Prediction of Surge and Swab Pressure Profile for Flow of Yield Power Law Drilling Fluid Model through Eccentric Annuli
Surge and swab pressure computation is very important in drilling hydraulics. Most blowout problem in oil wells have been as a result of surge and swab pressures developed from running or pulling of tubular goods in liquid-filled bore hole. Excessive surge pressures can fracture the geological formation, while excessive swab can result in blowouts. In this work the analysis of steady state, laminar couette flow of non-Newtonian yield power law drilling fluid model (Herschel-Bulkley) is used to compute the surge and swab in Eccentric annuli. A slot flow model was first of all developed for a yield power law fluid in a concentric annulus, this model equation formed the basis of this work. And in solving for an eccentric annulus, the mathematical concept of conformal mapping was applied. A suitable mathematical bilinear function was applied in mapping the original eccentric plane, for a particular eccentricity ratio, to a concentric (zero eccentricity ratio) plane. By applying a suitable iterative technique the various pressure values were obtained and plots of dimensionless pressures versus dimensionless flow rate or radii were made. From which for a particular eccentricity ratio, fluid behavior index, shear stress and consistency index, the corresponding surge or swab can be obtained.