Gas expansion equations

Basic gas laws:

• where P ₁ = formation pressure, psi

• P ₂ = hydrostatic pressure at the surface or any depth in the wellbore, psi

• V ₁ = original pit gain, bbl

• V ₂ = gas volume at surface or at any depth of interest, bbl

• T ₁ = temperature of formation fluid, degrees Rankine ( R = F + 460)

• T ₂ = temperature at surface or at any depth of interest, degrees Rankine

Basis gas law plus compressibility factor:

• where Z ₁ = compressibility factor under pressure in formation, dimensionless

• Z ₂ = compressibility factor at the surface or at any depth of interest, dimensionless

Shortened gas expansion equation:

• where P ₁ = formation pressure, psi

• P ₂ = hydrostatic pressure plus atmospheric pressure (14.7 psi), psi

• V ₁ = original pit gain, bbl

• V ₂ = gas volume at surface or at any depth of interest, bbl

Hydrostatic pressure exerted by each barrel of mud in the casing

With pipe in the wellbore:

• Example: Dh ? 9-5/8 in. casing ? 43.5 lb/ft = 8.755 in. ID

• Dp = 5.0 in. OD

• Mud weight = 10.5 ppg

• 

• psi/bbl = 19.93029 0.052 10.5 ppg

• psi/bbl = 10.88

With no pipe in the wellbore:

• Example: Dh ? 9-5/8 in. casing ? 43.5 lb/ft = 8.755 in. ID

• Mud weight = 10.5 ppg

• 

• psi/bbl = 13.429872 ...