(52d) Mathematical Models for Characterizing and Predicting Heat Flux Profiles in Ethylene Cracking Units

Reasonable uniformity of heat flux is an important criterion for the performance of ethylene cracking units. An appropriate heat-flux-profile specification balances a variety of considerations including run length, conversion efficiency, and tube life. It is possible to characterize normalized heat flux profiles as a function of two parameters: the elevation at which the maximum heat flux occurs (z_max) and the heat flux at the floor (y₀). In turn, these two parameters are determined by operating conditions and furnace and burner design ? statistically, all are significant contributors to y₀ and z_max. This highlights the need to work with burner design engineers to predict the heat flux profile at the earliest possible stage in the design of ethylene units.

This paper presents mathematical heat-flux models for hearth and hearth+wall firing cases. The derivation proceeds from a jet-theory analogy and a global energy balance on the furnace. The model establishes similarity conditions for field and test units and may be used to generate real-time heat flux curves from flue-gas temperatures. These results have been incorporated into a state-of-the-art configuration program which is also described.