Flow In Porous Media Research Articles

Characterization of N2 foam flow with in-situ capillarypressure measurements in a high-permeability homogeneous sandpack: effect of surfactant concentration and flowrate

Determining the capillary pressure during foam flow in porous media is important because bubbles are thought to coalesce by lamella rupture as the "limiting capillary pressure" is approached. In this study, the role of surfactant concentration on capillary pressure and apparent viscosity of a foam flowing, at different flowrates, through porous media was explored. An in-house capillary-pressure probe was constructed, and it was utilized to characterize the capillary pressure of a foam flowing in a 145-Darcy homogenous sandpack. In-situ capillary pressures were determined for seven foam-quality-scan experiments with different gas velocities and surfactant concentrations. By comparing the test results, collected under different flowrates and surfactant concentrations, the apparent viscosity and the capillary pressure decreased for a quality greater than the transition foam quality, at the peak of apparent viscosity. The transition foam quality increases with increasing surfactant concentration and flow rate. For the slowest velocity, a minimum surfactant concentration is required to generate strong foam. While above this minimum surfactant concentration, foam-apparent viscosity is similar for different surfactant concentrations at the same velocity.

Gradient flows of interacting Laguerre cells as discrete porous media flows

Gradient flows of interacting Laguerre cells as discrete porous media flows

Gravity stabilized drainage in porous media with controlled disorder

This work presents an experimental, numerical, and theoretical investigation of slow drainage processes in porous media, focusing on systematic variations in pore-scale disorder. We examine a system comprising a monolayer of cylinders in a quasi-two-dimensional (2D) geometry, where the medium's disorder is controlled via a disorder parameter, ε. By systematically altering ε, we randomly shift the positions of the cylinders and analyze the resulting effects on the gravity stabilized invasion front. Our results show that increasing ε has a significant impact on the stable width of the invasion front, with this width scaling with the disorder parameter according to an exponent β=0.57, which closely matches the theoretical value predicted by percolation theory for 2D systems. Additionally, we derive a reciprocal relationship between the dimensionless fluctuation number and the disorder parameter ε. Moreover, we find a correlation between the invasion front width and the size of trapped clusters in the system, and we explore how pore disorder affects the air saturation left behind the invasion front. Both our experimental and numerical findings exhibit exponent values that align with theoretical scaling predictions. This study advances the current understanding of multiphase flows in porous media by specifically addressing the influence of pore-scale disorder on the morphology of invasion fronts. Published by the American Physical Society 2025

Microscopic simulations of oil–water two-phase flow in high-porosity and low-permeability carbonate porous media

The pore types in carbonate reservoirs are highly diverse, and a detailed characterization of the flow behavior of oil–water two-phase flow at the pore scale within different pore storage types holds significant importance. In this work, digital core reconstruction based on computed tomography scanning technology has quantitatively characterized the micro-pore structures of these rocks, and typical core samples representing diverse pore storage types have been selected for microscopic visualization simulation studies. Utilizing the volume of fluid method, we conducted visual simulations of oil–water two-phase flow in porous media. Comparisons were made under varying conditions of wettability, displacement pressure, and viscosity ratio regarding breakthrough time, residual oil distribution, and changes in residual oil saturation, revealing the dynamic flow characteristics of oil–water phases within different pore types during water flooding. The results demonstrate that complex pore-throat structures (large pores, small throats) significantly reduce the displacement efficiency during microscopic water flooding. Specifically, moldic pores exhibit high permeability, leading to oil phase retention; biological chamber pores (intraparticle pores) are characterized by the most pronounced high-porosity and low-permeability features, with numerous blind-end voids and poor connectivity, resulting in limited displacement effectiveness, whereas intergranular dissolution pores show good connectivity, achieving more efficient oil recovery. The mobility of the water phase among the three pore types follows the order: intergranular dissolution pores > moldic pores > biological chamber pores. Furthermore, improvements in wettability, increased displacement pressure, and reduced oil–water viscosity ratio serve to optimize the flow process at the microscopic level, thereby enhancing overall oil recovery efficiency.

Simulation on detachment and migration behaviors of mineral particles induced by fluid flow in porous media based on CFD-DEM

Simulation on detachment and migration behaviors of mineral particles induced by fluid flow in porous media based on CFD-DEM

Meshless spline-based DQ methods of high-dimensional space–time fractional advection–dispersion equations for fluid flow in heterogeneous porous media

Meshless spline-based DQ methods of high-dimensional space–time fractional advection–dispersion equations for fluid flow in heterogeneous porous media

Dual-fractal nuclear magnetic resonance to relative permeability conversion: A novel framework for multiphase flow characterization

Based on dual-fractal theory, this paper proposes a novel methodology to transform nuclear magnetic resonance (NMR) measurements into relative permeability model, thereby realized the challenge of accurately quantifying multiphase fluid flow in dual-fractal porous media. The novel relative permeability model integrates a multitude of parameters associated with the microscopic pore architecture of porous media. It can be verified through case studies that the newly constructed relative permeability model demonstrates excellent applicability. Furthermore, we have discovered a correlation between the segmentation characteristics of the relationship between the pore radius (r) and transverse relaxation time (T2) in low-permeability sandstone reservoirs and the number of peaks in the NMR curve. Specifically, the single-peak type can usually be divided into two segments, while the multi-peak type can generally be divided into three segments. The comprehensive fractal dimension (Dc) derived from the weighting method effectively captures the holistic core heterogeneity. The characteristics of small diameter pores are particularly sensitive to variations in the pore tortuosity fractal dimension (Dτ), the pore structure fractal dimension (Df), Dc, and ε (represents the pore size ratios). Given that the wetting phase preferentially occupies small pores, its relative permeability is significantly affected by these parameter changes. Conversely, the non-wetting phase mainly flows through large pores and is thus less influenced by changes in these parameters.

The Gibbsian permeability model of porous media

A first-principles equation quantifying the permeability of fluid flow through a porous medium is developed. Existing treatments, like the popular Kozeny–Carman permeability equation, are phenomenological models, which are based on scaling arguments of one-dimensional flow. This paper shows that basic multi-dimensional flow effects make the Kozeny–Carman permeability inaccurate. The current model is based on second law considerations following Gibbs' thermodynamic equation and is generally valid for multi-dimensional porous media geometries and flows. Examples are used to illustrate the accuracy and relative simplicity of the new Gibbs permeability model against the Kozeny–Carman approach. In practice, the new model allows the permeability to be calculated with a single experimental trial compared to the multiple trials needed with D'Arcy's original method and that are required to calibrate the Kozeny–Carman model.

Hybrid solver with deep learning for transport problem in porous media

In this work, a hybrid solver with deep learning is proposed for numerical modeling of fluid flow in porous media. The classical simulation procedure is complemented with a neural network model to obtain an initial guess for fluid saturation that is closer to the solution in the Newton–Raphson iterative algorithm. The simulation setup is a 3-dimensional immiscible two-phase flow with fluid motion caused by multiple production and injection wells. Approximation of the initial guess with a neural network model accelerates the numerical modeling up to 14% in terms of nonlinear iterations. Extensive experiments with dynamic and static reservoir features revealed that improving predictive accuracy does not necessarily improve fluid modeling. Different training procedures (e.g., different loss functions) and feature spaces (e.g., more past time steps used) can lead to better prediction quality but a higher number of nonlinear iterations. These results demonstrate that not only the closeness to the solution, but also the spatial distribution of residuals affects the “quality” of the starting point in Newton’s method.

First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs

ABSTRACTWe present a model reduction approach for the real‐time solution of time‐dependent nonlinear partial differential equations (PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced‐order models for nonlinear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methods to deal with nonlinear terms. Furthermore, we introduce a first‐order empirical interpolation method (EIM) to provide an efficient approximation of the nonlinear terms in time‐dependent PDEs. We demonstrate the effectiveness of our approach on the Allen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two‐phase fluid flow in porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with both the Galerkin–Newton approach and hyper‐reduced models using the standard EIM.

Using a Plant Hydrodynamic Model, FETCH4, to Supplement Measurements and Characterize Hydraulic Traits in a Mixed Temperate Forest

AbstractSpecies‐specific hydraulic traits play an important role in ecosystem response to water stress; however, representation of biodiverse forest canopies remains a challenge in land surface models. We introduce FETCH4, a multispecies, canopy‐level, hydrodynamic model, which builds upon previous versions of the finite‐difference ecosystem‐scale tree crown hydrodynamics model (FETCH). FETCH4 simulates water transport through the soil, roots, and stem as porous media flow. Stomatal conductance is controlled by xylem water potential, which is resolved along the vertical dimension. A key feature of FETCH4 is a multispecies canopy formulation, which uses crown and stem dimensional characteristics to allow the model to produce both tree‐level and plot‐level outputs and improves the representation of hydraulic traits and their variation among trees and species. We demonstrate the model's performance in a mixed temperate forest in Michigan with species of contrasting hydraulic strategies. We optimize species‐specific hydraulic parameters using a Bayesian optimization framework incorporating sapflow measurements. FETCH4 performed well in simulating sapflow of species with contrasting hydraulic strategies under conditions of water stress. In addition, the model was able to capture higher‐level emergent traits, such as drought sensitivity. Using FETCH4 in combination with available observations can provide unique insights about difficult to measure hydraulic traits and plant hydrodynamics.

A fully-implicit solving approach to an adaptive multi-scale model - coupling a vertical-equilibrium and full-dimensional model for compressible, multi-phase flow in porous media

Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the dynamics of a system. While conventional full-dimensional models have the ability to represent dynamics, they come at the cost of high computational effort. We aim to combine the efficiency of the vertical equilibrium model and the accuracy of the full-dimensional model by coupling the two models adaptively in a unified framework and solving the emerging system of equations in a monolithic, fully-implicit approach. The model domains are coupled via mass-conserving fluxes while the model adaptivity is ruled by adaptive criteria. Overall, the adaptive model shows an excellent behaviour both in terms of accuracy as well as efficiency, especially for elongated geometries of storage systems with large aspect ratios.

Fractional analysis of time-fractional Emden-Fowler model arising in fluid flow of porous media and physical sciences

Fractional analysis of time-fractional Emden-Fowler model arising in fluid flow of porous media and physical sciences

Effects of uneven proppant distribution in multiple clusters of fractures on fracture conductivity in unconventional hydrocarbon exploitation

During the unconventional hydrocarbon development, the irregular shaping and uneven sand concentration of proppants banks in the staged multi-cluster fracturing of horizontal wells are key factors determining the fracture conductivity and post-fractured well productivity. To compensate for the limitation of small-scale sand filled core conductivity research that cannot accurately reflect the fracture conductivity at the field scale, this study used the mixture model to investigate the proppant distribution in fractures after sand carrying fluid enters the multi-cluster fractures from a horizontal well section, and divided the fractures into several regions based on different sand concentration ranges inside hydraulic fractures. The mechanical parameters and permeability of the sand embankment in each region were regressed to the entire fracture. The closure and conductivity of field-scale fractures with non-uniform sand filled were studied using elastic mechanics theory and free and porous media flow theory. Effects of fracture width and height on the conductivity of field-scale fractures were analyzed. The results indicate that reducing the fracture width, from 10 to 6 mm, and fracture height, from 12 to 6 m, can increase the proportion of fracture areas with sand concentration from 12 to 15%; Configurations of areas with different sand concentrations in fractures are irregular, and some areas without proppant filling can be closed under the closure pressure of 70 MPa, causing the surrounded sand filling areas to fail providing flowing paths; Sand banks with proppant concentration between 0 and 6% at the top part of the fracture can provide a more permeable flow channel than the bottom part during the initial closure of the fracture. While sand banks with proppant concentration between 12 and 15% at the bottom of the fracture can maintain a higher permeability than the top part when the closure pressure reaches 70 MPa; Reducing the width and height of the fracture can still maintain a larger fracture width when the closure pressure exceeds 60 MPa.

High-Accuracy Parallel Neural Networks with Hard Constraints for a Mixed Stokes/Darcy Model.

In this paper, we study numerical algorithms based on Physics-Informed Neural Networks (PINNs) for solving a mixed Stokes/Darcy model that describes a fluid flow coupled with a porous media flow. A Hard Constrained Parallel PINN (HC-PPINN) is proposed for the mixed model, in which the boundary conditions are enforced by modified the neural network architecture. Numerical experiments with different settings are conducted to demonstrate the accuracy and efficiency of our method by comparing it with the methods based on vanilla PINNs for the mixed model.

Alternative Variational Iteration Elzaki Transform Method for Solving Time‐Fractional Generalized Burgers‐Fisher Equation in Porous Media Flow Modeling

ABSTRACTIn this paper, we have studied the time‐fractional generalized Burgers‐Fisher equation, which has applications in turbulence modeling, image processing, and biology. A new method called the alternative variational iteration Elzaki transform method (AVIETM) has been used to achieve the results. We employed the proposed method to obtain a solution for the time‐fractional generalized Burgers‐Fisher equation. The convergence and uniqueness of the solutions for the proposed method have been analyzed and discussed. The validity of the AVIETM is shown by numerical simulation and graphs. The method's accuracy have been shown by comparing the results to exact for various values of the fractional order. The obtained results demonstrate that the proposed AVIETM method is straightforward, highly accurate, and efficient.

Model-Reduction and Data-Assimilation Approach Enhances Carbon-Dioxide Plume Tracking

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 221411, “Accelerated Calibration and CO2 Plume Tracking at the Illinois Basin Decatur Project: A Dynamic Mode-Decomposition and Data-Assimilation Approach,” by James Omeke, SPE, Kassem Alokla, SPE, and Dimitrios Voulanas, SPE, Texas A&M University, et al. The paper has not been peer reviewed. _ Addressing climate change through carbon capture and storage (CCS) technologies requires advanced computational methodologies for subsurface carbon-dioxide (CO2) storage monitoring. This study focuses on the Illinois Basin Decatur Project (IBDP), a CCS demonstration pilot aimed at CO2 injection into a deep saline reservoir. A novel framework combining dynamic mode decomposition (DMD), a data-driven model-reduction technique, with direct data assimilation is introduced to streamline the calibration of CO2 plume evolution models. This approach enhances rapid tracking and overcomes the computational challenges of traditional high-fidelity numerical reservoir simulations known as the full-order model (FOM). Introduction DMD represents a superior approach for flow in porous media compared with most reduced-order models because of its ability to capture complex flow dynamics effectively. DMD excels in identifying key dynamic features, spatial and temporal scales, and localized regions crucial for flow behavior. It offers a data-driven method that can reproduce flow phenomena accurately with high fidelity, even in multiphase and multiscale heterogeneous porous-media scenarios. Additionally, advancements such as sparse DMD and local DMD enhance the accuracy and efficiency of DMD models. The adaptability and robustness of DMD in capturing intricate flow structures make it a preferred choice for studying flow dynamics in porous media during CO2 storage. The foundation of DMD lies in its ability to approximate the Koopman operator. The DMD technique and the Koopman operator are detailed in the complete paper. Workflow Description The steps of the workflow are detailed in the complete paper, including associated equations. Identifying permeability as the principal uncertainty in multilevel pressure measurements, the authors conducted six simulation cases using various permeability multipliers within the IBDP. These simulations, integral to the history-matching process of the used FOM, were designed to span the expected range of uncertainty. Each simulation was specifically influenced by a chosen permeability multiplier. This subsection of the complete paper details the following steps: - Reconstruction of the reduced-order model (ROM) of each FOM case using DMD - Interpolation of DMD modes and eigenvalues for pressure-trend prediction - Kalman filter optimization of permeability multipliers - History-matching of the FOM using the optimized permeability multiplier and construction of the ROM

A fully discrete finite element method for unsteady magnetohydrodynamic flow in porous media

A fully discrete finite element method for unsteady magnetohydrodynamic flow in porous media

Predicting filtration coefficient and formation damage coefficient for particle flow in porous media using machine learning

Predicting filtration coefficient and formation damage coefficient for particle flow in porous media using machine learning

Water absorption dynamics in medical foam: empirical validation of the Lucas–Washburn model

This study extends the Lucas–Washburn theory through non-equilibrium thermodynamic analysis to examine fluid absorption in medical foams used for hemorrhage control. As a universal model for capillary flow in porous media, the theory demonstrated strong agreement with experimental results, confirming its semi-quantitative accuracy. Minor deviations, likely due to material heterogeneity, were observed and explained, enhancing the theory’s applicability to real-world conditions. Our findings underscore the universality of the Lucas–Washburn framework and provide valuable insights for optimizing the design of medical foams, ultimately contributing to more effective bleeding control solutions in clinical applications.Graphic abstract