Development of an analytical model for contaminant emission rates from passive cavities: CFD-based assessment and application to wastewater facilities

• CFD simulations evaluate emission from 2D cavities under turbulent flow. • Three flow regimes identified based on D/L, ER and Reynolds number. • Closed and open cavities allow explicit ER correlation using D/L and Re . • Sh-based model describes transfer in closed and open cavities using D/L and Re . • Results apply to WWTPs for estimating odour emissions from surface tanks. Odour emissions from open tanks in wastewater treatment plants (WWTPs) are difficult to quantify in real facilities because long-term atmospheric variability, heterogeneous geometries, fluctuations in wastewater composition, and site constraints hinder the creation of reliable measurement datasets, leaving dispersion models without defensible source terms. To address this gap, we generated a large synthetic database with two-dimensional computational fluid dynamics (CFD) using a Reynolds-averaged turbulence model across representative WWTP geometries and wind conditions. Based on the CFD results, an analytical correlation for the emission rate ( ER ) was developed for the closed and open regimes, directly linking ER to the Reynolds number and cavity geometry aspect ratio. The proposed correlation reproduces the CFD database with RMSE = 4.99·10⁻⁵ mol/s, and R² = 0.932; a mesh-independence check indicates mesh-induced uncertainty below 1 % for the emission metric, supporting numerical robustness. Validation focused on the flow physics: simulated velocity fields were compared with published laboratory benchmarks for cavity-type flows, confirming the mean recirculation structures that control emission; direct emission measurements for passive tanks were not available, so emission magnitudes were checked for order-of-magnitude consistency against standard mass-transfer analogies. The approach assumes a simplified two-dimensional, neutrally stratified flow and may be less accurate where strong three-dimensionality, unsteadiness, or buoyancy effects dominate; targeted case studies considering more advanced modeling approaches and field measurements are identified as next steps to extend applicability to complex sites. However, the proposed expression provides a practical, fast source-term input for odour dispersion studies of passive WWTP sources within the calibrated range, enabling screening, sensitivity analysis, comprehensive odour impact assessments and integration into plant-scale modeling without case-by-case coefficient tuning.