Generalized Newtonian (Pseudoplastic) Flow in Stationary Pipes and Annuli

Abstract

Published in Petroleum Transactions, AIME, Volume 213, 1958, pages 325–332. Introduction The first paper in this series outlined practical methods for applying the theory of steady-state flow of an ideal Bingham plastic liquid through a circular pipe and axially through a stationary concentric annulus to the engineering analysis of friction loss problems. In the present paper the properties of another useful rheological model, the pseudoplastic generalized Newtonian liquid, are considered. The terminology applied to the rheological models is derived from the following classification of rheological models. The term "generalized Newtonian" is a class designation applied to models which do not have yield points but which exhibit a dependence on shear rate. The term "pseudoplastic" applies to a sub-group of models within this class which exhibit a decrease in "viscosity" with increasing shear rate. The term "power model" refers to a mathematical model proposed for describing the behavior of the pseudoplastic liquid. This model is of interest since certain of the salt saturated, oil emulsion, and "low solids" drilling fluids, inverted emulsion- and oil-base drilling fluids, aqueous gels, gelled crudes and blocking agents employed in hydraulic fracturing operations are of this type. The present treatment considers the equations describing steady-state Poiseuille flow through a circular pipe and a stationary concentric annulus, and Couette flow between concentric rotating cylinders for a particular pseudoplastic model. As in the previous paper it is demonstrated how these equations can be applied to engineering calculations of friction losses. Graphical procedures for recovering the various flow curves and example calculations are included. A method for simplifying turbulent-flow correlations is also proposed.