Critical assessment of the operator-splitting technique in solving the advection-dispersion-reaction equation: 2. Monod kinetics and coupled transport
In the first manuscript of this two-part series, the behavior of the inherent time-lag error in the operator-splitting technique has been discussed. However, the discussion has been limited to the advection-dispersion-reaction equation with first-order kinetics. In this manuscript, the discussion is extended to address the applicability of the operator-splitting technique in solving the advection-dispersion-reaction equation with Monod kinetics. The discussion also considers the two-species coupled transport problem. The results of the analysis show that the behavior of the time-lag error causing a mass balance error is rather similar to those observed with first-order kinetics. The time-lag error directly depends on the reaction rate, and hence, affects the oxygen equation due to the high rate of oxygen consumption. Also, the alternate operator-splitting scheme shows a greater accuracy compared to the normal operator-splitting technique. Upon observing such similarities, a concept of equivalent first-order reaction rate is derived. The equivalent reaction rate has been found to be extremely useful for predicting the time-lag error of the single- and two-species mass transport with Monod kinetics using the result of the first-order reaction problems obtained in the first manuscript.