Influence of pore throat ratio on imbibition dynamics (a) without crossflow and (b) with crossflow. Our theory and simulations do not rely on a specific pore morphology however, Ref. provides experimental images of an example stratified medium. The black resistors represent longitudinal flow, while red resistors represent transverse crossflow. Each stratum is modeled as a series of nodes separated by a distance Δ x and connected by resistors. The subscripts represent structural descriptors of each stratum i. Blue indicates wetting fluid and white indicates nonwetting fluid.
(a) Schematic of forced imbibition in a stratified medium with crossflow. Our results thus provide quantitative guidelines for predicting and controlling flow in stratified porous media, with implications for water remediation, oil/gas recovery, and applications requiring moisture management in diverse materials. We find that the breakthrough saturation of nonwetting fluid is minimized when the imposed capillary number Ca is tuned to a value Ca * that depends on both the structure of the medium and the viscosity ratio between the two fluids. By numerically solving these models, we examine the fluid dynamics and fluid saturation left after breakthrough. We address this gap in knowledge by developing an analytical model of imbibition in a porous medium with two parallel strata, combined with a pore network model that explicitly describes fluid crossflow between the strata. How such stratification impacts the fluid dynamics of imbibition, as well as the fluid saturation after the wetting fluid breaks through to the end of a given medium, is poorly understood.
While such flows are typically studied in homogeneous porous media with uniform permeabilities, in many cases, the media have multiple parallel strata of different permeabilities. Imbibition, the displacement of a nonwetting fluid by a wetting fluid, plays a central role in diverse energy, environmental, and industrial processes.
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