# Coil Tubing Calculations

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**Calculate ID:**

OD – (2 * Wall)

1.75 – (2 * .156) = 1.438 in

** **

**Calculate Area of Tubing Wall:**

( OD^{2 }– ID^{2 }) * p / 4 NOTE: (p/4 =.7854)

( 1.75^{2 }– 1.438^{2 }) * .7854 = .781 in^{2}

** **

**Calculate Tubing Weight Per Foot (Wall Thickness Unknown)**

((((OD^{2} – ID^{2}) * .7854) * 12)/ 231) * 65.5

((((2.875^{2} – 2.441^{2}) * .7854) * 12) / 231) * 65.5 =

** **

**Calculate Tubing Weight per foot:**

p * ( OD – Wall ) * Wall * 12 * .2833

p * ( 1.75 – .156 ) * .156 * 12 * .2833 = 2.656 lbs/ft

** **

**Calculate Buoyancy Factor:**

( 65.447 – Fluid Weight, lbs/gal ) / 65.447

( 65.447 – 8.33 ) / 65.447 = .873

** **

**Calculate Weight of Tubing in Fluid:**

Weight in Air * Buoyancy Factor

2.656 * .873 = 2.319 lbs/ft

** **

**Calculate Load Capacity @ Minimum Yield:**

( OD^{2} – ID^{2 }) * .7854 * Yield * SF

( 1.75^{2 }– 1.438^{2} ) * .7854 * 80,000 * .8 = 49,997 psi

** **

**Calculate Pressure Capacity:**

2 * ( Wall – .005 )* Yield / OD

2 * (.156 – .005 ) * 80,000 / 1.75 = 13,806 psi

** **

**Calculate Pipe Capacity in Barrels per Linear Foot:**

ID^{2} * .0009714

1.438^{2} .0009714 = .002009 bbls/ft

Multiply by Total Length for Total Capacity in Barrels

** **

**Calculate Annular Volume in Barrels per Linear Foot:**

(ID_{prod}^{2 }– OD_{coil}^{2 }) * .0009714

( 2.441^{2 }– 1.75^{2 }) * .0009714 = .00281316 bbls/ft

Multiply by Total Length for Total Capacity in Barrels

** **

**Calculate Annular Velocity, Ft/Min:**

GPM * 24.51 / (ID_{prod}^{2 }– OD_{coil}^{2 })

84 * 24.51 / ( 4.892^{2 }– 1.75^{2} ) = 98.7 ft/min

** **

**Time to Displace:**

Total Volume ,bbls / Pump Rate, bbl/min = Minutes

or

Total Volume ,gal / Pump Rate, gal/min = Minutes

**Calculate Fluid Pressure Gradient:**

Down Hole Pressure / Depth = psi/ft

or

Fluid Weight, lbs/gal * .05195 = psi/ft

** **

**Calculate Hydrostatic Pressure:**

Weight, lbs/gal * .05195 * Depth

9.6 * .05195 * 11,200 = 5591 psi

** **

**Calculate Bottom Hole Pressure:**

Well Head Pressure + Hydrostatic Pressure

2200 + ((9.6 * .05195 * 11,200)) = 7785.664 psi

** **

**Calculate Kill Fluid Weight:**

Weight, lbs/gal + [ Well Head Pressure / ( .05195 * Depth ) ]

9.6 + ( 2200 / ( .05195 * 11,200 ) ) = 13.4 lbs/gal

** **

**Calculate Stretch due to Weight in hole, feet :**

.0567 * ( Length / 1000 )^{2}

.0567 * (12000 / 1000)^{2} = 8.1648 Feet

** **

**Calculate a “Free Point” for stuck tubing or the length of free pipe**

L = Stretch in inches*(30000000*Area)/Force/12

**Stretch = **inches, from over-pull force

**Area = **cross-sectional area of CT pipe wall

**Force =**applied weight over weight of pipe in air to stretch the CT

Example:

CT OD = 1.5

CT ID = 1.282

Stretch = 120 inches

Force = 15000 lbs (Weight Indicator)

120 * 30,000,000 * .476 / 15000 /12 = 9520 feet.

** **

**Calculate Elongation Due to Temperature, feet :**

**Average Temperature :**

( Surface Temperature + Bottom Hole Temperature ) / 2

( 70 + 210 ) / 2 = 140 Deg. F

**D****T :**

**Average Temperature – Surface Temperature**

140 – 70 = 70 Deg. F

** **

Depth * .0000828 * DT / 12

9650 * .0000828 * 70 / 12 = 4.7 ft

** **

**Calculate Specific Gravity of oil from API :**

141.5 / ( 131.5 + API )

141.5 / ( 131.5 + 30 ) = .876

** **

**Calculate thermal gradient, Deg F / ft**

(Bottom hole Temperature – Suface temperature) / Depth

( 195 – 60 ) / 9800 = .00138 Deg F / ft

or .138 Deg F / 100 ft

or 1.38 Deg F / 1000 ft

**Calculate Pressure drop due to friction**

.000077 * MW ^{.8} * Q ^{1.8} * PV ^{2} * L / D ^{4.8}

.000077 * 8.33 ^{.8} * 42 ^{1.8} * 1 ^{2} * 10000 / 1.438 ^{4.8} = 613.2 psi

**For spooled tubing on the reel: add 10 % or x 1.1**

- * 1.1 = 674.5 psi or 67.4 psi /1000 ft

**MW = **Fluid weight in lbs/gal

**Q = **Flow rate in gal / min

**PV = **Plastic viscosity in centipois

**L = **Length of pipe to flow through in feet

**D = **Diameter of pipe to flow through in inches

** **

***NOTE: This is conservative compared to the Quality Charts**

** **

**PHYSICAL CONSTANTS:**

** **

**Viscosity of water = 1 centipoise**

** **

**API gravity of water = 10 Deg. API**

** **

**Fresh water n’ and k’ = 1.0 and .00002**

** **

**Fresh water weighs 8.33 lbs/gal**

** **

**1 cu. ft = 7.4805 gal**

** **

**Water weighs 8.33 * 7.4805 = 62.312565 lbs/cu. ft**

** **

**1 cu. ft = 12 in * 12 in * 12 in = 1728 cu. in**

** **

**Pressure = Force / Area**

** **

**62.312565 lbs / 144 sq in = .4327261458 lbf / sq in / ft or psi/ft**

** **

**.4327261458 psi/ft / 8.33 lb/gal = .05194791666 (.05195) thus the constant born .052**

** **

**1 bbl = 5.615 cu. ft = 42 gal**

** **

**1 gal of Liquid (Cryogenic) N2 expands to 93.11 SCF**

** **

**N2 expands 697 times ( more exact: 696.4 times)**

** **

**Calculate KCL in pounds for % Needed:**

Gallons x (Fluid weight) x % KCL wanted = lbs

80 bbl x 42 = 3360 gallons

3360 x 8.6_{ lbs/gal }x 2% = 578 lbs KCL

**Calculate rate of travel with coiled tubing **

**(Total bbl ÷ Pump rate in bbls/min = Total Minutes)**

**(Total Interval in feet ÷ minutes = ft/min)**

150 bbls Acid

200 ft Interval to Place Acid

150 bbls÷ 2 bbl/min = 75 mins.

200 ft Interval ÷75 minutes = 2.6 fpm

**To make 3 passes using same problem**

75 minutes ÷ 3 = 25 minutes

200 ft Interval ÷ 25 minutes = 8 ft/min each pass

**To Calculate Pump Rate**

**(Bore ^{2} x .7854 x Stroke x # of plungers)**

4^{2} x .7854 x 8 x 3 = 301.6 in^{3}

= 301.6 in^{3 }x (1gal ÷ 231 in^{3}) x (1 bbl ÷ 42 gals)

= .0312 bbl/rev

= 1 ÷ .0312 = 32.05 rev/bbl

Assume Operating range in the 80 to 90 % Efficiency Range

32.05 rev/bbl x .85% = 27.2 rev/bbl

2 bbl/min x 27.2 rev/bbl = 54.4 strokes/min

**Kill Wt Fluid: PPG = PSI / .05195 X depth**

** **

**(O.D. **^{2}** – I.D. **^{2}**) X .7854 X .05195 X 65.447 =**

** **

**(O.D. **^{2}** – I.D. **^{2}** )X 2.6703 = wt. per ft**