A Mathematical Model Of Electric Furnace Operations And Its Use For Control And Process Optimization

Through the simultaneous statement of Maxwell's equations. the turbulent Navier-Stokes equations and the differential thermal energy balance equation, a mathematical representation has been developed for heat transfer and fluid flow in electric arc furnaces. In broad outline the theoretical predictions appear to be consistent with experimental measurements. A discussion is presented of the general arc furnace control and optimization problem, together with the potential for the incorporation of the mathematical model given in the paper, into future control and optimization schemes. ELECTRIC ARC FURNACE STEELMAKING accounts for about 24% of the total steel produced in the U.S., consuming about 550kw-hr/ton of steel which amounts to about 1.4x1010 kw-hr annually. The percentage of steel produced by the electric arc furnace route has doubled since 1960 and is expected to increase further in the foreseeable future, particularly with the more extensive use of direct reduction technology. Table I shows, in terms of percentages, the principal items that contribute to the cost of running an electric arc furnace. It is seen that in addition to the fixed costs (labor, depreciation, taxes etc.) electrode costs and power consumption are the dominant inputs, and it follows that process changes that would ultimately reduce any of these cost components would have a significant impact on the efficiency of the operation. There are three main areas where progress in arc furnace design and operation must be directed in the next decade (Committee on Technology, 1981). 1. Increased furnace productivity 2. Reduction in processing cost 3. Improvement in the thermal efficiency of the furnace An estimate of the current operating efficiency of the electric arc furnaces may be obtained by comparing the theoretical minimum energy consumption per ton of steel with those achieved in operational practice. Theoretically 330-360 kw-hrs of electricity are required to melt one ton of cold scrap. For superheating, 8-12 kWh per 100°F are required. The actual energy requirements are given in Table II. It is seen that furnaces currently operate at 70-80% efficiency, with the major heat loss from the furnace resulting from the waste gases (Committee on Technology, 1981). While it is apparent that operational experience has produced a technology that is reasonably energy efficient this has been achieved in the almost complete absence of any detailed knowledge concerning the fundamental heat transfer mechanisms occuring in the furnace. The purpose of the present paper is to present a case for the usefulness of mathematical models in increasing the thermal efficiency of furnaces by investigating these heat transfer mechanisms and then combining this knowledge with existing electrode regulator mechanisms to produce truly efficient power cycles for melting and refining. In particular, existing mathematical models describing convection, radiation, and electro-magnetism in the furnace should be employed, and the development of optimization models which balance the cost of electrodes and energy against the thermal efficience of the furnace should be undertaken. Recent work in this laboratory (Szekely, McKelliget, 1981, 1982, 1983; Szekely, McKelliget, Choudhary, 1983) has made a useful start towards solving the problem of heat transfer within the electric arc furnace but the work still needs to be directly related to existing furnace power cycles and tested against plant scale measurements.