Hierarchical modeling of fractures for naturally fractured reservoirs
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Discrete Fracture Networks (DFN) models have long been used to represent heterogeneity associated with fracture networks but all previous approaches have been either in 2D (assuming vertical fractures) or for simple models within a small domain. Realistic representation of DFN on field scale models have been impossible due to two reasons - first because the representation of extremely large number of fractures requires significant computational capability and second, because of the inability to represent fractures on a simulation grid, due to extreme aspect ratio between fracture length and aperture. This thesis presents a hierarchal approach for fracture modeling and a novel random walker simulation to upscale the fracture permeability. The modeling approach entails developing effective flow characteristics of discrete fractures at micro and macrofracture scales without explicitly representing the fractures on a grid. Separate models were made for micro scale and macro scale fracture distribution with inputs from the seismic data and field observations. A random walker simulation is used that moves walkers along implicit fractures honoring the intersection characteristics of the fracture network. The random walker simulation results are then calibrated against high-resolution flow simulation for some simple fracture representations. The calibration enables us to get an equivalent permeability for a complex fracture network knowing the statistics of the random walkers. These permeabilities are then used as base matrix permeabilities for random walker simulation of flow characteristics of the macro fractures. These are again validated with the simulator to get equivalent upscaled permeability. Several superimposed realizations of micro and macrofracture networks enable us to capture the uncertainty in the network and corresponding uncertainty in permeability field. The advantage of this methodology is that the upscaling process is extremely fast and works on the actual fractures with realistic apertures and yields both the effective permeability of the network as well as the matrix-fracture transfer characteristics.