as the product between the average liquid film thickness from the simulation and the specific surface of the packing given by the manufacturer.
Figure 2.2 This schematic illustration depicts the flow of information between the three scales proposed in the modeling strategy presented by Raynal and Royon‐Lebeaud.
Source: Adapted from Raynal and Royon‐Lebeaud [6].
At the intermediate scale, one representative elementary unit (REU, the repeating unit that forms the geometry of the packing) was represented because the pressure drop per unit length in a limited set of REUs matches that of the entire column [10]. Raynal and Royon‐Lebeaud [6] proposed a single‐phase flow approach (with only gas phase) at the REU level, although in their case, information from the small scale would be fed into their REU set‐up in order to account for the effect of the presence of liquid. To do so, two modifications at the REU scale setup were introduced. On the one hand, instead of a non‐slip boundary condition on the packing walls, i.e. velocity equal zero, the authors established a fixed velocity (the gas–liquid interface velocity obtained at the small scale). On the other hand, and in order to compare their data with a set of experiments including gas and liquid flow, the authors corrected the F‐factor by the liquid hold‐up obtained from the average liquid film thickness of the small‐scale simulations. The F‐factor F is a measure of the kinetic energy of the gas phase that enters the packed bed and comes determined by the product between the superficial velocity and the square root of the gas‐phase density. The corrected value of the F‐factor F′ is obtained by dividing it over the volume occupied by the gas phase per unit volume of packing, that is, the complementary value of the liquid hold‐up. A greater F‐factor then, than that of a dry simulation, is obtained for the same value of the gas superficial velocity. This is in accordance with the narrowing effect that the presence of the liquid phase has on the channels through which the gas flows, and therefore, greater gas pressure drops are obtained upon wet conditions. These intermediate scale calculations allowed the authors to obtain the pressure drop coefficients K in the three coordinate directions as the ratio per unit length between the pressure drop ΔP and the superficial dynamic pressure of the gas phase.
Finally, the entirety of the absorber is considered at the full scale. The pressure coefficients calculated at the REU scale are the link between the latter and the full scale and are therefore introduced in the full‐scale simulations as an additional momentum sink in Eq. (2.2). The final outcome from this multi‐scale approach was the velocity field within the absorber, with the objective of avoiding the possibility of flooding and selecting the most appropriate gas distributor so as to minimize strong velocity gradients.
Other multi‐scale strategies have followed in order to model amine scrubbers, such as that presented by Sun et al. [11], who proposed a two‐scale approach partially based on CFD. At the REU‐scale three‐dimensional (3‐D) multiphase (gas and liquid), CFD simulations of a limited set of REUs of the commercial packing Mellapak 350X were used to obtain the stream split fraction coefficients and the effective wetted area ratio as a function of the liquid flow rate. The authors distinguished between four REU types, namely, inlet of the column, outlet, wall, and interior. From that stage, they mapped the entire set of REUs within the column, assigning an identifier based on their location and subsequently, introduced the parameters from the small‐scale calculations mentioned above into a mechanistic model. The final output was the liquid hold‐up distribution across the entire column, which is necessary to obtain the wet pressure drop by means of experimental correlations. Although not entirely based on CFD, the scale‐based approach reported by Sun et al. [11] proved that multiphase simulations with gas–liquid interface tracking via the VOF method are possible with the advent of computational capabilities with increased power. The use of the computationally costly VOF method was not restricted to 2‐D simulations at the corrugation level or 3‐D simulations over a simple inclined plate, but at the REU scale.
A number of other models falling under the umbrella of one of the three scales presented by Raynal and Royon‐Lebeaud [6] can be found in the literature, showcasing interesting characteristics of the flow within an amine scrubber. At the corrugation scale 2‐ and 3‐D simulations featuring the VOF algorithm have been used to study the fundamental hydrodynamics of rivulets and droplets. Some attempts to introduce the chemistry between carbon dioxide and the amine have also been reported in 2‐D by Haroun et al. [12] and in 3‐D by Sebastia‐Saez et al. [13]. At the REU scale, most of the studies have focused on obtaining the dry pressure drop of the packing, where an accurate selection of the appropriate turbulence model is crucial [14]. Finally, at the full scale, a big step forward has been taken by introducing the multiphase reactive flow on the porous Euler‐Euler approach. To accomplish this, Pham et al. [15] introduced mass and momentum source terms added to the Navier–Stokes equations. These are the terms marked as Smass and Smom in Eqs. (2.1) and (2.2), respectively, to account for the anisotropy of the packing. To include these source terms in the calculation, one can make use of a user‐defined function, like those used in commercial software such as ANSYS Fluent, or directly code their defining equations in an open‐source CFD software such as OpenFOAM or an in‐house code. The momentum source terms were accounted for the loss of momentum on both the liquid and the gas phase caused by the porous resistance, momentum exchange between both phases and liquid dispersion. For a complete description of the momentum source terms, the reader is referred to the work of Pham et al. [15]. Table 2.1 gathers information on CFD models related to amine scrubbers in terms of the scale used and the conclusions reached.
Table 2.1 Summary of published CFD studies concerning amine scrubbers.
| Authors | Simulation scale | Aspect studied | Short comment on conclusions |
|---|---|---|---|
| van Baten et al. [16] | REU (intermediate scale) | Quantification of axial and radial liquid dispersion on KATAPAK‐S commercial structured packing | Enhanced axial dispersion in the case of KATAPAK‐S relative to common packings |
| Petre et al. [17] | REU (intermediate scale) | Description and quantification of the main contributions to dry pressure drop | The most significant causes of pressure loss are elbow effect and jet splitting at packed bed entrance, elbow effect at column walls, elbow effect at layer transitions, and collision at crisscross junctions |
| Raynal et al. [18] | REU (intermediate scale) | Multi‐scale REU + corrugation scale study | Combining dry pressure drop from 3‐D REU‐scale and liquid hold‐up from 2‐D corrugation scale is a successful strategy to match wet pressure drop data obtained experimentally |
| Fernandes et al. [19, 20] | REU (intermediate scale) | Study of dry and wet pressure drop in a considerable number of REUs (whole column section) |
The geometry used encompasses one of the largest sets of REUs found in the literature along with that represented by Isoz and Haidl [21]. Wet pressure drop obtained assuming fully developed
|
