Proton-equivalent budgeting enables acid demand prediction and reflux control in partial nitrification/anammox-hydroxyapatite side-stream treatment

Acid–base regulation remains a major operational challenge in the treatment of ammonium-rich side-streams using partial nitrification/anammox-hydroxyapatite (PN/AMX-HAP) systems, where acid and alkalinity dosing are largely adjusted empirically despite the coupled effects of biological nitrogen conversion, mineral precipitation, reflux, and external acid compensation. Here, we developed an alkalinity-referenced proton-equivalent budgeting framework to quantify acid–base fluxes and predict chemical demand in a two-stage PN/AMX-HAP system treating digestate-derived liquid. The framework was organised into state, stoichiometric, and control layers. In the PN stage, ammonia-oxidising bacteria-driven ammonium oxidation was the dominant proton source, whereas simultaneous nitrification–denitrification partly offset the net proton load. The calculated PN proton-equivalent demand closely matched the measured value, achieving robust closure across loading conditions. Based on this closure, an alkalinity safety index was proposed to quantify the buffering margin for PN operation, with 1.22–1.51 indicating sufficient but non-excessive influent alkalinity. In the AMX-HAP stage, AMX and residual denitrification acted as proton-utilising processes, while HAP formation provided a minor mineral counterflux. Because internal stoichiometry alone could not explain the measured acid requirement under reflux operation, a dimensionless correction factor, A(R) , was introduced to bridge internal proton-equivalent demand and actual external acid dosing. The corrected framework predicted an external proton requirement of 9.84–11.6 mmol H + -eq g⁻ 1 NH 4 + -N and employed reflux-dependent operating windows that balance nitrite dilution and acid economy. Compared with pH-based and alkalinity-only predictors, the proton-equivalent budget showed higher accuracy and substantially lower bias for acid demand prediction. This framework shifts PN/AMX-HAP control from empirical pH or alkalinity correction toward mechanistic proton tracing, providing a quantitative basis for alkalinity assessment, acid dosing, reflux selection, and operational boundary definition in coupled nitrogen removal–phosphorus recovery systems.