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a porous layer, where the modified reaction kinetics was introduced to accommodate the effect of the catalyst. Figure 2.5a–c shows three parity plots between their numerical and experimental results, with fair agreement between them. Figure 2.5d shows a velocity contour plot and indicates the two areas mentioned above (the porous layer marked as a catalyst layer in the plot and the free flow zone at the center), whereas Figure 2.5e displays the computational mesh used. The reaction kinetics published earlier by Ohya et al. [60] were introduced in the software. In their experiments, the catalyst layer was formed using 8.5 wt% Ru–Cs/Al2O3. The model was successful in predicting the CO2 conversion percentage as a function of working temperature and pressure, which were compared to the data obtained experimentally.
Figure 2.5 (a) Parity plot showing the match between the numerical and the experimental results at atmospheric pressure, (b) at 5 bar, and (c) at 10 bar, (d) contours of axial velocity (legend in m s−1) at 250 °C and atmospheric pressure, and (e) image of the computational mesh used to obtain the numerical data.
Source: Engelbrecht et al. [59]. © Elsevier.
Engelbrecht et al. [59] thus used already published data for the reaction kinetics and introduced them on their numerical model, which was subsequently validated by direct comparison with their own experiments in terms of carbon dioxide conversion percentage. The authors not only confirmed their numerical setup as a useful tool, but also confirmed the data of Ohya et al. [60] as an adequate way of describing the reaction kinetics of the methanation reaction in the presence of 8.5 wt% Ru–Cs/Al2O3 catalyst. The added value of their simulation was therefore to spare the experimental load needed otherwise to obtain the reaction kinetics and on the other hand the insight provided in terms of variable contours and quick parametric sweep possibilities.
A similar methodology was developed by Alarcón et al. [61], who used their own experimental setup to obtain the reaction kinetics and introduced it into the simulation. They developed their model using the commercial software ANSYS Fluent and tested the effect of a catalyst formed with 15 wt% Ni as the active component and ceria as the promoter. Similarly, they only simulated one channel and defined both a free flow and a porous zone where the reaction kinetics were modified in order to account for the presence of the catalyst.
In both instances, the effect of the catalyst was thus indirectly considered by measuring the reaction kinetics and introducing their defining parameters in the simulation set‐up. The approximation of introducing the modified reaction kinetics in a porous bed is thus a well‐established trend in the literature, which can yield valuable insight into how a particular catalyst affects the development of a carbon conversion reaction.
Other numerical techniques might be useful for the numerical study of the methanation reaction in other types of reactors. In those cases where the methanation reaction occurs in a fluidized bed of catalytic powder, the Euler–Euler method and the more computationally expensive CFD‐DEM approach can be applied. Liu et al. for instance implemented the methanation reaction of carbon monoxide plus the water shift reaction in an Euler–Euler model of a fluidized bed using the solver twoPhaseEulerFoam, within the open‐source CFD library OpenFOAM. The main code was modified to accommodate the kinetic model proposed by Kopyscinski et al. [62]. The effect of feed composition and the catalyst inventory on the concentration profiles across the fluidized bed were obtained and compared to the experimental data of Kopyscinski et al. [63] showing fair agreement. Another instance of the application of the Euler–Euler method to the study of the methanation reaction was presented by Sun et al. [64], who used the specific purpose software MFIX to study the methanation reaction of carbon monoxide in a fluidized bed using the Euler–Euler approach. The effect of operating parameters and catalyst inventory are investigated and the reactor will get eventually optimized. An example of the use of the coupled CFD‐DEM model to analyze the hydrodynamics within a methanation fluidized bed reactor was presented by Wu and Tian [65]. DEM provides further insight as a result of the assessment of the behavior of single solid particles within the bed at the expense of a substantially increased computational time.
2.7 CFD for Biological Utilization: Microalgae Cultivation
As for the application of CFD to biological utilization of carbon dioxide for photosynthetic production of microalgae, the number of published studies is rather limited. One of the most recent and representative studies available is the work reported by Chatterjee [66]. This article is concerned with the internal hydrodynamics of a photo‐bioreactor (PBR) but ignores any other aspects such as the chemistry of the system or the distribution of light across the vessel, which is crucial to the efficiency of the process and depends on the shape of the PBR. Another assumption in this model is that the mass and weight of the microalgae formed in the process were neglected.
Chatterjee [66] carried out a comparative study between a bubble column reactor and a serpentine PBR configuration using ANSYS CFX‐14.0 (Euler–Euler multiphase approach) with time steps ranging from 0.1 to 2 seconds and grids with a number of nodes varying between 75k and 109k. The modeler needs to have special care with the development of the mesh, which must have an appropriate resolution relative to the size of the gas bubbles formed within the PBR. The other crucial aspect is the choice of the turbulence model. Given that the scope of this work is to assess the mixing parameters, the turbulent model must be selected carefully. Both the standard k–ε model and the Reynolds stress model (RSM) were tested. The latter option resulted in a better match between the CFD and the experimental data in terms of gas hold‐up and gas velocities throughout the reactor. The set‐up gave way to valuable maps of turbulence kinetic energy, velocity swirling strength, and gas hold‐up within the domain. The results show that the serpentine configuration gives way to more intense turbulence, which in turn should theoretically result in better microalgae growth rate.
Perhaps the most innovative CFD work concerning PBRs is, however, the article presented by Zhang et al. (2019), who carried out a CFD study of a bionic fractal‐inspired branch‐like PBR. Fractal shapes are the solution provided by Nature for those applications where a high area‐to‐volume ratio is required. They used a similar set‐up to that presented by Chatterjee [66], based on the Euler–Euler method for gas–liquid interface tracking combined with the k–ε turbulence model in order to compare the performance of fractal‐inspired branched geometries to that of common configurations such as multi‐tubular and serpentine. As for the spatial discretization, finer meshes were employed because of the tiny spaces formed in the successive branching generations of the fractal shape (5th branching generation with diameters in the order of the millimeter). A grid independence study was conducted using three non‐structured meshes (a coarse mesh with 1.30 m nodes, a medium mesh with 2.48 m nodes, and a fine one composed of 3.5 m nodes). The prospective user can thus have an approximation of the degree of grid refinement required in these simulations given the diameter of the channels and the number of nodes, which need substantial computational resources. The results of their model suggested that better mixing occurs when using the fractal shape relative to the multi‐tubular and serpentine configurations, together with small pressure drops (Figure 2.6).
The literature confirms thus, CFD modeling as a valuable tool to carry out preliminary proof of concept of innovative PBR shapes. An interesting proposal for further work would be, however, to use a multispecies approach including mass source terms to account for the consumption of