Developing process descriptor for biological nitrogen removal in wastewater treatment

Intelligent control offers great potential for optimizing wastewater treatment but often operates in isolation from first-principle process mechanisms. To bridge this gap, we develop a matrix equation encoding the stoichiometric causality of biological nitrogen removal (BNR) based on nitrogen mass conservation, serving as a process descriptor. This equation establishes a comprehensive computational framework that defines the parameter relationships between nitrogen flow distribution (NFD), process structure, and BNR performance. It allows to describe BNR processes configured with any combination of partial nitrification (PN), partial denitrification (PD), and anammox (A), a capability validated with experimental data. Importantly, the descriptor equations form the mathematical basis for understanding process's observability at stoichiometric level, identifying PN, PD, PN/A, and PD/A as four basic observable processes. This outcome provides an analytical approach of online sensor placement for designing observability in complex processes with more than three sub-processes. Additionally, the descriptor creates a deterministic mapping space linking NFD parameters to operating states, significantly reducing the dimensionality of uncertain parameter relationships for intelligent control models. This work presents a transformative tool for process analysis, observability design, and optimal control in wastewater treatment systems.