Chapter 4.Drilling hydraulics.ppt

7/25/2019 Chapter 4.Drilling hydraulics.ppt

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1

Wellbore Hydraulics,

Pressure Drop Calculations



2

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



3

)D(Dρ0.052 p p 1ii

n

1i

i0

−=

−+=

∑

Fig. 4-3.

A Complex

Liquid

Column

D#$%.#p

pD#$%.#p #

∆ρ=∆

+ρ=



4Fig. 4-4. Viewing the Well as a Manometer (U-

PP!MP = ?



5

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=∆



6

Buoyancy "orce # weight o$ $luid displaced &'rchimedes( %$# B!)

Figure 4-9. Hydrauli !ores ating on a



7

%$$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



(

%)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 )



)

Axil For!e% in *rill%"ring

"b # bit weight

"* / "* are pressure $orces



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$



11

%)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*,*++



12

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<



13

%)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+,+++



14

!ross,sectional area of collars(

22 in2.3190

17* ==

2

1

53773523 in...

' 'areaalDifferenti %

=−=

−= A:

A1

%)ample ; cont<d



15

*. '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



16

%)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



17

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



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



1)Fi/. 3,**. ';ial tensions as a function of depth for E;ample 3.4



2+

%)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>



21

A)ial oad with "BI2 # >=,+++ lb$



22



23

"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



24

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



26

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=∆

∆

=∆

∆=



27

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



2(

aminar "low o$ 3ewtonian "luids

*

F

L

V µ =

E;perimentallyA



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



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•



31

0hear 0tress &s 0hear Eate $or a

3ewtonian "luid

0lope o$ line = µ

.γ µ τ =



32

Apparent @iscosity

*pparent 4is%osit$ -

is t"e slope at ea%" s"ear rate, .((321

•••

γ γ γ

•

γ τ 0



33

ypi!l *rilling Fluid #%. 0e"onin,

Bingm nd oer L Fluid%

(lotte on linear paper)



34

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

•



35

otatin/@leeve

-iscometer



36

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



37

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



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



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; '



4+

9xmple

8/12

p300$

=

−= µ θ τ

2

$ &tl#&100=τ

θ

6

- 20

θ

3

- 12

&@ee 'ppendi; ')



41

:el ;"reng"



42

: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 :;)



43

: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



44

#elo!i"y ro$ile%

lminr $lo8

"ig 9-:> @elocity pro$iles $or laminar $low

'a( pipe $low and 'b( annular $low



45

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



46

&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



47

&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



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



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

−=



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

−=



51

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



52

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



53

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 =



54

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



55

'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



56

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



57

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



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



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 &



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 &



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 &



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 &



63


Pressure Drop 7n Drill !ollars


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.&



64

%$$ecti&e @iscosity in Collars( e ):

Eeynolds 3umber in Collars (N Re ):

#$ % 1.&in '$ %2.& in

+ % 1!t


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



65

#$ 1.&in '$ %2.& in

+ % 1!t


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



66

"riction Pressure Jradient (dP/dL) :

"riction Pressure Drop in Drill Collars :

#$ 1.&in '$ %2.& in

+ % 1!t


ft

psi519#.#

$.%89*.%$

$.*%8%9.*98##$93#.#

D9*.%$

-f

dL

dP %%

==ρ

=

2##8519#.#LdL

dPP

=∆

=∆

∆"d % 22

0si



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



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



6)



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



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



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



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



73



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



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



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



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



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



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



7)

y

#*(###

%(###

5(###

3(###

$(###

2(###

1(###

9(###

4(###

# $(### *#(### *$(### %#(### %$(###


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



(+

#*(###

%(###

5(###

3(###$(###

2(###

1(###

9(###4(###

*#(###

# $(### *#(### *$(### %#(### %$(###


P r e s s u r e

s , p s i

02A2IC

CIEC!A2I3J

Wellbore Pressure Pro$ile



(1

#

%(###

3(###

2(###

9(###

*#(###

*%(###

*3(###

# %(### 3(### 2(### 9(### *#(###

Pressure, psi

D e p t h ,

$

DEI02EI3J

A33!!0

&@tatic)

BI2

Pipe Flo Laminar



(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



(3



vfdp J

%ρ

n = 1.+

Chapter 4.Drilling hydraulics.ppt

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Transcript of Chapter 4.Drilling hydraulics.ppt