Mathematical Modelling of a Cupola Furnace

Mathematical Modelling of a Cupola Furnace In mineral wool production minerals are melted in a cupola furnace. The objective of the project is to develop a simulation model in order to be able to simulate different raw materials or other changes in operation, which are difficult or very costly to test on full-scale furnaces. The benefits from a model should be gaining knowledge of the operation of a cupola with the intention of optimising the operation. In a cupola furnace several complex phenomena take place: counter current flow of coke/rocks/melt and air, combustion and gasification of coke, preheating, melting and superheating of mineral raw materials and heat and mass transfer to/from the coke and rocks/melt. The phenomena are modelled with a distributed model. The model has been validated with full-scale experimental data.

Figure 1: ROCKWOOL production process. The cupola is a vertical shaft furnace similar to blast furnaces as illustrated in figure 2. Coke and raw materials are continuously charged to the top of the cupola and hot air is blasted through the tuyeres (nozzles) at the bottom of the furnace. The oxygen in the blast air is consumed in the combustion from the tuyeres and 0.5m up. Above this, where no oxygen is present the up flowing gas and combustion products heat the down flowing coke and raw materials and melt the raw materials. Below the tuyeres the melt is collected in a melt bath that is maintained at a certain level by a siphon.

Objectives The Ph.D. project was initiated because the thermal efficiency of cupola furnaces used in production of ROCKWOOL is very low, less than 50%. The cupola operation has been improved over the 70 years that the cupola has been used. However, in the last 10 years only minor improvements have been made. The developments have been trial and error. This project should provide new knowledge that can facilitate new improvements based on a more fundamental understanding of the process. Also the project should provide a tool for development and trouble shooting, i.e. a computerised model.

Figure 2: Scketch of a cupola furnace

The process

Experimental

ROCKWOOL is produced through the process illustrated in figure 1. To the left in the figure the coke and raw materials (rocks, briquettes, etc.) are charged into silos. From the silos the coke and raw materials are weighed onto a conveyor belt that transport it to the top of the cupola furnace. In the cupola the coke is combusted releasing heat that is utilised for heating and melting the raw materials. The melt runs from the cupola to the spinning machines where the melt is spun to fibers. The fibers are mixed with an organic binder and collected on a conveyor belt as wool. The conveyor belt runs through the curing oven where the binder is cured to give the wool its stable structure. Then only cutting and packing remains before the product is shipped to

the customer.

Lab-scale and full-scale measurements have been carried out in the project: The lab-scale measurements include measurements of the properties of coke and of raw materials. The measurement results where used as input to the mathematical model described next. The full-scale measurements include inputs to and outputs from the cupola and the temperature and gas composition inside the cupola as function of position. The full-scale measurements were used for calibration and validation of the mathematical model.

The Model The developed mathematical model is a distributed 1-D

static model. The model describes mass flow and temperature of the raw materials, coke and gas phase and

phase temperatures as function of vertical position. The figure shows good agreement of the modelled and measured temperatures indicating that the model is valid.

The model accounts for eight chemical reactions in the cupola: C + 1/2 O2 → CO C + H2O → CO + H2 C + CO2 → 2 CO CO + 1/2 O2 ↔ CO2 H2 + 1/2 O2 → H2O CaCO3 → CaO + CO2 FeO → Fe + ½O2 Fe2O3 → 2Fe + 1½O2 Heat transfer between the phases is modelled as convection and radiation and mass transfer is modelled as convection. The interactions are illustrated in figure 3.

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T / oC

the chemical composition of the gas phase.

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Distance from Tuyeres / m

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Figure 5: Gas temperature as function of vertical position in the cupola, modelled and measured.

Application

The model predicts mass flows, temperature and chemical composition based on the specified inputs.

The model can be used for investigating the cupola in several ways. The model is particularly useful for providing fast and cheap predictions of how operational changes affects the cupola.

The model contains a number of tunable parameters, e.g. a correction factor to the mass transfer to account for deviation from spherical shape of the particles. The tunable parameters were tuned for the model to fit the measured input/output data, i.e. the model was calibrated.

Figure 6 shows an example of the use of the model. Simulations have been made with varying oxygen content in the blast air and varying temperature of the blast air. The coke percentage in charge is then adjusted to maintain a certain temperature of the melt leaving the cupola.

q

q q

q

q q

Limestone

Melt

Rocks

Gas

Coke

Surroundings

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Figure 6 shows that the cupola is more sensitive towards changes in oxygen content in the blast air at low concentrations, and that the sensitivity is larger at a given oxygen concentration when the blast air is 500°C than when it is 800°C. This shows that under some circumstances oxygen enrichment may be beneficial, while under others it may not. No unambiguous conclusion can be drawn. 14

Figure 3: Heat and mass transfer interactions in the model (q: heat, m: mass).

Successful calibration of the model to input/output data does not guarantee that the model has captured the essential phenomena of the cupola. Thus the calibrated model was subsequently validated. The validation was made by comparing the experimental data obtained inside the cupola with model simulations. Figure 4 and 5 show examples of the validation.

Coke / %

Validation

500 oC 800 oC

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Figure 6: Coke percentage necessary to maintain a certain melt temperature as function of the oxygen concentration in the blast air

Figure 4 shows the CO content in the gas phase as function of vertical position. The figure contains modelled results and probe measurements. The probe measurements were made at the wall, at the centre and midway between the centre and wall. The figure shows that the modelled CO profile matches the measurements, indicating that the model is valid. 15 W all H alf w ay C entre M od el 10

C O / %

Conclusion A 1-D static model of a cupola furnace for stone wool production has been developed and successfully calibrated to experimental data and validate against other experimental data. The model can be used for fast and cheap investigation of the cupola.

Acknowledgements This project was carried out in collaboration with ROCKWOOL International A/S. Financial support for this project from ROCKWOOL International A/S the Danish Ministry of Business and Energy is gratefully acknowledged.

Edition finished: 1 May 2002

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Figure 4: Measured and modelled CO concentrations in the gas phase as function of vertical position. Figure 5 show modelled and measured gas

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O2 / %

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