Bifurcation Analysis of an Impulsive System Describing Partial Nitritation and Anammox in a Hybrid Reactor

Low-energy nitrogen removal under mainstream conditions is a technology that has received significant attention in recent years as the water industry drives toward long-term sustainability goals. Simultaneous partial nitritation-Anammox (PN/A) is one process that can provide substantial energy reduction and lower sludge yields. Mathematical modeling of the PN/A process offers engineers insights into the operating conditions necessary to maximize its potential. Laureni et al. (Laureni et al. Water Res. 2019, 14) have recently published a simplified mechanistic model of the process operated as a sequencing batch reactor that investigated the effect of three key operating parameters on performance (Anammox biofilm activity, dissolved oxygen concentration and fraction of solids wasted). The analysis of the model was limited, however, to simulation with relatively few discrete parameter sets. Here, we demonstrate through the use of bifurcation theory applied to an impulsive dynamical system that the parameter space can be partitioned into regions in which the system converges to different fixed points that represent different outcomes: either the washout of nitrite-oxidizing bacteria or their survival. Mapping process performance data onto these spaces allows engineers to target suitable operating regimes for specific objectives. Here, for example, we note that the nitrogen removal efficiency is maximized close to the curve that separates the regions in parameter space where nitrite-oxidizing bacteria washout from the region in which they survive. Further, control of solids washout and Anammox biofilm activity can also reduce oxygen requirements while maintaining an appropriate hydraulic retention time. The approach taken is significant given the possibility for using such a methodology for models of increasing complexity. This will enable engineers to probe the entire parameter space of systems of higher dimension and realism in a consistent manner.