AN ADVECTIVE TRANSPORT PERSPECTIVE OF BREAKTHROUGH CURVES AT THE RECOVERY WELLS

Investigation of contaminant transport in the field often use forced or natural gradient tracer tests. A forced gradient tracer test is carried out by artificially generating a forced flow field, often through a single or multiple pumping or injecting wells, then subsequently observe the change of the tracer concentration at a fixed point. Three different forced gradient tracer tests that are commonly employed by hydrogeologists are diverging, converging, and two-well tests. The forced gradient tracer test has the advantage of accelerating the process of transport, thus can obtain the result timely. In addition, it is often less expensive because it uses only a few wells or boreholes. Its disadvantage is that the non-uniform flow pathways have been introduced because of the usage of pumping or injecting wells, which make breakthrough curves much more difficult to interpret compare to that in the uniform flow field. As far as we know, there is no exact theory and closed-form analytical solutions that can describe the breakthrough curve in a forced gradient test because of the difficulty of incorporating the non-uniform flow into the transport equation. Theories based on small perturbations have been developed and broadly employed to interpret the forced gradient tests. This article will provide exact closed-form analytical solutions for two different kinds of forced gradient flows by neglecting the dispersion. The first is the two-well test with equal pumping and injecting rates, the second is the converging test with regional flow. The purpose is to assess the "apparent" breakthrough curves caused exclusively by the non-uniformity of the flow. These solutions can be used as the first cut calculations of concentrations in non-uniform flow fields. Because the solutions are exact, they can be used to test previous approximation theories such as the small perturbation method.