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Questions and Answers
What does the upper half of the ellipse construction represent in casing design?
What is the significance of setting the internal pressure to zero in the lower part of the ellipse?
Which variable in the equations provided directly relates to the material yield strength?
When plotting the lower part of the ellipse, what should be done with the negative values?
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How does increasing internal pressure affect axial stress according to the equation?
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What mathematical form do the solutions to the equations for both upper and lower halves of the ellipse take?
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Which condition is necessary for the formulation of the lower part of the ellipse?
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In the context of casing design, what does 'Ve x As' represent?
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What is the internal pressure at the surface calculated in the provided data?
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What is the value of the radial stress at r = di as derived in the calculations?
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What is the calculated value of axial stress (σa) according to the provided analysis?
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Which component is NOT used in the calculation of axial stress?
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What is the calculated maximum Von Mises stress (VM) from the analysis?
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What is the relationship between the yield stress and the derived design factor (DF) as per the calculations?
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In the context of the analysis provided, which of the following pressures is considered as external pressure at the surface?
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What is the significance of the dimensions used (6.094 in and 7 in) in the stress calculations?
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What is the formula for calculating collapse pressure?
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Which assumption is NOT part of the simplified procedure for collapse design?
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How is external pressure determined in collapse pressure calculations?
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What does the variable CSD represent in the collapse pressure formula?
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The expression for collapse pressure can incorporate which of the following units?
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Which factor would NOT contribute to an increase in collapse pressure?
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Why are the assumptions made in the collapse design procedure considered severe?
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Which calculation is necessary for determining collapse pressure using equation (5.2)?
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Study Notes
Formation and Surface Pressure
- Formation pressure (Pf) at Total Depth (TD): 12231 psi at 15,880 ft.
- Surface pressure calculation: 12331 – 0.184 x 15880 results in 9309 psi.
- At surface, internal pressure equals 9309 psi, external pressure is 0 psi.
Radial and Tangential Stresses
-
Radial stress at r = di:
[- \frac{6.094^2 \times 9309}{7^2 \times 6.094^2} = -9309 psi] -
Tangential stress calculation:
[ t = \frac{6.094^2 \times 9309 - 0}{\frac{7^2 \times 6.094^2}{6} \times (7 - 6.094) } = 67,591 psi]
Axial Stress Calculation
- Axial stress (a) formula:
[ a = \left( \frac{air , weight}{casing , cross-sectional , area} \right) - buouyancy , force ] - Inserting values:
[ a = \left[ \frac{32 \times 15880}{9.3173} \right] - \left[ 16 \times 0.052 \times (15880 - 12915) + 0.052 \times 12915 \times 15.6 \right] ]
Yielding 41,596 psi.
Von Mises Stress Calculation
- Von Mises stress formula:
[ VM = \frac{a + t + \sqrt{(t^2 + a^2)}}{2} ] - Substituting values yields 67,922 psi.
Factor of Safety (DF)
- Factor of Safety (DF) formula:
[ DF = \frac{Material , Yield , Stress}{VM} = \frac{110,000}{67,922} \approx 1.6]
Pressure Evaluations
- Internal pressures can be analyzed at various critical points along the casing string (e.g., top of cement or shoe).
- Axial stress equation:
[ a = 0.5 C_1 P_i + 0.5 C_1 P_i + 4 C_3 P_i^2 ] - The quadratic equation provides both positive and negative roots for internal pressure.
Ellipse Construction
- The lower part of the ellipse is created by setting internal pressure to zero and using material yield strength.
- Axial stress for external pressure defined as:
[ a = 0.5 C_2 P_e + 0.5 C_2 P_e + 4 C_4 P_e^2 ]
Collapse Pressure Calculation
- Collapse pressure is calculated as:
[ Collapse , Pressure = External , Pressure - Internal , Pressure ] - Typical assumptions for a simplified collapse design:
- Casing is assumed empty due to lost circulation.
- Internal pressure inside casing is zero.
- External pressure results from the mud density applied at the casing setting depth (CSD).
Conclusion
- Simplified formula for collapse pressure:
[ C = mud , density \times depth \times acceleration , due , to , gravity ]
In psi:
[ C = 0.052 \times mud , density \times CSD , (ft) ] - Recognize severe assumptions applied in this model occur only under special circumstances.
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