A New Prediction Model for Liquid Level in Blast Furnaces Based on Time Series Analysis F. S. V. Gomes, J. L. F. Salles, L. A. Wasem Abstract The operations of Blast Furnace in the steel industry involves high levels of uncertainty since the liquid level in the hearth can not be directly measured. This paper presents the methodology to obtain the model of the health level by measuring the Electromotive Force (EMF) on the blast furnace shell, which is strongly correlated with the hearth level. It describes the results achieved with the installation of a measurement system of the EMF signal, and details all procedures for identification of a new mathematical model using time series analysis. The model is used to forecast the hearth level behavior in up to 30 minutes in a Steel Shop located in Brazil. T I. INTRODUCTION HE blast furnace plays a fundamental role in the steel production process as it is the place where the iron ore and the reducing fuels (coal or coke) are transformed into hot metal, slag and gas. Hot metal is formed by the reduction of iron ore while slag is formed from the agglomeration of coal or coke minerals and ashes. The hot metal and the slag, due to their different density, do not mix and stay in separate areas in the lower part of the blast furnace (hearth) [1]. The flow of hot metal and slag inside the hearth of a blast furnace has an important function in the production process. This phenomenon involves the transport of mass and energy and affects the distribution of the gas flow. In general, these liquids suffer physical-chemical transformations and are radially redistributed during the descent to the hearth. The level of liquids in the hearth affects the production process of the blast furnace in two ways: (1) the liquids in the hearth affect the descent of the load meaning that the higher the liquid level, the more strongly the submerged coke will push the load up; (2) if the slag reaches the tuyere level (air intakes) and cannot be drained, the gas flow will be severely hindered, causing several problems such as the cooling of the furnace and/or the total obstruction of the tuyeres leading to the shutdown of the plant for repairs. Thus, the liquid level on the hearth has to be maintained under control and, if possible, constant and low. Even with good cast house practice there is variation in the liquid level of the hearth of up to one meter inside the blast furnace document The ideal operation of a cast house for a big and high production blast furnace is the This work was supported in part by the ArcelorMittal Tubarão. F. S. V. Gomes is with ArcelorMittal Tubarao, Serra-ES, Brazil (e-mail: flavio.gomes@arcelormittal.com). J. L. F. Salles is with Electrical Engineering Department-Federal University of Espírito Santo, CP 019001, Brazil (corresponding author. e-mail: jleandro@ele.ufes.br). L. A. Wasem is with ArcelorMittal Tubarao, Serra-ES, Brazil (e-mail: flavio.gomes@arcelormittal.com). continuous tapping, with similar tapping times for the heats, with an almost continuous slag flow. Since the taphole, when continuously opened wears increasing the flow, it is necessary to close the notches from time to time to prevent direct contact between the tuyeres and the tapholes (gas leakage). This procedure shortens the life of the refractory in this region as it involves substantial impacts and vibrations in blast furnace walls. The process of tapping the hearth is generally done based on operational experience and involves high levels of uncertainty due to the subjectivity involved. With the purpose of making this operation more reliable, [2] have proposed a mathematical model to estimate hearth level and to help decision making regarding the timing to open and close the tapholes. The discrete model of the time obtained in [2] was determined through a white box procedure, i.e., through the physics and geometry equations of the process. Aiming to correct model errors and improve level estimate, the Extended Kalman filter was developed from a first order autoregressive model that relates the level with the electromotive force generated in the shell. In this work a new approach is proposed based on black box modeling to estimate liquid level in the hearth, which is totally based on the analysis by time series methodology of the electromotive force generated in the shell. To obtain the level model, a system to measure the electromotive force and to filter the thermal component present in the series was implemented. The work shows that the filtered electromotive force signal allows the development of the ARMA model that adequately represents the behaviour of the liquid level in the hearth. The model is used to forecast in up to 30 minutes with good accuracy. That time is a quarter of a cast operation and allows operators to adjust the process in advance, if necessary. The forecast tool developed in this work is being used in the ArcelorMittal Tubarão Steel Shop located in Brazil and is helping the team of operators in the optimization of the blast furnace tapping process. II. THE BLAST FURNACE S HEARTH Due to the current demand for stable, safe and long nonstop production stretches, the permanent optimization of the blast furnace operation is more and more necessary. There is, especially, a clear demand for improvements in the tapping strategies in blast furnace processes. The most promising blast furnace liquid level evaluation system is the measurement of the electromotive force generated in the blast furnace shell, from now on called EMF. However, the techniques to measure and interpret this signal have not developed enough to make the system adequately reliable to
serve as basis to optimize the operation and alterations in the strategies for blast furnaces tapping [3]. The EMF is produced in the blast furnace due to the thermal and chemical processes occurring in the furnace. These processes generate electric cells in the region they occur due to the oxidation of the iron to form iron oxide and slag. The current produced by these cells migrates to the furnace shell through different resistances zones and heat gradients. The EMF measured in the blast furnace shell is an indicator of the thermal and chemical state of the furnace and also of the level of liquids in the hearth [4] - [7]. As seen in Figure 1, for a stable process, the current and consequently the differential potential that is measured in the shell (EMF) varies according to three components: the resistance of the coke layer (RCo) and the resistances of the hot metal (RG) and slag (RE). After tapping, the hearth is filled in its larger part by coke. When the liquid level in the hearth increases, the iron and the slag flow to the coke agglomerate, filling the spaces between them. This causes a reduction of the internal resistance and a corresponding increase of the measured EMF. When the blast furnace is tapped, the liquid level fall, the internal resistance increases and the measured EMF decreases [8]. It is known that alterations in the process parameters such as flow rate, pressure or blowing temperature also affect the EMF because they have a direct impact on the reduction process catalyzation [9]. The EMF signal has a good correlation with the tapping sequence and with the liquid level in the hearth as can be seen in Figure 2. Fig. 2. EMF behavior measured in relation to the drainage of the liquids from the hearth. During the time between two heats, the EMF signal increases because the hearth is filling up. After the opening of the taphole, the EMF still increases and only decreases when the slag starts to flow from the hearth. This is related to low drainage rates suggesting that the liquid rate of arrival in the hearth is higher than the extraction rate [9]. It is also verified that the start of the slag drainage corresponds to the highest signal (level) of liquids in the hearth. III. TIME SERIES Fig. 1. Electrical circuit equivalent to the generation of EMF in a blast furnace shell [4]. Some studies showed that the monitoring of EMF variation difference by means of two probes, one over the tuyere air ring level and other in the lower region of the hearth has a good correlation with the level of liquid in the hearth. The EMF measured shows a long term variation at the minimum level (end of tapping) and the maximum level (start of tapping). This variation may be related to hearth drainage variation or may be the result of changes in hearth thermal state [4]. The signal produced by the EMF generated between the hearth upper and lower points is very low (variations smaller than 1 milivolt) and consists of the sum of three components: basic, periodical and noise (high frequency). The first is related to the hearth thermal state, the difference of temperature between measurement points and also with the components contained in the hot metal and slag. The periodical component is associated with the filling and draining of the liquids from the hearth. The last is the consequence of the movement of materials in the furnace and should be filtered from the system [8]. The analysis of the time series allows the detection of regularities in the variables observation and finds the law defining them. Trough this analysis it is also possible to forecast future observations with accuracy. The basic idea behind the procedures that comes from the Babylonian years is that it is possible to decompose the time series in finite numbers of independent components that together present regularity and may be calculated beforehand. In this procedure it is necessary to have different independent factors impacting the variable. One of the model classes currently most used for the identification of time series is the ARIMA model class. The ARIMA models describe adequately, the stationary linear processes thus represented [10]: Z µ = ϕ a, φ = 1 t k t k k = 0 Where at is the white noise, parameters such as: 2 ϕ k k = 0 < 0 and, is a sequence of There are three specific cases of the model (1) that will be used ahead: (i) autoregressive process of order p: AR(p); (ii) moving averages process of order q: MA(q); (1) (2)
(iii) autoregressive process and moving averages of orders p and q: ARMA(p,q). A widely used methodology in the analysis of parametric models is known as Box and Jenkins approach which was created in 1970 and optimized in 1994 [11]. It consists in the adjustment of integrated autoregressive models and moving averages, ARIMA (p, d, q) to a set of data. The strategy of the design of the model is based on the iterative cycle below: (i) A class of models is specified for the analysis; (ii) There is an identification of the model based on the analysis of autocorrelations, partial autocorrelations and other criteria; (iii) The model parameters are estimated, usually by means of least squares; (iv) There is the checking or validation of the model found, trough the analysis of the residues, to know if it is suitable to the desired objective (forecast, for example). In case of problems in any of the above mentioned phase, all the cycle is repeated. The critical step of the process is the identification. This is split in three parts: (i) To check the need of a transformation in the original series, aiming to stabilize its variance (stationary series). This can be done through graphical analysis; (ii) To differentiate the series many times as necessary till the series become stationary, making the process reduced to one ARMA (p, q), easing the process; (iii) To identify the resulting ARMA process, through the analysis of the autocorrelations and partial autocorrelations of the analyzed process, comparing them to the respective behaviours of the AR, MA and ARMA theoretical models [10]. IV. RESULTS AND DISCUSSION As case study, we will use the Blast Furnace n.3 of ArcelorMittal, located in Vitoria (ES), Brazil. The preparation of the predictive tool for monitoring the liquid level inside blast furnaces hearth was developed through the following steps: installation of equipment, filtering of the liquid level signal, modeling of the level by time series, validation of the found model and forecast of the liquid level. A. Equipment Installation In this blast furnace, four sets of probes were installed in the shell, one set per taphole. These probes measure the difference between the electromotive forces generated in the shell of the lower (bottom of the hearth) and upper (above the tuyeres level) regions. The blast furnace uses a digital control system (DCS) for the integration and operation of all plant areas and processes. For the transmission of the monitoring system probe signals from the field level to the control system wireless technology equipments were used, integrated with DCS via Modbus digital protocol. With all the system integrated and after few adjustments, a signal that corresponds to the descriptions encountered in the specialized literature was found, i.e. a signal that increases when the tapholes are closed and decreases when open. In Figure 3 we also notice that the signal presents itself as being non-stationary due to its component related to the thermal and chemical state of the hearth, regardless of the good correspondence between openings and closings of the tapholes and slag flows with the descent and rise behavior of the EMF. Fig. 3. Behavior of the EMF measured in the blast furnace shell. Firstly we tried to model the FEM behavior through a transfer function (ARMAX model), what is very reasonable, since we have significant oscillations in the signal when occur openings or tappings in the tapholes or when there are variations in hot metal temperature. The model tested was a ARMAX(2,2,2) using two tapholes openings and hot metal temperature as process inputs showed non satisfactory results. This phenomenon is explained by the large number of variables that impact, directly or not, the EMF signal measured on the blast furnace shell and thus producing a disassociation with variables that, logically, would be highly impactful [9]. B. Liquid Level Filtering The EMF generated at the blast furnace shell is affected by diverse phenomena (liquid level, hearth s chemical and physical state, dead man s state, etc). This effect turns out to be doubly undesirable for the project because it makes the comparative analysis between the current and past tapping difficult and also makes the identification through time series impossible without the use of more complex transformations. Thus, for the separation of the EMF level signal inside the hearth, the detailed comprehension through the time and frequencies signal analysis is needed. The frequency analysis is shown in Figure 4.
iron ore continued for some time implying in the arrival of a small amount of liquid material in the hearth. Fig. 4. FEM signal behavior (frenquency domain). After this analysis we have identified that, for this blast furnace, the time periods corresponding to the level of liquids in the hearth are found between 100 and 180 minutes (length of time of heats at each taphole). Based in this information, the signal filtering was made centred in the frequencies that really interested (opening and closing of the tapholes) as shown in Figure 5. This filtering was done in the control system, through the association of first order low-pass and high-pass filters. Fig. 7. Filtered signal behavior during a blast furnace shutdown. On another occasion, shown in Figure 8, during an operational instability in which there were significant changes in the process, the filtered signal effectively represented the behavior of liquids inside the blast furnace without thermochemical interference, with no change in average signal. On this occasion, there was a change in the thermal state of the hearth, possibly due to high rate of injection of fuel (coke and coal) in a blast furnace. Fig. 5. Filtering of the liquid s signal via first order filters. As result of this filtering we obtained a stationary signal and with high independence to the thermo-chemical state of the hearth. Its behavior is shown in Figure 6. Fig. 6. Performance of the EMF filtered signal The same signal in the frequency domain (Fourrier Transform) demonstrated significant signal attenuation in frequencies outside the edges of the digital filter. Then, the filtered signal was made available to the plant s operators, because it presented the best correlation with the actual behavior of the liquids inside the hearth. Some interesting behaviors were possible to see after the filtering as shown in Figure 7. In this case, there was a blast furnace shutdown and, while the EMF decreased, the filtered signal gradually increased until it stays constant. This behavior is expected inside the blast furnace because, during the shutdown of the plant, the reduction process of Fig. 8. Filtered signal behavior during a blast furnace instability. C. Level Modelling by Time Series Using the filtered signal (stationary) we made the analysis of the autocorrelations and partial autocorrelations [11] to find a model of the ARMA family that satisfactorily describes the behavior. Based on these graphs and [11] methodology, we set the class of autoregressive models (AR) pure is the one that best fits this behavior. Therefore, we will build on the model of AR 15th order, or AR (15). After that, we made the estimates of the model parameters by using the least squares method focused in the forecast of one step ahead, obtaining the model that follows: Z = 1.72Z 1.12Z + 0.32Z 0.1Z + ( k + 1) ( k) ( k 1) ( k 2) ( k 3) 0.07 Z 0.04Z + 0.02Z 0.01Z + ( k 4) ( k 5) ( k 6) ( k 7) 0.03Z 0.01Z + 0.01Z 0.02Z + ( k 8) ( k 9) ( k 10) ( k 11) 0.04Z + 0.01Z 0.05Z ( k 12) ( k 13) ( k 14) (3) By analysing the characteristic equation (3) we can guarantee that the obtained model is stationary and reversible [11], thus proving that we may use it for forecasting. From the results found in the simulations, we started the implementation in the field, aiming to validate the model in the production process.
D. Model Validation The validation of the model comprises the analysis of the residues (errors between the actual and forecasted values) aiming to find the same characteristics (correlations) of white noise process. In case of failure in this task the model is considered adequate. After being implemented in the DCS, a series of liquid level data was collected (filtered series) and its respective estimate of one step ahead. As the sampling rate was of ten minutes, the forecasting of future results was done with this forecasting horizon. The first analysis is the graphic evaluation, shown in Figure 9, where one can notice that the forecast is very close of the actual signal, confirming the results obtained in the simulation. Fig. 9. Comparison between the liquid level and ARMA model found (field validation) for a 10-minute forecast. The residues analysis may be seen in Figure 10, where we verified that it presents low autocorrelation, nearing a white noise (low or no correlation between its values), which demonstrates that the series was well represented by the chosen ARMA model. found: Z = 0.47Z 0.23Z 0.01Z 0.12Z ( k+ 3) ( k ) ( k 1) ( k 2) ( k 3) 0.29Z 0.08Z 0.11Z 0.08Z + 0.17Z ( k 3) ( k 5) ( k 6) ( k 7) ( k 8) + 0.04Z 0.01Z 0.021Z 0.06Z ( k 9) ( k 11) ( k 12) ( k 13) The forecast obtained with the optimized model (4) presents satisfactory results. One could also notice that there is a good accuracy in the forecasting times when the maximum volume occurs, i.e., in the best moments for the tapping of the taphole. V. CONCLUSIONS (4) The knowledge and control of the liquid level inside the blast furnace hearth is an important operational parameter, because it involves the possibility of processes optimization and consequently the reduction of costs. The segregation of the EMF signals between thermal components and hearth level provided a new vision about the study of the problem, so far not found in the specialized literature. From the filtered signal it was possible to visualize of some level behaviours inside the hearth, which up to now were not represented by clean EMF. The new mathematical modelling of the liquid level through the time series allowed a greater knowledge of the process dynamics, besides the possibility of forecasting from this to a next forecasting horizon. (In the present study, 30 minutes ahead was achieved) with good accuracy. Based on this information, the operators now have an additional resource for decision making in operational instability situations. The model presented may be applied in several kinds of tasks, such as: specialist software inputs (users of processes), extension of the lifetime of the hearth due to the optimization possibility for the quantity of openings and closing of the tapholes, training of operators in more realistic simulation systems and the use of the model obtained as basis for future studies about fluids dynamics inside the hearth and its relations with the several variables of the hot metal production process. REFERENCES Fig. 10. Autocorrelation and partial autocorrelation of the residues of the 10- minute forecast with the AR(15) model found. E. Liquid Level Prediction The next step consisted in the obtainment of the model for the forecasting for 30 minutes in the future (three steps ahead). This forecasting tool was initially obtained by means of the Diophantina equation (Box et al, 1994), related to model (3). However, adjustments in the parameters of the predictive model were necessary to minimize the error variance of the taphole opening and closing. After this procedure, the following model was [1] M. Geerdes, H. Toxopeus and C.V.D. Vliet. Blast Furnace Ironmaking: An Introduction. IOS Press BV, Amsterdam, Netherlands, 2nd edition,2009. [2] H.Saxen and J. Branbacka. Dynamic model of liquid levels in blast furnace hearth. Scandinavian Journal of Metallurgy, 34, 116-121,2005. [3] R.J. Nightingale ;F.W.B.U Tanzil. Blast furnace hearth condition monitoring and taphole management techniques. La Revue de Métallurgie CIT, 6, 533-540, 2001. [4] V. Dorofeev and A. Novokhatskii. Origin of diference in electrical potencials on blast furnace shell. Steel in the U.R.S.S, 9-11,1985. [5] V.Y. Dubovik. Automatic monitoring of the state of the blast furnace wall. Izv. V.U.Z. Chernaya Metall, 4, 4-6,1982.
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