Gas behaves differently from fluid therefore you cannot use a simple hydrostatic formula to determine reservoir pressure. Gas is compressible but fluid is incompressible.
The formula to determine the bottom hole pressure of dry gas well is shown below;
Where; Pbh = bottom hole pressure in psia (absolute pressure)
Pwh = wellhead pressure in psia (absolute pressure)
H = true vertical depth of the well
Sg = specific gravity of gas
R = 53.36 ft-lb/lb-R (gas constant for API standard condition air)
Tav = average temperature in Rankin (Rankin = Fahrenheit + 460)
Example: The dry gas well is shut in and the well head pressure is 2,000 psig (gauge pressure). The average wellbore temperature is 160 F. Gas specific gravity is 0.75. The well is 9,000’ TVD and the wellhead is on land. Determine the bottom hole pressure and compare the result if you use a normal relationship from hydrostatic pressure calculation.
Pwh = 2,000 + 14.7 = 2,014.7 psia
H = 9,000 TVD
Sg = 0.75
Tav = 160 + 460 = 620 °R
Pbh = 2,471 psia
Pbh = 2,471 – 14.7 = 2,456 psig
If you use hydrostatic pressure calculation, the bottom hole pressure is calculated by the following equation.
Pbh = Pwh + (0.052 x average gas density (ppg) x TVD of the well, ft)
Average air density at 160 F is 6.404 x 10-2 (lb/ft3) = 8.56 x 10-3 ppg
Average gas density at 160 F = gas specific gravity x Average air density at 160 F
Average gas density at 160 F = 0.75 x 8.56 x 10-3 ppg = 6.42 x 10-3 ppg
Pbh = 2000 + (0.052x6.42 x 10-3x9,000)= 2003 psia
As you can see from the calculation, the hydrostatic pressure cannot be used to determine the bottom hole pressure of the dry gas well. It will give you inaccurate result.