DISCRETE TIME-AVERAGED AND LENGTH-AVERAGED SOLUTIONS OF THE ADVECTION-DISPERSION EQUATION

Solute concentrations obtained from displacement experiments in porous media frequently represent discrete values as a result of averaging o ver a finite sampling interval. For example, effluent curves are made up of time-averaged concentrations while volume-averaged concentration s are obtained from core samples. The discrete concentrations are ofte n described by continuous solutions of macroscopic solute transport eq uations such as the advection-dispersion equation (ADE). The continuou s solution is often shifted to describe the average concentration. Thi s paper compares continuous and time- or length-averaged solutions of the one-dimensional ADE cast in terms of flux-averaged and resident co ncentrations. Expressions for the time- and length-averaged concentrat ions are presented for solute applications described by Dirac delta or Heaviside functions (instantaneous and continuous releases of the sol ute) using four different combinations of solute application and detec tion modes. A temporal and spatial moment analysis was conducted to co mpare the traditional continuous description with the discrete time- o r length-averaged approach. Graphical and tabular data are presented t o evaluate the accuracy of continuous solutions of the ADE for determi ning transport parameters. Although significant errors may occur for e xtreme cases with low dispersion coefficients and large sampling inter vals, shifting the continuous solution by half the sampling interval g enerally yields results similar to those obtained with the time- or le ngth-averaged analysis. An advantage of averaged concentrations is tha t they permit greater flexibility to conduct experiments, since averag ed concentrations provide an exact description of the data regardless of the sampling interval.