AUTHORS: Kairui Li, N. N. Smirnov, Chengzhi Qi, A. B. Kiselev, Mingyang Wang
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This paper is focused on the evolution from the initial opening to the initial propagation of a preexisting-closed plane-strain hydraulic fracture. An implicit finite difference algorithm is proposed for avoiding solving this solid-liquid coupling nonlinear problem composed by lubrication equation for fluid flow and elasticity equation for fracture opening. By accurately estimating the main unknowns of the problem at each time step: estimating the length of fluid-zone by transient velocity of fluid front, the length of lag-zone by zero opening at the fracture tip, and the fracture opening at the next time step by the fluid volume conservation, the convergence velocity is deeply improved. In order to improve model accuracy, an adaptive time step method is adopted because of gradually decreasing velocity of fluid front. The relationship between grid length and time step is discussed for balancing convergence velocity and good accuracy, and a balance threshold determining scales of grid length and time step is given. Based on the improved implicit algorithm the evolution laws of the first stage from the initial opening to the complete opening and the second stage from complete opening to initial propagation are obtained
KEYWORDS: -Preexisting-closed plain-strain hydraulic fracture; Implicit algorithm; Adaptive time step
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