  Over the past few years, we developed a mathematically rigorous method to
study the dynamical processes associated to nonlinear Forchheimer flows for
slightly compressible fluids. We have proved the existence of a geometric
transformation which relates constant mean curvature surfaces and
time-invariant pressure distribution graphs constrained by the
Darcy-Forchheimer law. We therein established a direct relationship between the
CMC graph equation and a certain family of equations which we call
$g$-Forchheimer equations. The corresponding results, on fast flows and their
geometric interpretation, can be used as analytical tools in evaluating
important technological parameters in reservoir engineering.
