The goal of this project is to improve energy efficiency of industrial crushing and grinding operations (comminution). Mathematical models of the comminution process are being used to study methods for optimizing the product size distribution, so that the amount of excessively fine material produced can be minimized. The goal is to save energy by reducing the amount of material that is ground below the target size, while simultaneously reducing the quantity of materials wasted as 'slimes' that are too fine to be useful. This is being accomplished by mathematical modeling of the grinding circuits to determine how to correct this problem. The approaches taken included (1) Modeling of the circuit to determine process bottlenecks that restrict flowrates in one area while forcing other parts of the circuit to overgrind the material; (2) Modeling of hydrocyclones to determine the mechanisms responsible for retaining fine, high-density particles in the circuit until they are overground, and improving existing models to accurately account for this behavior; and (3) Evaluation of advanced technologies to improve comminution efficiency and produce sharper product size distributions with less overgrinding.