Development of a Non-linear Framework for the Prediction of the Particle Size Distribution of the Grinding Products

2022

Minerals

Self Cite

The aim of this study is to evaluate the effect that the size of grinding media exerts on ferronickel slag milling efficiency and energy savings. A series of tests were performed in a laboratory ball mill using (i) three loads of single size media, i.e., 40, 25.4, and 12.7 mm and (ii) a mixed load of balls with varying sizes. In order to simulate the industrial ball milling operation, the feed to the mill consisted of slag with natural size distribution less than 850 μm. Grinding kinetic modeling and the attainable region (AR) approach were used as tools to evaluate the data obtained during the ball milling of slag. Particular importance was given to the determination of the specific surface area of the grinding products, the identification of the grinding limit, and the maximum specific surface area which could be achieved when different grinding media sizes were used. The results showed that, in general, the breakage rates of particles obey non-first-order kinetics and coarse particles are ground more efficiently than fines. The AR approach proved that there is an optimal grinding time (or specific energy input) dependent on the ball size used for which the volume fraction of the desired size class is maximized. The use of either 25.4 mm balls or a mixed load of balls with varying sizes results in 31 and 24% decrease in energy requirements, compared to the use of balls with small size (12.7 mm).

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of Grinding Media Size on Ferronickel Slag Ball Milling Efficiency and Energy Requirements Using Kinetics and Attainable Region Approaches

2022

Minerals

Self Cite

“…In addition, the same figure reveals that the deviation from the linear theory is more evident for the larger particle sizes which are ground more efficiently than finer particles. The non-linearity of batch grinding systems has been experimentally observed by many researchers [34,35,49]. By comparing the plots of the remaining mass (%) fraction vs. grinding time obtained using different f c values (Figure 3a-c), it appears that for a certain grinding time, lower f c values result in a smaller amount of material which remains in each particle size.…”

Section: Resultsmentioning

confidence: 55%

“…where K is the grinding rate constant and t is the grinding time. Despite the fact that the first-order hypothesis is the most widely used approach to describe the grinding process in a ball mill and many studies have pointed out its advantages [31,32], deviation from the linear kinetics has been experimentally observed in several cases when different materials are used [33][34][35]. Based on the non-linear behavior, Alyavdin proposed that the following formula (Equation ( 3)) can be used in batch milling processes [36,37]:…”

Section: Introductionmentioning

confidence: 99%

Modeling of Bauxite Ore Wet Milling for the Improvement of Process and Energy Efficiency

2021

Circ.Econ.Sust.

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Size reduction is a necessary operation in mineral processing plants and provides the desired size for separation operations and the liberation of the valuable minerals present in ores. Estimations on energy consumption indicate that milling consumes more than 50 % of the total energy used in mining operations. Despite the fact that ball milling is an efficient operation, it is energy intensive, and its modeling is a great challenge. In the present experimental study, efforts are made to model wet milling of bauxite ores and identify the optimum material filling volume in the ball mill. Modeling is based on the characterization of the grinding products obtained after various grinding periods and the description of the particle size distributions using mathematical approaches, i.e., Gates-Gaudin-Schuhmann (GGS), Rosin-Rammler (RR), and logistic distributions. In addition, grinding kinetic models were applied to the experimental data in order to identify if the linear theory of the population balance model is valid during bauxite grinding. The experimental data revealed that the logistic distribution is a model that represents more reliably particle size distributions obtained after grinding and fits the experimental data better than the GGS and RR models. Regarding grinding kinetic analysis, it was found that grinding exhibits non-first-order behavior and the reduction rate of each size is time dependent. This experimental work is in line with the Sustainable Development Goal of UN, SDG12: Responsible Consumption and Production and aims to improve the efficiency of ore grinding and thus reduce energy requirements and the associated CO 2 emissions.

“…Recently, Petrakis and Komnitsas [33] developed a nonlinear framework for the prediction of the particle size distribution of the grinding products, where the linear theory of PBM was considered as a partial case. Based on this approach, the fundamental batch grinding mass balance equation was transformed into the well-known (6)…”

mentioning

confidence: 99%

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

Varouchakis

Mining, Metallurgy & Exploration

2023

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.