Mixture Diffusion in Nanoporous Adsorbents: Equivalence of Fickian and Maxwell−Stefan Approaches

Enhanced Recovery of Oil Mixtures from Calcite Nanopores Facilitated by CO2 Injection

Slow production, preferential recovery of light hydrocarbons, and low recovery factors are common challenges in oil production from unconventional reservoirs dominated by nanopores. Gas injection-based techniques such as CO2 Huff-n-Puff have shown promise in addressing these challenges. However, a limited understanding of the recovery of oil mixtures on the nanopore scale hinders their effective optimization. Here, we use molecular dynamics simulations to study the recovery of an oil mixture (C10 + C19) from a single 4 nm-wide calcite dead-end pore, both with and without CO2 injection. Without CO2 injection, oil recovery is much faster than expected from oil vaporization and features an undesired selectivity, i.e., the preferential recovery of lighter C10. With CO2 injection, oil recovery is accelerated and its selectivity toward C10 is greatly mitigated. These recovery behaviors are understood by analyzing the spatiotemporal evolution of C10, C19, and CO2 distributions in the calcite pore. In particular, we show that interfacial phenomena (e.g., the strong adsorption of oil and CO2 on pore walls, their competition, and their modulation of transport behavior) and bulk phenomena (e.g., solubilization of oil by CO2 in the middle portion of the pore) play crucial roles in determining the oil recovery rate and selectivity.

Structure-Transport Relationships of Water-Organic Solvent Co-transport in Carbon Molecular Sieve (CMS) Membranes

We explore the effects of the carbon molecular sieve (CMS) microstructure on the separation performance and transport mechanism of water-organic mixtures. Specifically, we utilize PIM-1 dense films and integrally skinned asymmetric hollow fiber membranes as polymer precursors for the CMS materials. The PIM-1 membranes were pyrolyzed under several different pyrolysis atmospheres (argon, carbon dioxide, and diluted hydrogen gas) and at multiple pyrolysis temperatures. Detailed gas physisorption measurements reveal that membranes pyrolyzed under 4% H2 and CO2 had broadened ultramicropore distributions (pore diameter <7 Å) compared to Ar pyrolysis, and pyrolysis under CO2 increased ultramicropore volume and broadened micropore distributions at increased pyrolysis temperatures. Gravimetric water and p-xylene sorption and diffusion measurements reveal that the PIM-1-derived CMS materials are more hydrophilic than other CMS materials that have been previously studied, which leads to sorption-diffusion estimations showing water-selective permeation. Water permeation in the vapor phase, pervaporation, and liquid-phase hydraulic permeation reveal that the isobaric permeation modes (vapor permeation and pervaporation) are reasonably well predicted by the sorption-diffusion model, whereas the hydraulic permeation mode is significantly underpredicted (>250×). Conversely, the permeation of p-xylene is well predicted by the sorption-diffusion model in all cases. The collection of pore size analysis, vapor sorption and diffusion, and permeation in different modalities creates a picture of a combined transport mechanism in which water-under high transmembrane pressures-permeates via a Poiseuille-style mechanism, whereas p-xylene solutes in the mixture permeate via sorption-diffusion.

Use of Boundary-Driven Nonequilibrium Molecular Dynamics for Determining Transport Diffusivities of Multicomponent Mixtures in Nanoporous Materials

The boundary-driven molecular modeling strategy to evaluate mass transport coefficients of fluids in nanoconfined media is revisited and expanded to multicomponent mixtures. The method requires setting up a simulation with bulk fluid reservoirs upstream and downstream of a porous media. A fluid flow is induced by applying an external force at the periodic boundary between the upstream and downstream reservoirs. The relationship between the resulting flow and the density gradient of the adsorbed fluid at the entrance/exit of the porous media provides for a direct path for the calculation of the transport diffusivities. It is shown how the transport diffusivities found this way relate to the collective, Onsager, and self-diffusion coefficients, typically used in other contexts to describe fluid transport in porous media. Examples are provided by calculating the diffusion coefficients of a Lennard-Jones (LJ) fluid and mixtures of differently sized LJ particles in slit pores, a realistic model of methane in carbon-based slit pores, and binary mixtures of methane with hypothetical counterparts having different attractions to the solid. The method is seen to be robust and particularly suited for the study of study of transport of dense fluids and liquids in nanoconfined media.

Structure and Gas Transport at the Polymer-Zeolite Interface: Insights from Molecular Dynamics Simulations

We investigate the structure of polyimide (PI) at the surface of a silicalite zeolite (MFI), as part of a model hybrid organic-inorganic mixed matrix membrane system, through equilibrium molecular dynamics simulations. Furthermore, we report a comparison of the adsorption and transport characteristics of pure components CO₂ and CH₄ in PI, MFI, and PI-MFI composite membranes. It is seen that incorporation of MFI zeolite into PI results in the formation of densified polymer layers (rigidified region) near the surface, having thickness around 1.2 nm, before bulklike behavior of the polymer is attained, contrary to empirical fits suggesting the existence of an approximately 1 μm thick interface between the polymer and filler. This region offers an extra resistance to gas diffusion especially for the gas with a larger kinetic diameter, CH₄, thus improving the CO₂/CH₄ kinetic selectivity in the PI-MFI composite membrane. Furthermore, we find that the kinetic selectivity of CO₂ over CH₄ in the rigidified region increases with temperature and that additivity of transport resistances in MFI, interfacial layer, and bulklike region of the polymer satisfactorily explains transport behavior in the composite sandwich investigated. The gas adsorption isotherms are extracted considering the dynamics and structural transitions in the PI and PI-MFI composite upon gas adsorption, and it is seen that the rigidified layer affects the gas adsorption in the polymer in the PI-MFI hybrid system. A significant increase in CO₂/CH₄ selectivity as well as gas permeability is observed in the PI-MFI composite membrane compared to that in the pure PI polymer membrane, which is correlated with the high selectivity of the rigidified interfacial layer in the polymer. Thus, while enhancing transport resistance, the rigidified layer is beneficial to membrane selectivity, leading to improved performance based on the Robeson upper bound plot for polymers.

On the Maxwell-Stefan approach to diffusion: a general resolution in the transient regime for one-dimensional systems

The diffusion process in a multicomponent system can be formulated in a general form by the generalized Maxwell-Stefan equations. This formulation is able to describe the diffusion process in different systems, such as, for instance, bulk diffusion (in the gas, liquid, and solid phase) and diffusion in microporous materials (membranes, zeolites, nanotubes, etc.). The Maxwell-Stefan equations can be solved analytically (only in special cases) or by numerical approaches. Different numerical strategies have been previously presented, but the number of diffusing species is normally restricted, with only few exceptions, to three in bulk diffusion and to two in microporous systems, unless simplifications of the Maxwell-Stefan equations are considered. In the literature, a large effort has been devoted to the derivation of the analytic expression of the elements of the Fick-like diffusion matrix and therefore to the symbolic inversion of a square matrix with dimensions n x n (n being the number of independent components). This step, which can be easily performed for n = 2 and remains reasonable for n = 3, becomes rapidly very complex in problems with a large number of components. This paper addresses the problem of the numerical resolution of the Maxwell-Stefan equations in the transient regime for a one-dimensional system with a generic number of components, avoiding the definition of the analytic expression of the elements of the Fick-like diffusion matrix. To this aim, two approaches have been implemented in a computational code; the first is the simple finite difference second-order accurate in time Crank-Nicolson scheme for which the full mathematical derivation and the relevant final equations are reported. The second is based on the more accurate backward differentiation formulas, BDF, or Gear's method (Shampine, L. F. ; Gear, C. W. SIAM Rev. 1979, 21, 1.), as implemented in the Livermore solver for ordinary differential equations, LSODE (Hindmarsh, A. C. Serial Fortran Solvers for ODE Initial Value Problems, Technical Report; https://computation.llnl.gov/casc/odepack/odepack_ home.html (2006).). Both methods have been applied to a series of specific problems, such as bulk diffusion of acetone and methanol through stagnant air, uptake of two components on a microporous material in a model system, and permeation across a microporous membrane in model systems, both with the aim to validate the method and to add new information to the comprehension of the peculiar behavior of these systems. The approach is validated by comparison with different published results and with analytic expressions for the steady-state concentration profiles or fluxes in particular systems. The possibility to treat a generic number of components (the limitation being essentially the computational power) is also tested, and results are reported on the permeation of a five component mixture through a membrane in a model system. It is worth noticing that the algorithm here reported can be applied also to the Fick formulation of the diffusion problem with concentration-dependent diffusion coefficients.