Dynamic Simulation and Control of the Bayer Process. A Review

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PROCESS DESIGN AND CONTROL Dynamic Simulation and Control of the Bayer Process. A Review Yousry L. Sidrak† Department of Chemical Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

In the Bayer process, used for the production of alumina from the bauxite ores, there are frequent disturbances and a large number of interacting processes which incorporate considerable dead time. The challenge to any alumina refinery is to maximize the production of alumina (plant flow and yield) and minimize the energy costs per ton of alumina subject to constraints on liquor sodium oxalate concentration, levels of silica in liquor, digester ratio, mud washer dilution, and particle size distribution in precipitation. In addition, liquor inventories and the surge volume must be maintained within high and low limits. As a result, steady-state operation is difficult to attain, and the refinery, in general, does not run at its optimal operating conditions. There are, however, major economic incentives, typically in excess of several million dollars per year, to stabilize the operation of the plant, and cost competitiveness is one crucially important strategic factor in the alumina industry. Bayer process simulation and process control are two important tools available for use by management and process engineers to evaluate and improve performance in their plants. This paper reviews the current simulation and control technologies in alumina refineries and the basis for the application of advanced control to various processes within a refinery. 1. Introduction 1.1. Bayer Process. The 100-year-old Bayer process continues to be the most economic means of producing alumina from bauxite ores. The broad outline of the process is shown diagrammatically in Figure 1. Here, in brief, is the sequence of operations:1 1. The bauxite is crushed, ground, and then digested with caustic liquor under suitable conditions of temperature and caustic-to-alumina molar ratio in the digester slurry. 2. The digestion slurry, consisting of sodium aluminate liquor and the insoluble residue, is cooled and diluted. The residue, in the form of coarse silica sand and red mud, is separated, washed in countercurrent decantation, and then discharged. A filtration stage ensures complete removal of any remaining residue. 3. The supersaturated sodium aluminate liquor is then cooled further and passed to the precipitation stage. Here, controlled precipitation of alumina trihydrate is achieved by seeding the agitated liquor with recycled hydrate crystals. 4. The deposited crystals are then classified according to size. The large crystals form the product hydrate, which is calcined to remove the water of hydration and stored. The medium-sized crystals are recycled to the precipitation stage as seed hydrate. The extremely fine crystals are dissolved in the process liquor and recycled to the precipitation stage. 5. The “spent” liquor is then recycled, via heat exchangers, to commence the next production cycle. The † E-mail: [email protected]. Current address: 23 Doreen Rogen Way, South Morang, Victoria, 3752 Australia.

“spent” liquor is concentrated by evaporation to allow the intake of wash water at the residue-removal stage of the process. 1.2. Bayer Process Constraints. 1. Level of Sodium Oxalate in Liquor. When this builds up to a critical supersaturated level, it coprecipitates, giving rise to fines generation by interfering with agglomeration in the precipitation circuit. This causes a serious problem with product quality and seed balance.2 Standard plant practice to handle this problem includes dropping caustic soda levels, raising the fill temperature, and extensive washing of seed, all of which increase cost or lower liquor productivity. It should be mentioned, however, that, for some bauxites, liquor organics are not an issue and the refinery caustic concentration is constrained by caustic corrosion limitations, particularly in digester heater trains. 2. Levels of Silica in Liquor. As well as extracting alumina from the bauxite, silica in the bauxite reacts to form the desilication solid product, sodalite, Na2O‚Al2O3‚2SiO2‚2H2O. The solubility of sodalite increases with increasing caustic concentration, liquor temperature, and liquor alumina content.3 Sodalite is a major source of unrecoverable caustic loss, and it either deposits as a scale in the digesters or is removed as a solid after extraction. Silica levels in the product and, therefore, in the pregnant liquor must be kept low to meet the alumina quality requirements. Further, high silica levels increase the rate of scale formation in the process heat exchangers, and an increased frequency of acid cleaning becomes necessary. Sodalite formation is, therefore, critical in controlling the pregnant liquor silica levels. 3. Digester Ratio. The caustic-to-alumina molar

10.1021/ie000522n CCC: $20.00 © 2001 American Chemical Society Published on Web 01/25/2001

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Figure 1. Flowsheet of the Bayer process.

ratio in the digester slurry is a critical operating parameter. The choice of a target ratio is balanced by two opposing factors. It is desirable to operate the plant at a target molar ratio that is as low as possible to ensure that production and processing efficiencies are not lost yet high enough for complete alumina extraction from the bauxite and stable processing to precipitation.4 4. Mud Washer Dilution. After flash cooling, the digestion slurry is unstable for red mud settling or precipitation and is stabilized by using the weak liquor from the red mud countercurrent decantation washing operations. The target dilution ratio is dictated by either product quality requirements of the alumina or liquor inventory regulation, with concentration control a secondary objective in the latter case. A higher caustic soda in the dilution slurry would result in a higher occluded soda in the alumina, whereas a lower caustic soda in the pregnant liquor decreases stability and may result in early precipitation of alumina hydroxide in the thickeners and security filtration areas. 5. Liquor Inventories and Surge Volume. These must be maintained with high and low limits. To maximize the production of alumina and minimize the

energy costs per ton of alumina, liquor flow has to be maximized while maintaining the liquor concentration.5 6. Particle Size Distribution in Precipitation. An important issue6 in the optimization of the Bayer precipitation section is the constraint to sustain a delicate balance between fine particle generation by nucleation and coarsening through particle growth and particularly agglomeration. In addition, quantitative treatment of mineral processes is, in general, more difficult than other process industries because it invariably involves multiple systems which include solid, liquid, gaseous, or vapor phases, is often subject to gross variations in feed properties, and frequently involves nonstoichiometric reactions. Moreover, mineral properties are more difficult to measure than chemical and physical parameters, and process instrumentation is not as well advanced. Scale formation and erosion of primary sensors are common, making accurate measurements of process parameters difficult. Given the above, it is perhaps not surprising that the disciplines of Bayer simulation and control have lagged some years behind other process industries.

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This paper reviews the current simulation and control technologies in alumina refineries and the basis for the application of advanced control to various processes within the refinery. 2. Dynamic Simulation of the Bayer Process 2.1. Bayer Digester. The main function of the digester is to carry out caustic digestion of the bauxite and to precipitate out the undesirable silicates. Indeed, most of the digestion takes place very quickly; the long residence time (30-40 min) is required to give the desilication product enough time to dissolve and then reprecipitate as a desilication product.7 Because this reaction accounts for the major loss of valuable chemicals, the digester model must describe this precipitation phenomenon quite well. Moreover, the simulation model should be able to describe the dynamic behavior of the digester molar ratio for, basically, the purpose of controlling it. The earliest attempt to simulate the dynamic behavior of the Bayer digester was reported by Riffaud and Magistry.8 Dynamic models of the process were constructed using the computer as an online data collection system. Rapid pulse changes in the input streams (bauxite, liquor-to-slurry mixer, and digester feed) and the resulting digester ratio as measured by a conductivity cell were recorded on a computer disk. Fourier analysis was then used to identify and establish the models from these tests. Hoffman7 reported a model of the digester plant that utilizes the modular approach to provide the representation of the nonlinear effects, in conjunction with another simulation executive involving the simultaneous equations approach. Langa et al.9 developed a model for the digestion units at Point Comfort, TX. The model determines the steam and raw material usage based on unit flow sheet, operating strategy, and operating parameters. The model developed by Colombe et al.10 consisted of two parts. The first part is an empirical steady-state model that reduces to a second-degree polynomial fitted to the data that result from a set of experiments using factorial design. The second part is a dynamic model that consists of the unit gain transfer function between the one process output, digester molar ratio, and the measured process inputs, i.e., solid concentration of the digester feed and its alumina content, feed flow rate of the digestion unit, temperature of the slurry leaving the digester train, molar ratio, and Na2O caustic concentration of the liquor fed to the digester train. Similar models have also been developed by Donaldson et al.,11 Chapman et al.,12 and Crama and Visser.6 Sidrak13 developed a simple, but accurate, simulation model for the digestion process. In that model, the complex chemical reactions were assumed to occur instantaneously at the time the bauxite slurry and the strong feed liquor enter the first digester in the digester train, with the rest of the time spent in the train constituting a dead time. The model has been validated using step response data from a real alumina refinery. 2.2. Clarification and Washing Area. The aim of the clarification14 is to separate the bulk of the red mud from the desanded slurry. The turbid liquor is pumped to security filtration, while the caustic soda in the red mud residue is recovered in a train of washers working on the principle of countercurrent decantation. A secondary target of the clarification is to have the solids

content in the mud at the bottom of the thickeners be as high as practicable to ensure low overflow liquid turbidity. Although the dynamics of batch settling of solids in tanks has been studied,15-18 there is no theoretically solid and empirically proven way of predicting thickener performance completely and reliably from measurements made on small samples of suspension. Sidrak19 developed a dynamic simulation model for a multistage, countercurrent washing system. The model was used to optimize the washing operations, to maximize the caustic soda recovery from the red mud, and to control washer tank levels.20 2.3. Precipitation Process. The main function of the precipitation system is to achieve controlled precipitation of alumina trihydrate by seeding the agitated, supersaturated sodium aluminate liquor leaving the thickeners area. Both the productivity and quality of the alumina trihydrate produced are dependent on the performance of the precipitation section. An important issue6 is the constraint to sustain a delicate balance between fine particle generation by nucleation and coarsening through particle growth and particularly agglomeration. Misra and White21,22 constructed a mathematical model of the precipitation step by combining kinetic relations for the crystallization of aluminum trihydroxide with mass, energy, and particle population balances. A model developed by Audet and Larocque23 predicts the alumina hydrate productivity and is based on theoretical concepts rather than empirical concepts. It takes into account the variation of equilibrium solubility during precipitation and the effect of main Bayer liquor impurities. Chapman et al.12 used SPEEDUP to develop a model for the dynamic population balance representing the change in the population density function due to the processes of crystal nucleation, growth, agglomeration, and breakage. Audet and Larocque24 and Groneweg25 reported a mathematical model that can predict the size distribution in every precipitation tank and in the classification area in dynamic mode. Crama and Visser6 developed a model based on a general formulation of crystallization using a discretized population balance26 of growing hydrate particles. It incorporates the effects of growth, nucleation, agglomeration, and seeding, taking into account plant-specific parameters. Kiranoudis et al.27 reported an object-oriented simulation of the precipitation plant which focused on studying the overall effects of certain design parameters on the entire plant efficiency. They reported that the precipitation of alumina in crystallizers is greatly affected by the corresponding soda concentration of the washing unit product stream. Furthermore, ambient temperature was found to be important to the precipitation kinetics, influencing negatively the quantitative precipitation but resulting in particle populations of higher mean diameter. 2.4. Flash Calciners. The main function of the flash calciners is to remove water molecules from the recrystallized alumina trihydrate, Al2O3‚3H2O, before the product is shipped. Le Page et al.28 applied statistical modeling techniques, based on pseudo-random binary input disturbing signals, to an alumina flash calciner. Pulse transfer functions were identified using linear regression,29 which allowed significant input variables to be determined. Time series analysis30 was applied to systems found to be SISO by linear regression, and


adequate stochastic/dynamic models were identified for the calciners. 2.5. Evaporators. The main function of the evaporators is to concentrate, by means of evaporation, the “spent” process liquor before it is recycled to commence the next production cycle. The concentration operation also allows the intake of wash water at the residueremoval stage of the process. Nothing much has been published on the modeling or control of the process evaporators. To et al.,31 however, studied the dynamic behavior of the evaporation stage of the liquor burning process associated with the Bayer process. The first stage of this process is a single-effect evaporator, in which a side stream of the main caustic liquor circuit is evaporated at high recycle rates, to achieve product of a specified density. The authors implemented the process simulation using symbolic algebraic software, Maple V.3. The equations used to model the evaporation were derived from mass and energy balances. The model is for a two-input, twooutput system representing an idealized description of a highly nonlinear, complex unit operation. The strict validity of the equations was not established. However, it is considered to provide an adequate description of the process for the purpose of the evaluation of control strategies. An uncertainty vector adjustment was developed32 to compensate for the adverse effects of modeling errors and, thereby, to improve the robustness of nonlinear control strategies. 2.6. Bayer Liquor Caustic Concentration. Leslie and Blair1 developed a comprehensive dynamic model of the concentration of caustic soda in the Bayer process liquor. The model provides quantitative information about the process which cannot be measured during normal operation as well as a means of designing and testing various operating procedures to obtain better control over unwanted fluctuations in the caustic concentration of the process liquor. The basic model is expressed in terms of the state-variable caustic concentration. The state-space model has been formulated to retain the basic configuration of the system to enable the effects of various process elements to be readily identified and monitored. For modeling purposes, the alumina refinery was viewed as a system of tanks interconnected by a network of liquor flows. The model showed reasonable agreement with the plant in terms of absolute caustic concentration, and very good correlation in terms of dynamic form. 3. Control of the Bayer Process 3.1. Bayer Digester. A crucially important controlled variable in the Bayer digester is the caustic-to-alumina molar ratio in the digester slurry leaving the train of digesters.4 Generally, a target ratio is set by plant production demands and the digestion process is operated to keep the target ratio steady. It is desirable to operate the digester at a target ratio that is as low as possible yet high enough for complete alumina extraction from bauxite and stable processing to precipitation. In many alumina refineries, the electrical conductivity of the digesters’ downstream process liquor is measured, and the measurement is used to determine the causticto-alumina molar ratio. With a reliable online measurement, feedback control systems have been developed to control a ratio setpoint by varying the bauxite slurry flow entering the digestion process.33 The existence, however, of long time delays on the digesters train may

Figure 2. Digester control system structure.

cause substantial degradation in the performance of the feedback controller. An economic method of applying feedforward control using complex but rigorous mathematical models, in conjunction with precomputed setpoint values, has been proposed by Fay.34 Precomputed setpoint values enabled the use of reliable deterministic mathematical models based on the two-dimensional time-dependent form of the transport equations expressing the conservation of mass, energy, and momentum. The molar ratio was maintained by adjusting the bauxite per spent liquor ratio in the feed. The procedure resulted in an acceptable response time. A rule-based expert system for the diagnosis of process instrument and equipment problems associated with the Bayer digester ratio control has been reported by Langa.4 Sidrak13 reported the development of a feedforwardpredictive-feedback control scheme (Figure 2) that is based on a simple, but accurate, simulation model of the digester molar ratio. Both the simulation model and the closed-loop system have been tested and validated using real plant data. On a relative basis, this control scheme is easier to implement. Moreover, the feedforward term has been incorporated in the dead-time compensator reactor term, and the need to determine feedback parameters has been eliminated. The sensitivity of the feedback loop may be changed by inclusion of a proportionality factor, k, in the error term, ∆. Sensitivity analysis has shown the dependence of the closedloop performance on the model structure. The squared error integral and settling period were used as performance measures, indicating a good closed-loop performance. 3.2. Clarification and Washing Area. The purpose of control in the clarification area is to maintain a constant mud level in a network of thickener tanks, a high underflow mud density, and a low overflow turbidity, thus ensuring stabilization of the thickener opera-

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tion, improvement of the red mud washing efficiency in the washing area, and smoother security filtration. In the washing area, the purpose of control is to automatically stabilize red mud levels within the tanks of the washer train, thus improving the washing efficiency and removing one of the factors contributing to the difficulties encountered in the control of the operation of the train. Good level control is, perhaps, the most cost-effective way for a control engineer to improve plant operations.35 This is because inventories and feed rates are inextricably linked. An ultrasonic level controller, which controls the flow of liquids and free-flowing solids into storage vessels, tanks, reservoirs, etc., has been introduced by J. Jones Automation of Nottingham.36 Canney and Morari37 reported on the implementation and testing of an internal model controller (IMC) for the control of levels in stirred tanks. In the laboratory experiment, the IMC showed superior performance, was easier to tune, and was sufficiently robust to deal with significant gain and time delay errors, process nonlinearities, and valve hysteresis. Two averaging level controllers, the ramp controller and the optimal predictive controller, were reported to have been developed for a surge tank with improved disturbance filtering characteristics, as compared to previously reported averaging level controllers, for most of the disturbances considered.38 A model predictive optimal averaging level controller, which minimizes the maximum rate of change of outlet flow, provides integral action, and handles constraints on the tank level and outlet flow rate, has been designed and implemented on a surge tank.39 Lee et al.40 reported on the development of generic model control (GMC) for controlling the level of a surge tank. The overall algorithm is shown to be significantly lower in computational requirements than the previously proposed algorithm for surge tank control, and implementation is straightforward. An adaptive controller, which is embedded within a PC-based real-time control program, was applied to mould-level control for continuous steel slab casting.41 Friedman42 used a simple cascade control, which makes maximum use of the vessel surge capacity, to stabilize the tank level. Sidrak14 reported a regulatory and adaptive feedforward control to maintain a constant mud level in a network of thickener tanks by manipulating the underflow pump(s) speed. The evaluation of the closedloop performance of the controlled plant has been carried out using both computer simulation and manual testing in a central control room. The results have shown that the automatic control algorithm has performed as expected in handling disturbances, appearing in the rate of inflow from desilication and in partial and indefinite blockage of underflow pumps. However, as expected, the infrequent sampling of the feed, underflow density, and mud level in the thickener has introduced some errors in the control system, a result that reinforces the need for automatic mud-level sensors. In the countercurrent washing area, a classical feedforward-feedback control strategy, as well as an optimal controller, has been designed and implemented in a washer train.20 A comparison between classical and optimal control strategies, in the handling of typical disturbances, e.g., side-stream disturbances, has shown an improvement in the performance, over classical control strategy, achievable via the successful implementation of optimal control strategy with, almost, 50%

reduction, on the average basis, in the settling time and improved oscillatory behavior. 3.3. Precipitation Process. Control of the precipitation of alumina hydrate is a very important part of Bayer plant control because precipitation is mainly responsible for the size and strength of the product alumina. There are two purposes of precipitation control: 24 (a) control of agglomeration; (b) control of seed charges. Agglomeration is the critical step in the precipitation process. Parameters affecting agglomeration are wellknown, i.e., fine seed median size, seed charge, filtrate ratio, and temperature and, to a lesser extent, the residence time but less is known on the actual effect these have an agglomeration size. The current control of agglomeration is to lower or increase the solids content in the first agglomerator to increase or reduce agglomerate size. Hyprod24 was used to generate control charts that show optimum seed charge depending on the fine seed and filtrate ratio (feedforward type of control). The ultimate goal is to have automatic input of data in the model in order that the model suggests actions to take. The seed charge is controlled by adjusting the flow of seed and filtrate. The scanning laser microscope (SLM), which has proven itself in various process control applications in the mineral processing industry, has been applied to the control of the Bayer precipitation process.43 This technology measures particle size distribution directly inside a process stream. The sensor provides a complete size distribution; i.e., it senses the mean size as well as the over- and undersized components over a wide dynamic range. The sensor provides four programmable current outputs for real-time display of the most significant dynamic variables and for use in process control. An important issue6 in the optimization of the Bayer precipitation section is the constraints to sustain a delicate balance between the particle generation by nucleation and coarsening through particle growth and particularly agglomeration. In a steady state the number of particles removed as product and an additional loss in spent liquor clarification (very fine particles which are returned to digestion) equal the number of particles generated by the net balance of nucleation and agglomeration. To achieve optimum precipitation performance, various techniques have been applied in practice, such as (a) agglomeration of the finest seed fraction in a special zone of precipitators, (b) growth on new agglomerates, to deplete the liquor further, resulting in a high yield and a product with an acceptably low soda content in the resulting alumina, (c) realization of an optimum temperature profile with respect to economic precipitation yield, through the application of interstage coders, (d) the presence of enhanced surface area in the growth section which is accomplished, e.g., by effectively withdrawing an overflow with a lower solids density than that in the precipitator contents, and (e) classification of hydrate by hydrocyclones and thickeners for optimum seed recycle. Application of all of these techniques, developed by experience over long periods of time, has resulted in very complicated precipitation units wherein the many interrelations of process parameters and the resulting response are not transparent. Further development to improve the performance of the precipitation section is expected to be possible. The resulting flow sheets of such


a future precipitation section could be very complicated, and predictions on both yield and product quality are difficult to derive on currently based experience. Hence, modeling of the precipitation section, in particular concerning the particle numbers balance, has been regarded as a valuable process development and process control tool.24,44,45 However, most of the model descriptions reported focus on the mathematical presentation of the precipitation process. Less attention has been paid to the application of the models to plant practice, which demands a flexible and modular setup of the corresponding computer program. 3.4. Flash Calciners. The critical control objective in the calciner is the regulation of furnace temperature, because this determines the residual moisture content in the product alumina. As stated by Le Page et al.,28 statistically based identification and modeling techniques were successfully applied to the flash calciner, a process not considered suitable for classical step testing. It is expected that similar identification techniques can be applied throughout the Bayer process, particularly, to these areas having large time delays and time constants. This removes one of the major barriers to the wider use of model-based controllers within the alumina industry. Kohno and Itoh46 described the application of a statespace-derived controller to furnace temperature regulation. The controller was synthesized by fitting autoregressive models to captured plant data, by offline modeling. McIntosh et al.47 described upgraded process control systems implemented on rotary kiln calciners characterized by high-energy consumption. Classical first-order plus dead-time models were developed for the important processes within the kiln using step test methods. Control strategies were developed which incorporated feedforward terms and measures to minimize interactions. Mills48 described the regulation of the kiln hot end temperature, which is the apparent maximum temperature to which hydrate is exposed. An adaptive, pole-placement controller was used for temperature regulation. Duarte49 described a material and energy balance written for a fluidized bed calciner. Real-time data were transferred from a supervisory process control computer to a personal computer, where a spreadsheet program solved mass and energy balances. The spreadsheet was used to optimize calciner operation, based on energy consumption, but no advanced control scheme was presented. Mills et al.50 demonstrated the successful application of regulatory control techniques, dead-time compensation, and an explicit pole-placement selftuning control algorithm on an alumina calcining kiln. Figure 3 shows the general structure of the advanced control strategy with the following important features: (a) The cascade CO-O2 control strategy maintains the combustion efficiency. The inner O2 controller includes a Smith predictor51 for compensating the inherent dead time in this loop; (b) a self-tuning pole-placement hotend temperature controller adjusts the hydrate feed rate; (c) operator-set oil mass-flow adjustment, which effectively allows the operator to set throughput for the kiln; (d) feedforward compensation from both adjustments made in the kiln feed rate and oil flow rate to the draft controller. Improved performance of the COO2 control strategy incorporating the dead-time compensator was evident from the reduction in the oxygen content in the stack gas achieved because of the higher setpoint on the CO controller. In addition, the hot-end

Figure 3. Flash calciner control system structure.

temperature (HET) self-tuning controller has caused the narrowing of the HET histogram and the shifting of the mean to a more controlled position. The overall kiln stability, over a much wider range of throughputs, has led to the expectation of reduced energy consumption and more consistent product quality. Le Page et al.52 compared the performance of three control algorithms, proportional-integral-derivative (PID), dynamic matrix control (DMC), and self-tuning control (STC), in the regulation of the calciner furnace temperature at the Wagerup Alumina Refinery of Alcoa of Australia to assess the potential application of advanced control methods. The evaluation was carried out under both fixed and varying production conditions using process dynamic models obtained from identification experiments based on pseudo-random binary input disturbing signals.28 Measures were defined for controller performance, robustness, and complexity. DMC delivered the best performance, closely followed by the optimized PID controller. An explicit STC performed poorly, because the near minimum variance nature of the algorithm imparted too much control energy to the process. All three controllers performed significantly better than the PID control achieved with the tuning parameters currently implemented in the refinery. 3.5. Evaporators. The first stage of the liquor burning evaporation process is a single-effect evaporator,31 in which a side stream of the main caustic liquor circuit is evaporated at high recycle rates, to achieve product of a specified density. Evaporator flash tank inventory is also regulated but is of lesser importance. The process is open-loop unstable but controllable. A simplified process flow diagram is shown in Figure 4. Product

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Figure 6. Block diagram of multi-input, multi-output globally linearizing control structure.

Figure 4. Flowsheet of liquor burning process evaporator.

Figure 5. Evaporator feedback control by Su-Hunt-Meyer transformation.

density and flash tank inventory are each controlled by single-input single-output feedback loops that use proportional and integral (PI) action. The flow rate of the cooling water (QCW) is manipulated for density (FP) regulation, while the feed liquor flow (QF) is adjusted for inventory control (h). The two loops tend to interact and do not cope well with disturbances. Density deviations which impact on downstream operations are undesirable. Two main disturbances can be identified, which are the variation of the product flow rate (QP) caused by the downstream process and the reduction of recycle flow (QR) or heater feed flow (QHF) during a heater wash cycle. Three differential geometry-based nonlinear control strategies, including input-output linearization, generic model control,53 and Su-Hunt-Meyer transformation, were studied by To et al.31 on a simulation of the evaporation stage of the liquor burning process in the Bayer plant. The Su-Hunt-Meyer transformation54 maps the nonlinear system equations to the linear system in Brunsousky’s canonical form.55 Kravaris and Kantor56 showed that the exact feedback linearization of Isidori57 is equivalent to the Su-Hunt-Meyer approach when n ) r, where r is the relative order for the single-input single-output system. After the transformation variables are determined, the closed-loop performance can be found. A simple feedback control suggested by Hunt et al.54 can be implemented through the transformed linear system as shown in Figure 5. Kravaris et al.58 described a multi-input multi-output globally linearizing control structure (Figure 6) with the external linear and internal state feedback controller. The static state feedback law shown in Figure 6 is determined from input-output linearization of the nonlinear system with equal numbers of inputs and outputs. The investigations into implementing nonlinear control strategies on the evaporation stage of a liquor burning process revealed that the input-output linearization provided the best control performance against

a specified disturbance and modeling error. The SuHunt-Meyer transformation was comparatively less robust. All three strategies were shown to be able to provide better control than the classical linear one. Among the three nonlinear strategies, it was observed that, as a result of the design parameters, the inputoutput linearization provided comparatively flexible, robust, and effective control for the liquor burning process evaporator. It was observed that the generic model control is a subset of the input-output linearization. The simulation showed that nonlinear control technology could be implemented as easily as the traditional linear control theory once the mathematical background is understood. This confirms that nonlinear control has definite practical and economic value in industrial situations. 3.6. Bayer Liquor Caustic Concentration. One of the major variables to be maintained at a predetermined value in a Bayer cycle is the caustic soda concentration of the aluminate liquor.10 The digested bauxite slurry is mixed with a dilution liquor before entering agitated storage tanks. There are two approaches to regulate the Bayer liquor caustic concentration, namely, (1) manipulation of the rate of return of dilution liquor (this approach might have an impact on the refinery volume control) and (2) manipulation of the rate of return of dilution liquor to regulate the refinery volume and manipulation of the rate of raw caustic addition to the process to maintain the liquor caustic concentration. In the first approach, the flow rate of the dilution liquor controls the caustic soda concentration of the thickeners’ overflow. Suspension is then fed by gravity into thickeners. Information about operating conditions is very limited. The flow rate of the dilution liquor and the caustic soda concentration of the thickeners’ overflows are the only continuously measured variables. In addition, the flow rate of the liquor to be diluted can be valuably estimated from the flow rate of the suspension entering the digestion series of autoclaves. The dynamic models developed by Leslie and Blair1 and Colombe et al.10 both express dependence of the caustic soda concentration of thickener overflow on the conditions of feed to dilution. Identification of the step response obtained by computer simulation has resulted in a thirdorder transfer function with three identical time constants of 2.22 h and a time delay of 1.39 h. An internal model control has been designed, and simulations have shown10 a maximum transient deviation of 0.5% around the setpoint value with zero offset at steady state, for a 12% step decrease in the flow rate of liquor to be diluted. 3.7. Bayer Liquor Sodium Oxalate. Laboratory data2 on the apparent solubility of sodium oxalate in Bayer plant liquors are correlated with the pertinent variables by multiple regression analysis. The statistical analysis indicates that the apparent solubility of sodium oxalate in plant liquors is significantly affected by temperature and total alkali (total soda) and organic carbon concentrations. Organic solvents of low boiling point, such as alcohol, can be used effectively to control


sodium oxalate in Bayer liquor. Among the alcohols tested, methanol was found to be the most effective and butanol the least effective for lowering sodium oxalate concentrations. However, the complete miscibility of methanol in the aqueous phase requires a distillation step to recover the methanol. 3.8. Bayer Process Silica Levels. Silica3 is present in tropical bauxites in essentially two mineral forms, as the clay mineral kaolinite (Al2O3‚2SiO2‚2H2O) and as quartz (SiO2). Clay is normally the predominant silica-bearing mineral in the bauxite and is most easily attacked by caustic. Quartz is only attacked at the high digestion temperatures used to treat boehmitic bauxites (235-250 °C). The silica-bearing minerals in bauxites are responsible for process chemical losses, increases in process energy costs due to scaling of heat exchangers, and decreases in product quality. If present in large quantities, coarse quartz may cause sand disposal and equipment erosion problems. Paradoxically, clay will cause process problems if present in the bauxite in too large or too small a quantity. Too much clay results in unacceptable caustic losses while too little clay results in a high soluble silica level in process liquors with its attendant problems. In some bauxites, the clay content may be decreased by washing and screening of the crushed material. In cases of bauxites containing insufficient clay, a separate predesilication stage prior to the digestion stage may be incorporated into the process. When the bauxite contains an exceptionally low clay content, i.e., 0.1-0.5% SiO2, clay may actually have to be charged along with the bauxite. While contributing largely to process difficulties, silica in bauxite also has a beneficial role in the process by helping to control the carbonate and sulfate levels in the liquor. Both liquor impurities precipitate as part of the desilication product. A high silica in bauxite also means a greater amount of sodium hydroxide available for the chemical descaling of plant equipment. 4. Advanced Control of the Bayer Process and Its Benefits Advanced control5 and, in particular, multivariable predictive control have found widespread use within the petrochemical industry. Certainly within the last 10 years, considerable use has been made of this technology from installations on catalytic cracking to alkylation units. The challenge to any alumina refinery is to minimize the cost of production per ton of alumina consistent with safety and environmental considerations. This translates to maximizing the production of alumina (plant flow and yield) and minimizing the energy costs per ton of alumina. For the liquor circuit this equates to maximizing the liquor flow while maintaining liquor concentration. In addition, liquor inventories and surge volume must be maintained within high and low limits. Similarly, the mud washer dilution must be carefully controlled to maximize caustic recovery while minimizing the dilution. The Bayer circuit poses unique problems for control. Recovery of energy and caustic are what makes the Bayer process economically viable. This causes the unit processes to be highly interactive. Combined with long dead times, this causes problems for conventional control. Advanced control techniques in the form of

multivariable predictive control solves these problems. The robust nature of this controller handles model inadequacies experienced as a result of process variations such as scale buildup or feedstock variations. This type of control considers an entire process at a time, such as digestion or heat exchange. In this way the control objectives become those of the process. The process is kept within operational limits by the manipulation of variables that are not at their limits. Similarly, the process is optimized by pushing the process to the operational constraints. A well-designed approach to control of an alumina refinery would provide for an integrated approach. This is because of the circulatory nature of the Bayer circuit. To provide for the optimization of the circuit, it is necessary to combine control of individual units with the overall control. In this way no single process is maximized at the expense of the overall circuit throughput. The benefits’ figures given in this section are the result of long-term material and energy balances performed on each process individually and on the plant as a whole. 4.1. Plant-Wide Liquor Circuit Control. The liquor circuit consists of a continuous set of units and inventories in series. A bottleneck in one area requires a reduction in the total plant flow. This reduction is normally realized as a cut in the liquor feed to digestion. The dynamics around the circuit are long and variable. Operator action to alleviate a bottleneck is often too slow, resulting in a sharp uncontrolled cut in the digester feed. This upset then progresses through the other units in the circuit, causing instability and resulting in operation of the overall circuit at a safe throughput. Hence, the objective of control for this should be to provide automatic control of the liquor circuit flows and inventories. The solution to this is for one plant-wide optimizing controller. This controller would treat the inventories as controlled variables and the unit flows as manipulated variables. Inferred values for liquor concentration would be utilized. This application detects the potential problem and reduces plant flow in a controlled manner. Flows to the other units are reduced in parallel to maintain the liquor balance. The dynamic interactions between inventories are considered by the controller. Once the bottleneck is cleared the controller pushes the circuit flow back up to a maximum. In addition, the application sets the wash water based on the available surge volume and circuit concentration, thus maximizing the wash water flow and minimizing caustic losses. The application also controls the circuit concentration by manipulating the fresh caustic additions (Figure 7). A typical benefit to be expected from this application is a 2-4% increase in plant throughput. 4.2. Digestion. The control objectives are to achieve the target alumina-to-caustic ratio while maximizing throughput within the constraints imposed by levels, temperatures, etc. The solution is to utilize one multivariable predictive controller on each digester, which would manipulate the bauxite feed ratio based on a calculated value considering the above process disturbances. The estimate is corrected by the periodic laboratory feedback. The controller maximizes the liquor temperature prior to the digester. This reduces dilution from live steam injection into the digester. The blow-

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Figure 7. Bayer process master interaction.

off tank levels are controlled as throughput constraints. Additionally, the flow to each parallel unit is controlled by a total flow algorithm. This total flow control monitors constraints and efficiencies in each unit to determine the feed split. A typical benefit to be expected from this application is a 1-2% yield increase from improved ratio control. 4.3. Evaporation. The objectives of evaporation control are to (1) maximize throughput and evaporation, (2) control the liquor circuit concentration, and (3) minimize energy consumption. The solution is to utilize one multivariable predictive controller for the evaporation area. This controller would push evaporation against each of the constraints in order to maximize water removal. The temperature dynamics through the heaters is accounted for in the controller. A predicted concentration out of evaporation, based on duty, trims the fresh caustic additions. The controller optimizes the feed split/recycle between parallel units based on efficiency and dependent upon circuit configuration attempts to maximize recycle in order to maximize the liquor concentration. The temperature in the digester feed tank is controlled by manipulating the evaporator bypass. Typical benefits to be expected from this application are a 1% increase in the digester yield (from increased liquor concentration) and a decrease in the washer caustic loss (from increased wash water addition). 4.4. Liquor Heat Exchange. The objectives of control are to maintain precipitation inlet temperature while maximizing energy recovery. The solution is to utilize one multivariable predictive controller for all units. This control scheme then optimizes the flow through each of the heat-exchange passes in order to achieve the target precipitation inlet temperature. The outlet temperature is predicted based on the unit flows and efficiencies. In addition, it will maximize the heat transfer to spent liquor, thus improving the overall process energy efficiency. A typical benefit to be expected from this application is a stabilization of precipitation inlet temperature to better than 1 °C. 4.5. Mud Washer. The control objectives are to minimize caustic losses from the washers by manipulating the underflow densities while preventing washer trips. The solution is to utilize one multivariable predictive controller for each washer train. The control scheme would manipulate the washer underflows based on underflow density measurements. The flocculant, added to improve settling, is set in ratio to the incoming underflow. The washer rake torque is monitored to avoid washer trips. Wash water to the train is set by a plant-

wide liquor circuit, which is controlled based on evaporation and circuit concentration. The process has dead times on the order of 2-15 h. A change in underflow in the first washer, therefore, needs to be compensated for by a timely change in all underflows. To assist with this problem, the solution estimates the mud mass in each washer. This calculation is corrected with manual dips or level measurements if they exist. This assists the controller with the inventory management. A typical benefit to be expected from this application is a 1-2% reduction in caustic losses. 4.6. Calcination. Control objectives are to maintain alumina product qualities while minimizing energy consumption. The solution is to utilize one multivariable predictive controller for the calciner with a total feed flow algorithm to balance the flow among multiple calciners. The control scheme would primarily control the furnace and preheat burner temperatures. The control scheme detects feed changes and compensates for these with an increase in the fuel gas, allowing the temperature to be controlled closer to the target value. Residence time control is then applied to the holding vessel. The control scheme also monitors the “hot spots” inside the unit. Feed to multiple parallel calciners is determined by a total flow control algorithm. This total flow control monitors constraints and efficiencies in each unit to determine the optimum feed split. A reduction in the standard deviation of the specific surface area of alumina is anticipated with an energy savings of about 1%. 4.7. Milling Control. The control objective for an alumina milling circuit is to maximize mill throughput while maintaining a constant density of material to the slurry tanks. Generally, the digestion process is tolerant to some changes in grind size. The solution is to utilize specifically designed mill controllers. This uses a multivariable predictive controller to handle the interactions and long time delays. This is joined to a number of smart modules (dependent upon the milling type and configuration) to determine the optimum load set point, predict power excursions, etc. These smart modules include the use of a neural network and other techniques as required. Throughput benefits in excess of 2% have been observed with an additional power savings of over 5%. 4.8. Benefits Summary. There are a number of areas within a typical alumina refinery that are well suited to the application of advanced process control. Significant benefits can be derived from these by continuously pushing the various process limits. If a 1 million ton/year alumina refinery is considered, then approximate benefits of the application of advanced control can be determined as below: Assumptions. 1. 6 MW power is at a cost of $0.03/kWh/h. 2. Yield improvement in precipitation is due to tighter alumina-to-caustic ratio control. 3. Undigested bauxite is disposed of to mud lakes. 4. 1 °C precipitator fill temperature improvement is assumed to represent 1% yield improvement. 5. The energy consumed in calcination is 4 GJ/ton at a cost of $0.03/GJ. 6. Caustic loss to mud lakes is 200 g/ton at a cost of $200/ton.

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001 1155 Table 1. Dynamic Simulation and Control of the Bayer Process. A Review area

benefits

milling 5% digestion evaporation heat exchange

2%

calcination mud washing liquor stock control

1% 1% 0.5C 1% 1% 2%

benefits description throughput power saving yield improvement digester yield precipitator fill temperature energy savings caustic loss overall circuit throughput

$/year 1 000 000 80 000 500 000 500 000 500 000 120 000 400 000 1 000 000 total 4 180 000

7. Improvement in the digester throughput is production, and the value of the alumina is $200/ton. 8. The cost of production is $150/ton. Bradley et al.59 and Lalancette60 described the potential applications of the Internetsthe latest technology that enables simple and fast collection and distribution of datasto Bayer plant control. Applying standard Web authoring tools and techniques, the plant can easily distribute automation data to all users within the plant or corporation. These facilities range from live and historical data presentation to more advanced report repositories and data integration. The integration of the plant into the Web technology is achieved through the Process Information Web Server. 5. Conclusions This paper presented a comprehensive review of the current dynamic simulation and control technologies as they apply to alumina refineries. Advanced control techniques are directly applicable to a number of processes within an alumina refinery. The unit processes are generally highly interactive which, combined with the long process delay times, makes the processes difficult for operators to control at the optimum throughput. Traditional control does not handle these conditions well, making them ideally suited to the application of multivariable predictive control. This technique will stabilize the process, enabling optimization to maximize the overall circuit throughput. Benefits to be realized from this can be in excess of $4 million/year, and typical project paybacks are less than 6 months. It can be seen that the cost associated with advanced control is very effective when compared to capital equipment costs. For instance, a new 1 million ton/year refinery might cost on the order of $1 billion. This equates to $10 million/% of production. Advanced control techniques can generally achieve this same increase for less than $1 million, making it an attractive investment. Literature Cited (1) Leslie, R. A.; Blair, J. R. A Dynamic Model of the Stage II Tailings Leach Plant at Chingola. Proceedings of the 15th APCOM Symposiun, Brisbane, Australia, 1977; p 137. (2) The, P. J.; Bush, J. F. Solubility of Sodium Oxalate in Bayer Liquor and a Method of Control. Light Metals. Proceedings of Sessions, TMS Annual Meeting, Warrendale, PA, 1987; p 5. (3) Ostap, S. Control of Silica in the Bayer Process Used for Alumina Production. Can. Metall. Q. 1986, 25 (2), 101. (4) Langa, J. M. A Diagnostic Expert System for Bayer Digestion Ratio Control, Light Metals. Proceedings of Sessions, AIME Annual Meeting, Las Vegas, NV, 1989; p 9.

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Received for review May 26, 2000 Accepted November 17, 2000 IE000522N

Dynamic Simulation and Control of the Bayer Process. A Review

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