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Alongside amine scrubbing, calcium looping (CaL) has also proved a promising technology to be implemented commercially [38]. A CaL facility consists of two reactors: the carbonator and the calciner. In the carbonator, CO₂ is chemically trapped in CaO particles to form limestone (CaCO₃); the regeneration of the sorbent and subsequent release of CO₂ takes place in the calciner. CFD offers the possibility of studying the interaction between a particulate solid phase and a gaseous phase in a fluidized bed by means of the Eulerian multiphase method. Phase tracking using the Eulerian method is (similarly to the VOF method) accomplished by solving the volume fraction field. The difference between the VOF and the Eulerian method is that a single set of conservation equations is solved in the VOF method for all of the phases involved, whereas in the Eulerian method, a different set of conservation equations is solved for each phase in the system, thus enabling the description of granular flows. The Eulerian method has been widely used in the literature to model the flow within fluidized beds, while the VOF method has traditionally been reserved to tracking free interface problems such as the gas–liquid flow within a structured packing column. The work published by Atsonios et al. [39] is a good example of the capabilities of the Eulerian model to describe the fluid‐granular flow within a CaL plant. They developed a CFD Eulerian model of both the carbonator and the calciner and linked it to advanced thermodynamic models developed using Aspen Plus to account for the reaction kinetics. The CFD setup included the two‐fluid model and the energy minimization multi‐scale (EMMS) model for calculating the drag forces between the particulate and the gas phase. Figure 2.3 shows visually the details of the mesh and the results obtained including maps of solids volume fraction and species mass fraction. In linking both CFD and process simulations, the authors bridged the gap between continuum mechanics and process modeling. An alternative to feed the reaction kinetics from external sources is to implement them directly on the CFD software by way of mass source terms linked to the mass conservation equation (S_mass term in Eq. (2.1)). This however can result in unstable convergence or even divergence, and therefore, using the stiff chemistry solver in the CFD setup might be necessary.

The work of Atsonios et al. [39] proved that a CFD strategy based on the Eulerian method is a powerful tool to obtain values of the relevant variables in any spot within the calciner. Another approach to solve the multiphase fluid–particle flow in some carbon capture technologies is the discrete element method (DEM) and the dense discrete phase model (DDPM), which can also be combined with reaction kinetics. DEM is based on the application of Newton's laws of motion to a set of particles. Maps of particle size distributions can be obtained by using DEM (instead of the less descriptive maps of volume fraction that the Eulerian method delivers). DDPM on the other hand is based on a hybrid Eulerian–Lagrangian approach, where the solid phase is tracked thanks to the application of Lagrangian mechanics, while the continuous phase is described by the Eulerian approach. Comments on research articles dealing with carbon capture technologies based on particulate solids using CFD or DEM models are gathered in Table 2.2.

Figure 2.3 (a) Details of the space discretization of the calciner, (b) map of time‐averaged solids volume fraction, (c) map of time‐averaged CO₂ mass fraction, and (d) schematic of the carbonator and mass fractions of calcium carbonate and carbon dioxide versus riser height.

Source: Atsonios et al. [39]. © Elsevier.

Table 2.2 Summary of published CFD studies concerning carbon capture technologies based on adsorption into a particulate material.

Authors	Numerical technique	Capture technology modeled and short comment on findings
Abbasi et al. [40]	CFD Euler–Euler + PBM (population balance model)	MgO solid sorbent. Detailed maps of carbon dioxide concentration, reaction rates, and solid volume fraction
Ryan et al. [41]	CFD (Euler–Euler and Eulerian–Lagrangian)	Comparison between numerical techniques (ANSYS fluent Eulerian–Lagrangian results in unstable calculations)
Barelli et al. [42]	CFD (Euler–Euler)	CaO solid sorbent. Proof of concept of a novel reactor configuration. Maps of chemical species involved
Sornumpol et al. [43]	CFD (Euler–Euler)	Chemical looping. Maps of chemical species conversion
Kim et al. [44]	CFD (Euler–Euler). The lumped element model resulted in economy of computational resources	Mineral carbonation (Ca(OH)2 solution) in a bubble column. Maps of different species hold‐up and mass transfer rate were obtained
Chen et al. [45]	CFD (Euler–Euler)	Investigated pressure swing adsorption (PSA). Transient calculations of CO2 adsorption
Ghadirian et al. [46]	CFD (Euler–Euler)	Circulating fluidized bed (CFB) reacting loop. Contours of solid volume fraction. Transient carbon dioxide conversion rates were obtained
Wang et al. [47]	Dense discrete phase model (DDPM)	Potassium‐based solid sorbent. Maps of particle size distribution were obtained