Design and Analysis of Experiments
Design and Analysis of Experiments
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Although the Law of Diminishing Returns (LDR) has been established in Economics since the era of early economists such as Johann Heinrich von Thünen, Turgot, Thomas Malthus and David Ricardo, its validity in the fields of Engineering (and especially in Environmental Engineering, where Economics and Technology are merged) has not been adequately investigated. In this work, the validity of LDR in packed bed columns design/operation (used for wastewater treatment) is examined in two cases: decolorization by adsorption of dyes on lignocellulosic residues and BOD decrease by biochemical reaction within trickling filters. In the first case, dimensional analysis was used to provide empirical expressions where simulation mechanismic models were not satisfactory. For the same reason, already established semi-empirical models were used in the second case. The validity of the LDR was also proved in both biochemical treatment modes, once-through and with effluent partial recycling through a secondary thickener/clarifier, while in certain cases such validity is confirmed under a condition, which is quantitatively determined. From a methodological point of view, an algorithmic procedure has been developed to facilitate the investigation while an extension of this methodology to conventional chemical reactors is presented in the Discussion Section.