On the boundary conditions in tracer transport models for fractured porous underground formations

Abstract

A boundary condition traditionally used in analytical models for tracer or contaminant pulse transport in porous underground formations gives the tracer concentration at the injection border as a discontinuous function in time. It has recently been shown that this condition leads to a physically improper pulse behavior. Models using sounder boundary conditions are already available for non-fractured porous media, but not for fractured media, where the traditional condition is commonly employed which can potentially lead to errors. We develop two new formulations to describe tracer tests in fractured media. They set conditions (i) on the total amount of injected tracer and (ii) on the tracer flow. The new formulations are compared against the traditional debatable model by examining tracer breakthrough curve differences. It has been found that they are important at small Peclet numbers. Differences are analyzed in two ways, by (a) employing typical model parameter values, and (b) fitting the three models to the same field tracer data set, and comparing the resulting model parameter values. In the first case the breakthrough curve difference has been quantified at 25%, and in the field tests considered in the second case it was from 1% to 10%. In general these discrepancies are small, but could become significant in some cases.