Machine learning to predict effective reaction rates in 3D porous media from pore structural features

Large discrepancies between well-mixed reaction rates and effective reactions rates estimated under fluid flow conditions have been a major issue for predicting reactive transport in porous media systems. In this study, we introduce a framework that accurately predicts effective reaction rates directly from pore structural features by combining 3D pore-scale numerical simulations with machine learning (ML). We first perform pore-scale reactive transport simulations with fluid–solid reactions in hundreds of porous media and calculate effective reaction rates from pore-scale concentration fields. We then train a Random Forests model with 11 pore structural features and effective reaction rates to quantify the importance of structural features in determining effective reaction rates. Based on the importance information, we train artificial neural networks with varying number of features and demonstrate that effective reaction rates can be accurately predicted with only three pore structural features, which are specific surface, pore sphericity, and coordination number. Finally, global sensitivity analyses using the ML model elucidates how the three structural features affect effective reaction rates. The proposed framework enables accurate predictions of effective reaction rates directly from a few measurable pore structural features, and the framework is readily applicable to a wide range of applications involving porous media flows.

Lattice Boltzmann model with generalized wall boundary conditions for arbitrary catalytic reactivity

A lattice Boltzmann model for multispecies flows with catalytic reactions is developed, which is valid from very low to very high surface Damköhler numbers (Da_{s}). The previously proposed model for catalytic reactions [S. Arcidiacono, J. Mantzaras, and I. V. Karlin, Phys. Rev. E 78, 046711 (2008)PLEEE81539-375510.1103/PhysRevE.78.046711], which is applicable for low-to-moderate Da_{s} and encompasses part of the mixed kinetics and transport-controlled regime, is revisited and extended for the simulation of arbitrary kinetics-to-transport rate ratios, including strongly transport-controlled conditions (Da_{s}→∞). The catalytic boundary condition is modified by bringing nonlocal information on the wall reactive nodes, allowing accurate evaluation of chemical rates even when the concentration of the deficient reactant at the wall becomes vanishingly small. The developed model is validated against a finite volume Navier-Stokes CFD (Computational Fluid Dynamics) solver for the total oxidation of methane in an isothermal channel-flow configuration. CFD simulations and lattice Boltzmann simulations with the old and new catalytic reaction models are compared against each other. The new model demonstrates a second order accuracy in space and time and provides accurate results at very high Da_{s} (∼10^{9}) where the old model fails. Moreover, to achieve the same accuracy at moderate-to-high Da_{s} of O(1), the new model requires ∼2^{d}×N coarser grid than the original model, where d is the spatial dimension and N the number of species.

3-D Modelling and Experimental Comparison of Reactive Flow in Carbonates under Radial Flow Conditions

We use a two-scale continuum model to simulate reactive flow and wormhole formation in carbonate rocks under 3-D radial flow conditions. More specifically, we present a new structure-property relationship based on the fractal geometry theory, to describe the evolution of local permeability, pore radius, and specific area with porosity variation. In the numerical calculation, to improve the convergence rate, the heterogeneous medium in question is extended by adding a thin layer of homogeneous porous medium to its inlet. We compare the simulation results with the available experimental observations and find that they are qualitatively consistent with each other. Additionally, sensitivity analysis of the dissolution process with respect to acid injection rate and rock heterogeneity, including heterogeneity magnitude and correlation length, is presented.

Pore-scale simulations of concentration tails in heterogeneous porous media

The retention of contaminants in the finest and less-conductive regions of natural aquifer is known to strongly affect the decontamination of polluted aquifers. In fact, contaminant transfer from low to high mobility regions at the back end of a contaminant plume (i.e. back diffusion) is responsible for the long-term release of contaminants during remediation operation. In this paper, we perform pore-scale calculations for the transport of contaminant through heterogeneous porous media composed of low and high mobility regions with two objectives: (i) study the effect of permeability contrast and solute transport conditions on the exchange of solutes between mobile and immobile regions and (ii) estimate the mass of contaminants sequestered in low mobility regions based on concentration breakthrough curves.

Scaling up adsorption media reactors for copper removal with the aid of dimensionless numbers

Adsorption media may be used to sorb copper in an aquatic environment for pollution control. Effective design of adsorption media reactors is highly dependent on selection of the hydraulic residence time when scaling up a pilot-scale reactor to a field-scale reactor. This paper seeks to improve scaling-up technique of the reactor design process through the use of the Damköhler and Péclet numbers via a dimensional analysis. A new scaling-up theory is developed in this study through a joint consideration of the Damköhler and Péclet numbers for a constant media particle size such that a balance between transport control and reaction control can be harmonized. A series of column breakthrough tests at varying hydraulic residence times revealed a clear peak adsorption capacity at a Damköhler number of 2.74. The Péclet numbers for the column breakthrough tests indicated that mechanical dispersion is an important effect that requires further consideration in the scaling-up process. However, perfect similitude of the Damköhler number cannot be maintained for a constant media particle size, and relaxation of hydrodynamic similitude through variation of the Péclet number must occur.

Pore-scale study of transverse mixing induced CaCO₃ precipitation and permeability reduction in a model subsurface sedimentary system

A microfluidic pore structure etched into a silicon wafer was used as a two-dimensional model subsurface sedimentary system (i.e., micromodel) to study mineral precipitation and permeability reduction relevant to groundwater remediation and geological carbon sequestration. Solutions containing CaCl(2) and Na(2)CO(3) at four different saturation states (Ω = [Ca(2+)][CO(3)(2-)]/K(spCaCO(3))) were introduced through two separate inlets, and they mixed by diffusion transverse to the main flow direction along the center of the micromodel resulting in CaCO(3) precipitation. Precipitation rates increased and the total amount of precipitates decreased with increasing saturation state, and only vaterite and calcite crystals were formed (no aragonite). The relative amount of vaterite increased from 80% at the lowest saturation state (Ω(v) = 2.8 for vaterite) to 95% at the highest saturation state (Ω(v) = 4.5). Fluorescent tracer tests conducted before and after CaCO(3) precipitation indicate that pore spaces were occluded by CaCO(3) precipitates along the transverse mixing zone, thus substantially reducing porosity and permeability, and potentially limiting transformation from vaterite to the more stable calcite. The results suggest that mineral precipitation along plume margins can decrease both reactant mixing during groundwater remediation, and injection and storage efficiency during CO(2) sequestration.

Mesoscopic simulations of phase distribution effects on the effective thermal conductivity of microgranular porous media

This paper analyzes the phase distribution effects on the effective thermal conductivity (ETC) of multi-phase microgranular porous media using mesoscopic statistics based numerical methods. A multi-parameter random generation-growth method, quartet structure generation set (QSGS), is developed for replicating microstructures of multi-phase granular porous media based on the macroscopic statistical information, such as the volume fractions and the phase interactions. The phase distribution characteristics and the interphase connections are controlled by adjusting the related parameters. Then the energy transport equations through porous media are solved by a lattice Boltzmann method developed by us with multi-phase conjugate heat transfer considered. The results indicate that a smaller average particle size could lead to a larger effective thermal conductivity of two-phase porous media for a certain porosity. For the anisotropic media, if the larger directional growth probability is along the direction of temperature gradient, the effective thermal conductivity in the parallel direction is enhanced as a result, and that in the vertical direction will be weakened. For multi-phase porous media, the degree of phase conglomeration is determined by the phase interactions. A larger liquid-liquid interaction leads to a higher degree of liquid phase conglomeration and therefore a larger effective thermal conductivity of the porous media.

Mesoscopic predictions of the effective thermal conductivity for microscale random porous media

A mesoscopic numerical tool has been developed in this study for predictions of the effective thermal conductivities for microscale random porous media. To solve the energy transport equation with complex multiphase porous geometries, a lattice Boltzmann algorithm has been introduced to tackle the conjugate heat transfer among different phases. With boundary conditions correctly chosen, the algorithm has been initially validated by comparison with theoretical solutions for simpler cases and with the existing experimental data. Furthermore, to reflect the stochastic phase distribution characteristics of most porous media, a random internal morphology and structure generation-growth method, termed the quartet structure generation set (QSGS), has been proposed based on the stochastic cluster growth theory for generating more realistic microstructures of porous media. Thus by using the present lattice Boltzmann algorithm along with the structure generating tool QSGS, we can predict the effective thermal conductivities of porous media with multiphase structure and stochastic complex geometries, without resorting to any empirical parameters determined case by case. The methodology has been applied in this contribution to several two- and three-phase systems, and the results agree well with published experimental data, thus demonstrating that the present method is rigorous, general, and robust. Besides conventional porous media, the present approach is applicable in dealing with other multiphase mixtures, alloys, and multicomponent composites as well.