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.