Gasified Liquid Hydraulics

1
PETE 689 Underbalanced Drilling (UBD)

• Lesson 9
• Gasified Liquid Hydraulics
• Read UDM Chapter 2.7
• Pages 2.131- 2.179

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Gasified Liquid Hydraulics

• Reynolds number.
• Multi-phase flow.
• Pressure prediction
• Hole static pressure.
• Circulating pressure.
• Bit pressure drop.
• Hole Cleaning.

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Reynolds Number

• In practice the flow of gasified liquid is almost
  always turbulent (Reynolds number gt 4,000).
• Example water flowing up an 8½ hole with 5
  drillpipe.

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Reynolds Number

• Annular velocity of 7 ft/min would be sufficient
  for turbulent flow.
• AVs gt 100 ft/min are common in gasified liquid
  drilling.

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Reynolds Number
15.47 Dh?wVan µ
Re

• 2 .58

Where Dh hydraulic diameter of the annulus
(the difference between the hole and pipe
diameters) (inc). ?w liquid density
(ppg). Van average annular velocity
(ft/min). µ liquid viscosity (cP).
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Reynolds Number

• The consequences of turbulence in the annulus is
  that the rheology of gasified fluids has little
  effect on the annular pressure profile.
• This is at least true with un-viscosified base
  fluid and annular velocities are high.

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Multi-phase Flow

• At least three phases are present in the
  wellbore annulus.
• Liquid, gas and solids (cuttings).
• Liquids could be
• Mud.
• Oil.
• Water.

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Flow Regimes
Bubble Flow
Slug Flow
Churn Flow
Annular Flow
Flow Regimes for Two-Phase, vertical, Upward
Fluid Flow
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Flow Regimes
Flow Regime Map for Water/Air Mixture in Upward
Flow
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Flow Regimes
Horizontal flow patterns
GAS
(a) Bubble
(e) Slug
GAS
GAS
GAS
(f) Semi-Annular
(b) Plug
GAS
GAS
(g) Annular
(c) Stratified
GAS
(h) Spray
(d) Wavy
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Pressure Prediction

• HSP
• Annular friction.
• Bit pressure drop.
• Mud.
• Gasified mud.
• Drillstring pressure drop.
• Mud.
• Gasified mud.

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HSP
P1
ò


h
0
144
VdP
P2
2.59
Where V specific volume of the fluid
(ft3/lbm) P pressure (psia) P1 pressure at the
top of the column (psia). P2 pressure at the
bottom of the column (psia). H height (feet)
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HSP
In oilfield units, assuming ideal gas behavior
14.7S (Tavg 460)
520P
2.60 M 42MW
0.0764GS 2.61
Vm 5.61
Where Vm total volume (ft3) of gas/bbl liquid at
pressure. P pressure (psia). Tave average
temperature (oF). M mass of mixture (lbm/bbl) of
liquid. S volume of gas (scf/bbl) of mud. G gas
gravity. MW mud weight (ppg).
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HSP
For a static column of mixed gas and liquid in a
well of depth, h, Equation 2.59 can be rewritten
as
1 2117S (Tavg 460)dP M
520P

2.62
1 M
ò
ò
P1
P1
h 808dP
P2
P2
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Gas Volume
This can be integrated an re-arranged to find S,
the volume of gas (scf/bbl of liquid)
808 (Pb Ps) 42 hMW 0.0764h
4.071 (Tavg 460)ln (Pb/Ps)

2.63
S
Where Ps surface pressure (psia). Pb desired
bottomhole pressure (psia).
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Friction Forces
When the fluid column is flowing up the annulus,
work is done against friction between the fluid
and the annular walls (the hole wall, the
casings inside surface, and the drillstring).
Neglecting acceleration, the pressures at the top
and bottom of a vertical flowing column of fluid
are related to the fluids specific volume, the
height of the column and the energy lost to
friction, Wf , by
ò
P1
144 VdP h Wf 0
2.64
P2
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Fanning Friction Factor
Poettmann and Bergman related Wf to a fanning
friction factor, f
2.85 x 10-9fQ2V2mavg (Dh Ds)2 (Dh Ds)3
2.65
Wf
Where Q flow rate of liquid (gpm). Vmavg integrat
ed average of Vm between the surface and the
bottomhole pressures (ft3/bbl). Dh hole diameter
(inches). Ds drillstring diameter (inches).
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This relationship implies that an average
friction Factor is taken to represent frictional
effects up the full length Of the annulus.
Substituting Equation (2.65) into Equation (2.64)
and integrating, the following relationship
between well depth, surface and bottomhole
pressures is obtained
808 (Pb-Ps)4.071(Tavg460)ln(Pb/Ps)
(42MW0.0764GS) 1
h
2.85x10-9fQ2Vmavg2 (DhDs)2(Dh-Ds)3

2.66
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Reduced Reynolds Number
Poettman and Carpenter, 1952 15, determined the
friction factor, f, using a correlation with a
reduced Reynolds number for flow of gas and
liquid mixtures up gas wells. The reduced
Reynolds number, RePC was defined (in oil field
units) as
5.16x10-6MQ Dh Ds
RePC

2.67
Where Q liquid flow rate, stock tank (gpm).
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Reduced Reynolds Number
100
10
1
Friction Factor, f
0.1
0.01
0.001
1 10
100
Reduced Reynolds Number, RePC
Correlation between friction factor, f, and the
reduced Reynolds number, RePC (after Poettmann
and Carpenter, 195215).
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Gas Volume

• This correlation and equation 2.66 were used to
  compute the required air injection rate to give a
  BHP of 2,497 psi at 6000 in an 8½ X 4½ annulus
  at 350 gpm.
• Required 14.9 scf/bbl

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Gas Volume

• Equation 2.63 was used to calculate the volume of
  air to give the same BHP static.
• Required 13.4 scf/bbl.
• Poettmann and Bergman concluded that the
  difference is insignificant and a reasonable
  calculation of air rate for the desired BHP could
  be done assuming a static fluid column.

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CUBIC FEET OF AIR AT 14.7 PSIA AND 600F PER
BARREL OF NUC
180 170 160 150 140 130 120 110
100 90 80 70 60 50 40 30
20 10 0
AVERAGE FLUID COLUMN TEMPERATURE 1000
F (75-125) W Actual Fluid Weight Pounds Per
Gallon W Desired Effective Fluid Weight Pounds
Per Gallon
1000 2000 3000 4000
5000 6000 7000 8000
9000 10000
Drilling Depth in Feet
Air volumes required to achieve desired mud
weight reductions average fluid temperature
1000F (Poettmann and Bergman, 195514).
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Bit Pressure Drop

• Mud Red book
• Gasified Mud

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Bit Pressure Drop
Gasified Mud
G2 1 1 gcA2n ?b ?a
2.68
Pa Pb -
Where G mass flow rate of drilling fluid
(lbm/s). An total flow area of the nozzles
(feet). gc gravitational conversion factor (32.17
ft-lbm/lbf-s2). ?s fluids density above the bit
(lbm/ft3). ?b fluids density below the bit
(lbm/ft3). Pa pressure above the bit
(psfa). Pb bottomhole pressure below the bit
(psfa).

• This relationship neglects any energy loss
  through the nozzles due to frictional effects and
  any change in potential energy.

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Bit Pressure Drop
Gasified Mud

• Substituting equation 2.44 for the density of a
  lightened fluid this becomes

G2Fgo Po Po gcAn2?o Pb Pa
Pa Pb

2.69
-
Where Fgo volume fraction of gas in the liquid
under standard conditions. ?o density of the
fluid under standard conditions (pressure, Po)
(lbm/ft3).
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2000
Specifications Depth 6000 feet Hole Diameter 8
½ inches Drill Pipe 4 ½ inches Drill Collars 6
¼ inches Standpipe Injection
1800
1600
1400
1200
1000
Predicted Bottomhole Pressure (psia)
800
600
400
200
0
0 100 200 300 400 500 600
700 800 900 1000 Air Rate (scf/bbl)
Influence of gas and liquid injection rates on
predicted bottomhole pressures.
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14
Oil Injection _at_ 200 Liters/min 139.7 m m (5-1/2)
Int. casing 120.7 m m (4-3/4) Main Hz Hole
12
10
Optimum Point Minimum Achievable bottom Hole
Pressure for Specific Liquid Rate
8
Annular Bottomhole Pressure _at_ 2100m. (1000kPa)
6
4
Friction Dominated Nitrogen Wasting-Inefficient Mo
re Stable system Higher N2 rates or Gas Influx
Increases BHP
Hydrostatic Dominated Unstable Large Pressure
Changes Gas Influx Reduces BHP
2
0
0 10 20
30 40
50
Nutrition rate (stm3/min)
Pressure Dominance in a Multiphase Fluid System
(Saponja, 1995)
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14
Oil Injection 139.7 m m (5-1/2) Int.
Casing 120.7 m m (4 ¾) Main Hz Hole
12
10
8
Annular Bottomhole Pressure _at_ 2,100m. (1,000kPa)
6
4
Optimum Points
2
0
0 10 20
30 40
50
Nitrogen Rate (m3/min)
Optimum Condition for Different Liquid
Circulation Rates (Saponja, 1995)
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2500
Specifications Liquid Rate 350 gpm Depth 6,000
feet Drilled Diameter 8½ inches Drillpipe 4½
inches Drill Collars 6¼ inches Parasite string
at 2,000 feet
2000
1500
Predicted Bottomhole Pressure (psia)
1000
500
0
0 100 200 300 400 500 600
700 800 900 1000
AirRate (scf/bbl)
Comparison of bottomhole pressure predicted for
drillstring (standpippe) and annular (parasite
string) gas injection.
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10
1
9
0.9
8
0.8
7
0.7
0.6
6
Gas Fraction
5
0.5
Equivalent Circulating Density (ppg)
4
0.4
0.3
3
0.2
2
0.1
1
0
0
0 1000 2000 3000 4000
5000 6000
Measured Depth (feet)
Predicted Equivalent circulating densities and
gas volume fractions as functions of depth.
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8000
7500
7000
6500
Hole Problems Hole cleaning Inadequate Hole
Packed Off Not inidicated by Surface Pressure
6000
5500
Wiper Trip
5000
4500
Bottomhole Pressure
4000
Annular Pressure (kPa)
3500
3000
2500
2000
1500
1000
500
0
0 100 200 300 400 500 600 700
800 900 1000 1100 1200 1300 1400 1500 1600
1700 1800 1900
Time (min)
Comparison of dowhole and surface pressures
(after Saponja, 19957). To convert from kPa to
psi, multiply by 0.145.
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Hole Cleaning

• Settling velocity.
• Critical velocity.
• Settling velocity.
• Cuttings transport ratio.

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Settling Velocity
?c ?f ?f
Vt 92.6 dc
2.70
Where ?c cuttings density (ppg). ?b drilling
fluids average density, at the prevailing
temperature and pressure (ppg).
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Critical Velocity

• Guo assumed that the cuttings concentration in
  the annulus should not exceed some critical value
  if hole cleaning problems were to be avoided.
• Vc ROP/60Cc
• vc critical velocity, ft/min
• ROP rate of penetration, ft/hr
• Cc cuttings concentration, fraction

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Critical Velocity

• Taking the critical concentration as 4, cuttings
  would need to travel uphole with a velocity 25
  times greater than the penetration rate.
• For a penetration rate of 30 ft/hour, this
  corresponds to a velocity of 12.5 ft/min.

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350
300
250
200
Mud Flow Rate (gpm)
150
100
50
0
0 1000 2000 3000 4000
5000 6000 7000 8000
Air Injection Rate (cfm)
Gas and liquid injection rates required for
efficient cuttings transport (after Guo et
al.,199312) .
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Settling Velocity

• With a large annulus, the AV may not be such that
  turbulent flow can be achieved.
• We would then need to alter the viscosity of the
  fluid.

(?c ?f) 0.667 (?f µ)0.333
Vt 175dc
2.72


Where Vt terminal velocity (ft/m) dc average
cutting's diameter (inches) ?c cuttings density
(ppg) ?f fluids density above the bit
(lbm/ft3) µ fluids effective viscosity (i.e.
accounting for annular flow, cP)
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Settling Velocity

• For a 0.25 cutting with a density of 21 ppg
  falling through a fluid of density of 5 ppg.
• Maximum AV 15 ft/min.
• Settling velocity would have to be restricted to
  17.4 ft/min at a penetration rate of 30 ft/hr.
• This would require an effective viscosity of 160
  cP.

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Cuttings Transport Ratio
CTR Vt / Va Or CTR 1 (Vsl / Va)
Where CTR cuttings transport radio Vt transport
velocity, or velocity of the cuttings
(ft/sec) Va cuttings density (ppg) Vsl fluids
density above the bit (lbm/ft3)
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Cuttings Transport Ratio

• The velocity of the system is normally the mean
  velocity in the annulus determined by dividing
  the total flow rate of the various phases of the
  fluid by the cross-sectional area of the annulus.

Va M / (A) (?f)
Where M mass flow rate of fluid, lb/sec. A
cross-sectional area of the annulus, ft2 ?f
density of the fluid, lbm/ft3 Note These
units are for this equation only
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Cuttings Transport Ratio

• The CTR should be calculated throughout the
  annulus to ensure that adequate hole cleaning
  takes place at all points and that the cuttings
  are not packing off in the hole somewhere.
• A CTR of 1.0 implies perfect hole cleaning.
• If CTRgt0 cuttings are moving upward.
• CTR should be gt0.55

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Example
The following example suggested by Guo et all
illustrates how the Charts can be used to arrive
at an optimum solution for hydraulics. Example
Gasified-Fluid Hydraulics Solution Depth 5,0
00 ft Hole size 7 7/8-inc Max. ROP 60
ft/hr Rotary Speed 48 rpm D.P
Diameter 4½-inc Min. BHP (to avoid
collapse)1,250 psi
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Example

• Determine BHP requirements (given as 1,250 psi in
  this example).
• Determine expected cutting size.
• Enter the figure 3-3-10 at BHP 1,250 psi, and
  read the resulting intersection points with the
  curves for the four liquid flow rates to arrive
  at four combinations of liquid and gas rates that
  will give a BHP of 1,250 psi.

ds ROP/rpm (60 ft/hr)(12 in/ft)(1 hr/60
min) / . 48 rev/min ¼ in.
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2500
H 5.000 ft., Dh 7-7/5, Cp 4-½
2000
1500
Pbh, psi
1000
500
0
0 0.5 1 1.5 2
2.5 3 3.5 4 4.5
5 5.5 6 6.5 7
Qg. 1000 cfpm
Flowing Bottomhole Pressure vs. Gas Injection
Rate at 5.000 ft. (Guo et al., 1993).
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NOTE A family of curves exists, each member of
which covers a different set of conditions. The
additional curves are published in the Appendix
of this manual along with the curve above, as
Figures 3-3-10a through 3-3-10g.
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4. Plot the intersection points determined in
Step 3 on Figure 3-3-11. Connect the plotted
points and determine the resultant intersection
with the curve for ¼-in. diameter cuttings to be
230-gpm mud rate and 1,300-scfm air injection
rate.
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500
DEPTH 5000, HOLE 7-7/5, PIPE 4-1/2
400
300
MUD FLOW RATE. GPM
200
100
0
0 1
2
3
4
5
AIR INJECTION RATE, 1000 CFPM
Mud Flow Rate vs. Air Injection Rate at 5,000 ft.
(Guo et al., 1993).
Harold Vance Department of Petroleum Engineering
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NOTE A family of curves similar to that above,
each member of which describes a different set of
conditions, has been published in the Appendix of
this manual as Figures 3-3-11a through
3-3-11h. The flow and injection rates determined
in Step 4 represent the circulation rates that
should be employed to maintain a flowing BHP of
1,250 psi in this well while cleaning the hole
adequately.
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THE END
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