Mathematical Sciences: Numerical Analysis and Simulation of Reservoir Flows and Waves in Porous Media

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8903211 Douglas The principal investigators will study a variety of problems arising in numerical analysis and its applications to petroleum reservoir engineering and geophysics. In addition, they plan to establish the well-posedness of several models for reservoir simulation, including their derivation via homogenization techniques and the study of their regularity properties. Specifically, many questions related to several types of flows in naturally fractured reservoirs will be studied both theoretically and numerically. Included will be single-phase flows, two-phase immiscible flows, and miscible flows. The implementation of computational models for such flows will be carried out on parallel computers, after the models have been validated on workstations. A model for the propagation of waves in composite media consisting in part of elastic solids and in part of porous material saturated by a multi-phase fluid will be developed, beginning from basic physics and continuing through regularity and numerical approximation. The model will be applied to acoustic well-logging as an extension of current work on the Biot, single-phase model. THe numerical methods will be formulated so that parallel and vector computation is natural.