One-dimensional model of turbulent flow of non-Newtonian drilling mud in non-prismatic channels

One-dimensional model of non-Newtonian turbulent flow in a non-prismatic channel is challenging due to the difficulty of accurately accounting for flow properties in the 1-D model. In this study, we model the 1-D Saint-Venant system of shallow water equations for water-based drilling mud (non-Newtonian) in open Venturi channels for steady and transient conditions. Numerically, the friction force acting on a fluid in a control volume can be subdivided, in the 1-D drilling mud modelling and shallow water equations, into two terms: external friction and internal friction. External friction is due to the wall boundary effect. Internal friction is due to the non-Newtonian viscous effect. The internal friction term can be modelled using pure non-Newtonian viscosity models, and the external friction term using Newtonian wall friction models. Experiments were carried out using a water-based drilling fluid in an open Venturi channel. Density, viscosity, flow depth, and flow rate were experimentally measured. The developed approach used to solve the 1-D non-Newtonian turbulence model in this study can be used for flow estimation in oil well return flow.