Calculate the pressure (psig) at the bottom of a 7500 foot column of fluid for each of the following fluids:

a) Water

b) Drilling Mud (SG = 1.3)

c) Gas Lift column (S. G. = 0.85)

d) Natural Gas Column (SG = 0.6*) '*SG for Natural Gas is compared against air (density = 0.0765 lb / (cu ft))

Pressure at the botton of 7500 ft column is:

a) P (water) = 3256.508 psig

b) P (drilling mud) = 4229.035 psig

c) P (gas lift) = 18.092 psig

d) P (Natural gas) = 17.092 psig

Explanation:

hidrostatic pressure:

P = (d. f * g * h) + Po

∴ density of fluid (d. f) ≡ Kg/m³

∴ aceleration o gravity (g) = 9.807 m/s²

∴ column height (h) = 7500 ft * (m / 3.28084 ft) = 2285.99 m

∴ atmospheric pressure (Po) = 101300 Pa (Kg / m*s²)

specific gravity:

SG = d. f / d H2O (ref)

∴ d H2O = 997 Kg/m³

a) water:

⇒ P = (997 * 9.807 * 2285.99) + 101300

⇒ P = 22452844,88 Pa * (psig / 6894.76 Pa) = 3256.508 psig

b) Drilling Mud

⇒ SG = 1.3 = d. f / 997

⇒ d. f = 1296.1 Kg/m³

⇒ P = (1296.1 * 9.807 * 2285.99) + 101300

⇒ P = 29158182.16 Pa = 4229.035 psig

c) Gas lift column

⇒ SG = 0.85 = d. f / d. air (ref)

∴ d. air = 0.0765 Lb/ft³ = 1.23 Kg/m³

⇒ d. f = 1.23 * 0.85 = 1.0455 Kg/m³

⇒ P = (1.0455 * 9.807 * 2285.99) + 101300

⇒ P = 124738.755 Pa = 18.092 psig

d) Natural Gas column:

⇒ SG = 0.6 = d. f / 1.23

⇒ d. f = 0.738 Kg/m³

⇒ P = (0.738 * 9.807 * 2285.99) + 101300

⇒ P = 117845.003 Pa = 17.092 psig