A new group contribution method for mineral concentration processes

doi:10.1016/j.compchemeng.2014.12.009

Computers & Chemical Engineering

Volume 74, 4 March 2015, Pages 28-33

https://doi.org/10.1016/j.compchemeng.2014.12.009 Get rights and content

Highlights

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A group contribution model to predict the behavior of mineral concentration circuits is presented.
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The number of process groups is 143, which makes possible to represent over 274 million circuits.
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The model can estimate the recovery of concentration circuits with a maximum of 9 stages.
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The measured absolute error is 0.022 and the maximum error is 0.081.

Abstract

In this work, a group contribution model to predict the behavior of mineral concentration circuits is presented. The new model is an expansion and modification of an existing model in the literature (Sepúlveda et al., 2014). The modifications extend the number of process groups from 35 to 143, which makes it possible to extend the number of concentration circuits that can be represented from 1492 to over 274 million circuits and to increase the maximum number of stages from 6 to 9. The errors observed between the fitting and the prediction results of concentration circuits that were not included in the fitting verifies that the new model could be extremely useful in the design of mineral concentration circuits.

Introduction

Group contribution models assume that a certain property depends on the sum of the contributions made by structural groups. In this way, it is possible to estimate properties of many systems based on a reduced number of groups that constitute those systems. The primary application of these models is in designing chemical products that have the ability to form molecules based on groups of atoms. Additionally, these models have also been used to design separation processes based on fractional distillation (d’Anterroches and Gani, 2005) and recently to estimate the global recovery of concentration circuits (Sepúlveda et al., 2014). In this last work, a model was presented to estimate the recovery of 1492 circuits, which can incorporate 2–6 process stages, based on 35 process groups. To fit the model, data from 46 circuits were used. In the present work, this model is modified and extended to estimate the recovery of over 274 million concentration circuits, which can incorporate 2–9 concentration stages, based on 143 process groups. To fit the model, 293 concentration circuits were used. In addition to these advantages, the proposed contribution model includes circuit designs used in the process industry, the adjusted values α_i and β_i do not exhibit inconsistencies, and the model can relate the circuits from the database according to the number of process stages that are used.

Section snippets

Process groups

It is assumed that each concentration stage has two outlet streams: a concentrate and a tail. Fig. 1 shows a general diagram of the considered alternatives. The stages, rougher (R), cleaner₁ (C₁), cleaner₂ (C₂), and cleaner₃ (C₃), are defined as follows. Stage R processes the circuit feed, whose concentrate could be the final product or the feed to stage C₁. The concentrate generated by this last stage could be the final product or the feed to stage C₂. The concentrate generated in stage C₂

Recovery models

To estimate the circuit recovery, two models are proposed, which depend on the recovery values in the rougher stage (Sepúlveda et al., 2014). For high recoveries (0.63–1) and low recoveries (0.1–0.37) in the rougher stage, the following model is proposed: $R c_{j} = \frac{\sum_{i = 1}^{n} Λ_{i, j}}{\sum_{k = 1}^{9} r_{k} N_{T} + \sum_{k = 1}^{3} c_{k} N_{C} + \sum_{k = 1}^{2} s_{k} N_{S} + \sum_{k = 1}^{3} c s_{k} N_{C S}}$ where Rc_j is the recovery of species j in the circuit; Λ_i,j is the contribution of group i; N_T is the total number of groups in the circuit; N_C is the total number of cleaner stages in the

Fitting the models

The group contribution model was fitted using CONOPT-GAMS. The results are shown in Table 2, Table 3.

The measured absolute error (MAE, Eq. (4)) was used to quantify the difference between the predicted recovery and the recovery obtained by mass balance. $M A E = \frac{1}{N M} \sum_{i = 1}^{N} \sum_{l = 1}^{M} |R c_{i, l} - R b_{i, l}|$ where Rc_i,l is the recovery estimated by using group contributions, Rb_i,l is the recovery obtained from the mass balance, N is the number of circuits, and M is the number of cases. Table 4 shows the MAE obtained when

Example and validation

As an example, the recovery of two circuits that are not present in the database used to fit the model is estimated. Consider the circuits shown in Fig. 2, Fig. 3. The circuit of Fig. 2 can be partitioned into the groups [RC₁S₁], [S₁SC₁₁S₂], [S₂SC₁₁W], [C₁PCS₂₁], [SC₁₁CS₂₁S₁], and $[C S_{21} C_{1} S C_{11}]$ , and the circuit of Fig. 3 can be partitioned into [RC₁S₁], [C₁PCS₁₁], [S₁C₁W], and [CS₁₁PS₁]. Applying Eq. (1) the recoveries for the low and high ranges can be obtained: $R c_{1} = Λ_{R C_{1} S_{1}} + Λ_{S_{1} S C_{11} S_{2}} + Λ_{s_{2} S C_{11} W} + Λ_{C_{1} P C S}$

Conclusions

A group contribution model is presented in this work, which exhibits improvements with respect to the model by Sepúlveda et al. (2014) because it can estimate the recovery of species for a much greater number of concentration circuits and incorporates circuit designs that are used in industry. The model is based on the fact that the developed contribution model allows establishing relationships according to the number of stages of the circuits from the database, which then allows the circuit

Acknowledgments

Financial support from CONICYT (Fondecyt 1120794), CICITEM (R10C1004) and the Antofagasta Regional Government is gratefully acknowledged.

References (4)

L. d’Anterroches et al.
Group contribution based process flowsheet synthesis, design and modeling
Fluid Phase Equilib
(2005)
F. Lucay et al.
Separation circuits analysis and design using sensitivity analysis
Comput Aided Chem Eng
(2011)

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NoteA new group contribution method for mineral concentration processes