Submerged Gas Jet Penetration: A Study of Bubbling VersusJetting and Side Versus Bottom Blowing in Copper BathSmelting

JOEL P.T. KAPUSTA 1,2

1.—BBA Inc., 2020 Robert-Bourassa Blvd., Suite 300, Montreal, QC H3A 2A5, Canada.2.—e-mail: joel.kapusta@bba.ca

Although the bottom blowing ShuiKouShan process has now been widelyimplemented in China, in both lead and copper smelters, some doubts, ques-tions, and concerns still seem to prevail in the metallurgical community out-side China. In the author’s opinion, part of these doubts and concerns could beaddressed by a better general understanding of key concepts of submerged gasinjection, including gas jet trajectory and penetration, and the concept,application, and benefits of sonic injection in jetting regime. To provide someanswers, this article first offers a discussion on the historical developments ofthe theory and mathematical characterization of submerged gas jet trajectory,including the proposed criteria for the transition from bubbling to jetting re-gime and the application of the Prandtl–Meyer theory to submerged gas jets. Asecond part is devoted to a quantitative study of submerged gas jet penetrationin copper bath smelting, including a comparison between bubbling and jettingregimes, and side versus bottom blowing. In the specific cases studied, thecalculated gas jet axis trajectory length in jetting regime is 159 cm for bottomblowing, whereas it varies between 129 and 168 cm for side blowing forinclination angles of +18� to �30� to the horizontal. This means that sideblowing in the jetting regime would provide a deeper penetration and longergas jet trajectory than generally obtained by conventional bath smeltingvessels such as the Noranda and Teniente reactors. The theoretical results ofthis study do corroborate the successful high-intensity practice of the slagmake converting process at Glencore Nickel in Canada that operates underhigh oxygen shrouded injection in the jetting regime, and this would thensuggest that retrofitting conventional low-pressure, side-blowing tuyeres ofbath smelting and converting reactors with sonic injectors in jetting regimecertainly appears as a valuable option for process intensification with higheroxygen enrichment, without major process changes or large capital expendi-ture, i.e., no need for full reactor replacement.

INTRODUCTION

Research on submerged gas injection in pyromet-allurgy has produced a wealth of knowledge overthe last 60 years, with an apogee in the 1970s and1980s. In these golden decades for applied researchworldwide, both laboratory and plant trials wereconducted to elucidate critical aspects of submergedgas injection, leading to the discovery of distinctbubbling and jetting regimes, the characterizationof steady jetting conditions, or the quantification of

gas penetration into molten baths. In 1990, Brima-combe, Nakanishi, Anagbo, and Richards exhaus-tively documented the breadth of this newlyacquired global knowledge of the time in a 70-pageseminal paper on injection with more than 270references.1

Yet, despite numerous research breakthroughs ongas injection phenomena and some notable applica-tions that revolutionized the steelmaking industry,the copper bath smelting and converting practice incylindrical horizontal vessels has remained an

JOM, Vol. 69, No. 6, 2017

DOI: 10.1007/s11837-017-2336-4� 2017 The Minerals, Metals & Materials Society

970 (Published online April 7, 2017)

inherently inefficient bubbling process up until thelate 2000s. In that decade, China ENFI EngineeringCorporation (ENFI) and Dongying Fangyuan ofChina brought back to the forefront of the nonfer-rous metals industry the concept of sonic bottomblowing of highly oxygen enriched air, and applied itto copper matte smelting in their bottom blowingShuiKouShan (SKS) process in Vietnam andChina.2,3 Seasoned readers will certainly recall thatbottom blowing with shrouded tuyeres was inventedfor steelmaking by Savard and Lee in Canada in the1960s4–10 and industrially pioneered in nonferrousmetals by Lurgi in the 1980s, when they imple-mented lead sulfide smelting in Germany with theprocess conceived by Queneau and Schuhmann,which became known as the Queneau, Schuhmann,Lurgi, or Queneau–Schuhmann–Lurgi (QSL), pro-cess.11–14 For reference, in 2013, Kapusta15 andKapusta and Lee16 provided a fairly comprehensivehistorical perspective on the Savard–Lee tuyeredevelopment over three decades (1940s–1960s) andits subsequent adoption and adaptation from fer-rous to nonferrous pyrometallurgy in the followingfour and a half decades (1970s–present).

Although the SKS process has now been widelyapplied in China, with about 50 lead smelters andmore than 10 copper smelters in operation, withanother half dozen being under construction,according to Wu Shaohui of ENFI,17 some doubts,questions, and concerns continue to be raised in themetallurgical community outside China. Are theseconcerns legitimate, although typical for any newtechnology in its early deployment phase, or is theglobal nonferrous industry missing an opportunityfor a major step change? Although this article doesnot pretend or aim to provide a complete answer,reviewing specific aspects related to submerged gasinjection, however, presents an opportunity to chal-lenge the general understanding—or misunder-standing—around the concepts of bubbling andjetting regimes. In particular, the notions of gasjet trajectory and penetration are well worth revis-iting theoretically and practically as they trulydefine the differences in terms of process efficiencyand intensity between the traditional bubblingregime of the Noranda Reactor or Teniente Con-verter and the higher intensity jetting regime undersonic flow conditions of the SKS and QSL processesor the slag make converting (SMC) vessel.16

This article is composed of two main parts: (1) adiscussion on the historical developments of thetheory and mathematical characterization of sub-merged gas jet trajectory, including the proposedcriteria for the transition from bubbling to jettingand the application of the Prandtl–Meyer theory tosubmerged gas jet, and (2) a quantitative study ofsubmerged gas jet penetration in copper bathsmelting, including a comparison between bubblingand jetting regimes, and side versus bottomblowing.

SUBMERGED GAS JET TRAJECTORY

One limitation to higher oxygen enrichment ofblast air in smelting and converting vessels is theproportional increase in refractory erosion at thetuyere line. This refractory wear rate increasewith higher oxygen is generally attributed to themore intense oxidation reactions in the bathoccurring in the vicinity of the brick lining atand above the tip of the tuyeres. In that respect,the gas penetration—or lack of penetration—intothe bath has a significant impact on the life spanof the refractory lining, and consequently, it putsa stringent limit on the operating oxygen enrich-ment level compatible with a commercially viablereactor campaign length. This section will there-fore focus on the theory and mathematical char-acterization of submerged gas jet trajectory as afirst step toward predicting gas jet penetration incopper matte or white metal.

Early Mathematical Formulation

As a testament to the quality and originality ofthe research done in the 1960s and 1970s, themathematical formulation of a gas jet trajectory andpenetration into a liquid, developed by Themelis,Tarassoff, and Szekely18 and based on continuityand momentum balances, has served as a referencefor metallurgists around the world since its publi-cations in 1969. The formulation of their model topredict the axis trajectory of a gas jet inclined at anangle, h0, to the horizontal is provided in Eq. 1:

d2yr

dx2r

¼ 4

NFr�

tan2 hc

2

� �

cosh0

! ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 þ dyr

dxr

� �2s

x2rC: ð1Þ

with yr ¼ y=d0; xr ¼ x=d0; d0 is the tuyere orificediameter, NFr� is the modified Froude number, hc isthe cone angle or initial expansion angle, and C is theaverage gas fraction across the jet at xr given by Eq. 2where ql and qg are the liquid and gas densities:

C ¼1 � ql

qg

� �þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 � ql

qg

� �2þ16 ql

qgx2

r tan2 hc

2

� �r

8x2r tan2 hc

2

� � : ð2Þ

The modified Froude number, NFr� , is defined asfollows:

NFr� ¼qgu

2o

g ql � qg

� �do

where uo is the nominal gas jet velocity at the tuyereorifice, g is the acceleration of gravity, and do is thetuyere orifice diameter.

Equation 1 is a second-order nonlinear equationthat can be numerically solved with the Runge–Kutta method using the following boundaryconditions:

Submerged Gas Jet Penetration: A Study of Bubbling Versus Jetting and Side Versus BottomBlowing in Copper Bath Smelting

971

yr ¼ 0 at xr ¼1

2 tan hc

2

� � and

dyr

dxr¼ tan h0 at xr ¼

1

2 tan hc

2

� � :

The diagram on Fig. 1 illustrates a rising gas jettrajectory for a horizontal tuyere ðho ¼ 0Þ andprovides the mathematical characterization of themodel as developed by Themelis et al.18

To validate their model, Themelis et al.18 used anexperimental setup consisting of air injection intowater in Plexiglass models of a Peirce–Smith con-verter. With a long exposure photographic tech-nique, they visualized and measured the trajectoryof air jets into water at various tuyere diametersand gas velocities. Some of their photographs andone of their result graphs are reproduced forillustration in Figs. 2 and 3.

Early Evaluation of the Jet Cone Angle

One of the determining parameters in Eqs. 1 and2 to predict jet axis trajectory is the jet cone angle,i.e., the angle at which the jet cone expandsimmediately after exiting the tuyere. By using theirphotographic technique, in their experiments, The-melis et al.18 measured an average jet cone angle of20�. Applying this cone angle value in their jetpenetration formulation, they obtained a very goodagreement with their physical water model exper-iments. They believed that their air–water modelresults, including the cone angle value of 20�, couldbe extrapolated to the air–matte system of a Peirce–Smith copper converter. Nevertheless, Oryall andBrimacombe19 demonstrated that the physical prop-erties of the gas and liquid or molten bath had a

Fig. 1. Mathematical characterization of a rising gas jet trajectory.18

Fig. 2. Photographs of an air jet in water: (a) short time exposure (0.6 ms) illustrating the unstable jet, (b) long time exposure (5 s) visualizing thejet cone, and (c) long time exposure visualizing the influence of buoyancy.18

Fig. 3. Experimental results and predicted jet trajectory under theinfluence of buoyancy from Themelis et al.18 The dashed line rep-resents the calculated jet axis trajectory while the solid lines repre-sent the jet boundaries measured by long exposure photography.Note that Equation (22) on the figure corresponds to Eq. 1 in thisarticle.

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considerable impact on the jet dynamics. By com-paring air injection in water and mercury underisothermal conditions, Oryall and Brimacombe19

revealed that the jet cone angle in mercury rangedbetween 150� and 155�, a value more than seventimes greater than the angle of air jets in water. Byusing an electroresistivity probe combined with anoscilloscope, they discovered that the forward air jetpenetration in mercury was very limited. Althoughinjected horizontally, the air jets in mercuryappeared as if injected vertically.

Oryall and Brimacombe19 speculated that ifdensity were the controlling physical property,then the cone angle of ‘‘process jets’’ such as airinjected into copper matte, should have a valuebetween air jets in mercury and in water becausethe density of copper matte lies between that ofwater and mercury. This would give a cone anglein the 70�–100� range. Yet, they also pointed outthat if thermal expansion of the injected cold gasas a result of heat transfer from the hot moltenbath is taken into account, process jets shouldexpand faster than isothermal jets, and evenfaster if the reaction between the gas and bathis exothermic or produces a net increase in molesof gas, bringing the jet cone angle back to the150�–155� range.

Hoefele and Brimacombe20 discovered and delin-eated in the laboratory two regimes of flow: bub-bling and steady jetting. They complemented theirresearch by industrial measurements during nor-mal operation of a nickel converter at Inco’s (at thetime) Thompson Smelter in Manitoba and demon-strated that horizontally injected air into a con-verter was indeed discharging as discreet bubblesrising almost vertically, in a similar manner to airjets in mercury. One could then assume that thecone angle for air or oxygen enriched air injectedinto white metal or copper matte would have a valuein the range 100�–155�, and most likely in the upperportion of this range.

Transition from Bubbling to Jetting Regime

Applying Eq. 1 to predict a gas jet trajectoryunder bubbling regime is well established today. Infact, Asaki et al.21 refined the formulation for low-velocity conditions as they believed the assumptionof momentum conservation in the initial flow direc-tion of Themelis et al.18 may not hold for discretegas bubbles. On the other hand, to the best of hisknowledge, the author is not aware of publishedwork on the use of Eq. 1 for injection under jettingregime. In this respect, a key unknown is how todefine the cone angle for jetting, which is intrinsi-cally correlated to how the bubbling to jettingtransition is characterized. Various criteria havebeen proposed over the years, either based on themodified Froude number,20,22 the Mach num-ber,23,24 the ‘‘nominal’’ or underexpanded Machnumber,20,25–28 the fully expanded Mach number,29

or even, during industrial plant trials, a criterionbased on the minimum pressure necessary to keepthe tuyeres opened.30–32 The author has repeatedlybeen questioned over the years about his ownmethodology for designing punchless sonic injectorsand has experienced scepticism when respondingthat his criterion was not based on NFr� per se. Someexplanations are certainly warranted, and thisarticle offers an opportunity to provide them.

If Hoefele and Brimacombe20 were the first in theEnglish technical literature to delineate the flowregimes of bubbling and jetting as a function of NFr�

and the ratio of gas to liquid density, Sharma22

argued that their NFr� value range of 300–900 forthe bubbling to jetting transition was insufficient toavoid metal penetration into the tuyeres duringinert gas injection into molten iron or steel. Sharmaasserted that metal penetration in the tuyere wasindeed controlled by NFr� but not by the gas velocity,meaning not by the Mach number, and suggestedNFr� values of 2400–2500 or higher were necessary.Defining a criterion based on NFr� poses a problemas NFr� depends on the inverse of the tuyerediameter and on the gas and liquid densities. Thismeans that any NFr� criterion, such as that ofSharma,22 is only valid for a given gas–liquidsystem; i.e., given densities, and for a given tuyerediameter. Sharma’s criterion certainly held truewithin the context of his experiments and applica-tion of inert gas injection into molten iron and steelwith tuyeres of 1–3 mm in diameter. What wouldthen be the NFr� criterion for oxygen enriched airinjected into molten white metal with a 20–40-mmdiameter tuyere?

Seemingly in opposition to Sharma’s criterion,Farmer et al.29 stated that ‘‘it is generally agreedthat sonic velocity at the tuyere exit is required toattain jetting flow, thereby preventing the backflowof metal into the tuyere.’’ As a matter of fact,10 years earlier, Hoefele and Brimacombe20 hadobserved that for systems with a low gas-to-liquiddensity ratio, underexpanded flow conditions, andtherefore sonic velocity in the tuyeres, were neces-sary for steady jetting.

Based on the author’s experience, sonic flowconditions are indeed necessary but not necessarilysufficient. In that respect, Mori et al.25 stipulatedthat ‘‘the value of the critical gas-flow velocity is alittle bit larger than but very close to the nominalsonic velocity.’’ By accounting for the compressibil-ity property of gases, they derived a relationship forthe nominal Mach number, M0, as follows:

Po

Pmetal:¼

ffiffiffiffiffiffiffiffiffiffiffiffi2

kþ 1

r

M0 ð3Þ

where Po is the gas pressure at the tuyere exit,Pmetal. is the metallostatic pressure, and k is the gasspecific heat ratio CP/CV. Equation 3 becomes avery simple expression for the subsonic to sonicboundary at the critical condition Po = Pmetal.:

Submerged Gas Jet Penetration: A Study of Bubbling Versus Jetting and Side Versus BottomBlowing in Copper Bath Smelting

973

M0 ¼ffiffiffiffiffiffiffiffiffiffiffiffikþ 1

2

r

with M0 ¼ uo

að4Þ

where a is the sonic velocity at ambient tempera-ture. By applying their criterion for air injection(k = 1.4) into white metal, the subsonic to sonicboundary would occur at M¢ = 1.1, meaning steadyjetting would be obtained when the nominal Machnumber exceeds a value of 1.1. At this point,providing a definition of the nominal Mach numberis important to grasping its concept in full and thatof Hoefele and Brimacombe20 is both precise andconcise:

The nominal Mach number is defined, underconditions of underexpanded flow, to be theMach number that would obtain just beyondthe tip of the tuyere if the gas discharging fromthe tip accelerated uniformly in the flow direc-tion and attained the local pressure measuredat the tip. This, of course, is a fictitious numberbecause the gas undergoes a multidirectionalexpansion at the tip, but it gives a measure ofthe degree of underexpansion of the jet.

Prandtl–Meyer Theory Applied to SubmergedGas Injection

In compressible fluid flow theory, expansion wavesgenerated when a gas flow experiences a decrease inpressure are well described and characterized. Theseexpansion waves can be generated when, as perOosthuizen and Carscallen,33 ‘‘a supersonic gas flowpasses over a convex corner or when the end of a ductcontaining a gas at a pressure that is higher than inthe surrounding air is suddenly opened.’’ Such gasflows are called Prandtl–Meyer flows.

Applying the Prandtl–Meyer theory of expansionwave to sonic gas flow in a tuyere discharging intoliquid metal would certainly appear as a major leap.Based on the research work of Love et al.34 on gasdischarge into free air, Ozawa and Mori26,27 madethat leap and speculated that an underexpandedgas jet attaining sonic flow at the tuyere exit woulddischarge as a supersonic jet into molten metal.They derived the formulation to characterize thesupersonic jet initial expansion angle (or cone angle)and the fully expanded Mach number as follows:

hc ¼ 2

ffiffiffiffiffiffiffiffiffiffiffiffikþ 1

k� 1

r

tan�1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik� 1

kþ 1M2

exp : � 1� �r !

� tan�1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiM2

exp : � 1q� �

ð5Þ

M2exp : ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPexit

Pmetal:

� �ðk�1Þ=k kþ 1

2

� �� 1

" #2

k� 1

vuut ð6Þ

where Mexp. is the fully expanded Mach number ofthe supersonic jet and Pexit is the gas pressure at the

tuyere exit. By substituting Eq. 3 into Eq. 6, asimple relationship between Mexit and M¢ isobtained for air, oxygen, and nitrogen (k = 1.4) asfollows:

M2exp : ¼ 5:845M0 2=7 � 5: ð7Þ

Substituting the critical value of M¢ = 1.1 fromthe subsonic to sonic boundary of Mori et al.25 intoEq. 7 gives, interestingly, a value of Mexp. = 1.0.Equations 5 and 6 provide a means to calculate theinitial expansion angle of a gas jet injected intowhite metal under jetting conditions. Using valuesof Mexp. between 1.0 (calculated at M¢ = 1.1) and1.25 (corresponding to the criterion from Farmeret al.29) gives a cone angle of 0�–10�, which isconsiderably lower than the values of 150�–155� forinjection into white metal under bubbling regime.

In the author’s opinion, the necessary and suffi-cient condition for sonic injector design, includingfor matte smelting and converting, is that the fullyexpanded Mach number Mexp :, attains a criticalvalue larger than unity. This condition ensures thatthe gas flow reaches Mach 1, i.e., sonic velocity, atthe injector exit and that the gas flow is underex-panded. Although Mexp. is mathematically indepen-dent of the injector diameter or the liquid-to-gasdensity ratio, as opposed to NFr� , based on theauthor’s experience in sonic injection in both copperand nickel converting, the minimum or criticalvalue of Mexp. required for jetting is impacted bythe physical characteristics of the gas-molten bathsystem, particularly the gas flowrate and momen-tum and, therefore, indirectly to the injectordiameter.

Sharma,22 Farmer et al.,29 Ozawa et al.25–28 andBrimacombe et al.,19,20 all carried out their labora-tory work by using very small diameter tuyeres, inthe range of 1–5 mm, intended for gas injection intomolten iron and steel. Their criteria for jetting flowwere therefore developed and tested for small-diameter tuyeres. During plant trials of sonicinjection in the late 1990s in a nickel matteconverter at Falconbridge, now Glencore Nickel,the author had the opportunity to test the Prandtl–Meyer theory and the bubbling to jetting transitioncriteria based on Mexp: or M¢.35

As anticipated, blowing with tuyere diameterslarger than 18 mm had a marked impact on thecritical value of Mexp :, certainly resulting fromlarger gas inertia and momentum of the larger gasflowrate injected. In the course of several trialcampaigns, an optimum value was determined andtested. This new criterion for side blowing in nickelmatte, together with an annular space designcriterion, became a proprietary know-how thatensured the successful implementation of shroudedsonic injection in the Slag-Make Converter of Fal-conbridge36,37 and Hoboken converters at ThaiCopper,38,39 as well as of single-pipe sonic injectionin a Peirce–Smith converter at Lonmin Platinum.40

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SUBMERGED GAS JET PENETRATION

After discussing, in the previous section, thetheory and mathematical characterization of sub-merged gas jet trajectory, as a first step towardpredicting gas jet penetration in copper matte orwhite metal, this section provides a quantitativestudy of submerged gas jet penetration in copperbath smelting, first with a comparison betweenbubbling and jetting regimes, both in side blowing,and then between side versus bottom blowing, bothin the jetting regime. The process conditions andvessel dimensions chosen for this comparison aregiven in Table I. The gas jet axis trajectories arecalculated with Eq. 1, and the initial expansionangles for jetting are calculated with Eqs. 5 and 6.For this comparison, jet cone angles of 150� forbubbling (lower end of the 150�–155� range mea-sured by Oryall and Brimacombe19) and 20� forjetting (twice the angle from the critical angle ofFarmer et al.29) were chosen to remain on theconservative side and still demonstrate the differ-ence in forward gas penetration between the bub-bling and jetting regimes.

Bubbling Versus Jetting in Side Blowing

The effect of the jet cone angle on gas penetrationin the bubbling regime for side blowing is illustratedon Fig. 4. The curves on the figure represent theidealized centerline or axis of the gas jet trajectoryas calculated with Eqs. 1 and 2. The reader shouldremember that the actual jet has wider boundaries,as shown on Fig. 2, than this calculated gas jet axistrajectory. Qualitatively, penetration increases withdecreasing cone angle and the forward penetrationdistance from the tuyere tip obtained for the variouscone angles is in good agreement with the resultsfrom Themelis et al.18 Figure 5 provides a

comparison between the bubbling and jettingregimes for side blowing. Under the conditionsdetailed in Table I, the calculated gas penetrationunder the jetting regime for side blowing is aboutseven times larger than for bubbling, even with theconservative cone angles chosen. The impact of theinclination angle, the angle of the tuyeres inrelation to the horizontal, is illustrated on Fig. 6for side blowing in the jetting regime. A negativeangle, tuyeres inclined downward, gives a deeperand longer forward gas penetration until an incli-nation angle of about �18�. Beyond this inclinationangle, the forward penetration no longer increases.

Fig. 4. Effect of jet cone angle on gas penetration for bubbling sideblowing.

Table I. Model assumptions for gas jet penetration comparison in copper bath smelting

Vessel dimensionsVessel internal diameter (m) 4.00Average white metal level (m) 1.00Average slag level (bath depth) (m) 1.70

Side blowing Bottom blowing

Injection parametersTuyere/injector submergence (m) 1.00 1.55Tuyere/injector angle (to vertical) (�) 49 22Bath density above tuyere/injector

(mixture of slag and white metal) (kg/m3)4285 4775

Bubbling Jetting

Injection parametersTuyere/injector internal diameter 54 mm 40 mm (side)

36 mm (bottom)Blowing rate per tuyere/injector (Nm3/h) 1300 2300Tuyere/injector oxygen enrichment (%) 38 50Cone angle (initial expansion angle) (�) 150 20

Submerged Gas Jet Penetration: A Study of Bubbling Versus Jetting and Side Versus BottomBlowing in Copper Bath Smelting

975

Bubbling Versus Jetting in Side Blowing

A comparison of the gas jet axis trajectory for sideand bottom blowing, both in the jetting regime, isgiven in Fig. 7. Again, the curves on the figure rep-resent the idealized gas jet axis trajectory ascalculated with Eqs. 1 and 2. The graph clearlyshows that gas penetration away from the side wallin bottom blowing is essentially a result of thelocation of the tuyere tip deeper and closer to thecenter of the vessel compared to side blowing. The

gas jet axis trajectory is slightly curved because thestudied conditions are not truly ‘‘bottom blowing,’’the tuyere being at a 22� angle from the vertical.

Another element of comparison is the length ofthe gas jet axis trajectories, that can be calculatedwith the arc length numerical method using Simp-son’s rule. A longer trajectory length means a longertime for gas–bath interactions. The trajectorylengths calculated for side blowing are 129, 141,156, and 168 cm for inclination angles of +18�, 0�,�18�, and �30�, respectively. The trajectory lengthcalculated for bottom blowing is 159 cm, justslightly longer than for side blowing at an inclina-tion angle of �18�. If the calculated axis trajectorylengths are similar in this study for side blowing(�18� inclination) and bottom blowing (22� anglefrom vertical), the more significant difference inpractice, in the author’s opinion, resides on therecirculation matte and slag flow patterns gener-ated by side blowing compared with bottom blowing.A computational fluid dynamic (CFD) model, whichis beyond the scope of this article, would provideinsights into the recirculation matte flow within thevessel. Such a model would certainly be valuable toevaluate gas stirring capabilities, particularly ifconcentrate is added from the top via feed ports orchutes.

To visualize side and bottom blowing better, bothin the jetting regime, a scaled diagram of thesmelting vessel with the dimensions provided inTable I is presented in Fig. 8. The diagram offers acomparison of the gas jet trajectories for a sideblowing tuyere positioned at a 49� angle from thevertical and inclined by �18� from the horizontaland a bottom blowing tuyere positioned at a 22�angle from the vertical and installed radially. Once

Fig. 6. Effect of inclination angle on gas jet penetration for sideblowing jetting regime.

Fig. 7. Gas jet penetration for side versus bottom blowing in jettingregime.

Fig. 5. Gas jet penetration for bubbling (150�) versus jetting (20�) forside blowing.

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again, the ‘‘idealized’’ gas jet axis trajectory curvesin Fig. 8 represent the calculated axis trajectories.The actual gas jet boundaries widen as the gaspenetrates into the bath and away from the tuyeretip. The width of the gas jet depends on severalparameters, including the initial expansion angle,the gas and bath densities, as well as the tuyereorifice diameter, inclination angle, andsubmergence.

CONCLUSION

The following conclusions can be drawn from thisshort submerged gas jet penetration study of bub-bling versus jetting regimes and side blowing versusbottom blowing:

1. Operating under jetting conditions for sideblowing provides a major improvement com-pared with bubbling in terms of gas jet penetra-tion into the bath and away from the tuyere linerefractory, as shown in Fig. 5. In conventionallow-pressure injection, gas bubbles grow at thetip of the tuyeres and essentially rise verticallyabove the tuyere tips. With sonic underex-panded conditions, i.e., in the jetting regime,and depending on the tuyeres inclination angle,the results of this study show that the gas jetaxis penetrates 30–60 cm into the bath beforecurving upward as a result of buoyancy forces.

2. Retrofitting conventional low-pressure, side-blowing tuyeres of bath smelting (and convert-ing) reactors with sonic injectors in the jettingregime certainly appears as a very promisingoption considering the 30- to 60-cm gas jet axisforward penetration, the 129 to 168-cm gas jet

axis trajectory length, and the beneficial growthof a protective accretion at the tip of the sonictuyeres. Sonic injection would not only improvesmelting intensity but would also improve oxy-gen efficiency by minimizing or eliminatingleaks at the tuyere body connections (benefit ofpunchless operation). When appropriate, retro-fitting an existing bath smelting vessel would bemuch less capital intensive than replacing thatsmelting vessel.

3. Bottom blowing under the jetting regime doesprovide injection conditions with a long gas jetaxis trajectory through the bath at a muchgreater distance from the barrel wall andthrough a thicker layer of matte or white metal.These bottom blowing conditions should bebeneficial in terms of lower refractory erosionand high oxygen efficiency.

4. For both side and bottom blowing in the jettingregime, injectors must be designed and operatedto maintain sonic flow while ensuring the degreeof underexpansion is sufficient, yet not too large,so that the gas jet exiting at sonic velocity at thetip of the tuyere becomes supersonic immedi-ately after exiting the tuyere (Prandtl–Meyerflow).

From a purely theoretical perspective, this study ofgas jet penetration into molten copper baths mayseem incomplete to some readers, or even incorrect,since neither the Kelvin–Helmholtz (KH) andRayleigh–Taylor (RT) instabilities nor the impactof surface tension of the molten bath have beenconsidered. For instance, the wealth of literatureavailable, particularly in physics and fluid dynamics

Fig. 8. Scaled drawing of Cu smelting vessel with dimensions from Table I. Visualization of the calculated gas jet axis trajectories under jettingregime for side blowing (inclination of �18�) and bottom blowing (radial position).

Submerged Gas Jet Penetration: A Study of Bubbling Versus Jetting and Side Versus BottomBlowing in Copper Bath Smelting

977

journals, has shown that KH and RT instabilitiessignificantly impact air jet penetration into stag-nant water.

Nevertheless, two key differences between theair–water and air–molten copper systems in termsof gas jet behavior are the high temperature and the4- to 7-fold higher density of molten copper matteand slag compared to water. Although good modelsto predict air jet penetration into water have beendeveloped and validated by cold model experiments,the same cannot be said for air or oxygen injectioninto molten metals. At best, a gas jet penetrationtrend can be calculated for comparison purposes, asdone in this study.

The value of this present study and injectordesign approach, even if theoretically incomplete,is that sonic injectors designed by the author basedon the described Prandtl–Meyer flow theory, haveproven to work in commercial operations. Here, theterm ‘‘work’’ means that the injectors operate in apunchless mode, without blockage, at a constantcontrolled gas flowrate, with significantly lesssplashing, and with a life span sufficiently long toallow the process to be financially viable in aWestern economic model. So far, this has been goodenough for the author’s clients to meet their processimprovement goals.

Nevertheless, with a trend toward more and moredemanding constraints on the process operation toimprove the energy efficiency, work hygiene, andenvironmental footprint of copper smelting, con-verting, and refining vessels, gas injection technolo-gies have to continuously improve to maintain thepace of change. In that respect, the author wouldwelcome comments and suggestions from readers,particularly those experts in compressible fluiddynamics, on ways to better quantify the length ofpenetration of a gas jets into hot molten metals andslags. The objective is to continuously improve thedesign methodology for sonic injectors, particularlythose with exit diameters in the range of 25–50 mmwhere the gas momentum impact is large.

ACKNOWLEDGEMENTS

The permission and support from BBA to preparethis article is gratefully acknowledged.

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Submerged Gas Jet Penetration: A Study of Bubbling Versus Jetting and Side Versus BottomBlowing in Copper Bath Smelting

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