The analysis of tracer experiments conducted in divergent radial flow fields

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Abstract
Analytical models are developed to interpret tracer experiments conducted in divergent flow fields. The models account for the mixing of tracer in both the source and observation wells and for the diffusion of tracer into adjacent aquitards. A solution for the particular case of an observation well of infinitesimally small volume is also presented. Solutions are derived for both resident and flux concentrations and for macroscopically discontinuous conditions at both the inlet and outlet boundaries. The solutions for resident and flux concentration are identical when the mixing volume in the observation well is of finite volume. Two tracer experiments were conducted in a horizontally fractured shale to demonstrate the application of the new analytical models. Experiments were conducted with observation wells of finite volume and using a new sampling packer which eliminates the volume of the observation well. The results show that for experiments conducted in fractured media, the analytical model developed in this paper provides an improved fit to the shape of the concentration curve relative to models which do not account for mixing in the source and observation wells. Alternatively, by modifying the field method such that the volume of the observation well is eliminated using the sampling packer, either conventional models or the new model for concentration in the formation will provide equally suitable fits to the concentration data.