Interactions Between Viscous Fingering and Channeling for Unstable Water/Polymer Floods in Heavy Oil Reservoirs

Abstract Unstable floods and resulting viscous fingers remain a big challenge for reservoir simulation as the gridblock size is usually many orders larger than the viscous finger wavelength. This problem becomes especially pronounced with increasing applications of polymer and other chemical floods in the development of heavy oil reservoirs. Traditional reservoir simulators do not consider sub-grid viscous fingering effects and tend to overestimate the waterflood oil recovery. Using extremely fine grid models with centimeters size is unrealistic for field-scale simulations. While some researchers disregard viscous fingering by claiming that channeling dominates at the large scale for heterogeneous reservoirs, they miss the existence of viscous fingering at the small scale, which affects the displacement efficiency. To overcome this limitation, an effective-fingering model was developed to upscale fingering effects. The model divides each gridblock into three dynamic regions: two-phase flow, single phase oil flow, and bypassed-oil regions. Model parameters represent the maximum fraction of viscous fingering and the growth rates of different regions, which are used to modify flow functions. Model parameters from history match of a set of laboratory experiments show clear power-law correlations with a dimensionless viscous finger number, a function of viscosity ratio, velocity, permeability, interfacial tension, and core cross-sectional area. The correlation was achieved in the lab scale by considering homogeneous cores, and we extended it further to the field scale by performing high-order spatial accuracy numerical simulations at the intermediate scale using fine gridblock sizes roughly the same as that of the core. Geostatistical realizations of the permeability field were generated with various variances and correlation lengths. In a statistical way, we were able to quantify the viscous finger number valid for a gridblock at the field scale affected by various heterogeneities using the effective-fingering model. We also observed that channelized permeability distributions increase the viscous finger number drastically, showing the important role of channeling in such cases. This new model was applied to a field case with high heterogeneity undergoing water/polymer floods. We observed that the oil recovery was improved by the polymer slug because of the enhancement in both local displacement efficiency and sweep efficiency. In summary, we developed an upscaling model that provides a fresh-new insight on how to simulate unstable water/polymer floods at the field scale, which effectively accounts for the interplay of viscous fingering and channeling.