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 (Smass 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 |
2.4 CFD for Oxy‐fuel Combustion Technologies: The Application of Single‐Phase Reactive Flows and Particle Tracking Algorithms
Oxy‐fuel combustion is another technology that has also received a great share of attention in terms of CFD modeling, given its future potential as an economically viable carbon capture technique [48]. In burning fuel in an (almost pure) oxygen atmosphere instead of air, the products of the reaction are mainly water vapor and carbon dioxide. This results in extraordinary ease of separation of CO2 from the exhaust gas stream. CFD models of oxy‐combustion systems do not have a different setup from other combustion models, which consist mainly in a single‐phase, multispecies setup where the relevant reaction kinetics need to be specified. It is worth mentioning however that radiation models need to be incorporated because of the high temperatures attained within the burning chamber. Exceptions to the common single‐phase approach are the study of oxy‐fuel combustion of solid particulate fuels such as the work presented by Wu et al. [49], where the Eulerian approach discussed earlier was implemented in order to track the movement of the solid phase, and the work of Bhuiyan and Naser [50], who applied the Eulerian–Lagrangian method. Table 2.3 summarizes some recent CFD studies in oxy‐fuel technologies. Also, a look at the literature shows that some reported studies on oxy‐fuel CFD simulations have been combined with process simulations in co‐simulation strategies. Such is the work published by Edge et al. [54] and Fei et al. [55]. Co‐simulation is the object of the Section 2.8, where it will be discussed further because it can give way to enhanced numerical predictions with implications also in control engineering.
2.5 CFD for Carbon Storage and Enhanced Oil Recovery (EOR): The Link Between Advanced Imaging Techniques and CFD
In terms of carbon storage and enhanced oil recovery, CFD simulations can be applied at various scales in a way similar to the methodology discussed earlier in this chapter for amine scrubbers. The most interesting scale appears to be (according to the number of articles published) the small scale though, where it is possible to utilize the VOF method to analyze the flow across a small portion of a solid porous medium representing the geometry of the pores. In this direction, He et al. [56] studied the two‐phase flow between supercritical CO2 and water in the walls of a saline aquifer. The porous rock was assumed to be formed by detached spheres in a body‐centered cubic (BCC) arrangement. Their simulation setup allowed visualization of the displacement process (the porous medium was initially filled with water). The effect of wettability (i.e. contact angle), surface
