Casing Design with Flowing Fluids
- Robert Mitchell (Halliburton)
- Document ID
- Society of Petroleum Engineers
- SPE/IADC Drilling Conference and Exhibition, 1-3 March, Amsterdam, The Netherlands
- Publication Date
- Document Type
- Conference Paper
- 2011. SPE/IADC Drilling Conference and Exhibition
- 1.6 Drilling Operations, 1.6.1 Drilling Operation Management, 1.14.1 Casing Design
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- 503 since 2007
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Tubing forces and displacements have long been calculated for design purposes. Formulations, such as the Lubinski's buckling model, have the underlying assumption that the fluids are static. Adding the effects of fluid dynamics to the pipe force equilibrium problem is not as straight forward as one might think.
The key point is the loads generated by the fluid on the tubing. What information can we obtain from a simple balance of momentum of the fluid in bulk? For example, for flow inside a pipe, we can determine exactly the load exerted on the pipe by the flowing fluid in terms of only the fluid density, pressure, and momentum.
What might be the effect of fluid dynamics? Most papers have dealt with static fluids, but how are these static effects modified for a flowing fluid? Do we need to add a pressure gradient to the pipe buoyancy? How is fluid friction included in the pipe loading? How does fluid momentum affect the pipe? For curved pipes, we might expect a centrifugal force term. The answers to these questions are often surprising, even counter-intuitive.
In this paper, the general equations for the balance of fluid momentum are then combined with the equilibrium equation for the pipe. The effective force then emerges as a natural combination of pipe force and fluid-force terms. Pipe displacement is usually formulated in terms of the actual axial force, but the necessary modifications to this formulation are presented for the effective force.
The effect of fluid pressure on casing was not originally appreciated and still causes confusion today. The current understanding of the role of fluid forces can be traced to a paper by Klinkenberg (Klinkenberg, 1951). This paper resolved many of the questions about the effect of fluid pressures on the neutral point by examining a column immersed in liquid. In a written discussion of this paper, H.B. Woods expanded Klinkenberg's results by considering different internal and external pressures. In this analysis, he introduced many of the ideas later used by Lubinski (Lubinski, 1962) in the analysis of tubing buckling. Lubinski presented tubing-buckling equations based on a "fictitious" buckling force that included the effects of internal and external pressure but was developed for fluids of constant density. Chesney and Garcia (Chesney, 1969) recognized that the fictitious force could be expressed as:
EQUATION. . . . . . (1)
where Ff is Lubinski's "fictitious?? force (compression positive), Fa is the compressive axial force in the pipe, pi is the internal pressure, ri is the inside radius of the pipe, po is the external pressure, and ro is the outside radius of the pipe. The negative of the buckling force is called the effective tension or the effective force. For a summary of current thinking on fluid forces, see Aadnoy (Aadnoy, 2006).
The way fluid forces load the tubing has always been somewhat unclear. In this paper, the fluid forces are developed from the balance of momentum associated with fluid. The loads derived by this technique include the effects of fluid friction and fluid momentum. For example, it is far from obvious that equation (1) includes the effect of fluid friction. In this paper, we examine several cases including internal flow in tubing and external flow in an annulus. For these flow cases, we evaluate the shear loading as a result of fluid flow and compare the results to the stress analysis formulation using the effective tension.
The Effective Tension
The momentum balances given below were presented in (Mitchell, 2009).
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