*2.1. Structure and Renewal of the Dead Man*

As depicted in Figure 1, the dead man is located under the active coke zone beneath the cohesive zone. The upper part of the dead man, which is in the region between the raceways, is cone-shaped with a rounded top. The inclination from the apex of the dead man to the raceway plane is usually claimed to be associated with the repose angle of the coke particles that are charged [6], but also other factors (e.g., charging pattern [7], gas and liquid flow rates) may influence its state. Traditionally, the solid flow has been studied via small-scale experiments, but along with the emergence of more efficient software and hardware, it has recently become feasible to study the dead man formation and the flow of coke in the hearth via the Discrete Element Method (DEM).

The lower part of the dead man is in the region of the hearth where liquid iron and slag dripping from the cohesive zone accumulate before they are tapped out intermittently. Thus, the lower part of the dead man is submerged in a bath of liquid iron and slag, and is thus subjected to a buoyancy force that depends on how deeply the coke is submerged in the two liquids. Because of this, it is not straightforward to deduce the bottom shape and position of the dead man, especially taking into account the dynamic changes in the liquid levels during the tap cycle, as well as other operation

variables that may affect or interact with the buoyancy force. In principle, the bottom shape and position of the dead man can be estimated by balancing the forces acting on the dead man, whereby the buoyancy force (often) varies with the liquid levels. A majority of the studies on the estimation of the dead man bottom shape and position are summarized in a separate subsection. In this context, it should be mentioned that some authors use the term dead man only referring to its lower part (i.e., the region below the tuyere level), while others use the broader definitions used above (cf. Figure 1).

In the upper part beneath the active coke zone, the renewal of the dead man is relatively fast due to the short distance to the raceways where coke is intensively consumed. It has been clarified that there exists a small quasi-stagnant region in the center of the active coke zone where the coke particles descend slowly towards the raceways. Therefore, the dead-man porosity (and permeability) can be improved by feeding high-quality coke into the BF center [8–10]. It was also reported that the dead man can be lifted with a sufficient buoyancy force, and the coke right beneath the tuyere level can be "pushed" into the raceways. Renewal thus occurs as the "old" particles are forced to go out of the dead man and "new" particles enter to fill the voids through the upper surface of the dead man [11–15]. In the lower part, especially below the taphole level, it is, however, difficult for the coke to flow upwards into the raceways. Various other renewal mechanisms have been presented and the prevailing ones include FeO reduction, carbon solution loss and carbonization of liquid iron [16–20]. Data from a radioactive tracer test indicated that coke in the peripheral region within the hearth is consumed in 2–3 days, due to a more intensive flow of liquid iron that dissolves coke carbon. This number can be deduced from a simple carbon balance of the hearth, as follows: Consider a large BF with a hearth diameter of 14 m and a daily production rate of 9000 tons, where the hearth coke (85% carbon) occupies about 1000 m3, with a dead man voidage of ε = 0.35. If the iron that enters the hearth has a carbon content of 2.5% and a content of 4.5% at tapping, an average renewal rate of about 3 days is obtained. However, in the core region of the dead man, the coke is much more gradually dissolved, which is often claimed to occur within a few weeks [3]. It is expected that the dead man in the hearth is heterogeneous with respect to permeability, since the renewal processes are all strongly dominated by liquid flow and heat transfer, which are usually non-uniform in the hearth [21]. Another aspect that indicates a non-uniform permeability distribution is that smaller coke particles may move up and down with the hearth liquids in the voids formed between larger coke particles [5].

The permeability of the dead man can be estimated qualitatively by studying the residence time distribution of tracers injected through a tuyere, or via a probe inserted into the dead man at the tuyere level. The tracer particles dissolve in the iron and/or the slag and are measured in the runner afterwards. By analyzing the response of the tracer in the outflow, information about the flow pattern inside the hearth can be obtained. If the tracer particles are injected at different locations along the radius using a probe, the residence time can be used to evaluate the permeability of different zones of the hearth coke. In some industrial trials with radioactive coke particles, it was found that the core of the dead man in the hearth was very impermeable [22,23].

#### *2.2. Floating State of the Dead Man*

The bottom shape and position of the dead man depend on the liquid levels in the hearth and on the force acting on the bed from above. In a normal tap cycle, the liquid levels vary with varying outflow rates of iron and slag, due to the intermittent tapping, as the taphole is eroded during tapping, and because of the "competition" between iron and slag flow in the taphole [24]. Mainly based on balance equations of mass and force, the liquid levels in the BF hearth with two different dead man floating states were estimated and are shown in Figure 2, where the corresponding filtered electromotive force (emf) signals measured at the hearth shell are also depicted [25]. By comparison of simulated liquid levels and emf, Brännbacka [26] found that the iron level corresponds better to the emf signal. Comparing the maxima of the iron and slag level with the emf, this observation can also be confirmed in Figure 2. However, it should be mentioned that the variation in true liquid levels is very hard to measure, even though some indirect measuring methods have been proposed [27–29].

**Figure 2.** Estimated slag (upper solid curves) and iron (lower solid curves) levels in two BFs with different dead man floating states: sitting (upper panel) and floating (lower panel). Scaled emf signals (dashed curves) and the taphole levels (dotted lines) are also depicted. Reproduced with permission [25].

In an operating furnace, the dead man state in the hearth cannot be measured directly or monitored, owing to the high temperatures, wear, and extremely hostile environment. The dynamic behavior of the dead man has therefore mainly been investigated by utilizing scale models and/or mathematical models under simplified conditions. By visual inspection, it was found that the dead man moves vertically in a cyclic manner during a tap cycle [11,30]. The dead man sits completely on the hearth bottom (i.e., fully fills the hearth) when the liquid levels measured from the hearth bottom are low, while it floats to some degree of height or fully if the liquid levels are high, thus creating a free passage (i.e., coke-free zone) for the liquid flow. Since the iron, with a density of about 2.5 times that of slag, exerts a stronger buoyancy, it is generally considered that the distance between the hearth bottom and the inner end of the taphole ("sump depth") is decisive for dead man floating [31]. In the experimental runs with a pilot model where air was blown in through several tuyeres located in the sidewall and particles were discharged near the tuyeres (in order to mimic the coke consumption by combustion), the dead-man bottom was demonstrated to assume a profile with higher floating levels near the sidewall. This bottom shape has been confirmed in a set of quenched furnaces and two examples are presented in [32,33].

A sophisticated mathematical model [34] also taking into account BF hearth geometry and operation parameters categorized the floating state of the dead man into four different groups: (A) completely floating with a flat bottom, (B) completely floating, but floating higher near the wall, (C) partly floating at the wall, and (D) completely sitting. The results are shown in Figure 3a, where the hearth depth is defined as the distance between hearth bottom and the taphole level. It can be seen that the floating state of the dead man depends strongly on the hearth ("sump") depth and liquid level. The corresponding conditions of some Japanese furnaces were also examined by the mathematical model. As elucidated in Figure 3, the prevailing conditions (i.e., types B and C) of Japanese furnaces appear left of the vertical dashed line, while the aforementioned floating type A (i.e., completely floating with a flat bottom profile) appears right of the dashed vertical line, and is thus in conflict with the prevailing conditions.

**Figure 3.** Influences of liquid level and hearth depth on the dead-man state, where *Y*, *Z* and *R*<sup>H</sup> refer to the liquid level from hearth bottom, hearth depth, and hearth radius, respectively. (**a**) Critical liquid level as a function of hearth depth; (**b**) operating liquid levels of Japanese blast furnaces. Reproduced with permission [34].
