16. Cuttings Transport - Slip Velocity

8/17/2019 16. Cuttings Transport - Slip Velocity

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1

PETE 411

Drilling Engineering

Lesson 16

- Lifting Capacity of Drilling Fluids -- Slip Velocity -



2

Lifting Capacity of Drilling Fluids

- Slip Velocity -

Fluid Velocity in Annulus

Particle Slip Velocity

Particle Reynolds Number Friction Coefficient

Example

Iterative Solution Metod

Alternative Solution Metod

API RP !"# Metod



3

Read: ADE, Ch. 4 - all

HW #8: Due 10-14-05

Quiz A

Thursday, Oct. 11, 6 - 8 p.m. Rm. 101

!"sed ""$

1 %&uati"' sheet a!!"(ed, 8 1)*+ 11+ "th sides/

OT%: Quiz A*002 a'd the s"!uti"'

are "' the (e 3



4


Historically$ %en an operator felt tat

te ole %as not bein& cleared of cuttin&s

at a satisfactory rate$ e %ould'

Increase te circulation rate

(ic)en te mud *increase +P,PV-



5


ore recent analysis so%s tat'

(urbulent flo% cleans te ole better.

Pipe rotation aids cuttin&s removal.

/it %ater as drillin& fluid$ annularvelocities of !001!23 ft,min are

&enerally ade4uate *vertical %ells-



6


A relatively 5flat6 velocity

profile is better tan a

i&ly pointed one.

Mud properties can be

modified to obtain aflatter profile in laminar flo%

e.&.$ decrease n



#rilled cuttin&s typicallyave a density of

about 2! lb,&al.

Since te fluid density is

less tan 2! lb,&al te

cuttin&s %ill tend tosettle$ or 7slip8 relative

to te drillin& mud.slipfluidparticle VVV −=

Density ! Velocity

slipV

particleVfluid

9

V



Velocity Profile

(e slip velocity can be reduced by

modifyin& te mud properties suc

tat te velocity profile is flattened'

Increase te ratio *+P,PV-

*yield point,plastic viscosity- or

#ecrease te value of n



Plug Flo"

Plug Flo" is &ood for ole

cleanin&. Plu& flo% refers

to a 5completely6 flatvelocity profile.

(e s#ear rate is :ero%ere te velocity profile

is flat.



Participle Slip Velocity

$e"tonian Fluids%

(e terminal velocity of a small

sperical particle settlin&*slippin&- trou& a Ne%tonian

fluid under ;aminar flo%

conditions is &iven by S(<=E8S

;A/'

µρ−ρ

=2

sf ss

d-*!">v





Particle Slip Velocity

Sto)es8 ;a% &ives acceptable accuracy for a

particle Reynolds number ? 0.!

For Nre @ 0.! an empirical friction factor

may be used.

µρ

= ssf Re

dvA2>N



+#at forces act

on a settling

particle,

$on-

sp#ericalparticles

eperience

relati'ely

#ig#er drag

forces



Sp#ericities for Various Particle S#apes

S#ape Sp#ericity

./0 2.r #

./3 2r #

./4 r #

./05 r*4#

./20 r*10#

Cylinders

./34 4626

./33 266

Pris&

./1 Cu)e

./07cta#edron

1/.. Sp#ere

Sp#ericity 8

surface area of

spere of same

volume as particle

surface area of

particle





Particle 9eynolds $u&)er( fig/ 4/46

-d!0B.B.*E4...........!f

d>A.!v

f

sss

−

ρρ

=:n field units(

ased on real cuttin&s



Slip Velocity Calculation

using oore;s grap# <Fig/ 4/46=

!. Calculate te flo% velocity.

2. #etermine te fluid n and > values.

". Calculate te appropriate viscosity

*apparent viscosity-.

B. ?ssu&e a value for te slip velocity.

3. Calculate te correspondin&

Particle Reynolds number.



Slip Velocity Calculation

<using oore;s grap#=

D. <btain te correspondin& dra& coeff.$ f$

from te plot of f vs. Nre.

. Calculate te slip velocity and compare%it te value assumed in step B above.

>. If te t%o values are not close enou&$

repeat steps B trou& usin& te

calculated Vs as te assumed slip

velocity in step B.



Ea&ple

se *te modified- Moore8s metod tocalculate te slip velocity and te net particle

velocity under te follo%in& assumptions'

/ell dept' >$000 ft +ield point' B lbf,!00ft2

#rill pipe' B.36$ !D.D G,ft #ensity of Particle' 2! lbm,&al

Mud /ei&t' .! G,&al Particle diameter' 3$000 µm

Plastic viscosity' cp Circulation rate' "B0 &al,min

Hole si:e' 1,>6



20

Solution - Slip Velociy Pro)le&

1. Calculate the flow velocity

2. Determine the fluid n and K value

1174300300y =+=+=⇒−= p y p µ τ θ µ θ τ

18117300600300600 ! =+=+=⇒−= θ µ θ θ θ µ p

ft,sec"."23

-3.B>3.*BB>.2

"B0

-dd*BB>.2

4v

222

!

2

2

9

=

−=

−=



21

*!>,!!-lo&"."2lo&"2."n"00

D00 =

θθ

=

7101.0n =

2. Determine the fluid n and K value " cont#d

Solution - Slip Velociy Pro)le& - cont;d

cp.e4AB.DD=

3!!

!!-3!0*

3!!

-3!0*=

E!0!.0n

"00

=

=θ

=

(ADE)



22

!0!.0

!0!.0!

a

n

n!

9

!2a

020>.0

-!0!.0

!2*

"23."

3.B>3.

!BB

AB.DD

*B.!0-E4........... 020>.0

-n

!2*

v

dd

!BB

=

+

−=µ

+

−=µ

−

−

3. Calculate the a!!ro!riate vicoity


=

==

c!e$94.66

7 94.17

!

K

cpcpa

µ µ



23

ec%663.12

325.3

2

&&

'''

ft ===4. (ume a value for the li! velocity


5. Calculate the corre!ondin) *article +eynold ,o.

!E.AB

cm2.3B

in

m!0

cm

m3000.DD"-A2>*A.!-*!

dvA2>N

B

a

ssf Re

=

=

--

-

[ ] '52/$ 104$ s9e9e == /1969.0 in @ds =



24

Fro& grap#( f 8 2/.


6. tain the dra) coeff. f from the !lot of f v. ,re.

1f

d1/5'

f

sss

−=

1/66 ft*s./63's <<=

=

−=

f

./505 1

5/1

21/.

2/.

./15651/5 Vs

%<4/1.4d=EA/



25

B *ii- Assume

3 *ii- Particle

D *ii- From &rap$

*ii-

Subse4uent iterations yield 0.3D ft,s and

0.3D ft,s a&ain...

678.0v =

A.D2D>.0J.A2NRe ==

7.2f =

.etc.....s,ft3>.0.2

A3A.0vs ==

Solution - Slip Velocity Pro)le& - cont;d



26

!. Fully ;aminar'

Slip Velocity - ?lternate et#od

−= !

f

d!.>Av

f

sss

( )f s

a

2

ss

9

Re

Re

d>2.>v

K

N

B0f

'"N

-

−=

=

<



27

2. IntermediateK

K

N

22f

'"00N"

Re

Re

=

<<

!,"

af

2,"

f sss

9

-*

-*d2.A0v

-

−=




28

". Fully (urbulent'

%..$9e >


NOTE:

Check NRef

f sss

B

=B<Bd'

−=

1/0f =



29

For te above calculations'

d-4.*B.!0B.........E !f

d!.>Av

dvA2>N

f

sss

a

ssf Re

−=

=

-


NOTE: Check NRe



30

Slip Velocity - ?lternate et#od2

If te flo% is fully laminar$ cuttin&s transport isnot li)ely to be a problem.

et#od% 1/ Calculate slip velocity for Intermediate

mode

2. Calculate slip velocity for Fully (urbulentMode.

". Coose te lo"er 'alue/



31

*i- Intermediate'

ft,sec3B3.0!.AB-J*A.!

A.!-*2!J0.!ADAJ2.A0

v

-*

-*2.A0d

v

!,"

2,"

s

9

!,"af

2,"f ss

s

9

=

−

=

−= -

*ii- Fully (urbulent'

ft%ec0.7819.1

9.13210.19691.54v

3d1.54v

'

f

f

'

=−

=

−=

Ea&ple



32

Ea&ple - cont;d

Intermediate' Vs L 0.3B3 ft,sec

Fully (urbulent' Vs L 0.>! ft,sec

(e correct slip velocity is 0.3B3 ft,sec

a&rees reasonably %ell %it iterative metod on p.23

5194.17

1969.0545.01.9928 , Chec +e ==

Range OK



33

Slip Velocity - ?P: 9P 1D

Iterative Procedure

Calculate Fluid Properties$ n O =

Calculate Sear Rate

Calculate Apparent Viscosity

Calculate Slip Velocity

Example



34

Settling

Velocity

of Drilled

Cuttings

in +ater

FromAPI RP 13D

p.2



35

Calculation Procedure

!. Calculate ns for te settlin& particle

2. Calculate >s for te particle

". Assume a value for te slip velocity$Vs

B. Calculate te sear rate$ γs

3. Calculate te correspondin& apparent viscosity$ µes

D. Calculate te slip velocity$ Vs

. se tis value of Vs and repeat steps B1D until te

assumed and calculated slip velocities 5a&ree6



36

Slip Velocity - Ea&ple

ASSUMPTIONS:

3 RPM Reading R3 3 lbf/100 ft

100 RPM Reading R100 20 lbf/100 ft2

Particle Density ρp 22.5 lb/gal

Mud Density ρ 12.5 lb/gal

Particle Dia. = Dp 0.5 in





38


". Assume a value for te slip velocity$ Vs

Assume Vs 8 1 ft*sec

B. Calculate te sear rate$ γ!

p

SS

#

V!2=γ !

S sec0.2B3.0

!J!2 −==γ



39


3. Calculate te corresp. apparentviscosity'


!n

ssess=!00

−γ =µ

cp3.!B2BJ""D.DJ!00 !3B!".0

es ==µ −

µ

ρ

ρ

ρ

ρ

µ

=

ψ 1D

1De35.(52.<1D

e...24./.V

2

es

pp

p

./0

p

es./0

s



40



f ψ = 0.80 "hen:

Vs 8 ./.3 ft*sec Repea" !"ep! #$

µ

ρ

ρ

ρ

ρ

µ

=

1

D

1D460(161D.144/.V

2

es

pp

p

p

ess

=

14/143

0/120/.

10/12

0/22

0/.460(1610/120/.

4/143

.144/.V

2

s



41


%! & '.' *"+!ec

4. hear rate γ! & 1,.3$ !ec#1

5. (!!arent vicoity µe! & 1$2.$- cp

6. li! velocity %! & '.- *"+!ec

econ/ I"era"0on # !0ng

4. hear rate γ! & 1., !ec#1

5. (!!arent vicoity µe! & 1$.- cp

6. li! velocity %! & '.23 *"+!ec

Th0r/ I"era"0on # !0ng %! & '.- *"+!ec



42


%! & '.23 *"+!ec

4. hear rate γ! & 1.$ !ec#1

5. (!!arent vicoity µe! & 1$-.' cp

6. li! velocity %! & '.1, *"+!ec

For"h I"era"0on # !0ng

0p %eoc0"4 %! & '.1, *"+!ec

5 %! & 1.'4 '.'4 '.24 '.2 *"+!ec 6



43

Transport 9atio

QEfficiency(ransport

ft,min!20 velocityFluid ft,minA0 velocityParticle 'Example

!00JvelocityfluidvelocityparticleEfficiency(ransport

velocityfluidvelocityparticle Ratio(ransport

===

=

=





45

Potential Hole-Cleaning Pro)le&s

!. Hole is enlarged/ (is may result in

reduced fluid velocity %ic is lo%er

tan te slip velocity.

2. Hig# do"n#ole te&peratures may

adversely affect mud properties

do%nole.

T /e measured tese at te surface.U



46

Potential Hole-Cleaning Pro)le&s

". Lost circulation problems may preclude

usin& tic) mud or i& circulatin&

velocity. T#ic slugs may be te

ans%er.

B. Slo" rate of &ud t#icening 1 after it as

been seared *and tinned-trou& te bit no::les$ %ere te

s#ear rate is very i&.



T#e End

Lesson 16

- Lifting Capacity of Drilling Fluids -- Slip Velocity -

Documents

16. Cuttings Transport - Slip Velocity