A Prediction Model for Sustained Casing Pressure in B-Annulus for Shale Gas Well Induced by the Leakage of the Micro-Annulus at the Casing-Cement Sheath Interface

Abstract This paper proposes a prediction method for sustained casing pressure (SCP) in the B-annulus induced by gas leakage at the casing-cement sheath interface (CCSI). The cross-sectional area of microscopic leakage channels at the CCSI is first quantitatively characterized based on micro-contact finite-element simulation. Then, based on parallel-plate theory and the laminar-flow theory of incompressible viscous fluids as an engineering approximation, a gas leakage-rate prediction model through the CCSI is established. Finally, considering both the variation in gas leakage rate at the CCSI and gas accumulation at the wellhead, a coupled prediction model for gas leakage rate and SCP is developed using a recurrence method. The case study shows that the relative errors for the predicted stabilized SCP and SCP stabilization time are 7.09% and 1.9%, respectively, which validates the proposed model. Furthermore, a systematic parameter sensitivity analysis is conducted on the evolution laws of SCP in the B-annulus of a shale gas well. The results show that the elastic modulus and Poisson’s ratio of the cement sheath exert insignificant effects on SCP evolution. The roughness and axial leakage length at the CCSI significantly affect the SCP stabilization time by altering gas leakage resistance. Variations in the internal pressure of the production casing and wellbore temperature exert moderate effects on SCP evolution mainly by changing the interfacial contact pressure. The density of the annular protection fluid and the formation pressure, by altering the driving pressure difference for interfacial gas leakage, not only significantly affect the stabilization time of SCP but also evidently influence the final stabilized SCP value. To mitigate SCP risk in the B-annulus, reducing the roughness and ensuring sufficient effective cementing length at the CCSI, adopting cement sheaths with low elastic modulus and high Poisson’s ratio, and appropriately increasing the density of the annular protection fluid are recommended.