Transition From Viscous Fingering to Capillary Fingering: Application of GPU-Based Fully Implicit Dynamic Pore Network Modeling

Immiscible two-phase flow through porous materials exhibits different invasion patterns controlled by dynamic conditions, competition between the viscous and capillary forces, and the contrast between the fluids viscosities. Two distinct invasion patterns are viscous and capillary fingering. While the first one happens under unfavorable viscosity ratios at high injection rates, the second one happens when the viscous forces are very small compared to the capillary forces. Depending on whether the invasion is under the capillary fingering or viscous fingering regime, the remaining oil saturation and the effective permeability of the fluids can significantly change. The contribution of the present work has two key aspects: (a) It addresses how the remaining saturation changes at different flow rates (i.e., capillary numbers) for different unfavorable viscosity ratios in a three-dimensional system; (b) it presents a new dynamic pore network model using the fully implicit scheme which has been enhanced by the graphic processing unit (GPU) parallel computing. Additionally, the model has been carefully validated against micromodel experiments in both time and space, which to our best knowledge has not been reported in such detail in the literature. The results of the validated 3-D dynamic pore network model demonstrate the remaining saturation at the breakthrough time as a nonmonotonic trend with the imposed capillary number.