A new technique for accurately measuring two-phase relative permeability under non-Darcy flow conditions

Abstract A new steady-state technique for determining gas–water relative permeability curves for proppant packs under high confining stress conditions is presented. In this technique, a time domain reflectometry (TDR) device that can measure the saturation inside the proppant pack instantly and efficiently is introduced. De-aired water and nitrogen gas are simultaneously injected into the proppant pack under a desired confining stress, and the pressure drop and saturation are measured when steady-state conditions are reached. Two different proppant mesh sizes, 12/18 and 20/40, have been tested under four confining stresses ranging from 1000 to 4000 psi with repeatable and accurate results. In the majority of published techniques, two-phase relative permeability curves are determined by using Darcy׳s law. This might be accurate enough for low permeability formations under low flow rate conditions, but in high permeability fracture proppant packs, the non-Darcy flow effects, or inertial effects, cannot be neglected. Thus relative permeability curves neglecting inertial effects may lead to inaccurate predictions. In this paper, three flow models: the classic generalized Darcy׳s Law, the generalized Forchheimer flow model, and the two-phase Barree and Conway model ( Barree and Conway, 2007 ) are employed to calculate and compare the relative permeability results. The experimental results show that the non-Darcy flow effects on gas relative permeability are higher than those calculated using Darcy׳s Law. In addition, the various confining stress effects on water and gas relative permeability curves are also presented. A significant decrease in gas relative permeability and minor effects on water relative permeability occur as the confining stress increases. These results help to further understand the effects of multiphase flow in porous media.