**1. Introduction**

The blast furnace represents the most relevant process on the main route for ore-based production of iron in the steelmaking industry. An important part of the process is its lowest region, better known as the hearth, where molten iron and slag are collected before they are drained ("tapped") out through the tapholes. In large-size furnaces, this drainage procedure is carried out by opening alternating tapholes from where both liquid phases are tapped out simultaneously. Different tapping rates may occur, partly because of differences in the production or internal conditions in the hearth, leading to variation of the levels of the liquid phases. The outflow rates are anticipated to be lower in the beginning of the tapping, increasing as the drainage proceeds owing to erosion of the taphole. The erosion may be further induced by the arrival of newly produced hotter liquids that have not experienced heat loss to the hearth lining. The goal is to drain sufficient amounts according to observations and estimations to keep the liquid levels low in the furnace [1,2].

In large-scale operation, productivity and efficient operation of the casthouse might be jeopardized by the variation of operating factors. Some of the most common concerns are liquid-level fluctuations caused by production/extraction imbalance, and erosion of the hearth lining. Because of the complexity of the process and besides the lack of direct measurements, the understanding and control of the tapping procedure represent both difficult and essential tasks in order to ensure an efficient operation.

Earlier studies of alternating tapping practice presented differences in taphole length, amounts of liquids extracted, and hot metal temperature between the operating tapholes [1,3,4]. Even though some correlations among production variables and erosion of both lining and taphole were established, little is known about what induces such variations and how. Computational fluid dynamics (CFD) simulations were undertaken with the goal to clarify the relation between production variables, implicitly or explicitly suggesting that there may be considerable spatial distribution of the variables or differences depending on local conditions at the tapholes [5–8].

Many previous efforts have been made to shed light on the hearth fluid dynamics and the phenomena that occur during and between the taps. In contrast to earlier notions, the fact that iron can be drained to levels below the taphole was clarified in the 1980s by Tanzil et al. [9], who made small-scale experiments supported by computational analysis. The investigators showed that the flow of the viscous slag phase leads to a lower pressure in front of the taphole, which makes it possible to elevate iron from levels well below the taphole, thus leading to simultaneous outflow of the two liquid phases. Nouchi et al. [3] presented experimental work that associated slag ratio (mass ratio of slag to iron) with liquid levels and tap duration, as well as how the time corresponding to a maximum of the slag ratio shifted with changes in the conditions. Furthermore, the results showed that at constant conditions, the maximum slag ratio increases if low-permeability zones are present in the hearth. On the other hand, Nishioka et al. [10] pointed out that only taphole mud quality or erosion of the operating taphole could not explain the duration of the tapping and the fluctuations in the drainage rate. Even though some causal factors have been identified or suggested, little is reported about the occurrence or frequency of such fluctuations. Iida et al. [2] reached similar conclusions to Nishioka et al. [10], also suggesting that coke particle size and configuration in front of the taphole play important roles for the liquid outflow rates. These results indicate that local conditions at the taphole might cause such imbalance. Furthermore, in later efforts [1], the authors developed a mathematical model that led them to conclude that discrepancies between operating tapholes in terms of liquid drainage rate and tap duration were the result of local zones of low permeability. According to their model, the metal fraction depended on the vertical level of the iron–slag interface compared with the taphole level.

Several studies in the literature have presented models of hearth drainage [1,2,10–13]. A recent study by the present authors proposed a simple offline model simulating the liquid level fluctuations in a hearth with intermittent tapping [14]. By applying different conditions to each taphole, it was demonstrated that some outflow patterns and slag delays observed in a blast furnace could be mimicked. Thus, the model makes it possible to theoretically evaluate the role of different parameters. Furthermore, an online liquid-level model was also proposed based on similar simplifications and assumptions, but using estimates of the production and outflow rates [4]. The model considers a division of the hearth into pools with individual liquid levels. Its application indicated non-uniform drainage among the tapholes, as well as periods of accumulation and depletion of both iron and slag. However, certain drainage behaviors were observed that could not be explained by the models, so a deeper understanding of the hearth drainage behavior is needed. An analysis of the recurrence of outflow patterns and transition from one to another could provide some understanding of the blast furnace hearth state, even though irregularities frequently seen in the data make it difficult to identify and categorize the observations in an appropriate way. It is thus clear that a data-driven analysis of the liquids outflow patterns could be useful. The present paper addresses this very problem using principal component analysis to compress the information to make it easier to understand and illustrate.

#### **2. Principal Component Analysis**

The main purpose of principal component analysis (PCA) is to reduce the dimensionality of multivariate data. The method also provides guidelines on the number of components needed to represent the data in question with sufficient accuracy.

Consider a sample data *Y* of mean-centered measurements with *n* observations on *q* variables [15,16]. First, the linear combination *t*<sup>1</sup> = *Yp*<sup>1</sup> is found that accounts for the maximum variance subject to *p*1 <sup>=</sup> 1. This represents the first principal component. The second component is a combination defined by *t*<sup>2</sup> = *Yp*<sup>2</sup> that has the next greatest variance subject to *p*2 <sup>=</sup> 1 with the conditions that it is uncorrelated with, and orthogonal to, the first component *t*1. The following components are similarly determined. The sample principal component loading vectors *pi* are the eigenvectors of the covariance matrix of *Y*. PCA decomposes the observation matrix *Y* as

$$Y = TP^T = \sum\_{i=1}^{q} t\_i P\_i^T. \tag{1}$$

If a considerable part of the variation is represented by the contribution of a smaller number of components, these components can replace the original data.

The present paper aims to identify and classify iron and slag outflow patterns from a reference blast furnace by applying PCA to two data sets. The data representation in lower-dimensional components is presented in the following section in order to identify and visualize possible trends in the drainage patterns. Some interpretations of the results will also be presented with respect to hearth dynamics and tapping procedure.

#### **3. Method and Data Sets**

The data analyzed consists of two data sets, Data set 1 and 2, of three and six months worth of measurements of liquid outflow rates, respectively, from a large blast furnace with three tapholes, TH-1, TH-2, and TH-3. Between the end of Data set 1 and the beginning of Data set 2, 15 months of operation passed. The iron outflow rate was obtained from torpedo weighing, while the slag outflow rate was estimated based on measurements from the granulation unit. Both signals were available as one-minute averages. Considering the recorded times from the individual taps, the liquid outflow rate for each tapping was calculated, resulting in a total of 887 consecutive ones for Data set 1 and 1729 for Data set 2. From here on, individual tapping samples will be referred as taps, while tapping will refer to the drainage process.

### *3.1. Pre-Processing of the Data Set*

After visual inspection of the samples, systematic abrupt changes of the iron outflow rate (>5 tonne/min in a couple of minutes) were noticed, which did not agree with the overall trend. Such deviations were found to be caused by torpedo changes, so they were filtered out of the samples. The outflow samples were subjected to additional pre-processing conditions in order to discard samples that, owing to error in the measurements or records, could potentially corrupt the classification. Among these conditions were the following:


After excluding such samples, 776 taps remained in Data set 1 and 1463 taps in Data set 2, accounting for 87% and 86% of the original data sets, respectively. Nonetheless, the excluded samples were taken into account when estimating the slag delay (see below).

It was found to be appropriate to use a threshold for the outflow rate, set at 2% of the production rate, to indicate when the flow of the liquid in question (iron or slag) has started during the tap. This condition was needed as liquids from a tap often progressed in the runner to the torpedo and the granulation units for some minutes after the tapping ended, and so, based on this information, the moments when iron and slag started flowing out were noted, and the difference between these two times is called "slag delay" in what follows. Note that a negative slag delay means that slag starts flowing out first. The slag delay has an important meaning as it reflects the vertical location of the iron–slag interface in the hearth at the moment when the taphole is opened; therefore, it is an important feature to identify with the present method. Figure 1 illustrates two cases where different locations of the iron–slag interface determine which liquid phase will be "seen" first, that is, if the slag delay will

be positive or negative. The figure depicts the state of the interfaces just before the tapping ends (solid lines), just after the tap has ended and the interfaces have become horizontal (dotted lines) and the state just before the next tapping starts (dashed lines). In case (a), the right taphole has drained more slag and less iron, so the iron–slag interface is not significantly below the left taphole as the tapping ends, and while the tapholes are plugged, it rises above the left taphole. This will result in a positive slag delay in the following tap from the left taphole. As this taphole will start with iron-only flow, slag keeps on accumulating in the hearth, elevating the slag–gas interface. The duration of the tap is long and the iron–slag interface will have time to descend well below the taphole, eventually leading to the state depicted in the right panel, yielding a negative slag delay for the right taphole, as shown in case (b).

**Figure 1.** Illustration of two cases of slag delay: (**a**) positive slag delay (for the left taphole), (**b**) negative slag delay (for the right taphole).

PCA is a scale-dependent method. Thus, if the data matrix has variables of considerably bigger magnitude than others, these will have dominant weights in the sub-dimension. Therefore, the outflows were normalized by calculating the slag share, defined as

$$S\_{\rm slag}(i) = \frac{m\_{\rm slag}(i)}{m\_{\rm iron}(i) + m\_{\rm slag}(i)} \,\prime \tag{2}$$

where *i* denotes the time, while *m*iron(*i*) and *m*slag(*i*) are the corresponding mass flow rates of iron and slag from the furnace for the same time. The share of slag was considered an interesting variable, because work by other investigators has demonstrated that the hearth state may affect the distribution of the two liquids in the taps from multi-taphole furnaces [2,3,10]. Furthermore, in order to normalize the tap duration (defined as the time elapsed between the moment when the first liquid starts flowing out till the last liquid stops flowing out of the taphole), *S*slag was down-sampled to 10 average points, each representing one tenth of the duration of the tap. Thus, all taps were represented by ten values of the slag share, which facilitated a comparison between the results of different taps despite differences in tap duration. This down-sampling was found to yield an acceptable representation of the variable without losing much significant or relevant information. Thus, the vector length of the samples to be categorized was of 10. The method aims to identify outflow patterns within the production levels of the BF; therefore, both slag fraction and tapping duration were required to results pattern-dependent. Figure 2 presents a few examples from Data set 2 that depict some typical liquid outflow patterns, illustrating the phase that is first observed—hence, the start of the tap—and how the tap durations may vary. The top panels of Figure 3 show the corresponding slag shares calculated by Equation (2) for the same four taps. The lower panels of the figure show, using solid squares, the corresponding 10-point normalized curves. As seen from the four examples, the evolution of the share of slag in the outflowing liquid mixture may show quite different characteristics.

**Figure 2.** Examples of liquid outflow patterns from the Data set 2: (**a**) zero slag delay and 135 min tap duration, (**b**) negative slag delay and 170 min tap duration, (**c**) zero slag delay and 70 min tap duration, and (**d**) positive slag delay and 140 min tap duration.

**Figure 3.** Slag share for the taps presented in Figure 2. Upper panels: one-minute values obtained from the measurements. Lower panels: information discretized into 10 points (solid squares) and principal component analysis (PCA) reconstruction (open circles).

A preliminary study of the normalized outflow patterns showed differences between data sets and tapholes. Figure 4 shows the slag share for the 10 average points or variables of the data sets after preprocessing. Data set 1 is presented in Figure 4a, while Data set 2 is presented for comparison in two equivalent consecutive subsets of 720 and 763 taps in Figure 4b,c, respectively. The median curves for each taphole are depicted, as well as the median for the whole data set or subset and their corresponding 25th and 75th percentiles. The median for TH-1 in Data set 1 is seen to be similar to the 25th percentile of this dataset, while for TH-2, it is similar to the 75th percentile, particularly for variables 1 and 8–10. The median of TH-3 is, on the other hand, comparable to the global median. The median for the first subset of Data set 2 shows higher slag shares for all variables compared with Data Set 1, particularly for variable 1, where the median of TH-1 falls below the global median, while median of TH-2 falls above, and for TH-3 at the same level. Taphole median values are found above and below the global median in different orders for the other nine variables. In the second subset of Data set 2 (cf. Figure 4c), variable 1 shows a decrease from 0.35 to 0.23, with TH-1 and TH-2 medians below the global median and TH-3 above. Similar median curves are observed for variables 2–10 as in the first subset in Figure 4b.

**Figure 4.** Overall median curves of Data set 1 and 2 and median by taphole (TH), (**a**) Data set 1, (**b**) first half of Data set 2, (**c**) second half of Data set 2.

In summary, interesting variability is observed within and between the data sets, and between the different tapholes. This motivates the effort to identify the outflow patterns that may occur during certain periods and how they persist or develop during the operation of the blast furnace. Next, a systematic PCA-based analysis of the outflow patterns of the two data sets is presented.
