pete 203 drilling engineering drilling hydraulics
TRANSCRIPT
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PETE 203
DRILLING ENGINEERING
Drilling Hydraulics
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Drilling Hydraulics
Energy Balance
Flow Through Nozzles
Hydraulic Horsepower
Hydraulic Impact Force
Rheological Models
Optimum Bit Hydraulics
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Nonstatic Well Conditions
Physical Laws: Conservation of Mass Conservation of energy Conservation of
momentum Rheological Models
Newtonian Bingham Plastic Power – Law API Power-Law
Equations of State Incompressible fluid Slightly compressible
fluid Ideal gas Real gas
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Average Fluid Velocity
Pipe Flow Annular Flow
WHERE
v = average velocity, ft/s
q = flow rate, gal/min
d = internal diameter of pipe, in.
d2 = internal diameter of outer pipe or borehole, in.
d1 =external diameter of inner pipe, in.
2448.2 d
qv 2
122448.2 dd
qv
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Law of Conservation of Energy
States that as a fluid flows from point 1 to point 2:
QW
vvDDg
VpVpEE
21
2212
112212
2
1
In the wellbore, in many cases Q = 0 (heat) = constant{
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In practical field units this equation simplifies to:
fp pPvv
DDpp
21
22
4
1212
10*074.8
052.0
p1 and p2 are pressures in psiis density in lbm/gal.v1 and v2 are velocities in ft/sec.
pp is pressure added by pump between points 1 and 2 in psi
pf is frictional pressure loss in psi
D1 and D2 are depths in ft.
where
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Determine the pressure at the bottom of the drill collars, if
psi 000,3 p
in. 5.2
0 D
ft. 000,10 D
lbm/gal. 12
gal/min. 400 q
psi 1,400
p
1
2
DC
f
ID
p
(bottom of drill collars)
(mud pits)
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Velocity in drill collars
)(in
(gal/min)
d448.2
qv
222
ft/sec 14.26)5.2(*448.2
400v
22
Velocity in mud pits, v1 0
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400,1000,36.6240,60
400,1000,3)014.26(12*10*8.074-
0)-(10,00012*052.00p
PP)vv(10*074.8
)DD(052.0pp
224-
2
fp21
22
4-
1212
Pressure at bottom of drill collars = 7,833 psig
NOTE: KE in collars
May be ignored in many cases
0
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fp PPvv
DDpp
)(10*074.8
)(052.021
22
4-
1212
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0 P
v v0 P
0 vD D
f
n2p
112
Fluid Flow Through Nozzle
Assume:
4n
2n
412
10*074.8
pv and
v10*074.8pp
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If
95.0c 10*074.8
pcv
as writtenbemay Equation
d4dn
0 fP
This accounts for all the losses in the nozzle.
Example: ft/sec 305 12*10*074.8
000,195.0v
4n
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For multiple nozzles in //
Vn is the same for each nozzle
even if the dn varies!
This follows since p is the same across each nozzle.
tn A117.3
qv
2t
2d
2-5
bit AC
q10*8.311Δp
10*074.8
pcv
4dn
&
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Hydraulic Horsepower
HHP of pump putting out 400 gpm at 3,000 psi = ?
Power
pqP
A
qA*p
t/s*F
workdoing of rate
H
hp7001714
000,3*400
1714
pq HHP
In field units:
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Hydraulic Impact Force
What is the HHP Developed by bit?
Consider:
psi 169,1Δp
lb/gal 12
gal/min 400q
95.0C
n
D
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Impact = rate of change of momentum
60*17.32
vqv
t
m
t
mvF n
j
psi 169,1Δp
lb/gal 12
gal/min 400q
95.0C
n
D
lbf 820169,1*12400*95.0*01823.0Fj
pqc01823.0F dj
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Newtonian Fluid Model
Shear stress = viscosity * shear rate
A
F ,
L
VallyExperiment
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Laminar Flow of Newtonian Fluids
A
F
L
V
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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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Newtonian Fluid Model
Viscosity may be expressed in poise or centipoise.
poise 0.01 centipoise 1
scm
g1
cm
s-dyne1 poise 1
2
2cm
secdyne
.
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Shear Stress vs. Shear Rate for a Newtonian Fluid
Slope of line
.
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Example - Newtonian Fluid
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Example 4.16
Area of upper plate = 20 cm2
Distance between plates = 1 cm
Force req’d to move upper plate at 10 cm/s = 100 dynes.
What is fluid viscosity?
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Example 4.16
poise 5.0cm
sdyne5.0
10
52
1-
2
sec 10/1
dynes/cm 20/100
/
/
rate shear
stressshear
LV
AF
cp 50
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Bingham Plastic Model
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Bingham Plastic Model
- if
- if 0
if
yyp
yy
yyp
and y are often expressed in lbf/100 sq.ft
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Power-Law Model
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Power-Law Model
n = flow behavior index
K = consistency index
0 if K
0 if K1n
n
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Rheological Models
1. Newtonian Fluid:
2. Bingham Plastic Fluid:
rate shear
viscosityabsolute
stressshear
*)( py viscosityplastic
point yield
p
y
What if
y
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3. Power Law Fluid:
When n = 1, fluid is Newtonian and K = We shall use power-law model(s) to
calculate pressure losses (mostly).
n
)(K
K = consistency index
n = flow behavior index
Rheological Models
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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
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Summary of Laminar Flow Equations for Pipes and Annuli
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Fig 4.33: Fig 4.33: Critical Reynolds number for Critical Reynolds number for Bingham plastic fluids.Bingham plastic fluids.
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Fig 4.34: Fig 4.34: Fraction Factors for Power-law Fraction Factors for Power-law fluid model.fluid model.
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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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Total Pump Pressure
PUMP SC DP DC
B DCA DPA HYD
P P P P
P P P ( ΔP )
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Types of Flow
Laminar Flow
Flow pattern is linear (no radial flow)
Velocity at wall is ZERO
Produces minimal hole erosion
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Types of Flow - Laminar
Mud properties strongly affect pressure losses
Is preferred flow type for annulus (in vertical wells)
Laminar flow is sometimes referred to as sheet flow, or layered flow:
* As the flow velocity increases, the flow type changes from laminar to turbulent.
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Types of Flow
Turbulent Flow
Flow pattern is random (flow in all directions)
Tends to produce hole erosion
Results in higher pressure losses (takes more energy)
Provides excellent hole cleaning…but…
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Types of flow
Mud properties have little effect on pressure losses
Is the usual flow type inside the drill pipe and collars
Thin laminar boundary layer at the wall
Turbulent flow, cont’d
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
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Turbulent Flow - Newtonian Fluid
The onset of turbulence in pipe flow is characterized by the dimensionless group known as the Reynolds number
dv
N
_
Re
μ
dvρ928N
_
Re In field units,
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Turbulent Flow - Newtonian Fluid
We often assume that fluid flow is
turbulent if Nre > 2,100
cp. fluid, ofviscosity μ
in I.D., piped
ft/s velocity,fluid avg. v
lbm/gal density, fluid ρ where_
μ
dvρ928N
_
Re
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PPUMP = PDP + PDC
+ PBIT NOZZLES
+ PDC/ANN + PDP/ANN
+ PHYD
Q = 280 gal/min
= 12.5 lb/gal
Pressure Drop Calculations PPUMP
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"Friction" Pressures
0
500
1,000
1,500
2,000
2,500
0 5,000 10,000 15,000 20,000 25,000
Distance from Standpipe, ft
"Fri
ctio
n" P
ress
ure,
psi
DRILLPIPE
DRILL COLLARS
BIT NOZZLES
ANNULUS
2103
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Optimum Bit Hydraulics
Under what conditions do we get the best hydraulic cleaning at the bit? Maximum hydraulic horsepower?
Maximum impact force?
Both these items increase when the circulation rate increases.
However, when the circulation rate increases, so does the frictional pressure drop.
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Jet Bit Nozzle Size Selection
Nozzle Size Selection for Optimum
Bit Hydraulics:
Max. Nozzle Velocity
Max. Bit Hydraulic Horsepower
Max. Jet Impact Force
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Jet Bit Nozzle Size Selection
Proper bottom-hole cleaning Will eliminate excessive regrinding of
drilled solids, and
Will result in improved penetration rates
Bottom-hole cleaning efficiency
Is achieved through proper selection of bit nozzle sizes
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Jet Bit Nozzle Size Selection- Optimization -
Through nozzle size selection, optimization may be based on maximizing one of the following:
Bit Nozzle Velocity
Bit Hydraulic Horsepower
Jet impact force• There is no general agreement on which of these three parameters should be maximized.
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Maximum Nozzle Velocity
From Eq. (4.31)
i.e.
so the bit pressure drop should be maximized in order to obtain the maximum nozzle velocity
4b
dn 10*074.8
PCv
bn Pv
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Maximum Nozzle Velocity
This (maximization) will be achieved when the surface pressure is maximized and the frictional pressure loss everywhere is minimized, i.e., when the flow rate is minimized.
pressure. surface allowable maximum the and
rate ncirculatio minimum the at
satisfied, are above 2&1 whenmaximized is vn
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Maximum Bit Hydraulic Horsepower
The hydraulic horsepower at the bit is maximized when is maximized.q) p( bit
dpumpbit ppp
where may be called the parasitic pressure loss in the system (friction).
dp
bitdpump ppp
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Maximum Bit Hydraulic Horsepower
. turbulentis flow theif
cqpppppp 75.1dpadcadcdpsd
In general, wherem
d cqp 2m0
The parasitic pressure loss in the system,
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Maximum Bit Hydraulic Horsepower
0)1(p when 0
17141714
pump
1
mHbit
mpumpbit
Hbit
qmcdq
dP
cqqpqpP
dpumpbit ppp md cqp
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Maximum Bit Hydraulic Horsepower
when maximum is
1
1p when .,.
)1(p when .,.
d
pump
Hbit
pump
d
P
pm
ei
pmei
pumpd pm
p
1
1
0)1(p pump mqmc
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Maximum Jet Impact Force
The jet impact force is given by Eq. 4.37:
)(c0.01823
01823.0
d dpump
bitdj
ppq
pqcF
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Maximum Jet Impact Force
But parasitic pressure drop,
2201823.0
mdpdj
md
qcqpcF
cqp
)(c0.01823 d dpumpj ppqF
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Maximum Jet Impact Force
Upon differentiating, setting the first derivative to zero, and solving the resulting quadratic equation, it may be seen that the impact force is maximized when,
pd p2m
2p