Patzek et al. (2013, 2014) proposed the generalized physics-based scaling curve method as an alternative approach to the empirical decline curve analysis that predicted shale gas well production. Independently, (Patzek, 2019; Patzek et al., 2019) also introduced the Generalized Extreme Value statistics to evaluate cohorts of shale wells and their survival rates. In this work, we built a conceptual reservoir model of a typical, hydraulically fractured well in the northeast Pennsylvania Marcellus shale using a commercial reservoir simulator (CMG-GEM) to validate the generalized master curve numerically. We use the simulated gas production as the input data to estimate the generalized reservoir scaling curve, and we compare it to the master curve presented in Saputra et al. (2022). Our results reveal that the physical scaling method captures the physics behind gas production from mudrock plays. Our reservoir simulations agree with the master curve. We conclude that the simple method is an excellent alternative to the current industrial forecasting methods as it is computationally cost-effective, more flexible, and requires fewer input data. Also, the numerical reservoir simulations confirm the behavior of the generalized scaling curve with the variation of selected input factors. We complemented this study by conducting a global sensitivity analysis (GSA) to systematically examine the impacts of hydraulic fracture half-length and spacing, unstimulated shale permeability and gas adsorption on the variations of two master curve scaling parameters, the gas mass in the stimulated reservoir volume (M_SRV), and the characteristic pressure interference time (τ). GSA using a reservoir simulator is prohibitive. Therefore, we implement and validate a Gaussian process emulator that represents probabilistically the scaling parameters estimated from the reservoir simulation output. We calibrate the emulator with a small set of experiments sampled with a space-filling design. The conducted study provides new insights into the relationship between the production scaling variables M_SRV and τ and the reservoir parameters. The results reveal the high importance and nonlinear effects of the hydraulic fracture height, half-length, maximum gas volume adsorbed, and matrix porosity in varying the scaling variable M_SRV. Also, the unstimulated matrix permeability and the hydraulic fracture spacing contribute significantly to nonlinear variations of the scaling variable, τ. Finally, gas adsorption has a small effect on the cumulative gas produced but significantly affects the scaling factor M_SRV. Thus, gas adsorption becomes essential when estimating the ultimate recovery factor in the Marcellus shale wells.