Pore-level modeling of drainage: Crossover from invasion percolation fingering to compact flow

A pore-level model of drainage, which has been quantitatively validated, is used to study the effect of increased injection rate (i.e., increased capillary number) upon the flow, with matched-viscosity fluids. For small enough capillary number, the flows from the model correctly reproduce the flows from the invasion percolation with trapping (IPWT) model. As the capillary number is increased, the early-time flows mimic those of the IPWT-model, but then deviate towards compact flow at a characteristic time that decreases as the capillary number increases. That is, the larger the capillary number, the sooner the flow crosses over from IPWT flows towards compact (linear) flows.