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

主要研究人员将研究数值分析中出现的各种问题及其在石油油藏工程和地球物理学中的应用。此外，他们计划建立几个储层模拟模型的完备性，包括通过均质化技术推导模型和研究其规律性。具体来说，将从理论上和数值上研究与天然裂缝性储层中几种流动类型有关的许多问题。包括单相流、两相非混相流和混相流。这些流动的计算模型在工作站上得到验证后，将在并行计算机上执行。一个波在由弹性固体和多相流体饱和的多孔材料组成的复合介质中传播的模型将从基本物理开始，继续通过规则和数值近似。该模型将作为目前Biot单相模型工作的延伸，应用于声波测井。数值方法将被制定，使并行和矢量计算是自然的。

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.