IPR and Nodal Analysis
Enter reservoir pressure Pr, bubble point Pb and a test point (Pwf, q) to draw a composite Vogel or straight-line (PI) IPR, then enter a VLP table to find the operating point at the intersection.
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Educational tool for preliminary analysis. It is not a substitute for certified software or a qualified engineer’s review for major decisions.
Results
Calculation steps and intermediate values
Explanation and formulas
The IPR relates flowing bottomhole pressure Pwf to rate. Above the bubble point the flow is single-phase and the relation is linear: q = J (Pr − Pwf), where J is the productivity index.
Below the bubble point gas comes out of solution and the curve bends; Vogel (1968) gives an empirical equation. The composite form uses the straight line down to Pb and Vogel below it; J is derived from the test point whether it lies above or below Pb.
The VLP (vertical lift performance) curve is the bottomhole pressure needed to lift each rate to surface, usually from a multiphase-flow program. Its intersection with the IPR is the expected operating point.
Pwf < Pb : q = qb + (J·Pb/1.8) · [1 − 0.2 (Pwf/Pb) − 0.8 (Pwf/Pb)²], qb = J (Pr − Pb)
Test above Pb: J = q / (Pr − Pwf)
Test below Pb: J = q / [ (Pr − Pb) + (Pb/1.8)(1 − 0.2 x − 0.8 x²) ], x = Pwf/Pb
Saturated (Pr = Pb): q/qmax = 1 − 0.2 (Pwf/Pr) − 0.8 (Pwf/Pr)²
qmax = qb + J·Pb/1.8 ; operating point: Pwf_IPR(q) = Pwf_VLP(q)
Validation
Published example (Vogel; Ahmed, Reservoir Engineering Handbook, oil well performance chapter): saturated reservoir Pr = Pb = 2400 psi, test 100 STB/d at Pwf = 1800 psi. Book: qmax = 250 STB/d and q ≈ 211 STB/d at Pwf = 800 psi. Tool: 250.0 and 211.1 STB/d. Continuity of the composite curve at Pb and agreement with the straight line above Pb were also checked.
References
- Vogel, J.V. (1968). Inflow Performance Relationships for Solution-Gas Drive Wells. JPT 20(1): 83–92. SPE-1476-PA.
- Brown, K.E. (1984). The Technology of Artificial Lift Methods, Vol. 4. PennWell.
- Ahmed, T. (2019). Reservoir Engineering Handbook, 5th ed. — oil well performance chapter.
- Economides, M.J., Hill, A.D., Ehlig-Economides, C. & Zhu, D. (2013). Petroleum Production Systems, 2nd ed., Prentice Hall.