Dynamic modelling and predictive control for the sequential collaborative reactors of cobalt removal process under time‐varying conditions

Wang, Yalin; Xue, Yongfei; Huang, Kaimin; Cen, Lihui

doi:10.1002/cjce.23563

Cited by 4 publications

(10 citation statements)

References 34 publications

(49 reference statements)

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“…Actually, the four reactors interact, and the cobalt removal process can be regarded as a system with multiple interacting CSTR models; thus, it is necessary to study the synergistic relationships among the four reactors. In a specific time interval, the mass of zinc powder in reactor i can be calculated according to Equation (8) [27] :…”

Section: Scstr Model Of Cobalt Removal Processmentioning

confidence: 99%

“…orp , e eq,j , R, T c , l 1 , l 2 , l 3 , l 4 , and the parameters to be estimated are θ 2 ¼ ½f i j , E e , γ i j , p i j , q i j , χ i , δ, η i . Sun et al [10] estimated the values of f i j , E e , γ i j , p i j , and q i j , and Wang et al [27] reported δ and η i to be 2.9% and 1%, respectively. Therefore, the remaining unknown parameters are the mass-reaction surface coefficients χ i .…”

Section: Parameter Estimation Based On the Augmented State Equation A...mentioning

confidence: 99%

“…According to the mechanism analysis, the area in which cobalt ions are deposited is the reaction surface area, which is not the same as the total surface area of the zinc powder. [ 27 ] Considering the physical properties of zinc powder and assuming that the zinc powder particles are spherical and the reaction surface area is proportional to the mass of zinc powder in the solution:

S^{i} = χ^{i} \cdot W^{i}

where

χ^{i}

is the proportionality coefficient between

S^{i}

and

W^{i}

, which is called the mass‐reaction surface coefficient, and

W^{i}

is the mass of zinc powder in the solution.…”

Section: Analysis Of Cobalt Removal In Zinc Hydrometallurgymentioning

confidence: 99%

i

can be calculated according to Equation () [ 27 ] :

{\overset{W}{true}}^{i} (t) = {\overset{W}{true}}^{i, a} (t) + {\overset{W}{true}}^{i, b} (t) - {\overset{W}{true}}^{i, c} (t) - {\overset{W}{true}}^{i, d} (t) - {\overset{W}{true}}^{i, e} (t)

where

{\overset{W}{true}}^{i} (t)

{\overset{W}{true}}^{i, a} (t)

, and

{\overset{W}{true}}^{i, b} (t)

represent the zinc powder accumulated in reactor

i

, at the inlet of reactor

i

, and added to reactor respectively;

{\overset{W}{true}}^{i, c} (t)

is the outlet zinc powder of reactor

i

; and

{\overset{W}{true}}^{i, d} (t)

and

{\overset{W}{true}}^{i, e} (t)

represent the zinc powder participating in main Reactions ()–() and side Reactions () and () in reactor

i

, respectively.…”

Section: Dynamic Modelling Of Synergistic Reactors For the Cobalt Rem...mentioning

confidence: 99%

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Dynamic synergistic modelling for cobalt removal process in zinc hydrometallurgy and the research of parameter estimation based on unscented Kalman filter

Wang

Tang

et al. 2023

Can J Chem Eng

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The cobalt removal process with arsenic salt of zinc hydrometallurgy has serious non‐linearity, uncertainty, and mutual coupling. Its accurate dynamic modelling has always been a challenging problem. On the basis of in‐depth analysis of cobalt removal process and reaction mechanism, considering the cascade relationship between the reactors, a dynamic synergistic continuously stirred tank reactor (SCSTR) mechanism model of the cobalt removal process was constructed. Aiming at the unknown parameters in the SCSTR model, the idea of the Kalman filter was introduced, and the unknown parameters were characterized as unknown states; a method of estimating the unknown model parameters was developed using the augmented state equation and the unscented Kalman filter (UKF) algorithm. Simulation results with industrial data of a zinc smeltery showed that the parameter estimation model has high accuracy, and the estimated parameters can be used in the SCSTR model. An intensive simulation analysis of the dynamic characteristics of the complete SCSTR model was carried out to verify the influence of different input disturbances on the output ion concentration of each reactor, which demonstrated the excellent dynamic performance and potential of the model. Ultimately, according to the industrial calculation analysis, the SCSTR model has a guiding effect on the addition of zinc powder in the reactors, overcomes the blindness in the production process, and provides a momentous basis for the optimization control of the cobalt removal process.

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Section: Scstr Model Of Cobalt Removal Processmentioning

confidence: 99%

Section: Parameter Estimation Based On the Augmented State Equation A...mentioning

confidence: 99%

S^{i} = χ^{i} \cdot W^{i}

where

χ^{i}

is the proportionality coefficient between

S^{i}

and

W^{i}

, which is called the mass‐reaction surface coefficient, and

W^{i}

is the mass of zinc powder in the solution.…”

Section: Analysis Of Cobalt Removal In Zinc Hydrometallurgymentioning

confidence: 99%

i

can be calculated according to Equation () [ 27 ] :

{\overset{W}{true}}^{i} (t) = {\overset{W}{true}}^{i, a} (t) + {\overset{W}{true}}^{i, b} (t) - {\overset{W}{true}}^{i, c} (t) - {\overset{W}{true}}^{i, d} (t) - {\overset{W}{true}}^{i, e} (t)

where

{\overset{W}{true}}^{i} (t)

{\overset{W}{true}}^{i, a} (t)

, and

{\overset{W}{true}}^{i, b} (t)

represent the zinc powder accumulated in reactor

i

, at the inlet of reactor

i

, and added to reactor respectively;

{\overset{W}{true}}^{i, c} (t)

is the outlet zinc powder of reactor

i

; and

{\overset{W}{true}}^{i, d} (t)

and

{\overset{W}{true}}^{i, e} (t)

represent the zinc powder participating in main Reactions ()–() and side Reactions () and () in reactor

i

, respectively.…”

Section: Dynamic Modelling Of Synergistic Reactors For the Cobalt Rem...mentioning

confidence: 99%

See 2 more Smart Citations

Dynamic synergistic modelling for cobalt removal process in zinc hydrometallurgy and the research of parameter estimation based on unscented Kalman filter

Wang

Tang

et al. 2023

Can J Chem Eng

View full text Add to dashboard Cite

show abstract

“…A isoterma de Langmuir nesse caso mostrou um processo reversível, onde os processos de adsorção e dessorção pode ser controlada pela concentração hidrogeniônica empregada no meio reacional. Democrática do Congo, onde nunca houve uma transição pacífica de poder e o trabalho infantil ainda é usado em partes do setor de mineração [5][6][7] .…”

Section: Dedicatóriaunclassified

Estudo da extração hidrometalúrgica de matais de transição com nanopartículas superparamagnéticas funcionalizadas

Kaid¹

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Hydrometallurgical processing of strategic elements such as copper and cobalt is a subject of great relevance because of the economical and environmental issues involved. In this thesis, the interaction of superparamagnetic nanoparticles functionalized with ethylenediamine groups with transition metal ions, such as copper(II) and cobalt(II), has been investigated from the physico-chemical point of view, focusing on the adsorption kinetics and complexation equilibrium involved, aiming the understanding of magnetic nanohydrometallurgy applied to those systems. Also investigated was the influence of possible variables, such as the counter ions in solution and the adsorption selectivity observed in the comparison of different metal ions. Special emphasis was applied to the construction of adsorption isotherms using analytical methods (EDX) and zeta potentials measured in situ in aqueous solution. The proposed models in both cases, provided a critical view of the methodologies, showing the contrasts and the special role of the solvodynamic effects associated with the zeta potentials, including the formation of ion pairs at the nanoparticles slipping plane. The possible application of the systems in the development of magnetic affinity chromatography has also been demonstrated in the selective adsorption of mioglobin by the superparamagnetic nanoparticles containing copper ions. The Langmuir isotherm revealed a reversible process, in which the adsorption and desorption steps can be controlled by the pH of the reactional media.

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Distributed nonlinear model predictive control for cobalt removal process in zinc hydrometallurgy considering error compensation modelling

Wang

Tang

et al. 2023

Can J Chem Eng

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To address the strong nonlinearity, uncertainty, and mutual coupling in the cobalt removal process of zinc hydrometallurgy, an algorithm based on an improved genetic algorithm (GA) backpropagation (BP) neural network combined with distributed nonlinear model predictive control (NMPC) is proposed. This method was applied to improve the quality of the purification solution and reduce the consumption of zinc powder, overcoming the challenges faced by the current cobalt removal process. First, a synergistic continuously stirred tank reactor (SCSTR) model was constructed for the dynamic cobalt removal process. Second, aiming at the problem that a single SCSTR model has difficulty describing the process accurately, based on the highly nonlinear mapping ability of data‐driven models, a method that organically integrates the SCSTR model and an error compensation model based on the GA‐BP neural network was proposed (GA‐BP‐SCSTR) to provide a more accurate online prediction of the process indicators. Then, a distributed NMPC architecture was developed using the GA‐BP‐SCSTR model, control vector parameterization (CVP) technique, and sequential quadratic programming (SQP) algorithm to achieve the coordinated control of the cobalt removal process. Finally, simulation results of an actual site showed that the prediction accuracy of the GA‐BP‐SCSTR model was higher than those of other models. The proposed predictive control method can maintain the outlet cobalt ion concentrations at the set values while achieving accurate control of the zinc powder addition. This approach can provide guidance for on‐site production and eliminate the blindness of manual experience control.

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Dynamic modelling and predictive control for the sequential collaborative reactors of cobalt removal process under time‐varying conditions

Cited by 4 publications

References 34 publications

Dynamic synergistic modelling for cobalt removal process in zinc hydrometallurgy and the research of parameter estimation based on unscented Kalman filter

Dynamic synergistic modelling for cobalt removal process in zinc hydrometallurgy and the research of parameter estimation based on unscented Kalman filter

Estudo da extração hidrometalúrgica de matais de transição com nanopartículas superparamagnéticas funcionalizadas

Distributed nonlinear model predictive control for cobalt removal process in zinc hydrometallurgy considering error compensation modelling

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