Spreadsheet-based simulation of closed ball milling circuits M. Irannajad a , A. Farzanegan b, * , S.M. Razavian a a Amirkabir University of Technology, Mining, Metallurgical and Petroleum Engineering Department, Tehran, Iran b University of Kashan, Faculty of Engineering, Mining Department, Kashan, Isfahan 87317-51167, Iran Received 5 April 2006; accepted 11 August 2006 Available online 9 October 2006 Abstract Grinding, particularly at finer sizes to achieve the required degree of liberation or specific surface, is a critical unit operation in terms of energy consumption and process optimization. Nowadays, considering the significant developments made in computer hardware and software, using simulation programs to optimize design and operation of various ore treatment plants could be very beneficial to the mineral process engineers. Currently, there are a number of steady-state simulators that can be run under DOS TM or WINDOWS TM envi- ronments such as BMCS, MODSIM TM and JKSimMet TM . In this paper, COMSIM, a new simulator which runs under Excel spreadsheet will be introduced which uses a Population Balance Model (PBM) to simulate ball mills. Plitt and Nageswararao models have been used to describe the performance of hydrocyclones, which by linking to the ball mill model allow for closed-circuit simulations. To describe material flow through the ball mills, two tanks-in-series models called Weller’s model and one plug flow unit plus n perfect mixers units (1PF + nPM) model have been used. Utilizing Microsoft TM Excel TM capabilities such as graphics and VBA programming to implement new macro-based user functions, the authors developed an easy-to-use comminution simulation environment. By comparing the outputs of COMSIM with measured grinding data and previously existing simulators, particularly BMCS, its performance was firmly tested both in terms of accuracy and precision of obtained results. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Comminution; Grinding; Simulation; Spreadsheet; Modelling 1. Introduction Grinding process mathematical modelling and com- puter simulation particularly in mineral industry had been a very active research field for several past decades. This is due to the high consumption of electrical energy in com- minution circuits and low efficiency of operating mills especially in fine size range. The first attempts were made by Bond (1952) who introduced work index concept and developed an energy-based model of grinding mills as follow: W ¼ 10  W i 1 ffiffiffiffiffiffi P 80 p  1 ffiffiffiffiffiffiffi F 80 p   ð1Þ where W is the specific energy for grinding in kW h/ton, W i is the work index in kW h/ton, P 80 is the mill product d 80 size in lm and F 80 is the mill feed d 80 size lm. Given W, W i and F 80 , one can calculate the product size, namely, P 80 . This is one of the simplest models to predict the ground size. Traditionally, Eq. (1) has been the main tool to design new mills, even though it can only predict one point of the product particle size distribution, P 80 . Then, during 1960–1990, Population Balance Modelling (PBM) approach was extensively used to simulate grinding process, capable of predicting the full product particle size distribution. Recently, high fidelity simulation (HFS) approach which collectively refers to a number of model- ling methods such as discrete element modelling (DEM), computational fluid dynamics (CFD), discrete grain break- age (DGB) and finite element methods (FEM) has been the subject of many new researches in mineral processing (Herbst et al., 2002). In this paper, the authors explain 0892-6875/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2006.08.010 * Corresponding author. Fax: +98 361 5559930. E-mail address: a.farzanegan@kashanu.ac.ir (A. Farzanegan). This article is also available online at: www.elsevier.com/locate/mineng Minerals Engineering 19 (2006) 1495–1504