A population balance approach to predict the performance of continuous leaching reactors: Model validation in a pilot plant using a roasted zinc concentrate
Graphical abstract
Introduction
Leaching can contribute up to 30% of the total capital expenditure in a hydrometallurgy plant (Crundwell, 2005). The absence of accurate design methods resulted in excessive capital spending, poor control, and erroneous engineering decision-making. Historically, the determination of kinetic mechanisms has received great attention and it has provided important parameters for leaching design (Elgersma et al., 1992; Lampinen et al., 2015; Lapidus, 1992; Salmi et al., 2010). However, traditional kinetic models, such as the shrinking core model, were developed for monodispersed particles; thus, changes in operational parameters (e.g. the feed particle size distribution) could lead to large errors in plant design (Crundwell and Bryson, 1992). In addition, some of these traditional models have a limited industrial application since they are valid only for low solid/liquid ratios and constant acid concentrations (Doyle et al., 1987; Larba et al., 2013). Therefore, predicting a leaching plant performance has been a challenging task (Crundwell, 1995; Crundwell et al., 2013; Giona et al., 2002; LeBlanc and Fogler, 1987).
In order to overcome these limitations, several mathematical models have been proposed for leaching systems. The Population Balance (PB) has proved to be the most appropriate approach to model polydisperse systems (Crundwell et al., 2013; Dixon, 1996; Elduayen-Echave et al., 2019; Sepulveda and Herbst, 1978). Since it considers that the solid particles have a distribution of properties (e.g. size and composition), it can predicts the influence of these polydisperse particles in the reactors performance (Dixon, 1996, Dixon, 1995; Dorfling et al., 2013; Giona et al., 2002; Rubisov and Papangelakis, 1997). The PB approach has been applied with success to model several leaching systems, such as the continuous pressure leaching of sphalerite (Crundwell and Bryson, 1992) and the bacterial leaching (Crundwell, 2000, Crundwell, 1994a), which have led to excellent agreement between the predictions of the PB models and the data from pilot plants.
Nevertheless, in order to model continuous reactors, the flow patterns and the mixing conditions in the reactors should be accounted in the equations. To achieve this, several approaches are available, such as the Maximum Mixedness and the Segregated Flow (Crundwell, 1994b), which are associated to the two limiting regimes of micromixing. In the first one, all molecules of the same age remain together as they travel through the reactor and are not mixed with molecules of other ages. In other words, the inlet stream (or slurry) is broken into small finite volume elements that remain intact and behave as individual batch reactors during their passage through the reactor (Crundwell, 1994b). This regime corresponds to the Segregated Flow approach. In the second regime, molecules of different ages are completely mixed, on a molecular scale, as they enter the reactor, so all the particles leaving the reactor have the same age distribution and were completely mixed for the duration of their stay in the reactor, which correspond to the Maximum Mixedness approach (Crundwell, 2005; Fogler, 2016).
A theoretically comparison of these approaches has been done by Crundwell (1994b), who has demonstrated that the Segregated Flow and the Maximum Mixedness led to quite different results. Other authors (Crundwell, 2000; Rubisov and Papangelakis, 2000) validated experimentally their PB models, considering only the Maximum Mixedness condition. However, no previous work has compared the leaching data obtained from a pilot plant with the results generated by a PB model using both approaches (Segregated Flow and Maximum Mixedness), which is one of the objectives of this paper. In order to achieve this, the sulfuric leaching of a roasted zinc sulfide concentrate (RZC), in a pilot plant, was investigated and modeled. This system attracts attention since more than 85% of the world's zinc production is through the hydrometallurgical process (Habashi, 1997; Herrero et al., 2010; Hewitt and Wall, 2000), but it has not been comprehensively modeled. Although Doyle et al. (1987) modeled the leaching of zinc oxide, it was in diluted acid solutions and without using of the Population Balance. Balarini (2009) modeled the RZC leaching with the PB model, but no experimental verification was carried out. Other authors developed models for zinc sulfides, such the ones developed by Corriou et al. (1988) and Lampinen et al. (2015), but these models may not be adequate for the RZC leaching, since they work with pressure leaching in autoclaves, which involves other phenomena (e.g. gas-liquid equilibriums); then, quite different kinetics of that studied in present work. Therefore, in a previous work (Coelho et al., 2018), the first BP model for the RZC leaching resulted in an excellent agreement between the experimental data and the developed model, but only the batch leaching was studied.
In this context, the purpose of this paper is to apply the Population Balance to model the continuous leaching of a roasted zinc concentrate in sulfuric acid solutions, using the kinetic data and parameters determined for this system in the latter work (Coelho et al., 2018). Moreover, it is intended to validate this model with experimental data obtained in a pilot plant, and to investigate the flow patterns and mixing conditions in the reactors of this pilot plant by determining its residence time distributions (RTD). This allows comparing experimentally the Maximum Mixedness and the Segregated Flow approaches in the context of the PB modeling. Therefore, the validation of such model will contribute for further understanding of zinc leaching processes providing better techniques for plant design and control; since the PB model is capable to simulate industrial conditions, predicting the effect of several parameters in the reactor performance (e.g. the solid particles polydispersity, the acid consumption, and the feeding flow rate).
Section snippets
Population balance modeling
In order to model the continuous leaching of the roasted zinc concentrate (RZC), it was used a population balance (PB) for solid particles and one mass balance for the leaching agent (sulfuric acid). The kinetic parameters were determined in a previous work (Coelho et al., 2018), in which a PB model for the batch RZC leaching was experimentally validated.
Therefore, it is considered, initially, the general Population Balance for particles in a continuous system, according to Eq. (1) which
Residence time distributions (RTD)
The residence time distribution curves obtained for one single reactor of the pilot plant, for the feeding flow rate (υ0) of 0.21 and 0.41 L.min−1, are shown in Fig. 4. In this figure the RTD are presented as the normalized residence time distribution function (E(θ)) and it was also plotted the simulated RTD curves using the perfect mixer cell model (Ideal CSTR).
From Fig. 4, it can be seen that no bypassing (short-circuiting) occurred in the system, since no sharp early peaks or long tails were
Conclusion
In the present work, the Population Balance was applied to develop a model for the continuous leaching of a roasted zinc concentrate. The flow patterns and mixing conditions in the reactors were incorporated in the model using the Maximum Mixedness and the Segregated Flow approaches.
Experiments using a tracer in the liquid phase demonstrated that the flow patterns in the pilot plant reactors are similar to the ones observed in ideal continuous stirred-tank reactors (CSTR). Therefore, the
Nomenclature
- a
fraction of the inlet flow is exchanged with the stagnant zone (TISEx model)
- AAS
atomic absorption spectroscopy
average rate of particles birth
- C(t)
tracer concentration in the outlet stream
- C0
tracer concentration in the inlet stream
- CA0
molar concentration of the leaching agent (sulfuric acid) in the feed stream
- CAf
molar concentration of the leaching agent (sulfuric acid) in the outlet stream (liquor)
- CFe,f
molar concentration of iron in the outlet stream (liquor)
- CZn,f
molar concentration of zinc in
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001. The authors also acknowledge the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and the Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) for the support.
References (42)
- et al.
Importance of roasted sulphide concentrates characterization in the hydrometallurgical extraction of zinc
Miner. Eng.
(2008) - et al.
Roasted zinc concentrate leaching: population balance modeling and validation
Hydrometallurgy
(2018) - et al.
Thermodynamic and kinetic study of the pressure leaching of zinc sulfide in aqueous sulfuric acid
Hydrometallurgy
(1988) Mathematical modelling of batch and continuous bacterial leaching
Chem. Eng. J. Biochem. Eng. J.
(1994)Micro-mixing in continuous particulate reactors
Chem. Eng. Sci.
(1994)Progress in the mathematical modelling of leaching reactors
Hydrometallurgy
(1995)The leaching number: its definition and use in determining the performance of leaching reactors and autoclaves
Miner. Eng.
(2005)- et al.
The modelling of particulate leaching reactors- the population balance approach
Hydrometallurgy
(1992) - et al.
Dynamics of particle-size distributions in continuous leaching reactors and autoclaves
Hydrometallurgy
(2013) Improved methods for the design of multistage leaching systems
Hydrometallurgy
(1995)
The multiple convolution integral: a new method for modeling multistage continuous leaching reactors
Chem. Eng. Sci.
A new mass-based discretized population balance model for precipitation processes: application to struvite precipitation
Water Res.
Acidic dissolution of zinc ferrite
Hydrometallurgy
A closed-form solution of population-balance models for the dissolution of polydisperse mixtures
Chem. Eng. J.
Hydrometallurgical process development for the production of a zinc sulphate liquor suitable for electrowinning
Miner. Eng.
Kinetic model for direct leaching of zinc sulfide concentrates at high slurry and solute concentration
Hydrometallurgy
Citric acid as an alternative lixiviant for zinc oxide dissolution
Hydrometallurgy
Measurements of liquid phase residence time distributions in a pilot-scale continuous leaching reactor using radiotracer technique
Appl. Radiat. Isot.
Solution techniques for population balance equations as applied to heterogeneous aqueous processes in stirred tank reactors
Comput. Chem. Eng.
Sulphuric acid pressure leaching of laterites - a comprehensive model of a continuous autoclave
Hydrometallurgy
Mechanistic modelling of kinetics and mass transfer for a solid–liquid system: leaching of zinc with ferric iron
Chem. Eng. Sci.
Cited by (3)
A Mechanism-Based Semisupervised Online pH Estimation Approach for a Leaching Process
2022, IEEE Transactions on Instrumentation and MeasurementAdaptive process for improving leaching efficiency of germanium from secondary zinc oxide
2021, International Journal of Chemical Reactor Engineering