PETE 625 Well Control

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PETE 625Well Control

• Lesson 3
• Kicks and Gas Migration

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Contents

• Density of real gases
• Equivalent Mud Weight (EMW)
• Wellbore pressure before and after kick
• Gas migration rate - first order approx.
• Gas migration rate with temperature, mud
  compressibility and Z-factor considerations

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Assignments

• Homework 2
• Ch 1, Problems 1.11-1.21
• Read All of Chapter 1

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Density of Real Gases

• M molecular weight
• m mass
• n no. of moles
• gg S.G. of gas

(Real Gas Law)
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Density of Real Gases

• What is the density of a 0.6 gravity gas at
  10,000 psig and 200 oF?
• From Lesson 2, Fig. 1
• ppr p/ppc 10,015/671 14.93
• Tpr (200460)/358 1.84
• Z 1.413

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1.413
1.84
14.93
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Density of Real Gases

p 10,000 psig T 200 oF gg 0.6

• rg 2.33 ppg

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Equivalent Mud Weight, EMW

• The pressure, p (psig) in a wellbore, at a depth
  of x (ft) can always be expressed in terms of an
  equivalent mud density or weight.
• EMW p / (0.052 x) in ppg

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EMW
po0
0

• EMW is the density of the mud that, in a column
  of height, x (ft) will generate the pressure, p
  (psig) at the bottom, if the pressure at top 0
  psig
• or, at TD
• p 0.052 EMW TVD

x
TVD
p
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SICP 500 psig
After Kick
Before Kick
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Gas Migration

• Gas generally has a much lower density than the
  drilling mud in the well, causing the gas to rise
  when the well is shut in.
• Since the gas, cannot expand in a closed
  wellbore, it will maintain its pressure as it
  rises (ignoring temp, fluid loss to formation,
  compressibility of gas, mud, and formation)
• This causes pressures everywhere in the wellbore
  to increase.

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p1 p2 p3 ??
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Gas Migration

• Example 1.7 A 0.7 gravity gas bubble enters the
  bottom of a 9,000 ft vertical well when the drill
  collars are being pulled through the rotary
  table.
• Flow is noted and the well is shut in with an
  initial recorded casing pressure of 50 psig.
  Influx height is 350 ft.
• Mud weight 9.6 ppg.

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Gas Migration

• Assume surface temperature of 70 oF. Temp
  gradient 1.1 oF/100 ft. Surface pressure 14
  psia
• Determine the final casing pressure if the gas
  bubble is allowed to reach the surface without
  expanding
• Determine the pressure and equivalent density at
  total depth under these final conditions

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Gas Properties at Bottom

• First assumption BHP is brought to the
  surface
• Pressure at the top of the bubble
• P8,650 14 50 0.052 9.6 (9,000-350)
  4,378 psia
• T9,000 70 (1.1/100) 9,000 460
• 629 oR

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Gas Properties at Bottom

• ppc 666 psia
• Tpc 389 deg R
• ppr 4,378/666 6.57
• Tpr 629/389 1.62
• Z 0.925

pseudocritical - pseudoreduced
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Bottomhole Pressure

• rg 290.74,378 / (0.925 80.28 629) 1.90
  ppg
• DpKICK 0.052 1.9 350 35 psi
• BHP 4,378 35
• BHP 4,413 psia (surface press.?

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Pressure at Surface

• Assume, at first, that Zf 1.0 (at the surface)
• Then,

BOTTOM
SURFACE
so, po 3,988 psia (with Temp. corr.)
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Solution with Z-factor Corr.

• At surface
• ppr 3,988 / 666 6.00
• Tpr 530 / 389 1.36
• Zf 0.817
• p0 3,258 psia

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Solution with Z-factor

• A few more iterative steps result in
• Z0 0.705 and p0 2,812 psia
• At the surface
• rf 290.72,812 / (0.70580.28530)
• 1.9 ppg

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New BHP EMW

• New BHP 2,812 0.052 1.9 350 0.052
  9.6 8,650
• New BHP 7,165 psia
• EMW (7,165 - 14)/(0.052 9,000)
• EMW 15.3 ppg

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• 4,413 psia
• 4,378
• 3,988 (T)
• 3,258 (Z)
• 2,812 (Z)
• 2,024 (mud)

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Compression of Mud in Annulus vA 0.1 bbl/ft)

• DV compressibility volume Dp
• -6 10-6 (1/psi) 0.1(9,000-350)2,626
• DV -13.63 bbls
• Initial kick volume 0.1 350 35 bbls
• New kick volume 35 13.63
• 48.63 bbl

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Compression of Mud in Annulus

• From Boyles Law, pV const
• p2 48.63 2,812 35
• p2 2,024 psia
• p8650 poA poB poC
• Consider V,p,Z const. p,Z change mud comp.
• 2nd iteration ? . 3rd
• or, Is there a better way?

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Gas Migration Rate

• A well is shut in after taking a 30 bbl kick.
  The SIDPP appears to stabilize at 1,000 psig.
  One hour later the pressure is 2,000 psig.
• Ann Cap 0.1 bbl/ft
• MW 14 ppg
• TVD 10,000 ft

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Gas Migration Rate

• How fast is the kick migrating?
• What assumptions do we need to make to analyze
  this question?

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1 hr
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First Attempt

• If the kick rises x ft. in 1 hr and the
  pressure in the kick constant, then the
  pressure increases everywhere,
• Dp 0.052 14 x
• x (2,000 - 1,000) / (0.052 14)
• x 1,374 ft
• Rise velocity 1,374 ft/hr

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Gas Migration Rate

• Field rule of thumb 1,000 ft/hr
• Laboratory studies 2,000 6,000 ft/hr
• Who is right?
• Field results?
• Is the previous calculation correct?

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Second Attempt

• Consider mud compressibility
• Ann. capacity 0.1 bbl/ft 10,000 ft
• 1,000 bbl of mud
• Volume change due to compressibility and
  increase in pressure of 1,000 psi,
• DV 610-6 (1/psi) 1,000 psi 1,000 bbl
• 6 bbl

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Second Attempt

• i.e. gas could expand by 6 bbl, to 36 bbl
• Initial kick pressure
• 1,000 0.052 14 10,000 (approx.)
• 8,280 psig
• 8,295 psia

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Second Attempt

• A 20 expansion would reduce the pressure in
  the kick to 0.88,295
• 6,636 psia
• 6,621 psig
• So, the kick must have migrated more than 1,374
  ft!

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Second Attempt

• How far did it migrate in 1 hour?
• The pressure reduction in kick fluid
• 8,260 - 6,6211,659 psi
• The kick must therefore have risen an additional
  x2 ft, given by
• 1,659 0.052 14 x2
• x2 2,279 ft

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Second Attempt

• 2nd estimate 1,374 2,279
• 3,653 ft/hr
• What if the kick size is only 12 bbl?
• What about balooning of the wellbore?
• What about fluid loss to permeable formations?
  T? Z?...

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Example 1.9

• Kick occurs. After shut-in, initial csg. Press
  500 psig. 30 minutes later, p 800 psig
• What is the slip velocity if the kick volume
  remains constant?
• MW 10.0 ppg

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Simple Solution
Ignoring temperature, compressibility and other
effects.
What factors affect gas slip velocity, or
migration rate?
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Gas slip velocity

• The bubble size, and the size of the gas void
  fraction, will influence bubble slip velocity.
• The void fraction is defined as the ratio (or
  percentage) of the gas cross-sectional area to
  the total flow area.

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Gas slip velocity
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Gas slip velocity

• Bubbles with a void fraction gt 25 assume a
  bullet nose shape and migrate upwards along the
  high side of the wellbore concurrent with liquid
  backflow, on the opposite side of the wellbore

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Gas slip velocity

• Large bubbles rise faster than small bubbles
• Other factors
• Density differences
• Hole geometry
• Mud viscosity
• Circulation rate
• Hole inclination
• One lab study showed max. rate at 45o.