Bottom-up model of adsorption and transport in multiscale porous media

Coarse-Grained Modeling Using Neural Networks Trained on Structural Data

We propose a method of bottom-up coarse-graining, in which interactions within a coarse-grained model are determined by an artificial neural network trained on structural data obtained from multiple atomistic simulations. The method uses ideas of the inverse Monte Carlo approach, relating changes in the neural network weights with changes in average structural properties, such as radial distribution functions. As a proof of concept, we demonstrate the method on a system interacting by a Lennard-Jones potential modeled by a simple linear network and a single-site coarse-grained model of methanol-water solutions. In the latter case, we implement a nonlinear neural network with intermediate layers trained by atomistic simulations carried out at different methanol concentrations. We show that such a network acts as a transferable potential at the coarse-grained resolution for a wide range of methanol concentrations, including those not included in the training set.

Sorption-Deformation-Percolation Model for Diffusion in Nanoporous Media

Diffusion of molecules in porous media is a critical process that is fundamental to numerous chemical, physical, and biological applications. The prevailing theoretical frameworks are challenged when explaining the complex dynamics resulting from the highly tortuous host structure and strong guest-host interactions, especially when the pore size approximates the size of diffusing molecule. This study, using molecular dynamics, formulates a semiempirical model based on theoretical considerations and factorization that offer an alternative view of diffusion and its link with the structure and behavior (sorption and deformation) of material. By analyzing the intermittent dynamics of water, microscopic self-diffusion coefficients are predicted. The apparent tortuosity, defined as the ratio of the bulk to the confined self-diffusion coefficients, is found to depend quantitatively on a limited set of material parameters: heat of adsorption, elastic modulus, and percolation probability, all of which are experimentally accessible. The proposed sorption-deformation-percolation model provides guidance on the understanding and fine-tuning of diffusion.

Modeling transport and filtration of nanoparticle suspensions in porous media

Recently membrane filters have gained in significance due to the need to provide protection against airborne pollution. A question of importance, and some controversy, is the efficiency of filters for small nanoparticles with diameters below 100 nm as these are considered particularly dangerous due to possible penetration into the lungs. The efficiency is measured by the number of particles blocked by the pore structure after passing though the filter. To study the penetration into pores by nanoparticles suspended in a fluid, a stochastic transport theory based on an atomistic model is used to calculate particle density and flow within the pores, resulting pressure gradient, and filter efficiency. The importance of pore size relative to particle diameter and of the parameters of the pore wall interactions are investigated. The theory is applied to aerosols in fibrous filters and found to reproduce common trends in measurements. As particles enter the initially empty pores on relaxation to the steady state the small penetration measured at the onset of filtration increases faster in time the smaller the nanoparticle diameter. Control of pollution by filtration is achieved by strong repulsion of pore walls for particle diameters greater than twice the effective pore width. For smaller nanoparticles the steady-state efficiency decreases as the pore wall interactions weaken. Effective efficiency is increased when the suspended nanoparticles inside the pores combine into clusters of sizes greater than the filter channel width.

Nonlinear Reactor Design Optimization With Embedded Microkinetic Model Information

Despite the success of multiscale modeling in science and engineering, embedding molecular-level information into nonlinear reactor design and control optimization problems remains challenging. In this work, we propose a computationally tractable scale-bridging approach that incorporates information from multi-product microkinetic (MK) models with thousands of rates and chemical species into nonlinear reactor design optimization problems. We demonstrate reduced-order kinetic (ROK) modeling approaches for catalytic oligomerization in shale gas processing. We assemble a library of six candidate ROK models based on literature and MK model structure. We find that three metrics—quality of fit (e.g., mean squared logarithmic error), thermodynamic consistency (e.g., low conversion of exothermic reactions at high temperatures), and model identifiability—are all necessary to train and select ROK models. The ROK models that closely mimic the structure of the MK model offer the best compromise to emulate the product distribution. Using the four best ROK models, we optimize the temperature profiles in staged reactors to maximize conversions to heavier oligomerization products. The optimal temperature starts at 630–900K and monotonically decreases to approximately 560 K in the final stage, depending on the choice of ROK model. For all models, staging increases heavier olefin production by 2.5% and there is minimal benefit to more than four stages. The choice of ROK model, i.e., model-form uncertainty, results in a 22% difference in the objective function, which is twice the impact of parametric uncertainty; we demonstrate sequential eigendecomposition of the Fisher information matrix to identify and fix sloppy model parameters, which allows for more reliable estimation of the covariance of the identifiable calibrated model parameters. First-order uncertainty propagation determines this parametric uncertainty induces less than a 10% variability in the reactor optimization objective function. This result highlights the importance of quantifying model-form uncertainty, in addition to parametric uncertainty, in multi-scale reactor and process design and optimization. Moreover, the fast dynamic optimization solution times suggest the ROK strategy is suitable for incorporating molecular information in sequential modular or equation-oriented process simulation and optimization frameworks.

Wicking in Porous Polymeric Membranes: Determination of an Effective Capillary Radius to Predict the Flow Behavior in Lateral Flow Assays

The working principle of lateral flow assays, such as the widely used COVID-19 rapid tests, is based on the capillary-driven liquid transport of a sample fluid to a test line using porous polymeric membranes as the conductive medium. In order to predict this wicking process by simplified analytical models, it is essential to determine an effective capillary radius for the highly porous and open-pored membranes. In this work, a parametric study is performed with selected simplified structures, representing the complex microstructure of the membrane. For this, a phase-field approach with a special wetting boundary condition to describe the meniscus formation and the corresponding mean surface curvature for each structure setup is used. As a main result, an analytical correlation between geometric structure parameters and an effective capillary radius, based on a correction factor, are obtained. The resulting correlation is verified by applying image analysis methods on reconstructed computer tomography scans of two different porous polymeric membranes and thus determining the geometric structure parameters. Subsequently, a macroscale flow model that includes the correlated effective pore size and geometrical capillary radius is applied, and the results are compared with wicking experiments. Based on the derived correction function, it is shown that the analytical prediction of the wicking process in highly porous polymeric membranes is possible without the fitting of experimental wicking data. Furthermore, it can be seen that the estimated effective pore radius of the two membranes is 8 to 10 times higher than their geometric mean pore radii.

The difference between semi-continuum model and Richards' equation for unsaturated porous media flow

Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach is similar to the hybrid/multiscale modelling. Semi-continuum model is able to physically correctly describe diffusion-like flow, finger-like flow, and the transition between them. This article presents the limit of the semi-continuum model as the block size goes to zero. In the limiting process, the retention curve of each block scales with the block size and in the limit becomes a hysteresis operator of the Prandtl-type used in elasto-plasticity models. Mathematical analysis showed that the limit of the semi-continuum model is a hyperbolic-parabolic partial differential equation with a hysteresis operator of Prandl’s type. This limit differs from the standard Richards’ equation, which is a parabolic equation and is not able to describe finger-like flow.

Multiscale modeling of gas flow behaviors in nanoporous shale matrix considering multiple transport mechanisms

This study proposes a multiscale model combining molecular simulation and the lattice Boltzmann method (LBM) to explore gas flow behaviors with multiple transport mechanisms in nanoporous media of shale matrix. The gas adsorption characteristics in shale nanopores are first investigated by molecular simulations, which are then integrated and upscaled into the LBM model through a local adsorption density parameter. In order to adapt to high Knudsen number and nanoporous shale matrix, a multiple-relaxation-time pore-scale LBM model with a regularization procedure is developed. The combination of bounce-back and full diffusive boundary condition is adopted to take account of gas slippage and surface diffusion induced by gas adsorption. Molecular simulation results at the atomic scale show that gas adsorption behaviors are greatly affected by the pressure and pore size of the shale organic nanopore. At the pore scale, the gas transport behaviors with multiple transport mechanisms in nanoporous shale matrix are explored by the developed multiscale model. Simulation results indicate that pressure exhibits more significant influences on the transport behaviors of shale gas than temperature does. Compared with porosity, the average pore size of nanoporous shale matrix plays a more significant role in determining the apparent permeability of gas transport. The roles of the gas adsorption layer and surface diffusion in shale gas transport are discussed. It is observed that under low pressure, the gas adsorption layer has a positive influence on gas transport in shale matrix due to the strong surface diffusion effect. The nanoporous structure with the anisotropy characteristic parallel to the flow direction can enhance gas transport in shale matrix. The obtained results may provide underlying and comprehensive understanding of gas flow behaviors considering multiple transport mechanisms in shale matrix. Also, the proposed multiscale model can be considered as a powerful tool to invesigate the multiscale and multiphysical flow behaviors in porous media.

Lattice Boltzmann method for adsorption under stationary and transient conditions: Interplay between transport and adsorption kinetics in porous media

A numerical method based on the Lattice Boltzmann formalism is presented to capture the effect of adsorption kinetics on transport in porous media. Through the use of a general adsorption operator, canonical models such as Henry and Langmuir adsorption as well as more complex adsorption mechanisms involving collective behavior with lateral interactions and surface aggregation can be investigated using this versatile model. By extending the description of adsorption phenomena to kinetic regimes with any underlying adsorption model, this effective technique allows assessing the coupled dynamics resulting from advection, diffusion, and adsorption in pores not only in stationary conditions but also under transient conditions (i.e., in regimes where the adsorbed amount evolves with time due to diffusion and advection). As illustrated in this paper, the development of such an approach provides a simple tool to determine the reciprocal effect of molecular flow and dispersion on adsorption kinetics. In this context, the use of a Lattice Boltzmann-based approach is important as it allows considering porous media of any morphology and topology. Beyond fundamental implications, this efficient method allows treating real engineering conditions such as pollutant dispersion or surfactant injection in a flowing liquid in soils and porous rocks.

Wettability and capillary effects: Dynamics of pinch-off in unconstricted straight capillary tubes

We study the interfacial evolution of immiscible two-phase flow within a capillary tube in the partial wetting regime using direct numerical simulation. We investigate the flow patterns resulting from the displacement of a more viscous fluid by a less viscous one under a wide range of wettability conditions. We find that beyond a wettability dependent critical capillary number, a uniform displacement by a less viscous fluid can transition into a growing finger that eventually breaks up into discrete blobs by a series of pinch-off events for both wetting and nonwetting contact angles. This study validates previous experimental observations of pinch-off for wetting contact angles and extends those to nonwetting contact angles. We find that the blob length increases with the capillary number. We observe that the time between consecutive pinch-off events decreases with the capillary number and is greater for more wetting conditions in the displaced phase. We further show that the blob separation distance as a function of the difference between the inlet velocity and the contact line speed collapses into two monotonically decreasing curves for wetting and nonwetting contact angles. For the phase separation in the form of pinch-off, this work provides a quantitative study of the emerging length and timescales and their dependence on the wettability conditions, capillary effects, and viscous forces.

A multi-scale model for fluid transport through a bio-inspired passive valve

Tillandsia landbeckii is a rootless plant thriving in the hyper-arid Atacama Desert of Chile. These plants use unique cellulose-based microscopic structures called trichomes to collect fresh water from coastal fog. The trichomes rely on a passive mechanism to maintain an asymmetrical transport of water: they allow for the fast absorption of liquid water deposited by sporadic fog events while preventing evaporation during extended drought periods. Inspired by the trichome's design, we study fluid transport through a micrometric valve. Combining Grand Canonical Monte Carlo with Non-Equilibrium Molecular Dynamics simulations, we first analyze the adsorption and transport of a fluid through a single nanopore at different chemical potentials. We then scale up the atomic results using a lattice approach, and simulate the transport at the micrometric scale. Results obtained for a model Lennard-Jones fluid and TIP4P/2005 water were compared, allowing us to identify the key physical parameters for achieving a passive hydraulic valve. Our results show that the difference in transport properties of water vapor and liquid water within the cellulose layer is the basis for the ability of the Tillandsia trichome to function as a water valve. Finally, we predict a critical pore dimension above which the cellulose layer can form an efficient valve.

Impact of Nanoporosity on Hydrocarbon Transport in Shales' Organic Matter

In a context of growing attention for shale gas, the precise impact of organic matter (kerogen) on hydrocarbon recovery from unconventional reservoirs still has to be assessed. Kerogen's microstructure is characterized by a very disordered pore network that greatly affects hydrocarbon transport. The specific structure and texture of this organic matter at the nanoscale is highly dependent on its origin. In this study, by the use of statistical physics and molecular dynamics, we shed some new lights on hydrocarbon transport through realistic molecular models of kerogen at different level of maturity [ Bousige et al. Nat. Mater. 2016 , 15 , 576 ]. Despite the apparent complexity, severe confinement effects controlled by the porosity of the various kerogens allow linear alkanes (from methane to dodecane) transport to be studied only via the self-diffusion coefficients of the species. The decrease of the transport coefficients with the amount of adsorbed fluid can be described by a free volume theory. Ultimately, the transport coefficients of hydrocarbons can be expressed simply as a function of the porosity (volume fraction of void) of the microstructure, thus paving the way for shale gas recovery predictions.

Kinetic Accessibility of Porous Material Adsorption Sites Studied through the Lattice Boltzmann Method

We present here a computational model based on the lattice Boltzmann scheme to investigate the accessibility of active adsorption sites in hierarchical porous materials to adsorbates in a flowing liquid. By studying the transport and adsorption of tracers after they enter the pore space of the virtual sample, we characterize their kinetics as they pass through the pore space and adsorb on the solid-liquid interface. The model is validated on simple geometries with a known analytical solution. We then use it to investigate the influence of regular grooves or disordered roughness on the walls of a slit pore geometry, looking at the impact on adsorption and transport. In particular, we highlight the importance of adsorption site accessibility, which depends on the shape and connectivity of the pore space as well as the fluid flow profile and velocity.

Transport and adsorption under liquid flow: the role of pore geometry

We study here the interplay between transport and adsorption in porous systems with complex geometries under fluid flow. Using a lattice Boltzmann scheme extended to take into account the adsorption at solid/fluid interfaces, we investigate the influence of pore geometry and internal surface roughness on the efficiency of fluid flow and the adsorption of molecular species inside the pore space. We show how the occurrence of roughness on pore walls acts effectively as a modification of the solid/fluid boundary conditions, introducing slippage at the interface. We then compare three common pore geometries, namely honeycomb pores, inverse opal, and materials produced by spinodal decomposition. Finally, we quantify the influence of those three geometries on fluid transport and tracer adsorption. This opens perspectives for the optimization of materials' geometries for applications in dynamic adsorption under fluid flow.

Free Volume Theory of Hydrocarbon Mixture Transport in Nanoporous Materials

Despite recent focus on shale gas, hydrocarbon recovery from the ultraconfining and disordered porosity of organic matter in shales (kerogen) remains poorly understood. Key aspects such as the breakdown of hydrodynamics at the nanoscale and strong adsorption effects lead to unexplained non-Darcy behaviors. Here, molecular dynamics and statistical mechanics are used to elucidate hydrocarbon mixture transport through a realistic molecular model of kerogen [ Bousige, C.; et al. Nat. Mater. 2016 , 15 , 576 ]. Owing to strong adsorption effects, velocity cross-correlations between the mixture components and between molecules of the same species are shown to be negligible. This allows estimation of each component permeance from its self-diffusivity, which can be obtained from single-component data. These permeances are found to scale with the reciprocal of the alkane length and decrease with the number of adsorbed molecules following a simple free volume theory, therefore allowing mixture transport prediction as a function of the amount of trapped fluid.

Multiscale adsorption and transport in hierarchical porous materials

This review presents the state-of-the-art of multiscale adsorption and transport in hierarchical porous materials.

Unexpected coupling between flow and adsorption in porous media

We study the interplay between transport and adsorption in porous systems under a fluid flow, based on a lattice Boltzmann scheme extended to account for adsorption. We performed simulations on well-controlled geometries with slit and grooved pores, investigating the influence of adsorption and flow on dispersion coefficient and adsorbed density. In particular, we present a counterintuitive effect where fluid flow induces heterogeneity in the adsorbate, displacing the adsorption equilibrium towards downstream adsorption sites in grooves. We also present an improvement of the adsorption-extended lattice Boltzmann scheme by introducing the possibility for saturating Langmuir-like adsorption, while earlier work focused on linear adsorption phenomena. We then highlight the impact of this change in situations of high concentration of adsorbate.