Download - Chapter 4.Drilling hydraulics.ppt
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1
Wellbore Hydraulics,
Pressure Drop Calculations
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Wellbore Hydraulics
• Hydrostatics
• Buoyancy
• Pipe Tension vs. Depth• Effect of Mud Pressure
• Laminar and Turbulent Flo
• Pressure Drop !alculations " Bingham Plastic Model
" API Power-aw Model
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)D(Dρ0.052 p p 1ii
n
1i
i0
−=
−+=
∑
Fig. 4-3.
A Complex
Liquid
Column
D#$%.#p
pD#$%.#p #
∆ρ=∆
+ρ=
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4Fig. 4-4. Viewing the Well as a Manometer (U-
PP!MP = ?
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Figure 4.4
})9.0(10,000)16.7(1,000
)12.7(1,7008.5(300))10.5(7,000{0.052 p p 0a
−++++=
psig 0 p0 =
psig266,1 pa =∴
D#$%.#p ∆ρ=∆
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Buoyancy "orce # weight o$ $luid displaced &'rchimedes( %$# B!)
Figure 4-9. Hydrauli !ores ating on a
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%$$ecti&e 'buoyed( Weight
∴
ρ
ρ
−= s
f
e *++
Buoyn!y F!"or
#lid $or %olid &ody or n open-ended pipe'
sf
f
be
+
,+
-,+
F++
ρρ=
ρ=−= +e buoyed ei/ht
+ ei/ht in air
Fb buoyancy force
- volume of body
ρf fluid densityρs body density
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(
%)ample
For steel,
immerse in m!,
t"e #!o$an%$ &a%tor is'
/al0lbm.s 565=ρ)/al0lbm.& f 015=ρ
11*.#$.2$
#.*$**
s
f =
−=
ρρ
−
A drillstring weighs *++,+++ lbs in air
Buoyed weight # *++,+++ +..* # ..,*++ lbs
& 34# lbm0ft5 )
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)
Axil For!e% in *rill%"ring
"b # bit weight
"* / "* are pressure $orces
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1+
0imple %)ample - %mpty Wellbore
Drillpipe ei/ht *4.$ lbf0ft *#(### ft
6D $.### in
7D 3.%12 in
( )%%7D6D
3 ' −
π=
' $.%2$ in%
+ *4.$ lbf0ft 8 *#(### ft *4$(### lbf
A1IA 2%30I43, lb$
D % P 2 H ,
$ t
+ lb$ *56,+++ lb$
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%)ample - *6 lb7gal Mud in Wellbore
Drillpipe ei/ht *4.$ lbf0ft *#(### ft
6D $.### in
7D 3.%12 in
( )%%7D6D
3 ' −
π=
' $.%2$ in%
+ *4$(### , 3*(*## *$5(4## lbf
A1IA 2%30I43, lb$
D % P 2 H
, $ t
+ *4$(### lbf
Pressure at bottom #.#$% 8 *$ 8 *#(### 1(9## psiF P 8 '
1(9## 8 $.%2$
3*(*## lbf
*68,5++- 9*,*++
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A)ial 2ension in Drill 0tring
%)ample ' drill strin/ consists of *#(### ft of *4.$ :0ft drill
pipe and 2## ft of *31 :0ft drill collars suspended
off bottom in *$:0/al mud &Fb bit ei/ht #).
• +hat is the a;ial tension in the
drillstrin/ as a function of depth<
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%)ample
Pressure at top of collars
#.#$% &*$) *#(### 1(9## psi
Pressure at bottom of collars #.#$% &*$) *#(2## 9(%29 psi
Cross-sectional area o$ pipe,
%
%
%
5* in15.$ft
in*338
ft0lb34#
ft0lb$.*4 ' ==
1+,6++
A*
1+,+++
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!ross,sectional area of collars(
22 in2.3190
17* ==
2
1
53773523 in...
' 'areaalDifferenti %
=−=
−= A:
A1
%)ample ; cont<d
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*. 't *#(2## ft. &bottom of drill collars)
!ompressive force p '
5$1(%## lbf
= a;ial tension , 5$1(%## lbf >
2
2in2.3
in
l#& 268,8=
4
32
1
%)ample - cont<d
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%)ample - cont<d
2. *t 10,000 &t+ (top o& %ollars)
F - 2 / F2 / F #
- 17 l#m&t 600 &t / 357,200
- 88,200 / 357,200
- /269,000 l#&
4
32
1
F b = F BIT = 0
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5. 't *#(### ft , &bottom of drillpipe)
FT +*?+%?F*,F%,Fb
99(%## ? 19## lbf0in% 8 51.$in% , 5$1(%##
99(%## ? %4%($## , 5$1(%##
? %5($## lbf
4
32
1
%)ample - cont<d
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1(
3. 't @urface
FT +* ? +% ? F* , F% , Fb
*4.$ 8 *#(### ? 99(%##
? %4%($## , 5$1(%## , #
%*9($## lbf
'lternativelyA FT + '7 8 BF
%95(%## 8 #.11*# # :*=,896 lb$
4
32
1
%)ample - cont<d
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1)Fi/. 3,**. ';ial tensions as a function of depth for E;ample 3.4
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%)ample - 0ummary
*. 't *#(2## ft FT ,5$1(%## lbf =compression>
%. 't *#(### ? ft FT ,%24(### lbf =compression>
5. 't *#(### , ft FT ?%5($## lbf =tension>
3. 't @urface FT ?%*9($## lbf =tension>
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A)ial oad with "BI2 # >=,+++ lb$
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"or multiple no??les in parallel
@n is the same $or each no??le e&en i$the dn &aries
2his $ollows since ∆p is the same across
each no??le
t
n '**1.5
Cv =
2
2
t
%
d
,$
bit '!
C*#89.5** p
ρ=
*#8#13.9
pcv
3dn ρ∆
= −
Cd # +56
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Hydraulic Horsepower
/ o$ pump pu""ing ou" 4++ gpm " 3,+++ p%i = ?
Power, in $ield units
*1*3
###(583## HHP =
*1*3
pC HHP ∆
=
Hydraulic Horsepower o$ Pump # .++ hp
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Impact # rate o$ change o$ momentum
( )
lbf 9%#*24(*8*%3##84$.#8#*9%5.#F
pCc#*9%5.#F
2#8*1.5%
vCv
t
m
t
mvF
E
d E
n
E
==
∆ρ=
ρ=∆
∆
=∆
∆=
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aminar "low
Eheological Models etonian
Bin/ham Plastic
Poer,La &'DE G 'P7)
Eotational @iscometer
aminar "low in Wellbore
Fluid Flo in Pipes
Fluid Flo in 'nnuli
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2(
aminar "low o$ 3ewtonian "luids
*
F
L
V µ =
E;perimentallyA
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2)
0e"onin Fluid odel
n a etonian &l!i t"e s"ear stress is ire%tl$
proportional to t"e s"ear rate (in laminar &lo)'
i.e.,
"e %onstant o& proportionalit$, is t"e 4is%osit$
o& t"e &l!i an is inepenent o& s"ear rate.
=se%
12
µ cm
dyne
µ
•γ µ=τ
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3+
0e"onin Fluid odel
is%osit$ ma$ #e epresse in poise or %entipoise.
poise#.#*centipoise*
scm
/*
cm
s,dyne*poise*
%
=
−==
2cmsecdyne •
γ
τ=µ•
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0hear 0tress &s 0hear Eate $or a
3ewtonian "luid
0lope o$ line = µ
.γ µ τ =
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Apparent @iscosity
*pparent 4is%osit$ -
is t"e slope at ea%" s"ear rate, .((321
•••
γ γ γ
•
γ τ 0
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ypi!l *rilling Fluid #%. 0e"onin,
Bingm nd oer L Fluid%
(lotte on linear paper)
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eologi!l odel%
1. etonian Fl!i'
2. ing"am lasti% Fl!i'
viscosityplastic
pointyield
p
y
=µ
=τ
"at i& τ y =0?
•γ µ=τ
•
γ µ+τ=τ py
rateshear
viscosityabsolute
stressshear
=γ
=µ=τ
•
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otatin/@leeve
-iscometer
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Figure 3.6o""ing
#i%!ome"er
eome"er
e
etermine
r"eologi%al
properties
o& rilling
&l!is int"is e4i%e
n&inite
parallel
plates
" " "i l
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eome"er o""ionl
#i%!ome"er8
"ear tress - & (Dial :eaing)
"ear :ate - & (lee4e :;)
"ear tress - & ("ear :ate)
)(& γ τ =
Bate@hear the&H'MM')(of value
theondepends@tress@hear the)(T'I&
γ
τ
8<8
slee4e
&l!i
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3(
eome"er - &%e !%e
(:;) γ (se%/1) 3 5.11
6 10.22
100 170 200 30
300 511
600 1022
:; 1.703 - se%/1
9 l
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3)
9xmple
* rotational 4is%ometer %ontaining a Bingm pl%"i!
$luid gi4es a ial reaing o& 12 at a rotor spee o& 300:; an a ial reaing o& 20 at a rotor spee o& 600 :;
Compute plastic viscosity and yield point
12/20
300600 p
=
−= θ θ µ
%p8 p = µ
θ
6
- 20
θ
3
- 12
@ee 'ppendi; '
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4+
9xmple
8/12
p300$
=
−= µ θ τ
2
$ &tl#&100=τ
θ
6
- 20
θ
3
- 12
&@ee 'ppendi; ')
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:el ;"reng"
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:el ;"reng"
- s"ear stress at "i%" &l!i mo4ement #egins
= "e $iel strengt", etrapolate &rom t"e
300 an 600 :; reaings is not a goo
representation o& t"e gel strengt" o& t"e &l!i
= >el strengt" ma$ #e meas!re #$ t!rning t"e
rotor at a lo spee an noting t"e ial
reaing at "i%" t"e gel str!%t!re is #ro?en
(!s!all$ at 3 :;)
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:el ;"reng"
n &iel !nits,
7n practice( this is often appro;imated to
θ τ 06.1g =2&t100l#&
2&t100l#&
"e gel strengt" is t"e maim!m ial reaing"en t"e 4is%ometer is starte at 3 rpm.
τg = θmx,3
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#elo!i"y ro$ile%
lminr $lo8
"ig 9-:> @elocity pro$iles $or laminar $low
'a( pipe $low and 'b( annular $low
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FIt looGs liGe concentric rings o$ $luid
telescoping down the pipe at di$$erent &elocities
8D @iew o$ aminar "low in a pipe
- 3ewtonian "luid
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&le 4.3 - ;ummry o$ 9qu"ion% $or
o""ionl #i%!ome"er
0e"onin odel
a
5##θ=µ
Fr
#22.$%
=γ ⋅
5##a θ=µ
or
&le 4 3 ;ummry o$ 9qu"ion% $or
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&le 4.3 - ;ummry o$ 9qu"ion% $or
o""ionl #i%!ome"er
300
or
1 p $ 1
µ θ τ −=
rpm3atmag θ τ
=
Bingm l%"i! odel
300600 p θ θ µ −= )(
300
or
12
12
p θ θ µ −−=
p300$ µ θ τ −=
or
or
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4(
9xmple 4.22
@omp!te t"e &ri%tional press!re loss &or a 7A 5A
ann!l!s, 10,000 &t long, !sing t"e slot &lo
representation in t"e ann!l!s. "e &lo rate is 80
galmin. "e 4is%osit$ is 15 %p. *ss!me t"e &lo pattern is laminar.
. 6 *6
π
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4)
9xmple 4.22
"e a4erage 4elo%it$ in t"e ann!l!s,
)52.8(7
80
)2.8(
B4
222
1
2
2
C
−=
−
=
&ts1.3624 C
=
( ) 212
C
&
1000
4
E
p
−=
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5+
9xmple 4.22
( )51.0750 psi51
)57(1000
)000,10()362.1()15(D
E
pFp
2&
==∆
−==
f p
( )%
*%
J
f
dd*###
vK
dL
dp
−=
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2otal Pump Pressure
• Pressure loss in sur$ euipment
• Pressure loss in drill pipe
• Pressure loss in drill collars
• Pressure drop across the bit no??les
• 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 di$$erence 'ρ &aries(
2 $ $l
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2ypes o$ $low
Lminr
Fig. /30. Eaminar an t!r#!lent &lo patterns in a %ir%!lar pipe' (a) laminar
&lo, (#) transition #eteen laminar an t!r#!lent &lo an (%) t!r#!lent &lo
ur&ulen"
& l " Fl
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ur&ulen" Flo -
0e"onin Fluid
e o&ten ass!me t"at &l!i &lo is
"ur&ulen" i& 0re < 21++
%p.&l!i,o& 4is%osit$
in.D., pipe &ts4elo%it$,&l!ia4g. 4
l#mgalensit$,&l!iρ "ere
C
===
=
D
4ρ928
C
:e =
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2urbulent "low -
3ewtonian "luid
%$.*
%$.#
1$.* J 1$.#
f
d*9##
v
dL
dp µρ=
2urbulent "low -
Bingham Plastic "luid
%$.*
%$.#
p
1$.* J 1$.#
f
d*9##
v
dL
dp µρ=
( ) %$.**%
%$.#
p
1$.* J 1$.#
f
dd542(*
v
dL
dp
−
µρ=
( ) %$.*
*%
%$.#
1$.* J 1$.#
f
dd542(*
v
dL
dp
−µρ
=
In Annulus
In Pipe
'P7 P L M d l
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'P7 Poer La Model
G - %onsisten%$ inen - &lo #e"a4io!r ine
SHEARSTRESS
τpsi
τ = K γ n
SHEAR RATE, γ , sec-1
0
API EP *8D
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otatin/ @leeve -iscometer
@I0C4M%2%E
EPM
5*##
5##
2##
&PM 8 *.1#5)
0H%AE EA2%
sec -*
$.***1#.5
$**
*#%%
B4B
0%%@%
A33!!0
DEI
02EI3J
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Pressure Drop !alculations
• %)ample !alculate the pump pressure inthe ellbore shon on the ne;t pa/e( usin/ the
'P7 method.
• 2he rele&ant rotational &iscometer readingsare as $ollows
• 5 5 &at 5 PM)
• *## %# &at *## PM)
• 5## 54 &at 5## PM)
• 2## 2$ &at 2## PM)
P D P
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5(
PP!MP ∆PDP ? ∆PDC
? ∆PBI2 34KK%0
? ∆PDC7A33 ? ∆PDP7A33
? ∆PHLD
Q %9# /al0min
*%.$ lb0/al
Pressure Drop
!alculations
P"UM"
P D 7 D ill Pi 4D # 9 6 in
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5)
Power-aw Constant (n):
Pressure Drop 7n Drill Pipe
"luid Consistency Inde) (K):
A&erage BulG @elocity in Pipe (V):
4D # 96 in
ID # 8.= in
# **,9++ $t
151.#54
2$lo/5%.5
B
Blo/5%.5n
5##
2## =
=
=
2737.0
600 se%017.2
022,1
6511.5
022,1
11.5
cm
dyne R K
n
n ===
sec
ft##.9
19.5
%9#83#9.#
D
3#9.#-
%% ===
P D 7 D ill Pi #$ % 4 &
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6+
%$$ecti&e @iscosity in Pipe ( e ):
Pressure Drop 7n Drill Pipe
Eeynolds 3umber in Pipe (N Re ):
#$ % 4.&in '$ % .*
in+ % ,,4!t
n*n
en3
*n5
D
-42M*##
+
=µ
−
cP$5151.#83
*151.#85
19.5
9842#*1.%8*##
151.#*151.#
e =
+
=µ
−
2*2(2$5
$.*%8##.9819.584%9-D4%9
e
Be ==µ
ρ=
P D 7 D ill Pi #$ % 4 &
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61
NOTE: N Re > 2,100, so"riction "actor in Pipe (f):
Pressure Drop 7n Drill Pipe #$ % 4.&in '$ %.* in
+ % ,,4!t
/o
b
Beaf =
#1$4.#$#
45.5151.#lo/
$#
45.5nlo/
a =+
=
+
=
%24#.#1
151.#lo/1$.*
1
nlo/1$.*b =
−=
−=
##1*%2.#2*2(2
#1$4.#
af
%24#.#b
Be
===
P D 7 D ill Pi #$ % 4 &
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62
"riction Pressure Jradient (dP/dL) :
Pressure Drop 7n Drill Pipe #$ % 4.&in '$ %.* in
+ % ,,4!t
"riction Pressure Drop in Drill Pipe :
3##(**8#$951.#LdL
dP
P =∆
=∆
∆
"d0 % 11&
0si
ft
psi#$951.#
19.589*.%$
$.*%898##1*%2.#
D9*.%$
-f
dL
dP %%
==ρ
=
P D 7 D ill ! ll #$ % 1 &
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63
Power-aw Constant (n):
Pressure Drop 7n Drill !ollars
"luid Consistency Inde) (K):
A&erage BulG @elocity inside Drill Collars (V):
#$ % 1.&in '$ %2.& in
+ % 1!t151.#
54
2$lo/5%.5
B
Blo/5%.5n
5##
2## =
=
=
%
n
151.#n
2##
cm
secdyne#*1.%
#%%(*
2$8**.$
#%%(*
B**.$ ===
sec
ft%9.*9
$.%
%9#83#9.#
D
3#9.#-
%% ===
#$ % 1.&
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64
%$$ecti&e @iscosity in Collars( e ):
Eeynolds 3umber in Collars (N Re ):
#$ % 1.&in '$ %2.& in
+ % 1!t
Pressure Drop 7n Drill !ollars
n*n
en3
*n5
D
-42M*##
+
=µ
−
cP%*.59151.#83
*151.#85
$.%
%9.*9842#*1.%8*##
151.#*151.#
e =
+
=µ
−
91#(*5%*.59
$.*%8%9.*98$.%84%9-D4%9
e
Be ==µ
ρ=
#$ % 1.&P D 7 D ill ! ll
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65
#$ 1.&in '$ %2.& in
+ % 1!t
Pressure Drop 7n Drill !ollars
NOTE: N Re > 2,100, so"riction "actor in DC (f): b
Beaf =
/o
#1$4.#$#
45.5151.#lo/
$#
45.5nlo/
a =
+
=
+
=
%24#.#1
151.#lo/1$.*
1
nlo/1$.*b =
−=
−=
##$93#.#91#(*5
#1$4.#
af
%24#.#b
Be
===
#$ % 1.&P D 7 D ill ! ll
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66
"riction Pressure Jradient (dP/dL) :
"riction Pressure Drop in Drill Collars :
#$ 1.&in '$ %2.& in
+ % 1!t
Pressure Drop 7n Drill !ollars
ft
psi519#.#
$.%89*.%$
$.*%8%9.*98##$93#.#
D9*.%$
-f
dL
dP %%
==ρ
=
2##8519#.#LdL
dPP
=∆
=∆
∆"d % 22
0si
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67
Pressure Drop across oNNles
$3, % ,, 2nds
(in) $32 % ,,
2nds (in) $3 %
,2 2nds (in)
( )%%%%
%
*%****
%9#8$.*%8*$2P
++=∆
∆"3oles % ,21
0si
( ) %%
5
%
%
%
*
%
DDD
*$2P
++
ρ=∆
Pressure Drop
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6(
Pressure Drop
in D!0H6LE
'nnulus
$H#+5 % *.&in#$$6 % 1.&
in
+ % 1
Q = 280 gal/min
= 12.5 lb/gal*.&in
$ % * &Pressure Drop
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6)
Power-aw Constant (n):
"luid Consistency Inde) (K):
A&erage BulG @elocity in DC7H4% Annulus (V):
$H#+5 % *.&
in#$$6 % 1.&
in+ %1 !t
Pressure Drop
in D!0H6LE 'nnulus
$3*5.#5
%#lo/2$1.#
B
Blo/2$1.#n
5
*## =
=
=
%
n
$3*5.#n
*##
cm
secdyne552.2
%.*1#
%#8**.$
%.*1#
B**.$ ===
sec
ft9#9.5
$.2$.9
%9#83#9.#
DD
3#9.#-
%%%
*
%
%
=−
=−
=
$ % * &
Pressure Drop
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7+
%$$ecti&e @iscosity in Annulus ( e ):
Eeynolds 3umber in Annulus (N Re ):
$H#+5 % *.&
in#$$6 % 1.&
in+ %1 !t
cP%#.$$$3*5.#85
*$3*5.#8%
$.2$.9
9#9.58*33552.28*##
$3*5.#*$3*5.#
e =
+
−=µ
−
( ) ( )2##(*
%#.$$
$.*%89#9.58$.2$.94%9-DD4%9
e
*%
Be =−
=µ
ρ−=
n*n
*%
en5
*n%
DD
-*33M*##
+
−
=µ−
Pressure Drop
in D!0H6LE 'nnulus
$H#+5 % *.&
Pressure Drop
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71
/o
H#+5
in#$$6 % 1.&
in+ %1 !t
NOTE: N Re < 2,100 "riction "actor in Annulus (f):
#*$##.#2##(*
%3
%3f
Be
===
( ) ( ) ft
psi#$%22.#
$.2$.99*.%$
$.*%89#9.58#*$##.#
DD9*.%$
-f
dL
dP %
*%
%
=−
=−
ρ=
2##8#$%22.#LdLdPP =∆ =∆
∆
"d7hole % ,.1
0si
Pressure Drop
in D!0H6LE 'nnulus
Pressure Drop
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72
q = 280 gal/min
= 12.5 lb/gal
Pressure Drop
in DP7H4% Annulus
$H#+5 % *.& in
#$$" % 4.& in
+ %,,4 !t
Pressure Drop $H#+5 % *.& in
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73
Power-aw Constant (n):
"luid Consistency Inde) (K):
A&erage BulG @elocity in Annulus (V a ):
Pressure Drop
in DP7H4% Annulus
H#+5
#$$" % 4.& in
+ %,,4 !t
$3*5.#5
%#lo/2$1.#
B
Blo/2$1.#n
5
*## =
=
=
%
n
$3*5.#n
*##
cm
secdyne552.2
%.*1#
%#8**.$
%.*1#
B**.$M ===
sec
ft*41.%
$.3$.9
%9#83#9.#
DD
3#9.#-
%%%
*
%
%
=−
=−
=
Pressure Drop
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74
%$$ecti&e @iscosity in Annulus ( e ):
Eeynolds 3umber in Annulus (N Re ):
p
in DP7H4% Annulus
n*n
*%
en5
*n%
DD
-*33M*##
+
−
=µ−
cP23.41$3*5.#85
*$3*5.#8%
$.3$.9
*41.%8*33552.28*##
$3*5.#*$3*5.#
e =
+
−
=µ−
( ) ( )#33(*
23.41
$.*%8*41.%8$.3$.94%9-DD4%9
e
*%
Be =−
=µ
ρ−=
Pressure Drop
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75
/o 0si
Pressure Drop
in DP7H4% Annulus
NOTE: N Re < 2,100 "riction "actor in Annulus (f):
#%%44.##33(*
%3
%3f
Be
===
( ) ( ) ft
psi#*535.#
$.3$.99*.%$
$.*%8*41.%8#%%44.#
DD9*.%$
-f
dL
dP %
*%
%
=−
=−ρ
=
3##(**8#*535.#LdLdPP =∆ =∆
∆"d07hole % ,&.2 0si
P D C l
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76
Pressure Drop Calcs
- 0!MMAEL -
PP!MP ∆PDP ? ∆PDC ? ∆PBI2 34KK%0
? ∆PDC7A33 ? ∆PDP7A33 ? ∆PHLD
PP!MP 22$ ? %%1 ? *(#%2
? 5% ? *$5 ? #
PP!MP # *,5*= *=6 # :,*+8 psi
P = ∆P + ∆P + ∆P
:,*+8 psi
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77
PP!MP # *,5*= *=6
# :,*+8 psi
∆PH8$ #
P"UM" = ∆P$/ + ∆P33 + ∆PH8$
∆P$/ = ∆P$" + ∆P$6 + ∆P:'T 3#;;+5/
22$ ? %%1 ? *(#%2 *(4*9
psi∆P33 = ∆P$6733 + ∆P$"733
5% ? *$5 *9$
P
#+
N"rictionN Pressures
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7(
#
$##
*(###
*($##
%(###
%($##
# $(### *#(### *$(### %#(### %$(###
Cumulati&e Distance $rom 0tandpipe, $t
N
" r i c t i o n N P r e s s u r e , p s i
DEIPIP%
DEI C4AE0
BI2 34KK%0
A33!!0
Hydrostatic Pressures in the Wellbore
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7)
y
#*(###
%(###
5(###
3(###
$(###
2(###
1(###
9(###
4(###
# $(### *#(### *$(### %#(### %$(###
Cumulati&e Distance $rom 0tandpipe, $t
H
y d r o s t a t i c P r e
s s u r e , p s i
BHP
DEI02EI3J A33!!0
Pressures in the Wellbore
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(+
#*(###
%(###
5(###
3(###$(###
2(###
1(###
9(###4(###
*#(###
# $(### *#(### *$(### %#(### %$(###
Cumulati&e Distance $rom 0tandpipe, $t
P r e s s u r e
s , p s i
02A2IC
CIEC!A2I3J
Wellbore Pressure Pro$ile
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(1
#
%(###
3(###
2(###
9(###
*#(###
*%(###
*3(###
# %(### 3(### 2(### 9(### *#(###
Pressure, psi
D e p t h ,
$
DEI02EI3J
A33!!0
&@tatic)
BI2
Pipe Flo Laminar
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(2
Pipe Flo , Laminar
7n the above e;ample the flo don thedrillpipe as turbulent.
Inder conditions of very hi/h viscosity(
the flo may very ell be laminar.
NOTE: if N Re < 2,100, then
"riction "actor in Pipe (f):
BeF
*2f =
D9*.%$
-f
dL
dP %ρ
=
Then and
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(3
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vfdp J
%ρ
n = 1.+