Date of Graduation


Document Type


Degree Type



Statler College of Engineering and Mineral Resources


Mining Engineering

Committee Chair

Qingqing Huang

Committee Co-Chair

Yi Luo

Committee Member

Yi Luo

Committee Member

Berk Tulu


This study evaluates the coal liberation behavior using silica as the grinding media by assessing the effects of four operating factors including nominal feed size, media size, shaft speed and grinding time, each of three levels on two response variables, the product P80 and the specific energy. The coal material used in this study was mixed-phase particles commonly referred to as middlings, sampled from dense medium circuit at the Leatherwood preparation plant in Kentucky. One-third fractional factorial design of resolution III was implemented. Since silica was obtained in three standard size ranges as per manufacturer’s design, media size was qualitative while other factors were quantitative.

The experiment was custom designed, and the results were analyzed with JMP statistical software. Both ash analysis of the grind products and the shape analysis of the media before and after the grinding tests indicate no media degradation occurred during the grinding process. Statistical analyses were initially performed to determine the operating parameters that significantly influence the product P80 and the specific energy. For the product P80, feed size has a p-Value of 0.001 at a five-percent significance level. In addition, the normal probability plot of effect estimates also shows feed size deviates from the straight line. Hence, only feed size amongst the four operating factors has a significant effect on the product P80. However, for specific energy, grinding time and shaft speed have p-Values of 0.03 and 0.05, respectively at a five-percent significance level. This is also corroborated on the normal probability plot of effect estimates where only grinding time and shaft speed deviate from the straight line. Therefore, only grinding time and shaft speed significantly influence specific energy.

Based on the mathematical models that were further developed, it can be deduced that the product P80 decreases with decreasing feed size and vice versa. On the other hand, the specific energy decreases with decreasing grinding time and shaft speed and vice versa. Irrespective of other factors investigated in this study, the lowest and highest product P80 (4.5 microns and 137.5 microns, respectively) were measured when the nominal feed size was at its low level (25 microns) and high level (250 microns), respectively. In the same vein, the lowest and highest specific energy (16 kWh/ton and 416 kWh/ton, respectively) were obtained when grinding time and shaft speed were at their low levels (16 minutes and 200 rpm) and high levels (64 minutes and 400 rpm), separately.

Finally, the batch grinding process was numerically simulated with the population balance model using the experimental data. Particle swarm optimization, a stochastic algorithm in MATLAB was used to iteratively fit the model to the experimental data with a mean squared error of 0.01. The selection and breakage function parameters of Leatherwood coal were determined as 0.05, 4.98, -2.03 and 1.34, 0.06, 10.15, respectively.