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Channel fracturing revolutionarily changes continuous sanding into discontinuous distribution by wrapping proppant particles with a degradable fiber and then injecting these packs or pillars into the formation. Channel fracturing creates open channels between pillars and substantially increases the fracture conductivity. The pulse time of injecting proppants can influence pillar spacing, thereby changing the opening of the fracture. Under different formation conditions, determining a proper pulse time to improve the wellbore productivity is the key problem in channel fracturing.

On the basis of Hertz contact theory, we assume that a proppant pillar is a standard cylindrical indenter. We also calculate the penetration depth beneath the original surface. In this manner, we obtain the residual fracture width under a certain confining stress. This residual fracture width serves as our optimization objective. Then, by combining …