Susan Schrader (Dept. of Petroleum Engineering, MT Tech)

5/5/2022  3:10pm

Abstract:

Darcy’s Law is a fundamental equation of fluid flow in a porous and permeable media and is the starting point for the derivation of essential models for subsurface flow modeling. Darcy’s Law relates the flow velocity to the pressure gradient, viscosity of the fluid, and the permeability - the ability of the medium to conduct fluid. Darcy’s Law can be used to accurately model flow in cases where the fluid is incompressible and the flow is steady state.

This talk begins by presenting the extension of Darcy’s Law to time dependent models with a slightly compressible fluid. This is achieved by combining Darcy’s Law with Conservation of Mass and an appropriate fluid model that relates the fluid density to the pressure. This more versatile model is a cornerstone of reservoir engineering, as it can be applied to gases and to liquids with dissolved gases at high pressures. Numerical solutions of this model are presented. However, as interest grows in flow through low permeability media in areas such as oil and gas production, CO2 sequestration, soil science, and filtration, laboratory work indicates that Darcy’s Law might not accurately model the observed behavior. Based on these observations, modifications to Darcy’s Law have been developed that alter either the pressure gradient or viscosity for more accurate models.

 This work proposes to extend these new models to both allow for time dependent flow and to allow for compressible fluids in a similar fashion as done for Darcy’s Law. Two potential new flow models are described, one based on a modification of the velocity term in Darcy’s Law, and the other requiring a threshold pressure gradient to be reached before flow begins.

 A future goal of the research is to determine if these new flow models can better predict the behavior of slightly compressible fluids in both time dependent and steady state regimes.   We describe a laboratory experiment that is designed to simulate the low permeability case.   Data from this experiment will be compared to simulation results from both the enhanced models and conventional models.