Modeling and Upscaling Unstable Water and Polymer Floods: Dynamic Characterization of the Effective Finger Zone
Authors: Luo Haishan , Mohanty Kishore K. , Delshad Mojdeh , Pope Gary A. 
Published: March 2016

Abstract
Upscaling of unstable immiscible flow remains an unsolved challenge for the oil industry. The absence of a reliable upscaling approach greatly hinders the effective reservoir simulation and optimization of heavy oil recoveries using waterflood, polymer flood and other chemical floods, which are inherently unstable processes. The difficulty in upscaling 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.
In a recent study based on abundant experimental data, it is found 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), which is a combination of viscosity ratio, capillary number, permeability, and the cross-section area of the core. Based upon this important finding as well as the features of unstable immiscible floods, an effective-finger model is developed in this paper. A porous medium domain is dynamically identified as three effective zones, which are two-phase flow zone, oil single-phase flow zone, and bypassed oil (isolated oil island) zone, respectively. Flow functions are derived according to effective flows in these zones. This new model is capable of history-matching a set of heavy-oil waterflood corefloods under different viscosity ratios and injection rates. Model parameters obtained from the history match also have a power-law correlation with the viscous finger number.
The build-up of this correlation contains reasonable physical meanings to quantitatively characterize the upscaled behavior of viscous fingering effects. Having such a correlation enables the estimation of model parameters in any gridblock of the reservoir by knowing the local viscous finger number in reservoir simulations. The model is applied to several heavy-oil field cases with waterfloods and polymer floods with different heterogeneities. Oil recovery in water flooding of viscous oils is overpredicted by classical simulation methods which do not incorporate viscous fingering properly. Simulation results indicate that the new model reasonably differentiates the oil recoveries at different viscous finger numbers, e.g., lower injection rate leads to higher oil recovery. In contrast, classical simulations obtain close oil recoveries under different injection rates or degrees of polymer shear-thinning, which is apparently incorrect for unstable floods. Moreover, coarse-grid simulations using the new model are able to obtain consistent saturation and pressure maps with fine-grid simulations when the correlation lengths are not smaller than the coarse gridblock size. Furthermore, it is well captured by the model that the shear-shinning polymer solution can strengthen the fingering in high-permeability regions due to increased capillary number and viscosity ratio, which is not observed in waterflood. As a whole, 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 EOR projects.