An approximate analytical solution for hydraulic fracture opening under non-uniform internal pressure


Because of the special non-uniform pressure distribution in hydraulic fracture, an especial hypothesis is proposed to get an approximate solution for the fracture opening, which satisfies the mixed boundary conditions on the fracture edges with the use of Bessel function integral properties. Error analysis of this approximate solution compared with the accurate solution is carried out. It is proved that the approximate solution is in good agreement with the accurate solution under the condition of this special pressure distribution in hydraulic-fracturing.