1

PETE 411Well Drilling

Lesson 26* Well Control *

* Variable Geometry *

2

Well Control-Variable Geometry

Initial Shut-In Conditions

Driller’s Method Kick at Casing Seat

Kick at Surface

Wait and Weight Method Kick at Casing Seat

Kick at Surface

3

Read:Applied Drilling Engineering, Ch. 4

Quiz B Thursday, Nov. 14, 7 - 9 p.m. Rm. 101

Closed Book1 Equation sheet allowed, 8 1/2”x 11” (both sides)

HW #14: Driller’s Method - due 11-11-02 HW #15: W&W Method - due 11-15-02

4

Example Problem

1. Determine the pressure at the casing seat at 4,000’ when using the old mud

(Driller’s) versus using the kill mud (Wait and Weight) to circulate a gas kick out of the hole.

2. Determine the casing pressure at the surface when the top of the gas bubble has just reached the surface, for the same two mud weights used above.

5

Example Problem

Well depth = 10,000’

Hole size = 10.5”

Drill pipe = 4.5”, 16.60 #/ft

Drill Collars = 8” * 3.5” * 500 ft Surface casing = 4,000’, 13-3/8”, 68 #/ft

Mud Weight = 10 ppg

Fracture gradient @ 4,000’ = 0.7 psi/ft

6

Example Problem

Shut in Annulus Pressure, SICP = 400 psi

Shut in Drillpipe Pressure, SIDPP = 200 psi

Pit level increase = 20 barrels (kick size)

Drop the Z terms but consider Temperature

T at surface = 70 deg. F

Temperature gradient = 1.2 deg.F/100 ft

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Initial (Closed-In) Conditions:

/gal#10 WeightMud Initial

bbl 20 Increase Level Pit

psi 400 SICP

psi 200 SIDPP

Initial mud gradient = 0.520 psi/ft

(0.052 * 10 = 0.520)

8

Initial (Closed-In) Conditions:

Pressure, Hole Bottom

psi 5,400)ft

psi520.0(*)ft 000,10(200P10,000

Collars, Drill outside Vol/ft Annular

gal 42

bbl

in 231

gal)in 12(in)85.10(

4v

2222

DC_Ann

bbl/ft 04493.0VDC_Ann ( 20.28 ft/bbl )

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4,000’

9,500’

10,000’

vdp.csg = 0.13006 bbl/ft

vdc,hole = 0.04493 bbl/ft

vdp,hole = 0.08743 bbl/ft

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Fluid, Kick ofHeight

ft 445bbl/ft 0.04493

bbl 20h 10,000

Fluid, Kick across Pressure cHydrostati

555,9*520.0400400,5P 0kick_10,00

psi 4 31.P 0kick_10,00

Annulus,the in csHydrostati

0kick_10,00P 9,555 * 0.520 400 5,400

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Driller’s Method - kick at bottom

F = P * A = W

(2)--- PPPBHP MAK00 ΔΔ

area * PressureFluid Kick of Weight

2222

in)85.10(4

*in

lb31.4

lb 1,141 W

12

4,000’

9,500’

10,000’

9,555’

PB = P 10,000 = 5,400 psi

445’

SIDPP = 200 psiSICP = 400 psi

31.4psi

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Driller’s Method - kick at csg. seat

What is the pressure at 4,000 ft when the top of the kick fluid first reaches that point?

4,0004,000 P

1,098,444h

650

4604870*

P

5,400*20h*0.08743

4,0004,000

10,000

4,000

4,000

10,00010,0004,000 T

T*

P

P*V V

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4,000’

9,500’

10,000’

Driller’s Method

Top of Kick at Casing

Seat

P = 5,400 psi

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Driller’s Method - kick at csg. seat

Again,

in4.510.54

lbs 1,141

area

weightP

22K_4,000

π

MAK_4,0004,000 PPPBHP ΔΔ

P K_4,000 = 16.1 psi

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Driller’s Method - kick at csg. seat

4,0004,000 P

1,098,444*(0.52)P2,264

4,0004,000 h*0.523,120P5,384

)h(6,000*0.5216P5,400 4,0004,000

MAK_4,0004,000 PPPBHP ΔΔ

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Driller’s Method - kick at csg. seat

0.7 psi/ft 0.6233 psi 2,493 P4,000

2

571,191*42,2642,264P

0.52

4,000

0571,191P 2,264P 4,00024,000

This results in the quadratic Eqn:

With the solutions:

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Driller’s Method - Top of Kick at Casing Seat

4,000’

9,500’

10,000’

BHP = 5,400 psi

P4,000 = 2,493 psi

h4,000 = 441 ftP = 16 psi

4,0004,000 P

1,098,444h

P0,ann = ?

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4,000’

9,500’

10,000’

Driller’s Method

Top of Kick at Surface

We need two equations…

P0 = ?

BHP = 5,400 psi

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Driller’s Method - kick at surface

When the bubble rises, it expands. The volume of the bubble at the surface is given by:

(1)--- P

084,677h

o0

46012070

46070

P

540020h)13006.0(

00

000,10

0

0

000,10000,100 T

T

P

PVV (Z = const.)

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Driller’s Method - kick at surface

psi 1110.85P K0 Δ

222K,0

in 4.512.4154

lb 1,141

area

weightP

π

Δ

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Driller’s Method - kick at surface

From Eq. (2),

But, from Eq. (1),0

0

00

P

677,084h

)h(10,000*0.5211P5,400

MAK00 PPPBHP ΔΔ

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Driller’s Method - kick at surface

0084,352P189P 02

0

Quadratic equation . . .

352,084PP115,2005,400 200

00 P

677,08410,0000.5211P5,400

So,MAK00 PPPBHP ΔΔ

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Driller’s Method - kick at surface

2

)084,352)(4(189189P

2

12

0

psi 695psi 34.695P0

ft 974 h0

74.97334.695

084,677h0

4,000’

9,500’

10,000’

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Driller’s Method - kick at surface

psi 2,280

111,574695

P974)(4,000*0.52PP KO04,000

Δ

psi 2,280

3,120-5,400

)000,4000,10(*)52.0(PP

,elyAlternativ

000,104,000

( = 0.57 psi/ft )

4,000’

9,500’

10,000’

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Driller’s Method. Top of Kick at Surface

4,000’

9,500’

10,000’

h0 = 974 ftPK,0 = 11 psi

P0,ann = 695 psi

P 4,000 = 2,280 psi

P10,000 = ?

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Calculate the pressure at 4,000 ft when the top of the bubble reaches this point.

Volume of bubble at 4,000 ft

Wait and Weight Method- kick at casing seat

10,000

4,000

4,000

10,00010,0004,000 T

T

P

PV V

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Wait and Weight Method

Top of Kick at Casing

Seat

Kill Mud

Old Mud

4,000’

9,500’

10,000’

BHP = 5,400 psi

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W&W - Pressure at top of kick at 4,000 ft

650

578

P

5,40020h(0.08743)

4,0004,000

10,000

4,000

4,000

10,00010,0004,000 T

T

P

PV V

(7)--- ΔPΔPΔPPBHP M1MK_4,0004,000

(6)--- P

1,098,444h

4,0004,000

Also,

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Wait and Weight Method - kick at surface

Capacity inside drill string

= DP_cap. + DC_cap.

bubble. thebelow mud gal

# 10.0 ofQuantity

bbl 141

ft 500*ft

bbl0.0119ft 9,500*

ft

bbl0.01422

4,000’

9,500’

10,000’

BHP = 5,400 psi

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W&W - Pressure at top of kick - kick at 4,000 ft

bbl/ft 0.08743

bbl 141*10*052.0P M

psi 839P M

psi 16P before, As K_4,000

10,000 * 0.052

SIDPP Wt.Mud Old MudKill of Density

gal

# 10.380.3810.00 KWM

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W&W - Pressure at top of kick - kick at 4,000 ft

4,0004,000

4,000M1

h(0.5398)2,36883916P5,400

0.08743

141h6,000*10.38*0.052ΔP

ΔPΔPΔPPBHP M1MK_4,0004,000

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W&W - Pressure at top of kick - kick at 4,000 ft

4,000000 4 P

1,098,444(0.5398)P2,177

0592,940P 2,177P 4,00024,000

2

940,592 * 4177,2177,2P

5,02

000,4

psi/ft 0.61 psi 2,422 P 4,000

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4,000’

9,500’

10,000’

Wait and Weight Method

Top of Kick at Surface

Kill Mud

Old Mud

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Wait and Weight Method - kick at surface

Volume of gas bubble at surface:

10,000

0

0

10,00010,0000 T

T

P

PV V

650

530

P

5,40020h*0.13006

00

P

677,084h

00

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Wait and Weight Method (Engineer’s Method) - kick at surface

Assume all 10 lb/gal mud is inside the 13 3/8” csg. Then the height of 10 lb mud:

M1MK0010,000 PPPPP ΔΔΔ

ft 1,084 bbl/ft0.13006

bbl 141.0h M

psi 11P K,0 ΔAs before,

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Wait and Weight Method (Engineer’s Method) - kick at surface

psi 564 1,084*10*0.052ΔPM

Hydrostatic head across the mud columns:

Old Mud:

Kill Mud:

1,084)h(10,000*10.38*0.052P 01M

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Hydrostatics in Annulus W&W Method - kick at surface

00

00

M1MK0010,000

h(0.5398)P12.14

)h(8,916*0.539856411P5,400

ΔPΔPΔPPP

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Wait and Weight Method kick at surface

psi 611 610.59 P

2

365,490 * 41212P

0365,49012PP

P

677,084(0.5398)P12

0

2

1 2

0

020

00

From Eq. 4, substituting for h0

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Height of Bubble at Surface

ft 1,109

610.59

677,084

P

677,084h

00

Wait and Weight Method- kick at surface

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Check Pressure at 4,000 ft- kick at surface

psi/ft 0.54 psi 2,161

1,093)-1,109-(4,000* 10.38*0.052

56911611

ΔPΔPΔPPP M1MK004,000

Looks OK

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Wait and Weight MethodTop of Kick at Surface

Kill Mud

Old Mud

4,000’

9,500’

10,000’

h0 = 1,109 ftPK,0 = 11 psi

P0,ann = 611 psi

P 4,000 = 2,161 psi

P10,000 = ?

POld Mud = 569 psi

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Summary

Driller’s Engineer’sMethod Method

Bubble at 10,000 ft

400 400 P

2,480 2,480 P

0

4,000

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Summary

Driller’s Engineer’sMethod Method

Top of Bubble at 4,000 ft

342 413 P

2,422 2,493 P

0

4,000

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Summary

Driller’s Engineer’sMethod Method

Top of Bubble at surface

611 695 P

2,161 2,280 P

0

4,000

46

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Why the difference?

48

Wait and Weight Method

Kick Intensity, ppg

Max

imu

m C

asin

g P

ress

ure

, p

si

49

Cas

ing

Pre

ssu

re,

psi

Pump Strokes

Kick Intensity, ppg

50

Cas

ing

Pre

ssu

re,

psi

Volume of Mud Pumped, bbl