Hydraulic Model for Accelerated Flows Through Porous Medium in the Form Drag-Dominated Regime

The pressure drop for steady uniform flows (UF) through low permeability porous media—packed bed of particles (balls and rods) and sand $(K<10−7m2)$—is predicted using the existing global Hazen-Dupuit-Darcy (HDD) hydraulic model, composed of the viscous and form drag terms. In this work, experiments are performed to generate pressure drop data for accelerated steady flows through porous media for a wide range of low permeability $(10−9<K<10−7m2)$⁠, low porosity (ϕ < 0.4) in the form drag-dominant (λ ≫ 1) flow regime. Using the data, the global spatial acceleration effect that arises due to channel cross section variation is shown to be unaccounted for in the existing global HDD model resulting in inaccurate prediction of pressure drop, with more than 80% error in such situations. A modified hydraulic model is developed, introducing geometric parameters in the drag terms in the existing hydraulic model, to account for the acceleration effects. By comparing the results with experimental data, the proposed modified hydraulic model is shown to predict the pressure drop for accelerated flows in porous media in the form drag-dominant regime, with less than 10% error.