BAKER HUGHES - Drilling Fluids Reference Manual

Hydraulics
Other Models
Three other mathematical models have been developed which, at low shear rates, exhibit behavior
intermediate between that of the Bingham Plastic and Power Law Models. These models are, in
effect, hybrid models of the Bingham Plastic and Power Law Models. These are the Casson Model,
the Robertson-Stiff Model, and the Herschel-Bulkley Model. These mathematical models are
represented by the equations where,
Casson
τ = shear stress
τ o = yield stress
μ ∞ = plastic viscosity
γ = shear rate
K = consistency factor
γ o = shear rate intercept
n = flow behavior index
τ = [ τȯ 5 + ( μ ∞ γ ) .5 ] 2
The Casson Model is a two-parameter model that is widely used in some industries but rarely applied
to drilling fluids. The point at which the Casson curve intercepts the shear stress axis varies with the
ratio of the yield point to the plastic viscosity.
Robertson-Stiff
τ = K( γ o + γ) n
The Robertson-Stiff Model includes the gel strength as a parameter. The model is used to a limited
extent in the oil industry. This model is one of the two options available for hydraulics calculations in
ADVANTAGE Engineering.
Herschel-Bulkley
τ = τ o + K( γ
n )
The Herschel-Bulkley Model is a Power Law Model that includes a yield stress parameter. The
Herschel-Bulkley Model gives mathematical expressions which are solvable with the use of
computers. As a consequence the Helschel Bulkley model is more widely used than previously as it is
seen to more accurately describe most fluids than the simpler Power Law and Bingham models.
Therefore, it is being widely used for hydraulics calculations both by Baker Hughes Drilling Fluids
and other companies. Difficulties are still experienced making correlations between drilling fluid
parameters measured in the field and hydraulic calculations.
Reference Manual
Baker Hughes Drilling Fluids
1-20 Revised 2006