Sulfate diffusion in coal pillar: experimental data and prediction model

The stability of coal pillar dams is crucial for the long-term service of underground reservoirs storing water or heat. Chemical damage of coal dams induced by ions-attacking in coal is one of the main reasons for the premature failure of coal dams. However, the diffusion process of harmful ions in coal is far from clear, limiting the reliability and durability of coal dam designs. This paper investigates sulfate diffusion in coal pillar through experimental and analytical methods. Coal specimens are prepared and exposed to sulfate solutions with different concentrations. The sulfate concentrations at different locations and time are measured. Based on experimental data and Fick’s law, the time-dependent surface concentration of sulfate and diffusion coefficient are determined and formulated. Further, an analytical model for predicting sulfate diffusion in coal pillar is developed by considering dual time-dependent characteristics and Laplace transformations. Through comparisons with experimental data, the accuracy of the analytical model for predicting sulfate diffusion is verified. Further, sulfate diffusions in coal dams for different concentrations of sulfate in mine water are investigated. It has been found that the sulfate concentration of exposure surface and diffusion coefficient in coal are both time-dependent and increase with time. Conventional Fick’s law is not able to predict the sulfate diffusion in coal pillar due to the dual time-dependent characteristics. The sulfate attacking makes the coal dam a typical heterogeneous gradient structure. For sulfate concentrations 0.01–0.20 mol/L in mine water, it takes almost 1.5 and 4 years for sulfate ions to diffuse 9.46 and 18.92 m, respectively. The experimental data and developed model provide a practical method for predicting sulfate diffusion in coal pillar, which helps the service life design of coal dams.