Radial fracture in a three-phase composite: Application to wellbore cement liners at early ages

Abstract

Little understanding exists between the early-age stress developments in a wellbore cement sheath and its risk of impairment. During hydration, the cement morphology and pore-pressure changes induce eigenstresses in the solid and pore volumes. Utilizing these stresses as the driving mechanism of fracture, this paper formalizes the inspection of a radial crack in an elastic cement sheath constrained by an inner steel casing and an outer rock formation. The solution is constructed in the framework of analytic function theory and seeks the Green’s function for an edge dislocation in the intermediate cement phase. A dislocation pile-up along the line of fracture constructs a singular integral equation for the crack opening displacement derivative, from which the energy release rate is readily deduced.Under the uniform development of eigenstresses, the stiffness ratios of steel-to-cement and rock-to-cement generally predict the crack to initiate along the steel-cement interface. Here, the impacts of (i) a rigid bond and (ii) a sliding interface with no shear are assessed. This leads to the primary result of the paper: the potential for radial fracture is substantially mitigated by ensuring the shear connection between the steel casing and the cement sheath.