Spatiotemporal distribution model for zinc electrowinning process and its parameter estimation
|
摘要
This paper focuses on the distributed parameter modeling of the zinc electrowinning process(ZEWP)to reveal the spatiotemporal distribution of concentration of zinc ions(CZI)and sulfuric acid(CSA)in the electrolyte.Considering the inverse diffusion of such ions in the electrolyte,the dynamic distribution of ions is described by the axial dispersion model.A parameter estimation strategy based on orthogonal approximation has been proposed to estimate the unknown parameters in the process model.Different industrial data sets are used to test the effectiveness of the spatiotemporal distribution model and the proposed parameter estimation approach.The results demonstrate that the analytical model can effectively capture the trends of the electrolysis reaction in time and thus has the potential to implement further optimization and control in the ZEWP.
This paper focuses on the distributed parameter modeling of the zinc electrowinning process(ZEWP)to reveal the spatiotemporal distribution of concentration of zinc ions(CZI)and sulfuric acid(CSA)in the electrolyte.Considering the inverse diffusion of such ions in the electrolyte,the dynamic distribution of ions is described by the axial dispersion model.A parameter estimation strategy based on orthogonal approximation has been proposed to estimate the unknown parameters in the process model.Different industrial data sets are used to test the effectiveness of the spatiotemporal distribution model and the proposed parameter estimation approach.The results demonstrate that the analytical model can effectively capture the trends of the electrolysis reaction in time and thus has the potential to implement further optimization and control in the ZEWP.
This paper focuses on the distributed parameter modeling of the zinc electrowinning process(ZEWP)to reveal the spatiotemporal distribution of concentration of zinc ions(CZI)and sulfuric acid(CSA)in the electrolyte.Considering the inverse diffusion of such ions in the electrolyte,the dynamic distribution of ions is described by the axial dispersion model.A parameter estimation strategy based on orthogonal approximation has been proposed to estimate the unknown parameters in the process model.Different industrial data sets are used to test the effectiveness of the spatiotemporal distribution model and the proposed parameter estimation approach.The results demonstrate that the analytical model can effectively capture the trends of the electrolysis reaction in time and thus has the potential to implement further optimization and control in the ZEWP.
引文
[1]ZHANG Bin,YANG Chun-hua,ZHU Hong-qiu,LI Yong-gang,GUIWei-hua.Kinetic modeling and parameter estimation for competing reactions in copper removal process from zinc sulfate solution[J].Industrial&Engineering Chemistry Research,2013,52(48):17074-17086.
[2]SUN Bei,GUI Wei-hua,WU Tie-bin,WANG Ya-lin,YANGChun-hua.An integrated prediction model of cobalt ion concentration based on oxidation-reduction potential[J].Hydrometallurgy,2013,140:102-110.
[3]HERRERO D,ARIAS P L,GüEMEZ B,BARRIO V L,CAMBRAJ F,REQUIES J.Hydrometallurgical process development for the production of a zinc sulphate liquor suitable for electrowinning[J].Mineral Engineering,2010,23(6):511-517.
[4]BARTON G W,SCOTT A C.Scale-up effects in modelling a full-size zinc electrowinning cell[J].Journal of Applied Electrochemistry,1992,22(8):687-692.
[5]MAHON M,PENG S,ALFANTAZI A.Application and optimization studies of a zinc electrowinning process simulation[J].Canadian Journal of Chemical Engineering,2014,92:633-642.
[6]WANG Ya-lin,Gui Wei-hua,YANG Chun-hua,HUANG Tai-song.Intelligent modeling and optimization on time-sharing power dispatching system for electrolytic zinc process[J].Transactions of Nonferrous Metals Society of China,2000,10(4):561-565.
[7]BAHRAM B,JAVAD M.Statistical evaluation and optimization of zinc electrolyte hot purification process by Taguchi method[J].Journal of Central South University,2015,22(6):2066-2072.
[8]YANG Chun-hua,DECONINCK G,GUI Wei-hua,LI Yong-gang.An optimal power-dispatching system using neural networks for the electrochemical process of zinc depending on varying prices of electricity[J].IEEE Transactions on Neural Network,2002,13(1):229-236.
[9]BARTON G W,SCOTT A C.Industrial applications of a mathematical model for the zinc electrowinning process[J].Journal of Applied Electrochemistry,1994,24(5):377-383.
[10]MAHON M,WASIK L,ALFANTAZI A.Development and implementation of a zinc electrowinning process simulation[J].Journal of Applied Electrochemistry,2012,159(8):D486-D492.
[11]ZHANG Qi-bo,HUA Yi-xin,DONG Tie-guang,ZHOU Dan-gui.Effects of temperature and current density on zinc electrodeposition from acidic sulfate electrolyte with H2SO4 as additive[J].Journal of Applied Electrochemistry,2009,39(8):1207-1216.
[12]GUI Wei-hua,YANG Chun-hua,CHEN Xiao-fang,WANG Ya-lin.Modeling and optimization problems and challenges arising in nonferrous metallurgical processes[J].Acta Automatic Sinica,2013,39(3):197-207.
[13]DENG Shi-jun,YANG Chun-hua,LI Yong-gang,ZHU Hong-qiu.On-line prediction model for concentrations of zinc ion and sulfuric acid in zinc electrowinning process[J].Chinese Journal of Chemical Engineering,2015,66(7):2588-2594.
[14]GUI Wei-hua,ZHANG Mei-ju,YANG Chun-hua,LI Yong-gang.Energy consumption optimization of zinc electrolysis process based on hybrid particle swarm algorithm[J].Control Engineering of China,2009,16(6):748-751.
[15]CHARTON S,DUHAMET J,BORDA G,ODE D.Axial dispersion in pulsed disk and doughnut columns:A unified law[J].Chemical Engineering Science,2012,75(0):468-477.
[16]LI Han-xiong,QI Chen-kun.Modeling of distributed parameter systems for applications-A synthesized review from time-space separation[J].Journal of Process Control,2010,20(8):891-901.
[17]BONIS I,XIE Wei-guo,THEODOROPOULOS C.Multiple model predictive control of dissipative pde systems[J].IEEE Transactions on Control Systems Technology,2014,22(3):1206-1214.
[18]XIANG Xiu-qiao,ZHOU Jiang-zhong,LI Mo,LUO Zhi-meng,LIChao-shun.Improved algorithm about NSFOT[J].Applied Mathematics&Computation,2009,215(3):881-888.
[19]STANKOVIC A M,LEV-ARI H,PERISIC M M.Analysis and implementation of model-based linear estimation of dynamic phasors[J].IEEE Transactions on Power System,2004,19(4):1903-1910.
[20]ABBASBANDY S,KAZEM S,ALHUTHALI M S,ALSULAMI HH.Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation[J].Applied Mathematics&Computation,2015,266:31-40.
[21]LEPIK U.Solving fractional integral equations by the Haar wavelet method[J].Applied Mathematics&Computation,2009,214(2):468-478.
[22]LI Yuan-lu,SUN Ning.Numerical solution of fractional differential equations using the generalized block pulse operational matrix[J].Computers&Mathematics with Applications,2011,62(3):1046-1054.
[23]MALEKNEJAD L,SOHRABI S,BARAJI B.Application of2D-BPFs to nonlinear integral equations[J].Communications in Nonlinear Science&Numerical Simulation,2010,15(3):527-535.
[24]YU Shou-yi,CAO Yue-bin,ZHOU Xuan.Parameter identification for vertical quench furnace control system based on orthogonal function[J].Control Engineering of China,2009,16(3):251-253.
[25]PAN Jun-li,WEN Yue-hua,CHENG Jie,PAN Jun-qing,BAIZhang-li,YANG Yu-sheng.Zinc deposition and dissolution in sulfuric acid onto a graphite-resin composite electrode as the negative electrode reactions in acidic zinc-based redox flow batteris[J].Journal of Applied Electrochemistry,2013,43:541-551.
[26]YU Jiang-xian,YANG Han-xi,AI Xin-ping,CHEN Yong-yan.Effect of anions on the zinc electrodeposition onto glassy-carbon electrode[J].Russian Journal of Electrochemistry,2002,38(3):321-325.
[27]SUNG BAE KIM,LEE Y.Diffusion of sulfuric acid within lignocellulosic biomass particles and its impact on dilute-acid pretreatment[J].Bioresource Technology,2002,83(2):165-171.
[28]LI Yong-gang,GUI Wei-hua,TEO KOK LAY,ZHU Hong-qiu,CHAI Qin-qin.Optimal control for zinc solution purification based on interacting CSTR models[J].Journal of Process Control,2012,22(10):1878-1889.
[2]SUN Bei,GUI Wei-hua,WU Tie-bin,WANG Ya-lin,YANGChun-hua.An integrated prediction model of cobalt ion concentration based on oxidation-reduction potential[J].Hydrometallurgy,2013,140:102-110.
[3]HERRERO D,ARIAS P L,GüEMEZ B,BARRIO V L,CAMBRAJ F,REQUIES J.Hydrometallurgical process development for the production of a zinc sulphate liquor suitable for electrowinning[J].Mineral Engineering,2010,23(6):511-517.
[4]BARTON G W,SCOTT A C.Scale-up effects in modelling a full-size zinc electrowinning cell[J].Journal of Applied Electrochemistry,1992,22(8):687-692.
[5]MAHON M,PENG S,ALFANTAZI A.Application and optimization studies of a zinc electrowinning process simulation[J].Canadian Journal of Chemical Engineering,2014,92:633-642.
[6]WANG Ya-lin,Gui Wei-hua,YANG Chun-hua,HUANG Tai-song.Intelligent modeling and optimization on time-sharing power dispatching system for electrolytic zinc process[J].Transactions of Nonferrous Metals Society of China,2000,10(4):561-565.
[7]BAHRAM B,JAVAD M.Statistical evaluation and optimization of zinc electrolyte hot purification process by Taguchi method[J].Journal of Central South University,2015,22(6):2066-2072.
[8]YANG Chun-hua,DECONINCK G,GUI Wei-hua,LI Yong-gang.An optimal power-dispatching system using neural networks for the electrochemical process of zinc depending on varying prices of electricity[J].IEEE Transactions on Neural Network,2002,13(1):229-236.
[9]BARTON G W,SCOTT A C.Industrial applications of a mathematical model for the zinc electrowinning process[J].Journal of Applied Electrochemistry,1994,24(5):377-383.
[10]MAHON M,WASIK L,ALFANTAZI A.Development and implementation of a zinc electrowinning process simulation[J].Journal of Applied Electrochemistry,2012,159(8):D486-D492.
[11]ZHANG Qi-bo,HUA Yi-xin,DONG Tie-guang,ZHOU Dan-gui.Effects of temperature and current density on zinc electrodeposition from acidic sulfate electrolyte with H2SO4 as additive[J].Journal of Applied Electrochemistry,2009,39(8):1207-1216.
[12]GUI Wei-hua,YANG Chun-hua,CHEN Xiao-fang,WANG Ya-lin.Modeling and optimization problems and challenges arising in nonferrous metallurgical processes[J].Acta Automatic Sinica,2013,39(3):197-207.
[13]DENG Shi-jun,YANG Chun-hua,LI Yong-gang,ZHU Hong-qiu.On-line prediction model for concentrations of zinc ion and sulfuric acid in zinc electrowinning process[J].Chinese Journal of Chemical Engineering,2015,66(7):2588-2594.
[14]GUI Wei-hua,ZHANG Mei-ju,YANG Chun-hua,LI Yong-gang.Energy consumption optimization of zinc electrolysis process based on hybrid particle swarm algorithm[J].Control Engineering of China,2009,16(6):748-751.
[15]CHARTON S,DUHAMET J,BORDA G,ODE D.Axial dispersion in pulsed disk and doughnut columns:A unified law[J].Chemical Engineering Science,2012,75(0):468-477.
[16]LI Han-xiong,QI Chen-kun.Modeling of distributed parameter systems for applications-A synthesized review from time-space separation[J].Journal of Process Control,2010,20(8):891-901.
[17]BONIS I,XIE Wei-guo,THEODOROPOULOS C.Multiple model predictive control of dissipative pde systems[J].IEEE Transactions on Control Systems Technology,2014,22(3):1206-1214.
[18]XIANG Xiu-qiao,ZHOU Jiang-zhong,LI Mo,LUO Zhi-meng,LIChao-shun.Improved algorithm about NSFOT[J].Applied Mathematics&Computation,2009,215(3):881-888.
[19]STANKOVIC A M,LEV-ARI H,PERISIC M M.Analysis and implementation of model-based linear estimation of dynamic phasors[J].IEEE Transactions on Power System,2004,19(4):1903-1910.
[20]ABBASBANDY S,KAZEM S,ALHUTHALI M S,ALSULAMI HH.Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation[J].Applied Mathematics&Computation,2015,266:31-40.
[21]LEPIK U.Solving fractional integral equations by the Haar wavelet method[J].Applied Mathematics&Computation,2009,214(2):468-478.
[22]LI Yuan-lu,SUN Ning.Numerical solution of fractional differential equations using the generalized block pulse operational matrix[J].Computers&Mathematics with Applications,2011,62(3):1046-1054.
[23]MALEKNEJAD L,SOHRABI S,BARAJI B.Application of2D-BPFs to nonlinear integral equations[J].Communications in Nonlinear Science&Numerical Simulation,2010,15(3):527-535.
[24]YU Shou-yi,CAO Yue-bin,ZHOU Xuan.Parameter identification for vertical quench furnace control system based on orthogonal function[J].Control Engineering of China,2009,16(3):251-253.
[25]PAN Jun-li,WEN Yue-hua,CHENG Jie,PAN Jun-qing,BAIZhang-li,YANG Yu-sheng.Zinc deposition and dissolution in sulfuric acid onto a graphite-resin composite electrode as the negative electrode reactions in acidic zinc-based redox flow batteris[J].Journal of Applied Electrochemistry,2013,43:541-551.
[26]YU Jiang-xian,YANG Han-xi,AI Xin-ping,CHEN Yong-yan.Effect of anions on the zinc electrodeposition onto glassy-carbon electrode[J].Russian Journal of Electrochemistry,2002,38(3):321-325.
[27]SUNG BAE KIM,LEE Y.Diffusion of sulfuric acid within lignocellulosic biomass particles and its impact on dilute-acid pretreatment[J].Bioresource Technology,2002,83(2):165-171.
[28]LI Yong-gang,GUI Wei-hua,TEO KOK LAY,ZHU Hong-qiu,CHAI Qin-qin.Optimal control for zinc solution purification based on interacting CSTR models[J].Journal of Process Control,2012,22(10):1878-1889.