When tracers are used to analyse industrial processes, it is common to express the tracer concentration in the system output in terms of elapsed time, and then to calculate the mean residence time, variance and other parameters related to the time response.

Although the time response is generally used in interwell studies it has some problems that reduce its usefulness. Effectively, alterations in the pattern, such as variations in the injection rate, which are very common in any oilfield, result in a biased response curve.

To avoid this inconvenience, a good alternative is to express the tracer concentration as a function of the cumulative injected or produced water volume, which is rate independent. Nevertheless, time representation is often preferred because in many cases the volumetric data are not available.

Figure 29 shows time (a) and volumetric (b) responses for the same well. It is obvious that they are nearly identical since the cumulative volume was calculated from the injection flow rate, which in this case was quite stable.

The volumetric response in a production well when an instantaneous tracer injection has been performed is a measure of the pore volume swept by the injected water.

The tracer breakthrough is sometimes used as an indicator of the swept pore volume, but the mean of the distribution is a better locator because it represents the average volume swept by the injected water and takes into account the shortest as well as the longest paths followed by the tracer. Then:

C(V) dV

о

The swept volume arriving at a given well is equal to the average volume swept multiplied by the fraction of the injected water that reaches this production

weH f).