Two-Rate Flow Test, Variable-Rate CaseApplication to Gas-Lift and Pumping Wells
Authors: Odeh A.S. , Jones L.G. 
Published: December 2007

A disadvantage of the familiar two-rate flow test is that the flow rate during the two flow periods must be constant. Here is an extension of the method that can handle variable rate in the second flow period. The test is particularly well suited to wells that have been producing at stable rates for a relatively long time. Gas-lift or pumping wells usually qualify as prime candidates for this approach.

Introduction
Pressure buildup analyses are widely used to obtain Pressure buildup analyses are widely used to obtain reservoir data such as effective flow capacity of the formation. However, over the years several drawbacks, arising from the procedure of shutting in the well at the wellhead, have become apparent. The mathematics of pressure buildup analysis is based on the assumption that the well is shut in at the sand face, and that no production occurs after the well is shut in. In practice, the well is closed at the surface, and flow into the wellbore continues for a period of time. This is referred to as afterflow. Afterflow in some cases, especially in tight reservoirs, can last for many hours. This requires that the well be shut in for a long period so that data may be obtained that are free of afterflow. When the shut-in period is long, the loss in production may make it period is long, the loss in production may make it uneconomical to conduct a pressure buildup test. Drawdowns are free of afterflow. However, they suffer from two drawbacks. The first is the requirement that pressure be completely stabilized before the test is run. This means a full buildup must precede a drawdown. The second drawback is that the precede a drawdown. The second drawback is that the annulus unloads during the test, and this complicates the analysis. In 1963 Russell published the two-rate flow test, which is designed to eliminate the disadvantages of buildups and drawdowns. The two-rate flow test conducted on a flowing well does not require a shut-in period. Thus it is free of afterflow, and no loss in period. Thus it is free of afterflow, and no loss in production is incurred. The disadvantage of the production is incurred. The disadvantage of the two-rate flow test is that the flow rate during the second flow period must be constant. This is hard to achieve, and a small drift in the rate, if not accounted for, may lead to considerable error in the calculated results. This is so because a small drift in rate affects the slope of the straight line of the pressure vs log time function plot, and the results are very sensitive to the value of the slope, as reported by Selim. To eliminate some of the difficulties encountered in the two-rate test analysis, Selim proposed a modification that consisted of following the rate reduction (second rate) with a rate increase. The modification still requires constant-rate flow and results in lengthening the test time. In this paper we eliminate the disadvantages of the two-rate flow test and maintain its advantages by removing the constant-rate requirement during the second flow period. Thus the test is easier to run, and any fluctuation in rate is accounted for in the calculations. The two-rate flow test, variable-rate case, is suited to wells that have been flowing at stable rates for a period that is relatively long compared with the second period that is relatively long compared with the second flow period. It is also suitable when semisteady-state flow occurs during the first flow period. Pumping and gas-lift wells usually meet this requirement and are prime candidates for the test. In particular, the prime candidates for the test. In particular, the afterflow periods of buildup on these wells are readily analyzed with this approach.
JPT
P. 93