This research presents a new method to analyze production and well test data – the superposition-rate. The method was developed based on the well-accepted superposition principle. It is presented in a generalized form and is applicable to data in transient flow (including radial, linear, and bilinear) as well as in boundary dominated flow.

The superposition-rate method is validated by synthetic data generated from reservoir modeling. Moreover, a practical workflow of implementing the superposition-rate in production data and well test analysis is presented. Last, real field examples are utilized to demonstrate the practicality of superposition-rate.

A thorough comparison between the superposition-rate and superposition-time methods is presented. The superposition-rate shows advantages over the superposition-time. A key improvement of the superposition-rate in quality diagnostics and data analysis is that it does not modify time scale. Consequently the superposition-rate keeps all production data in the sequence of their occurrence.


Analysis of rate and pressure data relies on the solutions of flow equation in porous media derived using constant boundary condition. All wells can exhibit one of the two constant boundary conditions: constant production rate or constant flowing pressure. For well testing operations, the flow period is typically controlled, and constant rate solutions are chosen to analyze well testing data. On the other hand, for production operations, the flowing pressure often declines rapidly and becomes constant during a prolonged period. As a result, constant pressure solutions are considered to be more useful in analyzing production data, particularly for wells in unconventional reservoirs. However, there are numerous situations where both rate and flowing pressure continuously decline, or make step changes (discontinuously) during well testing and production operations. These variable-rate/variable-pressure issues are typically addressed using superposition.

The superposition principle is effective in converting variable-rate/variable-pressure data to its equivalent constant boundary solution. The classical way to apply the superposition principle is to use a time function, namely superposition-time. It involves manipulation of time in accordance with the changes in rates and flow durations. Valuable as this procedure is, it suffers from many disadvantages: for instance, after manipulation, the resulting time will have been shuffled back and forth. This makes the data's sequence difficult to be tracked and identified, and subsequently causes problems in data quality diagnostics. This is particularly evident in the presence of outliers.

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