For subsea applications, hydrostatic pressure exerted by the hydraulic fluid must be accounted for calculation.
In this case, we assume water depth at 1500 ft, therefore hydrostatic pressure exerted by hydraulic fluid (hydraulic fluid pressure gradient = 0.445 psi/ft) = 0.445×1500 = 668 psi. Besides of that, the concept for calculation is as same as surface accumulator. So please take a look about how to calculate usable volume per bottle as following steps.
Step 1 Adjust all pressures for the hydrostatic pressure of the hydraulic fluid:
Pre-charge pressure = 1000 psi + 668 psi = 1668 psi
Minimum system pressure = 1200 psi + 668 psi = 1868 psi
Operating pressure = 3000 psi + 668 psi = 3668 psi
Step 2 Determine hydraulic fluid required to increase pressure from pre-charge pressure to minimum system pressure:
Boyle’s Law for ideal gase: P1 V1 = P2 V2
1668 psi x 10 = 1868 x V2
16,680 ÷1,868 = V2
V2 = 8.93 gal
It means that N2 will be compressed from 10 gal to 8.93 gal in order to reach minimum operating pressure. Therefore, 1.07 gal (10.0 – 8.93 = 1.07 gal) of hydraulic fluid is used for compressing to minimum system pressure.
Step 3 Determine hydraulic required increasing pressure from pre-charge to operating pressure:
P1 V1 = P2 V2
1668 psi x 10 gal = 3668 psi x V2
16,680 ÷ 3668 = V2
V2 = 4.55 gal
It means that N2 will be compressed from 10 gal to 4.55 gal in order to reach operating pressure. Therefore, 5.45 gal (10.0 – 4.55 = 5.45 gal) of hydraulic fluid is used for compressing to operating pressure.
Step 4 Determine usable fluid volume per bottle:
Usable volume per bottle = Total hydraulic fluid/bottle – Dead hydraulic fluid/bottle
Usable volume per bottle = 5.45 – 1.07
Usable volume per bottle = 4.38 gallons
Reference book: Well Control Books