Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion

Abstract

Quantification of mass and heat transport in fractured porous rocks is important to areas such as contaminant transport, storage and release in fractured rock aquifers, the migration and sorption of radioactive nuclides from waste depositories, and the characterization of engineered heat exchangers in the context of enhanced geothermal systems. The large difference between flow and transport characteristics in fractures and in the surrounding matrix rock means models of such systems are forced to make a number of simplifications. Analytical approaches assume a homogeneous system, numerical approaches address the scale at which a process is operating, but may lose individual important processes due to averaging considerations.Numerical stability criteria limit the contrasts possible in defining material properties. Here, a hybrid analytical-numerical method for transport modeling in fractured media is presented. This method combines a numerical model for flow and transport in a heterogeneous fracture and an analytical solution for matrix diffusion. By linking the two types of model, the advantages of both methods can be combined. The methodology as well as the mathematical background are developed, verified for simple geometries, and applied to fractures representing experimental field conditions in the Grimsel rock laboratory.

GEM-Selektor geochemical modeling package: revised algorithm and GEMS3K numerical kernel for coupled simulation codes

“…Applications are in the fields of groundwater and surface hydrology, water resources, geotechnics, radioactive waste disposal, geothermal energy, and CO 2 storage [7,30,35,46,47,51,54,60,63]. The concept of OpenGeoSys is a distributed open source scientific software development that should benefit from joint efforts of all involved groups.…”

The effect of spatial aperture variations on the thermal performance of discretely fractured geothermal reservoirs

“…The approach to use hybrid FEM and boundary integral representations is not new and our developed model was influenced by such works as Zhou et al (2009), which studied the effect of thermoelastic stresses in a geothermal reservoir. Other hybrid numerical and analytical methods have been derived before, Cheng et al (2001) used their developed methodology to model multi-dimensional heat effects in geothermal reservoirs and McDermott et al (2009) used their hybrid model to solve…”

“…They further showed how the mean flow rate was either enhanced or inhibited, depending on the orientation of the applied pressure drop. Transport properties such as dispersion have also been studied in self-affine fractures (Plouraboué et al 1998;Drazer and Koplik 2002;McDermott et al 2009;Auradou et al 2010). Numerical studies exhibit non-Gaussian transit time distribution with long tails (Drazer and Koplik 2002) and experiments with Newtonian and shear thinning fluids showed that geometric/hydraulic dispersion is dominant at low Péclet numbers with the dispersion coefficient on the order of the Péclet number (Auradou et al 2010).…”

Uncertainty analysis of thermo-hydro-mechanical coupled processes in heterogeneous porous media

“…THM processes in fractured-porous media occur at extremely different length and time scales, i.e. relatively fast advection in fractures and very slow diffusion into the porous medium [35]. Therefore, high performance computing (HPC) is absolutely indispensable to cope with the extreme computational costs for uncertain fractured-porous media concepts.…”