Determination of minimum permeability plateau and characteristic length in porous media with non-Darcy flow behavior

A mathematical model has been formulated to determine the minimum permeability plateau and characteristic length in porous media with non-Darcy flow behaviour. More specifically, two new parameters are first defined to respectively include effect of minimum permeability plateau and characteristic length on non-Darcy flow behaviour across the completion with consideration of wellbore storage and skin effects. The newly formulated mathematical model is solved by discretizing the convolution integral and material balance equation, and then validated by simplifying it to the traditional Forchheimer model. The pressure together with its corresponding derivative type curves for both buildup and drawdown tests can be reproduced to examine effects of both wellbore storage and non-Darcy flow across the completion. The pressure derivative response with non-Darcy flow across the completion has been found to have a steep slope since the non-Darcy effect is increased after the wellbore-storage-dominated period. Such steep derivatives resulting from the increased non-Darcy effect cannot be observed from the existing models based on Darcy׳s law. In particular, the non-Darcy parameter depending on flow rate is found to dominate the shape of the derivative curves. Compared to the drawdown derivative curves, there exists a larger gap in the buildup derivative curves, indicating that buildup tests are more appropriate than drawdown tests for type curve matching non-Darcy flow behaviour.