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A cautionary note on implications of the well-mixed compartment assumption as applied to mass balance models of chemical fate in flowing systems



A convenient, simple, and widely used approach for modeling the fate of a chemical in a flowing environmental or biological system is to simulate the system as comprising one or more well-mixed boxes, also known as continuous stirred tank reactors (CSTRs). In principle, any desired level of accuracy can be achieved by increasing the number of boxes. However, highly segmented systems require more input data, they are more computationally intensive, and the results may be more difficult to interpret. Thus there is a tendency to minimize the number of boxes, especially in screening level models. Whereas in the hydrology and engineering literature there is an appreciation of the mathematical errors associated with applying the well-mixed box concept, we believe that these errors are often underappreciated when modeling certain environmental systems. Here, we briefly review the implications of these errors in multimedia models, river and lake simulations, atmospheric transport, flow in soils, gastrointestinal absorption, and metabolism in the liver. The key conclusion is that if over 25% of the chemical entering a box is removed, applying this well-mixed assumption can lead to substantial error. We recommend that results obtained when this criterion is violated be treated with caution.