A Capillary Model for Predicting Saturated Hydraulic Conductivity of Ion-Adsorption Rare Earth Ore Based on Improved Kozeny–Carman Equation

Abstract

During the in-situ leaching process of ion-adsorption rare earth ore, the seepage velocity of the leaching solution is one of the core problems in studying the leaching efficiency. The determination of the saturated hydraulic conductivity is of great significance to reveal the leaching process. The classical Kozeny–Carman (KC) equation is widely employed to predict the hydraulic conductivity of sandy soils. However, in the equation, the effect of tortuosity on the hydraulic conductivity is not considered, and the specific surface area is difficult to determine in practice. In this study, the capillary model for predicting the saturated hydraulic conductivity of ion-adsorption rare earth ore was established. First, we assumed that all the pores in the ore body are a series of parallel and tortuous capillaries with equal diameters. Based on the assumption and Hagen–Poiseuille’s law, the KC equation was improved by introducing the tortuosity. Second, the constant head permeability tests were carried out to derive the seepage velocity and hydraulic head loss under the steady seepage state. According to the experimental results, the diameter of the capillary was calculated with Darcy's formula. Then we obtained a linear-fit relationship between capillary diameter and porosity to express the specific surface area variation with porosity. Third, by validating with experimental data, when the pore shape coefficient is 0.4, the saturated hydraulic conductivity calculated by the capillary model is in good agreement with the tested value. The proposed model can be considered to have a satisfactory capability to predict the saturated hydraulic conductivity of ion-adsorption rare earth ore.