Presentation materials
Porous media naturally exhibit a heterogeneous structure including two different spatial scales: The pore/micro-scale is the fundamental scale, on which flow and reactive transport processes take place whereas the macro-scale, i.e. the scale of the porous medium, is of practical relevance for geoscientific applications. What is more, mineral dissolution and precipitation alter a porous...
In this talk we derive a homogenized model for a reaction-diffusion equation describing mineral precipitation/dissolution in an evolving porous micro-domain, consisting of a fluid phase and a solid phase build by periodically distributed spherical solid grains. The evolution of the micro-domain depends on the concentration at the surface of the grains, leading to a free boundary value problem...
Single-phase macroscopic flow in a rigid porous medium is traditionally described by classical Darcy's law which can be formally derived by upscaling the pore-scale flow equation in the creeping incompressible flow regime and the no-slip condition at the solid-fluid interfaces. However, there are many situations for which fluid release from the surface into the pores or, conversely, absorption...
Multiphase flow and reactive transport are important in many applications, in particular in porous media. We consider the incompressible flow of two immiscible fluids in the presence of a solid phase changing due to precipitation and dissolution. We employ a ternary phase-field model on the pore scale, extending widespread models for two fluid phases by including a solid phase.
We upscale...
A porous medium is a highly complex domain, in which various processes can take place at different scales. Here we consider a phase-field approach to model the evolution of the evolving interfaces at the micro-scale. After applying a formal homogenization procedure, a two-scale phase-field model is derived, describing the averaged behavior of the system at the Darcy scale (the macro-scale)....
There is an increasing interest in solvers for phase-field models of brittle fracture [2]. The
governing equations for this problem originate from a constrained minimization of a non-convex energy functional, and the most commonly used solver is a staggered scheme. This method shows robustness in comparison to the monolithic Newton method, however, the staggered scheme often requires many...
The development of continuum reactive transport models in porous media traces back to mid-80’s when the theoretical framework to consider reactions in mass transport equations was outlined. Since their establishment, the operator-splitting (OS) approach has been frequently used due to its easy implementation and computational efficiency in large scale simulations including complex chemical...
The simulation of coupled fracture flow and deforming porous medium is a
challenging problem in reservoir engineering. Common examples are
hydraulic simulations or hydro-fracking. Some of the challenges arise
due to the difference in properties of the mathematical models used in
each of the subdomains. Solving the problem using a monolithic approach
leads to an ill-conditioned system of...
Whereas extraction of hydrocarbons from the subsurface typically involves transport phenomena over large distances (e.g, in-between injection and production wells), transport of geothermal heat during extraction and storage is chiefly confined to the proximity of wells. This indicates significantly reduced computational efforts by considering only a region of interest around the wells. In this...
Modeling and simulation of flow, transport and geomechanics in the subsurface porous media is an effective approach to help make decisions associated with the management of subsurface oil and gas reservoirs, as well as in other wide application areas including groundwater contamination and carbon sequestration. Accurate modeling and efficient, robust simulation have always been the main...
Whether naturally- or artificially-induced due to human activities, decreasing or increasing of suction in multiphase-fluid-saturated porous materials can lead to enormous changes in their thermo-hydromechanical properties. In this, both the mathematical description and the numerical modeling of the coupled problem present a challenging task. The presentation considers the following two...
Modeling and simulation of multiphase flow in porous media have been a major effort in reservoir engineering and in environmental study. One basic requirement for accurate modeling and simulation of multiphase flow is to have the predicted physical quantities sit within a physically meaningful range. For example, the predicated saturation should sit between 0 and 1 while the predicated molar...
In a fractured porous medium, the fractures are often characterised by their anisotropic shape. For example, in a two-dimensional situation, the fractures are long and thin formations, in which the medium properties may differ considerably when compared to the corresponding ones in the adjacent blocks. For the numerical simulation of flow in porous media, a commonly adopted strategy is to...
We consider a porous medium in a semi-infinite domain, saturated with saline water. The top boundary is subject to evaporation of water but where the solute stays behind, while the bottom boundary has an inflow of water with the background solute concentration. This leads to an accumulation of solute near the top boundary. As the density of the water increases with larger solute concentration,...
While near-surface geothermal energy applications for the heating and
cooling of buildings have been in use for decades, their practical adoption is
limited by the energy transport rates through soils. Aquifers provide a means
to use convective heat transport to improve heat transfer between the building
and the aquifer. However, the solid matrix in the aquifer is carbonaceous...
We study the performance of a membrane filter represented by a pore network based on two criteria: 1) total volumetric throughput and 2) accumulated foulant concentration. We first formulate the governing equations of fluid flow on a general network, and we model adsorptive fouling by imposing an advection equation on each pore (edge) and imposing conservation of fluid and foulant volumetric...
We consider an extension of Discrete Fracture Matrix (DFM) models to compositional two-phase Darcy flows in fractured porous media.
The model is hybrid-dimensional, i.e. fractures are treated as surfaces of co-dimension one, and accounts for phase transitions and Fickian diffusion. It is based on physically consistent transmission conditions across matrix fractures (m-f) interfaces resulting...
This work deals with the application of the Balancing Domain Decomposition based on Constrains (BDDC) method to unsteady two-phase flow problems in porous media.
We briefly describe the spatial discretization of the problem which is based on the mixed-hybrid finite element method (MHFEM) and semi-implicit time discretization.
Then, we describe the BDDC method, in detail discuss the...
Super absorbents are swelling to thousands of percent of strain. Apart from the important industrial applications of these materials, the scientific understanding of electromechanical coupling in these ionized gels are paramount in the scrutiny of mechanotransduction of biological tissue. Regular finite deformation finite element codes fail to simulate these extremely large deformations [6]. A...
Simulation problems linked to the fabrication and degradation of Ceramic-Matrix Composites involves a precise knowledge of effective heat and mass transfer properties of porous media at the fiber scale and the fabric scale. When dealing with complex reinforcement architecture, predictive tools have to be able to handle large 3D images, including the capability to modify them through...
In This work, we combine Generalized Multiscale Finite Element Method (GMsFEM) with a reduced model based on Discrete Fracture Model (DFM) to resolve the difficulties of simulating fluid flow in fractured porous media while efficiently and accurately reduce the computational complexity resulting from resolving the fine scale effects of the fractures. The geometrical structure of the fractures...
We develop a space-time mortar mixed finite element method for
parabolic problems modeling flow in porous media. The domain is
decomposed into union of subdomains with non-matching grids and
different time steps. The space-time variational formulation couples
mixed finite elements in space with discontinuous Galerkin in time.
Continuity of flux across space-time interfaces is imposed...
The multiscale hybrid mixed finite element method (MHM-H(div)), previously developed for Darcy’s problems, is extend for coupled flow/pressure and transport system of two-phase flow equations on heterogeneous media under the effect of gravitational segregation. It is combined with an implicit transport solver in a sequential fully implicit (SFI) manner. The MHM-H(div) method is designed to...
We present a first-order finite element method with mass-lumping and flux upwinding, to solve the immiscible two-phase incompressible flow problem in porous media. The primary unknowns are the wetting phase pressure and saturation. Recently, the theoretical convergence analysis of the method was derived in [1]. Here, we propose a comprehensive computational methodology and extend the scheme to...
Richards equation is commonly used to model the flow of water and air through soil, and it serves as a gateway equation for multiphase flow through porous domains. With pressure
where $S:[-\infty,\infty]\to...
In this contribution, we present a new numerical solution of a two-phase compressible Darcy's flow of a multi-component mixture in a porous medium. The mathematical model consists of mass conservation equation of each component, extended Darcy's law for each phase, and an appropriate set of the initial and boundary conditions. The phase split is computed using the constant temperature-volume...
Experimental and theoretical studies indicate that nonlinear dynamical processes are inherent into flow and transport through fractured porous media. However, numerical predictions based on commonly applied numerical models using classical Darcy’s, Richards’ and Fick’s concepts may significantly deviate from real transport processes in porous media. The goal of this paper is to demonstrate an...
Drying of porous media is traditionally described by macroscopic continuum models. In this frame, the partially-saturated porous medium is treated as homogeneous continuum and the fluid transport is driven by gradients of spatially-averaged quantities (such as moisture content) and controlled by non-linear (effective) parameters (such as moisture transport coefficient). The boundary conditions...
