Casing Collapse Pressure for Non-zero Internal Pressure Condition (Effect of Internal Pressure on Collapse) Jiang Wu Chevron ETC August, 2011 API specifies casing collapse rating primarily based on casing collapse test data. The casing collapse test is conducted with zero internal pressure inside the casing (Fig. 1). The external pressure which collapses the casing with zero internal pressure is defined as the casing collapse pressure or casing collapse rating: = (1) is casing collapse pressure, and is casing external pressure. Fig. 1 Zero internal pressure case. Fig. 2 Non-zero internal pressure case. For some casing design applications, there is an internal pressure inside the casing (Fig. 2) and we need to design the casing for large external pressure and prevent casing collapse. The casing collapse pressure at this case is traditionally calculated by directly reducing the internal pressure from the external pressure: = - (2) is casing external pressure, and is casing internal pressure. Chevron has been using Eq. 2 in casing collapse design on operations worldwide successfully for many years. However, another equation to calculate the casing collapse pressure for non-zero internal pressure case is listed in API 5C3/ISO 1400 and used in Landmark casing design software Stresscheck and tubular analysis software Wellcat: 1
= - (1-2t/D)* (3) is casing external pressure, is casing internal pressure, t is casing wall-thickness, and D is casing outside diameter. This Eq. 3 is simply to consider the internal pressure load () is acting on the casing internal diameter (d) and can t be directly reduced from external pressure, but reduced by a proration involving with d/d ratio: d* /D = (1-2t/D)* (4) The Eg. 3 gives a slightly larger casing collapse pressure () than that from Eq. 2. Which equation should be correct to use in calculating casing collapse pressure in non-zero internal pressure case? To answer this question, let us take look at the following models in Fig. 3. Model 1 is a piece of casing in atmosphere condition, while the model 2 is a piece of casing in hydrostatic pressure condition with pressure all around. Model 1 Model 2, Fig. 3 Casing in atmosphere condition vs. casing in hydrostatic pressure all around. Both casing in model 1 and model 2 are in Neutral stress condition or zero Von Mises equivalent stress condition, and if we would apply additional external pressure to both models (Fig. 4), they should collapse at the same additional external pressure (). This is because the change of stress that results in collapse is the same on the addition of external pressure () to model 1 and model 2. 2
Model 1 Model 2 Fig. 4 Adding the same additional external pressure to collapse both models. For Model 1, we have the collapse pressure = or = (1) For Model 2, we have the collapse pressure = + or = - (2) This verifies that the direct deduction of internal pressure from the external pressure (Eq. 2) can be the correct collapse pressure for pipe collapse design on non-zero internal pressure case, together with an added hydrostatic axial tension (Ff) to compensate to the hydrostatic axial compressive load in building Model 2, which is equal to applying the internal pressure to the cross-section area of the casing, as shown in Application Model in Fig. 5: Ff = 3.14159/4*(D^2 d^2)* (5) 3
Actual condition Hydrostatic Addition Application Model - - Fig. 5 Casing collapse pressure and hydrostatic axial tension for non-zero internal pressure case. Note this added hydrostatic axial tensile load is to take into account of the effect of internal pressure on pipe collapse together with using the direct differential pressure as pipe collapse pressure (Eq. 2). Although we know casing axial tension load may reduce the casing collapse strength, the combination of this added hydrostatic axial tension and the casing real axial load should normally be an axial compression load under casing/tubing collapse design condition and no reduction on casing collapse strength should occur. This is because the casing real axial load is normally a very large compression load under casing collapse condition. The following example of 13 5/8 liner PBR collapse pressure/load calculation may help understand how it works. 4
For the above 13 5/8 liner hanger PBR, the worst case discharge (WCD) condition for collapse design is: PBR OD: 14.375 PBR ID: 13.523 PBR External pressure: 13,505 psi PBR Internal pressure: 7,230 psi PBR real axial load: - 13505*3.14159/4*(14.375^2-13.523^2) = - 252,114 lb (compressive) PBR fictitious axial tension load from internal pressure: 7230*3.14159/4*(14.375^2-13.523^2) = 134,971 lb (tensile) PBR combined axial load: - 252,114 + 134,971 = -117,143 lb (compressive, will not reduce PBR collapse strength) PBR collapse pressure: 13505 7230 = 6275 psi. If we would use Eq. 3, the PBR collapse pressure becomes 6704 psi (6.8% higher than 6275 psi). 5
Conclusion 1. The direct differential pressure or the direct reduction of internal pressure from external pressure (Eq. 2) is the correct casing/tubing collapse pressure to use for non-zero internal pressure condition, which can be used for any size and weight and grade of casing, with an associated hydrostatic axial tension equal to the product of the internal pressure and the pipe cross-section area; 2. The associated hydrostatic axial tension (Eq. 5) due to the present of internal pressure will normally not cause a reduction of casing collapse strength, as the combination of the real axial load under the collapse design condition and the associated hydrostatic axial tension load together is normally still an axial compression load; 3. Casing collapse design may simply use the direct differential pressure or the direct reduction of internal pressure from external pressure (Eq. 2), without bothering to include the associated hydrostatic axial tension, based on the above statement of conclusion No.2, unless it becomes necessary for verifying the combined axial load as compressive; 4. When there is no internal pressure, such as designing casing collapse with void pipe condition, the direct differential pressure is obviously the collapse pressure (no difference on Eq. 2 and 3), and no associated hydrostatic axial tension will be added; 5. The above analysis and conclusion will also apply to tubing collapse design. 6