Study of delayed creep fracture initiation and propagation based on semi-analytical fractional model

•Corresponding J and C* integrals have the same structure in Laplace space.•A semi-analytical inverse Laplace transform method was developed for Heaviside function.•Delayed initiation and propagation is very important for improving the well production.•Incremental fracture length created the creep is highly controlled by the net pressure in the operation. Fractional calculus has been widely used in the study of constitutive equation of geomaterials. However, a simple and convenient method for dealing with the viscoelastic problem based on fractional model efficiently and accurately is still absent. In this paper, constant stress assumption was employed to obtain the corresponding J and C* integrals in Laplace space and a semi-analytical inverse Laplace transform method based on Stehfest inverse Laplace transform was developed to apply inverse Laplace transform to Heaviside function. In conjunction with the semi-analytical superposition model for calculating the stress and displacement fields around the crack (or fracture), a model for simulating the delayed initiation and propagation of creep fracture was developed. The simulation results show that: the incremental fracture length enlarged by the delayed initiation and propagation is very important for connecting the reservoir rocks and improving the well production. J integral of hydraulic fracture tip will decrease first and then become to be periodic in the later shut-in period; its amplitude and frequency are governed by time-independent elastic theory and time-dependent creep rate. The incremental creep fracture length is not determined by the fractional order. However, the propagation rate of the creep fracture will be highly risen by the increasing of the fractional order.