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

TL;DR

This paper introduces a geometric approach using constant mean curvature graphs to model nonlinear flows in porous media, offering a new tool for reservoir engineering analysis.

Contribution

It presents a novel differential geometric framework linking pressure distributions to constant mean curvature surfaces for nonlinear flow modeling.

Findings

Provides a geometric interpretation of nonlinear flows in porous media.

Enables evaluation of reservoir parameters using differential geometry.

Bridges PDE solutions with geometric surface analysis.

Abstract

This work represents an application of constant mean curvature graphs (as solutions of the mean curvature PDE) to non-linear non-Darcy flows in porous media. It relates time invariant pressure distribution graphs to graphs of constant mean curvature surfaces. This differential geometric interpretation provides an important tool for evaluating technological parameters in reservoir engineering.