Anisotropic Permeability in Fractured Reservoirs from Joint Inversion of Seismic AVAZ and Production Data

Anisotropic effective medium theory (for homogenization of fractured/composite porous media under the assumption of complete scale-separation) can be used to map the effects of sub-grid (or sub-seismic) fractures onto the grid-scale. The effective poroelastic stiffness and hydraulic permeability tensors that determines the seismic amplitude versus angle-azimuth (AVAZ) and production data (provided that one has information about the overburden and the porous matrix, as well as suitable tools for seismic forward modelling and fluid flow simulation) can therefore be viewed as functions of a relatively small number of parameters related with the fractures (e.g., fracture density and azimuthal orientation). In this paper, we develop a rock physics-based Bayesian method for joint inversion of seismic AVAZ and production data with respect to these parameters of the fractures. Within this stochastic framework, the expectation value of the effective permeability tensor is given by an integral of an effective medium approximation (derived by using rigorous integral equation or Green’s tensor function methods) weighted by the posterior probability density function over the allowed values of the parameters of the fractures. The present work complements those of Will et al. (2005), Jakobsen et al. (2007) and Jakobsen and Shahraini (2008) in the sense that we are using different inversion methods, seismic attributes and/or (rock physics) models of the fractured reservoir. Our interdisciplinary method for characterization of sub-grid fractures can in principle be applied to rather complicated models of fractured reservoirs (e.g., involving multiple sets of fractures characterized by different fracture densities and orientations, etc.). However, the initial (synthetic) modelling and inversion results presented here are associated with a relatively simple model of a fractured reservoir in which a single set of vertical fractures are located within sub-set of the (piecewise constant) reservoir model (that can in principle be identified using complementary methods). We have analysed synthetic AVAZ and production data contaminated with different amounts of normal distributed noise, and managed to recover the (unknown parameters of the fractures) effective permeability tensors with good accuracy. The results show clearly that the incorporation of seismic anisotropy attributes into the history matching process helps to reduce the uncertainties of the estimated permeability tensors.