Self-consistency of a heterogeneous continuum porous medium representation of a fractured medium

A possible approach to representing fractured rocks is to use heterogeneous continuum porous medium (CPM) models in which each grid block has an effective permeability appropriate to represent the network of fractures within the block. It needs to be demonstrated that the approach is self-consistent; that is, the effective permeability on a length scale larger than the grid blocks derived using the heterogeneous CPM model is close to that derived directly from the underlying network model. For models based on the Borrowdale Volcanic Group at Sellafield in the United Kingdom and the granite at Aspo in Sweden, it is shown that the use of heterogeneous CPM models is self-consistent, both for models using effective permeabilities determined directly from the underlying network of discrete features model and for models based only on the correlation structure of the effective permeability on the length scale of the grid blocks.