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Abstract The impact of wettability on the co-moving velocity of two-fluid flow in porous media is analyzed herein. The co-moving velocity, developed by Roy et al. (Front Phys 8:4, 2022), is a novel representation of the flow behavior of two fluids through porous media. Our study aims to better understand the behavior of the co-moving velocity by analyzing simulation data under various wetting conditions. We analyzed 46 relative permeability curves based on the Lattice–Boltzmann color fluid model and two experimentally determined relative permeability curves. The analysis of the relative permeability data followed the methodology proposed by Roy et al. (Front Phys 8:4, 2022) to reconstruct a constitutive equation for the co-moving velocity. Surprisingly, the coefficients of the constitutive equation were found to be nearly the same for all wetting conditions. On the basis of these results, a simple approach was proposed to reconstruct the relative permeability of the oil phase using only the co-moving velocity relationship and the relative permeability of the water phase. This proposed method provides new information on the interdependence of the relative permeability curves, which has implications for the history matching of production data and the solution of the associated inverse problem. The research findings contribute to a better understanding of the impact of wettability on fluid flow in porous media and provide a practical approach for estimating relative permeability based on the co-moving velocity relationship, which has never been shown before. 

AbstractElectrokinetic in-situ recovery is an alternative to conventional mining, relying on the application of an electric potential to enhance the subsurface flow of ions. Understanding the pore-scale flow and ion transport under electric potential is essential for petrophysical properties estimation and flow behavior characterization. The governing physics of electrokinetic transport is electromigration and electroosmotic flow, which depend on the electric potential gradient, mineral occurrence, domain morphology (tortuosity and porosity, grain size and distribution, etc.), and electrolyte properties (local pH distribution and lixiviant type and concentration, etc.). Herein, mineral occurrence and its associated zeta potential are investigated for EK transport. The new Ek model which is designed to solve the EK flow in complex porous media in a highly parallelizable manner includes three coupled equations: (1) Poisson equation, (2) Nernst–Planck equation, and (3) Navier–Stokes equation. These equations were solved using the lattice Boltzmann method within X-ray computed microtomography images. The proposed model is validated against COMSOL multiphysics in a two-dimensional microchannel in terms of fluid flow behavior when the electrical double layer is both resolvable and unresolvable. A more complex chalcopyrite-silica system is then obtained by micro-CT scanning to evaluate the model performance. The effects of mineral occurrence, zeta potential, and electric potential on the three-dimensional chalcopyrite-silica system were evaluated. Although the positive zeta potential of chalcopyrite can induce a flow of ferric ion counter to the direction of electromigration, the net effect is dependent on the occurrence of chalcopyrite. However, the ion flux induced by electromigration was the dominant transport mechanism, whereas advection induced by electroosmosis made a lower contribution. Overall, a pore-scale EK model is proposed for direct simulation on pore-scale images. The proposed model can be coupled with other geochemical models for full physicochemical transport simulations. Meanwhile, electrokinetic transport shows promise as a human-controllable technique because the electromigration of ions and the applied electric potential can be easily controlled externally. Graphical abstract 

Abstract Various researchers have studied fluctuations in pore‐scale phase occupancy during multiphase flow in porous media using synchrotron‐based X‐ray microcomputed tomography (micro‐CT). However, the impact of these fluctuations on the concept of a representative volume is not yet fully understood. In this study, we performed spatial and temporal averaging of multiphase flow experiments visualized with synchrotron‐based micro‐CT, focusing on oil saturation as the key parameter to determine a representative time‐and‐space average. Our findings revealed that a saturation value representative of both time and space was achieved during fractional flow experiments in drainage mode with fractional flows of 0.8, 0.5, and 0.3. Furthermore, we computed a range of relative permeabilities on the basis of whether momentaneous saturation or time‐and‐space averaged saturation was utilized for direct simulation. Our results highlighted the importance of time‐and‐space averaging in determining a representative relative permeability and indicated that the temporal and spatial scales covered in a typical micro‐CT flow experiment were sufficient to obtain a representative saturation value for sandstone rock under intermittent flow conditions. 

Abstract Wettability is one of the critical parameters affecting multiphase flow in porous media. The wettability is determined by the affinity of fluids to the rock surface, which varies due to factors such as mineral heterogeneity, roughness, ageing, and pore-space geometry. It is well known that wettability varies spatially in natural rocks, and it is still generally considered a constant parameter in pore-scale simulation studies. The accuracy of pore-scale simulation of multiphase flow in porous media is undermined by such inadequate wettability models. The advent of in situ visualization techniques, e.g. X-ray imaging and microtomography, enables us to characterize the spatial distribution of wetting more accurately. There are several approaches for such characterization. Most include the construction of a meshed surface of the interface surfaces in a segmented X-ray image and are known to have significant errors arising from insufficient resolution and surface-smoothing algorithms. This work presents a novel approach for spatial determination of wetting properties using local lattice-Boltzmann simulations. The scheme is computationally efficient as the segmented X-ray image is divided into subdomains before conducting the lattice-Boltzmann simulations, enabling fast simulations. To test the proposed method, it was applied to two synthetic cases with known wettability and three datasets of imaged fluid distributions. The wettability map was obtained for all samples using local lattice-Boltzmann calculations on trapped ganglia and optimization on surface affinity parameters. The results were quantitatively compared with a previously developed geometrical contact angle determination method. The two synthetic cases were used to validate the results of the developed workflow, as well as to compare the wettability results with the geometrical analysis method. It is shown that the developed workflow accurately characterizes the wetting state in the synthetic porous media with an acceptable uncertainty and is better to capture extreme wetting conditions. For the three datasets of imaged fluid distributions, our results show that the obtained contact angle distributions are consistent with the geometrical method. However, the obtained contact angle distributions tend to have a narrower span and are considered more realistic compared to the geometrical method. Finally, our results show the potential of the proposed scheme to efficiently obtain wettability maps of porous media using X-ray images of multiphase fluid distributions. The developed workflow can help for more accurate characterization of the wettability map in the porous media using limited experimental data, and hence more accurate digital rock analysis of multiphase flow in porous media. 

Ion transport within saturated porous media is an intricate process in which efficient ion delivery is desired in many engineering problems. However, controlling the behavior of ion transport proves challenging, as ion transport is influenced by a variety of driving mechanisms, which requires a systematic understanding. Herein, we study a coupled advection–diffusion–electromigration system for controlled ion transport within porous media using the scaling analysis. Using the Lattice–Boltzmann–Poisson method, we establish a transport regime classification based on an Advection Diffusion Index (ADI) and a novel Electrodiffusivity Index (EDI) for a two-dimensional (2D) microchannel model under various electric potentials, pressure gradients, and concentration conditions. The resulting transport regimes can be well controlled by changing the applied electric potential, the pressure field, and the injected ions concentration. Furthermore, we conduct numerical simulations in a synthetic 2D porous media and an x-ray microcomputed tomography sandstone image to validate the prevailing transport regime. The simulation results highlight that the defined transport regime observed in our simple micromodel domain is also observed in the synthetic two- and three-dimensional domains, but the boundary between each transport regime differs depending on the variation of the pore size within a given domain. Consequently, the proposed ADI and EDI emerge as dimensionless indicators for controlled ion transport. Overall, our proof-of-concept for ion transport control in porous media is demonstrated under advection–diffusion–electromigration transport, demonstrating the richness of transport regimes that can develop and provide future research directions for subsurface engineering applications. 

This study aims to bridge length scales in immiscible multiphase flow simulation by connecting two published governing equations at the pore-scale and continuum-scale through a novel validation framework. We employ Niessner and Hassnaizadeh's [“A model for two-phase flow in porous media including fluid-fluid interfacial area,” Water Resour. Res. 44(8), W08439 (2008)] continuum-scale model for multiphase flow in porous media, combined with the geometric equation of state of McClure et al. [“Modeling geometric state for fluids in porous media: Evolution of the Euler characteristic,” Transp. Porous Med. 133(2), 229–250 (2020)]. Pore-scale fluid configurations simulated with the lattice-Boltzmann method are used to validate the continuum-scale results. We propose a mapping from the continuum-scale to pore-scale utilizing a generalized additive model to predict non-wetting phase Euler characteristics during imbibition, effectively bridging the continuum-to-pore length scale gap. Continuum-scale simulated measures of specific interfacial area, saturation, and capillary pressure are directly compared to up-scaled pore-scale simulation results. This research develops a numerical framework capable of capturing multiscale flow equations establishing a connection between pore-scale and continuum-scale simulations. 

Flow fluctuations that are commonly associated with multiphase flow in porous media are studied using concepts from non-equilibrium thermodynamic and statistical mechanics. We investigate how the Green–Kubo formulation of the fluctuation dissipation theorem can be used to predict the transport coefficient from the two-phase extension of Darcy's law. Flow rate-time series data are recorded at the millisecond timescale using a novel experimental setup that allows for the determination of flow fluctuation statistics. By using Green–Kubo relations, a transport coefficient is predicted based on the integrated autocorrelation function. Notably, this coefficient aligned closely with the total effective phase mobility computed using Darcy's equation for multiphase flow, particularly in scenarios where a linear relationship between flow rate and pressure gradient was observed. Our results open a new field of coefficient explorations where microscale fluctuations during multiphase flow are directly linked to macroscale parameters.