Abstract This work develops a unified, dimensionless framework for comparing reacting systems that are geometrically similar but differ in size, particle size distribution (PSD), and internal pore structure of the solid reactant, with emphasis on hydrometallurgical heap leaching. For two heaps operated under dynamically similar hydrodynamic conditions, the dimensionless residence time distribution (RTD) of the liquid is identical. However, differences in PSD and internal porosity break microscopic similarity and can strongly alter heap-scale conversion. Using the shrinking-core model (SCM), we show how a PSD induces a distribution of particle-scale Damköhler numbers that controls the heap-averaged conversion. We derive explicit change-of-variable expressions mapping a PSD in particle diameter to Damköhler-number distributions for (i) external film (convection) control, (ii) intraparticle diffusion control, and (iii) mixed control approximated by additive resistances. We then couple SCM kinetics to dual-porosity hydrology (mobile/immobile liquid domains) and identify the additional dimensionless groups governing interporosity exchange. Two numerical examples illustrate the approach: (1) transforming a lognormal PSD into external- and diffusion-controlled Damköhler distributions, and (2) a toy column/heap calculation comparing conversion trajectories for different PSDs under film versus diffusion control. Finally, we outline a practical workflow for column-test interpretation, combining SCM diagnostics with tracer-derived RTD and exchange parameters. The framework explains the heightened sensitivity of diffusion-controlled systems to PSD tails and dual porosity and provides a compact set of dimensionless groups for robust scale-up from columns to industrial heaps.
Juan J. Segura (Sun,) studied this question.