Resistance And Deformation Of Tubular Goods Under Non-Uniform And Combined External Loads
Authors: El-Sayed A.A.H. 
Published: March 2010

Abstract
The effect of non-uniform external load on the collapse resistance and radial deformation of well casings is discussed. Three types of external loads are dealt with:uniform,non-uniform, andcombined uniform and non-uniform.
The stress distribution within the wall of the pipe and the radial deformation of the cross section were determined with the help of known solutions from the mathematical theory of elasticity. Von Mises criteria were applied to determine the pipe's collapse resistance. Two empirical equations based on computer calculated results were derived to calculate the uniform and non-uniform collapse resistance of casing pipes.
The results showed that both the resistance and radial deformation of pipes depend on the steel's strength and the diameter-thickness- ratio. Increasing the steel's strength or decreasing the diameter-thickness-ratio increased the pipe resistance and decreased the radial deformation under uniform external load. The collapse resistance of pipe exposed to non-uniform external pressures were reduced by 72.6 to 88.7% compared to uniform external pressure and the radial deformation increased by about 100%. This could result in collapsed casing with drilling or production equipment getting stuck inside the casing. Applying combined uniform and non-uniform external pressures reduced the pipe's collapse resistance relative to non-uniform external pressure, but decreased the radial deformation of the pipe. Field measurements of radial deformation using caliper log or sonic log can help predict the non-uniformity of external pressure outside the casing as well as the possibility of casing collapse. The empirical equations fitted the computer calculated data with an absolute error range from 0.1 to 0.5%.

Introduction
Non-uniform pressure is the major cause of easing collapse in most wells penetrating viscoplactic evaporate formations such as salt. Non-penetrating pressure can occur in the presence of regional movement by the evaporates and exists in boreholes having an irregular shape resulting form washouts. As a result of washouts, an adequate fill of the annulus with cement may be difficult to obtain and loading the casing may occur due to salt flows. Figure 1 shows the possible pressure conditions resulting form salt flows in wells (1).
Non-uniform pressure can be divided into three categories(2):A uni-directional load applied on half of the outer surface of the casing, uniformly distributed along a diameter with a corresponding load in the opposite direction on the other half, together with hydrostatic pressures on the inner and/or outer surfaces.Opposing line load on the outer surface, together with hydrostatic pressure on the inner and/or outer surfaces.Line oad on one end of pipe diameter combined with complete restraint to radial deformation at the other end of the diameter, together with hydrostatic pressure on the inner and/or outer surfaces.
The foregoing three pressure conditions are special cases. More complex combinations may result from the superposition of two or more load types. The first condition is the predominant one in most oil and gas wells penetrating salt formation. The second and third conditions occur at the beginning of salt flow.