THE DILEMMA OF CHOOSING BOUNDARY CONDITIONS IN COLUMN TRACER TESTS

Solute transport in a column is probably one of the most fundamental problems investigated in contaminant hydrology and soil physics. From a physical point of view, whatever boundary conditions used must satisfy the mass balance requirement. However, a careful revisit of literature shows that this requirement is not always satisfied. The boundary condition could impose great influence upon transport in a column, particularly when the so-called Peclet number is small. There are three types of boundary conditions to choose for transport in a column. Among them, only the third-type boundary condition satisfies the mass balance requirement rigorously, thus is a better choice for the inlet boundary. The question is on how to deal with the outlet boundary. At present, there are several different ways to do it. One way is to use a zero concentration gradient at the outlet, the so-called Danckwerts' condition (the model A). The other way is to treat the finite length column as a part of an infinitely long column and to calculate the concentration at the outlet based on a formula developed for an infinitely long column (the model B). A dilemma appears after a careful check of different models. The model A satisfies the mass balance requirement but was found to fit with experimental data poorly. The model B, on the other hand, does not satisfy the mass balance requirement, but usually agrees well with the experimental data. So, the question is: which model to choose? To resolve the dilemma, one must check the advection-dispersion equation (ADE) that uses the Fick's law to describe the hydrodynamic dispersion. According to Taylor's transport theory, the dispersion coefficient varies linearly with time at the beginning and tends to its asymptotic, Fickian value after a travel length of a few correlation lengths. Therefore, for a finite column whose length is not much greater than the dispersivity value, the transition zone in which solute transport is non-Fickian could consist of a significant portion of the column length. It is such non-Fickian transport in the column that is responsible for the failure of the model A. To resolve the dilemma, one must carry out non-Fickian transport study to deal with the transition zone. It is our hypothesis that if the non-Fickian transport analysis succeeds, one will find that the mass balance requirement is satisfied in the model B.