Lesson 7 Foam Drilling Hydraulics-3

8/12/2019 Lesson 7 Foam Drilling Hydraulics-3

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Harold Vance Department of Petroleum Engineering

Lesson 7

Foam Drilling HydraulicsRead: UDM Chapter 2.5 - 2.6

Pages 2.75-2.130MudLite Manual Chapter 2

Pages 2.1-2.14

PETE 689

Underbalanced Drilling(UBD)


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Foam Drilling Hydraulics

Benefits of foam drilling.Rheology.Circulating pressures.

Limitations of foam drilling.Homework # 2.


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Benefits of Foam DrillingHigh viscosity allows efficientcuttings transport.

Gas injection rates can bemuch lower than dry gas ormist drilling.

Low density of foam allowsUB conditions be establishedin almost all circumstances.


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BHP tends to be higher than drygas or mist operations and

penetration rates maybe reduced.But, penetration rates are stillmuch higher than conventional.

Low annular velocities reducehole erosion.

Benefits of Foam Drilling


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Higher annular pressures withfoam than with gasses canpotentially reduce mechanical

wellbore stability.Even if air is used as the gas, foamdrilling can prevent downhole fires.

Probably the greatest benefit offoam drilling is the ability to liftlarge volumes of produced liquids.

Benefits of Foam Drilling


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Rheology

Two factors that have thegreatest impact on the flowbehavior of foams are qualityand flow rate.Foam viscosity is largelyindependent of the foamingagents concentration in theliquid phase.


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When viscosifying agents are addedto the liquid phase, the foam

viscosity increases with increasingliquid phase viscosity.Foam rheology is not very sensitive

to other flow variables

Rheology


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Einstein (quality from 0 to 54%)

mf = m(1.0+2.5 )

Where mf = f oam viscosity.

m = v iscosity of base liquid.= f oam quality (fraction).

Rheology


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Hatschek (quality from 0 to 74%)

mf = m(1.0+4.5 )

Hatschek (quality from 75% to 100%)

mf = m(1.0/{1 - 0.333 })

Rheology


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Mitchell (quality from 0 to 54%)

mf = m(1.0+3.6 )

Mitchell (quality from 54% to 100%)

mf = m(1.0/{1 - 0.49 })

Mitchell also assumed Bingham Plastic behavior.

Rheology


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Yield stress innormally expressedin units of lbf/100sf

Rheology

Plastic viscosity and yield point of foam as functions of foamquality (after Mitchell, 1971 6).

F o a m

V i s c o s

i t y ( c

P )

Foam Quality (fractional)

20

18

16

14

12

10

8

2.5

4

2

0

0 0.2 0.4 0.6 0.8 1

F o a m

Y i e l

d S t r e s s

( p s f

)

2

1.5

1

0.5

0

6


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RheologyPlastic Viscosity and Yield Strength of Foam(Krug,1971)

Quality Plastic Yield Strength0 1.02 0

0-25 1.25 0

25-30 1.58 0

30-35 1.60 035-45 2.40 0

45-55 2.88 0

55-60 3.36 0

60-65 3.70 14

65-70 4.30 2370-75 5.00 40

75-80 5.76 48

80-86 7.21 68

86-90 9.58 100

90-96 14.38 250


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RheologyPower- Law Fluid Properties of Foam

Foam Quality,Percent Gas by

Volume

Consistency Index,

k

Flow BehaviorIndex,

n 65-69 2.766 0.29069-71 2.777 0.295

72-73 2.8716 0.293

74-76 2.916 0.295

77-78 3.343 0.273

79-81 3.635 0.26284-86 4.956 0.214

89-91 5.647 0.200

91-92 6.155 0.187

94-96 3.325 0.290

96-97.7 2.566 0.326


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Rheology

E f f e c

t i v e

V i s c o s i t y

( c P )

1000

100

10

1 10 100 1000 100001

Shear Rate (s -1 )

80 Quality Foam


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Rheology

E f f e c t

i v e

V i s c o s

i t y ( c P

)1000

100

10

1 1 10 100 1000 10000

Shear Rate (s -1 )

1000090 Quality Foam


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E f f e c t

i v e

V i s c o s

i t y ( c P

) 1000

100

10

1000095 Quality Foam

1 10 100 1000 10000

Shear Rate (s -1 )

Rheology

1


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Rheology - Stiff Foam

Effective viscosity of stiffened nitrogen-based fracturing foam, 80and 90 quality (after Reidenbach et al., 1986 6)

A p p a r e n

t P i p e v i s c o s i

t y ( c P )

1000

100

10

10000

10 100 1000 10000

Shear Rate (s -1 )


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The particular rheological model touse may depend on the applicationof the fluid.

One argument is that the closer thefluid is to be a pure liquid system(low foam qualities) the more likelyis that the fluid will act like aBingham Plastic.

Rheology


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Empirical evidence shows that:

In laminar flow the fluid acts morelike a Bingham Plastic.While in turbulent flow the fluid

acts more like a Power Law Fluid.

Rheology


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Cuttings Transport

Lifting forces acting on a 0.1875-inch diameter sphere for differentquality foams (after Beyer et al., 1972 4)

Liquid Volume Fraction0 0.2 0.4 0.6 0.8 1

R e l a t

i v e

L i f t i n g

F o r c e

1

0.10

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Relative Velocity 2

Relative Velocity 1


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Cuttings Transport (Moore)

V t = 4,980 d

c2

V t = 175d c

In laminar flow:

c- fe

( c- f ) 2/3( f e) 1/3

In transitional flow:


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V t = 92.6 d c c - f f

In fully turbulent flow:Cuttings Transport (Moore)

(2.54)


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Where: V t terminal velocity of a cutting (ft/min.)

Dc the cuttings diameter (inches). c the cuttings density (ppg).

f the drilling fluids density (ppg). e the fluids effective viscosity at the

rate flowing up the annulus (cP).

Cuttings Transport


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Cuttings Transport A cuttings Reynolds number, N

Rec can be

expressed as:

15.47 f v td ceNRec =

Theoretically, flow past the cutting will be

Laminar if N Rec < 1Transitional if 1 < N Rec < 2,000

Turbulent if NRec

> 2,000.


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If flow is laminar, an increase in foamviscosity with increasing quality willdominate the reduction in foam density,

and the terminal velocity will decreasewith increasing foam quality, until thefoam breaks down into mist.

Cuttings Transport

V t = 4,980 d c2 c- f

e Laminar flow


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If the flow is turbulent, the terminalvelocity is independent of the foamsviscosity.The terminal velocity will increasewith increasing foam quality due toreduction in density. In fully turbulentflow:

Cuttings Transport

V t = 92.6 d c c - f f

Fully turbulent flow


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For typical foam drilling conditions,flow past a 1/2 diameter cutting in a60 quality foam at nearly 10,000 wastransitional.The terminal velocity was computed tobe ~60 feet per minute. In transitionalflow:

Cuttings Transport

V t = 175d c ( c- f ) 2/3( f e) 1/3

Transitional flow


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In transitional flow, the terminal velocity issensitive to the density difference betweenthe cutting and the foam, as well as theeffective viscosity of the foam.

This is probably why foam does not showas much increase in cuttings transportcapacity (over water) as might be expectedfrom its viscosity.

Cuttings Transport

V t = 175d c ( c- f ) 2/3( f e) 1/3

Transitional flow


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Circulating Pressures

Strongly influenced by viscosity andquality.Both viscosity and quality changewith changing pressure.


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Predicted influence of water inflow on bottomhole pressure(after Millhone et al., 1972 24 )

B o t t o m

h o l e P r e s s u r e

( p s i

)

Formation Fluid Influx (BWPH)

400

500

300

200

100

0

0 5 10 15 20 25 30 35 40 45

Foam Gas/LiquidRates (scfm/gpm)

100/40

400/40100/10

400/10

Well Productivity


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A i r V o l u m e

R a t e

( s c f m

) a n d

W a t e r

R a t e

( g p m )

1050

1200

900

750

600

450

300

150

0 2000 4000 6000 8000 10000 12000

150

140

130

120

110

100

90

80

700

Recommended air and liquid injection rates and predicted injectionpressures for foam drilling (after Krug amd Mitchel, 1972 19 ); no inflow

continued

Depth (feet)

I n j e c t

i o n

P r e s s u r e

( p s i

)


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Suggested air and liquid (mud) injection rates for stiff foam drilling(after Garavini et al., 1971 7)

Air Injection Rates (cfm)50 75 100 125 160 175 200 225 250 275 300 325 350 375 400 425 450

35 30 25 20 15 10 5 0Mud Injection Rates (gpm)

H o l e

D i a m e t e r (

I n c h e s

)

18

17

16

15

14

13

12

11

10

98

l


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0 2000 4000 6000 8000 10000 12000

Predicted bottomhole pressures during foam drilling, no inflow(after Krug and Mitchell, 1972 19 ).

B o t

t o m

h o l e P r e s s u r e

( p s i

)

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

0


Depth (feet)


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Power-Law Fluid Model PressuresGuo et al. (1995) set out a

procedure that can be used tocalculate BHP generated by foamsystems in a multi-step process.

This procedure assumes the fluidbehavior the Power-Law model.



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1. Determine the desired foamvelocity and foam quality at thebottom of the hole. Calculate the

corresponding volumetric flow rateof gas and liquid (e. g., thevolumetric flow of gas is simply thelocal flow rate multiplied by thefractional foam quality) at the holebottom, Q gbh and Q lbh respectively,in ft 3/sec.



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Circulating Pressures2. After specifying a desired foam

quality at the surface in theannulus (usually 95-96%),

calculate the required ratio ofbottomhole to surface usingthe equation:

Pbh /P s=(z bh Tbh s{1- bh })/(Z sTs bh {1- s})


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Where: P = pressure, lb f /ft 2

z = dimensionless gascompressibility factor.

T = absolute temperature, 0R

= foam quality fraction.The subscripts bh and s refer to bottomholeconditions and surface conditions, respectively.


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Where: l = density of the liquid phase, lb m /ft 3 .

Dv = true vertical depth at the bottomholelocation, ft.

R` = universal gas constant,R g/(Molecular weight) air , lb m /lb mmol,

R g is 1,545 lb f ft/lb mmol 0R and R`= 53.3 for air.

The subscript av refers to average condition .


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4. Calculate the bottomhole pressureusing the equation:

Pbh = Ps(P bh /Ps)

Where: All factors were defined earlier.



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5. Calculate foam density at bottomholeconditions using:

( fbh ) = (1- bh ) l+ gbh bh

Where: fbh = density of foam atbottomhole, lb m /ft 3 .

gbh = density of gas atbottomhole, lb m /ft 3 .

gbh = P hb /R`Z bh Tbh


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6. Calculate the mass low rate offoam using:

Mf , lb m / sec = f Qf

Where:Qf = volumetric flow rate of

foam, ft 3/sec.


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7. Average foam density can then becalculated using:

fav = P bh /D v 8. The average foam velocity will be:

vfav , ft/sec = M f /A a favWhere: A a = cross-sectional area of

the annulus, ft 2.



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9. Then the average foam quality canbe determined using:

av = ( l fav ) / ( l gav )

Where:

gav = P av / (R`Z av Tav )


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Circulating Pressures10. Table 3-4-3 (UDOM-Signa), can

be used to determine theconsistency index, k , and theflow behavior index, n , based

on the average foam qualityfrom Step 9.


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11. The effective foam quality can then be estimated based on average

conditions, according to Moore

(1974) using the following equation:

e = K ({2n+1}/3n) n(12v fav /{D-d}) n-1

Where: D = wellbore diameter, ft.d = drillpipe diameter, ft.



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12. Calculate the Reynolds numberusing:

R e = v fav (D-d) fav / e

13. Then calculate the friction factor

with:f = 24 / R e


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14. The pressure loss due to friction canthen be calculated using;

P f = 2 f vfav fav Lh/(g c{D-d})

Where:

Lh = length of the hole, ft.

g c = gravity, 32,174 lb mft/lb f sec 2


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15. The total BHP can then beupdate (p bhu ) by adding thefriction pressure loss to thehydrostatic BHP determinedin Step 4 above:

Pbhu = P bh + P f


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16. The surface pressure can then beupdate (P su ) using the equationfrom step 4 above:

P su = P bhu ( P bh /P s)

17. Repeat Steps 7 through 16 untilthe update BHP nearly equals thebeginning BHP.



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Injection Rates

Guo et al. not only developed a

simple method of determining thebottomhole and surface annularpressures with a foam system, theyalso described how to continueusing the technique to determineflow rates, or injection rates of thegas and liquid phases of the foam.

Power-Law Model Fluid Injection Rate


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Injection Rates

Finally, they described the use of thetechnique to ensure the cuttings arebeing carried out of the holeadequately.Guo et al. carried their processthrough four additional steps thatcontinue from the process describedabove. The remaining steps for aPower-Law model fluid are:

j i


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Injection Rates18. Using the BHP calculated with the Guo

et al. method, P bh , and the gas flowrate estimated in Step 1 above usingthe desired foam quality, Q ghb ,

calculate the gas flow rate at thesurface using the equation:

Qgs = (P bh /P a)(T a /T bh )(Q gbh /Z bh )

Where: P a = ambient pressure, lb f /ft 2

Ta = ambient temperature, 0R


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Injection Rates

19. Determine desired trouble-freecuttings concentration at the

surface, C d , (usually 4-6%), anduse it to calculate the requiredcuttings transport velocity, V tr , inft/sec, similar to the methoddescribed in the section ongasified fluids.


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Injection Rates

This transport velocity should becalculated at a critical point in the

wellbore, most likely at the top ofthe collars.

This will necessitate calculating

the annular pressure at thecritical point using the techniquedescribed above for BHP.


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Injection Rates

The following equation can thenbe use to calculate transport

velocity at the critical point:

V tr =(ROP/C d)(Z cr /Z d)(T cr /Td)*..

( d/ cr )(P d/P cr )

Where: ROP = rate of penetration, ft/sec.The subscripts cr and d refer to the critical point and the cuttings

delivery point (usually the surface), respectively.


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Injection Rates

Also note that the pressure, foamquality, foam density, and foamvelocity must be calculated at thecritical point using Steps 7through 16 in section Power-LawFluid Model Pressures.


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Injection Rates

20. The cuttings terminal settlingvelocity must then be determined,based on the particle Reynolds

Number, calculated using:Re p = ( f d c V ts )/ e

Where: f = density of foam, lb m /ft 3

d c = diameter of a single cutting, ft

e = effective viscosity of foam, lb m /ft-sec


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Injection Rates

The particular equation for theterminal cuttings velocity, Vts, isdetermined by the flow regime of thefluid. The fluid will either be in viscousflow (Re p


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Injection Rates

Note that in the previous sectionreferenced here, the methods werethose described by Bourgoyne et al.,

and the ranges for viscous, transition,and turbulent flow were slightlydifferent.

Also, in the earlier section theterminal settling velocity, V ts wasreferred to as the slip velocity, V sl


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21. The minimum foam velocity requiredto lift the given cutting size can thenbe calculated using:

V f , ft/sec = (V tr + V ts )

Where is a correction factor for wellboreinclination. When the wellbore is vertical, is1.0; when the wellbore is horizontal, is 2.0

Injection Rates


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Injection Rates

22. The final step is to compare thevelocity calculated in Step 21 with thevelocity assumed and specificoriginally in the calculation of theBHP (step 1 under Power-Law FluidModel Pressures ). If the calculated

required foam velocity is less thanthe velocity assumed and specificabove, then the hole is beingcleaned.


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Injection Rates

Otherwise, the hole will not becleaned. A higher value will needto be specified in step 1 above,and the entire procedure willneed to be repeated.


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Limitations of Foam Drilling

Corrosion when air is used as thegas.

Saline formation waters increasecorrosion.H2S or CO 2 in the formationincreases corrosion.Wellbore instability.

MechanicalChemical


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Homework # 2

Using the graphical methoddetermine:

BHP Air injection rateWater injection rateInjection pressure

For the well in Homework # 1.


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Homework # 2, cont.

Repeat using the 22 step

process described in handout(and this presentation).

Due October 6, 2000

Lesson 7 Foam Drilling Hydraulics-3

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