Electromagnetic (EM) Heat Exchangers (HX) are systems which convert EM energy into heat or mechanical work. One potential design consists of a porous lossy ceramic material heated by EM waves saturated with a compressible gas coolant. EM heating of ceramics is nonlinear, since the loss factor is temperature dependent. Designing such EM HXs requires an understanding of the coupling between...

In this talk we present a novel way to mathematically frame the concept of *ecological memory* of plant water stress in the context of root water uptake in the unsaturated flow equation.

As reported in [1], ecological memory can be defined as “the degree to which an ecological process is shaped by its past modifications of a landscape”. Inspired by recent eco-hydrological papers (see in...

We present a fully coupled chemo-hydro-mechanical variational phase field model for simulating fracture initiation and propagation, including chemical reactions in cementitious systems. In a staggered approach, we coupled three subprocesses: (i) fluid flow in porous media, (ii) reactive transport, and (iii) mechanical deformation of fractured porous media using the variational phase...

Defense and energy applications ubiquitously involve multiscale and multiphysics systems. The accurate modeling of these systems, critical to achieve superior performances and optimized designs, has challenged generations of computational physicists due to the mathematical and numerical complexities involved in the development of their computable representations. One of the fundamental...

When viscous dominated fluid -> fluid displacements in a porous medium take place, and the viscosity of the displacing fluid is significantly lower than that of the displaced fluid, then an instability occurs known as viscous fingering (VF). The 2 fluids may be completely miscible or immiscible but in porous media the more complex phenomenon to reproduce both experimentally and in numerical...

In order to study the efficiency of the various forms of trapping including mineral trapping scenarios for CO$_2$ storage behavior in deep layers of porous media, highly non-linear coupled diffusion-advection-reaction partial differential equations (PDEs) including kinetic and equilibrium reactions modeling the miscible multiphase multicomponent flow have to be solved. We apply the globally...

Non-equilibrium modeling is relevant in several physics of coupled processes, flow and transport of fluids situations in homogeneous and heterogeneous porous media systems, for instance, subject to phase transitions, hysteresis and chemical reactions, among many others complex systems (see, e.g. [1,3,4,5,6] and the references cited therein). To model the dynamics of these phenomena, the...

In recent years, we have seen increasing attention paid to multiphase flow in subsurface porous media due to issues related with enhanced oil recovery, geothermal technology, unconventional oil/gas reservoirs, geological carbon sequestration, and subsurface storage of hydrogen. One key effort prior to constructing the mathematical model governing the compositional multiphase flow is to...

Successful large-scale compositional reservoir simulation requires robust and efficient equilibrium calculations. In recent years a large number of papers have been published on the topic of three-phase vapor-liquid-aqueous (VLA) equilibria

which frequently appear in hydrocarbon reservoirs. The presence of the aqueous phase increases the probability of equilibrium calculations to have issues....

We consider a mathematical model for saturated flow and reactive transport in a porous medium. In this model, the absolute permeability of the medium depends on the solute concentration. Due to this, the fluid velocity depends on the unknown concentration. On the other hand, the solute is transported by the fluid, so the concentration is dependent on the fluid velocity. This yields a fully...

Multiphase flow and transport in porous media typically is simulated by solving an elliptic or parabolic flow equation together with hyperbolic transport equations. In case of tight coupling, either a fully implicit solution algorithm is required, or very small time steps have to be employed, if a sequential algorithm is used. Here, a new solution approach is presented, which relies on a...

We develop a mixed finite element computational model for the interaction between a free fluid and a poroelastic medium . The free fluid flow is governed by the time-dependent incompressible Navier-Stokes equations, while the poroelastic region is governed by the Biot system. A Lagrange multiplier method is employed to impose weakly the continuity of flux. Under a small data condition,...

Conventional numerical modeling techniques, with finitely resolved length and time scales, need specific treatments to include the effects of unresolved physics and solution discontinuities. In this regard, their applications to multi-scale problems involving transport in fractured media are no different. Lagrangian particle-tracking methods provide a compelling alternative to the Eulerian...

Fractures in the geological formations can propagate and slide when the in-situ compressive stress state changes. As for the compressive nature of the stress, shearing (i.e., Mode II mechanical failure) is the dominant fracture propagation mechanism. In addition, geological formations entail several fractures which can also cross each other. To avoid the use of excessively high-resolution...

The problem of solidification with macro-segregation and the formation of freckles is usually a complicated one that involves mass, momentum, heat, and species transfers between the solid, mushy, and liquid phase regions [1]. In several natural and industrial applications, the quantitative description of phase change, chemical heterogeneities, and multi-phase and multi-component flows serve an...

The aim of this talk is to present the derivation of the new effective boundary condition for the fluid flow in a domain with porous boundary. We start from the Stokes system in a domain with an array of small holes on the boundary and on each hole we impose an appropriate dynamic condition, namely the value of the normal stress corresponding to the exterior conditions. The goal is to obtain...

We present in this talk an effective model for transport processes in periodically perforated elastic media, taking into account also cyclic elastic deformation as it occurs e.g. in lung tissue due to respiratory movement. The underlying microscopic problem consists of a linear elasticity equation for the displacement within the Lagrangian framework, posed on a fixed domain and a diffusion...

The dynamic behavior of multiphase flow in gas-solid-liquid mixture systems plays an important role in various applications of petroleum industry, biochemical processing, chemical and metallurgical industry, food technology, water treatment, and sub-seabed CO2 storage and its understanding can provide insights in various phenomena like rain deposition, landslides and degradation of heritage...

Dissolution of solid mineral in porous media due to the introduction of reactive fluids is of utmost importance for a wide range of subsurface applications, including CO2 storage, geothermal systems, fuel cell technology, and enhanced oil recovery. The conditions of the injection process as well as the mineral properties strongly influence the resulting dissolution pattern, leading to compact,...

Nitrogen fertilization is vital for productive agriculture and efficient land use. However, globally, approximately 50% of the nitrogen applied is lost to the environment, causing inefficiencies, pollution, and greenhouse gas emissions. Rainfall and its effect on soil moisture are the major components controlling nitrogen losses in agriculture. Thus, changing rainfall patterns could accelerate...

Structural changes of the pore space and clogging phenomena are inherent to many porous media applications. However, related mathematical investigations remain challenging due to the degeneration of the hydrodynamic parameters. In this research, we apply an appropriate scaling of the unknowns and work with porosity-weighted function spaces. This enables us to prove solvability of a coupled...