Abstract Summary (Max 250 words)
Rotary disc contactors (RDCs) are widely used for liquid–liquid extraction, but quantifying axial back-mixing in multi-stage units remains difficult. Here, CFD-generated tracer pulse responses are combined with a stage-wise N-CSTRs-in-series model with back-mixing to identify effective mixing parameters for a multi-stage RDC. Transient CFD simulations were performed for 25 operating points spanning multiple flow-rate ratios and rotor speeds in a five-stage geometry. Outlet tracer signals were converted to residence-time distributions (RTDs) via baseline correction, area normalization, and nondimensional time. RTDs were fitted using peak-weighted least squares with explicit tail handling to reduce bias toward long-time data. A local search over the back-mixing coefficient k, coupled with discrete exploration of the number of ideal stages N, yields robust fits and enables automated parameter selection across cases. The fitted curves reproduce both peak location and decay, and a weighted R-squared metric provides a consistent indicator of fit quality. Sensitivity analyses show that k largely controls peak shape, motivating localized k-segmented searches and fixed-N sweeps to stabilize estimation across operating conditions. For each condition, the workflow returns k, N, and mean residence time tau, summarized as heat maps to reveal operating-condition dependence. The framework is transparent, reproducible, and transferable to other staged liquid–liquid contactors, supporting model-based design and scale-up.
