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PETE 411 Well Drilling. Lesson 9 Drilling Hydraulics - Hydrostatics. Drilling Hydraulics - Hydrostatics. Hydrostatic Pressure in Liquid Columns Hydrostatic Pressure in Gas Columns Hydrostatic Pressure in Complex Columns Forces on Submerged Body

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Pete 411 well drilling

PETE 411Well Drilling

Lesson 9

Drilling Hydraulics

- Hydrostatics


Drilling hydraulics hydrostatics
Drilling Hydraulics - Hydrostatics

  • Hydrostatic Pressure in Liquid Columns

  • Hydrostatic Pressure in Gas Columns

  • Hydrostatic Pressure in Complex Columns

  • Forces on Submerged Body

  • Effective (buoyed) Weight of Submerged Body

  • Axial Tension in Drill String sA = FA/A


Read applied drilling engineering ch 4 drilling hydraulics to p 125

Read:Applied Drilling Engineering, Ch.4 (Drilling Hydraulics) to p. 125

HW #4

ADE #1.18, 1.19, 1.24

Due Monday, Sept 23, 2002


Drilling hydraulics applications

WHY?

Drilling Hydraulics Applications

  • Calculation of subsurface hydrostatic pressures that may tend to burst or collapse well tubulars or fracture exposed formations

  • Several aspects of blowout prevention

  • Displacement of cement slurries and resulting stresses in the drillstring


Drilling hydraulics applications cont d

Drilling Hydraulics Applications cont’d

  • Bit nozzle size selection for optimum hydraulics

  • Surge or swab pressures due to vertical pipe movement

  • Carrying capacity of drilling fluids


Pete 411 well drilling

ppore < pmud < pfrac

Well Control

Fig. 4-2. The Well Fluid System


Forces acting on a fluid element

Forces Acting on a Fluid Element

F1 =

F2 =

F3 =

FWV = specific wt.

of the fluid


Pressures in a fluid column
Pressures in a fluid column

  • At equilibrium, S F = 0

0 = F1 + F2 + F3

(p = rgh)


Incompressible fluids

Incompressible Fluids

Integrating,


Incompressible fluids1

Incompressible Fluids

In field units,

1’ x 1’ x 1’

cube


Incompressible fluids2

p0

D

Incompressible fluids

p

If p0 = 0 (usually the case except during well control or cementing procedures)

then,


Compressible fluids

T = temperature, R

r = density, lbm/gal

M = gas molecular wt.

m = mass of gas

Compressible Fluids

…………… (1)

…………… (2)

…… (3)

But,

p= pressure of gas, psia

V= gas volume, gal

Z = gas deviation factor

n = moles of gas

R = universal gas constant = 80.3

…… (4)

from (3)


Compressible fluids1

Compressible Fluids

T = temperature, oR

r = density, lbm/gal

M = gas molecular wt.

m = mass of gas, lbm

p= pressure of gas, psia

V= gas volume, gal

Z = gas deviation factor

n = moles of gas

R = universal gas constant, = 80.3


Compressible fluids2

From Eqs. (2) and (4):

Compressible Fluids

Integrating,

Assumptions?


Example

Example

Column of Methane (M = 16)

Pressure at surface = 1,000 psia Z=1, T=140 F

(i) What is pressure at 10,000 ft?

(ii) What is density at surface?

(iii) What is density at 10,000 ft?

(iv) What is psurf if p10,000 = 8,000 psia?


Example i

Example (i)

(i) What is pressure at 10,000 ft?


Example cont d

Example cont’d

(ii) What is density at surface?

(iii) What is density at 10,000 ft?


Example1

Example

(iv) What is psurf if p10,000 = 8,000 psia?


Fig 4 3 a complex liquid column

Fig. 4-3. A Complex Liquid Column


Pete 411 well drilling

Pa = ?

Fig. 4-4. Viewing the Well as a Manometer



Buoyancy force weight of fluid displaced archimedes 250 bc

Buoyancy Force = weight of fluid displaced (Archimedes, 250 BC)

Figure 4-9. Hydraulic forces acting on a foreign body


Effective buoyed weight

Effective (buoyed) Weight

Buoyancy Factor

Valid for a solid body or an open-ended pipe!


Example2

Example

For steel,

immersed in mud,

the buoyancy factor is:

A drillstring weighs 100,000 lbs in air.

Buoyed weight = 100,000 * 0.771 = 77,100 lbs



Simple example empty wellbore

Drillpipe weight = 19.5 lbf/ft 10,000 ft

Simple Example - Empty Wellbore

0 lbf

195,000 lbf

OD = 5.000 in

ID = 4.276 in

DEPTH, ft

A = 5.265 in2

AXIAL TENSION, lbf

W = 19.5 lbf/ft * 10,000 ft = 195,000 lbf


Example 15 lb gal mud in wellbore

Drillpipe weight = 19.5 lbf/ft 10,000 ft

Example - 15 lb/gal Mud in Wellbore

- 41,100

0

153,900

195,000 lbf

OD = 5.000 in

ID = 4.276 in

DEPTH, ft

A = 5.265 in2

AXIAL TENSION, lbf

F = P * A

= 7,800 * 5.265

= 41,100 lbf

Pressure at bottom = 0.052 * 15 * 10,000 = 7,800 psi

W = 195,000 - 41,100 = 153,900 lbf


Anywhere in the drill collars axial tension wt pressure force bit wt

Anywhere in the Drill Collars:Axial Tension = Wt. - Pressure Force - Bit Wt.


Anywhere in the drill pipe axial tension wts pressure forces bit wt

Anywhere in the Drill Pipe:Axial Tension = Wts. - Pressure Forces - Bit Wt.

FT


Axial tension in drill string

Axial Tension in Drill String

Example

A drill string consists of 10,000 ft of 19.5 #/ft drillpipe and 600 ft of 147 #/ft drill collars suspended off bottom in 15#/gal mud (Fb = bit weight = 0).

What is the axial tension in the drillstring as a function of depth?


Example3

A1

Example

Pressure at top of collars = 0.052 (15) 10,000

= 7,800 psi

Pressure at bottom of collars = 0.052 (15) 10,600

= 8,268 psi

Cross-sectional area of pipe,

10,000’

10,600’


Example4

A1

Example

Cross-sectional area of collars,

A2


Example5

4

Example

3

2

1. At 10,600 ft. (bottom of drill collars)

Compressive force = pA

= 357,200 lbf

[ axial tension = - 357,200 lbf ]

1


Example6

4

Example

Fb = FBIT = 0

3

2

2. At 10,000 ft+ (top of collars)

FT = W2 - F2 - Fb

= 147 lbm/ft * 600 ft - 357,200

= 88,200 - 357,200

= -269,000 lbf

1


Example7

4

Example

3

2

3.At 10,000 ft- (bottom of drillpipe)

FT = W1+W2+F1-F2-Fb

= 88,200 + 7800 lbf/in2 * 37.5in2 -357,200

= 88,200 + 292,500 - 357,200

= + 23,500 lbf

1


Example8

4

Example

3

2

4. At Surface

FT = W1 + W2 + F1 - F2 - Fb

= 19.5 * 10,000 + 23,500

= 218,500 lbf

Also: FT = WAIR * BF = 283,200 * 0.7710

= 218,345 lbf

1



Example summary

Example - Summary 4.9

1. At 10,600 ftFT = -357,200 lbf [compression]

2. At 10,000 + ftFT = -269,000 lbf [compression]

3. At 10,000 - ftFT = +23,500 lbf [tension]

4. At SurfaceFT = +218,500 lbf [tension]