A Comparative Study of the Cement Sheath Integrity Based on the Linear and Hyperbolic Drucker-Prager Strength Criteria
Authors: Zhang Y. T. , Song L. A. , Zhao H. , Shan Y. L. , Yan X. F. , Huang X. , Zhao Y. P. 
Published: September 2023

ABSTRACT
Cement sheath is of vital importance in well life. It prevents inter-zonal cross-flow and provides support for the casing. Considering the complicated environments under down hole condition, numerical simulation plays an important role in cement sheath integrity evaluation. Accurate description of the mechanical behavior of cement sheath becomes increasingly important. This paper presents an investigation about the failure criteria of cement stone. In order to predict the strength characterization of different cement stones, a series of uniaxial tension and triaxial compression experiments were conducted for cement stone. Based on the experiment results, both linear Drucker-Prager(D-P) and hyperbolic D-P criteria were used to predict the failure of cement stone. A coupled thermo-mechanical finite element model is used to evaluate the cement sheath integrity during the hydraulic fracturing under high temperature condition. The experiment results indicate that the hyperbolic D-P criteria show better precision than the linear D-P criteria for both compression shear and tensile failure.

INTRODUCTION
In the early days of oil and gas industry, compressive strength was the only mechanical property cared about by the engineer, and it was usually designed base on the experience of the engineer. As the cementing technology develops, large scale simulators were used to simulate the casing-cement-formation loading and behavior downhole (Jackson and Murphey, 1993). With the increasing demands of oil and gas resource in recent years, the underground condition is becoming more and more complicated, which pose a challenge for the cement sheath integrity evaluation. It is very hard for the simulators to reproduce the loading and geometry the cement sheath beard at the bottom hole. The high temperature and high pressure will not only make the cost of simulator very expensive, but also introduce security challenges.
In contrast, numerical calculation is more flexible and easier to use, it plays an important role in mechanical properties optimization and cement sheath integrity evaluation (Bosma et al., 1999; Garnier et al., 2007). The first numerical calculation model was an analytical model (Thiercelin et al., 1997), the casing-cement-formation system was described with a plane strain model. The influence of temperature and pressure change for cement sheath integrity was studied. The numerical simulation such as finite element method(FEM) and finite difference method(FDM) are also used to perform mechanical evaluation for the cement sheath, they are always used to study more complicated problems, such as the failure of the cement sheath around the perforations (Lu et al., 2016) and the debonding of the interface between the cement sheath and the formation (Feng et al., 2016). The cement sheath fatigue failure also have a significant impact on the quality of cement and result in wellbore integrity issues, the artificial neural network is used to predict the fatigue failure of the cement sheath (Zheng et al., 2022).