A critical analysis of classical design equations for waste stabilization lagoons and other wastewater treatment systems

This paper analyzes the applicability of classical equations to the design of waste stabilization lagoons and to other wastewater treatment processes based on the structure removed BOD load = a X applied BOD load + b, where BOD is biochemical oxygen demand. Although the emphasis is on waste stabilization lagoons, this type of equation is presented by several researchers describing wastewater treatment processes, used worldwide, and cited in virtually all textbooks in the field of wastewater treatment. However, the equation has a problem of bias in its structure because the so-called independent variable (applied loan) is not actually independent; it is implicitly present in the dependent variable (removed load, which is equal to applied load minus effluent load). By definition, the equation can achieve high correlation coefficients because it is a good predictor of removed load. However, the more important variables effluent load and removal efficiency are not well estimated by this equation, undermining its intended applicability. This conclusion is supported by results obtained in a simplified didactic example with a small data set and a Monte Carlo simulation with a large data set (500 values).