lesson 7 foam drilling hydraulics-3
TRANSCRIPT
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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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Circulating Pressures
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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Circulating Pressures
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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Circulating Pressures
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
Circulating Pressures
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.
Circulating Pressures
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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.
Circulating Pressures
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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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Circulating Pressures
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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Circulating Pressures
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.
Circulating Pressures
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Circulating Pressures
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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Circulating Pressures
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.
Circulating Pressures
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Circulating Pressures
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.
Circulating Pressures
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Circulating Pressures
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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Circulating Pressures
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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Circulating Pressures
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.
Circulating Pressures
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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