Development and application of analytic element method for estimation of effective hydraulic conductivity of anisotropic porous formations
Suribhatla, Raghavendra M.
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Effective hydraulic conductivity of heterogeneous formations is an important parameter for describing average flow and transport at the formation scale. In this dissertation, the main objective is to estimate effective conductivity of highly heterogeneous statistically anisotropic porous formations using accurate numerical simulations of flow. Stochastic models of the heterogeneous formations are constructed based on a multi-indicator representation of conductivity structure. The models consist of spheroidal inclusions oriented along principal axes of anisotropy and embedded in an anisotropic background conductivity. The corresponding flow problem is formulated based on the analytic-element method and solved using a scaling approach. Analytic expressions are developed for head and specific discharge due to multiple interacting spheroidal inclusions embedded in anisotropic background conductivity. Explicit linear relations between the various coefficients in analytic expressions are derived, allowing for highly efficient and accurate simulations of flow through tens of thousands of inclusions. Following the development of analytic-element solutions, the classical solution for effective conductivity based on effective medium approximation is tested against accurate numerical simulations of flow in highly heterogeneous anisotropic domains. All the numerical simulations consist of 50,000 inclusions placed according to periodic placement schemes, yielding high volume fractions of inclusions (0.5 and 0.7) and extending over hundred conductivity integral scales. The results show that the effective medium approximation is exact for the simulated multi-indicator models.