Modeling and Upscaling Unstable Water and Polymer Floods: Dynamic Characterization of the Effective Viscous Fingering

The upscaling of unstable immiscible flow remains an unsolved challenge for the oil industry. The absence of a reliable upscaling approach hinders effective reservoir simulation and optimization of heavy-oil recoveries by use of waterflood, polymer flood, and other chemical floods, which are inherently unstable processes. The difficulty in scaling up unstable flow lies in estimating the propagation of fingers smaller than the gridblock size. Using classical relative permeabilities obtained from stable flow analysis can lead to incorrect oil recovery and pressure drop in reservoir simulations. Extensive experimental data in water-wet cores indicate that the heavy-oil recovery by waterfloods and polymer floods has a power-law correlation with a dimensionless number (named viscous-finger number in this paper), a combination of viscosity ratio, capillary number, permeability, and the cross-sectional area of the core. On the basis of the features of unstable immiscible floods, an effective-fingering model is developed in this paper. A porous-medium domain is dynamically identified as three effective regions, which are two-phase flow, oil single-phase flow, and bypassed-oil region, respectively. Flow functions are derived according to effective flows in these regions. Model parameters represent viscous-fingering strength and growth rates. The new model is capable of history matching a set of heavy-oil waterflood corefloods under different conditions. Model parameters obtained from the history match also have power-law correlations with the viscous-finger number. This model is applicable to water-wet reservoirs; it has not been tested for mixed-wet and oil-wet systems, low-interfacial-tension (IFT) environments, low permeability, and heavy-oil reservoirs with free gas cap. In reservoir simulations, having such a correlation enables the estimation of model parameters in any gridblock of the reservoir by knowing the local viscous-finger number. The model was first applied to a heavy-oil field case with channelized permeability by waterfloods. Simulation results with the new model indicated that viscous fingering strengthened the channeling. Also, the new model shows that a lower injection rate leads to a higher oil recovery. In contrast, oil recovery in waterflooding of viscous oils is overpredicted by classical simulation methods that do not incorporate viscous fingering properly. We further showed that coarsegrid simulations with the new model were able to obtain saturation and pressure maps consistent with fine-grid simulations. The new model was then used to model a real field case in the Pelican Lake heavy-oil field. It was able to match the field-production data without major adjustment of reservoir/fluid properties from the literature, showing its competence in capturing subgrid viscous-fingering effects. Overall, the new model shows encouraging capability to simulate unstable water and polymer floods in heavy-oil reservoirs, and hence can facilitate the optimization of heavy-oil enhanced-oil-recovery (EOR) projects.