where λ is the mean free path and L the length scale of the problem, gives a rule of thumb as to when to apply either methodology, with continuum mechanics being applicable when Kn < 1. Continuum mechanics is of interest for the study of the unit operations within a CCSU process. For instance, it is useful when the modeler needs to perform a preliminary proof of concept of a packed bed column or an oxy‐fuel burner and needs to represent its entire geometry. In some applications, however, it is unfeasible to perform a continuum mechanics simulation of the entire unit process, and thus, a multi‐scale approach might be necessary owing to computational capacity limitations. This becomes clear for the case of packed bed columns, where the intricate geometry requires the use of different scales depending on the variable to be studied.
Figure 2.1 Time and length scales of the simulation methods available for CCSU processes from quantum mechanics to molecular dynamics, continuum mechanics, and process engineering simulations.
The application of continuum mechanics to fluid flows gives way to the Navier–Stokes equations. As of today, the analytical solution of these equations is known only upon some restrictive assumptions, and therefore, numerical methods must be applied in the majority of cases of interest. The study of the numerical solving of the Navier–Stokes equations conforms the discipline known as computational fluid dynamics (CFD). Although historically the term CFD has referred to the numerical solving of the Navier–Stokes equations, it has been expanded recently to include the study and development of Lattice Boltzmann methods. The development of CFD kicked off within the field of aeronautics but has rapidly entered into other fields such as chemical engineering with the advent of increased computing power and refined algorithms capable of describing multiphase flows, chemical reactions, interface tracking, diffusion, etc.
The Navier–Stokes equations result from a mass and momentum balance on an infinitesimal control volume within the fluid being studied. The mass conservation equation reads
where ρ is the density of the fluid, t denotes the time,
where flow incompressibility is assumed and p denotes pressure, τ is the viscous stress tensor,
Finally, on the opposite end of the time‐ and length‐scale spectrum, process engineering simulations perform mass balances coupled with the equations that define the functioning of each device within an entire plant or part of it. The body of literature dealing with the application of process simulations in the field of CCSU is considerable, and as of today, process simulations remain the most widely used simulation approach in the field of CCSU. Process simulations are used to test new plant configurations, for instance, and give a general overview of the techno‐economic viability of CCSU processes, although the information lacks detail on the physical phenomena taking place within each unit process.
Simulations can therefore give valuable insight into CCSU technologies, which would be otherwise rather expensive to obtain if only experimental methods were to be applied. This chapter aims at providing the reader with a summary of the capabilities of CFD simulation techniques across the field of CCSU, from carbon capture to sequestration and utilization. Particular emphasis is to be put on those specifics that have already undergone comprehensive validation, with the aim of letting the reader know the applications where these models can be applied most confidently.
2.2 Multi‐scale Approach for CFD Simulation of Amine Scrubbers
As of today, amine scrubbing in packed columns remains the most advanced method for CO2 capture, having been deployed commercially for some years [5]. Accordingly, it has also received the greatest attention in terms of CFD modeling among all of the CCSU methods available. High‐fidelity simulations of the entire absorber describing the reactive multiphase flow within are, however, far beyond computational capacity. For this reason, the CFD modeling of amine scrubbers must be undertaken using a multi‐scale perspective. Although at present, the boundaries between scales are very clear in every CFD study on structured packings, these boundaries will be blurred in the future with the upcoming of more powerful computational resources.
An interesting multi‐scale approach for amine‐based absorbers was proposed by Raynal and Royon‐Lebeaud [6], and reviewed by Raynal et al. [7], who divided the modeling in the three scales illustrated in Figure 2.2. First off, two‐dimensional (2‐D) simulations were used at the small scale to represent the gravity‐driven liquid flow falling down the corrugations of the packing by using an interface tracking numerical technique named Volume‐of‐Fluid (VOF) method. The latter introduces an additional conservation equation for a colour function f, the volume fraction, which varies within the closed interval from 0 through 1. Cells within the mesh with values at both ends of that range correspond to either phase, whereas values in between correspond to the interface. The VOF method has proved a useful tool for the description of a number of free surface interface problems across many engineering fields. It ideally requires however the use of adaptive grids or in the case of fixed grids at least a greater resolution in those cells that are expected to contain the interface [8]. This requirement comes motivated by the discontinuous character of gas–liquid interfaces in Nature, whereas an unnatural transition area between phases appears instead of a sharp interface when using the VOF algorithm. The results can therefore be affected by substantial errors if the mesh is not treated conveniently in the vicinity of the interface. Moreover, the VOF method is characterized by the assumption that the density and viscosity assigned to the interface cells are volume fraction averaged. There is therefore some variability in the density along the computational domain that results in the appearance of additional mass and momentum source terms in the conservation equations. The implications of these additional source terms are yet to be assessed and are minimized when extra mesh refinement is introduced [9]. The average film thickness and the gas–liquid interface velocity were the direct output from the calculations at the small scale
