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.