Chapter 2: Drilling Hydraulics. Introduction . One of the primary functions of drilling fluid is to carry drilled cuttings from the bit face, up the annulus, between the drillstring and wellbore, to surface
in the bit.
The pressure required to circulate the fluid through the drillstring and annulus are often called sacrificial pressure losses, they do not contribute anything to the drilling process
The ejection of the fluid through the nozzles in the bit also results in significant pressure loss but does perform a useful function(it helps to clean the drilled cuttings from the face of the bit.
Pt = Total pressure (psi)
Q = flow rate (gpm)
This expression for hydraulic horsepower is a general expression and can also be used to express the power which is expended in sacrificial losses and the power that is used to pump the fluid through the nozzles of the bit.
The primary function of the drilling fluid is to carry the drilled cuttings to the surface. In order to do this the velocity of the fluid in the annulus will have to be high enough to ensure that the drilled cuttings are efficiently removed.
If these cuttings are not removed the drillstring will become stuck and theoretical optimization will be fruitless.
Considerations with respect to optimization should therefore only be addressed once the minimum annular velocity for which the cuttings will be removed is achieved.
Only then, should any further increase in fluid flowrate be used to improve the pressure loss across the nozzles of the bit and therefore the hydraulic power at the bit face.
Vt = Va - Vs
Vt = transport velocity
Va = annular velocity
Dh = hole diameter
ODp = outside diameter of pipe
In this type of flow, layers of fluid move in streamlines or laminae. There is no microscopic or macroscopic intermixing of the layers. Laminar flow systems are
generally represented graphically by streamlines.
In turbulent flow there is an irregular random movement of fluid in a transverse direction to the main flow. This irregular, fluctuating motion can be regarded as
superimposed on the mean motion of the fluid.
In laminar flow, fluid layers flow parallel to each other in an orderly fashion.
This flow occurs at low to moderate shear rates when friction between the fluid and the channel walls is at its lowest. This is a typical flow in the annulus of most wells.
This flow occurs at high shear rates where the fluid particle move in a disorderly and chaotic manner and particles are pushed forward by current eddies. Friction
between the fluid and the channel walls is highest for this type of flow. This is a typical flow inside the drillpipe and drillcollars.
Unlike laminar flow, mud parameters (viscosity and yield point) are not significant in calculating frictional pressure losses for muds in turbulent flow.
occurs when the fluid flow changes from laminar to turbulent or vice versa.
group and is known as the Reynolds number. In field units:
Fig. 4-30. Laminar and turbulent flow patterns in a circular pipe: (a) laminar flow, (b) transition between laminar and turbulent flow and (c) turbulent flow
In a Newtonian fluid the shear stress is directly proportional to the shear rate (in laminar flow):
The constant of proportionality, is the viscosity of the fluid and is independent of shear rate.
Viscosity may be expressed in poise or centipoise.
Apparent viscosity =
is the slope at each shear rate,
1. Newtonian Fluid:
2. Bingham Plastic Fluid:
What ifty = 0?
API RP 13D
K = consistency index
n = flow behaviour index
analogous to the apparent viscosity.
When attempting to quantify the pressure losses inside the drillstring and in the annulus it is worth considering the following matrix:
Calculate the velocity of a fluid flowing through a 5" 19.5 lb/ft drillpipe (I.D.= 4.276") at 150 gpm.
b. Determine the pressure loss in the above situation if the fluid is a Bingham Plastic fluid with a plastic viscosity of 20 cp, a yield point of 15 lb/100 sq. ft and density is 10 ppg.
c. Calculate the pressure loss in the above situation if the fluid was a Power Law fluid with an non-Newtonian Index of 0.75 and a consistency index of 70 eq cp
b. If the fluid in the above situation is a Bingham Plastic fluid with a plastic viscosity
of 20 cp, a yield point of 15 lb/100 sq. ft and density is 10 ppg the pressure loss in
the pipe will be:
a. The velocity of a fluid flowing through a 5" 19.5 lb/ft drillpipe (I.D. = 4.276") at 150 gpm is:
c. The pressure loss in the above situation if the fluid was a Power Law fluid with an non-Newtonian Index of 0.75 and a consistency index of 70 eq cp would be:
Turbulent Flow of Newtonian Fluids in PipesThe equation for the pressure losses in turbulent flow of a Newtonian fluid in a pipe is derived from incorporating a control factor in the pressure loss equation:
1. the change in pressure due to a change in elevation is negligible.
2. the velocity vo upstream of the nozzle is negligible, compared with the nozzle velocity vn
3. the frictional pressure loss across the nozzle is negligible.
The exit velocity predicted for a given pressure drop across the bit, ΔPb, is never realised.
The discharge coefficient may be as high as 0.98 but the recommended value is 0.95.
This assumes that the best method of cleaning the hole is to concentrate as much fluid energy as possible at the bit.
This assumes that the most effective method is to maximise the force with which the fluid hits the bottom of the hole.