Geometric framework for modeling nonlinear flows in porous media, and its applications in engineering

Our work is focused on certain theoretical aspects of non-linear non-Darcy flows in porous media, and their application in reservoir and hydraulic engineering. The goal of this paper is to develop a mathematically rigorous framework to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. Using fundamental geometric methods, we have proved the existence of a nonlinear scaling operator which relates constant mean curvature surfaces and time invariant pressure distribution graphs constrained by the Darcy-Forchheimer law. The hereby obtained properties of fast flows and their geometric interpretation can be used as analytical tools to evaluate important technological parameters in reservoir engineering.