This paper describes the development of a model for predicting tracer returns under variable flow rate conditions. The model is based on the one-dimensional advection dispersion equation. The model is used to define interwell connectivity and the extent to which it can be applied for fracture dominated reservoirs is explored.

The main conclusion is that if the dominant flow paths between well pairs do not intersect, then this method works well, and a convolution relationship exists between the injected and produced tracer concentration. The key discovery is that the convolution is in terms of cumulative flow between each well pair (as opposed to time).

The interwell connectivity is represented by a kernel function, which can be estimated via deconvolution. A nonparametric kernel estimation method is illustrated by deconvolving synthetic data generated from a discrete fracture network simulation. The results are verified using both cross validation and by comparison to known solutions.

The discussion concludes with an example where the dominant fractures do intersect, which shows how the model becomes overly cumbersome, and practically infeasible for such cases. Qualitative reasoning is given for why, for complex fracture systems, it is challenging to find a unique transfer function between well pairs from tracer return data, at variable flow rate conditions. In spite of this complication however, the models seems to provide reasonable predictions. Two key reasons for obtaining such reasonable results are that, the model does take into account both the time delay and dispersion associated with tracer, as well as a transformation of time into cumulative flow.

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