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Two modeling paradigms have been shown to be effective in modeling the dynamics of multi-phase heat exchangers. The more complex finite control volume approach accurately captures the distributed nature of the system parameters; while the simpler moving boundary lumped parameter approach uses effective parameter values to create a more control-oriented model. However, parameter tuning of these simpler models can be time and data intensive. This paper presents an approach to apply model reduction techniques to the finite control volume models to extract an optimal choice of effective parameters for use in the simpler control oriented models. The process can be repeated over a wide range of operating conditions to obtain maps of effective parameters which can be used to create a low-order, first principles nonlinear model of the dynamics. A key advantage of these approaches is retention of the physical nature of the system states which are lost when using standard model reduction procedures.