Deviation from Darcy Law in Porous Media Due to Reverse Osmosis: Pore-Scale Approach

Abstract

Shale and tight hydrocarbons are vital to global energy dynamics. The fluid flow in sub-micron pores of tight oil reservoirs varies from bulk fluid flow. The Darcy law is widely accepted to model creeping flow in petroleum reservoirs. However, traditional reservoir modeling approaches fail to account for the sub-micron mechanisms that govern fluid flow. The accuracy of tight oil reservoir simulators has been improved by incorporating the influence of sub-micron effects. However, there are still factors that affect sub-micron fluid mobility that need investigation. The influence of a chemical potential gradient on fluid flow in sub-micron pores was modeled by solving Darcy and the transport and diluted species equations. The findings indicate that when a chemical potential gradient acts in the opposite direction of a hydraulic pressure gradient (reverse osmosis), there exists a limiting pressure threshold below which a non-linear flow pattern deviating from the Darcy equation is observed. Furthermore, the simulation based on tight reservoir pore parameters shows that when the effect of a chemical potential gradient is added, the resultant flux is 8–49% less. Hence, including the effect of the chemical potential gradient will improve the accuracy of sub-micron pressure dynamics and flow velocity.