BAKER HUGHES - Drilling Fluids Reference Manual

HYDRAULICS
D 2 = hole diameter, in.
D 1 = outside pipe diameter, in.
ρ = fluid density, lb m /gal
μ ea
= effective viscosity in the annulus, cp
n = power law constant for the
a
annulus
Flow Regime and Critical Reynolds Number
As discussed in the Rheology section of Chapter 2, fluid flow may be laminar, transitional, or
turbulent. In the experiments conducted by Osborne Reynolds in 1883, he found in observing the
flow of water in a circular pipe that the onset of turbulent flow began at a calculated Reynolds
Number of 2000 and was completely turbulent flow at a Reynolds Number of 4000. He then
defined a Reynolds Number between 2000 and 4000 as transitional flow – neither completely
laminar nor turbulent.
Since drilling fluids don't behave exactly like the flow of water, the Reynolds Numbers at which
flow changes from laminar to turbulent flow is not the same as water. The following equations
have been developed to determine the critical Reynolds Number (Rec) at which the flow regime
changes.
Laminar Flow
Rec < 3470 – 1370n
Transitional Flow
3470 – 1370n ≤Rec ≤4270 – 1370n
Turbulent Flow
Rec > 4270 – 1370n
Critical Flow Rate
In the drilling operation, it is usually desirable to have laminar flow in the annulus. In order to have
laminar flow, the critical Reynolds Number for laminar flow (3470 – 1370n a ) in the annulus must
not be exceeded. It is then easy to calculate the critical flow rate for the critical Reynolds Number
in two steps.
First, obtain the critical velocity by solving the following equation:
Where:
V
c
⎡
⎢
⎢
=
⎢
⎢
⎢
⎣
( 3470 −1370
)( 100)
928ρ
( D − D )
V c = critical annular velocity, ft/sec.
2
na
1
K
a
⎡ 2n
a
+ 1⎤
⎢ ⎥
⎣ 3n ⎦
⎡ 144 ⎤
⎢ ⎥
⎣D
2
− D1
⎦
a
1−n
a
na
⎤
⎥
⎥
⎥
⎥
⎥
⎦
1
2−na
BAKER HUGHES DRILLING FLUIDS
REFERENCE MANUAL
REVISION 2006 9-13