Effect of Eccentricity, Voids, Cement Channels, and Pore Pressure Decline on Collapse Resistance of Casing

Abstract

Abstract Conventional collapse design is based upon uniform external pressure loading. Conventional design considers pore pressure and does not account for the effects on casing stresses from the external cement sheath and surrounding formation. In addition, the conventional design does not predict the collapse load of non-uniform loaded casing that arises from imperfect cement jobs and formation voids. This paper presents the results of a finite element study of casing subjected to external, non-uniform loading. These loads include the effects of cement channels and voids, surrounding formation voids, and pore pressure decline in those voids. A better understanding of these common downhole conditions will help to better understand the resultant stress fields and enable a more accurate determination of the necessary collapse strength of casing. Introduction Conventional collapse design fails to account for the collapse stresses present in non-uniform loaded casing. Cement channels and voids, formation voids, or eccentrically centered casing may cause non-uniform loading. The conventional casing design is based on the strengths predicted by the equations of the American Petroleum Institute. API's collapse resistance calculation is divided into four different equations based on the outside diameter to thickness ratio. These four equations are derived by both empirical and analytical methods. These equations are reasonably accurate assuming the collapse load is applied uniformly on the casing. This paper investigates the effects of non-uniform loading on collapse resistance by using finite element analysis (FEA). The study focused on the following non-uniform loading conditions:eccentrically centered casing,voids in cement and formation,channels in the cement, anddeclining pore pressure in voids. A better understanding of these common downhole conditions will help to analyze the induced collapse stresses and enable a more accurate determination of the necessary collapse resistance of casing. A two dimensional FEA model was verified against exact analytical solutions and then extended to capture the effects of cement, formation and non-uniform loading conditions. Material Properties Material properties define the strength and amount of deflection of a body. There are two different elastic properties called modulus of elasticity, Young's modulus, E, and modulus of rigidity, G. Materials are called elastic when, upon the release of stress, the material returns to its original shape. These elastic materials obey Hooke's law:Equation 1 The third elastic strain property is called Poisson's ratio (?) and expresses the ratio of the lateral strain to the axial strain. Its value is between zero and one half. Poisson's ratio varies with the material and is 0.3 for steel and 0.5 for an incompressible fluid (e.g. water). All three elastic constants are related to each other by equation 2:Equation 1 Finite Element Analysis In FEA, a geometrically or physically complex system is discretized into simple geometrical shapes. These shapes, called elements, are used to calculate the physical system's distortion and stresses under various conditions. Material properties such as Young's modulus, Poisson's ratio, etc. are assigned to each element. The continuous functions that describe the complex shape are replaced by piecewise approximations and expressed as unknown values at specific points on the element called nodes. Many structural analysis problems deal with the displacement of loaded bodies. First the displacement is calculated, then the strain is computed, and finally the stress is evaluated by use of a stress-strain relationship, like Hooke's law for elastic deformations.