Effect of Non-uniform Loading
When the formation flows under the action of overburden pressure, it is more likely that the casing will be subjected to non-uniform loading as shown in Fig. 4.24. Nonuniform loading is generally caused by inadequate filling of the annulus with cement, which leaves the casing partially exposed to the flowing formation. Generally, two effects of nonuniform loading of casing are recognized: curvature and point-load effects (Nester et al., 1955).
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CEMENT |
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DRILLING FLUID |
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Arrows indicate salt movement |
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Fig. 4.24: Point loading effect due to the flow of salt. (After Cheatham and McEver, 1964.) |
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TIME = t + At |
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Fig. 4.25: Curvature effect due to the salt flow. (After Cheatham and McEver, 1964.) |
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TIME = t |
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COMBINED LOADING DUE TO FORMATION FLUID AND SALT FLOW (p ) |
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CEMENT |
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UNIFORM LOADING DUE TO FORMATION FLUID PRESSURE P02 OR Pf; p, — INTERNAL PRESSURE (a) |
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NON-UNIFORM LOADING DUE TO SALT FLOW {pf) (b) |
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(C) |
Fig. 4.26: Different modes of loading on composite casing. (After El-Sayed et al., 1989.)
The curvature effect is shown in Fig. 4.25. The accentuated irregular shape of the borehole axis is a result of washouts by the drilling fluid. At the in-gauge section of the hole, the flowing (salt) formation comes in contact with the pipe and restricts its movement. In the out-of-gauge section, particularly in sections where drilling fluid instead of cement surrounds the pipe, the formation continues to flow and closes the borehole. The flow of formation above or below the frozen point (gauge section of the hole or where there is an adequate filling of the annulus with cement) can cause severe bending loads.
Point loading generally occurs when the annulus is partially filled with cement ; the remaining volume is occupied by drilling fluid. When salt flows, the unsupported part of the casing is subjected to point loading (Fig. 4.25). As depicted in Fig. 4.26, p,-, and p02 are the hydrostatic heads due to the presence of drilling fluid in the annulus and borehole. The concentrated force represents the point loading by the formation and the resulting reaction forces on the opposite side of the casing (see Fig. 4.26(b)). Figure 4.26(c) represents the combined effects of uniform load due to drilling fluid (p02 and p,-,) and nonuniform load due to formation flow (pj). This imbalance can lead to radial deformation of the outer pipe and a severe loading situation.
In a theoretical study, El-Sayed and Khalaf (1989) showed that the radial deformation caused by nonuniform external loading is transmitted to the cement and the inner casing. This results in additional internal stresses in the cement and the inner pipe, and additional contact pressures on the surfaces between the outer pipe and cement, and the cement and inner pipe. The authors found that the non-uniform external loading could reduce the collapse resistance of the composite pipe by as much as 20 %.