Copyright <D IFAC Automation in the Steel Industry, Kyongju, Korea, 1997 A MATHEMATICAL MODEL OF THE HEAT LOSS OF STEEL IN A METALLURGICAL LADLE Tom P. F'redman * J. Torrkulla * H. Saxen· * Heat Engineering Laboratory, Abo Akademi University Biskopsgatan 8, FIN-20500 Abo, Finland E-mail: <tfredman/jtorrkul/hsaxen>@abo.fi Abstract: A mathematical model suitable as a tool for improving temperature control in the steel plant is presented. With this tool, a number of variables such as holding time, material choice and refractory layer thicknesses can be studied with regard to their influence on the steel temperature evolution during casting. In addition, the model can be used as a decision support and forms a basis for automation of temperature control. Copyright © 1998 IFAC Keywords: Mathematical models, Process simulators, Temperature control, Heat flows, Steel industry 1. BACKGROUND In modern steelmaking, after the introduction of the continuous casting process and new refrac- tory materials, steel temperature control within the narrow bounds called for by quality requi- rements has become increasingly demanding. As holding times for steel in the ladle have increased and process logistics often overrule thermal- and energy-efficiency aspects, improved strategies for heat loss estimation for the steel are necessary. Contemporary refractory materials with improved durability and longer campaign life are thermally inferior to traditional brick material, i.e. their heat conductivity and specific heat are larger, resulting in increased heat losses from the steel. Over mul- tiple ladle cycles this can result in unacceptably high shell temperatures for the ladle, introducing problems with shell buckling and lining separa- tion. 2. INTRODUCTION Over the years, a number of thermal models for ladle systems have been presented, ranging in complexity from simple correlations for steel tem- 193 perature drop variation with time, specific to a certain plant (Olika and Bjorkman, 1993) to more involved models (Austin et al., 1992b) accounting for stratification phenomena in the steel (Verhoog et al. , 1974), (Egerton et al., 1979), (Perkins et al., 1986), (Ilegbusi and Szekely, 1987), (Austin et al., 1992a) and (Neifer et al., 1993) and effects of stirring and ladle additions. Early contributions feature simulation of heat losses and refracto- ry temperature profiles on an analog computer (Paschkis, 1956), (Paschkis and Hlinka, 1957). In order to describe steel temperature variation with time it is necessary to formulate an energy balance equation for the steel in the ladle and integrate it at the desired time instant . Included in the balance are the heat loss terms due to radiation and convection from the slag surface and due to conduction to the refractory. Since there is a two- way coupling between the energy balance and the temperature profile in the refractory these, strictly speaking, have to be solved for simultaneously. Hence, an accurate heat balance for the steel requires good estimation of loss terms of which an essential component is the calculation of the heat loss to the ladle refractory. In a number of works this was done by numerical integration of