Buckling-induced lock-up of a slender rod injected into a horizontal cylinder

We investigate the buckling and post-buckling behavior of an elastic rod injected into a horizontal, frictional, cylindrical constraint through experiments, numerical simulations, and scaling analyses. Particular emphasis is given to the onset of helical buckling which can lead to lock-up and prevent further injection. This problem is of timely importance to the petroleum industry due to the prevalence of Coiled Tubing (CT) technology in horizontal wells. An experiment is developed at the desktop scale to allow for a precise exploration of parameter space, including the important effects of radial clearance and natural curvature of the injected rod. In parallel, we perform computer simulations derived from first principles, implementing a dynamic Kirchhoff rod model that includes the frictional interaction between the rod and constraint. Our numerical simulations allow a direct comparison with experiments, as well as a systematic exploration of the parameter space. Moreover, a scaling analysis is performed to identify the key dimensionless parameter(s) that justifies using these findings at the field scale, thereby enabling the direct application of the results from our desktop experiments and numerical simulations to a problem of industrial relevance.