Theoretical analysis of fracture conductivity created by the channel fracturing technique

The channel fracturing technique has been increasingly popular in recent years. It is of great significance in increasing fracture conductivity while reducing water and proppant consumption. Stable open channels are created inside the fractures by this technique, which allow hydrocarbons to flow through without too much resistance from proppant. However, both how to calculate the fracture conductivity and how the related influence factors work still lack enough study. In this paper, based on homogenization theory, an efficient model to calculate the effective permeability of channel-fracturing fractures is developed. Firstly, according to elastic contact theory, a simplified conceptual model is developed to represent the physical deformation of channel-fracturing fractures subjected to confining stress. In the fine scale, the coupled Darcy-Brinkman model is applied to simulate the fluid flow in fractures: the proppant pillars are considered as porous regions, in which flow is modeled by Darcy's equation, while Brinkman equation is used to describe the flow in the open channels between pillars. Then, the upscaling of these equations from fine scale to coarse scale is implemented based on homogenization theory. Thus, the effective permeability of channel fracturing fractures can be obtained eventually to evaluate the conductivity of fractures. Based on this model, the influence of different parameters is analyzed, including volume fraction of pillars, confining stress, pillars' distribution, etc.