4. Wellbore Hydraulics, Pressure Drop Calculations

7/18/2019 4. Wellbore Hydraulics, Pressure Drop Calculations

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1

PETE 661Drilling Engineering

Lesson 4

Wellbore Hydraulics,

Pressure Drop Calculations


2/85

2

Wellbore Hydraulics

Hydrostatics

Buoyancy

Pipe Tension vs. Depth Effect of Mud Pressure Laminar and Turbulent Flow

Pressure Drop alculations Bingham Plastic Model

API Power-Law Model


3/85

3

Assignments:

READ: ADE Ch 4

HW !": On the Web. - AxialTension

Due 09-20-04


4/85

4

)DD(052.0pp 1ii

n

1i

i0 =

+=

Fig. 4-3.

A Complex

Liquid

Column

D!"#.!p

pD!"#.!p !

=

+=


5/85

5Fig. 4-4. Viewing the Well as a Manometer (U-

PPUMP= ?


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6

Figure 4.4

})000,10(0.9)000,1(7.16

)700,1(7.12)300(5.8)000,7(5.10{052.00

++++= ppa

psig00=p

psig266,1pa =

D!"#.!p =


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7

Buoyancy Force = weight of fluid displaced$%rchimedes& #"! B'

Figure 4-9. Hydrauli !ores ating on a


8/85

8

Effectie !"uoyed# $eight

= sf

e ())

Buo!n" F!"#or

$!lid %or ! &olid 'od or !n open-ended pipe(

sf

f

be

)

*)

+*)

F))

=

== )e, buoyed wei-ht) , wei-ht in air

Fb, buoyancy force

+ , volume of body

f, fluid densitys, body density


9/85

)

E%ample

For steel,

immersed in md,

t!e "o#an$# %a$tor is&

-allbm.s 565='-allbm.$ f 015=

//(.!".0"

!.("((

s

f =

=

A drillstring weighs &''(''' l"s in air)

Buoyed weight = &''(''' * ')++& = ++(&'' l"s

$, 12! lbmft3'


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1*

Axi!l For"e& in +rillring

F"= "it weight

F&, F& are pressure forces


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11

imple E%ample - Empty $ell"ore

Drillpipe wei-ht , (2." lbfft (!&!!! ft

4D , ".!!! in

5D , 1.#/0 in

( )## 5D4D1

%

=

% , ".#0" in#

) , (2." lbfft 6 (!&!!! ft , (2"&!!! lbf

A.IAL /E0I10( l"f

2EP/3(

ft

' l"f &45(''' l"f


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12

E%ample - &5 l"6gal Mud in $ell"ore

Drillpipe wei-ht , (2." lbfft (!&!!! ft

4D , ".!!! in

5D , 1.#/0 in

( )## 5D4D1

%

=

% , ".#0" in#

) , (2"&!!! * 1(&(!! , ("3&2!! lbf

A.IAL /E0I10( l"f

2EP/3

(ft

' (2"&!!! lbf

Pressure at bottom , !.!"# 6 (" 6 (!&!!! , /&7!! psiF , P 6 %

, /&7!! 6 ".#0"

, 1(&(!! lbf

&57(4''- 8&(&''


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13

A%ial /ension in 2rill tring

E%ample % drill strin- consists of

(!&!!! ftof (2." 8ftdrillpipe and

0!! ftof (1/ 8ftdrill collarssuspended off bottom in ("8-almud

$Fb, bit wei-ht , !'.

)hat is the a9ial tension in the

drillstrin- as a function of depth:


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14

E%ample

Pressure at top of collars

, !.!"# $("' (!&!!! , /&7!! psi

Pressure at bottom of collars, !.!"# $("' (!&0!! , 7 psi

9ross-sectional area of pipe(

#

#

#

3( in/3."

ft

in(116

ftlb12!

ftlb".(2% ==

A&

1)4**,

6**,


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15

ross*sectional area of collars&

22 in2.'31'''90

1'7 ==

2

1

5377352'3 in...

%%areaalDifferenti #

===

A:

A1E%ample ; cont


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16

(. %t (!&0!! ft.$bottom of drill collars'

ompressive force , p %

, 3"/!! lbf

; a9ial tension , * 3"/!! lbf ee %ppendi9 %'


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42

:el ;#reng#


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43

:el ;#reng#

s!ear stress at !i$! %lid moement "egins

+!e #ield strengt!, etrapolated %rom t!e 300

and 600 :readings is not a good representation o%

t!e gel strengt! o% t!e %lid


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44

:el ;#reng#

n %ield nits,

5n practice& this is often appro9imated to

06.1g=2%t100/l"%

2%t100/l"%

+!e gel strengt! is t!e maimmdial reading!en t!e is$ometer is started at 3 rpm.

g= m!x/3


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45

$elo"i# ro%ile&

l!min!r %lo

Fig) 8-:>) @elocity profiles for laminar flow

!a# pipe flow and !"# annular flow


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It looGs liGe concentric rings of fluid

telescoping down the pipe at different elocitiesH

72 @iew of Laminar Flow in a pipe

- 0ewtonian Fluid


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!'le 4.3 - ;umm!r o% 9qu!#ion& %or

o#!#ion!l $i&"ome#er

0e#oni!n odel

a

3!!=

r

!00."#

=

3!!a =

or

!'le 4 3 ;umm!r o% 9qu!#ion& %or


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48

!'le 4.3 - ;umm!r o% 9qu!#ion& %or

o#!#ion!l $i&"ome#er

300

or

1p# 1

=

rpm3atmag

=

Bing!m l!i" odel

300600p = )(300

or

12

12

p =

p300# =

or

or


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4)

9x!mple 4.22

>ompte t!e %ri$tional pressre loss %or a 7? 5?

annls, 10,000 %tlong, sing t!e slot %lo

representation in t!e annls. +!e %lo rate is 80

gal/min. +!e is$osit# is 15 $p. ssme t!e %lopattern is laminar.

+H 5H &H6


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5*

9x!mple 4.22

+!e aerage elo$it# in t!e annls,

)52.''8(7

80

)d2.''8(d

@

222

1

2

2

A

=

=

%t/s1.362A

=

( ) 212

A

%

dd1000

B

dC

dp

=


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51

9x!mple 4.22

( )51.0750psi51

)57(1000

)000,10()362.1()15(D

dC

dpp

2%

==

==

fp

( )#(#

H

f

dd(!!!

vI

dL

dp

=

/ l P P


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52

/otal Pump Pressure

Pressure loss in surf) euipmentPressure loss in drill pipe

Pressure loss in drill collars

Pressure drop across the "it no??lesPressure loss in the annulus "etween the drill

collars and the hole wall

Pressure loss in the annulus "etween the drill

pipe and the hole wall

3ydrostatic pressure difference !aries#

/ f fl


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/ypes of flow

L!min!r

Fig. '30. Caminar and tr"lent %lo patterns in a $ir$lar pipe& (a) laminar

%lo, (") transition "eteen laminar and tr"lent %lo and ($) tr"lent %lo

ur'ulen#

' l # Fl


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ur'ulen# Flo -

0e#oni!n Fluid

-e o%ten assme t!at %lid %lo is

#ur'ulen# i% 0re < 21**

$p.%lid,o%is$osit#B

in.D.,piped%t/selo$it#,%lidag.

l"m/galdensit#,%lidE!ere

A

===

=

B

dE928

A

e =


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/ur"ulent Flow -

0ewtonian Fluid

#".(

#".!

/".(/".!

f

d(7!!

v

dL

dp =

/ur"ulent Flow -

Bingham Plastic Fluid

#".(

#".!

p

/".(/".!

f

d(7!!

v

dL

dp =

( ) #".((#

#".!

p

/".(/".!

f

dd320&(

v

dL

dp

=

( ) #".((#

#".!

/".(/".!

f

dd320&(

v

dL

dp

=

In Annulus

In Pipe

%P5 P L M d l


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%P5 Power Law Model

$onsisten$# inden %lo "e!aior inde

SHEARSTRESS

psi

= K n

SHEAR RATE, , sec-10

API P &72


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@otatin- >leeve +iscometer

@I91ME/E

PM

3(!!

3!!

0!!

$@PM 6 (./!3'

3EA A/E

sec -&

".(((/!.3

"((

(!##

B1B

LEE@E

A00ULU

2ILL

/I0J


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Pressure Drop alculations

E%amplealculate the pump pressure in thewellbore shown on the ne9t pa-e& usin- the %P5

method.

/he releant rotational iscometer readingsare as follows

@3 , 3 $at 3 @PM'

@(!!, #! $at (!! @PM'

@3!!, 32 $at 3!! @PM'

@0!!, 0" $at 0!! @PM'

P DP


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5)

PPUMP , P2P = P29

= PBI/ 01KKLE

= P296A00 = P2P6A00

= P32

# , #7! -almin

, (#." lb-al

Pressure Drop

alculations

P"UM"

P D 5 D ill Pi 12 = 8 5 in


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6*

Power-Law 9onstant $n%:

Pressure Drop 5n Drill Pipe

Fluid 9onsistency Inde% $&%:

Aerage BulG @elocity in Pipe $'%:

12 = 8)5 in

I2 = 7)+ in

L = &&(8'' ft

/3/.!32

0"lo-3#.3

@

@lo-3#.3n

3!!

0!! =

=

=

2737.0

600 se$017.2022,1

6511.5

022,1

11.5

cm

dyneRK

n

n ===

sec

ft!!.7

/7.3

#7!61!7.!

D

J1!7.!+

## ===

P D 5 D ill Pi #$ % 4 &


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Effectie @iscosity in Pipe $ e%:

Pressure Drop 5n Drill Pipe

eynolds 0um"er in Pipe $(Re%:

#$ % 4.&in'$ % .*

in+ % ,,4!t

n(n

en1

(n3

D

+20K(!!

+

=

cP"3/3/.!61

(/3/.!63

/7.3

7620!(/.#6(!!

/3/.!(/3/.!

e =

+

=

0(0&0"3

".(#6!!.76/7.362#7+D2#7

e

@e ==

=

P D 5 D ill Pi #$ % 4 &


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()*E: (Re+ ,-.., soFriction Factor in Pipe $/%:

Pressure Drop 5n Drill Pipe #$ % 4.&in '$ %.* in

+ % ,,4!t

/o

b

@eaf =

!/"2.!"!

23.3/3/.!lo-

"!

23.3nlo-

a =+

=

+

=

#02!.!/

/3/.!lo-/".(

/

nlo-/".(b =

=

=

!!/(#0.!0(0&0

!/"2.!

af

#02!.!b

@e

===

P D 5 D ill Pi #$ % 4.&


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Friction Pressure Jradient $dP0dL%:

Pressure Drop 5n Drill Pipe #$ % 4.&in '$ %.* in

+ % ,,4!t

Friction Pressure 2rop in 2rill Pipe:

1!!&((6!"73/.!LdL

dP

P =

=

"d0% 11&

0si

ft

psi!"73/.!

/7.367(.#"

".(#676!!/(#0.!

D7(.#"

+f

dL

dP ##

==

=

P D 5 D ill ll #$ % 1.&


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Pressure Drop 5n Drill ollars


Aerage BulG @elocity inside 2rill 9ollars $'%:

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

+ % 1!t/3/.!

32

0"lo-3#.3

@

@lo-3#.3n

3!!

0!! =

=

=

#

n

/3/.!n

0!!

cm

secdyne!(/.#

!##&(

0"6((."

!##&(

@((."K ===

sec

ft#7.(7

".#

#7!61!7.!

D

J1!7.!+

## ===

#$ % 1.&P D 5 D ill ll


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Effectie @iscosity in 9ollars$ e%:

eynolds 0um"er in 9ollars $(Re%:

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

+ % 1!t


n(n

en1

(n3

D

+20K(!!

+

=

cP#(.37/3/.!61

(/3/.!63

".#

#7.(7620!(/.#6(!!

/3/.!(/3/.!

e =

+

=

7/!&(3#(.37

".(#6#7.(76".#62#7+D2#7

e

@e ==

=

#$ % 1.&P D 5 D ill ll


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

+ % 1!t


()*E: (Re+ ,-.., soFriction Factor in 29 $/%: b@eaf =

/o

!/"2.!"!

23.3/3/.!lo-

"!

23.3nlo-

a =

+

=

+

=

#02!.!/

/3/.!lo-/".(

/

nlo-/".(b =

=

=

!!"71!.!7/!&(3

!/"2.!

af

#02!.!b

@e

===

#$ % 1.&P D 5 D ill ll


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Friction Pressure Jradient $dP0dL%:

Friction Pressure 2rop in 2rill 9ollars:

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

+ % 1!t


ft

psi3/7!.!

".#67(.#"

".(#6#7.(76!!"71!.!

D7(.#"

+f

dL

dP ##

==

=

0!!63/7!.!LdL

dPP

=

=

"d% 22

0si


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Pressure Drop across oles

$3,% ,, 2nds

(in) $32% ,,

2nds (in) $3%

,2 2nds (in)

( )#####

(#((((

#7!6".(#6("0P

++=

"3oles% ,21

0si

( )##3###

(

#

DDD

J("0P

++

=

Pressure Drop


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6)

Pressure Drop

in DH4LE

%nnulus

$H#+5 % *.&in#$$6 % 1.&

in

+ % 1

Q = 280 gal/min

= 12.5 lb/gal*.&in

$ % * &Pressure Drop


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7*



Aerage BulG @elocity in 29631LE Annulus $'%:

$H#+5 % *.&

in#$$6 % 1.&

in+ %1 !t

Pressure Drop

in DH4LE %nnulus

"1(3.!3

#!lo-0"/.!

@

@lo-0"/.!n

3

(!! =

=

=

#

n

"1(3.!n

(!!

cm

secdyne330.0

#.(/!

#!6((."

#.(/!

@((."K ===

sec

ft7!7.3

".0".7

#7!61!7.!

DD

J1!7.!+

###

(

#

#

=

=

=

$ % * &

Pressure Drop


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Effectie @iscosity in Annulus $ e%:

eynolds 0um"er in Annulus $(Re%:

$H#+5 % *.&

in#$$6 % 1.&

in+ %1 !t

cP#!."""1(3.!63

("1(3.!6#

".0".7

7!7.36(11330.06(!!

"1(3.!("1(3.!

e =

+

=

( ) ( )0!!&(

#!.""

".(#67!7.36".0".72#7+DD2#7

e

(#

@e =

=

=

n(n

(#

en3

(n#

DD

+(11K(!!

+

=

Pressure Drop

in DH4LE %nnulus

$ # % *.&

Pressure Drop


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/o

$H#+5 % *.&

in#$$6 % 1.&

in+ %1 !t

()*E: (Re1 ,-..Friction Factor in Annulus $/%:

!("!!.!0!!&(

#1

#1f

@e

===

( ) ( ) ftpsi

!"#00.!".0".77(.#"

".(#67!7.36!("!!.!

DD7(.#"

+f

dL

dP #

(#

#

=

=

=

0!!6!"#00.!LdLdPP ==

"d7hole% ,.1

0si

Pressure Drop

in DH4LE %nnulus

Pressure 2rop


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73

q = 280 gal/min

= 12.5 lb/gal

Pressure 2rop

in 2P631LE Annulus

$H#+5 % *.& in

#$$" % 4.& in

+ %,,4 !t

Pressure 2rop $H#+5 % *.& in


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74



Aerage BulG @elocity in Annulus $'a%:

Pressure 2rop

in 2P631LE Annulus

H#+5

#$$" % 4.& in

+ %,,4 !t

"1(3.!3

#!lo-0"/.!

@

@lo-0"/.!n

3

(!! =

=

=

#

n

"1(3.!n

(!!

cm

secdyne330.0

#.(/!

#!6((."

#.(/!

@((."K ===

sec

ft(2/.#

".1".7

#7!61!7.!

DD

J1!7.!+

###

(

#

#

=

=

=

Pressure 2rop


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Effectie @iscosity in Annulus $ e%:

eynolds 0um"er in Annulus $(Re%:

p

in 2P631LE Annulus

n(n

(#

en3

(n#

DD

+(11K(!!

+

=

cP01.2/"1(3.!63

("1(3.!6#

".1".7

(2/.#6(11330.06(!!

"1(3.!("1(3.!

e =

+

=

( ) ( )!11&(

01.2/

".(#6(2/.#6".1".72#7+DD2#7

e

(#

@e =

=

=

Pressure 2rop


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/o 0si

Pressure 2rop

in 2P631LE Annulus

()*E: (Re1 ,-..Friction Factor in Annulus $/%:

!##22.!!11&(

#1

#1f

@e

===

( ) ( ) ftpsi

!(313.!".1".77(.#"

".(#6(2/.#6!##22.!

DD7(.#"

+f

dL

dP #

(#

#

=

=

=

1!!&((6!(313.!LdLdPP ==

"d07hole% ,&.2 0si

P 2 9 l


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Pressure 2rop 9alcs)

- UMMA -

PPUMP , P2P = P29 = PBI/ 01KKLE

= P296A00 = P2P6A00 = P32

PPUMP , 00" = ##/ = (&!#0

= 3# = ("3 = !

PPUMP = &(4& &5 = :(&'7 psi

P"UM" = P$/ + P33 + PH8$

:(&'7 psi


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78

PPUMP = &(4& &5

= :(&'7 psi

PH8$, !

P"UM" = P$/ + P33 + PH8$

P$/ = P$" + P$6 + P:'T 3#;;+5/

, 00" = ##/ = (&!#0 , (&2(7

psiP33= P$6733 + P$"733

, 3# = ("3 , (7"

P

='

NFrictionN Pressures


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7)

!

"!!

(&!!!

(&"!!

#&!!!

#&"!!

! "&!!! (!&!!! ("&!!! #!&!!! #"&!!!

9umulatie 2istance from -tandpipe( ft

N

FrictionNPressure(psi

2ILLPIPE

2ILL 91LLA

BI/ 01KKLE

A00ULU

3ydrostatic Pressures in the $ell"ore


80/85

8*

y

!(&!!!

#&!!!

3&!!!

1&!!!

"&!!!

0&!!!

/&!!!

7&!!!

2&!!!

! "&!!! (!&!!! ("&!!! #!&!!! #"&!!!


3

ydrostaticPre

ssure(psi

B3P

2ILL/I0J A00ULU

Pressures in the $ell"ore


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81

!(&!!!

#&!!!

3&!!!

1&!!!"&!!!

0&!!!

/&!!!

7&!!!2&!!!

(!&!!!

! "&!!! (!&!!! ("&!!! #!&!!! #"&!!!


Pressure

s(psi

/A/I9

9I9ULA/I0J

$ell"ore Pressure Profile


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82

!

#&!!!

1&!!!

0&!!!

7&!!!

(!&!!!

(#&!!!

(1&!!!

! #&!!! 1&!!! 0&!!! 7&!!! (!&!!!

Pressure( psi

2ept

h(

f

2ILL/I0J

A00ULU

$>tatic'

BI/

Pipe Flow Laminar


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83

Pipe Flow * Laminar

5n the above e9ample the flow down thedrillpipe was turbulent.

Gnder conditions of very hi-h viscosity&

the flow may very well be laminar.

()*E: i/ (Re1 ,-.., then

Friction Factor in Pipe $/%:

@e

(0f =

D7(.#"

+f

dL

dP #

=

Then and


84/85

84


85/85

vfdpH

#

n = 1.*

4. Wellbore Hydraulics, Pressure Drop Calculations

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Transcript of 4. Wellbore Hydraulics, Pressure Drop Calculations