Читать книгу Engineering Solutions for CO2 Conversion - Группа авторов - Страница 33

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 in Raynal and Royon‐Lebeaud's work. Then, the authors estimated indirectly the total liquid hold‐up 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 S_mass and S_mom 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 film flow over the entire packing surface
Armstrong et al. [22]	REU (intermediate scale)	Effect of corrugation angle and F‐factor on dry pressure drop caused by friction	Adding the effect of corrugation angle in correlations improves dry pressure drop predictions
Owens et al. [23]	REU (intermediate scale)	Optimization of computational resources to simulate more effectively at the REU scale. Use of X‐ray computer tomography to generate geometries	Number of REU considerably increased to include half an element of Mellapak N250Y
Haroun et al. [24]	REU (intermediate scale)	Gas–liquid interface tracking in four REU geometries. Their approach constitutes a step forward toward integrating the corrugation and REU scales	Not only is the REU scale valid for representing the dry pressure drop per unit length but also the interface area versus liquid flow rate
Lautenschleger et al. [25]	REU (intermediate scale)	Single‐phase (gas) flow characteristics of novel packing PD‐10	Optimization of packing geometry to reduce pressure drop without jeopardizing mass transfer
Sebastia‐Saez et al. [26]	REU (intermediate scale)	Characteristics of multiphase gas–liquid flow on a limited set of REUs	Dependence between liquid flow rate and both gas–liquid interface area and liquid hold‐up successfully represented in a set of four REUs
Li et al. [27]	REU (intermediate scale)	Transition between corrugation and REU scale	Wet pressure drop and liquid hold‐up complemented with data obtained at the corrugation scale
Isoz and Haidl [21]	REU (intermediate scale)	Parametric study on the effect of slope of packing channels among others on the dry pressure drop. The authors used the imaging software Blender to obtain accurate representations of the column inner intricacies	Largest set of REUs along with that presented by Fernandes et al. [19, 20]
Yang et al. [28]	REU (intermediate scale)	Multiphase VOF gas–liquid flow within three piled REUs of Mellapak 250 Y. The work focuses on the effect of liquid flow patterns on the formation of dead zones	Portion of dead zones increased at high values of the Weber No. Wetted area highly affected by liquid flow rate but not by gas flow rate. The latter affects film stability and droplet formation
Asendrych et al. [29]	Full scale	Operating parameters including profiles of velocity of both phases, pressure liquid hold‐up, and species concentration by using the Euler–Euler multiphase method + mass source terms for chemical reactions	The model was validated in terms of CO2 capture efficiency by comparison to own experimental data
Niegodajew and Asendrych [30]	Full scale	Parametric 2‐D study of the entire column using the full‐scale porous medium approach	There is a mild effect of the carbon dioxide concentration at inlet conditions on the capture efficiency, which highlights the suitability of amine scrubbing on diverse scenarios (change of fuel, etc.)
Kim et al. [31]	Full scale	Effect of four modification factors in the Ergun equation related to the liquid hold‐up and the liquid load in order to determine the pressure drop	Good match between simulation and experimental results in terms of carbon dioxide conversion, wet pressure drop, and hold‐up using the new factors in the Ergun equation
Gu et al. [32]	Corrugation scale (small scale)	2‐D study of the effect of corrugation geometry on the hydrodynamics of liquid films	Research on surfactants and treatment of packing surface are crucial to obtain desired film flow patterns
Valluri et al. [33]	Corrugation scale (small scale)	2‐D multiphase study of gravity‐driven liquid films flowing down a corrugated textured solid surface (Mellapak) at low Reynolds numbers	The ratio between gas–liquid interface and specific packing area diminishes with increased surface roughness
Ataki and Bart [34]	Corrugation scale (small scale)	Morphology of rivulets in Rombopak 4M	Simulations used to develop or modify the degree of wetting, liquid hold‐up, and effective area
Haroun et al. [35]	Corrugation scale (small scale)	2‐D direct multiphase simulation of the formation of liquid recirculation areas in packing corrugation and its effect on mass transfer	Recirculation areas substantially affect the liquid hold‐up (liquid dead zones). Mass transfer not affected by the formation of recirculation areas
Iso et al. [36]	Corrugation scale (small scale)	Study of the effect of packing texture patterns on the gas–liquid interface area	To place ridges perpendicularly to the flow direction results in enhanced gas–liquid interface area
Sebastia‐Saez et al. [37]	Corrugation scale (small scale)	Study of the hydrodynamics of rivulet instabilities (braiding)	Braiding caused by interplay between surface tension and inertia and results in reduced interface area. Packing texture must be designed to hamper the effect of surface tension