In the process industries, cooling capacity is an important enabler for the facility to manufacture on specification product. The cooling water network is an important part of the overall cooling system of the facility. In this paper a cooling water circuit consisting of 3 cooling towers in parallel, 2 cooling water pumps in parallel, and 11 heat exchangers in parallel, is modelled. The model developed is based on first principles and captures the dynamic, non-linear nature of the plant. The modelled plant is further complicated by continuous, as well as Boolean process variables, giving the model a hybrid nature. Energy consumption is included in the model as it is a very important parameter for plant operation. The model is fitted to real industry data by using a particle swarm optimisation approach. The model is suitable to be used for optimisation and control purposes.

A derivation of a dynamic Electric Arc Furnace (EAF) model is shown in Bekker 1) and Bekker, Craig and Pistorius.2) This model describes the time-evolution of EAF furnace and off-gas system variables. A preliminary verification of this model with measurements taken from an industrial EAF, is discussed in Bekker, Craig and Pistorius. 3) In this note the Bekker model is improved and expanded to include some process variables not modelled previously. Improvements are made to the off-gas temperature model, and a slag foam depth model is added.The off-gas model as derived by Bekker 2) is sufficient as far as the CO production rate is concerned. The mass flow through the cooling duct is also fairly accurately modelled. The off-gas temperature model, however, still had room for improvement.There are two main processes in the cooling duct which affect the temperature of the off-gas mixture. Of these, combustion adds heat to the gas, and convective heat transfer to the duct sides extracts heat from the gas. The rates of both processes were initially modelled 2) as being proportional to the difference between the off-gas temperature at the entrance to the cooling duct, and the temperature of the cooling duct walls. These two processes were remodelled to better describe the mechanics of the heat transfer that occurs.In the duct the off-gas from the furnace mixes with the air from the atmosphere that enters at the slip-gap. The CO then combusts with oxygen that enters with the air. The mass fraction of CO in the off-gas (QC CO ) reacting with the O 2 gas in the cooling duct is given by Eq. (1), where g is given by Eq. (2)

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