Summary
The presence of a stochastic distribution of impermeable shale sheets strongly affects the production performance of a horizontal well. Oil recovery is drastically reduced, and its uncertainty is dramatically increased for a reservoir with high shale density and long correlation range. Construction of a probability distribution of the oil recovery based on many stochastic images requires extensive work and computation time. However, that probability distribution can be approximated easily if a single ranking parameter is assigned to each realization. Conventional effective vertical permeability, keV, which is based on vertical single-phase flow, was tested first because it governs horizontal-well productivity. This attempt was unsuccessful because of the inappropriate representation of inner and outer boundary conditions applied to the domain. Production-based effective vertical permeability, keV,p, which honors both inner and outer boundary conditions, was tried next. It successfully ranked each realization in terms of oil recovery after 10 years with excellent accuracy. The correlation between keV,p and recovery is independent of the shale density or correlation range. This study shows that honoring the appropriate boundary conditions to obtain a representative permeability is extremely important. The conventional permeability renormalization technique, in which either no-flow or constant-pressure boundaries are applied to coarse grids, fails for this reason.
