Design Factor Collapse The casing will experience a net collapse loading if the external radial load exceeds the internal radial load. The greatest collapse load on the casing will occur if the casing is evacuated (empty) for any reason.

Design Factor Collapse If external pressure exceeds internal pressure, the casing is subjected to collapse. Such conditions may exist during cementing operations or well evacuation. Collapse strength is primarily function of the material’s yield strength and its slenderness ratio, dn/t. Lame’s equations: Pe Pi ri ro r st sr dn t

Design Factor Collapse 5 6 pe, pi – external and internal pressure sr, st – radial and tangential stresses

Design Factors Collapse Equations (5) and (6) are used under no axial tension or axial compression. Data in Table 7.6 (Applied Drilling Engineering) apply only for zero axial tension and no pipe bending. The maximal tangential stress, stmax, occurs at the internal surface of the pipe where r = ri.

Design Factors Collapse Primary collapse loads are generated by the hydrostatic head of the fluid column outside the casing string. These fluids are usually drilling fluids and sometimes cement slurry. Casing is also subjected to sever collapse pressure when drilling through troublesome formations such as: plastic clays and salts. Strength of the casing under external pressure depends in: length, diameter, wall thickness of the casing and the physical properties of the casing materials (yield point, elastic limit, poisson’s ration, etc.).

Design Factors Collapse Casing having a low dn/t ratio and low strength, reaches the critical collapse value as soon as the material begins to yield under the action of external pressure. Casings exhibit ideally plastic collapse behavior and the failure due to external pressure occurs in the so-called yield range. Casing with high dn/t ratio and high strength, collapses below the yield strength of the material. In this case, failure is caused by purely elastic deformation of the casing. The collapse behavior is known as failure in the elastic range.

Design Factors Collapse Collapse regimes Yield Range Elastic Range Transition Range Stress Strain Plastic range

Design Factors Collapse The collapse strength criteria consist of four collapse regimes determined by yield strength and dn/t. Each criterion is discussed next in order of increasing dn/t. Yield strength collapse: Yield strength collapse is based on yield at the inner wall. This criterion does not represent a “collapse” pressure at all. For thick wall pipes (dn/t < 15), the tangential stress exceeds the yield strength of the material before a collapse instability failure occurs. Assumed that the pipe is subjected only to an external pressure pe. From eq. (6), the absolute value of tangential stress st is always greatest at the inner wall of the pipe. Hence, the yield strength collapse occurs at the inner wall: r = ri then equation (6) becomes:

Design Factors Collapse 8 9 7 Rearrange equation (8) gives equation (9) to calculate the critical pressure for yield strength collapse, Pcr

Design Factors Collapse Plastic collapse: Plastic collapse is based on empirical data from 2,488 tests of K-55, N-80 and P-110 seamless casing. No analytic expression has been derived that accurately models collapse behavior in this regime. The minimum collapse pressure for the plastic range of collapse is calculated by equation (10). 10

Design Factors Collapse Transition Collapse: Transition collapse is obtained by a numerical curve fitting between the plastic and elastic regimes. The minimum collapse pressure for the plastic-to-elastic transition zone is calculated by equation (11) 11

Design Factors Collapse Elastic Collapse: Elastic collapse is based on theoretical elastic instability failure; this criterion is independent of yield strength and applicable to thin-wall pipe (dn/t > 25). The minimum collapse pressure for the elastic range of collapse is calculated by using equation (12) Most oilfield tubulars experience collapse in the plastic and transition regimes. 12

Design Factors Collapse

Design Factors Collapse Apply only when axial stress is zero and no internal pressure

Design Factors Collapse Calculate F

Design Factors Collapse Example Compute the collapse pressure rating for 20’’, K-55 casing with a nominal wall thickness of 0.635’’ and a nominal weight per foot of 133 lbf/ft.

Design Factors Collapse Example Solution: dn/t = 20/0.635 = 31.49 This is the transition collapse

Design Factors Collapse

Design Factors Collapse Combined Stresses All the pipe strength equations previously given are based on a zero axial stress state. This idealized situation never occurs in oilfield applications because pipe in a wellbore is always subjected to combined loading conditions. The fundamental basis of casing design is that if stresses in the pipe wall exceed the yield strength of the material, a failure condition exists. Hence the yield strength is a measure of the maximum allowable stress. To evaluate the pipe strength under combined loading conditions, the uniaxial yield strength is compared to the yielding condition.

Design Factors Collapse Combined Stresses The most widely accepted yielding criterion is based on the maximum distortion energy theory, which is known as the Huber-Von-Mises Theory. This theory states that if the triaxial stress exceeds the yield strength, a yield failure is indicated. Note that the triaxial stress is not a true stress. It is a theoretical value that allows a generalized three-dimensional stress state to be compared with a uniaxial failure criterion (the yield strength).

Design Factors Collapse Combined Stresses 13 Where sY – minimum yield stress, psi sVME – triaxial stress, psi VME: Von Mises Equivalent sz, st, sr – axial tress, tangential stress, and radial stress, psi

Design Factor Collapse Combined Stresses Setting the triaxial stress equal to the yield strength and solving equation (13) give the results: Equation (14) is for the ellipse of plasticity. Combining Eq. (14) and eq. (6) together and let r = ri, will give the combinations of internal pressure, external pressure and axial stress that will result in a yield strength mode of failure. < 0 for collapse and > for burst 14

Design Factors Collapse Combined Stresses

Design Factors Collapse Combined Stresses As axial tension increases, the critical burst-pressure increases and the critical collapse-pressure decreases. In contrast, as the axial compression increases, the critical burst-pressure decreases and the critical collapse-pressure increases.

Design Factors Collapse Combined Stresses Example Compute the nominal collapse pressure rating for 5.5’’, N-80 casing with a nominal wall thickness of 0.476’’ and a nominal weight per foot of 26 lbf/ft. In addition, determine the collapse pressure for in-service conditions in which the pipe is subjected to a 40,000 psi axial tension stress and a 10,000 psi internal pressure. Assume a yield strength mode of failure.

Design Factors Collapse For collapse pressure rating, r = ri then eq. (6) becomes

Design Factors Collapse From eq. (14) with we have 14

Design Factors Collapse For in-service conditions of sz = 40,000 psi and pi = 10,000 psi Solving eq. (14) gives

Design Factors Collapse