Modeling and discretization of flow in porous media with thin, full-tensor permeability inclusions

When modeling fluid flow in fractured reservoirs, it is common to represent the fractures as lower-dimensional inclusions embedded in the host medium. Existing discretizations of flow in porous media with thin inclusions assume that the principal directions of the inclusion permeability tensor are aligned with the inclusion orientation. While this modeling assumption works well with tensile fractures, it may fail in the context of faults, where the damage zone surrounding the main slip surface may introduce anisotropy that is not aligned with the main fault orientation. In this article, we introduce a generalized dimensional reduced model which preserves full-tensor permeability effects also in the out-of-plane direction of the inclusion. The governing equations of flow for the lower-dimensional objects are obtained through vertical averaging. We present a framework for discretization of the resulting mixed-dimensional problem, aimed at easy adaptation of existing simulation tools. We give numerical examples that show the failure of existing formulations when applied to anisotropic faulted porous media, and go on to show the convergence of our method in both two-dimensional and three-dimensional.publishedVersio

Linear and nonlinear convection in porous media between coaxial cylinders

We uncover novel features of three-dimensional natural convection in porous media by investigating convection in an annular porous cavity contained between two vertical coaxial cylinders. The investigations are made using a linear stability analysis, together with high-order numerical simulations using pseudospectral methods to model the nonlinear regime. The onset of convection cells and their preferred planform are studied, and the stability of the modes with respect to different types of perturbation is investigated. We also examine how variations in the Rayleigh number affect the convection modes and their stability regimes. Compared with previously published data, we show how the problem inherits an increased complexity regarding which modes will be obtained. Some stable secondary modes or mixed modes have been identified and some overlapping stability regions for different convective modes are determined

Simulation of muon radiography for monitoring CO2 stored in a geological reservoir

Current methods of monitoring subsurface CO2, such as repeat seismic surveys, are episodic and require highly skilled personnel to acquire the data. Simulations based on simplified models have previously shown that muon radiography could be automated to continuously monitor CO2 injection and migration, in addition to reducing the overall cost of monitoring. In this paper, we present a simulation of the monitoring of CO2 plume evolution in a geological reservoir using muon radiography. The stratigraphy in the vicinity of a nominal test facility is modelled using geological data, and a numerical fluid flow model is used to describe the time evolution of the CO2 plume. A planar detection region with a surface area of 1000 m2 is considered, at a vertical depth of 776 m below the seabed. We find that 1 year of constant CO2 injection leads to changes in the column density of ≲1%, and that the CO2 plume is already resolvable with an exposure time of less than 50 days