BAKER HUGHES - Drilling Fluids Reference Manual

Hydraulics
Power Law Model
Most drilling fluids exhibit behavior that falls between the behaviors described by the Newtonian
Model and the Bingham Plastic Model. This behavior is classified as pseudo plastic. The
relationship between shear stress and shear rate for pseudo plastic fluids is defined by the power law
mathematical model,
where,
τ
=
K( γ
n )
τ = shear stress
K = consistency factor
γ = shear rate
n = flow behavior index
Figure 1-10 illustrates the flow curve for a pseudo plastic fluid.
Figure 1-10
Flow Curve for a Power Law Fluid
The two terms, K and n, are constants in the Power Law Model. Generally, K is called the consistency
factor and describes the thickness of the fluid and is thus somewhat analogous to effective viscosity.
If the drilling fluid becomes more viscous, then the constant K must increase to adequately describe
the shear stress/shear rate relationship.
Additionally, n is called the flow behavior index and indicates the degree of non-Newtonian behavior.
A special fluid exists when n = 1, when the Power Law Model is identical to the Newtonian Model. If
n is greater than 1, another type of fluid exists classified as dilatant, where the effective viscosity
increases as shear rate increases. For drilling fluids, the pseudo plastic behavior is applicable and is
characterized when n is between zero and one. Pseudo plastic fluids exhibit shear thinning, where the
effective viscosity decreases as the shear rate increases just like the Bingham Plastic Model. Figure
1-11 shows the flow curves for these values of n.
Reference Manual
Baker Hughes Drilling Fluids
1-16 Revised 2006