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Show Since the rates governing the formation and destruction of N O x are of the same order of magnitude as those governing mixing, the assumption that chemical reaction is fast compared to mixing is inaccurate for these species. To account for the rate of formation of these species in the model, additional equations governing the formation of thermal, prompt, and fuel N O x are solved in a "post process" analysis. These equations are de-coupled from the equations governing the turbulent flow field since the formation of these trace species has a negligible effect on the velocity field. Thus, the converged velocity field is used in the equations governing N O x. Since radiation is typically the most significant mode of heat transfer to the process coils in a process furnace, it is critical that the radiation field be accurately represented. Accurately simulating radiative transfer to specific regions in a system requires a model which can account for both absorbing-emitting radiation processes and complex system geometries, including arbitrary structures such as process coils. Additionally, it is desirable that any radiative model selected be computationally efficient in terms of execution time and storage to allow coupling with other routines in a comprehensive combustion model. REI's process heater model utilizes the discrete-ordinates method which has been shown to be a good choice for modeling radiation in combustion systems, both in terms of computational efficiency and accuracy. This method retains the directional dependency of the radiation intensity in a way that other flux models are unable to achieve, yet provides for a finite-difference or finite-volume solution that is more computationally efficient than zone methods and more deterministic than Monte Carlo methods. The development of the discrete-ordinates method and its application to a number of complex geometries (e.g., Adams, 1993; A d a m s and Smith, 1993) have been presented in the literature and serve to validate the use of this method in accurately modeling radiative heat transfer in process heaters (Adams, 1993; A d a m s & Smith, 1993; A d a m s & Smith, 1995). 2.2.2 Particle Phase Combustion Along with the capability of modeling gas phase combustion and turbulent transport, the model is also equipped to handle condensed phase turbulent transport, dispersion, and reaction. This capability makes possible the simulation of practical combustion processes which use solid particles, liquid droplets, or slurries as fuels in turbulent environments. In the context of modeling cracking furnaces, this capability makes possible the simulation of oil or coal fired furnaces or coke particle burnout within the radiant firebox during decoking operations. Predictions of simulations of this latter application are discussed in section 3.2. The turbulent transport of particles is solved for in a Lagrangian reference frame by modeling the time evolution of a probability density function (PDF) for the particle position. The value of this time evolving PDF, at any location, represents the probability of finding particles of the corresponding type and starting position, with that residence time, at that location in the flow field. This probability is used to obtain the expected number density of particles with the corresponding properties in each computational volume. The contribution to mass, momentum, and energy by these particles in each Eulerian computational cell is added dynamically while tracking the particle P D F to provide source terms which are coupled into the Eulerian gas phase transport equations. The mean particle position and its variance are expressed as ordinary differential equations, with the aerodynamic drag force 3 |