Nind (4), and Richardson and Shaw (3), have presented mathematical extensions of Vogel's (1) IPR. These mathematical manipulations result in a calculation of flow efficiency or a Vogel factor. This paper illustrates that these idealized mathematical manipulations are extremely sensitive to actual field data, and that the "Inverse" problem presented by these authors will often result in meaningless interpretations.


The IPR (Inflow Performance Relationship) reflects the productive capability of a well. It's the relationship between flow rate and producing sandface pressure. and depends, principally, on two factors namely. (i) the formation's transmissivity and (ii) the near-wellbore condition as expressed by the skin effect.

Vogel (1) and Standing (2) derived IPR's for oil reservoirs under various conditions. In general, these relationships are known to apply reasonably well to the majority of oil wells. Recently several authors, Richardson and Shaw (3) and Nind (4), have tried to extend these relationships, and to extract too much information from limited data. Their process is mathematically correct, but the results are often dramatically wrong as is illustrated in this paper. The explanation for this lies in the difference between the "Direct" problem and the "Inverse" problem.

Literature Review

Vogel (1) presented what is now recognized as a standard IPR Reference curve for oil wells. It was derived from the simulation of several saturated reservoirs, with zero skin effect. Standing (2) presented modifications of Vogel's curve to account for skin effects. He published a series of curves for flow efficiencies ranging from 0.5 to 1. 5. The curve with a flow efficiency equal to l was, of course, Vogel's curve.

Vogel(1) presented the equation of the references curve that gives a reasonable empirical fit of the computer simulations: <Equation Available In Full Paper>

Richardson and Shaw (3) generalized Vogel's equation by replacing the 0.2 above, by a parameter V, (for Vogel), called the quadratic curve factor, as shown below. <Equation Available In Full Paper=

They showed that if V and PR were known, a single flow test (q1 Pwf1) defines qmax and hence the IPR curve. If only the value of V were known, then two comtemporaneous tests could define both the IPR curve and PR. If a series of three tests were conducted on the well, the V could determined in addition to the IPR and PR.

Nind (.4) combined the work of Standing (2) and Vogel (1), and showed how the flow efficiency, F.E., of a well can be obtained from two production tests (q1, Pwf1, q2, Pwf2) on that well. His equations are summarized below: Equation Available in Full Paper


When using the standing flow efficiency corrections, it must be remembered that the flow efficiency determined from a buildup test often does not reflect near wellbore damage alone, but is significantly affected by the increased gas saturation near the wellbore due to gas breaking out of solution.

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