2.4.1. Response curves

A good sampling programme and the measurement of these samples with adequate detectors (high efficiency, low background and low statistical error) is the way to obtain good response curves which form the basis for further interpretation.

2.4.1.1. Tim e response

The time response is the graphic representation of the concentration of activity (after background subtraction and decay correction) as a function of time. A preprocessing of the experimental data can also be used in order to smooth the response.

From this curve, the cumulative response (recovered activity versus time) is derived by a simple numerical integration. The application of complex integration methods is not justified because of statistical dispersion in the original data and variations in the pattern parameters.

The example illustrated in Fig. 28 was taken from an actual field exercise and shows both instantaneous and cumulative response curves to HTO injection.

Concerning the cumulative response, the following expression gives the activity recovered up to an instant, ti:

Aif) _ f g(t) C (t) dt

0

where

A(t) is the total tracer recovery up to ti (kg or Bq);

g(t) is the production water flow rate as a function of time (m3/d);

C(t) is the tracer concentration as a function of time (kg/m3 or Bq/m3); ti is the elapsed time after the injection (d).

Information about the production flow rate is usually available in the oil company. Among the information obtained from the time response, tracer breakthrough is the first to be obtained. It is the time interval during which the tracer concentration exceeds the general background level of the samples.

The mean residence time is another important parameter. Its definition is identical to the one used in process studies, i. e. the ratio between the volume (V) involved in this process and the flow rate that feeds it (Q).

(9)

I tC(t) dt

t =^z (10)

I C (t) dt

Jo

The final time is the time in which the response reaches the general background level of the sample. However, in oilfield experiments it is very common to stop sampling before this point. Thus, the final time is evaluated from the extrapolated response curve. For extrapolation purposes the exponential function gives the best fit for the tail of the experimental curve.

Knowing the distance between injection and production wells it is easy to calculate the maximum, mean and minimum water velocities from the breakthrough, mean residence time and final time respectively.

The tracer recovery in each well is determined from the extrapolation of the cumulative response for time approaching infinity on the basis of the exponential approximation of the concentration curve. The fraction of injected tracer recovered in each well in the pattern (f) equals the fraction of the injected water that arrives at this well:

where Аш is the extrapolated tracer activity recovered in the well at time infinite and A is the injected activity.

The total tracer recovered in all the wells belonging to a given pattern should be identical to thequantity of tracer injected in order to obtain a perfect mass balance. However, tracer recovery is seldom higher than 80% and it can be as low as 20% for tritium, which is supposed to be an ideal tracer for water. There are three reasons for this behavior. Firstly, the tracer molecules continue moving towards second line wells and not all of them emerge from the wells immediately surrounding the injector, secondly the injected water pushes the oil to production wells and replaces it in the rock pores and finally, a fraction of the tracer mainly in the tail of the response curve suffers dilution that causes the concentration to fall under the detection limit. Sampling second line wells is a good idea in order to improve the mass balance and to gain additional information about the pattern under study.