A Mathematical Model for a Mineral Melting Cupola Furnace

This Ph.D. project was initiated to increase the knowledge about mineral melting cupola furnaces used for stone wool production. The product aimed at improving operation of existing cupolas.

The project's focuses on development of a first engineering principles mathematical model of a mineral melting cupola furnace used for stone wool production. Results from lab scale masurements were used as input to the model, and full scale measurements were used for calibration and vaildation of the model.

The coke property measurements ranked seven cokes relevant to stone wool production after reactivity towards CO₂, and correlated the reactivity to the manufacturing process of the coke It was found that cokes produced with a long baking time were the least reactive.

The raw material property measurements supplied enthalpy as function of temperature for nine raw materials used in stone wool production. an empirical model was developed to predict the enthalpy as function of temperature based on the chemical composition of the raw material.

The full scale measurements include masurements with probes inserted horizontallythorugh the wallin the hot part of the cupola and probes inserted vertically from the top of the cupola. The temperature and gas composition were measured and melt samples were collected with the wall probes. The gas temperature was measured with the top probes. Melt samples from the wall probes, collected through the tuyeres and at the furnace outlet were used to establish where the iron oxides in the raw materials are reduced to metallic iron. An operating cuploa was quenched to obtain a picture of the internal structure. E.g. the melt zone was found between 400mm and 750 mm above the tuyeres, and the bulk porosity was found not to contradict the expectation of 0.4 - 0.5.

The mathematical model developed is a static 1-D model that predicts temperatures, gas composition and mass flow rates of each phase as function of vertical position. The model accounts for seven chemical reactions for conversion of coke, O₂, C, CO, CO₂, H₂O, FeO, Fe₃O₂ and CaCO₃. Mass transfer is modelled as convection and heat transfer as convection and radiation. The differential equations were discretised using orthogonal collocation and the algebraic equations solved using Levenberg-Marquard and Neton-Raphson methods.

The mathematical model uses the measured properties of the coke and raw material. Full scale measurements formed the basis of the calibration, and the subsequent validation. The validation shoed that the model has captured the essential phenomena sufficiently detailed for predicting temperatures and gas composition in the cupola as function of the vertical position.
Application of the model show how different operating condiction affects process changes, so that a change can be beneficial under some circumstances but not under others. E.g. oxygen enrichment is more beneficial in terms of coke savings when the blast air temperature is 500 °C than 800 °C.