The design of accurate multiscale domain decomposition methods for channelized, high-contrast porous media remains as an important challenge in typical problems posed by the oil industry.
Here we investigate an improved version of the recently proposed Multiscale Robin Coupled method (MRCM) [1]. This method ensures weak continuity of both normal fluxes and pressure through the imposition of...
Non-overlapping domain decomposition multiscale methods have been succesfully applied to flows in porous media. Such remarkable class of methods seek to decompose the domain of the porous media flow equations in non-overlapping subdomains, solving smaller local problems in parallel, and one global interface problem, instead of a large coupled one. Usually the interface problem enforces the...
We are interested in the numerical approximation of partial differential equations of elliptic nature, in the context of incompressible two-phase flow problems in heterogeneous porous media. Numerical solutions of elliptic boundary value problems with high contrast and discontinuous coefficients are often expensive and time consuming, so efficient numerical methods are necessary. Indeed,...
In subsurface characterization using a history matching algorithm, we reconstruct the subsurface properties, such as distributions of permeability and porosity, with a set of limited data. As a history matching algorithm, Markov chain Monte Carlo (McMC) method is effective for reconstructing permeability and porosity fields. The McMC method is serial in nature due to its Markov property....
In data assimilation problems, various types of data are naturally linked to different spatial scales (e.g. seismic and electromagnetic data), and these scales are usually not coincident to the subsurface simulation model scale. Alternatives like down/upscaling [1] of the data and/or the simulation model can be used, but with potential loss of important information. To address this issue, a...
In the exploration of deep formations, alterations in pore pressure change the mechanical equilibrium of the porous medium leading to stress modifications which alter rock properties such as permeability and porosity and, consequently, the fluid flow pattern (Murad et al., 2013). The coupling of geomechanical effects and fluid flows is widely influenced by the natural rock heterogeneity...
Numerical simulations of immiscible two-phase flow in porous
media with dynamic capillary pressure and gravity interactions in
heterogeneous porous media are presented with a novel computational
method based on ideas introduced in [1]. We formulate and test
numerically a new two-dimensional fully coupled and implicit procedure
for numericaly solving two-phase transport problems...
Low frequency lattice vibrations (<100 cm-2) are indicators of variety of structural transformations in the metal-organic frameworks (MOFs) [1]. In the case of zeolitic imidazole frameworks (ZIFs) ZIF-4, ZIF-7 and ZIF-8, the terahertz vibrations which are responsible for such phenomena as gate opening mechanism, shear-induced deformations or breathing. ZIFs are promising materials not only for...
Highly non-linear, porous structures stand out by significant changes of their morphology, allowing to control, e.g., their size, shape and acoustic band gaps. A research area that still remains to be fully explored in this exciting class of functional materials is their interaction with pore fluids. For example, the local-flow phenomenon is well studied for rocks, describing a local exchange...
Metal wire mesh is used in a wide variety of filtration applications. The geometric pore size is the diameter of the largest spherical bead that can pass through such a mesh. It is a very important quality measure and is found by filtering spherical glass beads with the mesh. Here, we describe how the geometric pore size of a mesh can be reproduced by computer simulations with GeoDict. The...
In the formulation of multiscale methods for second order elliptic equations that are based on domain decomposition procedures, (see e.g. the Multiscale Mortar Mixed Finite Element Method (MMMFEM) [1], the Multiscale Mixed Method (MuMM) [2], Multiscale Robin Coupled (MRC) [3], the Multiscale Hybrid - Mixed Finite Element Method (MHM) [4]) typically the computational domain is decomposed into...
In this work, we show an alternative way of handling the spatially discontinuous capillary pressure models in two-phase flow in porous media. This topic is very challenging and has also been studied theoretically and numerically in recent works [1,2,3]. We propose a new numerical formulation, by combining mixed hybrid finite element and finite volume discretization strategies along with novel...
The Radial Basis Function generated Finite Differential (RBF-FD) is a meshless method that has attracted attention in the last decades by its flexibility in the numerical approximation of PDEs, simplicity of computational implementation and ease in the approach of complex geometries. It has already been successfully applied to various engineering problems such as heat transfer, electrostatics,...
In this talk, the speakers will introduce a high order flux-conservative finite element method for the fluid flow model equations in porous media. The numerical schemes are based on the classical Galerkin finite element method enhanced by a flux approximation on the boundary of a prescribed set of control volumes. The numerical approximations can be characterized as the solution of a...
