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Pressure Drop Calculations
1.7-1
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1.7-2
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1.7-3 For multiple nozzles in
parallel
Vn is the same for each nozzleeven if thedn varies!
This followssince Dp is the sameacross each nozzle.
t
nA117.3
qv
2
2
t
2
d
-5
bitAC
q10*8.311p
10*074.8
pcv
4dn D
&
Cd = 0.95
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1.7-4 Hydraulic Horsepower
of pump putting out 400 gpm at 3,000 psi = ?
Power, in field units:
1714
000,3*400HHP
1714
pqHHP
D
Hydraulic Horsepower of Pump = 700 hp
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1.7-5 What is Hydraulic Impact
Force
developed by bit?
If:
psi169,1p
lb/gal12
gal/min400q
95.0C
n
D
pqc01823.0F dj D
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1.7-6 Laminar Flow
Rheological Models
Newtonian
Bingham Plastic
Power-Law (ADE & API)
Rotational Viscometer
Laminar Flow in Wellbore
Fluid Flow in Pipes
Fluid Flow in Annuli
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Laminar Flow of Newtonian Fluids
A
F
L
V
Experimentally:
1.7-7
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1.7-8 Newtonian Fluid Model
In a Newtonian fluid the shear stress is directly
proportional to the shear rate (in laminar flow):
i.e.,
The constant of proportionality, is the viscosity
of the fluid and is independent of shear rate.
sec
12
cm
dyne
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1.7-9 Newtonian Fluid Model
Viscosity may be expressed in poise orcentipoise.
poise0.01centipoise1
scm
g
1cm
s-dyne
1poise1 2
2cmsecdyne
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1.7-10 Shear Stress vs. Shear Rate for aNewtonian Fluid
Slope of line
.
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1.7-11 Typical Drilling Fluid Vs. Newtonian,
Bingham and Power Law Fluids
0
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1.7-12 Rheological Models
1. Newtonian Fluid:
2. Bingham Plastic Fluid:
viscosityplastic
pointyield
p
y
What ify 0?
py
rateshear
viscosityabsolute
stressshear
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1.7-13Rotating
Sleeve
Viscometer
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1.7-14 Figure 3.6Rotating
Viscometer Rheometer
We
determinerheological
properties
of drilling
fluids inthis device
Infinite
parallel
plates
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1.7-15 Rheometer
(Rotational Viscometer)
Shear Stress = f (Dial Reading)
Shear Rate = f (Sleeve RPM)
Shear Stress = f (Shear Rate)
)(f BOB
sleeve
fluid
RateShearthe(GAMMA),ofvalue
theondependsStressShearthe),TAU(
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1.7-16 Example
A rotational viscometer containing a Bingham plastic
fluidgives a dial reading of 12 at a rotor speed of 300RPM and a dial reading of 20 at a rotor speed of 600 RPM
Compute plastic viscosity and yield point
12-20
300600p
cp8p
600 = 20300 = 12
See Appendix A
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1.7-17 Example
8-12
p300y
2
y ftlbf/1004
600 = 20300 = 12
(See Appendix A)
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1.7-18 Gel Strength
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1.7-19 Gel Strength
= shear stress at which fluid movement begins
The yield strength, extrapolated from the
300 and 600 RPM readings is not a good
representation of the gel strength of the fluid
Gel strength may be measured by turning the
rotor at a low speed and noting the dial
reading at which the gel structure is broken
(usually at 3 RPM)
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1.7-20 Gel Strength
In field units,
In practice, this is often approximated to
06.1g 2ft100/lbf
2ft100/lbf
The gel strength is the maximum dial readingwhen the viscometer is started at 3 rpm.
g = max,3
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1.7-21 Velocity Profiles
(laminar flow)
Fig. 4-26. Velocity profiles for laminar flow:
(a) pipe flow and (b) annular flow
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It looks like concentric rings of fluid
telescoping down the pipe at different velocities
3D View of Laminar Flow in a pipe
- Newtonian Fluid
1.7-22
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1.7-23 Table 4.3 - Summary of
Equations for Rotational Viscometer
Newtonian Model
NaN
300
Nr
066.52
300a
or
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1.7-24 Table 4.3 - Summary of Equationsfor Rotational Viscometer
300
N
or
1pNy 1
rpm3atmaxg
Bingham Plastic Model
300600p )(NN
300
or
12 NN
12
p
p300y
or
or
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1.7-25 Total Pump Pressure
Pressure loss in surf. equipment
Pressure loss in drill pipe
Pressure loss in drill collars
Pressure drop across the bit nozzles
Pressure loss in the annulus between the drill
collars and the hole wall
Pressure loss in the annulus between the drill
pipe and the hole wall
Hydrostatic pressure difference ( varies)
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1.7-26 Pressure losses for laminar
flow.
2
500,1 d
V
dL
dP
2
12000,1 dd
V
dL
dP
dd
V
dL
dP yp
225500,1 2
122
12 200000,1 dddd
V
dL
dP yp
Newtonian Fluid Bingham Plastic Fluid
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1.7-27 Types of flow
Laminar
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
Turbulent
1 7 28 Turbulent
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1.7-28 Turbulent
Flow - Newtonian
Fluid
We often assume that fluid flow is
turbulent if Nre > 2100
cp.fluid,ofviscosity
inI.D.,piped
ft/svelocity,fluidavg.v
lbm/galdensity,fluidwhere
_
dv928N
_
Re
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Turbulent Flow -
Newtonian Fluid
25.1
25.075.1_
75.0f
d1800
v
dL
dp
Turbulent Flow -
Bingham Plastic Fluid
25.1
25.0
p
75.1_75.0
fd1800
v
dL
dp
25.112
25.0
p
75.1_75.0
f
dd396,1
v
dL
dp
25.112
25.0
75.1_75.0
f
dd396,1
v
dL
dp
In Annulus
In Pipe
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