Injection/casing pressure required to open valve

Input(s)

$\mathrm{P}_{\mathrm{bt}}$: Bellows or Dome Pressure at Valve Depth (psi)

$\mathrm{P}_{2}$: Production or Tubing Pressure at Valve Depth (psi)

$\mathrm{A}_{\mathrm{p}}$: Area of Valve Port or Seat (in. ${ }^{2}$ )

$\mathrm{A}_{\mathrm{b}}$: Area of Bellows (in. ${ }^{2}$ )

Output(s)

P1: Injection/Casing Pressure Existing at the Valve Depth (psi)

Formula(s)

$$ \mathrm{P} 1=\frac{\mathrm{P}_{\mathrm{bt}}-\left(\mathrm{P}_{2} *\left(\frac{\mathrm{A}_{\mathrm{p}}}{\mathrm{A}_{\mathrm{b}}}\right)\right)}{1-\left(\frac{\mathrm{A}_{\mathrm{p}}}{\mathrm{A}_{\mathrm{b}}}\right)} $$

Reference(s)

Beggs, H. D. 2003. Production Optimization using Nodal Analysis, OGCI and Petroskills Publications, Second Edition, Chapter 5, Page: 166.