Abstract
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.
Highlights
One-dimensional prediction of non-Newtonian turbulent effect is more challenging than 2-D and 3-D shallow water flow prediction
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
Haldenwang, Fread, power law (PL), HB, and Pierre Carreau (PC) model results are compared with experimental flow depth along the channel at a steady state (Fig. 5)
Summary
One-dimensional prediction of non-Newtonian turbulent effect is more challenging than 2-D and 3-D shallow water flow prediction. There can be two types of friction assumptions in non-Newtonian fluids: internal friction due to viscous effect and external friction due to channel boundaries (Jin and Fread 1997, Fread 1988, 1993). External friction from channel walls can, in 1-D modelling, be calculated from the Darcy–Weisbach equation, the Chezy equation, and the Manning formula (Manning 1891; Chow 1959; Akan 2006; Abdo et al 2018). This is similar to the Newtonian flow friction force from the walls. F = 16∕Re∗ is widely used for the rectangular-channel friction factor for a fully developed non-Newtonian laminar flow. Propagated due to high flow rates, wall friction, shape of the channel, and viscous forces
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