drainage model of multi-taphole blast furnaces · a drainage model of a multi-taphole hearth of a...

Drainage Model of Multi-taphole Blast Furnaces

MAURICIO ROCHE, MIKKO HELLE, JAN VAN DER STEL, GERARD LOUWERSE,JOOST STORM, and HENRIK SAXEN

A drainage model of a multi-taphole hearth of a (large) blast furnace operated by alternatetappings has been developed. The model, which is based on a simplified treatment of thepressure losses in the dead man, taphole entrance and taphole, can estimate the liquid levels andoutflow rates of the two liquid phases in quasi-stationary and dynamic states. The sensitivity ofthe results to changes in the conditions, such as taphole length and diameter, dead-manporosity, as well as in the model parameters is illustrated. The effect of asymmetric conditions atthe two tapholes, and dynamic responses of particular interest are also illustrated and discussed.The results of the model are finally compared with findings from a reference blast furnace wherethe outflows rates of iron and slag are routinely estimated, demonstrating that several of thetypical outflow patterns observed in the furnace can be at least quantitatively reproduced. Thisdemonstrates the feasibility of the model as a tool for gaining deeper insight into the complexdrainage with alternating tappings and the evolution of the liquid levels in the hearth of largeblast furnaces.

https://doi.org/10.1007/s11663-020-01857-1� The Author(s) 2020

I. INTRODUCTION

THE blast furnace is the primary unit in theproduction chain where iron ores are processed toliquid iron before the conversion into steel. The processcan be characterized as a huge chemical reaction withsimultaneous heat and mass transfer and chemicalreactions. The multi-phase flow is extremely complex,and different regions are characterized by the presenceof different phases that interact. In the lowest part, thehearth, the main product (molten iron also called hotmetal) and the by-product (molten slag) are accumu-lated with the lighter slag floating on top of the heavieriron. The liquids are tapped intermittently throughtapholes that are drilled through the hearth sidewallrefractory and closed by a gun injecting taphole clay.The furnace drainage is complex since both liquidphases are drained through the same taphole.[1] Infurnaces with large hearth diameter multiple tapholesare used. Large furnaces typically have three or fourtapholes, and it is common to use two of themalternately, keeping the remaining one(s) idle. After

operating two tapholes a number of weeks one or bothof them may be replaced and another taphole pair startstapping. Since the conditions inside the hearth are harsh,with aggressive molten phase at high temperature, it isnot possible to measure the internal state. Thus, e.g., theinternal levels of the liquids are unknown. The condi-tions are further complicated by the fact that the liquidsin the hearth only occupy the void between a coke bedthat extends (close) to the hearth bottom. This coke bed,called dead man, has largely unknown properties, andthe way in which it affects the internal liquid flows is notobvious. In particular, the conditions in front of thedrilled taphole are important, because the liquidsaccelerate on their way towards the taphole, whichmeans that the main internal pressure drop occursrelatively close to the entrance of the taphole. Due to theabove reasons, the blast furnace tapping process ischallenging and a lack of deep understanding of thephenomena still limits the success of controlling thedraining process.[2]

The outflow patterns are known to be complicated.The flow, which is mainly induced by the gas pressure inthe furnace, experiences viscous and inertial losses bothin the dead man and in the taphole, where the lattercontributes by the major part. However, as the moreviscous slag flows out, a considerable pressure dropoccurs already in the coke bed, lowering the staticpressure in the immediate vicinity of the taphole. Thismakes it possible to drain iron to levels well below thetaphole during the simultaneous outflow of both phases,and also to lift iron from levels below the taphole even intaps that start with slag-only outflow.[3] The viscous

MAURICIO ROCHE, MIKKO HELLE, and HENRIK SAXENare with the Process and Systems Engineering Lab., Abo AkademiUniversity, 20500 Abo, Finland. Contact e-mail: [email protected] JANVAN DER STEL, GERARD LOUWERSE, and JOOST STORM arewith Tata Steel, Research and Development, 1970CA IJmuiden, TheNetherlands.

Manuscript submitted February 7, 2020.Article published online May 11, 2020.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 51B, AUGUST 2020—1731

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losses in the slag also lead to a declivity of the slag-gasinterface towards the taphole, and as a result consider-able quantities of slag may remain in the hearth after thetapping ends: the taphole is usually plugged after gasstarts bursting out. These matters complicate thedynamics of the liquids in the hearth. In addition, largefurnaces may show spatial variation in the liquid levelscaused by differences in the dead-man porosity, e.g.,impermeable regions caused by coke degradation, accu-mulation of coke fines or insufficient carburization rateof the hot metal.[4]

Due to the complexity of the hearth drainage, severalinvestigators have tackled the problem by small-scaleexperiments or mathematical modeling. The fact thatthe iron-slag interface may descend well below thetaphole was first pointed out and demonstrated inlaboratory scale in Australia by Tanzil and co-work-ers.[3] The findings partly revised the earlier results onslag drainage presented by Fukutake and Okabe.[5,6]

The work in Australia was continued by Zulli,[7] whorefined the expressions of the residual slag by consider-ing the motion of both interfaces. These findings wereused in a model by Nightingale et al. for estimating thecoke-bed voidage in operating blast furnaces.[8] Opber-ger and Toxopeus[9] developed a simplified hearthdrainage model inspired by findings in industrial fur-naces, assuming a full mixing of the two phases in thetaphole, using average liquid properties to estimate thepressure drop. The authors reported outflow patterns ingeneral agreement with observations from a large blastfurnace. Based on the main findings of Nightingaleet al.,[8] Brannbacka et al.[10] developed a simplifiedmodel for simulation of hearth drainage in small(one-taphole) blast furnaces, considering a possiblemotion of the dead man caused by the buoyancy forcesof the hearth liquids. This conceptual model was shownto be able to estimate whether the dead man sits or floatsin operating blast furnaces.[11,12] Shao and Saxen[13] laterextended the model to consider the pressure drop in theslag by integrating the Kozeny-Carman equation infront of the taphole, and the pressure drop in thetaphole using a model based on fully stratified flow ofiron and slag. The authors demonstrated how the modelcould be used to select drill-bit diameter to achieve agiven (aim) duration of the taps in a simulated one-tap-hole furnace.

Nouchi et al.[14] studied hearth drainage experimen-tally in the laboratory with a three-dimensional modeland clarified cases where the dead-man floating level washigh and or the central part of the dead man wasclogged. The simplified drainage model developed in thework was later applied by Iida et al.,[15,16] who, likeearlier investigators,[9] considered iron and slag to befully mixed in the taphole. The pressure loss in front ofthe taphole was determined by a one-dimensional flowmodel through a ‘‘porous plug’’, the length of which wasadapted to yield outflow rates in agreement withobservations in large Japanese blast furnaces. A mul-ti-pool model was applied to consider spatial differencesin the liquid levels and the authors studied the effect ofimpermeable zones. They hypothesized that a division ofthe hearth into two or three pools of different

permeability could explain the observed drainage imbal-ance in the reference furnaces. Saxen[17] developed asimilar quasi-stationary two-pool hearth model repre-senting the regions around the operating tapholes andstudied how the cross-pool flows and dead-man floatingwould affect the liquid levels. In this model, theinter-cast period was taken to be sufficiently long tojustify the assumption of iron-only flow in the beginningof the taps and the outflow rates of iron and slag werefixed based on the production rates to satisfy thematerial balances. Roche et al.[18] developed a two-zonemodel with variable pool size and studied the effect ofvarious variables and asymmetry on the liquid levels.The outflow patterns were pre-set based on observationsfrom a reference blast furnace.Mathematical models based on a more detailed

description of the fluid flows have also been reported.Nishioka et al.[19] studied the liquid levels and flowpatterns in quasi-stationary state by a three-dimensionalCFD model considering the taphole as a pipe (ofgrowing diameter due to taphole erosion) with mixedflow of iron and slag. The shares of iron and slag in thetaphole were taken to be equal to the correspondingshares in the computational cell next to the tapholeentrance in the hearth. To the best of the presentauthors’ knowledge, the model by Nishioka et al. is theonly rigorous CFD model in the literature by which theconditions during consecutive taps of iron and slag havebeen simulated. Obvious challenges in the CFD model-ing are the different length scales of the system and thesimultaneous drainage of two liquid phases, as well toproperly describe the conditions in the porous bed infront of the taphole. Recently, attempts have been madeto understand the operation of the hearth by consideringnot only fluids but also the motion of coke by acombination of CFD and the Discrete Element method(DEM). Bambauer et al.[20] simulated the whole (butdown-scaled) blast furnace by CFD-DEM, including thehearth with one liquid phase, and demonstrated how theliquid levels and dead-man coke evolved along the tapcycle. Vango et al.[21] studied single drainage patterns ofa three-dimensional hearth with iron and slag, where thecoke particles were allowed to move along with liquidflow and buoyancy.In summary, considerable efforts have been spent in

clarifying the changes of the liquid levels in and outflowsof iron and slag from the blast furnace hearth, both withpilot models and numerical methods of different degreesof sophistication. However, the models’ results haveonly been compared to single measured outflow patternsand little work has been reported on model-basedanalysis of the different drainage patterns that areobserved in real blast furnaces.[22,23] The computationalrequirement of CFD models still seems prohibitive forusing this technique to mimic the drainage patternsobserved in the real operation, considering the fact thatseveral tap cycles have to be simulated until a quasi-sta-tionary state is reached. Furthermore, it is also ofinterest to study dynamic responses, e.g., at disturbancesor when the internal hearth conditions gradually change.Even though some studies have considered the flow inthe taphole in a more realistic way, the large differences

1732—VOLUME 51B, AUGUST 2020 METALLURGICAL AND MATERIALS TRANSACTIONS B

in the flowrates in the hearth and taphole call for a largenumber of computational cells, and the description ofthe interfaces is particularly problematic and susceptibleto numerical problems.

These challenges inspired the present investigators todevelop a fast model that still considers most of theimportant features of the problem at hand, for simulat-ing the liquid levels and outflows for a hearth with twooperating tapholes. Section II of the paper presents theassumptions made in the modeling and the mainequations. Section III illustrates some results of themodel under different conditions. In Section III–A, theconditions at the two alternating tapholes are assumedto be identical, while they are different in the results ofthe following subsection. Section III–C briefly studiesdynamic behavior. An interesting comparison of thedrainage patterns of a large blast furnace and theoutflows predicted by the model is provided in Sec-tion IV, demonstrating the feasibility of the model.Finally, some concluding remarks and lines of futuredevelopment are provided in Section V.

II. MODEL

A. Background

In large blast furnaces with multiple tapholes, theoutflows may show different types of patterns and alsoindividual differences may occur or disappear suddenlyor gradually.[22] A reason for this is that for a hearthoperated with a short inter-cast period, the iron-slaginterface may not have time to rise above the othertaphole before it is opened, yielding slag-first taps(showing ‘‘negative slag delays’’, tsd<0). Conversely, ifthe iron-slag level does not descend low enough beforethe tap ends, the next tap may start with simultaneousoutflow of iron and slag, or even with iron-first flow (i.e.,‘‘positive slag delay’’, tsd>0) which is characteristic ofsingle-taphole BFs. The order in which the phases aredrained out is likely to play a role for the tapping rates,since the pressure and local conditions at the tapholeinlet are affected by the liquid levels. The model outlinedin the following sections tackles this problem in asimplified way using basic fluid mechanics.

B. Main Assumptions

The mathematical model is based on the followingmain assumptions:

1. The volumes of iron and slag in the hearth arecharacterized by overall levels, zir and zsl

2. For every time moment, the outflows are taken to bein a quasi-stationary state.

3. The hearth diameter (dh) and the voidage (eh) of thedead man are given and the dead man is assumed tosit on the hearth bottom.

4. The inflow rate of iron to the hearth, _mir;in, and theslag (mass) ratio, cin, are given.

5. The taphole diameter (dth), length (lth), angle ofinclination (ath) and erosion rate (eth) are given foreach taphole.

6. Two tapholes are alternated with an inter-cast time,tpl, during which both tapholes are closed.

7. Simple conditions are applied to determine the pha-ses that initially flow out when the taphole is opened.

8. The tapping ends when the gas-slag interface locallybends down to the taphole.

C. Basic Equations

The model tracks the dynamic changes of the iron andslag levels in the hearth by describing the outflow rate ofthe two phase, considering the conditions in front of andin the taphole. Figure 1 illustrates the BF hearth and themain variables and parameters of the model.Iron and slag enter the hearth at given mass flow

rates. The liquid levels in the hearth are expressed as thevertical distance from the inner end of the taphole,which thus acts as the reference point (z ¼ 0). The rateof changes in the liquid levels are expressed by differ-ential mass balance equations, written as

dzirdt

¼ _mir;in � _mir;out

qirAheh; ½1�

dzsldt

¼ dzirdt

þ cin _mir;in � _msl;out

qslAheh; ½2�

where qir and qsl are the iron and slag densities, andAh ¼ pd2h=4 is the cross-section area of the hearth.The mass outflow terms, _min;out and _msl;out, in Eqs. [1]

and [2] are expressed through pressure balances for thetwo liquids between the hearth and the surroundingcasthouse. These balances are split into two parts,expressing the conditions in the hearth and in thetaphole.

pg ¼ pth � gqslzsl þ Dpbed;sl þ Dpent;sl; ½3�

pg þ gqsl zsl � zirð Þ ¼ pth � gqirzir þ Dpbed;ir þ Dpent;ir;

½4�

pth ¼ p0 � gqjlth sin ath þ Dpth;j; j ¼ ir; sl;mix: ½5�

In Eqs. [3] and [4], the left-hand-sides express thepressure at the slag-gas and iron-slag interfaces farfrom the taphole, pth is the pressure at the entrance ofthe taphole, p0 is the atmospheric pressure, whileDpbed;j and Dpent;jare the pressure losses in the deadman and at the entrance of the taphole for phase j(¼ sl; ir). The pressure balance over the taphole,Eq. [5], applies to the cases where only iron, onlyslag, or a mixture of both flows out simultaneously;Dpth;j expresses the pressure loss in the taphole.Figure 1(a) shows a hearth state where both phasesare tapped simultaneously.The pressure drop of the liquids in the dead man is

obtained from the Ergun equation[24]


dp

dx¼ 150

lj 1� eð Þ2

dcUð Þ2e3uj þ 1:75

qj 1� eð ÞdcUð Þe3 u2j ; j ¼ ir; sl,

½6�

where lj and uj are the viscosity and velocity ofphase j, dc and U are the diameter and shape factor ofdead-man coke, and e is the voidage of the coke bedin front of the taphole. This equation was applied tothe system depicted in Figure 1(b), using r as thespatial coordinate. The cross-section area for the flowis that of a hemisphere, giving the local average

velocity uj ¼ _Vj= 2pr2� �

, where _Vj ¼ _mj=qj� �

is the

volume flow rate of phase j. Integrating Eq. [6] fromthe hearth radius (rh) to a minimum radius (rmin)

Zrmin

rh

150lj 1� eð Þ2

dcUð Þ2e3uj þ 1:75

qj 1� eð ÞdcUð Þe3 u2j

!

dt; j ¼ ir; sl,

½7�

yields for the pressure loss

Dpbed;j ¼ 150lj 1� eð Þ2

2p dcUð Þ2e31

rmin� 1

rh

� �_Vj

þ 1:75qj 1� eð Þ

12p2 dcUð Þe31

r3min

� 1

r3h

� �_V2j ;

j ¼ ir; sl:

½8�

Since the taphole diameter in the blast furnace is notmuch larger than the (coke) particles of the bed, it isunreasonable to assume that a porous bed of uniformproperties extends to the taphole, as this would give andexcessive pressure drop as the flow converges. Therefore,the integration limit rmin was set clearly off the tapholeentrance (cf. Figure 1(b)); it can be seen as a model

parameter, or physically as a taphole ‘‘entrance void’’,by which different degrees of contact of the coke bedwith the taphole can be considered.In the case where only one phase (iron or slag) flows

out, the entrance loss in Eq. [3] can be written as

Dp 1ð Þent;j ¼ kent

qj2u2th;j; ½9�

where kent is an entrance loss factor and uth;j is thevelocity in the taphole. However, the case with simul-taneous outflow of iron and slag, and particularly theone where the iron-slag interface is clearly below thetaphole, requires further consideration because theflow of iron is constrained by the slag phase. With ref-erence to Figure 2(a), it is clear that the entrance

Fig. 1—(a) BF hearth and its main variables and parameters in the model and (b) top view illustrating region for integration of bed pressureloss.

Fig. 2—Definition of the geometry for estimating the entrance lossfor iron for the case where the overall iron level is below thetaphole: (a) vertical cross-section and (b) horizontal cross-section.


resistance to iron flow grows as iron is drained deeperbelow the taphole. To consider the effect of the con-verging region, another entrance-loss term was intro-duced

Dp 2ð Þent;ir ¼ kup

qir2

_Vir

Aup

� �2

¼ kupqir2u2up; zir � 2dth: ½10�

The velocity of the iron phase (uup) is obtained bydividing the volume flow rate by a cross-section area,(Aup) at a vertical level two-taphole a certain distance(2dth) below the taphole, as indicated in Figure 2. Closeto the taphole the iron-slag interface was assumed to fallon a quarter of a circle with a radius equal to thedistance between the taphole and the overall iron-slaginterface. This defines the radius, rup, of the semi-circu-

lar region with the cross-section area Aup ¼ pr2up=2.A similar procedure was applied to the case where

slag is drained together with iron even though theoverall iron level is above the taphole.[3,14,25] For this, acorresponding entrance-loss term is

Dp 2ð Þent;sl ¼ kdown

qsl2

_Vsl

Adown

� �2

¼ kdownqsl2u2down;

zir � 2dth:

½11�

Finally, the overall entrance loss in Eqs. [3] and [4] isgiven by

Dpent;j ¼ max Dp 1ð Þent;j;Dp

2ð Þent;j

� �: ½12�

Finally, the pressure loss in the taphole was taken tobe that in a rough pipe, defined as

Dpth;j ¼ fjlthdth

qj2u2th;j; i ¼ ir; sl;mix ½13�

where fj is the friction factor. This factor is given byEq. [14a] for laminar flow and by the Cole-brook-White equation[26] of Eq. [14b] for turbulentflow

fj ¼64

Rej; Rej � 2300; ½14a�

1ffiffiffifj

p ¼ �2 log2:51

Rejffiffiffifj

p þ n3:7dth

!

; Rej>2300: ½14b�

In Eq. [14b], n is the roughness of the taphole, and theReynolds number is given by

Rej ¼uth;jqjdth

lj; j ¼ ir; sl;mix: ½15�

The velocity uth;j was calculated based on the corre-sponding volumetric flow and the taphole cross-sectionarea. For the case where iron and slag flow outsimultaneously, qmix and lmix were obtained as meanvalues based on the volumetric shares of the two phases.Even though it may be argued that the two phases arenot mixed but stratified[13,27] or that they show even

more complex flow patterns,[28] this assumption wasjustified its computational simplicity and as the sameapproach has been made by other investigators in thefield.[9,15,19] The taphole diameter is obtained byintegrating

ddthdt

¼ eth; ½16�

using dth ¼ dth;ini as the initial condition when the tap-hole is opened.

D. Outflow Cases and Tap-End Conditions

After a period when the tapholes have been plugged,and a taphole is opened, the vertical level of theiron-slag interface zir was used to determine the initialphase(s) to flow out by the simple condition that onlyiron flows out if zir � zth � dth=2, only slag if zir<�Dzmix and otherwise both iron and slag. Obviously, thiscondition is strongly simplified, so a possible revision ofit is undertaken in the next time step based on theprevious solution. In case of iron-only flow, an ansatz ismade that also slag starts flowing out at a volume flowrate given as a share, b, of the production rate (i.e.,_Vsl ¼ b _msl;in

qsl) and the pressure balance of the slag

phase in the hearth (Eq. [3]) is solved with respect to pth.If the value is higher than the taphole pressure deter-mined in the previous solution, simultaneous outflow ofiron and slag is assumed to occur. Likewise, in case of aninitial slag-only flow, the ansatz is that also iron startsflowing out at a volume flow rate given by_Vir ¼ b _mir;in

qir, and the pressure balance of the iron

phase (Eq. [4]) is solved with respect to pth. If the value ishigher than the taphole pressure of the previoussolution, simultaneous outflow of iron and slag isassumed to occur.In the model the tap end is defined as the time when

the gas-slag interface can locally bend down to thetaphole. This requires that the pressure loss of slag in thebed and at the taphole entrance balances the head of theslag layer, i.e.,

Dpbed;sl þ Dpent;sl � qslgzsl: ½17�

When this conditions is satisfied, the taphole isplugged and kept close for a time period of tpl, afterwhich the taphole is changed and the procedure isrepeated. It should be noted that a transition fromtwo-phase to one-phase flow was banned in the model,since such changes were rarely observed in the referencefurnace and could give rise to fluctuating solutions in themodel.

E. Numerical Aspects

The model was implemented in Matlab. The differ-ential Eqs. [1] and [2] were discretized and solved by anexplicit scheme using a time step of one minute. Thenonlinear algebraic Eqs. [3] through [5] combined withEqs. [8] through [15] were solved numerically with

respect to the two unknowns (pth; _Vsl) for time steps of


slag-only flow, (pth; _Vir) for iron-only flow, and to the

three unknowns (pth; _Vsl; _Vir) for time steps where bothliquids were tapped. Non-negativity of the unknownswas imposed by applying variable transformations.After setting the geometry and model parameters aswell as the initial and boundary conditions, the systemwas run until a quasi-stationary state was reached. Thisusually occurred within 5 tap cycles, depending on theinitial liquid levels and parameter settings. In some casesthe dynamic response to a change was of interest, andthen the change was introduced after a quasi-stationarystate had been reached. A typical simulation time for a2500-minute case (comprising about 15 tap cycles) is oneminute on a standard laptop.

III. RESULTS

The model described in Section II was applied tostudy the evolution of the liquid levels and the outflowrates under different conditions. The sensitivity of themodel to its parameters was also studied to gain anunderstanding of the primary factors that affected thestate of the hearth. The simulation results of this sectionare complemented by practical findings reported inSection IV.

In the present study, the model was applied to studythe hearth of a large blast furnace, where two tapholesare alternately used with a short inter-cast period. Thebase-case conditions and parameter settings are pro-vided in Table I. The geometric parameters (hearthdiameter, taphole length and diameter), production rate,slag ratio and blast pressure were estimated from typicalvalues of large blast furnaces (partly from Rocheet al.[18]), and the material properties (iron and slagdensities and viscosities, taphole roughness, coke parti-cle size and shape factor, as well as bed voidage) fromvalues used in similar numerical studies of the blastfurnace hearth in the literature. The time the tapholewas plugged was taken to be 6 minutes, which representsa typical ‘‘fast’’ switching between tapholes.[18] Theentrance loss factor was set low due to the assumed voidat the taphole entrance, while the values used for theadditional loss factors (kup; kdown) were set by trial anderror to yield reasonable transitions between the twoentrance-loss equations in Eq. [12]. As there are prac-tically no means of directly quantifying the progress oferosion of the taphole, most investigators have simplyassumed values that give rise to calculated outflows inagreement with observed tapped quantities.[9,15,19] Thevalue used in the present study (eth ¼ 3:3� 10�6m=s) issomewhat higher than that used by other investigators.

The results to be reported include the evolution of theoverall levels of iron and slag in the hearth, the outflowrates, normalized by dividing them by the inflow rates,the duration of the tap, ttap, the slag delay, tsd, as well asthe mass ratio of slag in the outflow, cout. For thepurpose of illustration, the results for every second tap,referred to as taps from taphole 2 (TH2), have beendepicted by dotted lines. In all the graphs, the results foriron and slag are denoted by red and blue lines,

respectively, while for the inter-cast period a black lineis used. In the dynamic examples, the outflows are notnormalized as the inflows (may) vary.Key drainage indices of the cases are collected in

Table II. It must be stressed that taps with slag delaysclose to zero, tsdj j ¼ 1, in practice would be equivalent totaps where the two liquids appear simultaneously in therunner because these values may arise merely due to theprocedure applied in Section II–D to select the initialphase(s) to drain.

A. Identical Conditions at the Tapholes

In the first part of the study, identical conditions wereimposed on the two tapholes and their vicinities, so theresulting tap cycles (liquid levels and outflow rates)should be identical. The first example is the Base case,which simulates the drainage using the conditions andparameter settings of Table I. Figure 3(a) illustrates theresulting slag and iron levels (blue and red lines in thetop panel) and the normalized outflow rates (samecolors, bottom panel) for a period of 450 minutes ofquasi-stationary operation. The outflows were thusnormalized by dividing them by the inflows, whichmeans that for values less than one the phase in questionis accumulated while for values above one it is depleted.The slag level is seen to be 2-3 m above the taphole whilethe iron level varies above and below the taphole,yielding a tapping time of ttap ¼ 156 minutes and no slagdelay; the two liquids start flowing out simultaneously(cf. Table II). The bottom panel shows an interestingoutflow behavior: the iron outflow gradually increasesbut levels out later in the tapping. By contrast, the slagoutflow is moderate initially, then decreases to aminimum about 25 minutes into the tap, followed byan almost linear increase, reaching a final level of abouttwice the production rate. Similar patterns werereported by Nouchi et al.[14] in their small-scale drainageexperiments using fluoride (as ‘‘iron’’) and paraffin (as‘‘slag’’), by simplified drainage models,[9,16] by CFDmodels considering both iron and slag flow,[19] as well asin measurements from operating multi-tapholefurnaces.[16,19]

The effect of slag viscosity on the results is studied bychanging it by � 0:15 Pa s from the base-case value,Figures 3(b) and (c) show the result of an increase and adecrease of viscosity, respectively. The increased slagviscosity lowers the iron level but raises the slag level,while the opposite holds true for a decrease in slagviscosity. This is due to the fact that the pressure at thetaphole decreases with the slag viscosity, which makes itpossible to drain iron from lower levels, but simultane-ously the end level of the slag is raised (cf. Eq. [17]). Inthe former case, slag is the first phase to flow out, butthe iron is only marginally delayed. The effect on the tapduration is minor due to the shifting of the twointerfaces in opposite directions. However, the effecton the outflow patters is considerable: the higher slagviscosity increases the share of slag in the initial part ofthe tap while a lower viscosity decreases the share. In thelatter case, the slow initial outflow rate is due to the high


iron-slag interface level, but the lower flow resistanceleads to a strong slag flow in the later parts of the tap.This demonstrates the complex effect of the internalconditions on the liquid outflows, where the flowresistance in the coke bed, at the taphole entrance andin the taphole interplay. An interesting detail worthnoting is that the case with low slag viscosity shows ashort period of iron-only flow in the very beginning ofthe tap, but the outflow rate is only marginally higherthan it is when the slag outflow has started. Thus, theadditional slag flow does not substantially affect thepressure drop in the taphole. The fact that the ironoutflow rate only slightly dropped as slag enters thetaphole was observed also in one-taphole blastfurnaces.[29]

The effect on the production rate is studied inFigure 4, which shows the impact of an increase in thehot metal production rate from 11,000 t/day to12500 t/day (Figure 4(a)) and an increase in the slag

ratio from 0.2 to 0.25 (Figure 4(b)). The increase in theproduction rate leads to longer tapping time (increasingby 27 minutes from the Base case), larger amplitudes ofthe liquid levels, and a higher slag level. The liquidoutflow patterns are very similar to those of the Basecase. An increase in the slag ratio by 50 kg per ton of hotmetal raises the maximum slag level by almost 0.5 m butconversely lowers the iron level, as the share of slag inthe outflow must increase (to close the material bal-ances). The tapping time increases by 13 minutes, butiron and slag still start flowing practically at the samemoment.In the practical operation of the blast furnace, the

taphole length varies and mainly depends on the localflow conditions in the hearth and the quality of thetaphole clay. The length can be affected by the volumeof the injected taphole clay, but it is not always possibleto extend the taphole since the formation of the‘‘mushroom’’ at its inner end requires a good contact

Table I. Conditions and Model Parameters for the Base Case

Variable or Parameter Value Unit Variable or Parameter Value Unit

_mir;in 11,000 t/day lth 3 mcsl 0.2 — dth;ini 0.064 mqir 6700 kg/m3 eth 3.3 9 10�6 m/sqsl 2400 kg/m3 n 0.003 mlir 0.006 Pa s pgas 3.2 9 105 Palsl 0.35 Pa s p0 1.01 9 105 Padh 14 m tpl 6 mineh 0.35 — e 0.35 —dc 0.035 m kent 0.05 —U 0.6 — kup 0.05 —e 0.35 — kdown 0.05 —rmin 0.1 m a 10 degb 0.01 — Dzmix 3dth m

Table II. Perturbed Terms and Key Drainage Indices for the Examples Presented in Figs. 3 Through 10

Perturbed Term Value Unit Tap Duration (min) Slag Delay (min) Slag Ratio Figures

(Base case) — — 156 0 0.2 3(a)lsl 0.5 Pa s 155 � 1 0.2 3(b)lsl 0.2 Pa s 157 1 0.2 3(c)_mir;in 12,500 t/day 182 0 0.2 4(a)cin 0.25 — 168 � 1 0.25 4(b)lth 4 m 195 1 0.2 5(a)lth 2 m 105 0 0.2 5(b)dth;ini 0.058 m 199 0 0.2 6(a)dth;ini 0.070 m 122 1 0.2 6(b)e 0.39 — 159 0 0.2 7(a)e 0.31 — 150 1 0.2 7(b)rmin 0.075 m 153 20 0.2 8(a)rmin 0.15 m 159 � 5 0.2 8(b)lth;1 lth;2 3 2 m 155 106 1 � 1 0.19 0.22 9(a)dth;1* dth;2** 0.064 0.058 m 158 148 1 � 1 0.20 0.20 9(b)e1 e2 0.3 0.4 — 122 176 � 1 20 0.19 0.21 10(a)rmin;1 rmin;2 0.10 0.15 m 140 171 � 8 1 0.25 0.16 10(b)

*Taphole length: lth;1 ¼ 3 m.**Taphole length: lth;2 ¼ 2 m.


Fig. 3—Iron and slag levels (zir, zsl) and normalized outflow rates (mi,out/mi,in): (a) Base case, (b) increased (lsl ¼ 0:50 Pa s) and (c) decreased(lsl ¼ 0:20 Pa s) slag viscosity. i = ir (red), i = sl (blue) (Color figure online).

Fig. 4—Iron and slag levels (zir, zsl) and normalized outflow rates (mi,out/mi,in): (a) increased overall production rate ( _mir;in ¼ 12; 500 t=day) or (b)increased slag ratio (cin ¼ 0:25). i = ir (red), i = sl (blue) (Color figure online).


Fig. 5—Iron and slag levels (zir, zsl) and normalized outflow rates (mi,out/mi,in): (a) longer (lth ¼ 4 m) or (b) shorter (lth ¼ 2 m) taphole. The innerends of the two tapholes appear on different levels due to the taphole length difference. i = ir (red), i = sl (blue) (Color figure online).

Fig. 6—Iron and slag levels (zir, zsl) and normalized outflow rates (mi,out/mi,in): (a) smaller (dth;ini ¼ 0:058 m) or (b) larger (dth;ini ¼ 0:070 m) initialtaphole diameter. i = ir (red), i = sl (blue) (Color figure online).


Fig. 7—Iron and slag levels (zir, zsl) and normalized outflow rates (mi,out/mi,in): (a) larger (eh ¼ e ¼ 0:39) or (b) smaller (eh ¼ e ¼ 0:31) coke-bedvoidage. i = ir (red), i = sl (blue) (Color figure online).

Fig. 8—Iron and slag levels (zir, zsl) and normalized outflow rates (mi,out/mi,in): (a) smaller (rmin ¼ 0:075 m) or (b) larger (rmin ¼ 0:15 m) tapholeentrance void. i = ir (red), i = sl (blue) (Color figure online).


between the clay and the coke bed.[30] A strongperipheral flow of the liquids in the hearth, which maybe the result of a clogged core of the dead man, is knownto lead to a shorter taphole. The effect was investigatedby changing the length by ± 1 m from the base-casevalue: these would represent extreme values encounteredin the practical operation. Figure 5(a) demonstrates thatthe increase, as expected, prolongs the tap considerably(by almost 40 minutes) and therefore also yields largeramplitudes of the liquid levels. The longer taphole alsoshifts the inner end of the taphole downward, whichlowers the liquid levels (with respect to the furnacebottom). The slag level rises somewhat, but the change isnot dramatic. The outflow patters largely remain as inthe Base case, but the minimum exhibited by the slagoutflow is more pronounced. For the short taphole(Figure 5(b)) the tap duration decreases by 50 minutes,which brings down the liquid-level amplitudes and theoverall slag level. Along with this change, the share ofiron flowing out during the initial part of the tap isincreased. For both cases, the tap starts with practicallysimultaneous flow of iron and slag.

One of the few variables that can be used to directlyaffect the drainage is the taphole drill diameter. Theeffect of the initial taphole diameter is illustrated inFigure 6, which shows the simulated drainage using drilldiameters with ± 4 mm offset from the base-case value.The decreased diameter (Figure 6(a)) naturally prolongsthe tap (here by more than 40 minutes) and yields higherslag levels in the hearth. The initial outflow rate of ironis somewhat lower and the rate of slag is higher than inthe Base case, and the outflow patters are strikinglysimilar to those for the case with a long taphole (cf.Figure 5(a)). Conversely, an increased diameter (Fig-ure 6(b)) lowers the slag level and raises the iron level inthe hearth, which increases the iron flow in the begin-ning of the tap. The slag outflow rate no longer shows aminimum but increases monotonously. The primaryeffect of the larger taphole diameter is that the tapduration decreases (Table II).

Closely related to the above is the role of tapholeerosion. After increasing or decreasing the rate from thebase-case value the main effect was found to be only onthe duration of the taps, while the outflow patternsremained practically unchanged.

The voidage of the dead man plays an important rolefor the liquid levels; a lower voidage means largerchanges in the liquid levels as there is less space for theliquids in the bed. The voidage also affects the pressuredrop in the bed, particularly close to the tapholes. Theeffect of voidage is seen in Figure 7, which shows theresults for the cases where the overall voidage eh waschanged by ± 0.04 from the base-case value. The samechange was implemented in the local voidage (e) in frontof the tapholes. Such changes could be due to changes incoke quality, or in the residence time of coke in theupper furnace. The outflow patterns are very similar tothe one obtained after perturbing the taphole diameter,but the effect is lesser on the tap duration. The slag levelis seen to be strongly affected by the voidage change(through Eq. [8]).

The local conditions of the dead man part in front ofthe taphole strongly affect the pressure loss in the bedbecause of the converging flow. This is the main reasonwhy the integration limit, rmin, in the model is impor-tant. However, the conditions in front of the taphole areunknown in practice, and may also be subject to changebecause of accumulation of coke fines[4] or dissolution ofthe carbon in coke due to high liquid flow rates.[15,31]

Furthermore, as the taphole drill breaks through thewall it affects the conditions both of the mushroom andthe coke bed, inducing stochastic variations. To studythe effect, the value of the radius of the taphole entrancevoid was changed to rmin ¼ 0:075 m and rmin ¼ 0:15 mwith results illustrated in Figure 8. A small void region(cf. Figure 8(a)) increases the pressure drop in the bed,which elevates the liquid levels. It is worth noting thatthe iron level is raised considerably, and it lies above thetaphole level throughout the tap. Thus, the iron-slaginterface has to bend downward to let out slag, and thisoccurs after a slag delay of tsd ¼ 20 minutes. This ismade possible by the inertial term of the Ergunequation, which results in a sufficient pressure losscreated by the iron flow in the bed. As slag starts flowingout, the iron outflow rate drops slightly, but increasesslowly during the rest of the tap. The slag outflow, inturn, increases strongly and linearly. By contrast, in thecase where the taphole entrance void is larger (Fig-ure 8(b)), the outflow order is interchanged: slag is thefirst phase to flow out (tsd ¼ � 5 minutes) due to a lowlevel of the iron-slag interface, which is at or below thetaphole during the whole tap.

B. Different Conditions at the Tapholes

In the practical operation, symmetry of the conditionsat the alternating tapholes cannot be guaranteed asdifferences in the hearth state may arise due to sponta-neous voidage changes caused by the accumulation ordissolution of fines, or liquid flow-path shifts caused bylining erosion or buildup of skull on the hearth wall andbottom. Asymmetry may also arise from a non-uniformsupply of blast and auxiliary reductants to the raceways,or from channeling of the liquid supply from the upperpart of the dead man. Particularly in large blastfurnaces, with hearth diameters clearly above 10 m,impermeable zones may affect the liquid levels and theflows to the tapholes. Small-scale experiments[14,15] andsimulations models[15,17–19] have been applied to studythe expected results of such asymmetry. Roche et al.[22]

studied the outflow patterns of iron and slag in a largethree-taphole blast furnace and classified the normalizedoutflow share of slag by principal component analysis.The authors found large changes in the drainage fromdifferent tapholes, including strong imbalance andgradual changes in the outflow patterns.With the aim of gaining understanding about the

factors in the complex draining system that could liebehind such asymmetry, some cases were simulated withthe model after imposing asymmetric conditions at thetapholes. Figure 9(a) shows the quasi-stationary state ofthe hearth for a furnace where the lengths of the twooperating tapholes (subscripts 1 and 2) differ, i.e., lth;1 ¼


3 m and lth;2 ¼ 2 m, and their corresponding tapholeentrance levels in gray solid and dotted lines, respec-tively. Some imbalance is seen to arise, where the firsttaphole (TH1) that has the nominal length (solid lines),exhibits the same outflow patterns as in the Base casewith unchanged duration, while the duration of tapsfrom TH2 is clearly shorter (106 min). TH2 also drainsmore slag since the iron-slag interface lies below thetaphole, but the short tap duration leaves the final ironlevel close to the level of TH1, which promotes iron flowwhen TH1 is opened.

In practice, the effect of a short taphole can becounter-acted by selecting a smaller drill diameter. Sincethe taphole resistance is roughly proportional to thelength and to the square of the velocity (and volumeflow rate), we have Dpth � lthd

�4th . Thus, a gross estimate

of how to reduce the taphole diameter in the shortertaphole can be obtained. Denoting the desired(base-case) taphole length by lth and dimeter by dth,

we have dth ¼ dth

ffiffiffiffilthlth

4

q¼ 0:064 m

ffiffi23

4

q 0:058 m. Thus,

the diameter of TH2 should be decreased by 6 mm.The liquid levels and outflows for the revised case aredepicted in Figure 9(b), showing results that are quitesimilar to those of the Base case (cf. Figure 3(a)) Themodel predicts a small positive slag delay for TH1 and anegative one for TH2 due to their different levels. Thetap durations are 158 and 148 minutes, and the slag

share tapped from the two tapholes (cout;1 and cout;2)match the slag ratio in the inflow (Table II), so thetaphole diameter correction has restored the balance.Finally, two other sources of asymmetry are studied.

Since the local voidage of the coke bed may vary withtime, the role of a different voidage at the two operatingtapholes was investigated by changing their values by± 0.05 from the base-case value. It should be noted thatthe overall voidage of the deadman, eh, was assumed to beunaffected as the induced changes only concern theregions close to the tapholes, so the total liquid levels inEqs. [1] and [2] are not affected directly but only thepressure drop in Eq. [8]—Figure 10(a) shows that a clearimbalance has arisen. The lower coke-bed voidage at TH1(e1 ¼ 0:30) gives rise to a tap of short duration, becausethe tap-end condition of Eq. [17] is satisfied at an earlymoment due to the large value of Dpbed. The longerduration of the tap from TH2 is the result of a combi-nation of high starting liquid levels and low end levels(due to a low value of Dpbed in Eq. [17]). The different tapdurations and different levels of the iron-slag interface atthe moment when the taphole is opened lead to funda-mentally different outflow patterns of the two liquids.Iron and slag start flowing out simultaneously and atpractically equal normalized rates from TH1, and therates of increase are not very different. The slag outflowfrom TH2, in turn, is delayed (tsd;2 ¼ 20 minutesÞ, afterwhich it grows strongly and linearly.

Fig. 9—Iron and slag levels (zir, zsl) and normalized outflow rates (mi,out/mi,in) with different taphole lengths (lth;1 ¼ 3 m; lth;2 ¼ 2 m): (a) sametaphole diameters and (b) smaller diameter in TH2. Note that the inner ends of the two tapholes appear on different levels. i = ir (red), i = sl(blue) (Color figure online).


The other reason for asymmetry studied is the extent ofthe taphole void region. By keeping the size unchanged atTH1, but extending it to rmin ¼ 0:15 m at TH2, the stateillustrated in Figure 10(b), showing some similarities, butalso some differences, compared to the state after thebed-voidage change (Figure 10(a)). However, the slag levelis lowered due to the smaller flow resistance, and also theiron level is shifted downwards. This yields a long tapduration for TH2, which lowers the iron level so much thatthere is a clear period of slag-only flow (tsd;2 ¼� 8 minutes) as TH1 is opened. This taphole is charac-terized by a particularly strong initial outflow of slag. As aresult of this, cout is much higher in TH1 than in TH2,where the initial slag outflow rate is very low.

To gain a further understanding of the complexinteraction of different factors on flow, the evolution ofthe main pressure-loss terms during the progress of thetap was analyzed. Figure 11(a) illustrates the contribu-tion by the viscous (solid lines) and inertial (dashedlines) terms in Eq. [8] as well as the pressure drop in thetaphole (black line, right ordinate scale) for the Basecase. Iron and slag have been depicted by red and bluelines for the coke-bed pressure drop. The taphole is seento represent the clearly largest term (218-270 kPa). Thisloss term increases slightly initially, but shows a decreaseduring the second part of the tap, largely due to tapholeerosion which lowers the velocities. In the hearth, theinertial term is the clearly dominating one for iron, dueto a low viscosity and high density. For slag, the viscousterm is more important, but the role of the inertial termgrows along with the increasing slag outflow.

The corresponding terms for the asymmetric casewhere rmin for the two tapholes differ (cf. Figure 10(b))are depicted in the lower two panels of Figure 11. TH1(Figure 11(b)) shows a lower pressure drop in thetaphole. The strong initial slag outflow during the firstminutes yields higher viscous and inertial losses in thebed, which suddenly decrease when iron starts flowingout. Simultaneously, the pressure drop in the tapholeincreases abruptly (by about 40 kPa), balancing thechange. For the remaining parts of the tap, the behavioris quite similar to that of the Base case, but the shorterdraining time limits the erosion of the taphole and hencealso the loss terms. For TH2 (Figure 11(c)), the largerradius of the taphole void region (rmin;2 ¼ 0:15 m)results in smaller pressure losses in the hearth, but thestrong initial iron outflow during indicates the role ofthe inertial term.

C. Dynamic Effects

Even though the primary aim is to keep the conditionsin the hearth as stable as possible, occasional events ordisturbances temporarily perturb the state. It is there-fore interesting to use the model to analyze the dynamicresponse of the hearth. Some examples of the dynamicbehavior of the liquid levels and outflows are thereforepresented, inspired by the findings in the analysis ofprocess data from the reference blast furnace (cf.Section IV). It should be noted that short-term dynam-ics (e.g., acceleration of the fluids) are disregarded, and

Fig. 10—Iron and slag levels (zir, zsl) and normalized outflow rates (mi,out/mi,in) for different coke-bed conditions at the tapholes: (a) differentvoidage (e1 ¼ 0:4; e2 ¼ 0:3) and (b) different size of taphole void regions (rmin;1 ¼ 0:1 m; rmin;2 ¼ 0:15 m). i = ir (red), i = sl (blue) (Colorfigure online).


that base-case settings (Table I) were used for allvariables and parameters, except the perturbedquantities.

In some situations, it is not possible to open thetaphole due to external constraints (e.g., runner main-tenance problems or lack of torpedo cars) and if theexpected duration of the disturbance is short, the blastvolume is not decreased. Figure 12 shows a case wherethe hearth was run into a quasi-stationary state before adisturbance was introduced by keeping the tapholeplugged 14 minutes longer than the base-case valuebetween the first and second tap; the taps in thefigure have been numbered for convenience. The out-flows show that iron is the first phase to flow out(tsd ¼ 17 minutes), the slag ratio of the tap is lower(cout ¼ 0:17), and the maximum iron and slag levels areelevated by about 0.15 and 0.6 m, respectively. Theresulting tap lasts about 10 minutes longer, giving timefor the iron to descend to practically the same verticallevel as after a ‘‘normal’’ tap. Therefore, the system

rapidly re-assumes its original quasi-stationary state. Asomewhat more complex disturbance is introduced afterthe third tap in the figure, where the production rate(dashed lines) is decreased linearly within two hours to8120 t=day, kept at this level during six hours, andincreased linearly back to the original level in 4 hours.For simplicity, the furnace gauge pressure (pgas � p0)was decreased in proportion to the production rate. Thedecreased production rate results in a substantial des-cent of the liquid levels in the hearth and in shorterdurations of the taps. As the iron level descends, theshare of slag in the outflow increases (to a maximum ofcout ¼ 0:26 for the sixth tap), but when the productionrate increases, the opposite occurs, and the share of slagin the outflow decreases (to a minimum of cout ¼ 0:17for the ninth tap). At the end of the depicted period, thesystem is back in its normal quasi-stationary state.The final example of dynamics studies the effect of a

3.5-hour stoppage and a longer inter-cast periodbetween taps #3 and #4. With reference to the lowerpanel of Figure 13, the furnace pressure is decreasedlinearly within two hours (after t ¼ 1000 minutes), keptat the ambient pressure during two hours, and rampedup to the normal furnace pressure in three hours. Toconsider the time lag of the liquids between the tuyerelevel and the hearth, the production rate was variedproportionally to the gauge pressure with a delay of30 minutes. The taphole was kept closed until 1.5 hourshad elapsed after the pressure started to increase.The outflows show interesting ‘‘deformed’’ patterns

for the last tap (#2) before the stoppage, due to thedecrease in liquid inflows and furnace pressure. The firsttap after the stoppage (#3) has a strong iron outflow anda clear slag delay (tsd 50min). Hence, this tap drains

Fig. 12—Liquid levels (zir and zsl) and inflow and outflow rates(dashed and solid lines) of iron and slag (mir and msl). Inter-castperiod between taps #1 and #2 is prolonged from 6 to 20 min.Production rate is decreased after tap #3, kept lower for 6 h, andthen increased linearly back to the original level in four hours.Base-case setting of all other variables.

Fig. 11—Pressure-drop terms in the coke bed (Eq. [8]) and in thetaphole (Eq. [13]): (a) Base case, as well as (b) drainage fromTH1and (c) TH2 for the case with asymmetric size of the tapholeentrance void region, rmin (cf. Figure 10(b)).


considerably less slag (cout 0:16). The longer inter-castperiod that follows delays the slag outflow of the nexttap (#4) even more (tsd ¼ 57min) and extends itsduration to almost ttap ¼ 180min: The slag share risesslightly and in the fifth tap it is cout ¼ 0:25. After this,the value gradually decreases towards cin. The outflowscan be better understood by studying the liquid levels inthe upper panel of Figure 13. In the final tap (#2) beforethe stoppage, the liquids descend to low levels, but thelevels increase considerably during the period when theproduction has commenced but the tapholes are keptclosed (black lines). The high iron level gives rise to aslag delay of tap #3. Due to the long inter-cast periodthat follows between taps #3 and #4, the slag level raisesfurther, yielding a long tap (#4) during which the ironlevel descends well below the taphole. This is the reasonwhy two taps (#3 and #4) with cout<cin are followed bytaps with cout>cin.

IV. OUTFLOWS IN A THREE-TAPHOLE BLASTFURNACE

This section presents a comparison with some of thefindings of the simulation study with process data fromBF 7 of Tata Steel Europe in IJmuiden, the Netherlands,which is a large (dh ¼ 14m) three-taphole blast furnace.In this furnace, the outflow rates of iron and slag are‘‘measured’’ by differencing of results from frequentweighing of the torpedoes and measurement informa-tion from the slag granulation units. The former signal isconsidered fairly accurate, while the latter is known tobe more uncertain.[23] Despite potential inaccuracies, thesignals reported in the historical database of the steel

plant were used as such in this study. In analyzing theresults, one should keep in mind that time lags caused bythe main trough and runner may occur. The refractorystate during the present campaign was estimated by aninverse heat-transfer model,[32] and based on this hearthgeometry a force balance was stated and solved,indicating that the dead man is likely to sit in BF7.[33]

The outflows from the furnace was analyzed by Rocheet al.[18] for a three-month period from early 2016holding more than 800 taps. The data set, together withanother more extensive one (> 1400 taps), was laterstudied in a classification of the liquid outflow patternsby principal component analysis.[22] These studiesdemonstrated that the outflow patterns may changegradually or abruptly, and that imbalance between thetwo operating tapholes may occur. Figure 14 shows theslag delay for the taps during the former data period.The values were calculated by noting the time differencebetween the moments when slag and iron started flowingout for every tap. For about 15 pct of the taps, thereported outflows were so irregular that a slag delaycould not be determined, and the value was assumed tobe zero for these. The figure illustrates that there arevery few positive delays except very small ones(tsd 2 0; 2ð �min), which may be apparent ones due tothe delays of the liquids in the trough and runners, andlarge ones due to longer inter-cast periods or stoppages(cf. Figures 12 and 13). By contrast, the negative slagdelays were frequent and exhibited certain pat-terns.[18,22,23] For instance, there were periods (aroundtaps 180, 225, 420 and 580 in Figure 14) where onetaphole drained slag first while in the other the liquidsstarted flowing out simultaneously, or there was a slagdelay of 1-2 minutes). Such imbalance was found toappear and disappear suddenly, e.g., in conjunction withtaphole changes, or gradually with time.[34]

Figures 15(a) through (c) show the (slightly filtered)normalized outflow rates of six consecutive taps withalternating tapholes. The first taphole (TH1, left column)drains slag first at a rate at least twice the production rate.

Fig. 13—Liquid levels (zir and zsl) and inflow and outflow rates(dashed and solid lines) of iron and slag (mir and msl). Theproduction is ramped down and up prior to and after a 3.5-hstoppage, respectively. A longer inter-cast period occurs betweentaps #3 and #4. Base-case setting of all other variables.

0 100 200 300 400 500 600 700 800Tap number

-20

-10

0

10

20

30

40

50

t sd (

min

)

Fig. 14—Observed slag delays in the reference furnace for a 3-monthperiod.


The slag delay reported in the lower right corner of thepanels falls in the range tsd 2 �10;�3½ �min. Throughoutthe taps, slag is the dominating liquid (expressed in thisnormalized way) drained from this taphole, with a share ofcout 0:26. By contrast, iron and slag start draining at thesame time from the other taphole (TH2, right panels) andthe share of slag is much lower (cout 0:11). Anotherexample from a later period is given by the pair inFigure 15(d), where the differences in the slag share aresmaller. It is interesting to compare these patterns with thesimulatedones, andparticularlywith those ofFigure 10(b),which have been reproduced in Figure 15(d). Thus, asproposed earlier by the present authors,[22,23,34] the condi-tions at the inner end of the taphole may explain thedraining imbalance without further differences in perme-ability of the dead man as suggested in earlier studies.[15,18]

Also other features of the simulated outflows areobserved in the measurements from the furnace. Thetaps in Figures 16(a) and (b) resemble the simulatedoutflow patterns for several different cases, e.g., thosefor smaller taphole diameter or smaller coke bed

voidage, shown in Figures 16(c) and (d), respectively(reproduced from Figures 6(a) and 7(b)). The trendsseen in the two consecutive taps in Figure 17(a) resemblethose for the simulated system with different tapholelengths, shown in the Figure 17(b) (reproduced fromFigure 9(a)).Finally, a comparison of the dynamic response of the

reference furnace hearth with the simulated counterpartis made, starting with the disturbances already studiedin Figure 12. Figure 18(a) shows the effect of a longerinter-cast period of about 20 minutes (clearly longerthan the average, which is 6 minutes) before tap #363.The slag delay of the tap is of the same order as theprolonged inter-cast period, in agreement with thefindings presented in Figure 12. The effect of a reductionand increase in the blast volume, which was found to bea recurring event in the process data analyzed, is seen inFigure 18(b), Even though the outflow rates varyconsiderably from tap to tap, a common feature withthe simulated counterpart presented in Figure 12 is thatthe share of slag increases in the outflow for the periodwhen the production rate is low.

Fig. 15—(a through d) Normalized outflows of iron (red) and slag(blue) for two sets of consecutive taps of the reference furnace usingalternating tapholes, showing a clear imbalance in iron and slagdrained and (e) simulated flows for different rmin reproduced fromFig. 10(b) (Color figure online).

Fig. 16—Normalized outflows of iron (red) and slag (blue): (a, b)two single taps and similar outflows for the simulated system with(c) smaller dth and (d) bigger eh taken from Figs. 6(a) and 7(b)(Color figure online).

Fig. 17—Normalized outflows of iron (red) and slag (blue): (a) apair of consecutive taps and (b) simulated for the case with differentlth taken from Fig. 9(a) (Color figure online).


The drainage at a stoppage is presented in Figure 19,where the evolution of the production rate is similar tothe one used in the simulation of Figure 13. Comparisonof the outflows of the figures reveals several commonfeatures, despite some discrepancies. The simulated ironoutflow before the stoppage (for tap #408) resembles thesimulated counterpart, while the slag outflows differ.For the two taps after the stoppage (#409 and #410) theobserved slag delays are similar to those in Figure 13,and the iron outflow rate is clearly above the productionrate (dashed red line). In conclusion, the similarities areencouraging, demonstrating the general feasibility of themodel.

V. CONCLUSIONS AND FUTURE WORK

A simulation model of the draining of the hearth of amulti-taphole blast furnace has been developed. Themodel is based on basic fluid mechanics and a set ofsimplifying assumptions that are justified for the systemunder study. It describes the evolution of the overalllevels of iron and slag in the hearth and the outflow rates

of the two liquids during tappings of the furnace. Specialattention was paid to describing the region in front ofthe taphole to be able to consider the pressure drops ofiron and slag, which is a prerequisite of modeling theoutflows. The arising model has been illustrated by a setof examples, where the sensitivity of the simulated liquidlevels and outflows is studied with respect to changes inthe conditions and to some model parameters. Asym-metry that arises if the conditions at/of the twoalternating tapholes are different has also been studied,as well as the system’s dynamic response to distur-bances. To verify the model, the liquid outflow ratesmeasured in a reference blast furnace were used forcomparison, revealing that several of the simulatedoutflow patterns also occurred in the real process,including strongly asymmetric performance of the twooperating tapholes with respect to slag drainage andoutflow order of the liquids. The model has demon-strated the important role played by the taphole lengthand diameter, as well as the internal conditions (e.g., bedvoidage) and in particular the state of the coke bed infront of the taphole, where a majority of the pressurelosses in the bed are located. The sensitivity analysis hasdemonstrated that the duration of the tap may vary upto one hour and that the share of slag tapped from thealternating tapholes in case of asymmetry may differsubstantially.Overall, it can be concluded that the model relatively

successfully reproduces the drainage patterns observedin the real process. Because the model is fast, it ispossible to study a multitude of both quasi-stationaryand dynamic cases of interest. The operating point ofthe hearth was found to be robust, so the dynamicresponse to short disturbances usually brought thehearth back to its original state in five taps. Thisindicates that the important features of the fluidmechanics have been captured relatively well. Themodel has been able to explain why taps in the referencefurnace often show no slag delay (i.e., both liquids startflowing simultaneously) and why negative slag delaysare clearly more frequent than positive ones (the latterones usually being the result of longer inter-castperiods). The model also explains why taps that start

Fig. 18—Inflow and outflow rates (dashed and solid lines) of iron and slag for two sets of consecutive taps from the reference furnace: (a) effectof longer inter-cast time and (b) effect of temporary decrease in production rate.

Fig. 19—Inflow and outflow rates (dashed and solid lines) of ironand slag for consecutive taps, including a 3.5-h stoppage for thereference furnace.


with slow iron flow only (clearly below the productionrate) may still drain slag after a few minutes, eventhough the iron level rises: the pressure loss in the ironflow in front of the taphole is sufficient to bend theiron-slag interface down to let out also slag. It has alsobeen demonstrated that the slow initial outflow of ironin taps that start with slag is a result of two factorsassociated with a low iron level: the narrow paththrough which iron has to flow (cf. Figure 2) increasesthe velocity and therefore the pressure loss, and the headdifference (i.e., �gqirzir in Eq. [4]), which decreases thedriving pressure difference imposing the flow. Further-more, it has been demonstrated that the conditions atthe entrance of the taphole can explain why asymmetryarises in the draining of slag from two alternatingtapholes, without the occurrence of impermeable zonesin the more central parts of the dead man.

Naturally, some challenges still remain to be tackledin the model. One is that there is a number of modelparameters that have simply been given ‘‘suitable’’values without a solid theoretical or practical justifi-cation. In experimenting with the parameters, it wasfound that similar drainage patterns could beobtained for different combinations of the modelparameter values. Thus, another set of parametervalues than those used in the present work may bemore appropriate. A complication in the verificationof the model is the large variations in the drainageobserved in the real process. Obviously, manystochastic matters influence the outflows. Forinstance, viscous fingering[35] is known to play a rolein the final phases of slag drainage, and may maketaps much shorter than expected based on the overallliquid levels. Another problem is that the outflowsrates of iron and slag are not available in manyplants, and where available, at least the slag measure-ment is inaccurate and difficult to calibrate. Likewise,the liquid levels cannot be measured directly, andindirect techniques, such as emf and strain gauges,[36]

are susceptible to noise and drift, which makes it hardto verify the model’s results.

The general findings and the drawbacks notedabove indicate some directions for future work. Themismatch between the observed and simulated out-flows that occurred in certain situations could beaddressed by revising the formulation of the pres-sure-loss equations, and particularly those concerningthe entrance loss. Since the drainage patterns in thereference furnace were sometimes found to showgradual changes,[22,34] it would be natural to developthe model to automatically adapt to the observeddrainage patterns and in this way provide a physicalon-line explanation of the hearth state. Anotherinteresting application of the model is to use it forfinding ways to balance the outflows if asymmetrictaps occur. In furnaces with a high sump depth, themodel could also be extended to consider a possiblefloating of the dead man by a simple revision of theliquid-level equations.[10,12] Finally, if the model isapplied to furnaces using overlapping taps, the logicalconditions concerning the shifts between the numberof phases being drained should be revised.

ACKNOWLEDGMENTS

Open access funding provided by Abo AkademiUniversity (ABO). The research leading to these re-sults has received funding from the European Union’sResearch Fund for Coal and Steel (RFCS) researchprogram under Grant Agreement No. 847332, and thesupport is gratefully acknowledged.

OPEN ACCESS

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LIST OF SYMBOLS

ROMAN

A Cross-section area, m2

d Diameter, me Taphole erosion rate, m/sf Friction factorg Gravitational acceleration, m/s2

j Index for phase (ir, sl, mix)l Length, mm Mass, kgp Pressure, Pat Time, minutesu Velocity, m/sV Volume, m3

x General spatial variablez Vertical coordinate, m

GREEK

a Angle, degb Initial outflow rate as share of inflow ratee Coke-bed voidagec Slag ratio, kg slag/kg ironl Viscosity, Pa sF Particle shape factorq Density, kg/m3

n Taphole roughness, m


http://creativecommons.org/licenses/by/4.0/

SUBSCRIPTS

1,2 Indices for alternating tapholesbed Coke bedc Cokedown Downward flowent Entrancej Index for phase (ir, sl)h Hearthin Inflowir Ironmin Lower limitmix Liquid mixtureout Outflowpl Plugged timesd Slag delaysl Slagtap Tapping timeth Tapholeup Upward flow. A dot above a symbol denotes a flow rate

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