Burst-Induced Stresses in Cemented Wellbores
- W.W. Fleckenstein (Colorado School of Mines) | A.W. Eustes III (Colorado School of Mines) | M.G. Miller (Colorado School of Mines)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling & Completion
- Publication Date
- June 2001
- Document Type
- Journal Paper
- 74 - 82
- 2001. Society of Petroleum Engineers
- 2.2.2 Perforating, 1.6 Drilling Operations, 4.1.2 Separation and Treating, 4.1.5 Processing Equipment, 1.14.3 Cement Formulation (Chemistry, Properties), 3 Production and Well Operations, 1.14.1 Casing Design, 1.14 Casing and Cementing
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This paper presents the results of a finite element study of the resistance to burst pressure. Results from the 2D model quantify the effects of various mechanical properties of cement on a cemented wellbore. Comparison of the predicted stresses with experimental results demonstrated that ductile cement is far less likely to crack radially from high internal burst pressures than a brittle cement. It is demonstrated that the in-situ formation stresses acting on the cemented wellbore greatly affect the burst resistance of the cemented wellbore.
The industry acknowledges that there is an increase in the burst resistance of cemented pipe vs. uncemented pipe; but the effects of cement and formation mechanical properties, and in-situ stresses are not well understood. This paper presents the results of a finite element study of the resistance of casing to internal burst pressure under a variety of conditions. This will provide for better design understanding of the stress conditions developed in casing under burst loading.
2D stress-distribution model results are presented in graphical and tabular format for a variety of geometrical and mechanical material properties of formations, cement slurries, and casing combinations.
A better understanding of the true stress profile in cemented pipe allows for less expensive decisions concerning casing design parameters and safety-factor criteria. Applications using the burst resistance of the cemented pipe as a system as opposed to using the burst resistance of free pipe can include deeper drilling with thinner-walled pipe, smaller rigs, and better casing integrity decisions for refracturing candidates.
In casing design, standard practice is to design the casing while ignoring the cement effects, despite the industry's acknowledgment that there is a positive cement effect on the required strength of casing. A primary reason for this method of casing design is that previously, no method was available to determine the magnitude of this positive effect. This paper focuses on a method for determining the magnitude of the stresses in the casing, cement, and formation as a system and shows how cement enhances the ability of a casing string to resist burst pressures.
There are no standard casing design criteria for burst resistance. The American Petroleum Institute (API) publishes a bulletin1 of the formulas and calculations for casing properties that defines internal yield resistance as the lower of the internal yield resistance of the pipe or the internal yield resistance of the coupling. API's burst-pressure rating for the casing body is based on Barlow's equation, relying on the minimum yield stress of steel, the physical dimensions of the pipe, and a minimum tolerance to calculate a burst-pressure rating.
The objective of this paper is to model accurately the cased-borehole environment and simulate the effects of realistically constraining the ballooning of cemented casing caused by internal burst pressure. A better understanding of these stresses acting upon casing and the surrounding cement sheath will help quantify the risks so that more informed casing and cement job designs can be made. The risks associated with stimulation operations involving existing casing and high treating pressures will be better understood.
Finite Element Analysis
To study the effects of constraining the expansion of casing caused by internal burst pressures, the finite element analysis (FEA) method was chosen. The FEA method of analysis is a numerical technique to obtain approximate solutions to partial differential equations.2 The method is applied to a system by spatially discretizing the system and solving the FEA mathematics simultaneously across the geometry. The resulting matrix of equations describes the physical interactions at specified points called nodes, based on the relevant material mechanical properties and the applied boundary conditions. Computer hardware and software has advanced rapidly to the point that complex modeling can be accomplished with a desktop computer in a reasonable length of time. This allows practical analysis of problems in multiple dimensions.
The method is not tied to any specific discipline, but can be applied to many types of problems. Thermal analysis and structural and fluid mechanics are a few of the many applications.
The FEA method has the advantages of versatility and general applicability. Various shapes and sizes of objects can be described mathematically, and interactions between those objects can be solved. Irregular shapes can be approximated, allowing shapes with ill-defined boundaries to be analyzed. Several different materials with separate mechanical properties can be modeled easily.
In FEA, a continuous physical system is discretized into a series of finite elements. These elements are composed of a series of nodes at specified intervals. At the location of these nodes in structural mechanics, deflections and stresses are calculated. A series of equation matrices are solved, allowing each node to affect the deflection and stress at each other node. As the mesh becomes finer in this analysis, the increments between nodes become smaller, increasing the size and complexity of the system of matrices that must be solved. A larger number of nodes increases the number of calculations necessary to solve the system of equations.3
3D analysis is the most intuitive method for analysis. However, it is also computationally complex and prone to errors if the boundary conditions are not applied correctly. 2D and 1D models are less computationally intense and less prone to application error. However, they can lead to misunderstanding of the solution except under certain conditions.
There are three cases when 2D analysis is appropriate for the elastic analysis of solids: plane strain, plane stress, and axisymmetry. These problems are simplifications of 3D elasticity problems under the following assumptions.
Body forces, if any, cannot vary in the direction of the body thickness.
Applied boundary forces do not have axial components, and the forces must be uniformly distributed across the thickness.
Loads may not be applied across the parallel planes bounding the top and bottom surfaces.
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