The primary goal of this research is to develop comprehensive analytical and numerical models for stress distributions around an inclined, cased wellbore by considering all wellbore processes, including amendments to models of other works. Most previous research has focused on individual wellbore processes rather than a comprehensive treatment which considers all wellbore processes simultaneously: a more realistic approach developed in this paper. To achieve this goal, this work utilizes an elastic approach by coupling a poroelastic, undrained condition and a steady state condition for stresses induced by wellbore temperature variations. The superposition principle is used to develop a comprehensive model, which is then applied to cement sheath failure. ABAQUS1 is utilized for numerical solutions to verify the comprehensive analytical model. These comprehensive models show analogous stress distribution results to those of previous models at each individual wellbore process when using the plane strain condition. However, ABAQUS model results show stress differences because the general plane strain model for the analytical solution and full 3D model for numerical solution are used. While there are differences between analytical and numerical solutions as noted, the comprehensive analytical model is a good alternate to costly numerical software programs, and it provides an improvement to plane strain models.
The petroleum industry drills inclined and/or horizontal wellbores for many purposes. The wellbores are completed using casing and cement to maintain wellbore integrity. Moreover, these completed wellbores often experience severe conditions that threaten the integrity of the wellbore: eccentric casing; large changes in wellbore pressure; large changes in wellbore temperature and so on. These conditions often intensify near wellbore stress states, which, in turn, influence wellbore stability, sand production, zonal isolation, and hydraulic fracturing. Most oil companies spend significant amount of money to prevent the loss of wellbore integrity. Therefore, proper modeling of the stress states around wellbores is an important step in evaluating the effectiveness of a drilling/completion strategy. For modeling stress states around wellbores, this work mainly focuses on two objectives: (1) develop comprehensive analytical and numerical models for an inclined cased wellbore; (2) apply the developed models to study causes of the cement sheath failure. The following section introduces some background information relevant to the objectives.
Generally, several processes are required to model the state of stress of an inclined cased wellbore. Three main processes are considered as shown in Fig. 1: Phase 2, 3 and 4. In this figure, Phase 1 shows the natural state of rock formation under in situ stresses before drilling. Phase 2 illustrates the process of drilling an inclined wellbore. Drilling itself causes several complicated processes. However, these can be simplified into two basic processes: plain excavation and wellbore pressure of the drilling mud. Bradley calculated the stress distribution around an inclined open wellbore through this simplification along with the assumption of linear elasticity of the formation, and applied them to wellbore failure [1]. It ignored the coupling between the rock matrix and the fluid contained inside.
