Philipp Lang

Permeability tensor of three‐dimensional fractured porous rock and a comparison to trace map predictions

The reduction from three- to two-dimensional analysis of the permeability of a fractured rock mass introduces errors in both the magnitude and direction of principal permeabilities. This error is numerically quantified for porous rock by comparing the equivalent permeability of three-dimensional fracture networks with the values computed on arbitrarily extracted planar trace maps. A method to compute the full permeability tensor of three-dimensional discrete fracture and matrix models is described. The method is based on the element-wise averaging of pressure and flux, obtained from a finite element solution to the Laplace problem, and is validated against analytical expressions for periodic anisotropic porous media. For isotropic networks of power law size-distributed fractures with length-correlated aperture, two-dimensional cut planes are shown to underestimate the magnitude of permeability by up to 3 orders of magnitude near the percolation threshold, approaching an average factor of deviation of 3 with increasing fracture density. At low-fracture densities, percolation may occur in three dimensions but not in any of the two-dimensional cut planes. Anisotropy of the equivalent permeability tensor varies accordingly and is more pronounced in two-dimensional extractions. These results confirm that two-dimensional analysis cannot be directly used as an approximation of three-dimensional equivalent permeability. However, an alternative expression of the excluded area relates trace map fracture density to an equivalent three-dimensional fracture density, yielding comparable minimum and maximum permeability. This formulation can be used to approximate three-dimensional flow properties in cases where only two-dimensional analysis is available.

A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics

A new approach to upscaling two-dimensional fracture network models is proposed for preserving geostatistical and geomechanical characteristics of a smaller-scale “source” fracture pattern. First, the scaling properties of an outcrop system are examined in terms of spatial organization, lengths, connectivity, and normal/shear displacements using fractal geometry and power law relations. The fracture pattern is observed to be nonfractal with the fractal dimension D ≈ 2, while its length distribution tends to follow a power law with the exponent 2 < a < 3. To introduce a realistic distribution of fracture aperture and shear displacement, a geomechanical model using the combined finite-discrete element method captures the response of a fractured rock sample with a domain size L = 2 m under in situ stresses. Next, a novel scheme accommodating discrete-time random walks in recursive self-referencing lattices is developed to nucleate and propagate fractures together with their stress- and scale-dependent attributes into larger domains of up to 54 m × 54 m. The advantages of this approach include preserving the nonplanarity of natural cracks, capturing the existence of long fractures, retaining the realism of variable apertures, and respecting the stress dependency of displacement-length correlations. Hydraulic behavior of multiscale growth realizations is modeled by single-phase flow simulation, where distinct permeability scaling trends are observed for different geomechanical scenarios. A transition zone is identified where flow structure shifts from extremely channeled to distributed as the network scale increases. The results of this paper have implications for upscaling network characteristics for reservoir simulation.

Hydraulic sealing due to pressure solution contact zone growth in siliciclastic rock fractures

Thermo-hydro-mechanical-chemical simulations at the pore scale are conducted to study the hydraulic sealing of siliciclastic rock fractures as contact zones grow driven by pressure dissolution. The evolving fluid-saturated three-dimensional pore space of the fracture results from the elastic contact between self-affine, randomly rough surfaces in response to the effective confining pressure. A diffusion-reaction equation controls pressure solution over contact zones as a function of their emergent geometry and stress variations. Results show that three coupled processes govern the evolution of the fracture’s hydraulic properties: (1) the dissolution-driven convergence of the opposing fracture walls acts to compact the pore space; (2) the growth of contact zones reduces the elastic compression of the pore space; and (3) the growth of contact zones leads to flow channeling and the presence of stagnant zones in the flow field. The dominant early time compaction mechanism is the elastic compression of the fracture void space, but this eventually becomes overshadowed by the irreversible process of pressure dissolution. Growing contact zones isolate void space and cause an increasing disproportion between average and hydraulic aperture. This results in the loss of hydraulic conductivity when the mean aperture is a third of its initial value and the contact ratio approaches the characteristic value of one half. Convergence rates depend on small-wavelength roughness initially and on long-wavelength roughness in the late time. The assumption of a characteristic roughness length scale, therefore, leads to a characteristic time scale with an underestimation of dissolution rates before and an overestimation thereafter.

A synthesis of approaches for modelling coupled thermal–hydraulic–mechanical–chemical processes in a single novaculite fracture experiment

Abstract The geological formation immediately surrounding a nuclear waste disposal facility has the potential to undergo a complex set of physical and chemical processes starting from construction and continuing many years after closure. The DECOVALEX project (DEvelopment of COupled models and their VALidation against EXperiments) was established and maintained by a variety of waste management organisations, regulators and research organisations to help improve capabilities in experimental interpretation, numerical modelling and blind prediction of complex coupled systems. In the present round of DECOVALEX (D-2015), one component of Task C1 has considered the detailed experimental work of Yasuhara et al. (Earth Planet Sci Lett 244:186–200, 2006), wherein a single artificial fracture in novaculite (micro- or crypto-crystalline quartz) is subject to variable fluid flows, mechanical confining pressure and different applied temperatures. This paper presents a synthesis of the completed work of six separate research teams. A range of approaches are presented including 2D and 3D high-resolution coupled thermo–hydro–mechanical–chemical models. The results of the work show that while good, physically plausible representations of the experiment can be obtained using a range of approaches, there is considerable uncertainty in the relative importance of the various processes, and that the parameterisation of these processes can be closely linked to the interpretation of the fracture surface topography at different spatial scales.

Development of approaches for modelling coupled thermal–hydraulic–mechanical–chemical processes in single granite fracture experiments

The geological formation immediately surrounding a nuclear waste disposal facility has the potential to undergo a complex set of physical and chemical processes starting from construction and continuing many years after closure. The DECOVALEX project (DEvelopment of COupled models and their VALidation against EXperiments) was established and maintained by a variety of waste management organizations, regulators and research organizations to help improve capabilities in experimental interpretation, numerical modelling and blind prediction of complex coupled systems. In the present round of DECOVALEX (D-2015), one component of Task C1 has considered the detailed experimental work of Yasuhara et al. (Appl Geochem 26:2074–2088, 2011), wherein three natural fractures in Mizunami granite are subject to variable fluid flows, mechanical confining pressure and different applied temperatures. This paper presents a synthesis of the completed work of six separate research teams, building on work considering a single synthetic fracture in novaculite. A range of approaches are presented including full geochemical reactive transport modelling and 2D and 3D high-resolution coupled thermo–hydro–mechanical–chemical (THMC) models. The work shows that reasonable fits can be obtained to the experimental data using a variety of approaches, but considerable uncertainty remains as to the relative importance of competing process sets. The work also illustrates that a good understanding of fracture topography, interaction with the granite matrix, a good understanding of the geochemistry and the associated multi-scale THMC process behaviours is a necessary pre-cursor to considering predictive models of such a system.