We develop a mathematical framework for analyzing coupled fluid flow, species transport, and heat transfer in pore-scale network models, where nonlinear interactions arise from pressure-driven flow, temperature-dependent chemical reactions along pore walls, and thermal exchange between pore fluid and solid matrix. Along each network edge, species transport undergoes diffusion and advection and...
Evaporation from porous media partially saturated with saline water can cause density instabilities to form. As water evaporates, the dissolved salt stays behind, which causes the salinity to increase near the top of the porous medium. This creates a gravitationally unstable setting, where density instabilities in the form of fingers can develop. Whether these density instabilities form,...
In this paper, we derive a new effective interface condition governing the transition between porous and free flow regions of a fluid domain via asymptotic analysis. The proposed non-standard condition represents a Darcy-type law acting across the imaginary interface, asserting that the trace of the free-flow velocity is proportional to the difference in stresses on both sides of the...
We propose a mathematical model of a high-performance liquid chromatography column across three length scales. We assume a column packed with porous particles, which adsorb the solute on their internal surfaces. We consider three scales: inside the porous particles, the packed particles and interstitial fluid scale, and the column scale (see figure). Chemical interactions are taken into...
Proton exchange membranes (PEMs) has a crucial role in determining the fuel cell efficiency, durability, and performance of PEM fuel cells and water electrolysers. It governs proton transport while simultaneously acts as electronic insulators and gas separators. The current state of the art system employs composite membranes to enhance its efficiency manifold. Conventional macroscopic...
The Richards equation, a nonlinear elliptic–parabolic equation, is widely used to describe infiltration in porous media. We present a finite element method for solving the Richards equation by introducing a bounded auxiliary variable that removes unbounded terms from the weak formulation. The formulation is discretized with a semi-implicit scheme, and the resulting nonlinear system is solved...
Modelling unsaturated flow in porous media is challenging due to the strong nonlinearity and spatial heterogeneity of the Richards equation. Conventional finite difference and finite element methods often face difficulties related to mesh generation, numerical integration, and grid sensitivity, particularly when applied to complex geometries. To address these limitations, this study presents a...
In this talk, we introduce an enhanced discretization method for incompressible two-phase Darcy flows in heterogeneous porous media with discontinuous capillary pressures. The model is expressed in the total-velocity formulation, leading to a coupled system consisting of a degenerate parabolic equation for the non-wetting phase saturation and a pressure equation governing the total...
Recently, a new approach for simulating buoyant two-phase flow and transport in porous media was proposed, which is based on a coupled hyperbolic system. This new scheme incorporates Darcy’s law by adding a source term to the isothermal Euler equations combined with an additional equation for phase transport. The system allows for explicit simulations. It is solved in its hyperbolic form with...
Optimal-order convergence in the H1 norm is proved for an arbitrary Lagrangian–Eulerian (ALE) interface tracking finite element method (FEM) for the sharp interface model of two-phase Navier–Stokes flow without surface tension, using high-order curved evolving mesh. In this method, the interfacial mesh points move with the fluid’s velocity to track the sharp interface between two phases of the...
Slip flow in porous media is encountered in many applications involving gas flow (when Knudsen effects become significant) or even liquid flow when an effective boundary condition at the pore walls replaces no-slip flow over rough surfaces [1]. The macroscopic model describing flow with slip effects in homogeneous porous media takes the form of Darcy’s law in which the effective (or apparent)...
We model a porous medium as a random pore network and focus on how the medium’s internal structure affects its flow and adsorptive behavior (see the figure for an example of considered membrane structure). A particular emphasis is on modeling suspension flow, where particles adsorb onto the pore walls. We start by formulating the governing equations of fluid flow on a general network. Then, we...
Modeling flow and transport in large, heterogeneous networks—such as fractured, karstic, or pore-scale systems—often requires substantial model reduction while preserving global hydraulic behavior. We propose a systematic coarse-graining framework for resistor networks that combines resistance-distance–based upscaling with gradient-based optimization to construct physically consistent coarse...
Coupled geomechanical deformation and fluid flow phenomena arise in a wide range of subsurface processes, such as reservoir compaction, subsidence, and fault reactivation. Accurate and efficient simulation of these phenomena requires robust and consistent numerical formulations capable of capturing hydro-mechanical (HM) behavior in porous media. This study presents a detailed comparative...
A variational gradient damage model for saturated poroelastic media with thermo-hydro-mechanical (THM) coupling and cohesive zone effect is proposed in this work. The model provides a unified and fully coupled description of gradient damage, poroelasticity, heat transfer and fluid flow, and is able to accurately capture the behavior of fracture process zone (FPZ) near the tip of quasi-brittle...
We present a computational framework for simulating tightly coupled thermo-hydro-mechanical processes in porous media, as encountered in subsurface energy and environmental applications. The model is based on a fully coupled, quasi-static thermo-poroelasticity model, capturing the mutual feedback between deformation, pressure, and temperature.
To solve this multiphysics system efficiently...
Coupled fluid-flow and geomechanical simulations are essential for assessing the safety and effectiveness of reservoir operations. In fractured reservoirs, the presence of a large number of fractures makes fully resolved 2D and 3D coupled simulations of flow and deformation computationally infeasible. In such settings, efficient reduced-order methods that accurately approximate the governing...
We consider flow in carbonate reservoirs containing karstified layers, characterized by partially enlarged fractures and high-permeability conduits formed through superimposed chemical dissolution along fracture intersections. The computational framework is based on a discontinuous Galerkin (dG) formulation applied to a modified system of mixed dimensional flow equations, which explicitly...
Accurate and scalable simulation of geological CO₂ storage requires resolving strong heterogeneity, evolving plume fronts, and fracture matrix interactions, without making large scale models computationally prohibitive. In this work, we develop a multiscale strategy built on the Algebraic Dynamic Multilevel (ADM) method and its extension to fractured systems through projection-based embedded...
Geological carbon storage (GCS) technology has become increasingly relevant due to global warming. Numerical simulations play a crucial role in understanding and implementing this technology, as well as in assessing long-term storage risks. To provide a common baseline for GCS numerical simulations, the Society of Petroleum Engineers launched the 11th Comparative Solution Project (SPE11)...
Recovering hidden causes from observable effects is a fundamental challenge in many scientific and engineering applications. Examples include inferring subsurface properties from magnetic field measurements in geophysics and reconstructing sharper images from blurred ones in medical imaging. These tasks are commonly formulated as inverse problems. Such problems are often ill-posed and lack...
Fractures dominate water migration and strongly affect thermal evolution and ice formation in porous media exposed to freeze-thaw cycles. These cycles create complex thermo-hydraulic interactions between fractures and their surrounding matrix, reshaping flow dynamics and phase transitions. Yet, coupled processes governing fracture-matrix exchange in complex fractured porous media remains...
Abstract:
The freezing of water in saturated porous media depends on characteristics such as pore size, grain distribution, and boundary conditions. In this constribution, we present mathematical models of the freeze/thaw process of a saturated soil sample at the laboratory scale and at the pore scale. These models are based on balance laws for mass, momentum, and enthalpy in porous...
The displacement of a wetting fluid by a non-wetting fluid in porous media is an ubiquitous process in multi-phase flow and typically gives rise to a transient propagating interface referred to as the drainage front. Such fronts occur in transient settings, including the injection of supercritical CO2 into brine-saturated geological formations and rapid drying of water-saturated clayey...
Geological carbon storage involves strongly coupled processes in which multiphase flow of CO$_2$ interacts with deformation of the porous matrix. While such poromechanical effects are known to influence pressure evolution, their role in the stability of CO$_2$ plume migration remains poorly understood and is often neglected in predictive models. In this work, we present a mathematical...
