2013 Volume 53 Issue 6 Pages 1106-1111
In order to get a safer and more reproducible slag yard practice, the cooling of slags from stainless steel production in a slag yard was studied. A numerical 1D model was used to predict the spatial and temporal evolution of the temperature in the yard. This model has been validated based on temperature measurements at the surface and in the bulk of an industrial yard consisting of 22 layers. Each new layer initially cools down, but is heated again as additional layers are poured on top. In the bulk of the yard, temperatures of over 1273 K can be maintained throughout the filling of the yard. This temperature is a function of the process parameters. The validated model was used to quantify the influence of the layer thickness and the interval between subsequent layers on the temperature evolution within the yard.
In pyrometallurgy, the most important by-product are slags. This liquid oxidic phase floats on top of the liquid metal during processing to prevent oxidation through metal-air contact, to reduce heat losses to the surroundings and to remove specific impurities from the molten metal.1) After separating the liquid metal and slag, the latter is cooled to room temperature, either by a fast granulation or through slow air-cooling,2) yielding a rock-like product.
The largest slag producer in pyrometallurgy is the iron and steelmaking industry, totaling 350 to 450 million tons of slag in 2010 (U.S. Geological Survey3)). In stainless steelmaking, the amount of slag is smaller, yet substantial, reaching over 9 million tons in 2010. This slag covers 10 to 15% of the total energy consumption during the steel processing4) and represents thus a potentially valuable source for heat recovery, for instance by coupling to granulation.5,6) Typically, however, slags in stainless steelmaking are cooled in a slag yard where slags from subsequent heats are poured one on top of another. After the slags have cooled sufficiently, they can be removed and new slags can be poured. However, the time required for the slags to cool below a certain temperature depends on the specific slag pit handling and may vary between different yards, making the excavation of a slag yard a potentially hazardous operation.
Although slag yard cooling is a simple, seemingly uncontrolled method, it offers some potential to influence the cooling rate. Two main parameters can be adjusted: the interval between subsequent layers and their thickness. The first is interesting in theory, but may be very hard to alter in practice, as the slag availability is secondary to the scheme of the meltshop. However, the layer thickness can be readily adjusted by changing the size of the slag yard. By knowing how both factors affect the cooling, it would thus be possible to estimate the temperature profile throughout the slag yard at all times. This knowledge can be used to improve the reproducibility of the slag yard practice, and it provides a decision tool to determine when the yard is cold enough to be emptied. Considering the fact that large volumes of slag may remain hot or even liquid for very long times,7) as a consequence of the low thermal conductivity and the associated large thermal gradients,8) this would represent a leap forward in overall safety during slag pit handling.
In this article, the influence of the time between subsequent layers and of their thickness is evaluated through a numerical model for the temperature evolution throughout the slag yard. This model has been validated with experimental temperature measurements in an industrial yard. First, the experimental setup and the slag yard practice are introduced. Next, the model is described. The subsequent sections compare the calculated and measured temperatures and discuss the model results for varying process conditions. In the final section the main findings are summarized.
A slag yard consists of a large pit into which the slag is poured by tilting a slagpot at one end. The hot slag will flow from one end to the other (Fig. 1). Typically, a layer covers most of the yard surface, although this can be influenced by the chemistry, temperature, viscosity and the amount of slag in one pot. By knowing the amount of slag and the yard size, the average layer thickness can thus be estimated. By adjusting the size of the yard, this thickness can be influenced. The frequency at which slag pots arrive depends on a number of factors which are harder to control. Foremost, the scheme of the meltshop dictates the slag availability. Next to that, the number of furnaces and the number of slag pits that are used simultaneously affect the frequency. In addition to these rather predictable parameters, a number of less well-defined, logistic factors have an influence, like the availability of personnel and machinery to transfer a slag pot from the deslagging stand to the yard and the associated transport time. Due to this combination of factors, it is very hard to pinpoint the time of slag pouring in practice.
Schematic of the slag yard (left: top view) and of the thermocouple lance (right: front view).
Schematic illustration of the variation of the calculation domain as a function of time.
The investigated yard measured 6 × 20 m and a total of 22 layers were poured in it, yielding a cumulative height of 1.4 m. Of these 22 layers, half came from the AOD, half from the EAF. The steel temperature after tapping from the EAF and AOD is on average 1873 K and 1953 K, respectively. As mentioned above, the time of pouring in the yard is secondary to the scheme of the meltshop and consequentially the time between subsequent layers may vary greatly between steel plants. In order to enhance the general validity of the presented data, all figures related to the industrial experiments, i.e. Figs. 3, 4, 5 and 10, use the typical interval between layers as a generic time unit. Depending on the specific steel plant, this ‘layer equivalent’ can range anywhere from a couple tens of minutes up to several hours. In the parameter analysis with the validated model (Figs. 6, 7, 8, 9), standard time units, in this case hours, are used.
Thickness of the experimentally investigated slag yard as a function of normalized time. The total yard thickness increases discontinuously each time a new layer is poured in the yard. One unit on the time axis corresponds to the average time between subsequent layers.
Comparison of measured and calculated temperatures at the surface of the slag yard as a function of time. One unit on the time axis corresponds to the average time between subsequent layers. The top figure shows a close-up of the bottom figure for the first five layers.
Comparison of measured (S1 and S2) and calculated temperatures in the bulk of the slag yard as a function of time at two positions: 0.07 m (top) and 0.27 m (bottom) from the yard bottom. One unit on the time axis corresponds to the average time between subsequent layers.
To measure the temperature in the yard, a concrete lance was positioned at 1.5 m from the side of the yard and at about 10 m from the point where the slag was poured. The lance had an external diameter of 0.08 m and 6 type-S thermocouples were positioned over the height of the lance, as shown schematically in Fig. 1. The lance extended for about 0.8 m in the soil. At 0.4 m below the yard bottom a transition was made from the thermocouple cables to compensation cables, which were led through an air-cooled tube outside of the yard where they were connected to the measuring equipment. Type-K thermocouples were positioned above this horizontal duct to ensure that the temperature of the compensation cables did not exceed 378 K, the range for reliable measurements. The surface temperature was monitored by using a thermal camera at regular times. 4 h 30 min after all layers had been poured, the slag was cooled by intensively spraying water on top of the yard. This intense cooling was continued for 24 h.
The model calculates the temperature evolution in a vertical 1D section through the slag yard. There are two main regions. The first is the soil, for which a layer of 1 m is considered, which can be assumed to be semi-infinite. The second is the slag yard, which consists of a number of slag layers. Whereas the thickness of the soil remains constant, the thickness of the yard can vary as a function of time. Mathematically, each layer in the yard is treated separately, and the boundary between two subsequent layers is treated explicitly. Figure 2 illustrates schematically the variation of the calculation domain as a function of time.
Mathematically, the soil and each layer in the yard can be treated equivalently, assuming heat transport by conduction only. In cartesian coordinates, the heat transport equation in a phase separated by the boundaries sx and sx+1 can be written as (Fig. 2):9)
Herein T is the temperature, x is the spatial coordinate, H = H(r, t) is the enthalpy in J/m3 and k is the temperature dependent thermal conductivity in W/(mK).
The Landau transformation was used to distribute the nodes over each layer.8) This transformation introduces a new non-dimensional position variable in each phase v = (x – sx(t))=(sx+1(t) – sx(t)) which rescales the real positions sx(t) ≤ x ≤ sx+1(t) to 0 ≤ v ≤ 1 at all times. The inherently conservative finite volume expressions for resolving the temperature profiles at a node i at position vi with control volume boundaries vi–1/2 and vi+1/2 are obtained by integrating the resulting expression over one spacestep and timestep. An implicit formulation is used to avoid any timestep related instabilities. Details on this methodology can be found in literature.10)
Assuming perfect thermal contact at all interfaces, the continuity of fluxes at the interface between two subsequent slag layers, A and B, can be expressed as:
At the bottom of the calculation domain, an adiabatic boundary condition is imposed:
At the top of the calculation domain, corresponding to the yard-air interface, the air-cooling must be accounted for. Therefore, one of the conductive fluxes in Eq. (2) is replaced by a convective and radiative flux, with h the effective heat transfer coefficient, TS the temperature of the top surface and Tair the temperature of the bulk air:
hc is the convective contribution to the heat loss, which will be determined by comparison with the experimental data, whereas hr is the radiative contribution,
Initially the domain consists of the soil at room temperature and one slag layer at a temperature of 1873 K. This initial temperature is taken constant for each new layer, irrespective of the layer-specific time between deslagging and pouring in the yard.
Details on the discretization of the governing equations are available in literature.10) The discretized set of equations is solved iteratively until convergence:
1. Assuming perfect thermal contact at all interfaces, the heat balance (2) is used to update the interface temperature;
2. The new enthalpy profiles are solved in all phases, accounting for conditions (3) and (4) at the domain boundaries.
The thermal conductivity of the slag and the heat transfer coefficient at the yard-air interface will be fitted with the experimental measurements. The temperature dependent enthalpy from the slag was extracted from the commercial thermodynamic databases FToxid and FACT53 using FactSage for a typical EAF slag composition (CaO 35–40, SiO2 25–35, MgO 5–10, Cr2O3 5–10, Al2O3 5–10 wt%). This data was used for each layer. The temperature dependent data accounts for the heat of solidification upon cooling and for possible transformations in the solid state assuming equilibrium cooling. Even though these possible phase transformations are not considered explicitly in the calculations, i.e. each layer is considered as one phase, the contribution from the latent heat is properly accounted for. The slag density was taken constant at 2650 kg/m3.12) The soil is assumed to have the same properties as the slag.
The slag yard was allowed to cool for several days after which the part behind the lance was removed. On the resulting cross section, the different layers could be distinguished. Figure 3 shows the measured yard thickness as a function of normalized time. The yard thickness increases discontinuously each time a new layer is poured. Only 20 out of a total of 22 layers were found at the excavation position, as confirmed by visual observations during pouring, showing that the fourth and thirteenth layer only covered part of the yard and did not reach the measurement lance. This behavior can be explained qualitatively through differences in slag temperature and thus viscosity in between layers, for instance due to a lower temperature upon tapping or as a consequence of longer transport times.
The thermocouples S1 and S2 yielded reliable temperature measurements during the period in which the first 9 layers were poured. At longer times, the air cooling of the compensation cable connections was not sufficient to maintain a low enough temperature. Between layers 14 and 17, temperatures as high as 423 K were measured. Thermocouples S3 till S6, which were at higher positions, had failed before the slag had reached their respective heights. About 0.67 m above the bottom of the yard, close to the position of thermocouple S3, the lance had broken, causing the rupture of the thermocouple wires at this location. This break supposedly took place between the pouring of the 8th and 9th layers. During the excavation, a large metallic plate was found to surround the concrete measuring lance at this height.
Analysis of the measured temperatures shows that the concrete lance influences the measurements by acting both as an insulator and as a conductor. It represents a thermal resistance between the slag yard and the thermocouple which must be heated before the measured temperature increases. As a consequence, the maximum measured temperature is lower than the maximum temperature of the yard immediately after the pouring of a layer. This effect is partially off-set due to the preheating of the part of the lance and thermocouple which is not immersed in the yard yet, both by conduction through the lance and by radiation from the yard.
Figure 4 shows the measured surface temperature in the region of the lance. The temperature evolves between 1248 K and 608 K. Immediately after pouring, the surface temperature drops very rapidly: minutes after pouring the average temperature is around 1073 K. At longer times, the temperature levels off at about 673 K. The predicted surface temperature for hc = 30 W/(m2K) was superimposed on Fig. 4, yielding good quantitative agreement. This value for hc is typical for slightly moving air9) and thus physically meaningful, considering the open structure and the wind at the slag yard.
Figure 5 shows the measured temperature at two locations in the slag yard. The temperature S1, close to the bottom of the yard, continues to drop as more heat is conducted away through the soil, though still exceeds 1173 K after 9 layer equivalents. The temperature S2, representative for the bulk yard, initially drops quickly, but increases when a new layer is poured on top and eventually levels off at 1323 K. The extent to which a new layer affects the temperature in layers below differs. For S1, which is at the bottom of a very thick layer, the new layers have no pronounced effect. For S2, which is in a much thinner layer, the pouring of layers 3, 4 and 5 (to a lesser extent), result in an increase in temperature.
The predicted temperatures for k = 1.25 W/(mK) are superimposed on the experimental data in Fig. 5. For both S1 and S2 the maximum measured and predicted temperatures differ significantly. This discrepancy can be at least partially explained through the cooling effect of the concrete lance, limiting the maximum measured temperature. Moreover, the thermal resistance composed of the concrete itself, as well as of possible air layers between the thermocouple and the concrete or between the solidified slag and the concrete, will affect the initial temperature evolution13) registered by the thermocouple. This assumption is supported by the observation that after an initial transient, the effect of this resistance becomes negligible and model and experiment agree well. The bottom part of Fig. 5 shows that slight differences in the exact thermocouple position significantly alter the temperature evolution during the initial transient, due to the low conductivity of the slag. Therefore, the converged bulk temperature is taken as the main reference for validation, showing a close match. The conductivity of 1.25 W/(mK) lies within the expected range for CaO–SiO2-rich slags.7)
The optimized values for hc and k were used to run the model for a set of idealized conditions, keeping the thickness and intervals constant throughout the yard. Consider a yard consisting entirely of 0.08 m thick layers poured at one hour intervals. Figure 6 shows the variation in temperature over the fourth layer. The temperature drop is most severe at the top of the layer, where heat is lost to the environment by radiation and convection. At the bottom of the layer, the temperature initially drops very fast, as it contacts the relatively cold surface of the slag layer beneath, but starts to increase as heat is conducted towards here from the hotter, middle part of the new layer. This middle part of the layer cools significantly slower than the bottom and top parts. Once a new layer is poured on top, the large temperature gradients are reduced and the entire layer reaches an almost constant temperature which is maintained for a long time.
Calculated temperature at three different places in the fifth slag layer (poured after 4 hours) of a hypothetical yard, consisting of 0.08 m thick layers poured at 1 hour intervals.
To evaluate the effect of the layer thickness, Fig. 7 shows the temperature profile over the entire slag yard for two different layer thicknesses at two times, just before a new layer is poured. When the interval between subsequent layers is kept constant at one hour, a thicker layer, having a larger thermal mass, results in a higher temperature in the bulk of the yard. This temperature can be maintained throughout the filling of the slag yard, as illustrated in Fig. 7. The bulk temperature after five layers remains approximately constant after another five layers have been poured on top. Only the wavy profile near the top of the yard, i.e. the large temperature gradients within the upper layers, are damped when additional layers are poured on top. For a thicker layer, more time is required for the temperature profile to flatten.
Calculated temperature profiles in a hypothetical yard after two different times (5 and 10 hours) and for two different layer thicknesses (0.08 and 0.16 m). The interval between subsequent layers is taken constant at one hour.
The model has been used to evaluate the influence of the layer thickness and the interval between subsequent layers on the temperature evolution. Three temperatures are evaluated: the temperature plateau in the bulk of the yard (cf. Figs. 6 and 7) and the minimum and average temperatures of a layer immediately before a new layer is poured on top. The former will influence the microstructural evolution on the long term, whereas the latter values are indicative for the initial cooling conditions. It must be noted that in certain cases (thin layers, long intervals) the temperature plateau is only obtained for a high number of layers or after long times.
Figure 8 shows the influence of the time interval between subsequent 0.08 m thick layers, yielding an almost linear relation with the different evaluated temperatures. A longer time interval results in larger heat losses before a new layer is poured, and thus lower characteristic temperatures.
Calculated influence of the time interval between 0.08 m thick layers on characteristic temperatures in the slag yard.
Figure 9 shows the influence of the layer thickness for a 1 hour interval in between subsequent layers. For thicknesses smaller than 0.1 m, the characteristic temperatures decrease significantly for decreasing thickness. When increasing the thickness over 0.1 m, the effect is limited and levels off.
Calculated influence of the layer thickness on characteristic temperatures in the slag yard for a 1 hour interval in between subsequent layers.
Figures 8 and 9 clearly show that the temperature in a yard varies greatly with the slag yard conditions. In industrial practice, the interval between layers and the thickness of these layers is typically not constant. As a consequence, the temperature will vary throughout the yard. To illustrate this, consider again the industrial experiment for which the thickness evolution of the yard is given in Fig. 3. Figure 10 shows the predicted temperature profile in this experimentally investigated yard at four times, i.e. for four different total yard thicknesses. Due to the low thermal conductivity of the slag, the temperature profile through the yard acts as a memory of the conditions that were used in a certain zone of the yard. For instance, at 0.6 m from the bottom of the yard, a number of thick layers were poured, resulting in a high temperature plateau. At 1 m from the bottom, several thin layers were poured, yielding a low temperature plateau. Even when several additional layers have been poured on top, this local maximum and minimum in the temperature profile are maintained.
Calculated temperature profile in the experimentally investigated slag yard at different times. One layer equivalent corresponds to the average time between subsequent layers.
This relatively simple 1D model with constant thermal conductivity and perfect thermal contact between all layers yields good agreement with experimental data and can be used as a predictive tool for slag yard cooling. There are, however, a number of restrictions to account for. First, in practice the conditions may vary strongly within one yard, as illustrated in Fig. 10. Even though the conditions required for a specific cooling profile can be theoretically determined, they may be hard to meet in practice. Second, water cooling is not considered in the model. A straightforward way to incorporate this, is by adjusting hc at the top surface. While this approach would result in faster cooling of the top part, it cannot account for the penetration of water in the bulk of the yard, and would thus underestimate the cooling rate.
A 1D model for heat transport was used to describe the cooling of a mixed EAF and AOD stainless steel slag yard. Fitting of the predicted data to measured temperatures at the surface and in the bulk of the slag yard yields physically relevant values for the convective heat transfer coefficient at the top, hc = 30 W/(m2K), and for the thermal conductivity of the slag, k = 1.25 W/(mK), respectively. It was found that under typical industrial conditions, a layer in the bulk of the yard reaches a constant temperature after an initial transient period. This temperature may stay over 1273 K throughout the filling of the yard. The influence of the interval between subsequent layers and their thickness on this temperature were evaluated with the model. The bulk temperature decreases almost linearly with increasing interval. For layers thinner than 0.1 m the temperature increases strongly with increasing thickness, whereas for layers thicker than 0.1 m the influence is limited. The model can be used in practice to estimate the time required to cool a yard with layers of different thickness below a certain temperature. This knowledge will contribute to improved reproducibility and safety during slag pit handling.