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the smallest time and length scales, quantum mechanics focuses on solving the equations of quantum theory, whereas molecular dynamics is based on the application of Newton's laws of motion to a limited set of molecules. Quantum mechanics and molecular dynamics thus provide information on the phenomena taking place at the subatomic and molecular level, respectively.

The application of quantum mechanics and molecular dynamics to the field of CCSU provides valuable data on fractional free volume (space between particles), diffusion coefficients, and a better understanding of the role of hydrogen bonds on the absorption of CO₂ into amino acid ionic liquids (AAILs) [1]; the mechanism for carbon dioxide sequestration within porous rocks [2]; the study of the phase change mechanism of biphasic solvents for CO₂ capture [3]; and the adsorption mechanism including selectivity of different gas molecules in porous matrices [4]. In conclusion, quantum mechanics and molecular dynamics provide a visualization of the diffusion and chemical bonding at the subatomic and molecular level and are of interest for the development and study of new solvents and solid sorbents and the evaluation of sequestering media both in terms of diffusion time and depth.

In some other instances, however, researchers might need to obtain a broader vision of the phenomena taking place at larger time and length scales. Having commented briefly on the capabilities of quantum mechanics and molecular dynamics, the next step toward greater length and time scales is given by the application of continuum mechanics, which assumes that matter is a continuum instead of being formed by discrete particles. There is thus a boundary in terms of length scale between the suitability of the use of molecular dynamics or continuum mechanics for a given problem. Generally speaking, continuum mechanics must be applied instead of molecular dynamics when the representative length scale of the phenomenon to be studied is greater than the mean free path of the particles; that is, when the length scale contains a large number of particles. The Knudsen number italic upper K n equals StartFraction lamda Over upper L EndFraction , 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.

Graph depicts the time and length scales of the simulation methods available for CCSU processes from quantum mechanics to molecular dynamics, continuum mechanics, and process engineering simulations.

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

(2.1) StartFraction partial-differential rho Over partial-differential t EndFraction plus nabla dot left-parenthesis rho ModifyingAbove v With right-arrow right-parenthesis equals upper S Subscript mass

where ρ is the density of the fluid, t denotes the time, ModifyingAbove v With right-arrow is the velocity vector associated with the infinitesimal control volume, and S_mass is a mass source term. Mass source terms are crucial to the description of reactive flows, as it occurs in CO₂ chemisorption in packed columns and in CO₂ utilization by chemical conversion, for instance. On the other hand, the momentum equation is the second Newton's law applied to the infinitesimal control volume, whereby the sum of forces equals its acceleration. The momentum balance in one of its simplest forms is expressed as

(2.2) rho StartFraction upper D ModifyingAbove v With right-arrow Over italic upper D t EndFraction equals minus nabla p plus nabla dot tau plus rho ModifyingAbove g With right-arrow plus upper S Subscript m o m

where flow incompressibility is assumed and p denotes pressure, τ is the viscous stress tensor, ModifyingAbove g With right-arrow is the acceleration of gravity, and D denotes the material derivative. Momentum source terms S_mom are helpful when the flow in a porous media is to be considered, for instance, as will be described in Section 2.2.

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

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