Large-Scale Averaging Analysis of Single Phase Flow in Fractured Reservoirs
Chen Zhangxin · SIAM Journal on Applied Mathematics · 1994
The method of large-scale averaging is introduced to derive and analyze the most general form of the dual-porosity model of single phase flow in naturally fractured reservoirs. The dual-porosity model contains the usual equations based on Darcy's law and the coupling terms representing the fluid transfer between the matrix and the fractures. A transient closure problem is developed to obtain and analyze the fracture and matrix permeability tensors and the fluid transfer terms. The spatial averaging theorem is presented from a mathematical point of view and proved rigorously by the distribution theory. The problem of wellposedness of the dual-porosity model is also considered. The techniques developed here are not restricted to either regular geometric fractures or spatially periodic reservoirs.