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Using X-ray computed microtomography, we have visualized and quantified the in situ structure of a trapped nonwetting phase (oil) in a highly heterogeneous carbonate rock after injecting a wetting phase (brine) at low and high capillary numbers. We imaged the process of capillary desaturation in 3D and demonstrated its impacts on the trapped nonwetting phase cluster size distribution. We have identified a previously unidentified pore-scale event during capillary desaturation. This pore-scale event, described as droplet fragmentation of the nonwetting phase, occurs in larger pores. It increases volumetric production of the nonwetting phase after capillary trapping and enlarges the fluid−fluid interface, which can enhance mass transfer between the phases. Droplet fragmentation therefore has implications for a range of multiphase flow processes in natural and engineered porous media with complex heterogeneous pore spaces. Significance Fluid displacement processes in carbonate rocks are important because they host over 50% of the world's hydrocarbon reserves and are aquifers supplying water to one quarter of the global population. A previously unidentified pore-scale fluid displacement event, droplet fragmentation, is described that occurs during the flow of two immiscible fluids specifically in carbonate rocks. The complex, heterogeneous pore structure of carbonate rocks induces this droplet fragmentation process, which explains the increased recovery of the nonwetting phase from porous carbonates as the wetting phase injection rate is increased. The previously unidentified displacement mechanism has implications for ( i ) enhanced oil recovery, ( ii ) remediation of nonaqueous liquid contaminants in aquifers, and ( iii ) subsurface CO ₂ storage.

This study investigates the impact of pore network characteristics on fluid flow through complex and heterogeneous porous media, providing insights into the factors affecting fluid propagation in such systems. Specifically, high-resolution or micro X-ray computed tomography (CT) imaging techniques were utilized to examine outcrop stromatolite samples of the Lagoa Salgada, considered flow analogous to the Brazilian Pre-salt carbonate reservoirs. The petrophysical results comprised two distinct stromatolite depositional facies, the columnar and the fine-grained facies. By generating pore network model (PNM), the study quantified the relationship between key features of the porous system, including pore and throat radius, throat length, coordination number, shape factor, and pore volume. The study found that the less dense pore network of the columnar sample is typically characterized by larger pores and wider and longer throats but with a weaker connection of throats to pores. Both facies exhibited less variability in the radius of the pores and throats in comparison to throat length. Additionally, a series of core flooding experiments coupled with medical CT scanning was designed and conducted in the plug samples to assess flow propagation and saturation fields. The study revealed that the heterogeneity and presence of disconnected or dead-end pores significantly impacted the flow patterns and saturation. Two-phase flow patterns and oil saturation distribution reveal a preferential and heterogeneous displacement that mainly swept displaced fluid in some regions of plugs and bypassed it in others. The relation between saturation profiles, porosity profiles, and the number of fluid flow patterns for the samples was evident. Only for the columnar plug sample was the enhancement in recovery factor after shifting to lower salinity water injection (SB) observed. •Investigating the impact of pore network characteristics on flow through heterogeneous porous media•Generating Pore Network Model (PNM) and quantifying the relationship between key features of the porous system using high-resolution CT scanning•Quantifiying the relationship between key features of the pore network for the complex porous system•Core flooding experiments coupled with medical CT scanning to assess flow patterns and oil saturation distribution

Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep learning to accelerate solute transport simulation. We employ Physics-informed Neural Networks (PiNN) with a periodic activation function to solve solute transport problems in both homogeneous and heterogeneous porous media governed by the advection-dispersion equation. Unlike traditional neural networks that rely on large training datasets, PiNNs use strong-form mathematical models to constrain the network in the training phase and simultaneously solve for multiple dependent or independent field variables, such as pressure and solute concentration fields. To demonstrate the effectiveness of using PiNNs with a periodic activation function to resolve solute transport in porous media, we construct PiNNs using two activation functions, sin and tanh, for seven case studies, including 1D and 2D scenarios. The accuracy of the PiNNs’ predictions is then evaluated using absolute point error and mean square error metrics and compared to the ground truth solutions obtained analytically or numerically. Our results demonstrate that the PiNN with sin activation function, compared to tanh activation function, is up to two orders of magnitude more accurate and up to two times faster to train, especially in heterogeneous porous media. Moreover, PiNN’s simultaneous predictions of pressure and concentration fields can reduce computational expenses in terms of inference time by three orders of magnitude compared to FEM simulations for two-dimensional cases.

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

Miscible and near-miscible flooding are used to improve the performance of carbon-dioxide-enhanced oil recovery in heterogeneous porous media. However, knowledge of the effects of heterogeneous pore structure on CO2/oil flow behavior under these two flooding conditions is insufficient. In this study, we construct pore-scale CO2/oil flooding models for various flooding methods and comparatively analyze CO2/oil flow behavior and oil recovery efficiency in heterogeneous porous media. The simulation results indicate that compared to immiscible flooding, near-miscible flooding can increase the CO2 sweep area to some extent, but it is still inefficient to displace oil in small pore throats. For miscible flooding, although CO2 still preferentially displaces oil through big throats, it may subsequently invade small pore throats. In order to substantially increase oil recovery efficiency, miscible flooding is the priority choice; however, the increase of CO2 diffusivity has little effect on oil recovery enhancement. For immiscible and near-miscible flooding, CO2 injection velocity needs to be optimized. High CO2 injection velocity can speed up the oil recovery process while maintaining equivalent oil recovery efficiency for immiscible flooding, and low CO2 injection velocity may be beneficial to further enhancing oil recovery efficiency under near-miscible conditions.

CO2-enhanced oil recovery (CO2-EOR) has gained prominence as an effective oil displacement method with low carbon emissions, yet its microscopic mechanisms remain incompletely understood. This study introduces a novel high-pressure microfluidic visualization system capable of operating at 0.1–10 MPa without confining pressure and featuring stratified porous media with a 63 μm minimum throat size to provide unprecedented insights into CO2 and CO2-foam EOR processes at the microscale. Through quantitative image analysis and advanced machine learning modeling, we reveal that increasing the CO2 injection pressure nonlinearly reduces residual oil saturation, achieving near-complete miscibility at 6 MPa with only 2% residual oil—a finding that challenges conventional thresholds for miscibility in heterogeneous systems. Our work uniquely demonstrates that CO2-foam flooding not only mobilizes capillary-trapped oil films but also dynamically alters interfacial tension and the pore-scale fluid distribution, a phenomenon previously underexplored. Support Vector Regression (R2 = 0.71) further uncovers a nonlinear relationship between the surfactant concentration and residual oil saturation, offering a data-driven framework for parameter optimization. These results advance our fundamental understanding by bridging microscale dynamics with field-applicable insights, while the integration of machine learning with microfluidics represents a methodological leap for EOR research.

Investigating the diffusion characteristics of leaked crude oil in heterogeneous porous media is crucial for accurately predicting the location of oil leaks from buried pipelines, emergency response, and reducing the hazards of pipeline leakage accidents. This study establishes a leakage model for buried pipelines using computational fluid dynamics methods to simulate multiphase flow in porous media, focusing on the effects of different backfill soil porosities and leakage velocity on oil diffusion and temperature field evolution. Results reveal that the diffusion process consists of acceleration, transition, and stabilization phases. At a leakage velocity of 1 m/s, the oil reaches the surface in 169 s, while velocities of 2 m/s and 3 m/s reduce this to 77 s and 48 s, respectively. Higher leakage velocities significantly increase diffusion speed, with the volume fraction of crude oil in backfill soil reaching 75.68%, 91.90%, and 95.99% at 1 m/s, 2 m/s, and 3 m/s, respectively, after 180 s. The temperature field of the soil porous media after leakage is not sensitive to changes in backfill soil porosity, and the leakage rate is one of the main factors driving changes in the temperature field.

In this study, we propose a constraint learning strategy based on interpretability analysis to improve the convergence and accuracy of the enriched physics-informed neural network (EPINN), which is applied to simulate two-phase flow in heterogeneous porous media. Specifically, we first analyze the layerwise outputs of EPINN, and identify the distinct functions across layers, including dimensionality adjustment, pointwise construction of non-equilibrium potential, extraction of high-level features, and the establishment of long-range dependencies. Then, inspired by these distinct modules, we propose a novel constraint learning strategy based on regularization approaches, which improves neural network (NN) learning through layer-specific differentiated updates to enhance cross-timestep generalization. Since different neural network layers exhibit varying sensitivities to global generalization and local regression, we decrease the update frequency of layers more sensitive to local learning under this constraint learning strategy. In other words, the entire neural network is encouraged to extract more generalized features. The superior performance of the proposed learning strategy is validated through evaluations on numerical examples with varying computational complexities. Post hoc analysis reveals that gradient propagation exhibits more pronounced staged characteristics, and the partial differential equation (PDE) residuals are more uniformly distributed under the constraint guidance. Interpretability analysis of the adaptive constraint process suggests that maintaining a stable information compression mode facilitates progressive convergence acceleration.

The retention of contaminants within low-conductivity regions such as clay lenses and aquitards can greatly affect groundwater remediation processes. The aim of this study was to experimentally investigate the effects of the geometry of low-conductivity zones, conductivity contrast, and flow regime on solute flushing. We conducted a series of flushing tests in cylindrical models containing a cylindrical low-conductivity zone (i.e., low-K zone) embedded in a highly conductive medium (i.e., high-K zone). Seven models comprising four high-conductivity-contrast (SL, SS, LL, and LS), one medium-contrast (LLM), one low-contrast (LLL), and one homogeneous (H) models were considered. Experiments were conducted at two flow rates (Q = 0.6 and 26 cm3/min) for each heterogeneous model (SL, SS, LL, LS, LLM, and LLL) to compare the flushing processes in different flow regimes. First, we verified the validity of our experiments by comparing the results of the H model from an analytical solution with our experiment. The results of the high-contrast models showed that for a diffusion-dominated regime (Q = 0.6 cm3/min), the pore volume injected (PVI) required to flush out solute mass was much smaller than that in an advection-dominated regime (Q = 26 cm3/min). To evaluate the pore volumes required to flush out solutes for the four high-contrast models, we introduced a parameter P0.01, which is defined as the PVI needed for the relative concentration to become 0.01 at the middle of the low-K zone. P0.01 decreases with increasing the specific surface area of the low-K zone for diffusion-dominated regimes, while it increases with increasing the length of the low-K zone for advection-dominated regimes. We also determined the importance of the effect of K contrast on solute retention by comparing the results of three different models of K contrast (LL, LLM, and LLL).

In this paper, we study the dissolution of a porous formation made of soluble and insoluble materials with various types of Darcy-scale heterogeneities. Based on the assumption of scale separations, i.e., the convective and diffusive Damköhler numbers are smaller than certain limits which are documented in the paper, we apply large-scale upscaling to the Darcy-scale model to develop large-scale equations, which are used to describe the dissolution of porous formations with Darcy-scale heterogeneities. History-dependent closure problems are provided to get the effective parameters in the large-scale model. The large-scale model validity is tested by comparing numerical results for a 1D flow problem in a stratified system and a 2D flow problem in a nodular system to the Darcy-scale ones. The good agreement between results at Darcy and large scales shows the robustness of the large-scale model in representing the Darcy-scale results for the stratified system, even when the dissolution front is very sharp. Large-scale results for the nodular system represent satisfactorily the averaged Darcy-scale behaviors when the dissolution front is relatively thick, i.e., when model assumptions are satisfied, while there may be as expected some discrepancy generated between direct numerical simulations and large-scale results in the case of thin dissolution front. Overall, this study demonstrates the possibility of building a fully homogenized large-scale model incorporating dissolution history effects, and that the resulting large-scale model is capable to catch the main features of the Darcy-scale results within its applicability domain. Article highlights Large-scale model is developed for the dissolution of heterogeneous porous media, taking dissolution history effect into account. A sequential algorithm is proposed for the solution of effective mass exchange coefficient and effective permeability tensor. The large-scale model is validated for stratied and nodular systems.