One of the most general form of IPR model below bubble-point pressure:
(1) | \Psi^n(p_b) - \Psi^n(p_{wf}) = (q - q_b) \left[ \frac{1}{(q_\mathrm{max}-q_b)} \cdot \Psi^n(p_b) + \frac{(q-q_\mathrm{max}) (a_0 + a_1 \, q)}{ b_0 + b_1 \cdot q + b_2 \cdot q^2} \right], \ \ H(q) = \frac{\sum_{k=1}^m a_k \, q^k}{\sum_{k=1}^{m+1} b_k \, q^k}, \ \ , \quad p_b > p_r > p_{wf} |
where
p_{wf} | bottom-hole pressure (BHP) |
p_b | bubble-point pressure |
q | sandface flowrate |
q_\mathrm{max} | Absolute Open Flow (AOF) |
\Psi(p) | pseudo-pressure function specific to fluid type |
n | pseudo-pressure curvature |
a | laminar flow coefficient |
b | turbulent flow coefficient |
It needs well tests at least three different rates to assess \{ a \, , \, b, \, p_r \} but obviously more tests will make assessment more accurate.
See also
Petroleum Industry / Upstream / Production / Subsurface Production / Subsurface E&P Disciplines / Field Study & Modelling / Production Analysis / Productivity Diagnostics / Inflow Performance Relation (IPR)
[ Richardson and Shaw IPR @ model ] [ Wiggins IPR @ model ]
References
- Vogel, J. V. (1968, January 1). Inflow Performance Relationships for Solution-Gas Drive Wells. Society of Petroleum Engineers. doi:10.2118/1476-PA
- Archer, R. A., Del Castillo, Y., & Blasingame, T. A. (2003, January 1). New Perspectives on Vogel Type IPR Models for Gas Condensate and Solution-Gas Drive Systems. Society of Petroleum Engineers. doi:10.2118/80907-MS
- Seidle, J. P., & Erickson, D. J. (1993, January 1). Use of Vogel's Inflow Performance Relation for Coal Wells. Society of Petroleum Engineers. doi:10.2118/26201-MS