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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

Foam Drilling Hydraulics

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

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.

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.

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.

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.

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

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).

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)

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.

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).

Rheology

Plastic Viscosity and Yield Strength of

Foam(Krug,1971)

Rheology

Power- Law Fluid Properties of Foam

Rheology

80 Quality Foam

1000

100

Effective Viscosity (cP)

10

1

1 10

100 1000

10000

Shear Rate (s-1)

Rheology

90 Quality Foam

10000

1000

Effective Viscosity (cP)

100

10

1

1 10

100 1000

10000

Shear Rate (s-1)

Rheology

95 Quality Foam

10000

1000

Effective Viscosity (cP)

100

10

1

1 10

100 1000

10000

Shear Rate (s-1)

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)

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.

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.

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)

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

Cuttings Transport (Moore)

In fully turbulent flow

v

?c - ?f ?f

Vt 92.6 dc

(2.54)

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).

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.

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

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

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

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

Circulating Pressures

- Strongly influenced by viscosity and quality.
- Both viscosity and quality change with changing

pressure.

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)

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

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)

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).

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.

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.

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)

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.

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

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.

Circulating Pressures

4. Calculate the bottomhole pressure using the

equation Pbh Ps(Pbh/Ps) Where

All factors were defined earlier.

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

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.

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.

Circulating Pressures

9. Then the average foam quality can be

determined using Gav (?l ?fav) /

(?l ?gav) Where ?gav Pav /

(RZavTav)

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.

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.

Circulating Pressures

12. Calculate the Reynolds number using

Re vfav (D-d)?fav /µe 13. Then

calculate the friction factor with

f 24 / Re

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

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

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.

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.

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

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

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.

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.

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.

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.

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

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.

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

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

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.

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.

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

Homework 2

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

Homework 2, cont.

- Repeat using the 22 step process described in

handout (and this presentation). - Due October 6, 2000