Analytical up-scaling of small-scale permeability using a full tensor

An analytical method is developed to calculate an effective permeability tensor for a grid block by accounting for small-scale heterogeneity within the grid block. The method honours both the location and the orientation of the smallscale heterogeneity. Effective permeability tensors calculated using the analytical method and a numerical method show excellent agreement. Single phase flow simulations show that the effective permeability tensor method outperforms nontensor scale-up techniques in predicting the fluid flow distances in cases of general permeability anisotropy. The tensor method was also applied to two-phase flow simulations and it was shown that it retains the directionality in preferential flow paths after up-scaling.