Many types of drilling mud are classified as non-Newtonian fluid which is the behavior between Newtonian fluid model and Bingham Plastic model. The relationship between shear rate and shear stress is defined by the power law model shown below:
Where
= shear rate
K = consistency factor
= shear rate
n = flow behavior index
This articles demonstrates how to determine pressure losses through drill string.
To determine pressure drop while the drilling mud is passing through a circular pipe (drill pipe and drill collar), you can calculate pressure loss with the following equation:
Assumptions:
Turbulent viscosity = 3 cp
Friction factor = 0.378(Q/D)-0.14
The first equation has a coefficient (C) to take into account the friction and the geometry of the bore ID.
Where:
P = pressure loss, psi
L = length of pipe, ft
W = mud density, ppg
Vf = viscosity correction factor
PV = plastic viscosity, centipoises
Q = flow rate, gpm
Di = inside diameter of pipe, inch
C = general coefficient for internal diameter of pipe
