## 2 Modeling  
The SE-SMR process was modeled in Aspen Plus using the Fluidbed block, which describes a simplified one-dimensional and isothermal fluidized bed fluid mechanics to simulate the carbonator/reformer. This block takes into account particle size and density, terminal velocity, vessel geometry, chemical reactions, and the interaction with the fluid dynamics. Several correlations are automatically implemented to calculate minimum fluidization velocity, transport disengagement height (TDH), and solids drag and elutriation. The FluidBed is schematized by two zones: a lower dense bed and an upper freeboard zone. When considering chemical reactions, the gas phase is modeled as a plug flow and the solids as perfectly mixed, with the balances performed in single cells approximated to a CSTR. In the Aspen 'Properties' section, the components are listed and defined with a 'Type' describing their nature and the applied thermodynamic models, in our case the gaseous species (CH\({}_{4}\), H\({}_{2}\)O, CO, CO\({}_{2}\), and H\({}_{2}\)) as 'CONVENTIONAL' and the solids as 'SOLID' type. Still, an appropriate 'Property method' must be chosen, namely the set of estimation methods used by the software to calculate thermodynamic and transport properties of the components: the 'Ideal' model was used for simulations involving low pressures, while for high pressures, the SRKKD model (Soave-Redlich Kwong-Kabadi-Danner) was used, which is more suitable for modeling real gases. Moving on to the simulation section, the main flowsheet and chemical reactions are defined. The flowsheet is shown in Figure 1. In this preliminary study it was chosen not to model the whole circulation loop including the regeneration process in a second interconnected reactor. This work therefore strictly focused on the sorption-enhanced effect in the reformer due to the utilization of a fresh CaO sorbent. The reported Aspen flowsheet consists of two reactors: a fluidized bed reactor (FB) and an RGibbs reactor, which calculates the equilibrium concentrations through the minimization of the Gibbs free energy of the species involved in the process. The latter was used to compare the performance of the more realistic FluidBed reactor with kinetic limitations with that of an ideal thermodynamic equilibrium reactor. The 'SOLIDS' stream contains the selected catalyst (Ni/Al\({}_{2}\)O\({}_{3}\)) and the sorbent (CaO). This stream was duplicated resulting in two equal flows, S-IN and S1, fed to the FluidBed and the RGibbs reactors, respectively. The GAS stream was also duplicated for the same reason, and contained the steam and methane reactants mixture. The design specifications for the FluidBed block were set to 0.129 m and 5 m for the diameter and the height, respectively, with a bed inventory of 5 kg and considering Geldart B solid particles in a size range of 400-600 \(\upmu\)m.  
Among the possible reactions that can take place in a SMR process, three main reactions are generally considered: steam reforming to CO (1), steam reforming to CO\({}_{2}\) (2), and water gas shift (3). In the 'Reactions' section of the simulation environment, the name and type of kinetics and the chemical reactions need to be specified. Calculator blocks are used in the simulations to manipulate the expressions to have the Aspen required structures and units. The selected kinetics follow two main models: Power Law for the carbonation, and the Langmuir-Hinshelwood-Hougen-Watson (LHHW) model for the other simulated reactions. After the implementation of the reaction stoichiometry, the parameters to define a kinetic factor, a driving force expression, and, for the LHHW reactions, an adsorption expression are required in the 'Reactions' section. The kinetics of the reactions implemented in this work were taken from the well-known [PERSON] study [25].