Ind. Eng. Chem. Res. 2003, 42, 911-919
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Gas-Liquid Mass-Transfer Coefficients in Steel Converters M. Martı´n,† C. Blanco,† M. Rendueles,‡ and M. Dı´az*,† Department of Chemical Engineering and Environmental Technology, University of Oviedo, C/ Julia´ n Claverı´a 6, 33071 Oviedo, Spain, and Project Management Area, C/ Independencia 13, 33004 Oviedo, Spain
The steel converter, a gas/steel/slag process operating at high temperature, is one of the largest three-phase reactors. Mass transfer between the different phases has a major influence on the elimination of impurities from the hot metal. The aim of the present study was to determine and obtain useful estimations of the gas-liquid transport coefficients for this important system. Because of the difficulty of obtaining experimental data from an actual converter, a detailed analysis was carried out in an analogous cold model, although some comparative values were also obtained in a real converter. Lance blowing, alone or in combination with bottom blowing, is not extensively treated in the literature. Mass-transfer coefficients were obtained by physical methods in a cold model, as well as from hot steelmaking industrial results using kinetic models. In addition, the effects of the blowing flow rates were studied, including an analysis of their influence on these mass-transfer coefficients. 1. Introduction The steel converter can be considered as a three-phase reactor, gas-steel-slag, in which reactions for the removal of C, Mn, Si, S, and P take place. These impurities are removed as oxides through reaction with the oxygen dissolved in the iron or the FeO formed in the slag. The oxides of silicon and phosphorus are fixed by the addition of CaO. MnO and CaS are removed through the slag, and CO and CO2 are removed through the gases. Figure 1 shows a simplification of the refining reactions that take place inside the steel converters as considered in this work. To determine the efficiency of the refining, it is necessary to consider the conditions of mixing in the converter, as well as the mass- and heat-transfer phenomena that influence the velocities and selectivities of the simultaneous reactions taking place. The main characteristic of the LBE (lance bubbling equilibrium) process of steelmaking is that, in addition to oxygen top blowing (LD process), there is also injection of an inert gas into the melt during or after the refining period through a porous plug. The injection of this small quantity of inert gas produces a significant improvement in the refining process, which is attributed to the lower mixing time1 obtained and other related phenomena when bottom blowing is simultaneously employed. Thus, gas stirring is introduced to enhance inclusion removal, homogenizing the melt and increasing the rate of mass transfer between the different phases present in the reactor by providing an increase in the contact area between these phases. The study of a large number of combined blowing processes shows that simultaneous bottom blowing of small quantities of an inert gas during the LD process leads to an oxidation state similar to that reached when a much higher oxygen flow rate is blown solely through the top of the reactor.2-4 * To whom correspondence should be addressed. Fax: 34985103434. E-mail:
[email protected]. † University of Oviedo. ‡ Project Management Area.
Figure 1. Synthesis of the reactions and phases under consideration in the steelmaking process.
In the steel converter, a large number of masstransfer processes are produced between the gaseous and liquid phases, such as carbon removal, gas elimination, and hydrogen or nitrogen absorption. Nitrogen can be scarcely absorbed from the atmosphere into the steel, and the steel is reoxidized in the plume zone, where the injected gas displaces the slag layer. In some cases, nitrogen can be employed as the bubbling gas instead of as an inert gas to reduce costs, in which case nitrogen is absorbed both from the atmosphere and also from the injected gas. Thus, knowledge of the mass-transfer coefficients is important because the reoxidation of the liquid steel is improved by the mass transfer that occurs.2 No data on mass-transfer coefficients in this system could be found in the literature, where studies on this system report only the effects of the gas flow rate or other operation variables; nor have experimental results been tested. In the literature, it is possible to find values of the mass-transfer coefficients in bubble columns (gas-liquid reactors with bottom blowing), but it must be emphasized that there is a considerable geometric difference between this type of reactor and the steel converter, where the depth is not much greater than the diameter as is typical in bubble columns. This means that the hydrodynamics in the two types of
10.1021/ie020177x CCC: $25.00 © 2003 American Chemical Society Published on Web 01/21/2003
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reactors are different and thus have a major influence on the mixing and mass-transfer processes. With regard to top blowing, very few data5 are available on the masstransfer coefficient when the gas is blown through a lance over the surface, and it is even more difficult to find data for combined top-bottom blowing systems. Some of the main industrial problems that have to be considered in this subject are (a) the conditions of blowing; the effects of top, bottom, and combined blowing; and the best operating gas flow rate to achieve adequate levels of the final steel and (b) the effect of power agitation, which establishes a relationship between the gas blown and the height of the lance with respect to the mass-transfer coefficient in the steel converter. This parameter determines the most adequate conditions of gas flow and lance height. However, a number of other additional subjects remain as real industrial effects that are quite impossible to simulate in cold models. These are emulsion and foam effects or agitation and transport effects produced by CO and CO2 desorption after reaction. The aim of this paper is thus to evaluate the values of the gas-liquid mass-transfer coefficients in an actual steel converter system to obtain information that can be used to improve the design and operation of the process. The gas- and liquid-side mass-transfer coefficients (kGa and kLa, respectively) were experimentally determined in a laboratory cold model designed for a study of the hydrodynamic similarities between the different types of blowing (bottom, top, and combined) when the gas flow rate is modified. For the aim of comparison, mass-transfer coefficients were obtained from industrial plant data, and two different models were employed to determine the mass-transfer coefficient in the real reactor: the carbon model and a more complete model with average temperatures for the main species involved. Finally, the values obtained employing both reactors were compared so as to study the similarities between the determined values. 2. Experimental Method The steel converter process is primarily designed to control the levels of carbon that give rise to the main characteristics of steel and, in a complimentary way, to reach the desired final levels of Si, Mn, S, and P in the steel. Removal of these impurities is achieved by oxidation with oxygen that is blown from the top of the reactor into the iron bath, according to the oversimplified scheme
(C + Si + Mn + S + P + Fe) + oxygen f CO + SiO2 + MnO + SO2 + P2O5 + FeO Both a sufficient supply of oxygen from the gas and a high gas-liquid mass-transfer coefficient are essential to accomplish the process and must be controlled in the operation of the reactor. In Figure 1 is presented a scheme of the reactions that take place in the converter, showing the three phases steel, slag, and gas and the three nuclei of reaction: the oxygen dissolved in the steel, the FeO, and the lime added to remove impurities in the slag. The volumetric gas-liquid mass-transfer coefficient was calculated using data from a steel factory employing kinetic models, fitting the values of the coefficients to the results of the plant operation. Two kinetic models were used to determine the kLa value: (a) In the first
model, only the removal of carbon (the main consumer of oxygen) was considered. The kinetics of carbon oxidation for these reactions can be expressed in terms of the mass-transfer coefficient. The volumetric masstransfer coefficient is thus obtained by fitting data from 220 reactions from the LBE process using the initial and final carbon concentrations and the sublance data, with the mass of hot metal (250 ton) and the amount of oxygen consumed in each operation (1.20 ton/min). (b) Second, a complete model was considered that takes into account the oxygen consumption due to oxidation of all affected species. Then, 30 blowings were tested, the obtained values were fitted to the model, and an expression for kLa was obtained for a given lance height and amount of oxygen blown. Because of the high temperatures reached during the process of refining, measurement of the data needed to improve the process from the dynamic point of view is very difficult, and therefore, a cold model was employed for a detailed study of the effect of various process parameters. Gas-liquid mass-transfer coefficient determinations in the cold model can be useful not only to test models and operations but also to extrapolate the conditions of reaction, because of the facility of testing the effects of different variables in the cold model. A 1/10 length-scale laboratory cold model of a real 250-ton converter was built. Once geometrical analogy had been established, physical and dynamic analogies could be introduced through the selection of fluids and additives in the water-air-oil system used to simulate the steel and slag properties. The liquidside and gas-side mass-transfer coefficients were then determined using different gas flow rates under top, bottom, and combined blowing conditions. The liquidside mass-transfer coefficient was determined by the oxygen absorption method. To decrease the initial concentration of oxygen in the liquid bulk, an appropriate amount of Na2SO3 was added to reach a uniform oxygen concentration of approximately 0.8 mg/L. The air was then blown into the reactor, and the variations in the concentration of oxygen were recorded as a function of time. The gas-side mass-transfer coefficient was determined by a humidification method. Humidity measurements before the entry of the gas into the reactor and after the exit of the gas from the reactor were carried out employing a Vaisala HM34 thermohygrometer (humidity/temperature probe). 3. The Cold Model To design a scale model, the closest geometrical and dynamic analogies must be maintained. Fixing the same values of certain selected dimensionless quantities on both scales allows the results to be extrapolated to the true scale if the relations involving these quantities are the controlling factors for the efficiency of the process. (a) Geometric Analogy. A linear relationship between the actual converter and the cold model was employed for all dimensions of the steel converter. The geometrical analogy was also maintained for the height of the lance above the level of the metallic bath. The values of the geometrical parameters used for the cold model, as well as the most significant relationships among these parameters, are reported in Table 1. The total capacity of the reactor was 250 L, although only 25% was employed (63 L) to simulate the operating conditions of the steelmaking process. The geometrical similarity between the real steel converter and the cold model is shown in Figure 2.
Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003 913 Table 1. Characteristic Geometrical Parameters geometric analogy
lance diameter (cm)
lance hole diameter (cm)
lance height (cm)
reactor diameter (cm)
bottom blowing Tuyeres equivalent diameter (mm)
bath depth (cm)
base surface (m2)
bath free surface (m2)
bottom blowing surface (cm2)
real converter cold model
18.3 1.8
7.4 0.7
220-380 21.5-37.5
630 63
3.15a 2.1
220 22.2
19.5 0.19
31.2 0.3
49.9 0.5
a
Diameter of each orifice of the porous unit. Table 2. Summary of the Physical Properties of the Real System
Figure 2. Comparison between the real steel converter and the cold model.
Figure 3. Bottom and top blowing devices.
In the real converter, the bottom blowing device is made up of 16 porous units, each of which is composed of 40 holes, as can be seen in Figure 3a. Therefore, in the real converter, the surface available for the injection of gas in bottom blowing is approximately 312 mm2/ porous unit, i.e., 49.9 cm2. Because the scale factor employed in the construction of the model was 0.1, each porous unit in the scale model consisted of 3.12 mm2 of
phase
density F (kg/m3)
viscosity µ (cP)
surface tension (dyne/cm)
steel
7150
5.85
slag
3061
71.02
σsteel ) 1046 σsteel/slag ) 806 σslag ) 360
free area for the gas flow. To obtain a bubble diameter approximately equal to the diameter of the bubbles in the real converter, the height of the trapeze was maintained constant in the laboratory model, h ) 1.08 mm. Thus, the bottom blowing device was composed of 16 holes with an equivalent diameter of 2.1 mm. In Figure 3a, the distribution of the holes both in the real converter and in the cold model can be seen. The oxygen that produces the oxidation of the hot metal is injected into the top of the converter through a lance ending in a convergent-divergent nozzle. Figure 3b shows a detail of the nozzle in the cold model. Similarly, in the cold model, the lance is formed by a 2.1-cm-diameter tube ending in a multinozzle with four holes. (b) Other Analogies. Physical Analogies: Density, Viscosity, and Surface Tension. Table 2 presents the physical properties of the real system (density, viscosity, and surface tension) considering the steel, slag, and gas phases.6-10 The simulation of the different phases coexisting in the real converter was carried out employing a threephase system (water-vaseline-air) where the steel phase was represented by water, the slag phase was represented by a light medicinal oil of vaseline, and the gas phase was represented by air. The steel phase present in the real converter was simulated in the cold model by water, as the viscosity of water is of the same order as that of the hot metal mixture, 0.2-8 cP.11 Table 3 shows the characteristic values of the steel and slag phases, as well as some relationships between the properties of the cold model and of the real system, selected because these relationships appear in equations that describe the movement of particles. The values of µ-1 and σ, easy to simulate using surfactants and viscosifiers, are also indicated in Table 3. Dynamic Analogies. According to Szekely and Themelis,12 it is possible to define three types of regimes: viscosity-controlled, surface-tension-controlled and gravity-controlled. The gravity-controlled regime is of great interest in the modeling of the steel converter because the utilization of this type of control has been justified in liquid systems when the free liquid surface is subjected to an interference, in this case, a highpressure gas jet that impinges on the surface. Because it is not possible to fix all of the dimensionless quantities, the most important forces in the system must be considered so as to determine which value is to be maintained constant. In this case, the Froude number was considered the most adequate, because this dimensionless quantity relates the inertial forces of the system
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Table 3. Physical Properties of the Model Used and Existent Relationships with the Real Model viscosity relations density relations
system
relative magnitude
interaction evolution of bubbles into steel
L-G
L′-G
exit of steel drops into the converter atmosphere motion of gas bubbles through the slag motion of slag drops in the air
( ( ( (
) ) ) )
FL - F G FL
1/2
FL - F G FG
1/2
FL′ - FG FL′
1/2
FL′ - FG FG
1/2
average real value
average model value
0.099
0.999
59.78
0.999
39.11
26.44
20.47
4. Gas-Liquid Mass-Transfer Coefficient from Data from the Industrial Converter As mentioned above, the values of the mass-transfer coefficient were calculated using two models: a carbon removal model and a complete model for the removal of the most important species. The basis and schemes for both of these approaches are presented below. (a) Carbon Model. The evolution of the oxygen mass-transfer coefficient was studied considering the hot metal as consisting fundamentally of iron and carbon. The elimination of carbon takes place through the reaction13
C + 1/2O2(g) f CO(g) General considerations for the model are as follows: complete mixing is assumed in the steel converter as a result of top and bottom blowing, all of the carbon is removed through the gases and none is removed through the slag, and the volume of reaction in the steel converter remains constant. Diffusion or chemical reaction, depending on the percentage of carbon within the bath, might control the process. The expression for the rate of the carbon oxidation process thus obtained is
1 1 1 + zkLaC/A k′C
surface tension average real value
average model value
relative magnitude (dyne cm-1)
average real value
average model value
(µsteel)-1
0.171
1-0.025
σG-L
1046
20-75
(µslag)-1
0.014
0.023
σG-L′
360
0.998
to the gravitational forces, and in this type of reactor, with top blowing, the gravitational forces exert a major influence. The operative procedure of the simulation for calculating the gas flow rates to be employed in the cold model was based on maintaining the same Froude number (Fr ) v2/gd) as in the real plant. The Froude number was determined for the operation of the real system, and this value was applied to the cold model, so that the only unknown terms were the gas flow rates and the top and bottom blowing could be calculated. Using this approach, the values obtained for the cold model from the average real operating conditions were QT ) 0.046 m3/s for top blowing and QB ) 2074 L/h for bottom blowing. In accordance with these values, the intervals of flow rates employed for the two types of blowing in these experiments were QT ) 0.028 880.0637 m3/s for top blowing and QB ) 500-5403 NL/h for bottom blowing.
rc )
relative magnitude (N-1 m3 s-1 × 10-3)
(1)
32
When integrated for a discontinuous reactor, the amount of oxygen consumed for a given amount of carbon oxidation is obtained as indicated in eq 2,14 where z is the stoichometric coefficient for oxygen
MO2,total 1 Cf 1 ln + (Cf - Co) ) b Co c W
(2)
The equation was fitted with data from a total of 220 blowings from a steelmaking converter (the same one as simulated in the cold model), LD-III Aceralia, using the actual values of initial carbon concentration, final carbon concentration, mass of hot metal, and mass of oxygen consumed in each one of the operations. The values obtained for the kinetic constant and the masstransfer coefficient, considering average values for the amount of oxygen blown, mass, and volume of the reactor were k ) 0.13 s-1 and kLa ) 0.032 s-1, respectively. (b) Complete Model with Average Temperature. A mathematical model of the simultaneous evolution of C, Si, Mn, S, P, and O for combined-blowing steelmaking based on elemental mechanistic considerations was developed. The model based on mechanistic considerations and reasonable approaches gives good concentration curves close to the experimental points, once the constants are evaluated. The hypotheses used in the model are that the components are all loaded at a single initial moment, complete mixing of the phases occurs, and the kinetics is always first-order in each reactant. The oxygen solubility is a function of temperature, and the oxygen mass-transfer coefficient has a given value for each agitation power and lance height. Additionally, the approaches used for the component removal reactions are described briefly as follows:14 (1) Carbon is assumed to be removed only by the gas phase under consideration, as indicated previously, (2) Silicon reacts analogously to carbon, although more quickly (and more exothermically), so that its removal is diffusion-controlled. (3) Manganese in the steel phase reacts reversibly with FeO in slag, giving Fe (steel) and MnO (slag). This reaction is considered instantaneous when it can be justifed that DMn[Mn] , zDFeO[FeO]* for the forward reaction and DMnO[MnO]* , DFe[Fe] for the reverse reaction. (4) Phosporous is also removed through an interfacial reaction between the steel and slag, that is affected by several factors such as temperature and FeO/P2O5 ratio; we have considered Dp[P] , zDFeO[FeO]*. (5) Sulfur is removed through the reaction of
Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003 915
SFe with CaO (slag), but this reaction only occurs after a given time, so a certain activation acts; we have considered here that an increase in temperature is the activation term. The basic kinetic equations considered are as follows
dMSi ) -0.878k(O-L)asteelMOL* dt
(3)
-kL(O-L)asteelMOL*k′MC dMC ) dt kL(O-L)asteelMOL* + k′MC
(4)
dMMn ) -0.765kL(FeO-L)asteelMFeOL* + dt 0.984kL′(Fe-L′)aslagMFeL′* (5) dMP ) -0.172kL′(P-L′)aslagMFeOL′* dt
( )
Ea dMSFe M ) Ao exp dt RT SFeL
(6)
(7)
Data from the LD-III steelmaking plant of the Aceralia Company (Spain) were used to check the validity of the model, including the concentrations of carbon, manganese, phosphorus, sulfur, and silicon and the amounts of oxygen blown for different blowing times in accordance with the strategy of the simulation. The simultaneous kinetic equations were solved for the different values of the concentrations of the components measured at different times in the plant for the given analyzed blowing configurations using the characteristic constants for each reaction as parameters, that is, the kinetic constants and the mass-transfer coefficients. The values of these constants were optimized in accordance with a theoretical profile. During the process, it is difficult to obtain process data as a function of time. Instead, three points are available: initial, final (around 20 min), and intermediate (about 2 min before the end). To optimize the elimination profiles, it is necessary to know the concentration data for each element, and theoretical profiles from the bibliographic data were initially considered to obtain the parameters. When the parameters, kinetic contants, and the different mass-transfer coefficients are optimized, a statistical study determines the validity of the proposed model. An average optimized value for the oxygen gas-liquid mass-transfer coefficient with the experimental data was found to be about kLa ) 0.17 s-1. The oxygen mass-transfer coefficient between gas and steel (G-L), is a function of the lance height, h, and the agitation power per mass unit, . The agitation power is calculated from the lance height, temperature, pressure, and gas flow rate. An increase in the agitation power (or gas flow rate) or bath temperature or a decrease in the lance height causes an increase in the G-L transport coefficients. The effect of the lance height is nevertheless different for slag-metal reactions, which can run faster with higher lance heights. The values of the mass-transfer coefficients kLa depend on the power input and the lance height via kLa ∝ ahb. The positive effect of can be transformed into the effect of G and T (gas flow rate and temperature, respectively), whereas the height of the lance decreases the kLa value. An interesting point is that a given kLa
Figure 4. Variation of the oxygen concentration with time for three gas flow rates under bottom blowing conditions.
value can be obtained with different values of G-h pairs. Thus, to obtain a given yield per unit time, optimal theoretical strategies of simultaneously reducing the gas flow rate and the height (corrosion and cost problem) can be proposed. Real existing blowing trajectories are a result of considering all of the operating issues, so that continuously decreasing the height is a frequent trajectory option. It must also to be indicated that an increase in kLa (at a low h value) favors the removal of components such as carbon, silicon, or phosphorus but also increases the quantity of FeO formed, giving rise to a loss of metallic efficiency and increasing both the amount of oxygen in the bath and the final temperature. 5. Gas-Liquid Mass-Transfer Coefficient from the Cold Model (a) Liquid-Side Mass Transfer. If the concentration at equilibrium is related to the concentration in the gaseous phase by means of Henry’s law, H ) C/AG/C/AL, then the relationship between the global mass-transfer coefficient and the individual coefficients can be expressed as
1 1 1 ) + KL kL HkG
(8)
In the case of gases with low solubilities, the liquid film controls the mass transfer (kL ≈ KL). Considering complete mixing and carrying out a mass balance for the aqueous phase,15-17 it is possible to determine the value of kLa from the variation of the oxygen concentration with time
∫CC o
O2
dCO2 / (CO 2
- CO2)
) kLa
∫tt dt o
(9)
The shape of the variation of the oxygen concentration with time is shown in Figure 4 for the three gas flow rates employed under bottom blowing conditions. The steady state is soon reached when the highest gas flow rate is employed. For bottom, top, and combined blowing, the effect of the type of blowing on the value of the liquid-side
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Table 4. Operating Conditions during Bottom, Top, and Combined Blowing bottom blowing
top blowing
QB (NL/h) 1008 P gw (atm) P ow (atm) PT (mbar) ye (%) ys (%) Ye (kg of vapor/ kg of dry air) Ys (kg of vapor/ kg of dry air) G ˆ ′ (kg of dry air/s) Tge (°C) Tgs (°C) a
0.0232 0.0250 994 16.6 93.2 0.002
0.0251 0.0262 994 16.6 95.6 0.002
0.0151 3.31 × 19.1 21.3
2028
0.0282 0.0239 996 16.6 95.3 0.0019
0.0163 10-4
6.65 × 18.5 21.5
3054
0.0263 0.0272 997 16.5 96.6 0.0019
0.0147 10-4
1.01 ×
QT 4160
0.0241 0.0250 997 16.6 96.6 0.0021
0.0170 10-3
21.2 24.9
1.38 × 16.7 22.7
5403
0.0156 10-3
1.78 × 18.0 21.3
QB (NL/h)
0.0353 0.0455 0.0637 0.0201 0.0228 988 45.6 88.1 0.0072
combined blowinga
(m3/s)
0.0215 0.0229 988 45.6 88.1 0.0073
0.0237 0.0245 988 45.8 93.6 0.0073
2028
3054
4160
0.0203 0.0225 995 27.8 90.4 0.0033
0.0224 0.0241 995 27.8 93.0 0.0033
0.0230 0.0247 995 27.7 93.3 0.0032
0.0130 0.0140 0.0155 0.0131 0.0145 0.0149 10-3
0.0406 0.0523 0.0733 0.0349 0.0353 0.0358 21.1 19.8
21.1 19.8
21.2 19.9
17.5 20.5
18.1 22.2
18.2 22.8
Top gas flow rate employed to carry out the experiments under combined blowing conditions was 0.0288 m3/s.
Figure 5. Effect of top blowing on the value of kLa.
mass-transfer coefficient was obtained for different gas flow rates. Figure 5 presents the variation of the values of kLa with the bottom gas flow rate. The mass-transfer coefficient increases as the bottom gas flow rate increases, as can be seen in this figure. On the other hand, Figure 5 also shows that the values of kLa are higher when combined blowing is employed and that the value of kLa is the greatest for the highest value of the top blowing gas flow rate. The agitation power received by the bath under combined blowing conditions is higher than that received in the case of bottom blowing. One of the parameters used to compare the cold model and the real converter is the gas blown velocity. This makes it interesting to study the variation of the masstransfer coefficient in terms of dimensionless quantities such as the Froude number, which seems to be the most adequate for examining the similarity between the two reactors. The use of the dimensionless Froude number is interesting because gravitational forces exert an important influence in this type of reactor and, consequently, they can have an important use in comparing similar systems to the real converter setup. Figure 6 presents the values obtained for kLa against the top blowing Froude number to show the influence of each type of blowing on the mass-transfer coefficient. This figure shows that the mass-transfer coefficient increases with the Froude number (i.e., the gas flow rate) and that the introduction of a bottom gas flow rate causes an increase in the value of kLa. In both Figures 5 and 6, it can be observed that combined blowing is
Figure 6. Effect of bottom blowing on the value of kLa.
Figure 7. Efficiency of each type of blowing.
the most convenient overall strategy in terms of mass transfer in comparison with either bottom or top blowing used separately. If issues such as blowing efficiency or energy use are considered, as in Figure 7, bottom blowing is found to be the main factor responsible for the mass-transfer process. The efficacy of this type of blowing (expressed as kLa/Q) is higher than that obtained by top or combined blowing. The height of the lance strongly affects the magnitude of the bottom blowing advantage, although this advantage in efficiency of bottom blowing should be general and should be maintained even with lower heights of top blowing.
Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003 917
Figure 8. Comparison of the values of kGa obtained for each type of blowing.
(b) Gas-Side Mass Transfer. The diffusion of oxygen through the gas-metal interface is the controlling factor in the carbon removal process, at least in the first stages of the process18,19 and once the temperature is high enough to increase the rate of reaction. In this study, the focus on the observable kinetics was on the liquid side of the G-L mass-transfer coefficient, but the relative importance of the gas-side resistances compared to the liquid-side resistances can be deduced from eq 9. Only if kLa , HkGa is the control in the liquid phase. In the case that the two values are similar in magnitude, the resistances in both phases play a role. No data on the gas-side mass-transfer coefficients, kGa, for top or combined blowing are available in the literature, so it is important that these values be determined. It is even more important to have some idea of these values so that the processes of absorption or stripping of other gases can be considered. The gas-side mass-transfer coefficient is determined by the humidification method, where the phenomenon is also gas-side-controlled. The kGa value in a well-mixed system can be obtained using the equation
G ˆ ′(Ys - Ye) ) kGa (P ow - P gw)/RT
(10)
Table 4 shows the operating conditions employed in the different experiments (when bottom, top, and combined blowing were employed). This table shows the values of the gas flow rates employed, as well as other operating characteristics, such as humidity and temperature. The values of kGa obtained for each type of blowing are given in Figure 8, which shows that the gas-liquid mass-transfer coefficient increases with the Froude number. This figure also shows that combined blowing (QT ) 0.0288 m3/s) is the most effective type of blowing, because the values obtained for the mass-transfer coefficient are higher even when the lowest bottom gas flow rate is employed. However, when energetic factors are considered, bottom blowing is the most efficient for mass transfer, as can be seen in Figure 9. This figure shows that the efficiency (expressed as kGa/Q) of this type of blowing is clearly greater than the efficiencies of the others types of blowing. (c) Comparison of the Mass-Transfer Coefficients. The values obtained in the cold model for kGa are much higher than the values obtained for kLa, about 100 times, in fact. The variation ranges for kGa are wider than those for kLa. The values obtained for the gas-side mass-transfer coefficient range from 0.50 to 10
Figure 9. Efficiency of each type of blowing (in combined blowing QT ) 0.0288 m3/s).
s-1, whereas the values obtained in this reactor for the liquid-side mass-transfer coefficient range from 0.004 to 0.024 s-1. The resistance to mass transfer in this reactor is fundamentally located on the liquid side (for H g 0.1). If an oxygen solubility in the liquid steel of 0.23% w/w is used (H ) 0.014), mass-transfer control in the liquid side is accomplished as long as 0.007-0.142 s-1 . 0.004-0.024 s-1 (kGaH . kLa) for values with low and high flow rates in the cold model. Although, at low flow rates the condition is rarely fulfilled, in general, this assumption is acceptable. The values obtained in the real steel converter for kLa, which averaged to 0.032 s-1 or 0.175 s-1 (for the carbon model or complete model, respectively), are higher than the values of the liquid-side mass-transfer coefficient obtained in the cold model, kLa ≈ 0.020 s-1. The kLa values thus present some differences, although they can be considered to fall in the same range, mainly when looking at the assumptions made in the analysis of the real process data. Consider, for example, the differences in the numbers of elements/reactions or in the time needed for the addition of the melting elements at the beginning of the industrial blowing process, which contributes not to carbon removal but to the steel-slag reactions. The higher values of kLa from the real model evaluations than from the cold model can be explained in different ways. Desorption of the gases CO and CO2 from the chemical reaction mixture increases the turbulence and interfacial area; in addition the production of foams in the real converter is important for mass transfer. It must be also considered that the higher temperatures increase the diffusivities, and consequently the mass-transfer coefficients, of the various species. 5. Conclusions Liquid-side (kLa) and gas-side (kGa) volumetric masstransfer coefficients for the G-L interface in a reactor with geometrical and physical analogies to a steel converter were determined. The effects of bottom and top combined blowing on the kLa and kGa values were established and compared in terms of energy efficiency. The mass-transfer coefficients increased with the Froude number or the gas flow rates; this behavior was similar in the two cases, ranging from 0.50 to 10 s-1 for kGa
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and from 0.004 to 0.024 s-1 for kLa in the range of gas flow rates simulating the blowing rates in the real plant. In the range of gas flow rates treated, combined blowing was the most convenient procedure from the point of view of mass transfer, as the highest values of the mass-transfer coefficient were obtained when this type of blowing was employed. However, if energetic considerations are made, bottom blowing was responsible for most of the mass-transfer process, as the efficiency of this type of blowing is higher than the efficiency obtained by either top or combined blowing. Data from a real plant steel converter were analyzed using two different approaches, considering the removal of only carbon or the removal of gaseous components with several complex assumptions. An initial diffusional regime and a mixed diffusional-kinetic regime at the end of the blowing were defined. The average kLa values obtained were 0.03 and 0.17 s-1, a difference that can be justified in terms of the different approaches introduced into the models. These values are lower than but comparable to that obtained from the cold model. The kLa and kGa ranges of values obtained in the cold model experiments justify the conclusion of mass-transfer control on the liquid side. The kLa values obtained with the cold model were slightly lower than those obtained in the real converter, depending on the type of blowing employed. Some of the physical differences contributing to this discrepancy are the unavoidable hydrodynamic differences between the two reactors (that is, the different values of surface tension and viscosity in the reactors) and the fact that there is no chemical reaction in the cold model, so that the effects caused by the desorption of CO and CO2 and the formation of foams on mixing (and therefore on mass transfer), in addition to the large differences in temperature affecting diffusivities, are not considered. Nomenclature
S′ ) liquid free surface, m T ) temperature, K Tge ) gas temperature at the entrance, °C Tgs ) gas temperature at the exit, °C t ) time, s V ) volume of reaction mixture, m3 W ) reaction mass, ton Xi ) molar fraction of component i Y ) absolute humidity in the gas phase, kg of vapor (kg of dry air)-1 v ) linear velocity of gas in the outlet point, m s-1 y ) relative humidity in the gas phase, % z ) stoichiometric coefficient Greek Symbols ) agitation power, W ton-1 µsteel ) steel viscosity, kg m-1 s-1 µslag ) slag viscosity, kg m-1 s-1 F ) liquid-phase density, kg m-3 σG-L ) gas-steel surface tension, dyne cm-1 σG-L′ ) gas-slag surface tension, dyne cm-1 Subscripts B ) bottom blowing e ) entrance f ) final concentration G ) gaseous phase (i-L) ) diffusivity of component i in phase L L ) liquid phase, steel L′ ) liquid phase, slag o ) initial concentration s ) exit T ) top blowing Superscripts * ) solubility value
Literature Cited
a ) interfacial area, A ) reaction area, m2 Ao ) preexponential factor, m3 mol-1 s-1 a ) interfacial area, m2 b ) fitting constant from eq 2 C ) concentration of carbon in the liquid iron, ton m-3 C /A ) solubility of gas in the liquid, ton m-3 c ) fitting constant from eq 2 D ) diffusivity, m2 s-1 D′ ) free surface diameter, m DL ) diameter of the lance hole, m d ) diameter of the outlet orifice, m do ) diameter of the gas blown orifice Ea ) activation energy (kJ mol-1) g ) acceleration of gravity, m/s2 G ˆ ′ ) mass flow of dry air at the entrance, kg s-1 h ) lance height (m) H ) Henry’s constant K ) global mass-transfer coefficient, m s-1 KG ) gas-side mass-transfer coefficient, m s-1 kL ) liquid-side mass-transfer coefficient, m s-1 k′ ) kinetic constant, s-1 Lo ) depth of the bath, m M ) mass, ton PT ) total pressure, atm P gw ) water pressure vapor at humidity temperature, atm P ow ) partial pressure of water vapor, atm Q ) gas flow rate, m3 s-1 R ) universal gas constant, J mol-1 K-1 ri ) rate of reaction of component i, mol m-3 s-1 m-1
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Received for review March 8, 2002 Revised manuscript received September 20, 2002 Accepted November 4, 2002 IE020177X
