Surge and swab pressures have been known to cause formation fracture, lost circulation, and well-control problems. Accurate prediction of these pressures is crucially important in estimating the maximum tripping speeds to keep the wellbore pressure within specified limits of the pore and fracture pressures. It also plays a major role in running casings, particularly with narrow annular clearances. Existing surge/swab models are based on Bingham plastic (BP) and power-law (PL) fluid rheology models. However, in most cases, these models cannot adequately describe the flow behavior of drilling fluids.

This paper presents a new steady-state model that can account for fluid and formation compressibility and pipe elasticity. For the closed-ended pipe, the model is cast into a simplified model to predict pressure surge in a more convenient way. The steady-state laminar-flow equation is solved for narrow slot geometry to approximate the flow in a concentric annulus with inner-pipe axial movement considering yield-PL (YPL) fluid. The YPL rheology model is usually preferred because it provides a better description of the flow behavior of most drilling fluids. The analytical solution yields accurate predictions, though not in convenient forms. Thus, a numerical scheme has been developed to obtain the solutions. After conducting an extensive parametric study, regression techniques were applied primarily to develop a simplified model (i.e., dimensionless correlation).

The performance of the correlation has been tested by use of field and laboratory measurements. Comparisons of the model predictions with the measurements showed a satisfactory agreement. In most cases, the model makes better predictions in terms of closeness to the measurements because of the application of a more realistic rheology model. The correlation and model are useful for slimhole, deepwater, and extended-reach drilling applications.

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