Upscaling of fluid flow in fractured rock masses
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Abstract
Numerical modeling of fluid flow is applied to assess hydraulic reservoir properties and their uncertainties for decades and thus proven to be an essential part of geo-resource exploration. Yet, one of its main challenges is how to properly translate flow from the pore- to the reservoir-scale - the so-called upscaling problem. For fractured reservoirs, where flow predominantly localizes in large individuals or connected networks of open discontinuities, this may be cumbersome, as their mechanically induced structures are often complex and inherently multi-scale. Field-data-constrained stochastic fracture network models with reduced-order discrete fracture representations are the most common approach to model multi-scale fracture systems in 3D. Upscaling their effective properties like permeability or porosity crucially relies on parametrizations prescribing an average flow behavior at the single fracture scale to model network-scale flow. Advancing the accuracy and applicability of these techniques to model fluid flow in fractured rock masses from the fracture to the network scale is the main scope of this thesis.
Initially, a new scheme to quantify the non-planar geometry of single fractures is established as a basis to derive a refined parallel plate parametrization from the results of numerous 3D Stokes flow simulations in synthetically generated fractures. The accuracy of this prediction scheme depends on the ratio between the fracture size and the length scale of the long-range correlations in its aperture field. Analyzing these correlation lengths in 3D-imaged, naturally occurring discontinuities revealed that simple linear relationships to their mean apertures serve as an approximation of this property in network-scale models. Prior knowledge of the fractures correlation length enables determining the lowest scale in the upscaling process, at which using reduced-order fracture network models with parameterized flow behavior accounting for in-fracture flow variability is statistically valid.
As a next step, the flow complexities in fracture intersections were explored in numerical simulations, revealing that they represent preferred pathways for fluid migration compared to the crossing fractures and that, if its orientation aligns with the applied pressure gradient and its length is close to the system size, it enhances effective permeabilities. A newly established pipe-flow parametrization scheme enables including these effects into network-scale simulations. There, computational limitations for networks with many fractures and incorporating hydraulic properties of the matrix represent current issues in discrete fracture network flow methods. Developing a new single continuum discretization method for discrete fracture networks that includes parametrizations for fracture and intersection flow to generate high-resolved grids of individual, fully anisotropic permeability tensors helps tackle these problems. Combining this with a newly developed, massively parallelized finite-element Darcy-flow code capable of incorporating anisotropic permeability tensors at the local scale improves the efficiency of upscaling hydraulic properties of fractured-porous media. Furthermore, the provided discretization guidelines help to avoid the resolution dependency of single continuum methods while conserving the anisotropic character of complex multi-scale fracture networks during the upscaling process.