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Mud Hydraulics Fundamentals 23

When n < 1, the Power Law model describes the behavior of pseudo
plastic fluids or Power Law fluids. When n =1,thePowerLaw model
describes the behavior of Newtonian fluids. When n > 1, the Power Law
model describes the behavior of dilatant fluids.
The flow behavior of the Herschel-Bulkley fluids described by their
model is expressed as
τ = τ y + K _γ n (2.4)

Obviously, this three-parameter model is a general model that can be
used to describe the behavior of all of the fluids shown in Figure 2.1.
Most drilling fluids are too complex to be characterized by the New-
tonian model. Fluids that do not exhibit a direct proportionality between
shear stress and shear rate are classified as non-Newtonian. Non-Newtonian
fluids that are widely used in the drilling industry are the plastic and
pseudo plastic fluids described by the Bingham plastic model and the
Power Law model. The Herschel-Bulkley model is widely used by office
engineers in designing fluid hydraulics.
These non-Newtonian fluids are thixotropic because the apparent vis-
cosity (shear stress divided by shear rate) decreases with time after the
shear rate is increased to a new value. This shear-thinning property is
verydesirableindrillingoperations becausewewantlow viscosityto
reduce the circulating pressure in normal drilling operations, and we
want high viscosity during circulation breaks to suspend drill cuttings in
the annulus. At present, the thixotropic behavior of drilling fluids is not
modeled mathematically. However, drilling fluids generally are stirred
before measuring the apparent viscosities at various shear rates so steady-
state conditions are obtained. Not accounting for thixotropy is satisfactory
for most cases, but significant errors can occur when a large number of
direction changes and dimension changes are present in the flow system.
In contrast to the plastic and pseudo plastic fluids, apparent viscosity of
dilatant fluids increases with increasing shear rate. Since this shear-thickening
property is not desirable in drilling operations, dilatant fluids are not pur-
posely used as drilling fluids, but sometimes pseudo plastic fluids become
dilatant fluids when significant amount of starchlike additives such as CMC
are added to the system.

2.2.3 Measurements of Rheological Properties
Various types of instruments can be used to measure the rheological
properties of fluids. The Fann 35 VG meter shown in Figure 2.3 is