Comparison of non-reactive solute transport models for the evaluation of fluid flow in packed beds with implications for heap leaching practice

Abstract

This study investigated the effects of mean particle size fraction, bottom particle size, particle porosity and wettability on solution scale preferential flow behaviour via step input tracer tests in drip irrigated, narrowly and mixed-sized beds under steady state fluid flux. Nine solute transport models were used to quantify this behaviour reflected in the residence time distribution (RTD) profiles. Four were empirical models: three compartmental model configurations (CM-1, CM-2, CM-3) and tanks-in-series (TIS) model. The remainder five models were semi-empirical: advection dispersion (AD), piston exchange (PE), piston exchange - diffusion variant (PE-D), piston dispersion and exchange (PDE) and piston dispersion and exchange - diffusion variant (PDED). The model fit results showed that the mono-porosity TIS, AD and CM-2 models were the worst performers, while the dual porosity PDE and novel PDE-D models achieved the lowest average error values across the various systems. Higher levels of particle wettability coupled with capillary effects produced peculiar RTD curves that were relatively more difficult for the mono-porosity models to simulate. The model parameters investigated included the longitudinal dispersion coefficient ($D_{\mathrm{ds}}$), dead to total volume fraction ($V_D/V_T$), dynamic to total saturation fraction (${\beta }_d/{\beta }_T$), overall mass transfer coefficient ($K_{m}a$) and maximum diffusional pore length ($X$). The results showed that an increase in the average particle size within the beds led to higher $V_D/V_T$, $D_{\mathrm{ds}}$ and $X$ values, but lower ${\beta }_d/{\beta }_T$ and $K_{m}a$ values. These indicate an overall increase in solution scale preferential flow behaviour. Decreased capillary suction and connectivity between particle pores and inter-particle voids were deemed responsible for the results. Higher levels of particle porosity acted as a buffer against these effects. Overall, the results highlight the benefit of the addition of fines (0.1–1 mm particles) during the agglomeration process in heaps to help reduce solution scale preferential flow behaviour and increase liquid hold-up. This is more necessary when the ore has low to moderate levels of porosity (surface area: $<$2 m²/g) and will also increase the modelling options available as most models performed better fitting data from such beds.