20. Terminology

TERMINOLOGY AND FORMLAE

ContentsContents Page Page

Page 1 of 7

Appendix II

December 1996

Rev E

1 Basic Terminology ....................................... 12 Constants ..................................................... 2

2.1 Forces ............................................... 22.2 Area ................................................... 32.3 Volume .............................................. 3

3 Formulae ...................................................... 33.1 Area ................................................... 33.2 Volume .............................................. 4

OIL AND GAS WELL COMPLETIONS

CONFIDENTIALITY

This manual section is a confidential document which must not be copied in whole or in part ordiscussed with anyone outside the Schlumberger organisation.

The petroleum industry has accepted several abbreviations for values used in completion calculations. This appendixsection contains some of the more commonly used abbreviations and formulae.

1 Basic Terminology

L = Depth (in. or ft)

As

= Cross-sectional area of the tubing wall (in2)A

p= Area of packer seal bore (in2)

Ai

= Area of tubing ID (in2)A

o= Area of tubing OD in (in2)

ß = Coefficient of thermal expansion, in (.0000069 in/in/°F for steel) or .000082 in/ft/°F

∆Pi

= Change in tubing pressure at packer (psi)∆P

o= Change in annulus pressure at packer (psi)

∆Pia

= Change in average tubing pressure (psi)∆P

oa= Change in average annulus pressure (psi)

∆t = Change in average tubing temperature (°F)∆L

1= Piston effect length change

∆L2

= Buckling effect length change∆L

3= Ballooning effect length change

∆L4

= Temperature effect length change∆L

am= Length change due to applied mechanical force

∆Lt

= Total length change = (∆L1 + ∆L

2 + ∆L

3 + ∆L

4 + ∆L applied)

E = Modulus of elasticity, in psi (30,000,000 for steel)

F1

= Force – piston effect (Bouyancy)

3.3 Liquid Gradients ................................ 43.4 Gas Gradients ................................... 4

4 Tubing String Weights .................................. 44.1 Hookload ................................................ 44.2 Ballooning ............................................. 54.3 Ballooning Force ................................... 64.4 Temperature Effect ............................... 6

5 Total Force and Length Changes ..................... 6

Appendix II Rev E

Page 2 of 7 December 1996

OIL AND GAS WELL COMPLETIONSTERMINOLOGY AND FORMLAE

CONFIDENTIALITY


F3

= Force – ballooning effectF

4= Force – temperature effect

Fam

= Force – applied mechanicallyF

p= Packer to tubing force (F

1 + F

3 + F

4 + F

am)

Fa

= Force– applied, acting one end of tubing

I = Moment of inertia of tubing about its diameterI = Π (D4 - d4) in.4 where D is OD and d is ID

64

n = Distance to neutral point

σa

= Normal axial stressσ

b= Bending stress at the outer fiber

Pi initial

= Initial total tubing pressure at the packerP

o initial= Initial total annular pressure at the packer

Pi final

= Final total tubing pressure at the packerP

o final= Final total annular

r = Radial clearance between tubing OD and casing ID (in.) ID casing - OD tubing

2

R = Ratio of tubing OD to ID

So slackoff

= Tubing stress due to slack-off weight

Ws

= Weight of tubing per inch (lbm/in.)W

i= Weight of fluid in tubing (lbm/in.)

Wo

= Weight of displaced fluid (lbm/in.)

Fam

= (Applied mechanical) Can be Fs = slack off weight or F

t = tension applied

Si

= Tubing inner fiber stressS

o= Tubing outer fiber stresses

TJT = Top joint tension (tubing weight in air)TVD = True vertical depth (vertical distance perpendicular from rotary table to a

parallel line drawn from drilled depth).

2 Constants2.1 Forces

E = 30,000,000 = modulus of elasticity for steelβ = .0000069 in./in./°F = .000082 in/ft/°F = coefficient of thermal expansion for steelS = 207 psi = 0.0000069 x 1 x 30,000,0000.007 = Multiplying factor x pounds per cubic foot to find psi per foot (gradient)

Page 3 of 7


Rev E Appendix II

December 1996

CONFIDENTIALITY


0.052 = multiplying factor x pounds per gallon to find psi per foot (gradient)0.554 = Density of methane (CH4)0.650 = Density of dry natural gas0.850 = Density of carbon dioxide (CO2 )0.967 = Density of nitrogen2.718 = e = Natural logarithm base

1 gal Water (pure) = 8.34 lbm/gallon

1.000 gr/litre = Density of pure water

1.000 gr/litre = Density of air

0.434 psi/ft = Gradient for pure water

10° API = 8.34 lbm/gal

or (+) = Indicated positive forces (weight applied)or (-) = Indicates negative forces (tension applied)

2.2 Area

0.7854 = Multiplying factor x diameter2 to find square units in a circle144 = Square inches per square foot

2.3 Volume

0.02381 bbl = 1 gallon0.1337 ft3 = 1 gallon0.1781 bbl = 1 ft3

5.6146 ft3 = 1 oilfield barrel7.48 gal = 1 ft3

42 gal = 1 oilfield barrel1728 = Cubic in. per cubic ft

3 Formulae3.1 Area

Area = Length x WidthArea of a circle = 0.785 x diameter2

Annular area = Area casing ID - Area of tubing OD

0.0034 = 1 gal 0.1337 ft3 1728 in3 in3

0.785 x # x 1 x gal x 1ft3 = #

( )

( )

Appendix II Rev E



CONFIDENTIALITY


3.2 Volume

Volume (Cylinder) = 0.785 x diameter2 x depth

Annular Volume = Volume casing ID - displacement of tubing OD

3.3 Liquid Gradients

psi/ft = 61.28/(131.5 + ˚API)

3.4 Gas Gradients

(Pressure at given depth) 0.2085 x Gas Gravity x DepthF = e

Average Temp + 460

F x surface pressure = Pressure at depth

Gas gradient = (Pressure at desired depth - surface pressure)/depth at desired location

4 Tubing String Weights

Tubing string weight = Tubing Weight x Tubing String Depth (in air) (#) (#)/ft (ft)

Tubing string weight = Tubing Weight - Total Pressure x Tubing Cross Sectional Area(in fluid) (#) in air (#) (psi) (in.2)

4.1 Hookload

Hookload = Tubing string weight + all positive or negative buoyancy forces + any formation pressures (in air) acting on the tubing string.

= (Tubing weight x tubing length) - [Po(Ao - Ap) + P1(Ap - A1)]

Piston force F1 = [(Ap - Ao) x (∆Po)] - [(Ap - Ai) x (∆Pi)] (may be positive or negative)

Piston effect length change = ∆L1 = F1 x L (may be positive or negative)

E As

Buckling factor = Ap x (∆Pi - ∆Po)

Adjusted tubing weight (#/in) = Ws + Wi - Wo

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Rev E Appendix II

December 1996

CONFIDENTIALITY


Length change due to buckling if (n) is greater than (L):

L L∆L2A = (∆L2) x x 2 -

n n

(n) is greater than (L)

Length change due to slack-off: ∆Ls = (Fs) (L) + (r)2 (Fs)2

(E) (As) (8) (E) (I) (Ws + W1 - Wo)

Force change due to tension: Ft = (∆Lt (E) (As) (L)

4.2 Ballooning

Initial average tubing pressure: Pia initial = (Initial applied tubing pressure + Pi initial)2

(Ap) x [(Pi final - Po final)]n =

(Ws + Wi - Wo)

Weight of fluid in tubing (#/in): Wi = .0034 x (Tubing ID)2 x (Weight of fluid in tubing #/gal)

Weight of fluid in annulus (#/in):Wo = .0034 x (Tubing OD)2 x (Weight of fluid in annulus #/gal)

Length change due to tension: ∆Lt = (Ft) (L)(E) (As)

Final average tubing pressure: Pia final = (Final applied tubing pressure + Pi final)2

Change in average tubing pressure: ∆Pia = Pia final - Pia initial

Initial average annular pressure: Pia initial = (Initial applied annular pressure + Po initial)2

Length Change Due to Buckling ∆L2 = (r)2 (Ap)2 (∆Pi - ∆Po)2

(-8) (E) (I) (Ws + Wi - Wo)Length from packer to neutral point:

Appendix II Rev E



CONFIDENTIALITY


Initial average tubing temperature (°F): ta initial = Initial Surface Temp (°F) + Initial BHT (°F)2

Change in average annular pressure: ∆Poa = Poa final - Poa initial

Final average annular pressure: Pia initial - (Initial Applied Annular Pressure + Po initial)2

4.4 Temperature Effect

Average tubing temperature (°F): ta = Surface Temp (°F) + Bottom - Hole Temp (°F)

2

Bottom-hole temperature (°F): BHT = Surface Temp (°F) + 1.6 (˚F) x TVD (ft) 100 ft

1.6 The average geothermal gradient used if a gradient for the particular area is not known.

Final average tubing temperature (°F): ta final = Final Surface Temp (°F) + final BHT (°F)2

Change in average tubing temperature: ∆t = ta final - ta initial

Temperature force: F4 = (207) (As) (∆T)

Change in the tubing length: ∆L4 = (L)* (β) (∆T)

*L = Length of tubing (in.)

5 Total Force and Length Changes

Length

For slack-off weight applied: ∆L total = ∆L1 + ∆L

2 + ∆L

3 + ∆L

4 + ∆Ls

For tension applied: ∆L total = ∆L1 + ∆L

2 + ∆L

3 + ∆L

4 + ∆Lt

∆L3 = (.2) (L) x (R2 ∆Poa - ∆Pia)

107 (R2 - 1)

F3 = (.6) x [(∆Poa + Ao) - (∆Pia + Ai)]

4.3 Ballooning Force

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Rev E Appendix II

December 1996

CONFIDENTIALITY


(Pi final - Po final) 2 (Pi final - R2 Po final)

2

So = [3] x + + (σa) ± (σb) (R2 - 1) (R2 - 1)

Force

For slack-off weight applied: Fp = F

1 + F

3 + F

4 + F

s

For tension applied: Fp = F

1 + F

3 + F

4 + F

t

Tubing string fiber stresses

Actual force buoyancy on cross sectional end area of tubing:

Fa = [(Ap - Ao) x (Po final)] - [Ap - Ai) x (Pi final)]

Top joint tension = (Tubing string weightair) + (Fa) - (Fp)

Tubing joint strength =

(Tubing joint minimum cross sectional area) x (tubing yield strength) slack-off forces on tubing outer wall

So slackoff = Fs + (OD Tubing) (r) (Fs)

As (4) (I)

Normal axial stress (psi)a

= (Fp - Fa)

As

(OD tubing) (r)Bending stress at the outer fiber: σb = x {[Ap (∆Pi - ∆Po)] + [Fp]}

((4)) (I)

(R2) (Pi final - Po final) 2 (Pi final - R2 Po final) σb

2

Si = [3] x + + (σa) ± (R2 - 1) (R2 - 1) R

Tubing inner fiber stress (psi):

Tubing outer fiber stress (psi):

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20. Terminology