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)
\(where,\ \)\(\tau\ :measures\ shear\ stess\ in\ \ \ \ lb/100\text{ft}^{2}\),\(YP\ :Yield\ Point\), \(PV\ :Plastic\ Viscosity\ \),\(\gamma\ :measures\ shear\ rate\ in\ \ \ \ \ \ \sec^{-1}\)