Miscible and immiscible multiphase flow in deformable porous media

Incompressible immiscible multiphase flows in porous media: a variational approach

We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measures with prescribed mass endowed with some tensorial Wasserstein distance. We show the convergence of the approximation obtained by a minimization scheme à la [R. Jordan, D. Kinderlehrer & F. Otto, SIAM J. Math. Anal, 2...

Algebraic Dynamic Multilevel (ADM) Method for Immiscible Multiphase Flow in Heterogeneous Porous Media with Capillarity

Flow in porous media pore-network models and multiphase flow

In the last 3 years there has been a huge increase in the use of pore-scale modeling to study multiphase flow and transport in porous media. Starting from single pore models of fluid arrangements, computations of relative permeability, interfacial area, dissolution rate and many other physical properties have been made. Combined with a realistic description of the pore space, predictive modelin...

Modeling Multiphase Flow with Phase Transitions in Porous Media

A new approach to model multiphase flow in porous media with phase appearance and disappearance is to use nonlinear complementarity constraints. In addition to the standard mass balance equations for mulitphase flow, a set of complementarity constraints are added in order to handle the phase transitions. This results in a larger system of nonlinear equations, which is non-smooth in general. The...

Numerical Modeling of Multiphase Flow in Porous Media

The simultaneous flow of immiscible fluids in porous media occurs in a wide variety of applications. The equations governing these flows are inherently nonlinear, and the geometries and material properties characterizing many problems in petroleum and groundwater engineering can be quite irregular. As a result, numerical simulation often offers the only viable approach to the mathematical model...