Oil–air biphasic flow has been simulated at the scale of an entire potato tuber tissue using a Kinetic Monte‐Carlo (KMC) formulation parameterized on microscopic observations. Extrapolations to more general configurations are proposed by combining the proposed KMC framework with oil momentum equations integrated at microscopic scale. Branched percolation routes in three‐dimensional honeycomb arrangement of cells are explored using a first‐passage algorithm. Three major applications are presented. KMC simulations are first considered to homogenize sparse dynamic observations at the scale of isolated cells up to the scale of a full tissue. The second application investigates the effect of cell damages on oil uptake. Finally, our general KMC formulation was successfully compared with a diffusive model of oil uptake. Comprehensive rules to set the distribution parameters of all quantities (kinetic and structure parameters) from scarce observations or general assumptions are discussed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2329–2353, 2015