The interfacial area transport equation (IATE) is an important constitutive relation for closure of the interfacial transfer terms in the two-fluid model. In spite of this, the current level of model validation for interfacial area transport models does not approach the rigor of the two-fluid model formulation. Typically the constants in the bubble coalescence and breakup kernels of the IATE are determined using a very subjective methodology. In order to provide a more rigorous and thorough benchmark of the models, a new approach is used in this paper. A full one-dimensional two-fluid model code is developed for vertical flows in large diameter channels. The code is largely based on the methodology used in TRAC-PF1/MOD2 (Spore, et al., 1993), however the interfacial drag is predicted using the interfacial drag model of Ishii and Zuber (1979). The IATE derived by Smith, et al. (2012) has been implemented. This code is then used to predict flow conditions matching the experimental data of Schlegel, et al. (2012; 2014). By making incremental changes in the various empirical constants the Hessian matrix of the IATE with respect to the many empirical constants, representing the error surface of the IATE, is numerically approximated. This allows the use of a Gauss-Newton algorithm to solve the Pareto optimization problem, when an appropriate objective function has been defined. The results of this analysis provide a rigorous mathematical and statistical basis for the benchmarked constants, in addition to a detailed sensitivity analysis for the various bubble coalescence and disintegration mechanisms.