A novel open-source framework for automatic flocculation kinetics and retention time modelling using image analysis and swarm intelligence

Automatic detection of flocculation kinetic mechanisms and total hydraulic retention time (THRT) in multi-chamber systems in series is essential for seamless water treatment modelling. This study presents the first open-source tool for modelling flocculation kinetics and THRT in multi-chambers systems, with their sensitivity to image analysis. This study introduces three key novelties: (1) a non-derivative Secant method for simulating THRT, (2) use of Particle Swarm Optimization (PSO) algorithm to facilitate curve fitting technique for modelling flocculation kinetic coefficients, and (3) automatic retention time modelling directly from floc images, including sensitivity to threshold-based image segmentation. The proposed Secant method demonstrated greater robustness compared to the existing Newton-Raphson method (N-R), as it avoided convergence in cases where the N-R produced negative retention times. The PSO algorithm produced results comparable to the Bayesian approach, with aggregation coefficients of 2.773 × 10−4 and 1.905 × 10−4, and breakage coefficients of 1.186 × 10−6 and 2.656 × 10−6, at low and high velocity gradients ( G ), respectively. Flocculation kinetics at low G has steady aggregation followed by a dynamic equilibrium, while high G exhibited rapid formation of fragile flocs, followed by dominant breakage mechanism, and a later lower equilibrium. Scaled G for multi-chamber systems showed that reactor configurations with an immediate low G in the second chamber resulted in an average 50 % decrease in THRT. Finally, aggregation and breakage coefficients were sensitive to image segmentation thresholds, but THRT sensitivity is limited. The deployed model is accessible to improve flocculation modelling for multi-chambers in series (https://flocxion-application.onrender.com).