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 u sed in the solution of the advection-dispersion-reaction equation (ADR E), especially in the presence of biological decay, where the scales o f transport and biological decay are far apart. The OST introduces a t ime-lag between the advection-dispersion and reaction stages by splitt ing the ADRE causing a breakdown of the physics of the problem, thus l imiting its applicability. In this work, the applicability of the oper ator splitting technique is studied in parts. This first manuscript ad dresses the critical limitations of the operator-splitting technique a s 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 s plitting. The assessment is based on mass balance errors, deviations o f concentration prediction and sensitivities of concentration deviatio ns. The results show that the splitting introduces an inherent error i ndependent of the discretization errors. This inherent error increases with reaction rate and time-lag, and the overall errors can be reduce d by using the alternate operator-splitting technique suggested by pre vious researchers.