Time-variable functions

Laboratory and field experiments have shown that dispersivity is one of the key parameters in contaminant transport in porous media and varies with elapsed time. This time-dependence can be shown using a time-variable dispersivity function. The advantage of this function as opposed to constant dispersivity is that it has at least two coefficients that increase the accuracy of the dispersivity prediction. In this study, longitudinal dispersivity values were obtained for the conservative NaCl solute transport in a laboratory porous medium saturated with tap water. The results showed that the longitudinal dispersivity initially increased with time (pre-asymptotic stage) and eventually reached a constant value (asymptotic stage). Four functions were used to investigate the time variations of dispersivity: linear, power, exponential and logarithmic. In general, because of the linear increase of dispersivity during a long time of transport, the linear function with R2=0.97 showed better time variations than the other three functions; the logarithmic function, having an asymptotic nature, predicted the asymptotic stage successfully (R2=0.95). The ratio of the longitudinal dispersivity to the medium length was not constant during the transport process and varied from 0.01 to 0.05 cm with elapsed time.