxide (CO 2) in ionic liquids under normal processing and conditioning pressures for natural gas fluids. COSMO-RS was used to predict the unsymmetrical activity coefficients for CO 2 in ILs, and the Peng–Robinson equation of state was used to calculate the CO 2 fugacity coefficient. Using these two quantities, a correlation was developed which can be used to extrapolate solubilities for ILs where experimental data is not available. This study shows that the molecular mass of the ILs is an effective parameter to correlate the Henry's constant of CO 2.

Equilibrium Studies on the System H<sub>2</sub>O-H<sub>2</sub>O<sub>2</sub>-CO(NH<sub>2</sub>)<sub>2</sub>-C<sub>3</sub>H<sub>8</sub>

The phase equilibrium of the quaternary system H2O-H2O2-CO(NH2)2-C3H8 with gas hydrate formation had been studied at high pressure and low temperature. The temperature and pressure of gas hydrate formed from different hydrogen peroxide concentration aqueous were determined at adding surfactants and no surfactants separately. It was concluded that the equilibrium pressure of gas hydrate formation was increasing with the increase of the hydrogen peroxide concentration, the urea concentration and the temperature, the mother liquor amount entrained in the gas hydrate after liquid separation by sinking was very high when surfactants was not added, but the equilibrium pressure of gas hydrate formation was decreased and the mother liquor amount entrained in gas hydrate was also decreased when surfactants was added to the system. In addition, the equilibrium pressure of gas hydrate formation in the quaternary system H2O-H2O2-CO(NH2)2-C3H8 was calculated according to Chen-Guo thermodynamic model, improved UNIFAC mathematical equation and Aasberg-Peterson fugacity coefficient model. The calculated data was in agreement with the experiment data.

Thermodynamics of B(OH) 3 in the vapor phase of water: Vapor–liquid and Henry's constants, fugacity and second cross virial coefficients

Available experimental data are employed to determine: (1) the enthalpy of formation, Δ f H°, of B(OH) 3, in the ideal gas state; (2) the value of the Krichevskii parameter, ( ∂ P / ∂ x 2 ) T , V , x 2 = 0 c for boric acid in water; (3) values of the vapor–liquid distribution constants and Henry's constants for H 3BO 3 at infinite dilution in water for temperatures between 273.15 K and T c . The obtained information allows calculation of the fugacity coefficients for boric acid in the vapor phase of water and second cross virial coefficients for interactions between molecules of H 2O and B(OH) 3 at temperatures between 450 and T c .

Thermodynamic modeling of CO 2 and H 2S solubilities in aqueous DIPA solution, aqueous sulfolane–DIPA solution, and aqueous sulfolane–MDEA solution with electrolyte NRTL model

A thermodynamic model developed for CO 2 and H 2S solubilities in aqueous MDEA solution is extended to cover CO 2 and H 2S solubilities in aqueous DIPA solution, aqueous sulfolane–DIPA solution, and aqueous sulfolane–MDEA solution. The model makes use of the 2009 version of the electrolyte NRTL model for liquid phase activity coefficient calculations and the PC-SAFT equation of state for vapor phase fugacity coefficient calculations. The NRTL binary parameters for the molecule–electrolyte pairs required for the H 2O–DIPA–CO 2 ternary and the H 2O–sulfolane–DIPA–CO 2 quaternary are regressed against the solubility data of CO 2 in aqueous DIPA solution and aqueous sulfolane–DIPA solution, respectively. The NRTL binary parameters for the molecule–electrolyte pairs required for the H 2O–DIPA–H 2S ternary and the H 2O–sulfolane–DIPA–H 2S quaternary are regressed against the solubility data of H 2S in aqueous DIPA solution and aqueous sulfolane–DIPA solution simultaneously. The NRTL binary parameters for the electrolyte–electrolyte pairs involved in the H 2O–DIPA–CO 2–H 2S quaternary are regressed against the solubility data of the acid gas mixtures in aqueous DIPA solution. Likewise, the NRTL binary parameters for the sulfolane–electrolyte pairs required for the H 2O–sulfolane–MDEA–CO 2 quaternary and the H 2O–sulfolane–MDEA–H 2S quaternary are regressed against the solubility data of the acid gases in aqueous sulfolane–MDEA solution. The predicted enthalpies of acid gas absorption are compared favorably with the literature data available for the H 2O–DIPA–CO 2 system, the H 2O–DIPA–H 2S system, and the H 2O–sulfolane–MDEA–CO 2 system.

Investigation on isobaric vapor liquid equilibrium for acetic acid + water + ( n-propyl acetate or iso-butyl acetate)

Isobaric vapor–liquid equilibrium (VLE) data for acetic acid + water, acetic acid + n-propyl acetate, acetic acid + iso-butyl acetate, acetic acid + water + n-propyl acetate, acetic acid + water + iso-butyl acetate are measured at 101.33 kPa with a modified Rose still. The nonideal behavior in vapor phase caused by the association of acetic acid are corrected by the chemical theory and Hayden–O’Connell method, and analyzed by calculating the second virial coefficients and apparent fugacity coefficients. The VLE data for acetic acid + water, acetic acid + n-propyl acetate, and acetic acid + iso-butyl acetate are correlated through the NRTL and UNIQUAC models using the nonlinear least square method. The obtained NRTL model parameters are used to predict the ternary VLE data. The ternary predicted values obtained in this way agree well with the experimental values.

CO2 Absorption in Aqueous Piperazine Solutions: Experimental Study and Modeling

In this work, new solubility data of CO2 in aqueous piperazine (Pz) solutions were measured over a temperature range from T = (287.1 to 313.1) K and for amine concentrations from m = (0.10 to 2.00) mol·kg−1. The CO2 partial pressure was kept within PCO2 = (0.11 to 525.17) kPa using a vapor−liquid equilibrium (VLE) apparatus based on a static-synthetic method. These experimental data and those found in the literature for the ternary system Pz−CO2−H2O were correlated using a model combining the virial equation of state to calculate the fugacity coefficients with a modified Pitzer's thermodynamic model for the activity coefficients. With the new extended interaction parameters βi,j0 and βi,j1 that cover a wide range of temperature, CO2 partial pressure, and amine concentration, the model is able to correlate satisfactorily the available reliable experimental solubility data.

Development of a Kinetic Model for Supercritical Fluids Fischer−Tropsch Synthesis

Kinetic models for Fischer−Tropsch synthesis (FTS) were derived to express the reaction behavior in either conventional reaction media (gas-phase) or nonconventional media (near-critical and supercritical solvent media). These models we developed from experimental data generated from a commercial alumina supported cobalt catalyst (15% Co/Al2O3) in a fixed bed reactor. Two models were developed: the first one assumes ideal gas phase behavior for the gas phase reaction and uses partial pressures to express reactant and product concentrations in rate expressions while the second model accounts for the nonideal behavior of the reaction mixture under elevated pressures via the utilization of fugacity parameters and fugacity coefficients. The fugacity coefficients were estimated from a modified Redlich−Kwong−Soave equation of state. A comparison was conducted between the estimated kinetic parameters from the fugacity-based kinetic model and the partial pressure based kinetic model. The heat of adsorption of car...

XSEOS: An evolving tool for teaching chemical engineering thermodynamics

XSEOS – excess Gibbs energy models and equations of state – is an Excel ® add-in for computing properties with thermodynamic models often used in chemical process design. The program is free, has open source, and runs on a platform, Excel, commonly available in personal computers. The main targets are undergraduate and graduate courses in chemical engineering thermodynamics whose syllabi include phase and chemical equilibrium calculations, but XSEOS may also be useful for research. The thermodynamic models available in XSEOS allow computing excess or residual properties, and activity or fugacity coefficients of pure components and mixtures (with any number of components). The recent addition of several methods to characterize petroleum fluids and to estimate surface tensions extends the potential application of the package to oil refining and petroleum engineering courses. We also report assessments of XSEOS's use in assignments and course projects, based on feedback provided by students.

Third Bose fugacity coefficient in one dimension, as a function of asymptotic quantities

In one of the very few exact quantum mechanical calculations of fugacity coefficients, [L.R. Dodd, A.M. Gibbs. J. Math. Phys. 15 (1974) 41] obtained b 2 and b 3 for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For b 2, we have shown [A. Amaya-Tapia, S.Y. Larsen, M. Lassaut. Mol. Phys. 103 (2005) 1301–1306. < arXiv:physics/0405150>] that Dodd and Gibbs’ result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in one dimension. Now, we develop an exact expression for b 3 - b 3 0 (where b 3 0 is the free particle fugacity coefficient) in terms of sums and differences of three-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a Distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the twofold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel. The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.

Solid–liquid–gas equilibrium of the naphthalene–biphenyl–CO 2 system: Measurement and modeling

The first and last melting points (FLMP) method was employed to measure the melting temperature–composition ( T – w ) data at solid–liquid–gas (SLG) equilibrium for the naphthalene–biphenyl–CO 2 system. Results show that the system's phase diagram is simple eutectic under all investigated pressures (0.1, 3.0, 6.0 and 8.0 MPa), and the system's eutectic composition is almost constant. The ( T – w ) data measured with a high-pressure differential scanning calorimetry are in good agreement with these from FLMP. The semi-predictive model using solubility data (SMS) and the calculation model combining with G E models (CMG) for binary systems were extended to this ternary system. For the SMS model, the Peng–Robinson equation of state (PR-EoS) with the van der Waals one-fluid mixing rule was used to correlate the solubility data of the two solutes in CO 2 to obtain the two interaction parameters k 12 and k 13 and calculate the fugacity coefficients of the solutes in the liquid and vapor phases; the UNIFAC method was also applied to the activity coefficient of the solutes in the liquid phase. For the CMG model, the PR-EoS combining respectively the MHV1, LCVM, and modified LCVM (mLCVM) mixing rules was applied to the fugacity coefficients of the solutes. Results show that the CMG model with MHV1 gives the best prediction of the system's SLG equilibrium, while the SMS model and the CMG model with mLCVM provide comparable and acceptable results.