4.2.4. Period 2.4

Period 2.4 represents seven days of quite stable and uniform operation (Figure 9d, taps 800–880), where TH-1 operates throughout the period, TH-2 ends, and TH-3 starts its operation in the beginning of the period. TH-1 and TH-2 initially display a slightly positive slag delay and a mean slag share of 0.2, and as TH-3 is introduced, a positive slag delay is also expected. However, local conditions or operating actions result in a high iron share for TH-3, inducing imbalance as explained in Figure 1. At tap 820, TH-3 drains according to the mean pattern without slag delay, and the high iron share of TH-2 is counteracted by a shift in outflow of TH-1 to a higher slag share. The variations in C3 for all tapholes are small (Figure 10). After TH-2 is taken out of operation, the other tapholes show stable outflows, but TH-1 drifts towards a state with negative slag delay.

### 4.2.5. Periods 2.5 and 2.6

Period 2.5 (Figure 2e) represents a nine-day segment (taps 970–1040) that holds both positive and negative slag delays, but the slag share varies little. It can be argued that similar drainage conditions prevail at the tapholes with a uniform distribution of the liquids in the hearth. However, at the point where TH-1 is substituted by TH-2 (before tap 1020), its iron drainage has become poor: TH-1 experiences problematic taps much more often than TH-2 and TH-3. As a result, TH-2 drifts to a higher iron share and positive slag delay by tap 1020. Even though TH-2 drains enough iron, the tap duration is short, suggesting that slag is also poorly drained. As a consequence, both TH-2 and TH-3 show a higher slag share in the outflows by tap 1040. The imbalance of the drainage system is also seen in C3, but for taps 1050–1250, a more stable operation is noticed. This can be compared to similar segments following periods with a larger variation, for example, taps 350–600 and taps 800–100.

Finally, Period 2.6 is studied, which represents the nine-day segment with taps 1260–1340. During this period, TH-1 starts operating, while TH-3 ends. As also seen in Period 2.4, when both operating tapholes show iron-first tapping (i.e., positive slag delay), the "incoming" taphole will also do so. The initial imbalance in the share of slag drained between TH-1 and TH-2 vanishes by tap 1310, when TH-3 has already been taken out of operation. TH-1 maintains a long positive slag delay until tap 1340, while TH-2 shifts to a negative one, but towards the end of Data set 2, the outflows of the two tapholes fall close to the mean.

### **5. Results of PCA and Liquid Level Model**

The large hearth diameter in multi-taphole blast furnaces may give rise to zones of different coke-bed permeability, which leads to differences in the local conditions and liquid levels [18,19]. A mathematical model was developed by the present authors [14] and applied to study the effect of different parameters and variables on the liquid levels and drainage process. The hearth was modelled as two interconnected pools of liquids, where communication factors can control the flow from one taphole zone to the other. Figure 1 illustrates the states of a hearth with good communication between the zones, resulting in uniform liquid levels (except the in/declining parts in the vicinity of the tapholes). A sensitivity analysis of the model was conducted to evaluate the effect of parameters on the tap duration and slag delay. Therefore, some findings from the earlier study can be associated with the PCA results presented here.

For instance, the model shows that poor iron communication increases the tap duration and slag delay (Periods 2.1, 2.3, and 2.4), while poor slag communication does not change the tap duration, but results in a negative slag delay (Periods 1.3 and 2.3). Asymmetric cases, where the pool sizes are different, give rise to conditions resembling those observed during periods when one taphole ends its operation and another is taken into use. Roche et al. [14] demonstrated that the asymmetric cases are characterized by more negative slag delay (for one taphole) and longer tap duration (for the other). This is observed in periods where the "incoming" taphole shifts from an initially positive slag delay to a slight negative one after some taps (Periods 1.3, 2.1, 2.2, and 2.4).

Changes in the conditions in front of the taphole due to the interaction between the injected mud and the coke bed [5] could potentially alter the internal level of the taphole with respect to the slag–iron interface, causing differences in the slag delay and tap duration between operating tapholes. The final declivity of the gas–slag interface is affected by the slag viscosity and coke diameter [20–22], which may vary with time and affect the tap duration, and, therefore, the liquid levels, triggering some imbalance.

Regardless of the conditions in the hearth, the outflow from one taphole will affect the outflow of the other. A sensitivity study of the outflow parameters by the model suggests that the system is prompted to changes in slag delay and tap duration when different outflow patterns are imposed on one taphole. A slower initial drainage rate of iron from one taphole yields a positive slag delay and longer tap duration for the other, which, in turn, leads to a negative slag delay for the first taphole because of low liquids levels (cf. Figure 1). This behavior is seen in several periods where the outflow patterns are found in opposite regions of the (C1, C2) plane (Periods 1.1, 1.2, 1.3, 2.4, and 2.6). On the other hand, a slow initial drainage rate of slag from one taphole yields slightly negative slag delays in both tapholes and longer tapping. This seems to be the case with tapholes ending their operation when compared with the operating one (Periods 1.3, 2.1, and 2.5). As observed in the results, the outflow patterns diverge as a result of a triggering factor, but often converge after some period of operation towards the mean pattern as the systems reaches balance again (as seen in Periods 1.2, 1.4, 2.2, and 2.4). A constant monitoring of the variables during operation, for example, iron production, liquid outflows, and slag delay, is a key to keep such imbalances within reasonable limits.

#### **6. Summary of the Analysis**

For the taps in the two data sets analyzed, TH-1 entered into operation four times, while TH-2 and TH-3 entered three times. Even though the data sets analyzed were quite extensive, the number of taphole changes was still limited, and it is thus difficult to draw general conclusions about the draining conditions of the taphole that is brought into operation. However, it can still be deduced that if the taphole that enters into operation is located farther off (here, TH-1 or TH-2) and the liquids are not in balance, it likely leads to more imbalance in the drainage. This is particular notable for TH-1 in Periods 1.1, 2.1, and 2.6. This effect can be caused by smaller random effects, for example, in the conditions in the coke bed at the taphole inlet that accentuate the characteristics of the pattern when a taphole starts operating. Thus, an existing drainage imbalance sets the incoming taphole in an extreme initial state. On the other hand, when the drainage of the system is balanced, the operation of the incoming taphole is not very different, even though it often initially shows some discrepancy in terms of (typically positive) slag delay and slag share. This suggests that inactivity of a taphole gradually leads to different conditions in the hearth in the vicinity of it. In the reference BF, the taphole length was found to be initially considerably longer for the fresh taphole compared with the ones that had been operating. As for the end of the operating period of a taphole pair, more extreme drainage patterns were often observed. In the steel works in question, the incoming and outgoing tapholes were operated alternately for a few taps, most likely to induce a smooth transition, but disturbances were still seen. This also supports the hypothesis that different local conditions in the hearth may arise, such as different liquid levels and differences in the hearth-coke permeability. The model-based analysis of the liquid levels referred to in Section 5 indicated that the effective pool of the hearth that is drained may grow during tapping [14]. Such distribution of volumes would not only lead to different outflow patterns, but could also induce zones with different permeability with impact on lining and taphole erosion.

Also, the results of C4 for Data set 1 and C3 for Data set 2 are interesting because of the cyclical trend seen for all tapholes. These principal components showed negative correlation with the tap duration in both data sets and for all three tapholes. As mentioned earlier, with an initial higher slag share in the outflow, the slag–gas interface descends more rapidly. Additionally, some variation of the slag share as the tapping evolves is expected as a result of taphole erosion. Another explanation is that the fluid dynamics of the system induces such behavior, for example, the fact that iron has to be elevated from levels below the taphole.

It should be stressed that the two-phase outflow, the unknown conditions of the coke bed and the taphole entrance, and the taphole erosion make it difficult to explain the dynamics of the system. In general, TH-3 showed a more uniform distribution of the samples around the mean pattern, most likely owing to its location in the hearth. When operating alternately with either of the other two tapholes, similar hearth conditions are expected because of their location. Further, TH-1 and TH-2 often showed opposite behavior in order to balance the drainage.

The liquid level model supporting the findings [14] has proposed some system parameters that affect the outflow patterns of iron and slag. In light of the information gained in the present study, there may be a need to re-evaluate the system with the model. A challenge is that every tapping seems to show individual features, but the results presented in this paper still reveal some general drainage patterns of the hearth, and interrelations between the drainage of two alternating tapholes. In particular, it would be interesting to understand the transition paths between different common or particular outflow patterns, which could be useful when an online model is developed. In order to present more conclusive interpretations, a larger number of samples is necessary, where each taphole is represented by a sufficient number of operating periods. Despite these limitations, the PCA-based tool must be considered efficient in illustrating and condensing the information from individual samples into a comprehensible and compact form. The tool can be used along with other information from the BF to analyze how the system reacts after stoppages of different duration, an increase or decrease in the production rate, interchanges of tapholes, changes of drill diameters, and other specific measures taken in the casthouse.

### **7. Conclusions**

Two data sets, corresponding to three and six months of operation of a blast furnace, were analyzed with respect to the drainage of the furnace hearth. The blast furnace studied has three tapholes (TH-1, TH-2, and TH-3) and the liquid outflow rates were calculated based on weighing of the torpedos (hot metal) and signals from the granulation unit (slag). After inspecting individual outflow rates throughout the data, certain outflow patterns were detected and some of them were found to recur. To simplify the interpretation, the share of slag in the outflow was taken as the variable of primary concern. After normalizing the tap duration, the evolution of the share of slag during the tapping was down-sampled to ten variables to filter out some noise. To further compress the information

and to make it possible to visualize the time evolution of the drainage patterns, principal component analysis (PCA) was applied to the data sets. The results of the compression were analyzed and the first two principal components were found to describe two relevant tapping features: the first principal component (C1) basically describes the slag delay (i.e., the length of the period of one-phase flow in the beginning of the tapping), and the second principal component (C2) describes the mean or end slag share for the tapping. To better analyze the results, one additional component was considered, which expresses how the slag share develops as both iron and slag are being drained. This component was found to be the fourth component (C4) in Data set 1 and the third component (C3) in Data set 2. For the sake of clarity, the results were post-processed into moving averages over the latest 20 taps. The results presented in the paper focus mainly on detecting diverging or converging behavior of the outflows of the operating tapholes based on the evolution of the principal components. The data sets were divided into different periods. TH-1 was found to display the most erratic patterns, followed by TH-2, while TH-3 exhibited less fluctuation. This is logical, as TH-3 is located between TH-1 and TH-2. Often, taphole changes were followed by draining imbalance, where the outflows from all three tapholes occasionally showed large fluctuations, which were seen as extreme values in the principal component space. After some time, the system typically stabilized, leading to drainage that corresponded to the mean outflow pattern. Even though the reason for the disturbances often remained unknown, the general behavior of the system could partly be explained by arguments based on fluid dynamics. To generalize the findings, a longer data set may be needed, because random events seem to have a considerable effect on the dynamics. Nonetheless, the PCA-based tool developed has proven to be useful in capturing the evolution of hearth drainage in a few key indices, which may be studied and analyzed in an attempt to gain further understanding of the complex industrial system at hand. To assess the usefulness of the PCA-based approach, it is proposed that the model should be implemented in the plant and the evolution of the (main) principal components could be studied and correlated with other BF variables. This will allow for gathering further experience on what affects the lower-dimensional representation of the liquids outflows and how the information could be utilized in the casthouse operation. In conjunction with further analysis, the accuracy of the estimated liquid outflow rates should also be evaluated, and, in particular, the quality of the estimated slag outflow rate.

**Author Contributions:** conceptualization, M.R. and H.S.; methodology, M.R.; software, M.R.; formal analysis, M.R., M.H., and H.S.; data curation, M.H.; writing—original draft preparation, M.R.; writing—review and editing, M.R., M.H., and H.S.; supervision, M.H. and H.S.; funding acquisition, H.S.

**Funding:** The research leading to these results had received funding from the European Union's Research Fund for Coal and Steel (RFCS) research program under grant agreement no. RFSR-CT-2015-00001, and this support is gratefully acknowledged.

**Acknowledgments:** The authors are grateful for the valuable questions, comments, and suggestions by the anonymous reviewers, which helped us to improve quality of the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
