Design Criteria for Casing in Stimulated Wells
The maximal allowable temperature at which the pipe body or joint yields is usually determined by using the classical theory proposed by Holliday (1969). According to Holliday, the maximal allowable casing temperature is given by the following relationship:
^casing ^surrounding 3” (3-112)
where:
AT = ^ + ^2 (4.113)
I ь
ared — reduced yield stress due to temperature and internal pressure
= [(сгут-)2 — 0.75 <j,] -0.5(j,.
<jyT = yield stress corrected for temperature (hot yield stress).
<7, = (Barlow’s equation, corrected for pipe imperfections.)
ay] = joint yield stress (cold yield stress).
Values of elevated yield stress, cryT, in tension, for different steel grades are presented in Table 4.8 (Goetzen, 1986). An iterative solution is necessary to determine the value of allowable casing temperature because the yield strength of the casing material is a function of temperature.
Equation 4.113 is derived based on the following assumptions:
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Table 4.8: Yield stress of different steel grades at elevated temperature. (After Goetzen, 1986; courtesy of ITE-TU Clausthal.)
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ST = standard, TR = thermal resistance
1. Casing is an elastic-perfect plastic material which: does not strain harden, but flows plastically; exhibits Bauschinger’s Effect; has yield strength in compression.
2. The coupling is as strong in compression as the pipe body at elevated temperature.
3. The tensile coupling strength is unaffected by thermal axial compressive strain.
4. Biaxial stress effects result only from internal pressure. There is no external casing pressure present.
5. Casing is fully cemented and, therefore, no axial displacement of pipe is expected.
The design method presented here is different from the traditional elastic method discussed in Chapter 3 because the casing is assumed to deform plastically. However, the successful application of plastic design requires the exclusion of creep rupture effects due to extremely high temperatures and it is, therefore, recommended that the design procedure should be limited to casing temperatures of 700 °F or less and that any increase in yield strength due to blue brittleness be neglected.
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450 400 350 300 250 200 150 100 50 |
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100 200 300 400 |
RADIUS (mm)
Fig. 4.33: Temperature distribution in a typical steam injection well. (After Sugiura and Farouq Ali, 1978.)
The exclusion of any effect of external pressure in the casing design may not be completely realistic for deep wells, i. e., below 5,000 ft. Thus, the design method is applicable to shallow wells where the casing is not subjected to collapse loads. The vast majority of the casing designs for thermal wells, however, have been based on this method and no serious casing failures have been reported (Goetzen, 1986).