If the reservoir pressure is above the bubble point and yet the flowing bottomhole pressure is below, a generalized inflow performance can be written. The following approach enables generation of an IPR that has a straight portion for pwf ≥ pb, and follows the Vogel equation for pwf < pb adapted to the straightforward logic found in Standing (1971). This can be done for transient, steady state, and pseudosteady state. First, qb, the flow rate where pwf = pb, can be written as
where pD is the transient dimensionless pressure drop or is equal to ln(re/rw) for steady state or ln(0.472 re/rw) for pseudosteady state.
The productivity index above the bubble point is simply
and is related to qv (denoted here as “Vogel” flow, qV) by
For pwf ≥ pb,
For pwf < pb,
When is less than or equal to the original bubble-point pressure, use Equation 3-55.
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