Critical assessment of the operator-splitting technique in solving the advection-dispersion-reaction equation: 1. First-order reaction

Operator-splitting technique (OST) is a common mathematical approach used in the solution of the advection-dispersion-reaction equation (ADRE), especially in the presence of biological decay, where the scales of transport and biological decay are far apart. The OST introduces a time-lag between the advection-dispersion and reaction stages by splitting the ADRE causing a breakdown of the physics of the problem, thus limiting its applicability. In this work, the applicability of the operator splitting technique is studied in parts. This first manuscript addresses the critical limitations of the operator-splitting technique as related to first-order decay, and the second manuscript extends the work to include coupled transport between hydrocarbon and oxygen with Monod kinetics describing biological decay. The critical assessment is performed to address the errors associated with the time-lag due to splitting. The assessment is based on mass balance errors, deviations of concentration prediction and sensitivities of concentration deviations. The results show that the splitting introduces an inherent error independent of the discretization errors. This inherent error increases with reaction rate and time-lag, and the overall errors can be reduced by using the alternate operator-splitting technique suggested by previous researchers