Fluid flow through porous media in the periphery of Darcy's Law
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Modern petroleum engineers have used many equations to describe the physics behind the fluid flow through porous media. Under ideal situations these equations, which form the basis of modern software, yield accurate results. However, ever so often engineers are faced with challenging problems that seemingly defy physics: be it a well test problem, a history matched simulation model, or even a tool as simple as the material balance. Upon further investigation, engineers have to concede to the simple explanation that the assumptions behind those equations were violated. Even further discomforting is the admission that engineers have not yet properly characterized the physics behind the fluid flow through porous media. Darcy’s pioneering work is at the heart of all equations related to porous media. Often engineers use it without question. The purpose of this dissertation is to expose some of the challenges to Darcy’s Law and provide scientific solutions to those problems. Specifically, following problems have been discussed: low velocity flow through porous media, non-Newtonian fluid flow through porous media, fluid dissipation across the closing fracture faces into the porous media, and high velocity flow through porous media. These problems have been studied under the scope of experimental setups, mathematical analysis and numerical simulation methods. New analysis methodologies are also proposed. Finally all of these problems have been anchored in real world by application to real field data. This work will help understand much of the challenges to engineers, where accuracy must be traded off in the interest of getting a solution to this problem. More importantly this dissertation will aid in understanding the conditions under which it would be acceptable to neglect some of the terms and more importantly the conditions under which neglecting complex features of fluid flow problems will lead to completely erroneous results.