An approximate semianalytical solution for tracer injection tests in a confined aquifer with a radially converging flow field and finite volume of tracer and chase fluid

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Abstract
An approximate analytical solution describing the movement of a conservative tracer of finite volume in a radially converging flow field is proposed. The solution is divided into two phases: injection and transport. During the injection phase, an injection of chase fluid immediately following the tracer is allowed. Hydrodynamic dispersion effects are assumed to be negligible during this phase. The geometry of the tracer plume is determined by a particle‐tracking technique. During the plume transport phase, the tracer plume is approximated by a series of contiguous pulses. An approximate analytical solution for each pulse has been derived through linearization of the transport equation. The approximate solution has been verified by comparison with numerical solutions. The distribution of tracer in space and time is obtained by summing the contributions from all the pulses. Four geometrical parameters governing the geometry of the tracer plume immediately after injection are presented and discussed. The solution shows that the geometry of the initial tracer plume has an effect on the breakthrough curves. The volume of tracer and chase fluid has to be taken into account in tracer test design and data analysis. Limitations of the proposed solution are also discussed.