Hierarchical modeling of flow in naturally fractured formations with multiple length scales

This paper describes hierarchical approach to modeling flow in a naturally fractured formation. Our model is based on calculating the effective permea bility of a fractured formation, as a function of grid block size, and usin g the results in a conventional finite difference flow simulator. On the ba sis of their length (l(f)) relative to the finite difference grid size (l(g )), fractures are classified as belonging to one of three groups: (1) short fractures (l(f) much less than l(g)), (2) medium-length fractures (l(f) si milar to l(g)), and (3) long fractures (l(f) much greater than l(g)). The e ffects of the fractures belonging to each class are computed in a hierarchi cal manner. The permeability contribution from short fractures is derived i n, an analytical expression and used as an enhanced matrix permeability for the next-scale (medium-length) calculation. The effective matrix permeabil ity associated with medium-length fractures is numerically solved using a b oundary element method. The long fractures are modeled explicitly as major fluid conduits. As numerical examples, tracer transport in fractured format ions was illustrated. The numerical results clearly indicated that effectiv e tensor permeability well represented directional, enhanced permeability i n fractured formations. The fluid-conduit formulation captured the efficien t fluid transport by long fractures.