Effective medium theories may be used for predicting the permeability and elastic properties of hydrocarbon reservoirs containing natural fractures, but need to be validated using numerical calculations. In this paper, three different types of stress boundary conditions are applied for a discrete fracture network (DFN) containing two sets of non-orthogonal vertical fractures. The variation of fracture aperture and compliance with stress is investigated, and the anisotropy in the effective permeability and seismic properties obtained from the simulations are compared with the predictions of effective medium theory. The nonlinear behavior of fractures observed in laboratory experiments is incorporated in the numerical method. Discrepancies between the permeability obtained from the simulations and from effective medium theory are attributed to an oversimplified treatment of fracture interconnectivity in the effective medium theory used. By contrast, the effective elastic compliances obtained from numerical simulation and effective medium theory are in good agreement, even for relatively complicated fracture networks. Although permeability anisotropy and seismic anisotropy both vary with stress, the relation between them is not simple.
As a result of the increasing stress that develops during burial, plate-shaped clay minerals in shales tend to align with planes oriented approximately perpendicular to the maximum stress direction. This partial alignment results in shale anisotropy, and this needs to be quantified to reliably extract reservoir fluid, lithology and pore pressure from seismic data and to understand time-to-depth conversion errors and non-hyperbolic moveout. The low aspect ratio pores between clay particles play an important role in determining the character of the anisotropy of shales and can be represented by a normal compliance BN and shear compliance BT that describe the deformation of the interparticle regions under an applied stress. The relations among the various anisotropy parameters for shales depend on the ratio BN/BT of these low aspect ratio pores. For perfectly aligned clay particles, Thomsen''s anisotropy parameter ? is a function only of the shear compliance BT, but ? and ? increase with increasing BN/BT. The presence of a fluid with non-zero bulk modulus in the regions between clay particles acts to decrease BN and may lead to significant reductions in e and d for sufficiently high fluid bulk modulus.
During oilfield drilling operations, the rock originally in the volume occupied by the wellbore is replaced by drilling fluid that exerts pressure on the borehole wall. This leads to a redistribution of stress in the vicinity of the wellbore, and may lead to yield of rock close to the borehole. This results in a decrease in stress near the borehole wall. This redistribution in stress is studied in this paper for a vertical well using a computational model that accounts for rock deformation and plastic strain in the near-wellbore region. The stress changes around the borehole lead to changes in elastic wave velocities that may be used to monitor the changes in stress that occur. The change in elastic wave velocities are sensitive to the mechanical properties of the rock, and may therefore be used to calibrate mechanical earth models used to predict rock failure due to production.