Moment analysis to estimate degradation rate constants from leaching experiments

First-order degradation rate constants (gamma) are often estimated from the results of solute leaching experiments by using curve-fitting procedures, However, uniqueness problems can make curve-fitting a challenging task if multiple parameters are estimated simultaneously, Several attempts have been made to compute gamma by employing batch degradation theory to analyze the results of leaching experiments. This theory requires an estimate of the mass recovery fraction (MRF) and the degradation time. The degradation time is replaced with an average solute travel time when batch theory is applied to the results of a leaching experiment, This approach is flawed because the simultaneous occurrence of sorption, dispersion, and convection confounds the time available for degradation in a leaching experiment, We have used statistical moments to show that when degradation follows first-order kinetics, the degradation time is an adjusted convection time (ACT), It is defined as the harmonic mean of m(I)/R and the convection time (L/v), where m(I) is the first moment of the breakthrough curve (BTC), a is the retardation factor, L is the length of the soil column, and v is the pore water velocity. The adjustment in the convection time scale is required because of the simultaneous occurrence of dispersion and degradation. We show that these two processes interact to reduce the true convection time for the leaching event (ACT < L/v), We have tested our result by generating artificial BTCs with known values of gamma and then successfully estimating gamma by obtaining the MRF and ACT from the generated BTC. We have outlined a procedure to estimate gamma from the information generated in a typical leaching experiment.