Attached growth biological treatment systems rely on a fixed medium over which wastewater is distributed, allowing micro-organisms to attach and form a stationary biological film (biofilm). As sewage percolates down through the filter medium, organic matter is absorbed and aerobically metabolized by the biofilm layer. When the biofilm grows excessively thick, oxygen access is restricted to the inner layer, creating anaerobic conditions that lead to sloughing off of the biological film. The performance of single-stage and two-stage trickling filters is traditionally evaluated using the empirical NRC (National Research Council) Equations . For a single-stage or first-stage high-rate trickling filter, the BOD removal efficiency ($\epsilon_1$) is expressed as: $$\epsilon_1 = \frac{1}{1 + 0.443 \cdot \sqrt{\frac{W_1}{V_1 \cdot F_1}}}$$ Where $W_1$ is the influent $\text{BOD}_5$ load to the filter ($\text{kg/day}$), $V_1$ is the volume of filter media ($\text{m}^3$), and $F_1$ is the ...