4.1.1. Period 1.1

Figure 7a shows the evolution of C1 versus C2 for Period 1.1 ranging from tap 40 to 150 and corresponding to 15 days of operation. Initially, TH-2 and TH-3 operate with stable outflow patterns with little variation for taps 40–70. TH-2 shows short negative slag delay (positive C1) where slag flows out first, while TH-3 shows a short positive slag delay (negative C1) where iron flows out first. This slight imbalance can be explained by the reasoning presented in Figure 1. By tap 70, both tapholes exhibit outflow patterns resembling the mean. However, at the time when TH-1 starts operating (after tap 100), TH-3 has shifted towards a higher slag share (positive C2). As TH-1 initially drains a relatively high share of iron, the system reacts to compensate for such an imbalance with TH-3. The balance before this moment and the imbalance that follows are also seen in C4 in the top panel of Figure 8. By tap 130, the drainage reaches a more stable distribution, with TH-1 showing a positive slag delay and TH-2 and TH-3 a negative slag delay. After TH-3 ends its operation, TH-1 and TH-2 show little variation, with TH-1 draining more iron than TH-2. One-day stoppages occur at taps 74 and 141, but do not affect the drainage patterns.

Figure 8, in turn, shows that C4 values higher than the mean occur when the tap duration is short. As seen in Figure 5, high C4 values correspond to a negative slope of slag share. Thus, if the slag share is high at the beginning of the tapping and, as a consequence, the descent of the slag–gas interface is rapid, a short tap duration can be expected because the moment when the slag–gas interface bends down to the taphole will end the tap [9] (cf. Figure 1). This holds true for TH-1 and TH-2 beyond Period 1.1.

### 4.1.2. Period 1.2

Figure 7b shows C1 versus C2 for taps 180–320, corresponding to the 16 days of operation in Period 1.2 that starts two days after the end of Period 1.1. Period 1.2, where TH-1 and TH-2 operate alternately, is particularly interesting because the tapholes are opposite (cf. Figure 6), so possible differences in the in-hearth conditions should be discerned during the period. The results indeed suggest drainage imbalance: at tap 180, TH-1 and TH-2 display similar patterns to those seen at the end of Period 1.1, that is, positive slag delay for TH-1 and negative for TH-2. For taps 180–210, the slag share decreases in TH-1, while it increases in TH-2 and the outflow patterns remain fundamentally different, but from tap 210 onward, the imbalance gradually disappears and the patterns become more similar. By tap 255, the two tapholes show patterns where the two liquids flow out simultaneously. TH-2 still drains a higher share of iron than TH-1, but the differences gradually become smaller, even though TH-1 still drains iron first while TH-2 drains slag first. As for C4, in Period 1.2 (like the previous period), a negative correlation is seen with the tap duration (cf. Figure 8). The taphole showing a larger C4 value changes from one to the other, in pace with the taphole showing the shortest tap duration. In the end of this period, all principal components considered approach the mean values for both tapholes, but the strong imbalance lasted for about 100 taps of operation of the taphole pair, reflecting the slow dynamics of the system.

**Figure 7.** First vs. second principal components progression (C1, C2) corresponding to Data set 1 at different tap labels. (**a**) Period 1.1, (**b**) Period 1.2, (**c**) Period 1.3, (**d**) Period 1.4.

**Figure 8.** Fourth principal component (C4, **top**) and average tap duration (**bottom**) corresponding to the four periods of Data set 1. Blue line (TH-1), red line (TH-2), and green line (TH-3).
