Non-linear flow reduction factor and effective permeability of fractal fracture network

In this study, we investigate flow behaviors in a subsurface reservoir with fractal fracture network when both laminar and non-linear flows may occur in different fractures. The objective is to investigate how the non-linear flows in some fractures affect overall network permeability. A new non-linear flow reduction factor is developed to quantify the overall effective permeability by two separate components related to fractal fracture network features and flow characteristics respectively. The non-linear flow reduction factor takes into account flowrate reduction due to non-linear effect that is related to the hydraulic gradient. The other component is mainly related to the network characteristics representing the permeability of the fractal fracture network. The critical Reynolds number is explicitly used to distinguish non-linear flow from laminar flow in individual fractures. The effects of network and flow characteristics, including fractal dimension, scaling coefficient and exponent, maximum fracture trace length, and hydraulic gradient, on the non-linear flow ratio and effective permeability are examined. Both the laminar flow effective permeability and non-linear flow effective permeability decrease with the increase in hydraulic gradient. After scaling by the non-linear flow reduction factor, the scaled effective permeabilities vary much less significantly with the hydraulic gradient compared with the non-scaled ones, especially for the non-linear flow portion. Although it is proposed based on the idea of non-linear flows, the newly developed factor can also capture the laminar flow effective permeability reduction due to the reduction in the number of fractures where laminar flows occur.