An Explicit and Continuously Differentiable Flow Equation for Non-Newtonian Fluids in Pipes

Abstract

Summary A simple model approximates Herschel-Bulkley (HB) non-Newtonian fluids in laminar flow in pipes. It is continuously differentiable and explicit in the frictional pressure gradient. Such properties are needed for control, real-time optimization, and prediction in drilling operations. The accuracy of the new model is evaluated by comparing it with a numerical implementation of the implicit HB model and some representative approximations used in the literature. Very little loss in accuracy is experienced compared with the implicit solution.