A new dual-porosity/dual-permeability model with non-Darcian flow through fractures

The presence of fractures is associated with high oil or water productivity as well as high contaminant vulnerability. Consequently, it is important to develop a technique for properly modeling fractured formations. The recent dual-porosity/dual-permeability approach uses Darcian flow through both matrix and fractures. Unfortunately, Darcian flow applies to creeping flow only. It is well known that the fluid velocity through fractures is often too high for the flow to be Darcian. This paper reports results of a new formulation which uses the Forchheimer equation to describe fluid flow through fractures and couples this equation with Darcyʹs law in order to describe flow through the matrix. Results are compared with those of the conventional Darcian dual-porosity/dual-permeability formulation. Results show a considerable difference between the two models. However, the discrepancy between the two models is less for a given range of parameters. Results of a series of numerical runs are presented in order to show the behavior of the new model for a range of different flow parameters, such as matrix permeability, fracture width, and fracture spacing. The scaling up problem of fluid flow is considered with a series of numerical runs for a field scale. Results show that the flow prediction is consistent only if the fracture width is not scaled up using the conventional approach. Finally, steady-state results are compared with field observations and a good agreement between the two is observed.