AN IMPROVED APPROXIMATION FOR SPHERICAL DIFFUSION OF TRITIUM IN RELATIVELY DRY SOIL

A study by Smiles et al. [1995] investigated the spread of tritium in relatively dry soil, using a spherically symmetrical diffusion equatio n with radioactive decay to model the evolution of tritium profiles fr om the initial release of tritium in a uniform concentration over a sm all spherical volume of soil. They found that numerical cancellation e rrors affected the accurate evaluation of the analytical solution of C arslaw and Jaeger [1959], and they used a point source solution as an approximation to the solution for the correct initial conditions. We d erive a new and more accurate approximation, based on the principle th at the concentration distribution ''forgets'' the precise initial cond itions and is determined mainly by the total quantity of tritium and t he spatial variance of the distribution. The actual distribution is ap proximated by that from a point source which started spreading some ti me before the actual release time, and the value of the time shift whi ch gives the correct variance is found.