Temperature effect on non-Darcian flow in low-permeability porous media

Abstract

The Darcy’s law specifies a linear relation between the Darcy velocity of a fluid flow and the pressure gradient that drives the flow. However, in low-permeability porous media, the velocity of a fluid flow exhibits a nonlinear dependence on the imposed pressure gradient, which is referred to as the non-Darcian flow behavior. Temperature has been postulated to affect the threshold pressure gradient of a non-Darcian flow; however, the supporting data is very limited due to the challenges in conducting flow experiments in low-permeability porous media. In this study we for the first time report a systematic measurement of the threshold pressure gradient under various permeabilities and temperatures. The results show that a higher temperature leads to a lower threshold pressure gradient under the same permeability and a faster reduction of the threshold pressure gradient with increasing permeability. The experimental data are fitted to a two-parameter model we previously developed to determine the parameters, h0 and a, which characterize the interfacial fluid-solid interactions and the transition between the Darcy and non-Darcian regimes. Both h0 and a decrease with an increasing temperature. The lower value of h0 under a higher temperature leads to the faster decline of threshold pressure gradient with increasing permeability. This is the first comprehensive experimental study that measured the threshold pressure gradient under multiple different permeabilities and temperatures, which generated the first laboratory dataset of this kind. The experimental data and the model constrained here allow for systematic predictions of both Darcy and non-Darcian flows for a general set of low-permeability porous media under various temperatures and pressure gradients, which have important applications to geological disposal of nuclear waste, hydrocarbon extraction from shale, and contaminant remediation in clay-rich formations.