Applicable conditions and analytical corrections of plane strain assumption in the simulation of hydraulic fracturing

Plane stain assumption is widely used in the simulation of the distribution of stress and displacement around hydraulic fractures. According to the comparison of the solutions of elliptical fracture and plane stain fracture, the applicable conditions of plane strain assumption were discussed and the correction method was put forward. On the basis of the past research, a classical stress and displacement solution around a flat elliptical fracture was deduced, fulfilled and corrected. In comparison with the plain strain fracture solution, simulating results show that if taking plane strain assumption into consideration in the fracture height profile, the difference between the elliptical fracture solution and plane strain solution is negligible when the ratio between fracture length and fracture height is larger than 10, and the above critical value could be relaxed to 5 in some simulations which normal stress perpendicular to fracture face plays a decisive role. The plane strain fracture solution is accurate enough when the above critical value is satisfied, the correction of the plane strain fracture solution is needed when the length-height ratio is small. The correction charts of the additional initial stress of the horizontal well with an open-hole and the width of a single fracture were drawn under different length-height ratios. The fracture width of pseudo three dimension propagation models is easier to be modified by the correction charts.