Injection/casing pressure required to open valve

Input(s)

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

P2\mathrm{P}_{2}: Production or Tubing Pressure at Valve Depth (psi)

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

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

Output(s)

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

Formula(s)

P1=Pbt(P2(ApAb))1(ApAb)\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.


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