Stress distribution of cased elliptical hole with high fluid pressure: Analytical expression

Abstract

It's not uncommon that the high pressure fluid is injected within the cased wells, such as well test and hydraulic fracturing process. Recently, the circular model and numerical simulation are usually used to calculate the stress distribution in such circumferences. However, the interfaces of a cased hole are not circular but elliptical. Moreover, the numerical simulation method requires a large amount of computing and is not easy to generalize. Therefore, based on the complex stress function, this study obtained an analytical solution model of stress distribution in a cased hole with internal pressure. Consequently, the following conclusions are obtained: (1)The elliptical model can describe stress distribution more accurately, and predict the occurrence of plastic damage in the cement sheath earlier. (2) As injecting pressure increases, the probability of casing collapse first decreases and then increases. Under the conditions of this paper, the turning point is 71 MPa (3) In formations with higher in-situ stress ratio and fracture pressure, cement sheath and casing being collapsed and interface debonding are more likely to occur. In formations with higher brittleness, the cement sheath is prone to be damaged. Other complex situations are more likely to occur in formations with lower brittleness. (4) The elastic modulus and Poisson's ratio of casing and cement sheath should be lower. And the wellbore diameter should be as large as possible. Moreover, under the conditions of this paper, the optimal casing thickness is 10.54 mm. The proposed analytical model will be useful for casing program design.