Forced imbibition in stratified porous media: Fluid dynamics and breakthrough saturation

Imbibition, the displacement of a nonwetting fluid by wetting fluid, plays central role in diverse energy, environmental, and industrial processes. While this process is typically studied homogeneous porous media with uniform permeabilities, many cases, have multiple parallel strata different permeabilities. How such stratification impacts dynamics imbibition, as well saturation after breaks through to end given medium, poorly understood. We address gap knowledge developing an analytical model imbibition medium two strata, combined pore network that explicitly describes crossflow between strata. By numerically solving these models, we examine left breakthrough. find breakthrough minimized when imposed capillary number Ca tuned value Ca$^*$ depends on both structure viscosity ratio fluids. Our results thus provide quantitative guidelines for predicting controlling flow stratified media, implications water remediation, oil/gas recovery, applications requiring moisture management materials.