Slide 1*
= π x r x r
= π x D/2 x D/2
= π D2/4
Answer in Square Units.
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I.E. X-Section Area = (D2 x 0.7854) – (d2 x 0.7854)
As 0.7854 is common to both sets of brackets we can simplify this equation.
X-Section Area = 0.7854 x (D2 – d2)
The Cross-Sectional area is the difference in area between the larger circle and the smaller circle.
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Tubing & Casing are classified according to 4 criteria.
OD (inches or millimetres)
Grade ( A letter followed by a number e.g. N-80)
Thread
The grade tells you the strength of the material.
E.G. N-80 means the yield strength of the steel is 80,000 psi.
P-110 means the yield strength of the steel is 110,000 psi.
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Grade & Yield Strength of Steel
Example:- Red Book Section 200, page 10. 3 1/2” N-80 10.3# Tubing.
OD = 3.5”, ID = 2.922” Grade = 80000psi.
Pipe yield = 0.7854 (3.502 – 2.9222) x 80,000 psi
= 2.915 sq. in. x 80,000 lbs/sq.in.
= 233,227lbs.
≅ 233,000lbs
The Grade of the steel refers to the yield of the steel in Lbs/sq in.
∴ We can use this in conjunction with the X-Sectional Area to work out the joint yield strength of the tubing or casing.
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Answer in Cubic Units.
= 0.7854 x D2 x Height
Answer in Cubic Units
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Diameter in inches
Height/Length in Feet
Volume in Barrels
Volume
H/LFeet
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Hydrostatic Pressure
The Pressure Due to the Height of a Column of Fluid.
The only Two things that effect Hydrostatic pressure is the height (TVH) & the Density of the Fluid Column.
Pressure
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Hydrostatic Pressure
The Pressure Due to the Height of a Column of Fluid.
The only Two things that effect Hydrostatic pressure are the (TVH) & the Density of the Fluid Column.
Pressure
Depth is measured in Feet & Density is measured in Lbs/Gallon or ppg.
∴ We need to be able to Convert the Density to a
Hydrostatic Pressure Gradient.
We do this by dividing the fluid density (ppg) by
19.25
The Gradient of a Fluid is the weight of a 1 Foot High 1” square column of the Fluid.
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Determine Fluid Hydrostatic Pressure Gradient
Start with rectangular tube (closed on bottom and open on top)
Fill with one gallon of fluid
Height of fluid measures 231 inches
Pressure
1”
1”
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Determine Fluid Hydrostatic Pressure Gradient
Convert 231 inches to 19.25 ft (gradient of interest is psi/ft)
To solve for the hydrostatic pressure gradient of any density fluid: Fluid density (ppg) ÷ 19.25 in²/ft
Example: 10 ppg ÷ 19.25 in²/ft = 0.5194805 psi/ft hydrostatic pressure gradient
Pressure
1”
1”
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Fresh water has been assigned the Specific Gravity of 1.
Specific Gravity is a dimensionless figure! It is actually a ratio.
Any thing heavier than fresh water will have a Specific Gravity greater than 1.
Anything lighter than water will have a Specific gravity less than 1.
This ratio helps us when we are working out hydrostatic pressures.
E.G.: If the fluid has a S.G. of 0.85, then its gradient will be 0.85 of the gradient of fresh water.
I.E.: 0.433 psi/ft x 0.85 = 0.368 psi/ft.
Pressure
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0API Gravity
Fresh water has been assigned the oAPI (American Petroleum Institute) Gravity of 10.
When measured on their scale it gave a reading of 141.5.
∴ We have to use the following equation to convert oAPI Gravity to a Specific Gravity
___141.5__ = Specific Gravity 131.5 + oAPI
E.G.: API Gravity = 38o
= _141.5 = 0.835 169.5
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Pressure created by the weight of a column of fluid.
Applied Pressure ?
The Pressure applied to a system with a pump or by the Formation.
Felt equally throughout a closed liquid system.
Total Pressure ?
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Pressure Due to a Column of Gas
Gas is Compressible so its gradient will change according to depth and the Gravity of the gas concerned.
To make life easier for us Non Mathematicians, we use a correction Factor Chart when working out pressure at depth.
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IntersectDepth RowColumn &Where G.G. By the factor
Surface Pr.MultiplyPressureDownholeTo find the
FactorsCorrectionGradientGas
Surface Pr.MultiplyPressureDownholeTo find the
FactorsCorrectionGradientGas
Surface Pr.MultiplyPressureDownholeTo find the
FactorsCorrectionGradientGas
Surface Pr.MultiplyPressureDownholeTo find the
FactorsCorrectionGradientGas
∴Pressure @ Depth = (6000psi x 1.3201) = 7920.6psi
N.B. 7920.6 = Total Pressure, Hydrostatic Pressure =1920.6psi