First-passage-time transfer functions for groundwater tracer tests conducted in radially convergent flow

Forced-gradient groundwater tracer tests may be conducted using a variety o f hydraulic schemes, so it is useful to have simple semi-analytic models av ailable that can examine various injection/withdrawal scenarios. Models for radially convergent tracer tests are formulated here as transfer functions , which allow complex tracer test designs to be simulated by a series of si mple mathematical expressions. These mathematical expressions are given in Laplace space, so that transfer functions may be placed in series by simple multiplication. Predicted breakthrough is found by numerically inverting t he composite transfer function to the time-domain, using traditional comput er programs or commercial mathematical software. Transport is assumed to be dictated by a radially convergent or uniform flow field, and is based upon an exact first-passage-time solution of the backward Fokker-Planck equatio n. These methods are demonstrated by simulating a weak-dipole tracer test c onducted in a fractured granite formation, where mixing in the injection bo rehole is non-ideal. (C) 2000 Elsevier Science B.V. All rights reserved.