Adriana Paluszny

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.

How tough is brittle bone? Investigating osteogenesis imperfecta in mouse bone.

The multiscale hierarchical structure of bone is naturally optimized to resist fractures. In osteogenesis imperfecta, or brittle bone disease, genetic mutations affect the quality and/or quantity of collagen, dramatically increasing bone fracture risk. Here we reveal how the collagen defect results in bone fragility in a mouse model of osteogenesis imperfecta (oim), which has homotrimeric α1(I) collagen. At the molecular level, we attribute the loss in toughness to a decrease in the stabilizing enzymatic cross‐links and an increase in nonenzymatic cross‐links, which may break prematurely, inhibiting plasticity. At the tissue level, high vascular canal density reduces the stable crack growth, and extensive woven bone limits the crack‐deflection toughening during crack growth. This demonstrates how modifications at the bone molecular level have ramifications at larger length scales affecting the overall mechanical integrity of the bone; thus, treatment strategies have to address multiscale properties in order to regain bone toughness. In this regard, findings from the heterozygous oim bone, where defective as well as normal collagen are present, suggest that increasing the quantity of healthy collagen in these bones helps to recover toughness at the multiple length scales.

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 Sensitivity Study of the Effect of Image Resolution on Predicted Petrophysical Properties

Micro-CT scanning is a nondestructive technique that can provide three-dimensional images of rock pore structure at a resolution of a few microns. We compute petrophysical properties on three-dimensional images of benchmark rocks: two sandstones (Berea and Doddington) and two limestones (Estaillades and Ketton). We take scans at a voxel size of approximately 2.7

Finite-Element Modeling of the Growth and Interaction of Hydraulic Fractures in Poroelastic Rock Formations

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Pore-scale imaging and modelling

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Hybrid finite element–finite volume discretization of complex geologic structures and a new simulation workflow demonstrated on fractured rocks

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