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22 Part I Liquid Drilling Systems

The Bingham plastic model is used to describe the flow behavior of
Bingham plastic fluids. The model is expressed as
τ = τ y + μ _γ (2.2)
p
where
2
τ y = yield point (YP), lb/100 ft or Pa
μ p = plastic viscosity (PV), cp or Pa-s

Apparently, the Bingham plastic model is a linear model that does not
describe the flow behavior of the Bingham plastic fluid in the low-shear-rate
region. The discrepancy is shown in Figure 2.2. The model parameter yield
point (τ y ) overestimates the gel strength (τ s )of fluid.
The behavior of both the pseudo plastic fluid and the dilatant fluid
can be described by the so-called Power Law model expressed as
τ = K _γ n (2.3)
where

K = consistency index, cp or Pa-s
n = flow behavior index, dimensionless

200
Bingham plastic model
180
Low-rate behavior
160

140
Shear Stress 120

100
80
τ y
60
τ
40 s
20
0 0.5 1 1.5 2 2.5 3
Shear Rate
Figure 2.2 The Bingham plastic model does not describe the flow behavior of the
Bingham plastic fluid in the low-shear-rate region.