The April-June, 1976 edition of the Journal of Canadian Petroleum Technology contains a paper titled ‘Determination of the "Gas Free" Liquid Level and the Annular Gas Flow Rate For a Pumping Well.’ This paper summarizes the theory of the method and expands it to include the determination of the actual pumping rate. This enables the operator, with a single test, to evaluate the pumping system as well as to determine the inflow performances of the well.


At the time of publication of the first paper on this subject less than 20 field tests had been carried out. Since then the testing techniques have improved and now more than 200 tests have been run and analyzed. This paper reviews the theory, presents new test procedures, and discusses two actual field tests.


The mass balance equation for gas flowing in and out of a system such as the annulus of a pumping well is as follows:

Equation (1) (Available in full paper)


q1 = Annular gas flow rate

q2 = Gas Rate through the critical Flow prover both measured in Mscf/D

Using the test procedure described in the first Article1 the volume of gas in the annulus for the constant level case is related to the flow rate through the critical flow prover as follows:

Equation (2) (Available in full paper)

where m is the slope of the buildup or drawdown in psi/min.

For a constant bottom hole pressure the volume of gas in the annulus is related to the flow rate through the critical flow prover as follows:

Equation (3) (Available in full paper)

in which C is the product of the liquid gradient and the annular capacity.

The annular gas rate can be shown to be as follows, for either the constant level or constant pressure cases:

Equation (4) (Available in full paper)

The equations (1), (2) and (3) are derived in the aforementioned paper.1 Equation (4) appears in two patent applications.2,3

Test Procedures

Figure 1 shows the installation of a critical flow prover and a continuous recording pressure gauge on a typical pumping well. Briefly, the test procedure is co first open Valve 1 and close Valve 2. Pressures are recorded for a sufficiently long period to obtain a gradient, then the critical flow prover is opened and a second slope recorded. The prover is then closed until a third slope is registered. Finally, the pumping unit is shut in and a fourth gradient obtained.

If damage calculations are to be carried out, the well is left shut in; if not, the unit is restarted and the test is complete. If the recorder is left on when the pumping unit is started a fifth slope can be measured.

Figure 2 shows the pressure responses for the various phases of the test. The first slope is caused by the annular gas flow pressuring up the system when the annulus valve (Valve 1) is closed. The second slope is always less than the initial slope as the annulus gas rate is reduced by the amount vented through the prover.

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