Physical Consistency of Axial-Dispersion Boundary Conditions and Tanks-in- Series Models for Multi-Compartment Wastewater Treatment Reactors

<title>Abstract</title> <p>Accurate hydrodynamic representation is essential for interpreting residence time distribution (RTD) data and for developing reliable reactor-scale models of multi-compartment wastewater treatment systems. However, the tanks-in-series (TIS) model and axial-dispersion (AD) formulations are often applied as standard RTD tools, with hydrodynamic parameters then inferred without explicit evaluation of whether the underlying transport and boundary assumptions are physically consistent with the reactor system. This study evaluates the physical consistency and predictive performance of the TIS model and AD formulations with different boundary conditions (BCs), using tracer data from a 6-L, eight-chamber anaerobic baffled reactor as a representative multi-compartment system. The reactor was operated at hydraulic retention times of 93–366 min and under changes in temperature, dissolved-solids concentration, suspended-solids concentration, and reactor scale. The AD formulations based on BC I, which applies inlet flux balance and a zero-gradient outlet, and BC III, which neglects inlet dispersion and assumes an infinite downstream domain, provided the most consistent representation of the experimental RTDs. They produced identical responses and achieved the lowest average NRMSE values: 14% across the HRT-based tests and 10% across most environmental and geometric conditions, compared with 30–31% for AD with open boundary conditions and 16–17% for TIS. Although TIS reproduced some hydrodynamic descriptors, its ideal-mixing structure gave less consistent RTD-shape agreement and can misrepresent transport in compartmentalised reactors. Breakthrough time was poorly predicted by all reduced-order formulations, showing that short-circuiting is controlled by local flow pathways not captured by global RTD models.</p>