Related papers: Numerical Methods for Flow in Fractured Porous Med…
The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry…
Propagation of transient mechanical waves in porous media is numerically investigated in 1D. The framework is the linear Biot's model with frequency-independant coefficients. The coexistence of a propagating fast wave and a diffusive slow…
In this work, phase-field modeling of hydraulic fractures in porous media is extended towards a global-local approach. Therein, the failure behavior is solely analyzed in a (small) local domain. In the surrounding medium, a simplified and…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
We outline the main ideas behind the numerical modelling of soft-flowing crystals, with special attention to their application to microfluidic devices for the design of novel mesoscale porous materials.
Geo-materials such as vuggy carbonates are known to exhibit multiple spatial scales. A common manifestation of spatial scales is the presence of (at least) two different scales of pores, which is commonly referred to as double porosity. To…
We propose a workflow based on physics-informed neural networks (PINNs) to model multiphase fluid flow in fractured porous media. After validating the workflow in forward and inverse modeling of a synthetic problem of flow in fractured…
Shear dilation based hydraulic stimulations enable exploitation of geothermal energy from reservoirs with inadequate initial permeability. While contributing to enhancing the reservoir's permeability, hydraulic stimulation processes may…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation…
In this paper, we consider the complex flows when all three regimes pre-Darcy, Darcy and post-Darcy may be present in different portions of a same domain. We unify all three flow regimes under mathematics formulation. We describe the flow…
The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a…
It is of great concern to produce numerically efficient methods for moisture diffusion through porous media, capable of accurately calculate moisture distribution with a reduced computational effort. In this way, model reduction methods are…
This article is a follow up of our submitted paper [11] in which a decomposition of the Richards equation along two soil layers was discussed. A decomposed problem was formulated and a decoupling and linearisation technique was presented to…
A continuum model of crack propagation is presented and discussed. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic and viscoelastic effects are…
In the mathematical modelling of compactional flow in porous media, the constitutive relation is typically modelled in terms of a nonlinear relationship between effective pressure and porosity, and compaction is essentially poroelastic.…
Fluid injection and production cause changes in reservoir pressure, which result in deformations in the subsurface. This phenomenon is particularly important in reservoirs with abundant fractures and faults because the induced slip and…
We introduce a partitioned coupling approach for iterative coupling of flow processes in deformable fractures embedded in a poro-elastic medium that is enhanced by interface quasi-Newton (IQN) methods. In this scope, a unique computational…
This papers deals with a construction and convergence analysis of a finite difference scheme for solving time-fractional porous medium equation. The governing equation exhibits both nonlocal and nonlinear behaviour making the numerical…
Phase field model (PFM) is an efficient fracture modeling method and has high potential for hydraulic fracturing (HF). However, the current PFMs in HF do not consider well the effect of in-situ stress field and the numerical examples of…
We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy-Forchheimer law while that in the surrounding matrix is governed by Darcy's law. We give an appropriate mixed,…