A double exponential model for biochemical oxygen demand

Biochemical oxygen demand (BOD) exertion patterns in anaerobically treated farm dairy wastewater were investigated on a laboratory scale. Oxygen uptake was typically characterised by a period of rapid oxygen exertion, a transitional “shoulder” phase and a period of slower activity. A multi-species model, involving rapidly degradable and slowly degradable material, was developed, leading to a double exponential model of BOD exertion as follows: where t is time, and are apparent ultimate BOD (BODu) values, and k1 and k2 are rate constants. The model provided an improved description of BOD exertion patterns in anaerobically treated farm dairy wastewater in comparison to a conventional single exponential model, with rapidly degradable rate constant values (k1) ranging from 2.74 to 17.36 d−1, whilst slowly degradable rate constant values (k2) averaged 0.25 d−1 (range 0.20–0.29). Rapidly and slowly degradable apparent BODu estimates ranged from 20 to 140 g/m3 and 225 to 500 g/m3, respectively, giving total BODu levels of 265–620 g/m3. The mean square error in the curve fitting procedure ranged between 20 and 60 g2/m6, with values on average 70% lower (range 31–91%) than those obtained for the single exponential model. When applied to existing data for a range of other wastewaters, the double exponential model demonstrated a superior fit to the conventional single exponential model and provided a marginally better fit than a mixed order model. It is proposed that the presence of rapidly degradable material may be indicated from the value of the first rate constant (k1) and the time to 95% saturation of the first exponential function. Further model development is required to describe observed transitional and lag phases.