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

Abstract

This paper describes hierarchical approach to modeling flow in a naturally fractured formation. Our model is based on calculating the effective permeability of a fractured formation, as a function of grid block size, and using the results in a conventional finite difference flow simulator. On the basis of their length (lf) relative to the finite difference grid size (lg), fractures are classified as belonging to one of three groups: (1) short fractures (lf≪ lg), (2) medium‐length fractures (lf ∼ lg), and (3) long fractures (lf≫ lg). The effects of the fractures belonging to each class are computed in a hierarchical manner. The permeability contribution from short fractures is derived in an analytical expression and used as an enhanced matrix permeability for the next‐scale (medium‐length) calculation. The effective matrix permeability associated with medium‐length fractures is numerically solved using a boundary element method. The long fractures are modeled explicitly as major fluid conduits. As numerical examples, tracer transport in fractured formations was illustrated. The numerical results clearly indicated that effective tensor permeability well represented directional, enhanced permeability in fractured formations. The fluid‐conduit formulation captured the efficient fluid transport by long fractures.