Fracture Model Reduction and Optimization for Forchheimer Flows in Reservoir

TL;DR

This paper develops a reduced model for flow in fractured reservoirs with Forchheimer nonlinearities, proving its accuracy and using it to optimize fracture design for enhanced capacity.

Contribution

It introduces a low-dimensional coupled model for Forchheimer flows in fractures and applies it to optimize fracture geometry and properties.

Findings

Reduced model accurately approximates high-dimensional flow.

Optimal fracture design enhances reservoir capacity.

Method applicable to isotropic and anisotropic Forchheimer flows.

Abstract

In this study, we analyze the flow filtration process of slightly compressible fluids in fractured porous media. We model the coupled fractured porous media system, where the linear Darcy flow is considered in porous media and the nonlinear Forchheimer equation is used inside the fracture. Flow in the fracture is modeled as a reduced low dimensional BVP which is coupled with an equation in the reservoir. We prove that the solution of the reduced model can serve very accurately to approximate the solution of the actual high-dimensional flow in reservoir fracture system, because the thickness of the fracture is small. In the analysis we consider two types of Forchhemer flows in the fracture: isotropic and anisotropic, which are different in their nature. Using method of reduction, we developed a formulation for an optimal design of the fracture, which maximizes the capacity of the fracture in the reservoir with fixed geometry. Our method, which is based on a set point control algorithm, explores the coupled impact of the fracture geometry and beta-Forchheimer coefficient.