A comprehensive buckling model, a group of fourth order non-linear ordinary differential equations, was derived by applying the principle of virtual work. Lateral friction force is included in this model. The equations were normalized to make the solutions independent of the wellbore size, type of pipe and mud. The critical sinusoidal buckling load of tubing with different boundary conditions typically seen in drilling and well completion applications was analyzed based on the analytical solution of the linearized buckling equation. The results show that the effect of the boundary conditions can be neglected when the dimensionless length of tubing is greater than 5π. The authors further investigated the effects of friction on sinusoidal buckling by applying the principle of virtual work. The critical conditions for initiating sinusoidal buckling were determined by a group of three non-linear equations. A perturbation solution of these non-linear equations was obtained. It was found that the critical loads for sinusoidal buckling will increase by 30% to 70% for friction coefficients between 0.1 to 0.3. The authors also conducted an experimental study. The experimental results, including both data obtained by the authors and results published by other researchers, support the proposed model.

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