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Molecular dynamics simulations are carried out to study the two-phase behavior of the n-decane+water system in the presence of methane, carbon dioxide, and their mixture at reservoir conditions. The simulation studies were complemented by theoretical modeling using the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) and density gradient theory. Our results show that the presence of methane and carbon dioxide decreases the interfacial tension (IFT) of the decane+water system. In general, the IFT increases with increasing pressure and decreasing temperature for the methane+decane+water and carbon dioxide+decane+water systems, similar to what has been found for the corresponding decane+water system. The most important finding of this study is that the presence of carbon dioxide decreases the IFT of the methane+decane+water system. The atomic density profiles provide evidence of the local accumulation of methane and carbon dioxide at the interface, in most of the studied systems. The results of this study show the preferential dissolution in the water-rich phase and enrichment at the interface for carbon dioxide in the methane+carbon dioxide+decane+water system. This indicates the preferential interaction of water with carbon dioxide relative to methane and decane. Notably, there is an enrichment of the interface by decane at high mole fractions of methane in the methane/decane-rich or methane/carbon dioxide/decane-rich phase. Overall, the solubility of methane and carbon dioxide in the water-rich phase increases with increasing pressure and temperature.Additionally, we find that the overall performance of the PC-SAFT EoS and the cubic-plus-association EoS is similar with respect to the calculation of bulk and interfacial properties of these systems.

We perform molecular dynamics simulation study of CO, methane, and their mixture in the presence of brine over a broad range of temperature (311-473 K), pressure (up to about 100 MPa), and NaCl concentration (up to about 14 wt %). The general decrease in the interfacial tension (IFT) values of the CH-brine system with pressure and temperature is similar to that obtained for the corresponding CH-water system. The IFT of methane and brine is a linearly increasing function of salt concentration, and the resulting slopes are dependent on the pressure. A similar behavior as methane is observed for such systems containing CO and CO-CH mixture. The IFT of CO and brine increases linearly with increasing salt content; however, the resulting slopes are independent of pressure. The simulations show that the presence of CO decreases the IFT values of the CH-water and CH-brine systems, but the degree of reduction depends on the amount of CO in each sample, which is consistent with experimental evidence. These IFT values show a linear correlation with the amount of CO, and the resulting slopes are dependent on the temperature and pressure. Furthermore, our results for the mole fractions of the different species in the CO-CH-water system at 323 K and 9 MPa are in agreement with those of experiments. The mole fractions of methane and CO in the water-rich phase decrease with increasing salt concentration, whereas that of HO in the methane- or CO-rich phases remains almost unaffected in all of the studied cases. Our results could be useful because of the importance of carbon dioxide sequestration and shale gas production.

Using grand canonical Monte Carlo (GCMC) simulations, we study the adsorption behavior of CH 4 , CO , and their mixtures at 298.15 K and pressures up to 50 bar in Na-, Cs-, and Ca-montmorillonite clays in the presence of water. Montmorillonite clays in the presence of preadsorbed water, preferentially adsorb CO 2 over CH 4 during both pure component and mixture adsorption. The atomistic model we have used, gives good agreement with available single-component experimental adsorption isotherms, for CH 4 and CO 2 molecules adsorbed onto montmorillonite clays in the presence of water. We observe the general trend that the presence of increasing preadsorbed water content in the clay interlayers, reduced adsorption amounts of pure CH 4 and CO 2 molecules. With a relatively large basal spacing (d= 30Å), the favorability of adsorption of CO 2 by montmorillonite at relatively low pressures and intermediate water contents has been demonstrated using simulations. GCMC simulation is also used to assess the effect of water on the adsorption of N 2 /CH 4 , H 2 S/CH 4 , CO 2 /N 2 , and CO 2 /H 2 S binary mixtures in Na-montmorillonite clay. The ideal adsorbed solution theory is shown to agree well with the observed adsorption capacities and selectivities of mixtures in Na-montmorillonite clay.

Molecular dynamics simulations were performed to study the bulk and interfacial properties of methane + n-decane, carbon dioxide + n-decane, and methane + carbon dioxide + n-decane systems under geological conditions. In addition, theoretical calculations using the predictive Peng-Robinson equation of state and density gradient theory are carried out to compare with the simulation data. A key finding is the preferential dissolution in the decane-rich phase and adsorption at the interface for carbon dioxide from the methane/carbon dioxide mixture. In general, both the gas solubility and the swelling factor increase with increasing pressure and decreasing temperature. Interestingly, the methane solubility and the swelling of the methane + n-decane system are not strongly influenced by temperature. Our results also show that the presence of methane increases the interfacial tension (IFT) of the carbon dioxide + n-decane system. Typically, the IFT of the studied systems decreases with increasing pressure and temperature. The relatively higher surface excess of the carbon dioxide + n-decane system results in a steeper decrease in its IFT as a function of pressure. Such systematic investigations may help to understand the behavior of the carbon dioxide-oil system in the presence of impurities such as methane for the design and operation of carbon capture and storage and enhanced oil recovery processes.

We perform grand canonical Monte Carlo simulations to study the detailed molecular mechanism of intercalation behavior of CO2 in Na-, Ca-, and Mg-montmorillonite exposed to variably hydrated supercritical CO2 at 323.15 K and 90 bar. The simulations indicate that the intercalation of CO2 strongly depends on the relative humidity (RH). The intercalation of CO2 in the dehydrated interlayer is inhibited, followed by the swelling of the interlayer region due to uptake of water and CO2 as the RH increases. In all of the hydrated clay samples, the amount of the intercalated CO2 generally decreases as a function of increasing RH, which is attributed mainly to the weakening of the interaction between CO2 and clay. At low RH values, Ca- and Mg-montmorillonite are relatively more efficient in capturing CO2. The amount of CO2 trapped in all clay samples shows similar values above RH of ∼60%. Molecular dynamics simulations show that the diffusion coefficient of each species generally increases with increasing RH due to the associated expansion of the interlayer distance of the clay. For all the hydrated samples, the diffusion coefficients of CO2 and water in the interlayers are mostly comparable due to the fact that CO2 molecules are well solvated. The diffusion of CO2 in each hydration state is mostly independent of the type of cation in accordance with the fact that CO2 molecules hardly migrate into the first hydration shell of the interlayer cations.

Molecular dynamics simulations and theoretical analysis were carried out to study the bulk and interfacial properties of carbon dioxide−methane−water and carbon dioxide−methane−brine systems under geological conditions. The density gradient theory with the bulk phase properties estimated using the cubicplus-association (CPA) equation of state (EoS) can well describe the increase in the interfacial tension (IFT) of the CO 2 −water system in the presence of methane. The theoretical estimates of species mole fractions in the carbon dioxide−methane−water system are in good quantitative agreement with the experimental results. Furthermore, simulations of carbon dioxide−methane−brine system show that the IFT of the CaCl 2 case is generally higher than that of the NaCl case. This is probably due to the stronger hydration of Ca 2+ ions and their stronger repulsion from the interface as compared to Na +. While the overall shape of the ionic profiles is not much affected by the ion type, the water profiles show a local enrichment at the interface in the system with CaCl 2. In contrast to the case of NaCl, the slopes of the plots of IFT vs CaCl 2 concentration are dependent on temperature. Species mole fractions in the carbon dioxide−methane−brine system predicted by combining the CPA EoS with the Debye-Hückel electrostatic term are in good agreement with simulation results. 2

For solving reactive transport problems in porous media, we analyze three primal discontinuous Galerkin (DG) methods with penalty, namely, symmetric interior penalty Galerkin (SIPG), nonsymmetric interior penalty Galerkin (NIPG), and incomplete interior penalty Galerkin (IIPG). A cut-off operator is introduced in DG to treat general kinetic chemistry. Error estimates in L 2 (H 1 ) are established, which are optimal in h and nearly optimal in p. We develop a parabolic lift technique for SIPG, which leads to h-optimal and nearly p-optimal error estimates in the L 2 (L 2 ) and negative norms. Numerical results validate these estimates. We also discuss implementation issues including penalty parameters and the choice of physical versus reference polynomial spaces.1. Introduction. Discontinuous Galerkin (DG) methods employ discontinuous piecewise polynomials to approximate the solutions of differential equations, with boundary conditions and interelement continuity weakly imposed through bilinear forms. Even though they often have larger numbers of degrees of freedom than conforming approaches, DG methods have recently gained popularity for a number of attractive features [19,3,4,23,27,11,25,26,9,18,15]: (1) they are element-wise conservative; (2) they support general nonconforming spaces including unstructured meshes, nonmatching grids and variable degrees of local approximations, thus allowing efficient h-, p-, and hp-adaptivities; (3) they tend to have localized errors, allowing sharp a posteriori error indicators and effective adaptivities; (4) they have less numerical diffusion; (5) they treat rough coefficient problems and effectively capture discontinuities in solutions; (6) they are robust and nonoscillatory in the presence of high gradients; (7) with appropriate meshing, they are capable of delivering exponential rates of convergences; (8) they have excellent parallel efficiency since data communications are relatively local; (9) for time-dependent problems in particular, their mass matrices are block diagonal, providing substantial computational advantages if explicit time integrations are used. In addition, by a simple extension from the average of the fluxes on element faces, DG can provide a continuous flux field defined over the entire domain, allowing efficient coupling with conforming methods.Numerical modeling of reactive transport in porous media has important applications in hydrology, earth sciences, environmental protection, oil recovery, chemical *