BAKER HUGHES - Drilling Fluids Reference Manual

Baker Hughes Drilling Fluids
Continuity of Flow
Many hydraulic calculations in this manual require the use of the fluid velocity. It is important to
understand the difference between flow rate and velocity. Consider the flow of a liquid through a
pipe at a constant flow rate, as illustrated in Figure 1-6
Figure 1-6
Fluid Velocity is inversely Proportional to the Cross-Sectional Area of the Fluid
Conductor
An algebraic solution to the above diagram is described as follows:
Q flow = V 1 A 1 = V 2 A 2
If A 2 = ½ A 1
V 1 (2A 2 ) = V 2 A 2
V 1 = ½ V 2
Because drilling fluids are very nearly incompressible, the volumetric flow rate of fluid entering the
pipe must equal the volumetric flow rate leaving the pipe. This is the principle of continuity of flow.
The important result of this principle is that, at a constant flow rate, the fluid velocity is inversely
proportional to the area through which it flows. In other words, if the area decreases, the fluid
velocity must increase for a constant flow rate.
Mathematical Fluid Models
A mathematical fluid model describes the flow behavior of a fluid by expressing a mathematical
relationship between shear rate and shear stress. As described in the viscosity section, the shear
stress/shear rate relationship is a constant for Newtonian fluids.
For non-Newtonian fluids, however, the relationship between shear stress and shear rate is much more
complex. A generalized relationship for all non-Newtonian fluids has not been found. Instead,
various mathematical models have been proposed. These mathematical models do not describe the
behavior of non-Newtonian fluids exactly, but are merely close approximations.
Discussed below is a Newtonian Fluid Model which can be considered exact for Newtonian fluids,
and two non-Newtonian fluid models – the Bingham Plastic Model and the Power Law Model.
Additional models described are the Casson Model, the Robertson-Stiff Model, and the
Herschel-Bulkley Model.
Baker Hughes Drilling Fluids
Reference Manual
Revised 2006 1-11