Foam Drilling Hydraulics

1
Lesson 7
PETE 689 Underbalanced Drilling (UBD)

• Foam Drilling Hydraulics
• Read UDM Chapter 2.5 - 2.6
  Pages 2.75-2.130
  MudLite Manual Chapter 2
  Pages 2.1-2.14

2
Foam Drilling Hydraulics

• Benefits of foam drilling.
• Rheology.
• Circulating pressures.
• Limitations of foam drilling.
• Homework 2.

3
Benefits of Foam Drilling

• High viscosity allows efficient cuttings
  transport.
• Gas injection rates can be much lower than dry
  gas or mist drilling.
• Low density of foam allows UB conditions be
  established in almost all circumstances.

4
Benefits of Foam Drilling

• BHP tends to be higher than dry gas or mist
  operations and penetration rates maybe reduced.
• But, penetration rates are still much higher than
  conventional.
• Low annular velocities reduce hole erosion.

5
Benefits of Foam Drilling

• Higher annular pressures with foam than with
  gasses can potentially reduce mechanical wellbore
  stability.
• Even if air is used as the gas, foam drilling can
  prevent downhole fires.
• Probably the greatest benefit of foam drilling is
  the ability to lift large volumes of produced
  liquids.

6
Rheology

• Two factors that have the greatest impact on the
  flow behavior of foams are quality and flow rate.
• Foam viscosity is largely independent of the
  foaming agents concentration in the liquid
  phase.

7
Rheology

• When viscosifying agents are added to the liquid
  phase, the foam viscosity increases with
  increasing liquid phase viscosity.
• Foam rheology is not very sensitive to other flow
  variables

8
Rheology

• Einstein (quality from 0 to 54)
• mf m(1.02.5 G)
• Where mf foam viscosity.
• m viscosity of base liquid.
• G foam quality (fraction).

9
Rheology

• Hatschek (quality from 0 to 74)
• mf m(1.04.5G)
• Hatschek (quality from 75 to 100)
• mf m(1.0/1 - G0.333)

10
Rheology

• Mitchell (quality from 0 to 54)
• mf m(1.03.6G)
• Mitchell (quality from 54 to 100)
• mf m(1.0/1 - G0.49)
• Mitchell also assumed Bingham Plastic behavior.

11
Rheology
2.5
20
Yield stress in normally expressed in units of
lbf/100sf
18
2
16
14
1.5
12
Foam Yield Stress (psf)
10
Foam Viscosity ( c P)
1
8
6
0.5
4
2
0
0
0 0.2
0.4 0.6
0.8 1
Foam Quality (fractional)
Plastic viscosity and yield point of foam as
functions of foam quality (after Mitchell, 19716).
12
Rheology
Plastic Viscosity and Yield Strength of
Foam(Krug,1971)
13
Rheology
Power- Law Fluid Properties of Foam
14
Rheology
80 Quality Foam
1000
100
Effective Viscosity (cP)
10
1
1 10
100 1000
10000
Shear Rate (s-1)
15
Rheology
90 Quality Foam
10000
1000
Effective Viscosity (cP)
100
10
1
1 10
100 1000
10000
Shear Rate (s-1)
16
Rheology
95 Quality Foam
10000
1000
Effective Viscosity (cP)
100
10
1
1 10
100 1000
10000
Shear Rate (s-1)
17
Rheology - Stiff Foam
10000
1000
Apparent Pipe viscosity (cP)
100
10
10 100
1000
10000
Shear Rate (s-1)
Effective viscosity of stiffened nitrogen-based
fracturing foam, 80 and 90 quality (after
Reidenbach et al., 19866)
18
Rheology

• The particular rheological model to use may
  depend on the application of the fluid.
• One argument is that the closer the fluid is to
  be a pure liquid system (low foam qualities) the
  more likely is that the fluid will act like a
  Bingham Plastic.

19
Rheology

• Empirical evidence shows that
• In laminar flow the fluid acts more like a
  Bingham Plastic.
• While in turbulent flow the fluid acts more like
  a Power Law Fluid.

20
Cuttings Transport
1
0.9
0.8
0.7
0.6
Relative Velocity 2
Relative Lifting Force
0.5
0.4
0.3
Relative Velocity 1
0.2
0.1
0
0 0.2 0.4
0.6 0.8 1
Liquid Volume Fraction
Lifting forces acting on a 0.1875-inch diameter
sphere for different quality foams (after Beyer
et al., 19724)
21
Cuttings Transport (Moore)
In laminar flow
?c-?f µe
Vt 4,980 dc2
In transitional flow
(?c-?f)2/3 (?f µe)1/3
Vt 175dc
22
Cuttings Transport (Moore)
In fully turbulent flow
v
?c - ?f ?f
Vt 92.6 dc
(2.54)
23
Cuttings Transport
Where Vt terminal velocity of a cutting
(ft/min.) Dc the cuttings diameter
(inches). ?c the cuttings density (ppg). ?f the
drilling fluids density (ppg). µe the fluids
effective viscosity at the rate flowing up the
annulus (cP).
24
Cuttings Transport
A cuttings Reynolds number, NRec can be
expressed as
15.47?fvtdc µe
NRec

• Theoretically, flow past the cutting will be
• Laminar if NRec lt 1
• Transitional if 1 lt NRec lt 2,000
• Turbulent if NRec gt 2,000.

25
Cuttings Transport

• If flow is laminar, an increase in foam viscosity
  with increasing quality will dominate the
  reduction in foam density, and the terminal
  velocity will decrease with increasing foam
  quality, until the foam breaks down into mist.

?c-?f µe
Vt 4,980 dc2
Laminar flow
26
Cuttings Transport

• If the flow is turbulent, the terminal velocity
  is independent of the foams viscosity.
• The terminal velocity will increase with
  increasing foam quality due to reduction in
  density. In fully turbulent flow

Fully turbulent flow
v
?c - ?f ?f
Vt 92.6 dc
27
Cuttings Transport

• For typical foam drilling conditions, flow past a
  1/2 diameter cutting in a 60 quality foam at
  nearly 10,000 was transitional.
• The terminal velocity was computed to be 60 feet
  per minute. In transitional flow

Transitional flow
(?c-?f)2/3 (?f µe)1/3
Vt 175dc
28
Cuttings Transport

• In transitional flow, the terminal velocity is
  sensitive to the density difference between the
  cutting and the foam, as well as the effective
  viscosity of the foam.
• This is probably why foam does not show as much
  increase in cuttings transport capacity (over
  water) as might be expected from its viscosity.

Transitional flow
(?c-?f)2/3 (?f µe)1/3
Vt 175dc
29
Circulating Pressures

• Strongly influenced by viscosity and quality.
• Both viscosity and quality change with changing
  pressure.

30
Circulating Pressures
500
100/40
400
Foam Gas/Liquid Rates (scfm/gpm)
300
400/40
Bottomhole Pressure (psi)
100/10
200
400/10
100
Well Productivity
0
0 5 10 15 20
25 30 35 40 45
Formation Fluid Influx (BWPH)
Predicted influence of water inflow on
bottomhole pressure (after Millhone et al., 1972
24)
31
Circulating Pressures
1200
150
140
1050
130
900
120
750
Injection Pressure (psi)
600
110
Air Volume Rate (scfm) and Water Rate (gpm)
100
450
90
300
150
80
70
0
0 2000 4000 6000
8000 10000 12000
Depth (feet)
Recommended air and liquid injection rates and
predicted injection pressures for foam drilling
(after Krug amd Mitchel, 197219) no inflow
continued
32
Circulating Pressures
Mud Injection Rates (gpm)
35 30 25
20 15 10
5 0
18
17
16
15
14
Hole Diameter (Inches)
13
12
11
10
9
8
50 75 100 125 160 175 200 225
250 275 300 325 350 375 400 425
450
Air Injection Rates (cfm)
Suggested air and liquid (mud) injection rates
for stiff foam drilling (after Garavini et al.,
19717)
33
Circulating Pressures
5000
4500
4000
3500
3000
2500
Bottomhole Pressure (psi)
2000
1500
1000
500
0
0 2000 4000 6000
8000 10000 12000
Depth (feet)
Predicted bottomhole pressures during foam
drilling, no inflow (after
Krug and Mitchell, 197219).
34
Circulating Pressures

• Power-Law Fluid Model Pressures
• Guo et al. (1995) set out a procedure that can be
  used to calculate BHP generated by foam systems
  in a multi-step process. This procedure assumes
  the fluid behavior the Power-Law model.

35
Circulating Pressures
1.Determine the desired foam velocity and foam
quality at the bottom of the hole. Calculate the
corresponding volumetric flow rate of gas and
liquid (e. g., the volumetric flow of gas is
simply the local flow rate multiplied by the
fractional foam quality) at the hole bottom, Qgbh
and Qlbh respectively, in ft3/sec.
36
Circulating Pressures
2. After specifying a desired foam quality at the
surface in the annulus (usually 95-96),
calculate the required ratio of bottomhole to
surface using the equation
Pbh/Ps(zbhTbhGs1-Gbh)/(ZsTsGbh1-Gs)
37
Circulating Pressures
Where P pressure, lbf/ft2
z dimensionless gas
compressibility factor. T
absolute temperature, 0R G foam quality
fraction. The subscripts bh and s refer to
bottomhole conditions and surface conditions,
respectively.
38
Circulating Pressures
3. Calculate the surface annular pressure using
the equation
Ps (?l)(Dv)/(Pbh/Ps)(Gs/1-Gs)
...ln(Pbh/Ps)-GsDv/(RZavTav1-Gs)-1
39
Circulating Pressures
Where ?l density of the liquid phase,
lbm/ft3. Dv true vertical depth at the
bottomhole location, ft. R universal
gas constant, Rg/(Molecular
weight)air , lbm/lbmmol, Rg is 1,545
lbfft/lbmmol0R and R 53.3
for air. The subscript av refers to average
condition.
40
Circulating Pressures
4. Calculate the bottomhole pressure using the
equation Pbh Ps(Pbh/Ps) Where
All factors were defined earlier.
41
Circulating Pressures
5. Calculate foam density at bottomhole
conditions using (?fbh)
(1-Gbh)?l?gbhGbh Where ?fbh density of
foam at bottomhole, lbm/ft3. ?gbh
density of gas at bottomhole,
lbm/ft3. ?gbh Phb/RZbhTbh
42
Circulating Pressures
6. Calculate the mass low rate of foam using
Mf , lbm/ sec ?f Qf Where Qf
volumetric flow rate of foam, ft3/sec.
43
Circulating Pressures
7. Average foam density can then be calculated
using ?fav Pbh/Dv 8. The
average foam velocity will be vfav ,
ft/sec Mf/Aa ?fav Where Aa cross-sectional
area of the annulus, ft2.
44
Circulating Pressures
9. Then the average foam quality can be
determined using Gav (?l ?fav) /
(?l ?gav) Where ?gav Pav /
(RZavTav)
45
Circulating Pressures
10.Table 3-4-3 (UDOM-Signa), can be used to
determine the consistency index, k , and the
flow behavior index, n, based on the average
foam quality from Step 9.
46
Circulating Pressures
11. The effective foam quality can then be
estimated based on average conditions,
according to Moore (1974) using the following
equation µe K (2n1/3n)n(12vfav/D-d)n-1 W
here D wellbore diameter, ft.
d drillpipe diameter, ft.
47
Circulating Pressures
12. Calculate the Reynolds number using
Re vfav (D-d)?fav /µe 13. Then
calculate the friction factor with
f 24 / Re
48
Circulating Pressures
14. The pressure loss due to friction can
then be calculated using Pf 2fvfav
?favLh/(gcD-d) Where Lh length of the
hole, ft. gc gravity, 32,174 lbmft/lbf sec2
49
Circulating Pressures
15. The total BHP can then be update (pbhu) by
adding the friction pressure loss to the
hydrostatic BHP determined in Step 4 above
Pbhu Pbh Pf
50
Circulating Pressures
16. The surface pressure can then be
update (Psu) using the equation from step 4
above Psu Pbhu( Pbh/Ps) 17.
Repeat Steps 7 through 16 until the update BHP
nearly equals the beginning BHP.
51
Injection Rates
Power-Law Model Fluid Injection Rate

• Guo et al. not only developed a simple method of
  determining the bottomhole and surface annular
  pressures with a foam system, they also described
  how to continue using the technique to determine
  flow rates, or injection rates of the gas and
  liquid phases of the foam.

52
Injection Rates

• Finally, they described the use of the
  technique to ensure the cuttings are being
  carried out of the hole adequately.
• Guo et al. carried their process through four
  additional steps that continue from the process
  described above. The remaining steps for a
  Power-Law model fluid are

53
Injection Rates
18. Using the BHP calculated with the Guo et al.
method, Pbh, and the gas flow rate estimated in
Step 1 above using the desired foam quality,
Qghb, calculate the gas flow rate at the surface
using the equation
Qgs (Pbh/Pa)(Ta/Tbh)(Qgbh/Zbh) Where Pa
ambient pressure, lbf/ft2 Ta
ambient temperature, 0R
54
Injection Rates
19.Determine desired trouble-free cuttings
concentration at the surface, Cd, (usually 4-6),
and use it to calculate the required cuttings
transport velocity, Vtr, in ft/sec, similar to
the method described in the section on gasified
fluids.
55
Injection Rates

• This transport velocity should be calculated at a
  critical point in the wellbore, most likely at
  the top of the collars.
• This will necessitate calculating the annular
  pressure at the critical point using the
  technique described above for BHP.

56
Injection Rates

• The following equation can then be use to
  calculate transport velocity at the critical
  point

Vtr(ROP/Cd)(Zcr/Zd)(Tcr/Td).. (Gd/Gcr)(Pd/Pcr)
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.
57
Injection Rates

• Also note that the pressure, foam quality, foam
  density, and foam velocity must be calculated at
  the critical point using Steps 7 through 16 in
  section Power-Law Fluid Model Pressures.

58
Injection Rates
20.The cuttings terminal settling velocity must
then be determined, based on the particle
Reynolds Number, calculated using
Rep (?f dcVts)/µe
Where ?f density of foam, lbm/ft3 dc
diameter of a single cutting, ft µe
effective viscosity of foam, lbm/ft-sec
59
Injection Rates

• The particular equation for the terminal cuttings
  velocity, Vts, is determined by the flow regime
  of the fluid. The fluid will either be in viscous
  flow (Replt1), transition flow (1ltReplt2,000), or
  turbulent flow (Repgt2,000).
• The equations for Vts are described in more
  detail in Section Cuttings Transport.

60
Injection Rates

• Note that in the previous section referenced
  here, the methods were those described by
  Bourgoyne et al., and the ranges for viscous,
  transition, and turbulent flow were slightly
  different.
• Also, in the earlier section the terminal
  settling velocity, Vts was referred to as the
  slip velocity, Vsl

61
Injection Rates
21.The minimum foam velocity required to lift
the given cutting size can then be calculated
using Vf , ft/sec a (Vtr Vts)
Where a is a correction factor for wellbore
inclination. When the wellbore is vertical, a is
1.0 when the wellbore is horizontal, a is 2.0
62
Injection Rates
22.The final step is to compare the velocity
calculated in Step 21 with the velocity assumed
and specific originally in the calculation of
the BHP (step 1 under Power-Law Fluid Model
Pressures). If the calculated required foam
velocity is less than the velocity assumed and
specific above, then the hole is being
cleaned.
63
Injection Rates

• Otherwise, the hole will not be cleaned. A higher
  value will need to be specified in step 1 above,
  and the entire procedure will need to be repeated.

64
Limitations of Foam Drilling

• Corrosion when air is used as the gas.
• Saline formation waters increase corrosion.
• H2S or CO2 in the formation increases corrosion.
• Wellbore instability.
• Mechanical
• Chemical

65
Homework 2

• Using the graphical method determine
• BHP
• Air injection rate
• Water injection rate
• Injection pressure
• For the well in Homework 1.

66
Homework 2, cont.

• Repeat using the 22 step process described in
  handout (and this presentation).
• Due October 6, 2000