Frictional Pressure Losses for Annular Flow of Drilling Mud and Mud-Gas Mixtures

The calculation of single-phase and two-phase flowing pressure gradients in a well annulus is generally based on an extension of empirical correlations developed for Newtonian fluids in circular pipes. Various techniques for extending pipe flow correlations to an annular geometry have been presented in the literature which involve the representation of the annular well geometry with an equivalent circular diameter and the representation of non-Newtonian fluid behavior with an apparent Newtonian viscosity. Unfortunately, little experimental data have been available which would allow a comparison of the relative accuracy of the various proposed techniques. In this study, experimental pressure gradient data have been taken in two 6000-ft wells. Frictional pressure losses for single-phase flow (mud only) in two annuli were compared to values predicted by the Bingham plastic and power law models. These calculations utilized the equivalent diameters defined by the Crittendon criteria, the hydraulic diameter, and the slot approximation. Also, total pressure difference for two-phase flow was measured for one annular geometry. This data was compared to that predicted by the Poettmann and Carpenter, Hagedorn and Brown, Orkiszewski, and Beggs and Brill correlations. Comparison of experimental data with the various prediction techniques was favorable, each having advantage in certain situations. For the data investigated, the Crittendon criteria using a Bingham plastic model gave the best results. The two-phase flow data was best predicted by the Hagedorn and Brown correlation utilizing an equivalent hydraulic diameter.