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Current simulation technology for naturally fractured reservoirs is based on either the continuum or the discrete-fracture approach. The more commonly used continuum model can simulate complex recovery mechanisms. However, it uses a very simplified representation of the fracture system for calculating effective fracture permeability. The discrete-fracture flow method can handle complex fracture geometry. However, its use has been typically limited to basic flow calculations through a connected fracture system embedded in zero-matrix-permeability rock.We have developed a new technique for estimating the effective permeability of gridblocks used in conventional simulators. The idea behind this technique is to integrate the realism of fracture systems, as captured by discrete-fracture models, with the complexity of the flow calculations offered by continuum models. The end product of developing this technique is an efficient numerical code based on the boundary-element method. This code permits the fracture system to be complex and poorly connected, and it also includes the contribution from flow through the matrix rock. For fluid flow in the matrix rock, the fractures are treated as planar-source distributions. Periodic boundary conditions, for the flow properties, are used for the calculation of the effective permeability of individual gridblocks.We first use a simple fracture system to demonstrate the validity of our method and to evaluate the sensitivity of the results to matrix and fracture properties. We then use fracture statistics data from the Mesaverde sandstone, effective permeability values from our code, and a continuum simulator to calculate tracer-flow patterns for a more realistic system.

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We describe a hierarchical approach for modeling fluid flow in a naturally fractured reservoir with multiple length-scale fractures. Based on fracture length (lf) relative to the finite-difference grid size (lg), fractures are classified as belonging to one of three groups:short disconnected fractures (lf << lg),medium-length fractures (lf ~ lg), andlong fractures (lf >> lg). Effective grid-block permeabilities, associated with the short and medium length fractures, are used as input to a finite-difference simulator. We also present a separate transport equation for flow through long fractures to capture effects of large-scale high permeability pathways. Our new approach provides an improved means to include realistic and explicit fracture descriptions. Previously, Lough et al. (1997, 1998) developed a numerical method to compute the effective permeability of simulation grid-blocks with realistic fracture characterizations. Although this method handles generalized fracture geometries, it is numerically inefficient for the case where many small fractures exist. The method can also underestimate the flow contribution from long fractures. Assuming a linear potential gradient along the short fractures, we derive an analytical solution for the permeability contribution from short fractures. The solution becomes more accurate as fractures become randomly distributed and asymptotically small in length. The permeabilities from this analytical solution are used as the effective matrix permeability in computing a combined effective grid-block permeability that includes medium-length fractures. The method of Lough et al. is used for this computation. This hierarchical approach takes into account coupled flow between the rock matrix, short fractures and medium-length fractures. Long fractures are modeled explicitly in the reservoir simulator, using a transport equation that describes flow between long fractures and surrounding simulation grid-blocks. Simulation results from our new hierarchical approach are compared with those from the conventional dual porosity/permeability model. Numerical efficiency and accuracy are also examined.