A steady-state approach for evaluation of surge and swab pressures in flows with free surface boundary conditions

A new approach for predicting surge and swab pressures in open-ended pipes running in steady-state is proposed. In addition to the fluid flow through the annulus and drill pipe, the upper ends of drill pipe and annular space are assumed to be opened to the atmosphere, creating two free surfaces. The approach is based on the modified Bernoulli׳s equation applied to Bingham fluid flows. The pressure differences are not only due to viscous losses but also to fluid velocity differences, and to the fluid column weight differences. The model results are compared with measured data for a Newtonian fluid and the differences lie within an error range of 0% to +10%. A sensitivity analysis is conducted, depicting that the model depends on the Reynolds, Bingham and Froude numbers, and also on the pipe geometry (diameter ratios).