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A micro-continuum approach is proposed to simulate the dissolution of solid minerals at the pore scale under single-phase flow conditions. The approach employs a Darcy–Brinkman–Stokes formulation and locally averaged conservation laws combined with immersed boundary conditions for the chemical reaction at the solid surface. The methodology compares well with the arbitrary-Lagrangian–Eulerian technique. The simulation framework is validated using an experimental microfluidic device to image the dissolution of a single calcite crystal. The evolution of the calcite crystal during the acidizing process is analysed and related to the flow conditions. Macroscopic laws for the dissolution rate are proposed by upscaling the pore-scale simulations. Finally, the emergence of wormholes during the injection of acid in a two-dimensional domain of calcite grains is discussed based on pore-scale simulations.

We develop a probabilistic approach to map parametric uncertainty to output state uncertainty in first‐order hyperbolic conservation laws. We analyze this problem for nonlinear immiscible two‐phase transport in heterogeneous porous media in the presence of a stochastic velocity field. The uncertainty in the velocity field can arise from incomplete descriptions of either porosity field, injection flux, or both. This uncertainty leads to spatiotemporal uncertainty in the saturation field. Given information about spatial/temporal statistics of spatially correlated heterogeneity, we leverage the method of distributions to derive deterministic equations that govern the evolution of pointwise cumulative distribution functions (CDFs) of saturation for a vertical reservoir, while handling the manipulation of multiple shocks arising due to buoyancy forces. Unlike the Buckley‐Leverett equation, the equation describing the fine‐grained CDF is linear in space and time. Ensemble averaging of the fine‐grained CDF results in the CDF of saturation. Thus, we give routes to circumventing the computational cost of Monte Carlo simulations (MCS), while obtaining a pointwise description of the saturation field. We conduct a set of numerical experiments for one‐dimensional transport, and compare the obtained saturation CDFs, against those obtained using MCS as our reference solution, and the statistical moment equation method. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties, that is, standard deviation and correlation length of the underlying random fields, whereas the corresponding low‐order statistical moment equations significantly deviate from the MCS results, except for very small values of standard deviation and correlation length. Key Points Our cumulative distribution function method provides pointwise probabilistic descriptions of two‐phase transport, handling multiple shocks arising due to buoyancy forces Our results match Monte Carlo (MC) simulations and statistical moment equations for a wide range of statistical properties of the random inputs The numerical comparisons confirm the robustness and efficiency of our method over MC simulations and statistical moment equations

Geological carbon dioxide (CO2) storage is a means of reducing anthropogenic emissions. Dissolution of CO2 into the brine, resulting in stable stratification, increases storage security. The dissolution rate is determined by convection in the brine driven by the increase of brine density with CO2 saturation. We present a new analogue fluid system that reproduces the convective behaviour of CO2‐enriched brine. Laboratory experiments and high‐resolution numerical simulations show that the convective flux scales with the Rayleigh number to the 4/5 power, in contrast with a classical linear relationship. A scaling argument for the convective flux incorporating lateral diffusion from downwelling plumes explains this nonlinear relationship for the convective flux, provides a physical picture of high Rayleigh number convection in a porous medium, and predicts the CO2 dissolution rates in CO2 accumulations. These estimates of the dissolution rate show that convective dissolution can play an important role in enhancing storage security.

The paper presents a novel approach for uncertainty propagation in multicomponent two-phase displacements. This approach originates from and extends the frozen streamlines (FROST) distribution method for two-phase Buckley–Leverett displacements described in Ibrahima et al. (Transp Porous Media 109(1):81–107, 2015). The developed FROST method for multicomponent systems relies on the analytical solutions of gas–oil displacements provided by the theory of gas injection processes. With examples considering a stochastic porosity field in 1-D, we apply the developed framework to uncertainty propagation in three- and four-component systems to obtain the probability distribution of different compositions in space and time and verify that the results are in excellent agreement with the reference analytical Monte Carlo simulations.

The enormous growth in computational capabilities of recent years has made Navier–Stokes-based simulation of flow and transport in natural porous media possible. Because of the complex multiscale nature of porous media, however, full Navier–Stokes representation of the physics everywhere in the domain is not always feasible. Here, we employ, a filtering—or micro-continuum—approach to model the smallest length scales. The Darcy–Brinkman–Stokes (DBS) equation offers an appealing framework for this hybrid modeling. A general modeling framework based on the DBS equation is proposed. The approach is then used to bridge the gap between scales for several challenging problems, including flow in fractured media, pore-scale simulation with immersed boundary conditions, modeling of dissolution phenomena, and thermal evolution of oil shale.

A micro-continuum simulation framework is proposed to study the complex pore-scale dynamics associated with hydrocarbon recovery from shale gas. The model accounts for the presence of immiscible fluid phases and for transport mechanisms in the nanoporous structures including slip flow, adsorption, surface and Knudsen diffusion. We employ the concept of sub-grid models to simulate the transport phenomena in shale gas. Specifically, we use high-resolution FIB–SEM images that provide information on the spatial distribution of the minerals, resolved pore space, and sub-resolution porous regions. The model is used to investigate several production scenarios at the pore-scale. In one setting, the organic matter is in direct contact with a micro-crack; in the other setting, clay regions are sandwiched between the organic matter and the “open” crack. The simulations show that it is important to account for the presence of multiple immiscible fluid phases because they can play a critical role in hydrocarbon production from shale-gas formations both in terms of production rate and in terms of residual mass of hydrocarbon. Moreover, we show that, because of wettability conditions, the rate of hydrocarbon recovery, as well as the ultimate recovery, depends strongly on the spatial distribution of the kerogen and clay in the vicinity of the micro-cracks.

There is growing interest in using advanced imaging techniques to describe the complex pore-space of natural rocks at resolutions that allow for quantitative assessment of the flow and transport behaviors in these complex media. Here, we focus on representations of the complex pore-space obtained from X-ray microtomography and the subsequent use of such ‘pore-scale’ representations to characterize the overall porosity and permeability of the rock sample. Specifically, we analyze the impact of sub-resolution porosity on the macroscopic (Darcy scale) flow properties of the rock. The pore structure of a rock sample is obtained using high-resolution X-ray microtomography ( 3 . 16 3 μ m 3 / voxel ) . Image analysis of the Berea sandstone sample indicates that about 2 % of the connected porosity lies below the resolution of the instrument. We employ a Darcy–Brinkman approach, in which a Darcy model is used for the sub-resolution porosity, and the Stokes equation is used to describe the flow in the fully resolved pore-space. We compare the Darcy–Brinkman numerical simulations with core flooding experiments, and we show that proper interpretation of the sub-resolution porosity can be essential in characterizing the overall permeability of natural porous media.

Scale analysis of unstable density-driven miscible convection in porous media is performed. The main conclusions for instabilities in the developed (long time scales) regime are that (i) large-scale structures are responsible for the bulk of the production of concentration variance, (ii) variance dissipation is dominated by the small (diffusive) scales and that (iii) both the production and dissipation rates are independent of the Rayleigh number. These findings provide a strong basis for a new modelling approach, namely, large-mode simulation (LMS), for which closure is achieved by replacing the actual diffusivity with an effective one. For validation, LMS results for vertical flow in a homogeneous rectangular domain are compared with direct numerical simulations (DNS). Some of the analysis is based on the derivation and closure of the concentration mean and variance equations, whereby averaging over the ensemble of all possible initial perturbations is considered. While self-similar solutions are obtained for vertical, statistically one-dimensional fingering, triple correlation of concentration and scalar dissipation rate (rate at which the concentration variance decays due to diffusion) have to be modelled in the general case. For this purpose, an ensemble-averaged Darcy modelling (EADM) approach is proposed.

This manuscript presents a benchmark problem for the simulation of single-phase flow, reactive transport, and solid geometry evolution at the pore scale. The problem is organized in three parts that focus on specific aspects: flow and reactive transport (part I), dissolution-driven geometry evolution in two dimensions (part II), and an experimental validation of three-dimensional dissolution-driven geometry evolution (part III). Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex, and dissolFoam. These codes cover a good portion of the wide range of approaches typically employed for solving pore-scale problems in the literature, including discretization methods, characterization of the fluid-solid interfaces, and methods to move these interfaces as a result of fluid-solid reactions. A short review of these approaches is given in relation to selected published studies. Results from the simulations performed by the five codes show remarkable agreement both quantitatively—based on upscaled parameters such as surface area, solid volume, and effective reaction rate—and qualitatively—based on comparisons of shape evolution. This outcome is especially notable given the disparity of approaches used by the codes. Therefore, these results establish a strong benchmark for the validation and testing of pore-scale codes developed for the simulation of flow and reactive transport with evolving geometries. They also underscore the significant advances seen in the last decade in tools and approaches for simulating this type of problem.

X-ray micro-computed tomography (X-ray micro-CT) is widely employed to investigate flow phenomena in porous media, providing a powerful alternative to core-scale experiments for estimating traditional petrophysical properties such as porosity, single-phase permeability or fluid connectivity. However, the segmentation process, critical for deriving these properties from greyscale images, varies significantly between studies due to the absence of a standardized workflow or any ground truth data. This introduces challenges in comparing results across different studies, especially for properties sensitive to segmentation. To address this, we present a fully open-source, automated workflow for the segmentation of a Bentheimer sandstone filled with nitrogen and brine. The workflow incorporates a traditional image processing pipeline, including non-local means filtering, image registration, watershed segmentation of grains, and a combination of differential imaging and thresholding for segmentation of the fluid phases. Our workflow enhances reproducibility by enabling other research groups to easily replicate and validate findings, fostering consistency in petrophysical property estimation. Moreover, its modular structure facilitates integration into modeling frameworks, allowing for forward-backward communication and parameter sensitivity analyses. We apply the workflow to exploring the sensitivity of the non-wetting phase volume, surface area, and connectivity to image processing. This adaptable tool paves the way for future advancements in X-ray micro-CT analysis of porous media.