Pitzer Activity Coefficient Model Research Articles

Modelling the impact of geochemical reactions on hydrocarbon phase behavior during CO2 gas injection for enhanced oil recovery

CO2 injection in oil reservoirs offers the dual advantage of increasing oil recovery as well as storage to combat global warming. The injected CO2, however, may react with ions present in the brine as well as the rock. In this research, we present a model that quantifies the impact of these geochemical reactions on the phase behavior of hydrocarbon mixtures. A Gibbs free energy model is proposed that unifies different phase descriptions – the Peng–Robinson Equation of State (PR EOS) description for hydrocarbon phase components, the Pitzer activity coefficient model for aqueous components and an ideal solid phase. In particular, we illustrate the use of this model to determine the impact of geochemical reactions, introduced by the presence of an aqueous phase with ions and a solid calcite phase, on the phase envelope of CO2-nC14H30 mixture with different phase descriptions. The presented Gibbs free energy model is adaptable to different reservoir brines and can be used to assess the maximum impact of geochemical reactions during CO2 injection in different hydrocarbon reservoirs.

Modeling of the NH3–CO2–H2O vapor–liquid equilibria behavior with species-group Pitzer activity coefficient model

The vapor–liquid equilibria (VLE) model of the NH3–CO2–H2O system is crucial to the ammonia-based CO2 capture processes simulation and the proposition of innovation processes. Though traditional VLE models could describe the behavior of this system, they are always suffering too many regressed parameters and, more serious, the number of these parameters increases with the number of real species in the solution raised to the power of higher than 2. To conquer this problem, an upgraded thermodynamic model of the NH3–CO2–H2O system with the species-group Pizter activity coefficient model has been developed on the basis of the original model proposed by Krop (1999). Comparing with the commonly used activity coefficient models such as E-NRTL, extended UNIQUAC and original Pitzer model, the species-group Pizter activity coefficient model relates the parameters to the groups of species instead of real species in the solution, leading to significantly reducing the number of regressed parameters and simplifying the calculation. However, in the original model, the precipitation was not considered, which makes the validity of the model questionable, and the calculation of enthalpy, great importance for CO2 emission abatement processes, was also not taken into account. Therefore, in this work, the solid–liquid equilibria (SLE) of the NH4HCO3–H2O system were employed in the upgraded model to represent the precipitation and a new set of parameters were refitted against VLE data with genetic algorithm. The results indicate that this simplified thermodynamic model could satisfactorily describe the thermodynamic behavior of the NH3–CO2–H2O system.

Solubility of Li2CO3 in Na–K–Li–Cl brines from 20 to 90 °C

The solubility of Li2CO3 in Na–K–Li–Cl brines was measured by isothermal dissolution method within the temperature range of 20 to 90°C. It was found the solubility of Li2CO3 in all systems investigated decreased with increasing temperature. In NaCl and KCl solutions, the solubility of Li2CO3 initially increased to a maximum value and then decreased gradually with increasing solution concentration. However, the solubility of Li2CO3 in LiCl solutions decreased with increasing LiCl concentration due to the common ion effect of added Li+. New Pitzer activity coefficient model parameters for the Li+–CO32− ion pair were obtained by using experimental solubility data of Li2CO3 in pure water, and a new chemical model was built with the aid of Aspen Plus platform. The new model was shown to successfully predict the solubility of Li2CO3 in NaCl, KCl, LiCl and mixed NaCl–KCl solutions. Moreover, the new model could aid in analyzing the separation of lithium and magnesium in brines.

An Aqueous Thermodynamic Model for the Solubility of Potassium Ferrate in Alkaline Solutions to High Ionic Strengths from 283.15 to 333.15 K

Potassium ferrate, K2FeO4(cr), has numerous promising environmental applications. An aqueous thermodynamic model applicable to high ionic strengths is essential for guiding its applications. In this study, a thermodynamic model is developed for the solubility of K2FeO4(cr) in aqueous alkali metal hydroxide solutions, from 283.15 to 333.15 K to high ionic strengths, up to saturation of KOH and NaOH, based on the Pitzer activity coefficient model for aqueous species. The solubility products for K2FeO4(cr) at infinite dilution in the temperature range from 283.15 to 333.15 K were obtained. Based on the thermodynamic solubility product of K2FeO4(cr) at 298.15 and its temperature dependence, in combination with thermodynamic properties for $$ {\text{FeO}}_{4}^{2 - } $$ and K+ from the literature, standard thermodynamic properties of K2FeO4(cr) at 298.15 K and 0.1 MPa (1 bar) are derived for the first time as follows: Δf G 0 = −(896 ± 8) kJ·mol−1, Δf H 0 = −(1026 ± 4) kJ·mol−1, and S 0 = (130 ± 17) J·mol−1·K−1. Using the above thermodynamic properties for K2FeO4(cr), the potential presence or preservation of K2FeO4(cr) in the Martian soils under the conditions relevant to Mars were quantitatively evaluated. Thermodynamic calculations pertaining to the Martian conditions indicate that the presence or preservation of K2FeO4(cr) as a strong oxidant in the Martian soils can be supported.

Use of Adsorbed Solution theory to model competitive and co-operative sorption on elastic ion exchange resins

An Adsorbed Solution theory which takes into account non-idealities in both the adsorbed and the liquid phase was applied for the prediction of multi-component adsorption equilibria based on single component and binary mixture data. A novel non-iterative solution method was applied for the solution of the set of partly implicit model equations. The Pitzer activity coefficient model was used for the liquid phase and an empirical model for the adsorbed phase activity coefficients. Separation of concentrated acid lignocellulosic hydrolysates on an elastic strong acid cation exchange resin was used as a test system. The application is relevant in biorefineries when polysaccharides in wood are hydrolyzed to monosaccharides using concentrated sulfuric acid.It was found that the novel solution method for the equilibrium model can be applied successfully for complex multi-component systems; it is fast and easy to implement. The predictions of the thermodynamic model were validated with dynamic column experiments (pulse injections and loading/elution curves). Hereby, in the column mass balances, porosity fluctuations were taken explicitly into account. Satisfactory correlation between the calculated and experimental results was obtained. It was observed that the predictions of the model can be quite sensitive with respect to even minor inaccuracies in the calculated multi-component adsorption isotherms.

Chemical Modeling of Nesquehonite Solubility in Li + Na + K + NH4 + Mg + Cl + H2O System with a Speciation-based Approach

A chemical model, based on Pitzer activity coefficient model, is developed with a speciation approach to describe the solubility and chemistry of nesquehonite in concentrated chloride solutions. The chemical equilibrium constants for nesquehonite and aqueous species, i.e. MgCO03, MgHCO+3, and MgOH+, are precisely calculated as a function of temperature according to the Van't Hoff equation by use of standard Gibbs free energy, standard formation enthalpy and heat capacity. The most recent solubility data are regressed to obtain new Pitzer parameters with good agreement. The predictive ability of the new model is improved significantly in comparison with previous models. The behavior of speciation chemistry for nesquehonite in various chloride media is explained through this modeling work on the basis of the Mg/CO2−3 bearing species distribution, activity coefficient and pH changes.

Comment on “Thermodynamics of Solvent Extraction of Rhenium with Trioctyl Amine” (Fang, D.-w.; Gu, X.-j.; Xiong, Y.; Yue, S.; Li, J.; Zang. S.-l.J. Chem. Eng. Data2010,55, 424−427) and “Studies on Solvent Extraction of Perrhenate with Trialkylamine by Debye−Hückel and Pitzer Equations” (Fang, D.-w.; Gu, X.-j.; Xiong, Y.; Shan, W.-j.; Zang, S.-l.J. Chem. Eng. Data2010,55, 4440−4443)

Some concerns are raised regarding the value of the tabulated Pitzer activity coefficient model parameters for NH4ReO4 presented in two recent papers (Fang et al., J. Chem. Eng. Data2010, 55, 424−427 and Fang et al., J. Chem. Eng. Data2010, 55, 4440−4443). The use of these parameter sets is not recommended, as it leads to the calculation of activity coefficients which are inconsistent with the known behavior of similar salts.

Establishment of Uncertainty Ranges and Probability Distributions of Actinide Solubilities for Performance Assessment in the Waste Isolation Pilot Plant

AbstractThe Fracture-Matrix Transport (FMT) code developed at Sandia National Laboratories solves chemical equilibrium problems using the Pitzer activity coefficient model with a database containing actinide species. The code is capable of predicting actinide solubilities at 25 °C in various ionic-strength solutions from dilute groundwaters to high-ionic-strength brines. The code uses oxidation state analogies, i.e., Am(III) is used to predict solubilities of actinides in the +III oxidation state; Th(IV) is used to predict solubilities of actinides in the +IV state; Np(V) is utilized to predict solubilities of actinides in the +V state. This code has been qualified for predicting actinide solubilities for the Waste Isolation Pilot Plant (WIPP) Compliance Certification Application in 1996, and Compliance Re-Certification Applications in 2004 and 2009.We have established revised actinide-solubility uncertainty ranges and probability distributions for Performance Assessment (PA) by comparing actinide solubilities predicted by the FMT code with solubility data in various solutions from the open literature. The literature data used in this study include solubilities in simple solutions (NaCl, NaHCO3, Na2CO3, NaClO4, KCl, K2CO3, etc.), binary mixing solutions (NaCl+NaHCO3, NaCl+Na2CO3, KCl+K2CO3, etc.), ternary mixing solutions (NaCl+Na2CO3+KCl, NaHCO3+Na2CO3+NaClO4, etc.), and multi-component synthetic brines relevant to the WIPP.

Scaling prediction based on thermodynamic equilibrium calculation — scopes and limitations

A comprising thermodynamic approach is presented to investigate the behavior of saline solutions with respect to CaCO 3, CaSO 4 and SiO 2 scaling in water treatment processes. Thr Pitzer activity coefficient model is used to describe the aqueous species activities and the corresponding equilibrium reactions are solved to determine the saline solution composition. A well evaluated parameter set for the system H-Na-Ca-Mg-OH-Cl-CO 3-HCO 3-CO 2-SO 4-HSO 4-SiO 2 at 25°C is compiled and applied for calculation of the pure scale solubilities as well as mixture effects such as CaCO 3/CaSO 4 coprecipitation and silica adsorption. New data on silica removal dependant on the saline solution composition are used to estimate the ratio of silicate formation and silica adsorption onto other precipitating salts. Whereas the saturation states for pure scales are found to be well predictable at varying conditions, only qualtitative estimations for mixed scale formation can be achieved. Here, the predictability by thermodynamic equilibrium calculation is shown to meet its present boundary and its valuable service for understanding the mechanisms of scaling and the species involved is highlighted.

The Equilibrium Network: A New Approach for Simulation and Visualization of Aqueous Electrolyte Systems

A new simulation method for investigating mixed aqueous electrolyte systems at thermodynamic equilibrium is presented. Based on the commercial simulation package IPSEpro, a graphical procedure for assembling equilibrium systems followed by simultaneous solution of the underlying equation system was developed. At graphical setup, species and reactions objects are connected by the information of activity and stoichiometry in a network-like manner. Consequently, the resulting equations of mass action, the electro-neutrality and balance conditions are solved incorporating the Pitzer activity coefficient model and equilibrium constants from thermodynamic standard data. The method developed allows fast and flexible application of the complex thermodynamic principles to engineering tasks. The modeling approach and all basic models for graphical input and simultaneous solution of coupled equilibrium conditions are explained. For demonstration of the simulation method, example simulations for the systems of H2SO4-H2O, CaSO4-H2SO4-H2O and NaCl-CaSO4-CO2-H2O are described and evaluated successfully.

Modeling Multicomponent Ion Exchange: Application of the Single-Parameter Binary System Model

The single-parameter model for binary ion exchange equilibria is applied to the prediction of ternary and quaternary equilibria. This model is based on a statistical thermodynamic approach to exchanger-phase behavior, coupled with the Pitzer model for activity coefficients in aqueous solution and an explicit description of ion association phenomena. Exchange between alkali metal and alkaline earth cations on commercially available strong acid resins is investigated in the presence of a variety of nonexchanging anions. All systems can be predicted acceptably using parameters fitted to binary chloride-based systems. Model predictions from these parameters are highly accurate in many cases, while those systems that are not predicted as accurately from binary data are able to be described by recalculating one parameter using the ternary or quaternary data. This model fits all criteria required to be met by any description of ion exchange equilibria, and provides a simple yet highly effective approach to the description of equilibria in “real-world” ion exchange systems.

Thermodynamic solution model for trona brines

AbstractA thermodynamics solution model has been developed for concentrated trona brines over temperatures ranging from about 0°C to 200°C. The model was constructed by regressing on solubility data for the temperature‐dependent parameters in Pitzer's activity coefficient model. In addition, the model incorporates published thermochemical data for the solid salts and aqueous species. In some cases it was necessary to estimate solid salt heat capacities, but otherwise no adjustments were made in the thermochemical parameters. With one exception, the model provided an excellent fit to the data. The existence of a high‐temperature trona phase reported earlier cannot be reconciled with the model and is believed to be in error. The phase‐equilibrium diagram generated by the model appears suitable for design purposes.

Improved thermochemical data for computation of phase and chemical equilibria in flue-gas/water systems

A thermodynamic model for the computation of phase and chemical equilibrium in aqueous systems based on minimization of the Gibbs energy is developed using new thermochemical data and Pitzer's activity coefficient model. New data for the thermodynamic standard properties Δ f G 0, Δ f H 0and C p 0, are determined from our experimental results, which are based on the spectrometric in situ analysis of both the vapor and the liquid phase. The studies have been made in the concentration range pertinent to flue gas purification processes: p SO 2 between 0.01 and 1 kPa, c HCl up to 1 mol dm −3, c H 2SO 4 and c CaCl 2 up to 0.5 mol dm −3. The temperature varies from 298 to 333 K. In comparison with earlier data, a better correlation of important flue-gas/water subsystems like SO 2+water is achieved and a formerly proposed complexation of sulfur dioxide in the SO 2+HCl+H 2O system is confirmed. In particular, it is shown that on this basis the phase equilibria of SO 2+CaCl 2+H 2O and SO 2+HCl+H 2SO 4+H 2O can be predicted without further adjustment of parameters.

Solution Equilibria for Uranium Ore Processing: The BaSO 4-H 2SO 4-H 2O System and the RaSO 4-H 2SO 4-H 2O System

A radio-tracer determination of the solubility of BaSO 4 in H 2SO 4-H 2O mixtures was undertaken at temperatures of 25°C and 60°C. These were subsequently modelled using the Pitzer model for the activity coefficients, and estimates were made for Ba 2+-SO 4 2− and Ba 2+-HSO 4 − interaction parameters. The final model yields an excellent description of the solubility of BaSO 4 in H 2SO 4-H 2O mixtures up to 6 mol/kg and at both 25°C and 60°C. The logarithm of the thermodynamic solubility product constant (log K sp) for barite obtained by regression analysis was −10.02 ± 0.02 at 25°C and −9.68 ± 0.01 at 60°C. The values of the ion association constant derived from these data are 2.49 ± 0.03 at 25°C and 2.55 ± 0.1 at 60°C. The enthalpy of dissolution for BaSO 4 was estimated to be 17.6 ± 0.2 kJ mol −1. Literature solubility data for the RaSO 4-H 2SO 4-H 2O system have also been interpreted, using the Pitzer model for the necessary activity coefficients. The logarithm of the thermodynamic solubility product constant (log K sp) for radium sulfate obtained was −10.21 ± 0.06 at 25°C, while the value of the ion association constant derived is 2.76 ± 0.05 at 25°C. The high negative value of the Pitzer parameter β 2 obtained by regression analysis of these data suggests that the explicit recognition of a RaSO 4(aq) ion association species is to be preferred in this case.

Modeling mineral dissolution and precipitation in dual-porosity fracture-matrix systems

A dual-porosity chemical transport model is applied to saturated fractured porous media. In this model, transport through fractures is advection-dominated while transport within the matrix and between the matrix and the fractures is diffusion-dominated. Recent studies in the literature indicate that conservative tracers and radionuclides in these systems will be retarded by matrix diffusion even in the absence of chemical reactions. This study examines systems that include chemical reactions (e.g., dissolution/precipitation and aqueous complexation) and examines changes in retardation caused by precipitation. The two-dimensional simulation domain consists of a single fracture and the adjacent permeable matrix. The system is modeled using finite differences and a chemical equilibrium simulator based on the Villars-Cruise-Smith algorithm. A constant flow rate is assumed in the fracture, and diffusion rates are functions of the local matrix porosity. Results from simulations with idealized chemistry are presented and discussed to illustrate basic characteristics of this system. These characteristics include both advection-induced and diffusion-induced sequential dissolution/precipitation waves. Results are contrasted with limiting single porosity cases. An additional simulation using the Pitzer activity coefficient model illustrates the chemical retardation of a contaminant due to contaminant precipitation.

Equilibrium partial pressures of strong acids over concentrated saline solutions—I. HNO 3

Equilibrium partial pressures of HNO 3 have been measured at 25°C over concentrated aqueous solutions containing the ions H +, NO 3 −, SO 4 2−, K + , NH 4 + and Mg 2+. Measurements agree closely with predictions made using a Henry's Law constant of 2.45 × 10 6 mol 2 kg −2 atm −1 for the reaction HNO 3( g) = H ( aq.) + + NO 3( aq.) −, and the Pitzer activity coefficient model. The model is recommended for the calculation of solute and solvent activities in aqueous aerosols at high ionic strength, corresponding to equilibrium relative humidities greater than about 70 %. The following new parameters have been estimated for the model using the partial pressure measurements and other thermodynamic data: ψ H, Na, NO 3 , −0.003; θ NO 3, SO 4 , 0.0926; ψ NO 3, SO 4, K , −0.0046; ψ NO 3, SO 4, Na , 0.0066; ψ H, NH 4, NO 3 , −0.01; ψ H, K, No 3 3 , −0.01.

Equilibrium partial pressures of strong acids over concentrated saline solutions—II. HCl

Equilibrium partial pressures of HCl have been measured at 25°C over concentrated solutions containing the ions H + , Cl −, Mg 2+, NH 4 +, A1 3+, SO 4 2−, ClO 4 −, CH 3SO 3 −, and those of the alkali metals. Measurements agree closely with values predicted using a Henry's Law constant of 2.04 × 10 6mol 2kg −2atm −1 for the reaction HCl ( g) = H ( aq.) + + Cl ( aq.) −, and the Pitzer activity coefficient model. The following parameter values have been estimated for the model using the partial pressure and other thermodynamic data: θ H, Rb , −0.0120; ψ H, Rb, Cl , −0.012; θ H, NH 4 ,−0.01; ψ H, NH 4, Cl , −0.009; ψ H,NH 4,Br , −0.0104.

Hydrofluoric and hydrochloric acid behaviour in concentrated saline solutions

Ion-selective electrode measurements of mean NaF and Cl/F activities in concentrated NaCl media at 25 °C have been used to estimate Pitzer activity coefficient model parameters θCl,F(0.01), ψNa,Cl,F(0.002 33), and ψK,Cl,F(–0.003 3). Dissociation constants (K1) of HF and stability constants (K*) of MgF+ were determined in NaCl media at 25 °C up to I= 5.0 mol kg–1 and are described by: log K1=–3.165 + 1.81 I½/(1 + 3.73I½)– 0.06I- 0.0136I2 and log K*= 1.822 – 0.982I½/(1 + 0.328I½)+ 0.0713I+ 0.0169I2. Pitzer model parameters βMgF(0)(3.932), βMgF(1)(–25.17), and CφMgF(–5.294) were also derived. A Henry's law expression for the reaction HX(g)→ H+(aq)+ X–(aq)(KH/mol2 kg–2 atm–1) was applied to HCl (KH= 2.04 × 106) and HF (KH= 9.61). Partial pressures and speciation of the acids in acidified NaCl–MgCl2 media were then calculated over a range of concentrations. The results suggest that fluoride (as HF) is expelled preferentially to chloride from naturally acidified marine aerosols.