Pd-based membrane reformers have been substantially studied in the past as a promising reformer to produce high-purity H2 from thermochemical conversion of methane (CH4). A variety of research approaches have been taken in the experimental and theoretical fields. The main objective of this work is a theoretical modelling to describe the process variables of the Steam Reforming of Methane (SRM) method on the Pd-based membrane reformer. These process variables describe the specific aims of each equation of the mathematical model characterizing the performance from reformer. The simulated results of the mole fractions of components (MFCs) at the outlet of the Fixed Bed Reformer (FBR) and Packed-Bed Membrane Reformer (PBMR) have been validated. When the H2O/CH4 ratio decreases in PBMR, the Endothermic Reaction Temperature (ERT) is notably increased (998.32 K) at the outlet of the PBMR's reaction zone. On the other hand, when the H2O/CH4 ratio increases in PBMR, the ERT is remarkably decreased (827.83 K) at the outlet of the PBMR's reaction zone. An increase of the spatial velocity (Ssp) indicates a reduction in the residence time of reactant molecules inside PBMR and, thus, a decrease of the ERT and conversion of CH4. In contrast, a reduction of the Ssp shows an increase of the residence time of reactant molecules within PBMR and, therefore, a rise of the ERT and conversion of CH4. An increase of the H2O/CH4 ratio raises the conversion rate (CR) of CH4 due to the reduction of the coke content on the catalyst particles. Conversely, a reduction of the H2O/CH4 ratio decreases the CR of CH4 owing to the increase of the coke content on the catalyst particles. Contrary to the CR of CH4, the consumption-based yield (CBY) of H2 sharply decreases with the increase of the H2O/CH4 ratio. An increase of the ERT raises the thermochemical energy storage efficiency (ηtese) from 68.96% (ERT = 1023 K), 63.21% (ERT = 973 K), and 48.12% (ERT = 723 K). The chemical energy, sensible heat, and heat loss reached values of 384.96 W, 151.68 W, and 249.73 W at 973 K. The selectivity of H2 presents higher amounts in the gaseous mixture that varies from 60.98 to 73.18 while CH4 showed lower values ranging from 1.41 to 2.06. Our work is limited to the SRM method. In terms of future uses of this method, new works can be undertaken using novel materials (open-cell foams) and the physical-mathematical model (two-dimensional and three-dimensional) to evaluate the concentration polarization inside membrane reactors.