EP2212751B1 - Method and means for controlling an electrolysis cell - Google Patents

Method and means for controlling an electrolysis cell Download PDF

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EP2212751B1
EP2212751B1 EP08852151.3A EP08852151A EP2212751B1 EP 2212751 B1 EP2212751 B1 EP 2212751B1 EP 08852151 A EP08852151 A EP 08852151A EP 2212751 B1 EP2212751 B1 EP 2212751B1
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future
accordance
process variable
control
prediction
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EP2212751A4 (en
EP2212751A1 (en
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Steinar KOLÅS
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Norsk Hydro ASA
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    • C—CHEMISTRY; METALLURGY
    • C25—ELECTROLYTIC OR ELECTROPHORETIC PROCESSES; APPARATUS THEREFOR
    • C25C—PROCESSES FOR THE ELECTROLYTIC PRODUCTION, RECOVERY OR REFINING OF METALS; APPARATUS THEREFOR
    • C25C3/00—Electrolytic production, recovery or refining of metals by electrolysis of melts
    • C25C3/06—Electrolytic production, recovery or refining of metals by electrolysis of melts of aluminium
    • C25C3/20—Automatic control or regulation of cells

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  • the present invention relates to a method and means for controlling an electrolysis cell for production of aluminium.
  • the invention applies a non-linear model predictive control system (NMPC), where a model of the process is applied to predict the future behaviour of the process. Further, an estimator function is applied to produce estimates of process data in present time, based upon historical data.
  • NMPC non-linear model predictive control system
  • the benefits of the presented invention are that one is able to control the electrolysis cell such that the process variations are reduced. By that on is able to operate the electrolysis cell closer to operational targets and process limits, and to achieve lower emission to the surroundings combined with stable and more efficient production.
  • NMPC for controlling industrial processes is for instance known from the oil refinery industry, where this type of control has been widely applied.
  • EP 0211 924 discloses a method of controlling the alumina feed to reduction cells for producing aluminium. There is employed an adaptive control with parameter estimation and controller calculation based upon the separation theorem. As a process model there is used a linear model having two inputs and one output.
  • US patent 4,814;050 is representative for the state of the art linear controller that includes the use of an estimator that employs two sets of equations, namely, a time update algorithm that contains a dynamic model of the alumina mass balance of the cell and provides estimates of alumina concentration, and a measurement algorithm that uses a process feedback variable from the cell to modify the alumina estimate.
  • US 6 609 119 B1 relates to a neural control logic scheme based on prediction and pattern recognition techniques to control electrochemical processes such as aluminium electrolytic cells.
  • the predictive capacity of feedforward neural networks is used to predict the future values of decision variables to be used by the cell's control logic, enabling the control logic to apply anticipated actions to cells in different conditions, thus avoiding anode effects and improving cell stability.
  • the pattern recognition capacity of LVQ-type neural networks is used to provide a closed-loop control structure to the feeding of the cell as a function of cell resistance, alumina concentration and cell condition.
  • Controlling the alumina reducing process is challenging due to non-linear process characteristics, coupled mass and energy balance and few measurements.
  • bath temperature-acidity correlation It is well known in the aluminium community that both AlF 3 additions and the bath temperature have an influence on the acidity due to variation in side ledge thickness.
  • the relationship between the bath temperature and the acidity is referred to as bath temperature-acidity correlation, or simply the correlation line.
  • one (mathematical) model represents a theoretical representation of the Aluminium Electrolysis Cell.
  • the modeling methodology in the present invention is based on First Principle. This means that the model describing the process is based on fundamental understanding of the physics that describe heat and mass transfer relations and basic physical property relations. Modeling by First Principle usually takes the form of non-linear differential equations, and hence results in a non-linear model.
  • First Principle the mass and energy balance of the cell is described in such a manner that the time behavior of a chosen set of process variables and the relationship between them can be determined (or estimated).
  • the chosen set of process variable modeled is typical the side ledge thickness, mass of liquid bath and metal, concentration and mass of AlF 3 , concentration and mass of Al 2 O 3 , mass of sludge, bath temperature, cathode temperature, various heat flows, bath and metal height and pseudo resistance, to mention the most important ones.
  • the model represents an idealized framework, and will to a certain degree deviate from the physical process due to model uncertainty.
  • estimation techniques known as Kalmanfiltering is used.
  • Kalman filter state estimation is as such known from instance US patent 6757579 .
  • Kalman filter state estimation for the aluminium reduction cells is known from " Estimation of states in aluminium reduction cells applying extended kalman filtering algorithms together with a nonlinear dynamic model and discrete measurements" T.Saksvikronning, K.Vee, E.Gran (Light Metals 1976, pp. 275-286 )
  • the model uncertainty is adjusted for based on the information available in the measurements of process variables (a sub-set of all the process variables) and the process inputs.
  • the measurements are typically the pseudo resistance, bath temperature, cathode temperature, liquid bath and metal height and the concentration of AlF 3 .
  • the process inputs are typically the line current, added masses, anode movements and events (anode effect, metal tap, liquid bath tap/addition, anode change).
  • the outcome of the model adjustment is a more accurate estimation of the chosen set of process variables at the given time instance.
  • the Hall-Heroult process for aluminium production is the most used method by which aluminium is produced industrially today.
  • Liquid aluminium is produced by the electrolytic reduction of alumina ( Al 2 O 3 ) dissolved in an electrolyte, referred to as bath, which mainly consists of cryolite ( Na 3 AlF 6 ) .
  • bath which mainly consists of cryolite ( Na 3 AlF 6 ) .
  • a sketch of the alumina reduction cell is shown in Figure 1 .
  • alumina reduction cell hereafter referred to as the cell, one (S ⁇ derberg) or several (Prebake) carbon anodes are dipped into the bath. The alumina is consumed electrochemically at the anode.
  • the carbon anode is consumed during the process (theoretically 333 kg C/t Al).
  • the lower part of the cell, the cathode consists of a steel shell lined with refractory and thermal insulation. A pool of liquid aluminium is formed on top of the carbon bottom.
  • the cathode in the electrochemically sense, is the interface between the liquid aluminium and the bath, described by AlF 3 + 3 Na + + 3 e ⁇ Al + 3 NaF (2) and the total cell reaction becomes
  • Pure bath Na 3 AlF 6
  • the bath composition in a cell may typically be 6-13 [wt%] AlF 3 , 4-6 [wt%] CaF 2 , and 2-4 [wt%] Al 2 O 3 .
  • Lowering the liquidus temperature makes it possible to operate the cell at a lower bath temperature, but at the expense of reduced solubility of Al 2 O 3 in the bath, demanding good Al 2 O 3 control. It should be mentioned that if the concentration of Al 2 O 3 gets too low (less than approx.
  • anode effect the cell enters a state called anode effect.
  • anode effect the cell voltage increases from the normal 4-4.5V up to 20-50V.
  • Anode effect is a highly unwanted state, not only because it represents a waste of energy and a disturbance of the energy balance, but also because greenhouse gases ( CF 4 and C 2 F 6 ) are produced at the anode. Very often the anode effect requires a manual intervention of an operator.
  • the bath temperature during normal cell operation is between 940 °C and 970 °C.
  • the bath is not consumed during the electrolytic process, but some is lost, mainly during vaporization.
  • the vapour mainly consists of NaAlF 4 .
  • some bath is lost by entrainment of small droplets, and water present in the alumina feed reacts to form HF.
  • the gas is collected and cleaned in a gas scrubbing system. More than 98% of the AlF 3 is recovered in the scrubbing system and recycled back to the cells.
  • the content of sodium oxide ( Na 2 O ) and calcium fluoride ( Ca 2 F ) in the fed Al 2 O 3 neutralize AlF 3 .
  • the neutralized amount is also a function of the penetration of sodium into the cathode, and hence the cell age.
  • a 170 kA cell emits about 60 equivalent kg AlF 3 pr. 24 hours, and uses approximately 2500 kg Al 2 O 3 pr. 24 hours.
  • the amount of AlF 3 due to neutralization for a 170 kA cell is between 0 and 20 kg per 24 hour (dependent of cell age). However, since most of the AlF 3 is recycled, the real consumption of AlF 3 is very small compared to the consumption of Al 2 O 3 .
  • the composition of the side ledge is mainly pure Na 3 AlF 6 with some CaF 2 .
  • the thickness of the side ledge is a function of the heat flow through the sides, which is a function of the difference in bath temperature and liquidus temperature. Since it is assumed that the side ledge composition is mainly Na 3 AlF 6 , this means that the total mass of cryolite in the bath varies, while the masses of AlF 3 and Al 2 O 3 do not vary with the side ledge thickness. Further, since the concentration of an additive is the mass of the additive divided by the total mass of bath, the variation in the side ledge thickness introduces variation in the concentrations. Hence, the changes in the concentrations introduce changes in the liquidus temperature, which introduces changes in the superheat, affecting the side ledge thickness.
  • the challenge is thereby to ensure stable cell operations resulting in a stable protective side ledge, while minimizing energy input and maximizing production.
  • centralized or decentralised architectures To control the electrolysis cells there are two main hardware architectures, namely centralized or decentralised architectures.
  • the process control input is calculated by a centralized computer and distributed to local controlling devices on each aluminium electrolysis cell.
  • decentralized architectures a decentralized computer, usually located close to the aluminium electrolysis cell, calculates the process control input.
  • the dynamics in the mass of Al 2 O 3 is fast, and the control of the concentration of Al 2 O 3 has to deal with quick responses.
  • the control of the concentration of Al 2 O 3 is usually considered as an isolated problem.
  • the bath temperature is usually measured manually once a day or at least once a week. In some technologies, the bath temperature is possible to measure automatically.
  • the concentration of AlF 3 (acidity) is typically measured manually once or twice a week, while the concentration of Al 2 O 3 is not normally measured at all, only in conjunction with experiments.
  • R b is used as an input for the anode beam adjustment, and acts as a control variable in conjunction with the energy input to the cell.
  • control problem is a non-linear multivariable control problem, it is commonly solved as if it should be a linear non-multivariable problem. I.e. using linear, single loop controllers (i.e. one controller controls one process variable), typically one controller for alumina control, one for AlF 3 control and one for energy/bath temperature control.
  • linear, single loop controllers i.e. one controller controls one process variable
  • typically one controller for alumina control, one for AlF 3 control and one for energy/bath temperature control typically one controller for alumina control, one for AlF 3 control and one for energy/bath temperature control.
  • the measurements act as input to the controllers; the alumina controller typically uses the pseudo resistance measurement; the AlF 3 -controller uses a combination of AlF 3 and bath temperature measurements.
  • the output from an AlF 3 -controller could typically be c1(Tb-TbRef) + c2(AlF 3 - AlF 3 ref) , where c1 and c2 is technology specific constants.
  • Some technologies also use the bath temperature measurement to adjust the energy input (voltage) applied to the cell.
  • linear single loop controllers do not "co-operate" (not a multivariable control scheme), although some technologies do use a slight coupling between AlF 3 control and energy/bath temperature control. Also these linear controllers are bounded by a lot of heuristic and rules.
  • the present invention process control of Aluminium Electrolysis Cell:
  • Non-linear Model Predictive Control we understand the use of a non-linear dynamical model, state estimation (process variable estimation) and the solution of an online constrained non-linear optimisation problem to calculate the control inputs to the physical process. See also Fig. 3 .
  • FIG. 3 illustrates the building blocks in the invention.
  • the block labelled “Process” is meant to illustrate the physical process - one instance of the aluminium electrolysis cell. To the “Process” one is able to apply process control inputs (mass and energy) and measure some process outputs. The measurement could only be done up to a certain level of accuracy. The level of inaccuracy is described as "Measurement Noise”.
  • the block labelled “Estimator” contains a mathematical model of the "Process”. The “Process” is described by using “First Principle” modelling techniques, and results in several process parameters and process variables that are used in the estimation of the current value of the said variables. Also the model contains partial differential equations (PDE), which capture the time derivative of a selected sub-set of the process variables. This sub-set is called process states.
  • PDE partial differential equations
  • the discrepancy could be seen as uncertainty - here labelled "State Noise”.
  • the value of the process control inputs and the value of the measurements is also led as inputs to the "Estimator”.
  • the purpose of the "Estimator” is to calculate an estimate of the current process variables (process states, estimated parameters and measurements). Further, the estimated measurements are compared to the physical measurements, and the deviation is used to adjust the model such that the deviation is minimized. This technique is referred to as a Kalmanfilter estimation technique.
  • the estimated measurements, states and parameters are the output form the "Estimator”, and serves as an input to the non-linear model predictive control (NMPC) block.
  • the "NMPC” block uses a sub set of the estimated process variables (CV), usually in conjunction with some reference values and constraints, to calculate the optimal future process control input senario (MV) in order to move the process from the current working point (given by the estimate), to the working point given by the reference values.
  • the optimal future process control input senario would typically be within a finite future time frame. Since the strategy is operating in the discrete time frame, the optimal future process control input senario would be calculated each time step (say each 5 th minute), based up on updated process variable estimates, which also are available each time step.
  • the optimal control input scenario is found by solving an optimisation criterion by minimizing it with respect to predicted process variables, among others.
  • the predictions stem from using the non-linear dynamic model to predict the future values of the process variables.
  • the optimiser used is an optimiser that is able to solve non-linear constrained problems (typically SQP).
  • SQP non-linear constrained problems
  • the non-linear process model in the "NMPC" block is in this embodiment of the invention the same as the non-linear model in the "Estimator” block.
  • NMPC non-linear model of the aluminium electrolysis process is introduced.
  • the (non-linear) model has two important purposes - one is to estimate the current value of important process variables and measurements of the process, the second is to be used to predict the future values of the process variables and measurements (see figure 7 , to be further explained later).
  • a dynamic mathematical model of the electrolysis process is used to estimate important process variables.
  • the process variables could be variables that are not measured at all (side ledge thickness, mass of bath and metal, mass of AlF 3 , mass of Al 2 O 3 , concentration of Al 2 O 3 ) and process variables that are infrequently measured (concentration of AlF 3 , bath height, metal height and bath temperature).
  • process variables modelled is that estimates of the process variables are available almost continuously (for example each 5 th minute).
  • the NMPC uses the estimate from the estimator described above as a starting point (where we are). By comparing the estimate with selected set points (where we want to go) on a given set of process variables, the NMPC controller calculates the future control path in an optimal manner by the use of the model. The 'future' could be the next 24 hours. The first optimal control is then applied to the physical process. This scheme is then repeated each n th minute (n to be determined) (see Fig. 7 ).
  • the input to the controller is entirely based on estimated values, and not measured values directly. Further the controller utilizes the nonlinearity of the process, the coupling between the process variables, and the process dynamics together with process and controller constraints, and finds an optimal process control input, which is put onto the physical process. Also, in this embodiment of the invention the use of the NMPC is to directly calculate the process control inputs, and not some set points to secondary control loops or systems
  • the model used has 9 estimated process states, 7 measurements, 3 main and 10 additional process control inputs and some estimated process parameters. Further there is defined some calculated process variables.
  • the estimated process states are the side ledge thickness, bath temperature, mass of dissolved alumina in the bath, mass of dissolved aluminium fluoride in the bath, metal mass, the distance between the lower anode surface and the cathode, cathode temperature, mass of alumina sludge and mass of cryolite in the cell.
  • the measurements are the pseudo resistance, line current, bath temperature, concentration of aluminium fluoride, metal height, bath height and cathode rod temperature.
  • the main 3 process control inputs are the addition of alumina and aluminium fluoride and the anode movement.
  • the additional 10 process control inputs are information about the discrete events anode change, tap of metal, addition/removal of bath, crust covering, covering crust by alumina, addition of soda, crust brake, anode effect and anode problems.
  • the parameter estimated could be any, one or several, of the parameters needed to describe an aluminium electrolysis cell, but in present embodiment of the invention only the heat loss through the is estimated.
  • the other parameters are considered known and constant.
  • the most important calculated variables are mass of bath, alumina concentration, acidity, pseudo resistance, liquidus temperature, super-heat and anode-cathode distance.
  • the uncertainty related to the estimated process states and measurements is assumed Gaussian and additive.
  • the uncertainty in the control inputs is assumed Gaussian and relative.
  • the NMPC controller is used to control the Aluminium Electrolysis Cell and the aim is to control the energy and mass balance. Since there are three process inputs available (addition of alumina, addition of aluminium fluoride and anode movement) one can only expect to control three process variables to a desired value (set point). In the NMPC framework the process input is termed manipulated variables (MV).
  • MV manipulated variables
  • One of the challenges is then to select those three process variables that allow one to best control the mass and energy balance.
  • the following three process variables are chosen: alumina concentration, bath temperature and side ledge thickness.
  • These process variables are referred to as controlled variables or CVs, and is a sub set of all the process variables. Further the three process variables referred is associated with a reference (or a desired) value.
  • the mass of fluoride in the bath is also included in the CV, but without reference values. They are however assumed having a value between some determined minimum and maximum limits (see Table 3). Also it is important to note that the pseudo resistance has no dedicated reference value in this embodiment of the invention.
  • the NMPC is allowed to use the resistance value necessary to maintain the energy balance.
  • CVs The idea behind the selection of these process variables as CVs is that once the alumina concentration, the bath temperature and the side ledge thickness are determined the superheat is determined. When the superheat is determined, the liquidus temperature is determined and by that the mass of fluoride. Further the ACD is included in the CV in order to have the possibility to constrain the ACD because of safety related issues. For example it is considered as a serious safety concern if the anodes should leave the bath (high ACD).
  • the output from the Kalmanfilter as previously described is the best estimate of the current state of the process variables, and is used by the NMPC to define a starting point for the calculations to come.
  • the NMPC calculates an optimal future process input scenario U (t k ), U (t k+1 ), ..., U (t k+Nu ) in order to achieve the set point for the CVs within a chosen future discrete time of length N (prediction horizon).
  • t k is the present time (now)
  • t k +1 , ..., t k + Nu is the forward discrete time in the control horizon.
  • the interval t k to t k + N forms the prediction window.
  • only the first calculated process input U(t k ) from the optimal future process input scenario is put into effect on the physical process itself. This scheme is then repeated for example each 5 th minute.
  • the prediction model used in this invention is the same model as the model used in the estimator previously described, but now without the possibility to update the state estimates from measurements.
  • a criterion to be minimized is defined.
  • Constraints it should be understood methods for constraint handling if some constraints are violated.
  • T means the transpose.
  • the vector Z is composed of the future prediction of the controlled variables (CV).
  • Z - Z ref means the deviation.
  • the vector U is the future input scenario of all manipulated variables (MV), while ⁇ U is the difference between the present and the previous input scenario.
  • Equation (6) are all positive semi-definite and diagonal matrices, i.e. contains only positive or zero weights.
  • Q and S can bee seen as incorporated in W.
  • the purpose of the weight matrix Q is to control the behavior of the NMPC controller. Obviously increasing the weights in Q will increase the importance of controlling the CV to its set point and therefore reduce the set point deviation. By choosing different weights for the different CVs, one controls the priority between them. In this process the most important one is to achieve the desired alumina concentration, then the bath temperature and finally the side ledge thickness. This is reflected in the Q matrix with a large value in Q related to the alumina concentration, lower on the bath temperature and lowest on the side ledge thickness (see Table 3).
  • Equation (6) controls the cost of the use of the process inputs. Increasing the weights in S will suppress the use of the MV and relax the use of it. For example, with reference to Table 2 below, it is cheap to use alumina, a bit more costly to use anode movement and very expensive to use aluminium fluoride to achieve the desired set points.
  • Table 1 Input blocking - selected samples No Input Type Selected samples (sample numbers of 143) 1 Alumina feed Feedback 0, 4, 10, 24, 48, 96 2 Aluminium fluoride feed Feedback 0, 72 3 Anode movement for MPC Feedback 0, 12, 24, 48, 96
  • the points where the CV is evaluated against the reference are freely selected (see Table 4).
  • the parameterization of the input scenario may be selected individually for each MV (see Figure 7 ).
  • the algorithm is also illustrated in figure 4 to 7 .
  • Figure 4 illustrates that in the time t k (now) a new updated estimate of the CV's is available.
  • the updated estimate of the CV's is a subset of the estimate of the process variables.
  • the estimate of the process variables is the output available from the estimator (Kalmanfilter).
  • Z ref illustrates the set point for the CV.
  • MV illustrates the manipulated variables as defined earlier.
  • Figure 7 illustrates that in the time t k (now) the future optimal process control input scenario is calculated for the prediction window defined. Only U(t k ), the first process input combination for the optimal process control input scenario, is put onto the physical process. The current estimate of the process variables forms the starting point used in the prediction of the future time behavior of the process. The predicted CV is an extracted subset of the predicted time behavior of the process variables as given by the prediction model. Also the figure illustrates the control horizon and the prediction horizon. The control horizon could be smaller or equal to the prediction horizon. The control horizon stems from the cases when using input blocking. In such a case when the control horizon is smaller than the prediction horizon, it is assumed that the future optimal process control input value in the interval t k+Nu+1 to t k+N is equal to U(t k+Nu ).
  • Figure 6 illustrates that in the time t k (now) a new updated and corrected estimate of the CV's is available based on new measurements and inputs.
  • Figure 7 illustrates that in the time t k (now) a new future optimal input sequence is calculated for the prediction window defined based on the new updated CV. Only U(t k ), the first process input combination for the optimal future input sequence, is put onto the physical process.
  • the updated predicted CV is an extracted subset of the predicted time behavior of the process variables as given by the prediction model.
  • the dotted lines are the one from the last sample. Then repeat from Fig. 6 .
  • Table 2 Parametertuning related to the MV's No Input Type UMin uMax duMax S 1 Alumina feed Feedback 0 12 1.5 0.1 2 Aluminium fluoride feed Feedback 0 1.36 1.36 1800 3 Anode movement for MPC Feedback -20 20 8 20
  • Table 3 Parametertuning related to the CV's No Variable name Z min Z max Q Setpoint 1 Alumina concentration 2.3 4.5 250 3.0 2 Bath temperature 952 970 10 958.0 3 Side ledge thickness 20 160 0.4 100.0 4 Mass of fluoride 500 1600 0 N/A 5 Anode-cathode distance 0.02 0.04 0 N/A 6 Super heat 3.0 15.0 0 N/A
  • the chosen prediction horizon is typically 12 hours long. This has proven to give good results both on simulator and during online tests. This horizon is long enough that most variables have settled at the end of it.
  • the different controlled variables have different settling times, and are thus tuned differently in the prediction horizon.
  • the controller is tuned such that the added alumina mainly controls alumina concentration, anode movement mainly controls the temperature and the addition of aluminium fluoride mainly controls the side ledge thickness.
  • interactions and coupling between the variables are taken into account despite this tuning
  • Table 4 Parameterizing of the CV's No Variable name Active samples 1 Alumina concentration, 3:6:144 2 Bath temperature 24:6:144 3 Side ledge thickness 48:6:144 4 Mass of fluoride 12:6:144 5 Anode-cathode distance, 12:6:144 6 Super heat 12:6:144
  • 3:6:144 means that the 1 th value selected is sample nr 3, then each 6 th up till sample nr 144 (12 hours).
  • the idea behind the parameterization is that the CV is not changing faster than that the process dynamics is captured within the parameterization. By this, a selection of the sampling times is used and hence reduces the application's memory usage.
  • controller can be integrated in both decentralized and centralized control system architectures where said computer will have a software program dedicated to each pot or electrolysis cell due to the individual character of said cells.
  • the NMPC could be used to control the complete plant when dynamic current load is an issue.
  • the set point could be optimized such that the whole plant (all cells) could be operated in an optimum manner to lower the power consumption in defined periods during the day.

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EP2212751A4 (en) 2013-01-23
CN101868765A (zh) 2010-10-20
AR069355A1 (es) 2010-01-13
WO2009067019A1 (en) 2009-05-28
CN101868765B (zh) 2014-07-09
NZ585470A (en) 2012-05-25
AU2008326931A1 (en) 2009-05-28
EA018248B1 (ru) 2013-06-28
EA201000833A1 (ru) 2010-12-30
NO328080B1 (no) 2009-11-30
BRPI0820426A2 (pt) 2015-05-19
NO20075933L (no) 2009-05-20
ZA201003134B (en) 2011-04-28
CA2704551C (en) 2016-08-23
CA2704551A1 (en) 2009-05-28
EP2212751A1 (en) 2010-08-04
AU2008326931B2 (en) 2013-01-10

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