Reliability of the Non-linear Modeling in Predicting the Size Distribution of the Grinding Products Under Different Operating Conditions

Abstract

During the modeling of grinding systems, population balance modeling (PBM) which considers a constant breakage rate has been widely used over the past years. However, in some cases, PBM exhibited some limitations, and time-dependent approaches have been developed. Recently, a non-linear framework which considers the traditional linear theory of the PBM as a partial case was introduced, thus allowing the estimation of product particle size distribution in relation to grinding time or the specific energy input to the mill. In the proposed model the simplified form of the fundamental batch grinding equation was transformed into the well-known Rosin–Rammler (RR) distribution. Besides, the adaptability and reliability of the prediction model are among others dependent upon the operating conditions of the mill and the adjustment of the RR distribution to the experimental data. In this study, a series of grinding tests were performed using marble as test material, and the adaptability of the non-linear model was investigated using three loads of single size media, i.e., 40, 25.4, and 12.7 mm. The results indicate that the proposed model enables a more accurate analysis of grinding, compared to PBM, for different operating conditions.

Effect of Size-Distribution Environment on Breakage Parameters Using Closed-Cycle Grinding Tests

“…where S w is the specific surface area, ρ p is the particle density, D [3,2] is the mean surface area (Sauter mean diameter), and f, k are the surface and volume coefficients (for spheres f/k = 6). The power of the mill, P (kW), was calculated using Equation (10), proposed by Bond [37,38],…”

“…Its main purpose is to produce the desired size and liberate the minerals of interest from other invaluable constituents so that they can be efficiently separated [1]. However, comminution, especially grinding, is the most energyintensive process in mining operations, accounting for more than 50% of the total energy used [2][3][4]. Also, grinding is characterized by low efficiency and high carbon emissions.…”