Predicting effective viscosity of magnetite ore slurries by using artificial neural network Manik P. Deosarkar a, ⁎, Vivek S. Sathe b a Dept. of Chemical Engineering, Vishwakarma Institute of Technology, 666, Upper Indira Nagar, Bibwewadi, Pune-411037, Maharashtra, India b Dept. of Chemical Engineering, Dr. Babasaheb Ambedkar Technological University, Vidyavihar, Lonere 402103, Maharashtra, India abstract article info Article history: Received 26 March 2011 Received in revised form 19 December 2011 Accepted 25 December 2011 Available online 30 December 2011 Keywords: Viscosity models for slurry Solid volume fraction Particle size Effective viscosity Artificial neural network In this paper, we study the theoretical models for effect of various parameters used for predicting viscosity of magnetite ore slurry. These models are fitted using data collected from experiments conducted. These viscous slurries of magnetite ore have up to 30% solids (by weight). We prepared the slurry samples of magnetite in aqueous solutions of high viscosity powder of sodium salt of carboxy methyl cellulose (CMC) and guar gum. Average particle sizes of the four solid samples used were of 50, 52.3, 58.4 and 74.8 μm. The viscosity of slurry samples was measured using Brookfield DV-III + programmable rheometer. Once the experimental data was collected, we selected six different models for predicting viscosity; also we used artificial neural networks (ANN) for fitting the experimental data, and, trained the neural networks to predict viscosity for unknown samples. We have finally computed the root mean square errors (RMSE) between model predictions and cor- responding measured value of viscosity. The conclusions drawn and certain observations made are reported. © 2011 Elsevier B.V. All rights reserved. 1. Introduction The measurements of physical properties of solid–liquid slurries needed for several reasons. Flow of these complex fluids are frequent- ly encountered in many applications in industries and nature. Design and operation of slurry process calls for understanding the mechanism involved. The effect of slurry parameters is required to design such physical and engineering systems. We also note that for most of the slurry transport applications, the prediction of deposition velocities and rheological properties is essential in analysis of fluid transport and flow behavior. The recent studies have focused on preparing the slurries with maximum solid concentration, transportability of solids through pipeline, and the pressure drop and flow sampling [1–3]. There is a significant effect of solids concentration upon the slurry viscosity. At high solid concentrations, the rheological behavior of the slurry becomes complex. Several studies have shown the viscosity of slurry increases exponentially with solids concentration and become infinite at the maximum packing fraction [4–6]. The first equation re- lating the slurry viscosity to it solids content was due to Einstein [7]. This equation is a linear relation between the effective viscosity and the solid volume fraction of the slurry given as μ eff ¼ μ s μ f ¼ 1 þ 2:5ϕ ð1Þ where μ s is the slurry viscosity, μ f is suspending liquid viscosity and ϕ is the solid volume fraction. This Einstein's formula in Eq. (1) is valid only for very dilute suspensions. An extended validity of the Einstein's formula applicable to slur- ries with higher solid concentration can be discussed in terms of var- ious theoretical and empirical equations. The theoretical models in case of more complex fluids needing a deeper insight into the fluid behavior in general are usually variants of the Einstein's relation. This extended form of viscosity relation is expressed as a power series of higher order in ϕ and is μ eff : ¼ 1 þ k 1 ϕ þ k 2 ϕ 2 þ k 3 ϕ 3 þ ::::: ð2Þ Here k 1 ,k 2 ,k 3 … are the polynomial coefficients. These coefficients are functions of parameters such as particle–particle interactions and motion of solid particles, which can characterize a complex fluid such as slurry. Cheng and Law [4] have studied the parametric relations forming these polynomial coefficients and proposed a new viscosity model with five coefficients k 1, k 2, k 3, k 4, and k 5 . Several other empir- ical relationships have proposed to evaluate the effective viscosity of a suspension in higher concentration ranges. We cite a few examples as literature review. Rutgers [5] presented an extensive survey of these empirical correlations and has identified discrepancies in reported correlations modeling viscous behavior of slurry. The pa- rameters used in these correlations ϕ m and η are the maximum vol- ume fraction of solids and the intrinsic viscosity respectively. The maximum volume fraction of solids is a physical state or con- dition of any slurry at which the effective viscosity approaches infin- ity and the slurry behaves like a solid. As a general observation, only two extreme conditions can exist for the slurries. The first extreme condition is a suspension without particles, implying the effective vis- cosity is the same as the fluid viscosity. Another extreme condition Powder Technology 219 (2012) 264–270 ⁎ Corresponding author. Tel.: + 91 20 24202122; fax: + 91 20 24280926. E-mail address: mpdeosarkar@yahoo.com (M.P. Deosarkar). 0032-5910/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2011.12.058 Contents lists available at SciVerse ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec