Upscaling of Hydraulic Properties of Fractured Porous Media: Full Permeability Tensor and Continuum Scale Simulations

The simulation of flow and transport phenomena in fractured media is a challenging problem. Despite existing advances in computer capabilities, the fact that fractures can occur over a wide range of scales within porous media compromises the development of detailed flow simulations. Current discrete approaches are limited to systems that contain a small number of fractures. Alternatively, continuum approaches require the input of effective parameters that must be obtained as accurately as possible, based on the actual fracture network or its statistical description. In this work, a novel method based on the utilization of the Delta-Y transformation is introduced for obtaining the effective permeability tensor of a 2D fracture network. This approach entails a detailed description of the fracture network, where each fracture is represented as a segment with a given length, orientation and permeability value. A fine rectangular grid is then superimposed on the network, and the fractures are discretized so that each one of them is represented as a connected sequence of bonds on the grid with a hydraulic conductivity proportional to the ratio of effective permeability over fracture discretization length. The next step consists of the selection of a coarser rectangular grid on which the continuum simulation is performed. In order to obtain the permeability tensor for each one of the resulting blocks, the Delta-Y method is used. Finally, the resulting continuum permeability tensor is used to simulate the steady-state flow problem, and the results are compared with the actual flow pattern yielded by the fracture network simulation. The results obtained with both methods follow a similar flux pattern across the reservoir system. This shows that the proposed approach allows for efficient perform upscaling of hydraulic properties by honoring both the underlying physics and details of fracture network connectivity.