1.3.1 Bingham Plastic model
The Bingham Plastic model is a two parameter rheological model, which
was presented by Eugene C. Bingham in 1922. The model is used in the oil
and gas industry to portray the various flow physiognomies exhibited by
different drilling mud systems. The fluids and drilling mud systems,
which obey this law display, a liner shear stress versus shear rate
curve after an initial shear stress brink has been reached and they are
classified as Bingham Plastic fluids [3]. A desired drilling fluid
should have an as low as possible plastic viscosity, achieved by
minimizing the influx of colloidal solids to allow for rapid drilling
while on the other hand, the yield point must be high enough but not
excessive as this can lead to excessive pump pressure being needed to
break the gel, to transport cuttings and debris out of the hole. Authors
such as Herrick (1932), Babson and jones (1935) and Fitzpatrick (1955)
all preferred the Bingham Plastic model to describe drilling mud
systems. The Bingham Plastic model can be written arithmetically as
shown below.
\(\tau=YP+PV\ \left(\gamma\right)\) (3)
\(where,\ \)\(\tau\ :measures\ shear\ stess\ in\ \ \ \ lb/100\text{ft}^{2}\),\(YP\ :Yield\ Point\), \(PV\ :Plastic\ Viscosity\ \),\(\gamma\ :measures\ shear\ rate\ in\ \ \ \ \ \ \sec^{-1}\)