Simultaneous Predictions of Chemical and Phase Equilibria in Systems with an Esterification Reaction Using PC-SAFT

The study of chemical reactions in multiple liquid phase systems is becoming more and more relevant in industry and academia. The ability to predict combined chemical and phase equilibria is interesting from a scientific point of view but is also crucial to design innovative separation processes. In this work, an algorithm to perform the combined chemical and liquid-liquid phase equilibrium calculation was implemented in the PC-SAFT framework in order to predict the thermodynamic equilibrium behavior of two multicomponent esterification systems. Esterification reactions involve hydrophobic reacting agents and water, which might cause liquid-liquid phase separation along the reaction coordinate, especially if long-chain alcoholic reactants are used. As test systems, the two quaternary esterification systems starting from the reactants acetic acid + 1-pentanol and from the reactants acetic acid + 1-hexanol were chosen. It is known that both quaternary systems exhibit composition regions of overlapped chemical and liquid-liquid equilibrium. To the best of our knowledge, this is the first time that PC-SAFT was used to calculate simultaneous chemical and liquid-liquid equilibria. All the binary subsystems were studied prior to evaluating the predictive capability of PC-SAFT toward the simultaneous chemical equilibria and phase equilibria. Overall, PC-SAFT proved its excellent capabilities toward predicting chemical equilibrium composition in the homogeneous composition range of the investigated systems as well as liquid-liquid phase behavior. This study highlights the potential of a physical sound model to perform thermodynamic-based modeling of chemical reacting systems undergoing liquid-liquid phase separation.

Atomistic simulation framework for molten salt vapor–liquid equilibrium prediction and its application to NaCl

Knowledge of the vapor–liquid equilibrium (VLE) properties of molten salts is important in the design of thermal energy storage systems for solar power and nuclear energy production applications. The high temperatures involved make their experimental determination problematic, and the development of both macroscopic thermodynamic correlations and predictive molecular-based methodologies are complicated by the requirement to appropriately incorporate the chemically reacting vapor-phase species. We derive a general thermodynamic-based atomistic simulation framework for molten salt VLE prediction and show its application to NaCl. Its input quantities are temperature-dependent ideal-gas free energy data for the vapor phase reactions and density and residual chemical potential data for the liquid. If these are not available experimentally, the former may be predicted using standard electronic structure software, and the latter may be predicted by means of classical atomistic simulation methodology. The framework predicts the temperature dependence of vapor pressure, coexisting phase densities, vapor phase composition, and vaporization enthalpy. It also predicts the concentrations of vapor phase species present in minor amounts (such as the free ions), quantities that are extremely difficult to measure experimentally. We furthermore use the results to obtain an approximation to the complete VLE binodal dome and the critical properties. We verify the framework for molten NaCl, for which experimentally based density and chemical potential data are available in the literature. We then apply it to the analysis of NaCl simulation data for two commonly used atomistic force fields. The framework can be readily extended to molten salt mixtures and to ionic liquids.

A Review of Geochemical Modeling for the Performance Assessment of Radioactive Waste Disposal in a Subsurface System

Radionuclides are inorganic substances, and the solubility of inorganic substances is a major factor affecting the disposal of radioactive waste and the release of concentrations of radionuclides. The degree of solubility determines whether a nuclide source migrates to the far field of a radioactive waste disposal site. Therefore, the most effective method for retarding radionuclide migration is to reduce the radionuclide solubility in the aqueous geochemical environment of subsurface systems. In order to assess the performance of disposal facilities, thermodynamic data regarding nuclides in water–rock systems and minerals in geochemical environments are required; the results obtained from the analysis of these data can provide a strong scientific basis for maintaining safety performance to support nuclear waste management. The pH, Eh and time ranges in the environments of disposal sites cannot be controlled, in contrast to those under experimental conditions in laboratories. Using a hypothetical error mechanism for the safety assessment of disposal sites may engender incorrect assessment results. Studies have focused on radionuclide reactions in waste disposal, and have offered evidence suggesting that these reactions are mainly affected by the geochemical environment. However, studies have not examined the thermodynamics of chemical reactions or interactions between water and minerals, such as the surface complexation and adsorption of various nuclide-ion species. Simple coefficient models have usually been applied in order to obtain empirical formulas for deriving Kd to describe nuclide distributions in the solid or liquid phase in water–rock geochemical systems. Accordingly, this study reviewed previous research on the applications of geochemical models, including studies on the development of geochemical models, sources of thermodynamic databases (TDBs) and their applications in programs, the determination of the adequacy of TDBs in surface complexation models and case studies, and the selection and application of activity coefficient equations in geochemical models. In addition, the study conducted case studies and comparisons of the activity coefficients derived by different geochemical models. Three activity coefficient equations, namely the Davies, modified Debye–Hückel, and Pitzer equations, and four geochemical models, namely PHREEQC, MINEQL+, MINTEQA2, and EQ3/6, were used in the study. The results demonstrated that when the solution’s ionic strength was <0.5 m, the differences in the activity coefficients between the Davies and modified Debye–Hückel equations were <5%. The difference between the Pitzer and Davies equations, or between the Pitzer and modified Debye–Hückel equations in terms of the calculated activity coefficients was <8%. The effect of temperature on the activity coefficient slightly influenced the modeling outputs of the Davies and modified Debye–Hückel equations. In the future, the probability distribution and uncertainty of parameters of Kd and the equilibrium constant can be used in geochemical and reactive transport models to simulate the long-term safety of nuclear waste disposal sites. The findings of this study can provide a strong scientific basis for conducting safety assessments of nuclear waste disposal repositories and developing environmental management or remediation schemes to control sites marred by near-surface contamination.

Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media

Reactive transport plays an important role in various subsurface applications, including carbon dioxide sequestration, nuclear waste storage, biogeochemistry and the simulation of hydro–thermal reservoirs. The model couples a set of partial differential equations, describing the transport of chemical species, to nonlinear algebraic or differential equations, describing the chemical reactions. Solution methods for the resulting large nonlinear system can be either fully coupled or can iterate between transport and chemistry. This paper extends previous work by the authors where an approach based on the Newton–Krylov method applied to a reduced system has been developed. The main feature of the approach is to solve the nonlinear system in a fully coupled manner while keeping transport and chemistry modules separate. Here we extend the method in two directions. First, we take into account mineral precipitation and dissolution reactions by using an interior point Newton method, so as to avoid the usual combinatorial approach. Second, we study two-dimensional heterogeneous geometries. We show how the method can make use of an existing transport solver, used as a black box. We detail the methods and algorithms for the individual modules, and for the coupling step. We show the performance of the method on synthetic examples.

Toward a Spatiotemporal Understanding of Dolomite Dissolution in Sandstone by CO2-Enriched Brine Circulation

In this study, we introduce a stochastic method to delineate the mineral effective surface area (ESA) evolution during a recycling reactive flow-through transport experiment on a sandstone under geologic reservoir conditions, with a focus on the dissolution of its dolomite cement, Ca_1.05Mg_0.75Fe_0.2(CO₃)₂. CO₂-enriched brine was circulated through this sandstone specimen for 137 cycles (∼270 h) to examine the evolution of in situ hydraulic properties and CO₂-enriched brine-dolomite geochemical reactions. The bulk permeability of the sandstone specimen decreased from 356 mD before the reaction to 139 mD after the reaction, while porosity increased from 21.9 to 23.2% due to a solid volume loss of 0.25 mL. Chemical analyses on experimental effluents during the first cycle yielded a dolomite reactivity of ∼2.45 mmol m^-3 s^-1, a corresponding sample-averaged ESA of ∼8.86 × 10^-4 m²/g, and an ESA coefficient of 1.36 × 10^-2, indicating limited participation of the physically exposed mineral surface area. As the dissolution reaction progressed, the ESA is observed to first increase and then decrease. This change in ESA can be qualitatively reproduced employing scanning electron microscopy-image-based stochastic analyses on dolomite dissolution. These results provide a new approach to analyze and upscale the ESA during geochemical reactions, which are involved in a wide range of geoengineering operations.

Molecular Simulation of Chemical Reaction Equilibrium by Computationally Efficient Free Energy Minimization

The molecular simulation of chemical reaction equilibrium (CRE) is a challenging and important problem of broad applicability in chemistry and chemical engineering. The primary molecular-based approach for solving this problem has been the reaction ensemble Monte Carlo (REMC) algorithm [Turner et al. Molec. Simulation2008, 34, (2), 119-146], based on classical force-field methodology. In spite of the vast improvements in computer hardware and software since its original development almost 25 years ago, its more widespread application is impeded by its computational inefficiency. A fundamental problem is that its MC basis inhibits the implementation of significant parallelization, and its successful implementation often requires system-specific tailoring and the incorporation of special MC approaches such as replica exchange, expanded ensemble, umbrella sampling, configurational bias, and continuous fractional component methodologies. We describe herein a novel CRE algorithm (reaction ensemble molecular dynamics, ReMD) that exploits modern computer hardware and software capabilities, and which can be straightforwardly implemented for systems of arbitrary size and complexity by exploiting the parallel computing methodology incorporated within many MD software packages (herein, we use GROMACS for illustrative purposes). The ReMD algorithm utilizes these features in the context of a macroscopically inspired and generally applicable free energy minimization approach based on the iterative approximation of the system Gibbs free energy function by a mathematically simple convex ideal solution model using the composition at each iteration as a reference state. Finally, we additionally describe a simple and computationally efficient a posteriori method to estimate the equilibrium concentrations of species present in very small amounts relative to others in the primary calculation. To demonstrate the algorithm, we show its application to two classic example systems considered previously in the literature: the N₂-O₂-NO system and the ammonia synthesis system.