Meso-scale CFD study of the pressure drop, liquid hold-up, interfacial area and mass transfer in structured packing materials

International Journal of Greenhouse Gas Control 42 (2015) 388–399

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Meso-scale CFD study of the pressure drop, liquid hold-up, interfacial area and mass transfer in structured packing materials Daniel Sebastia-Saez a , Sai Gu a,∗ , Panneerselvam Ranganathan a , Konstantinos Papadikis b a b

School of Energy, Environment and Agrifood, Cranfield University, Cranfield MK43 0AL, United Kingdom Department of Civil Engineering, Xi’an Jiaotong-Liverpool University, Suzhou, Jiangsu Province 215123, PR China

a r t i c l e

i n f o

Article history: Received 11 May 2015 Received in revised form 18 August 2015 Accepted 21 August 2015 Keywords: VOF Structured packing Carbon capture CFD Reactive mass transfer

a b s t r a c t This work presents a meso-scale CFD methodology to describe the multiphase flow inside commercial structured packings for post-combustion CO2 capture. Meso-scale simulations of structured packings are often limited in the literature to dry pressure drop analyses whereas mass transfer characteristics and gas–liquid interface tracking are usually investigated at micro-scale. This work aims at testing further capabilities of meso-scale modeling by implementing the interface tracking instead of analyzing only the dry pressure drop performance with single-phase simulations. By doing so, it is possible to present also the hydrodynamics (i.e. liquid hold-up and interfacial area) for a small set of representative elementary units (REUs). The interest in interface tracking using commercial geometries lies on the fact that liquid hold-up and interfacial area have implications of capital importance on the overall performance of the absorber, hence the importance of developing a model to predict them accurately. The results show how the relationship, reported in the literature, between the liquid load and both the liquid hold-up and the interfacial area is reproduced by the present CFD methodology. Also, a more realistic visualization is accomplished with images of the inner irregularities of the flow (i.e. liquid maldistribution, formation of droplets and rivulets, etc.), which lie far from the prevailing assumption of the formation of a perfectly developed liquid film over the packing. Moreover, the effect of operating parameters such as the liquid load, liquid viscosity and liquid–solid contact angle on the amount of interfacial area available for mass transfer is also discussed. Finally, mass source terms are also included to describe the gas absorption into the liquid phase hence testing all the capabilities of micro-scale modeling at meso-scale. The present model could be further used for the analysis and optimization of other structured packing geometries. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

1. Introduction The International Energy Agency (IEA) has cataloged carbon capture and storage (CCS) as one of the main strategies deployed to mitigate global warming (Chakroun and Ghoniem, 2015). CCS encompasses the separation of CO2 from flue gas at large production points (e.g. power plants) and its storage in suitable geological formations. CO2 capture techniques include pre-combustion carbon capture, oxy-fuel technology and post-combustion carbon capture. Among them, post-combustion is the most widely used technology and consists in the CO2 removal after the combustion

∗ Corresponding author. E-mail address: s.gu@cranfield.ac.uk (S. Gu).

has taken place in a conventional way. Post-combustion CCS by means of chemical absorption with amines is the preferred method due to the possibility of being retrofitted to existing power plants and its high mass transfer effectiveness whilst giving low pressure drop values (Hosseini et al., 2012). Either structured or random packings are used for amine scrubbing, the former being preferred over random packings due to their high specific area (i.e. which goes up to 750 m2 /m3 ) and high void fraction (i.e. of up to 0.98). A CCS post-combustion amine scrubbing facility consists mainly of the absorber, where the reaction between the amine and the carbon dioxide takes place; and the stripper, where the regeneration of the amine is accomplished. The present work deals with the CFD modeling of the absorber. CFD has been proven to be a useful tool for the design of equipment with intricate inner geometries due to the subsequent reduction on

http://dx.doi.org/10.1016/j.ijggc.2015.08.016 1750-5836/© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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Nomenclature Latin symbols a Area per unit volume (1/m) D Diffusivity (m2 /s) F Volume fraction (–) Acceleration of gravity (m/s2 ) g h Liquid hold-up (–) k Mass transfer coefficient (m/s) Pressure (Pa) P S Mass source (kg/m3 /s) t Time (s) v Velocity (m/s) Concentration (kg/m3 ) y Greek symbols Packing void fraction (–) ε Angle between the packing wall and the vertical  direction (rad)  Interface curvature (1/m) Dynamic viscosity (Pa s)  Density (kg/m3 )   Surface tension (N/m) Exposure time (s)  Subscripts * Conditions at the interface eff Effective Gas g l Liquid b Bulk conditions

the experimental effort required. Also, CFD allows to further exploring the flow characteristics without any measurement probes interfering with the flow itself (Fernandes et al., 2009). The CFD modeling of a post-combustion CCS absorber equipped with structured packings is divided into three scales due to the current computational limitations: micro-, meso-, and macro-scale simulations (Raynal and Royon-Lebeaud, 2007). The capabilities and constraints of the three scales depend mostly on the computational resources available. The details usually covered by the three scales are summarized as follows. Micro-scale simulations have been mostly focused on the study of the interface between the gas and the liquid phases. The mass transfer, with and without chemical reaction, can be implemented at micro-scale at a reasonable computational cost. The chemical reactions of the CO2 -MEA system were implemented in our previous work, obtaining the CO2 concentration profiles in the liquid phase and predicting the values of the enhancement factor (Sebastia-Saez et al., 2015). The simulations were also able to reproduce the fact that the reaction occurs only at the gas–liquid interface, as indicated by the high value of the Hatta number associated with the chemistry of the system. The conclusion is that, although simulations at micro-scale can provide a good understanding of the phenomena associated with the reactive absorption into the amine solution liquid film, some effort has to be carried out to implement the same characteristics in actual commercial geometries (i.e. REUs at meso-scale) in order to extract more realistic and applicable conclusions. Meso-scale simulations feature a small set of REUs to study the dry pressure drop performance of the structured packing column (Owens et al., 2013). The fundamental principle of meso-scale simulations is that the pressure drop per unit length of a limited number of REUs is the same as for the entire column (Said et al., 2011).

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To extract the conclusions on the dry pressure performance, mesoscale simulations use a single-phase (i.e. gas phase) approach. Theoretically, it has been established that the pressure drop is the result of adding different components (Ding et al., 2015; Olujic et al., 2001): turbulent dissipation, direction changes near the walls, gas–liquid interaction at the interface, and the effect of the crisscross sections, which are the transition zones between two packing layers. The pressure drop due to turbulent dissipation is the dominant term and the one that can be implemented at meso-scale (Said et al., 2011). After the dry pressure drop is obtained with the simulations, the wet pressure drop is subsequently calculated using correction coefficients that take into account the presence of the liquid and the void fraction of the packing. The correction factors respond to the fact that the gas velocity increases under wet conditions due to the narrowing of the channels by the presence of the liquid, which at the same time produces a diminution on the void fraction. Thus, the acceleration of the gas phase due to the presence of the liquid leads to an increase on the pressure drop. Other important hydrodynamic parameters in structured packing reactors are the liquid hold-up and the interfacial area. The interfacial area is the contact area, available for mass transfer, between both the gas and liquid. The liquid hold up is the volume of liquid per unit volume of the structured packing. The total liquid hold-up inside the column is the result of adding two components: static and dynamic hold-up. The dynamic component is actually flowing whereas the static liquid hold-up remains inside the column, stuck at corners and dead spots and not being renewed with the flow (Zakeri et al., 2012a). An important consideration from the modeling point of view is that the total liquid hold-up is independent of the gas velocity until the loading point is reached. The loading point is the threshold beyond which both components, especially the static liquid hold-up, increase sharply hence increasing the pressure drop. The flooding point is reached if the gas flow rate is further augmented. Under flooding conditions the liquid cannot reach the bottom of the column and the solution starts overflowing through the top. Since the absorber is commonly operated at pre-loading conditions, in which the liquid hold-up is independent of the gas velocity, the latter has been neglected in the present study in the multiphase simulations. The dynamic component of the liquid hold-up constitutes the prevalent one and it is represented in CFD meso-scale simulations in this work. The importance of the influence of the liquid hold-up in the wet pressure drop performance of the column justifies the attempt to implement the interfacial tracking at meso-scale in order to quantify it. The simplest way of calculating the liquid hold-up is to multiply the liquid film thickness by the specific area of the packing. This assumes that a fully developed liquid film covers the entire surface of the structured packing. This assumption constitutes a good approximation to the actual value of the liquid hold-up measured in experimental tests and can be used in the aforementioned correction terms to get a valid idea about the wet pressure drop. Nonetheless, this assumption has been proven not to be accurate enough because of the appearance of the so-called liquid maldistribution phenomenon, which causes distortions in the flow that strongly affect the amount of liquid hold-up. Liquid maldistribution is the irregular distribution of liquid over the structured packing surface, which results in the fact that not all the surface of the packing is covered by the amine solution. Liquid maldistribution is more severe as cohesion forces (i.e. surface tension) within the liquid overcome the distortive forces (i.e. inertia), hindering the liquid spreading. The appearance of liquid maldistribution and liquid hold-up has been visualized with experimental techniques and reported in the literature. Basden et al. (2013) used neutron radiography whereas Fourati et al. (2012) used gamma ray tomography to visualize the heterogeneous distribution of the liquid along the packing and determined the liquid hold-up as a function of the

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radial and axial coordinates within the column. More recently, Olujic´ and Jansen (2015) quantified the large-scale liquid maldistribution in terms of the so-called maldistribution index (MI) at the whole-column level and defined it as the difference in the values of the liquid distribution found in a cross-section for various liquid loads. The authors reported three different types of liquid maldistribution such as chordal, peripheral and central blanking depending on the value of the MI. Thus, implementing the interface tracking method at mesoscale is key to interpret the occurrence of liquid maldistribution in the structured column and to understand the analysis of the liquid hold-up and interfacial area carried out in this work. Macro-scale simulations deal with the modeling of the entire column as a porous medium since the liquid dispersion takes place in a similar way both in porous media and in structured packings. Fourati et al. (2013) implemented an advection-diffusion model (i.e. analyzed in their previous work with gamma-ray tomography) to model the liquid dispersion with a CFD porous medium approach, showing a reasonable match with the experimental results. Macroscale simulations can also be used to study the influence of the internal geometry on the flow patterns inside the column. Finally, process simulations constitute a further modeling scale that does not use CFD techniques. In process simulations the interaction between the different devices that form a CCS plant is achieved. The components are treated as black boxes, making CFD studies a necessity in order to gain a deeper insight about flow characteristics inside the different pieces of equipment. Some studies linking process and CFD simulations are found in the literature. Fei et al. (2015) developed a co-simulation methodology to study the suitability of an existing power plant to implement oxy-fuel operation, taking into account the internal performance of the equipment. Reduced order models (ROMs) are developed using the Kriging method, which reproduces any potential operation scenario for the furnace from a limited number of CFD simulations. Both process and CFD simulations are mutually retrofitted to comprehensively describe the functioning of the power plant. The connection between the present CFD model and process simulations is advised as future work to obtain an integral CFD tool for the design and optimization of CCS amine scrubbing post-combustion facilities. The aforesaid description and discussion of the three scales strategy for the CFD modeling of structured packing columns highlight the importance of testing the capabilities of meso-scale to represent the liquid hold-up and the interfacial area with real geometries and not only at micro-scale domains. Therefore, the main purpose of this work is to test the implementation of the capabilities of micro-scale to meso-scale using a multiphase interface tracking CFD approach applied on commercial geometries. Some recent attempts have been made in this direction. Haroun et al. (2014) used the Volume of Fluid method (VOF) to track the gas–liquid interface over a single sheet of Mellapak 250.X. Since the interfacial area is said to have the highest influence on the overall performance of the packing, the authors focused on its study as a function of some operating parameters such as the contact angle and the liquid load. The simulations did not reproduce the real case scenario in which the metal sheets are confronted, resulting in contact points that heavily influence the liquid flow development. Recently, Basden (2014) presented a comprehensive analysis with experimental and numerical work for the characterization of structured packings. The effect of liquid density, contact angle, surface tension and liquid viscosity on the wetted area and the liquid hold-up for sections of MontzPak B1-300 was considered. The parametric study was carried out varying each one of the parameters separately whereas the rest were kept constant. The author reported that contact angle had the highest influence among all the operating parameters tested. The present study considers the

oxygen–water system whereas Basden (2014) studied absorption of CO2 in an aqueous NaOH solution. Also, Lautenschleger et al. (2015) developed a meso-scale CFD model including mass transfer to improve the pressure drop characteristics of structured packings whilst keeping the mass transfer performance but their simulations did not reproduce the interface between the fluids. Huang et al. (2015), developed a multiphase model to check the influence of the hydrodynamics characteristics on the pressure drop but for the case of layered wired gauze packings and not for structured packings. Therefore, although liquid hold-up and interfacial area have the highest importance in both pressure drop and mass transfer characteristics, the literature dealing with the gas–liquid interface tracking on commercial geometries has been observed to be scarce and needs to be expanded. The influence of the liquid–solid contact angle and the liquid viscosity is also assessed in this work. On the one hand, the influence of the contact angle seems to be well stated in the literature (Basden, 2014; Haroun et al., 2014) and a consensus appears that better wetting conditions give higher values of the interfacial area. This tendency is verified in the present study. On the other hand the influence of the liquid viscosity has also been assessed in the literature, showing contradictory conclusions. For instance, Tsai et al. (2009) studied the effect of viscosity and surface tension on the interfacial area, showing that the viscosity had practically no effect. Sidi-Boumedine and Raynal (2005) found that the viscosity has a strong influence on the liquid hold-up, resulting in a directly proportional relationship. Similarly Rizzuti et al. (1981) also found a strong relationship between the viscosity and the interfacial area. Bradtmöller et al. (2014) established that the effect is different depending on the flow regime considered (i.e. C-P liquid is found to be independent from it whereas at high viscosity film flow regions decrease in favor of flooded regions). Basden (2014) reported a small influence of the liquid viscosity on the wetted area and the liquid hold-up, with a decreasing tendency that has also been observed in the present work. In view of these contradictory results, more work needs to be done in order to throw light upon the effect of these operating parameters on the behavior of the multiphase flow. This work aims at contributing to palliate the lack of multiphase simulations at meso-scale and implements the VOF method to account not only for the single-phase gas flow prediction but also for the gas–liquid interface tracking. The results from the present model are compared with experimental correlations reported in the literature for the liquid hold-up and interfacial area of the MontzPak B1-250 packing. As an element of novelty, non-reactive mass transfer (i.e. between oxygen and water) is included on the multiphase simulations to study the influence of the liquid load on the absorption performance. The results ratify at meso-scale the relationship between the absorption rate and the liquid load already observed in our previous work at micro-scale (Sebastia-Saez et al., 2013) but with the realistic visualization of the flow provided by the interface tracking at meso-scale.

2. Computational model 2.1. Hydrodynamics model The simulations are performed using the commercial software ANSYS® FLUENT v14.0. This software uses the Finite Volume Method (FVM) to numerically solve the Navier–Stokes equations (i.e. continuity and momentum), which read as follows:

∇ · v = 0

(1)

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∂v + v · ∇ v ∂t

= −∇ P + ∇ 2 v + g + f

391

(2)

The standard k − ε turbulence model (Jones and Launder, 1972), is used to close the Navier–Stokes equations in the single-phase simulations carried out to study the dry pressure drop. The term f in the momentum equation accounts for any additional force acting on the fluid different from pressure, viscous stress and gravity. In the particular case of the present simulations, f represents the surface tension, which is calculated by means of the Continuum Surface Force (CSF) model (Brackbill et al., 1992) since it is especially suited for finite thickness Eulerian interfaces. The momentum source due to the surface tension is therefore calculated as: f = 

∇ F 0.5(l + g )

(3)

The free surface curvature is defined as:  = ∇ · nˆ =

1 |n|

 n

|n|





· ∇ |n| − (∇ · n)

(4)

Being nˆ the unitary normal vector whereas n is equal to the divergence of the volume fraction. The unitary normal vector in the cells next to the solid wall is calculated considering the solid–liquid contact angle, which in this case is equal to 70◦ . The gas–liquid interface is tracked using the VOF method, which is based on the concept of volume fraction. The volume fraction field is calculated by solving an additional transport equation:

∂F + v · ∇ F = 0 ∂t

Fig. 1. Computational domain and boundary conditions.

Fig. 1 shows a schematic of the computational domain and the boundary conditions used in the numerical set-up of the present simulations. The liquid load considered in the present study ranges from 0 to 265 m3 /m2 /h and covers the values found in both industrial facilities and experimental tests (Haroun et al., 2014). The gas load has been set to zero due to the fact that it does not affect the liquid hold-up at pre-flooding conditions, which is the normal operation regime. The simulations have been carried out at the Astral supercomputing facility at Cranfield University using 64 CPU cores in the case of the hydrodynamic simulations and 96 CPU cores in the case of mass transfer calculations.

(5) 2.3. Mass transfer theory

The value of the volume fraction ranges from 0 to 1, i.e. for gasand liquid-filled computational cells, respectively. Any cell whose volume fraction lies in between the aforesaid values belongs to the interface. After the volume fraction field is obtained, the interface is rebuilt using the Geo-Reconstruct algorithm. The density and dynamic viscosity that appear in the momentum equation are volume fraction averaged, as indicated by:  = Fl + (1 − F) g

(6)

 = Fl + (1 − F) g .

(7)

2.2. Numerical methodology An explicit scheme has been used whilst keeping numerical stability and reasonable values of the time step, ensuring an acceptable calculation time. A constant value of the Courant–Friedrichs–Levy condition (i.e. equal to 0.5) has been implemented to optimize the calculation time (Min and Park, 2011). The numerical set-up results in time-steps varying from 1 × 10−5 s to 1 × 10−6 s (i.e. for the cases with and without mass transfer, respectively). The computational domain consists of a set of 4 REUs, with a 2 × 2 s arrangement for the simulations describing the hydrodynamics whereas the mass transfer analysis is restricted to one single REU due to numerical resources economy. Said et al. (2011) carried out a study to check the mesh independence of the dry pressure drop. The authors study three tetrahedral meshes, with cell sizes of 1 mm, 0.6 mm and 0.5 mm, which ensure a good value of the y+ near the wall, i.e. between 1 and 3.5. The three meshes gave the same pressure drop results. A maximum element size of 0.5 mm is used in the present simulations, resulting in a mesh formed by 5,782,612 elements. The explicit formulation is considered for time discretization (Haelssig et al., 2010). PRESTO! and second order upwind schemes are used for pressure and momentum, respectively, spatial discretization. A first order upwind scheme is implemented for the spatial discretization of the turbulent kinetic energy. The SIMPLE scheme is used for the pressure–velocity coupling.

Mass transfer has been implemented using constant source terms based on Higbie’s penetration theory (Higbie, 1935), which considers the mass absorption as a transient process. Using Fick’s laws of diffusion and multiplying the mass flux by the effective area the following mass source term is obtained: Slg = kl aeff (yl∗ − yl,b )

(8)

The gas-side mass transfer resistance can be neglected since pure oxygen is used as the gas phase. The liquid-side mass transfer coefficient in Higbie’s penetration theory responds to the equation:



kl = 2

Dl



(9)

The diffusivity of oxygen in water (Dl ) is 2.1 × 10−5 cm2 /s and the value of the solute concentration at the interface is the solubility of oxygen in water at 20 ◦ C and atmospheric pressure (i.e. 8.5 × 10−6 in mass fraction). The effective area is calculated as the gradient of the volume fraction in each computational cell whereas the exposure time is obtained by means of the expression introduced by Raynal et al. (2009), who calculated it as the ratio between the distance traveled by the liquid from the inlet, and its velocity. 3. Results and discussion 3.1. Liquid hold-up and interfacial area prediction The liquid hold-up is an important parameter used to calculate other flow characteristics of structured packings such as the wet pressure drop and the gas–liquid effective velocity. The gas–liquid effective velocity is the velocity at the interface and is used to estimate the liquid side mass transfer coefficient via Higbie’s theory (Sidi-Boumedine and Raynal, 2005). Therefore, a good prediction of the liquid hold-up is crucial for a good mass transfer characterization of the packing. The liquid hold-up is also used to correct the dry pressure drop to obtain the actual pressure loss under wet

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Fig. 2. Liquid hold-up vs. liquid load.

conditions. In the present CFD simulations, the liquid hold up has been obtained as the volume within the domain whose computational cells have a value of the liquid volume fraction above 0.5, divided by the total volume of the computational domain. The liquid hold-up obtained in the present study is plotted against the liquid load in Fig. 2 and compared to previously reported exper´ (1991) and imental results from Fourati et al. (2012), Mackowiak Zakeri et al. (2012a). This graph covers the liquid load range for experimental tests, which reaches approximately 120 m3 /m2 /h. The range for lab-scale experimental rigs is normally smaller than the one found in pilot or industrial plants due to the size of the columns in each case. It has been found that the liquid hold-up increases with the liquid load as a general tendency. It has also been observed that the rate of change of the liquid hold-up is higher at low liquid loads whereas stabilization is found as the amount of liquid injected into the domain per unit time increases. The graph also highlights that the reported experimental results used for comparison purposes show a huge variation between them, which is accentuated for high liquid loads. The lowest liquid hold-up is calculated assuming the ideal case of the formation of a perfectly developed liquid film that fully covers the packing surface. The values of the liquid hold-up from the present CFD simulations match the reported experimental data at low liquid loads whereas the predictions are overestimated as the liquid load increases, presenting the biggest difference with respect to the ideal approximation among all the data series represented. This may be due to the fact that different flow patterns at the liquid inlet could be considered depending on the part of the absorber where the REU is located. In the case of the present study the liquid enters through the entire area of the upper boundary of the domain. This would be the case of the REUs located at the upper central part of the column, just below the exit of the liquid distributor. According to the experimental visualization carried out by Fourati et al. (2012), the highest values of the liquid hold-up are found in this area. In other parts of the column, the upper part of the REUs is not totally occupied by the liquid phase but by the droplets and rivulets that are formed within the domain and that can be visualized in Fig. 4. The results presented by Fourati et al. (2012) also overestimate previously reported experiments (Spiegel and Meier, 1992; Suess and Spiegel, 1992; Alix and Raynal, 2008) especially at

high liquid loads whereas, similarly to what has been reported in this work, the difference remains moderate at lower values. This difference between the various series of data can be notable. For instance, at a liquid load of 110 m3 /m2 /h, the highest experimental deviation corresponds to the correlation presented by Fourati et al. (2012), with a 45% error with the ideal approach as the base case whereas the present simulations show an 81% deviation. The error is reduced at low liquid loads, with the simulations practically matching the experimental results from Fourati et al. (2012) and with a 30% error with respect to the ideal approach for the case of 18 m3 /m2 /h. Additionally, the interfacial area is considered as the most important parameter influencing the mass transfer performance of the structured packing (Haroun et al., 2014). Fig. 3 shows a comparison plot between the reported literature (De Brito et al., 1994; Tsai et al., 2009; Gualito et al., 1997; Ataki and Bart, 2006; Siminiceanu et al., 2002) and the CFD predictions for the interfacial area against the liquid Reynolds number. It has been found that the rate of change is sharper at low Reynolds numbers whereas it diminishes as the liquid load increases. Wang et al. (2013) established that the interfacial area increases with the liquid load and is independent of the gas velocity, which reinforces the assumption of considering the gas phase as stagnant in the present work. The prediction from the present model matches the correlation developed by Siminiceanu et al. (2002) although a structured packing with a specific area of 750 m2 /m3 was used in their experimental work. It has also been found that the interfacial area from the present simulations is lower than the specific area of the packing, which in the case of MontzPak B1 250 is equal to 250 m2 /m3 , whereas bigger values were expected according to the literature due to the effect of the occurrence of droplets and rivulets, which increase the value of the interfacial area considerably (De Brito et al., 1994). A possible explanation for this is provided by (Bravo and Fair, 1982) who established that “the value of the effective area is composed not only by the wetted area over the packing but also by the area provided by suspended and falling droplets, gas bubbles within liquid puddles, ripples on the liquid film surface, and any contribution from film falling on the walls of the column”. The wetted area has been excluded from the present work, focusing only in the gas–liquid interfacial area, which is the actual area where the mass transfer takes place.

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Fig. 3. Interfacial area vs. Reynolds number.

It can be stated as a conclusion that the tendency is well reproduced for both liquid hold-up and interfacial area, showing the capability of the present model to predict these parameters. This prediction can be further used to optimize the pressure drop and the mass transfer performance of the packing. 3.2. Analysis of the liquid flow transient development Fig. 4 shows the transient development of the liquid flow within the structured packing for different liquid loads, ranging from 18 m3 /m2 /h to 265 m3 /m2 /h. This range of values covers both the experimental range and the liquid loads used in industrial facilities (Haroun et al., 2014). Pseudo-steady state conditions are reached when only slight changes around an average value occur for both the liquid hold-up and the interfacial area. For instance, for the case with 180 m3 /m2 /h, the interfacial area fluctuates between 116 m2 /m3 and 117 m2 /m3 whereas the liquid hold-up varies between 0.23 and 0.24 once pseudo-steady state is reached at 0.36 s flow time. The steady state conditions begin at different flow times depending on the liquid load. In particular, the higher the value of the liquid load the faster the steady state is reached. The transition to pseudo-steady state varies from 1 s for the case with a liquid load of 18 m3 /m2 /h to approximately 0.36 s for the case of 180 m3 /m2 /h. The images feature an isometric 3D view of the domain that shows the formation of irregularities in the liquid phase at an early stage of the flow development. The flow presents droplets and rivulets that appear inside the structured packing material, improving the gas–liquid interface availability. Generally, higher liquid loads give place to a fully connected flow regime, where it is more difficult to find liquid formations detached from each other. This regime is characterized by the appearance of appreciable areas of the packing fully covered by liquid, where a perfectly developed thin liquid film can be found (e.g. this is the case for a 265 m3 /m2 /h) liquid load. Elongated rivulets are prone to appear for lower liquid loads (e.g. 110 m3 /m2 /h). At this value of the liquid load, the initial accumulation of liquid at the inlet gives place not to areas with a thin liquid film but to a numerous set of thick rivulets. A discontinuity is therefore found between the upper and the lower half of the computational domain. This discontinuity begins to appear closer to the liquid inlet as the liquid load diminishes. Spherical formations are abundant for the case of 18 m3 /m2 /h. These

formations are detached from the main liquid flow stream early during the formation of the liquid flow pattern. The channels in the surface of any two consecutive structured packing sheets are disposed at a 90◦ angle, therefore, contact points between the metallic sheets exist at the center and at every corner of the REU, influencing the development of the flow regime. The droplets hit the contact points after their detachment from the main stream. This causes a further break-up of the liquid phase, giving place to round small droplets and elongated shapes adhered to the packing surface. This is easily visualized in the transversal plane snapshots showing the value of the volume fraction. The existence of these flow patterns was previously predicted by Bradtmöller et al. (2014), who define three different regimes: film flow, contact point (C-P) liquid and flooded regions. The three different flow regimes are established on the basis of the maximum and minimum Feret diameters of the liquid formations. Film flow consists of elongated and thin structures whereas C-P liquid areas and flooded regions are rounded, being the flooded regions bigger in size than C-P liquid areas. Similar flow regimes are observed in the isometric view of the results, where elongated liquid structures (i.e. film flow, along with droplets are reproduced). The film flow corresponds with the regime observed at high liquid loads whereas the rounded formations such as rivulets and droplets appear as liquid load diminishes. Rivulets are more likely to appear at intermediate liquid loads (e.g. 110 m3 /m2 /h) whereas C-P structures (i.e. small droplets) are found at the lowest liquid loads considered. In the droplets, the capillarity effects dominate over the shear stress induced by the surrounding air and the effect of gravity, reducing the interfacial area and giving a spherical shape as a result. Shear stress due to adhesion forces (i.e. contact angle) and viscosity overcomes surface tension near the wall, where film flow appears. Despite the fact that the capillarity effects tend to reduce the interfacial area of any particular liquid formation, the appearance of a large number of small droplets and rivulets have a beneficial impact on the total amount of gas–liquid exchange area on the domain. As it has been discussed earlier in this section, more round structures such as droplets and rivulets imply a substantial improvement in the interfacial area following the same principle as many other industrial processes (e.g. atomization, fluidized beds, etc.), which are based on the formation of extremely small and numerous liquid droplets to increase the interfacial area in a dramatic way.

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Fig. 4. (a–f) Transient development of the liquid hold-up. Volume fraction profiles.

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395

Fig. 5. Dry pressure drop vs. F-factor.

The most important conclusion that can be extracted from the visualization of the flow included in this section is that a perfectly developed liquid film is never achieved over the structured packing. Therefore, this assumption, widely used in the literature, is not accurate enough although it has been proven to be an acceptable approach. 3.3. Dry and wet pressure drop prediction The dry and wet pressure drop performances of the absorption column are important parameters to be optimized with CFD simulations since they constitute the most important energy penalty of the amine-based post-combustion CCS system along with the regeneration of the amine in the stripper. The procedure followed in the present work to calculate the wet pressure drop is analogous to the one usually followed in the literature. In this work, the values of the liquid hold-up obtained from the present multiphase simulations have been used to correct the gas velocity instead of taking the assumption of the perfectly developed liquid film. The standard procedure to obtain the wet pressure drop is summarized as follows: • The relationship between the dry pressure drop and the inlet gas flow is obtained by means of single-phase simulations for a particular packing geometry. • The liquid hold-up is calculated with the assumption of a perfectly developed film over the entire surface of the packing wall. Therefore, it is calculated as the product of the specific area of the packing times the liquid film thickness for a particular value of the liquid load. • The expression reported by Fernandes et al. (2009) is used to obtain the corrected value of the gas velocity, using the liquid hold-up calculated in the previous step:

vg,eff =

vg ε(1 − hl ) sin()

(10)

• The new value of the gas velocity is introduced in the dry pressure drop graph described in the first bullet point in order to obtain the value of the pressure drop considering the presence of the liquid phase (i.e. wet pressure drop).

Fig. 5 shows the dry pressure drop performance obtained from the present simulations as a function of the F-factor of the gas phase. The F-factor is a measure of the inertia of the gas phase and it can be calculated as: √ F-factor = vg  (11) The F-factor combines both the velocity and the density as a measure of the kinetic energy of the gas phase, which gives an idea of its capability to hold the liquid inside the packing. Air was used as the gas phase in these simulations, with a density of 1.225 kg/m3 and a viscosity of 1.7894 × 10−5 Pa s. The standard k − ε model with enhanced surface treatment was selected for turbulence modeling. The pressure drop was calculated as the difference in the averaged value of the pressure between the inlet and the outlet divided by the length of the domain. A good agreement with the experimental values found in the literature (Armstrong et al., 2013; Zakeri et al., 2012b) is accomplished. It has also been observed that the relationship between both parameters presents a parabolic shape, with a bigger slope as the F-factor grows. This trend appears to be representative of the fact that the pressure drop in any hydraulic conduct is proportional to the kinetic energy of the fluid (i.e. density and squared velocity). Fig. 6 presents the results for the wet pressure calculated with the liquid hold-up obtained in the present study and the correction factor represented by Eq. (10). The results are compared with the measurements carried out by Zakeri et al. (2012b) for the air/water system with two different liquid loads. The results are overpredicted by the model, the difference being higher as the F-factor increases. This may be attributed to the fact that the liquid hold-up obtained by the present model is also overpredicted. Nevertheless, the parabolic trend is also represented in both cases. As a conclusion, although the wet pressure prediction is not accurate enough, the present model can be used to compare the performance of different REU geometries. 3.4. Effect of the liquid viscosity on the interfacial area The differences in liquid viscosity can be considerable when solutions with various amine mass fractions are used in the process. In the case of monoethanolamine, the value of the dynamic viscosity (i.e. 24 cP) is substantially different from that of water.

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Fig. 6. Wet pressure drop vs. F-factor.

The influence of the liquid viscosity on the absorption process is an important aspect that should be considered for the optimization of structured packings. It has been reported in our previous studies at micro-scale that increasing the concentration of the amine has a beneficial impact on the reactive absorption of the column via the value of the reaction rate (Sebastia-Saez et al., 2015). Therefore, its impact on the interfacial area also needs to be assessed in order to determine whether there exists a double beneficial impact on the process (i.e. on both the interfacial area and the reaction rate). Fig. 7 shows the effect of the liquid viscosity (e.g. pure water and MEA concentration of 30 wt.% and 50 wt.%) on the interfacial area at the liquid load of 180 m3 /m2 /h. The results in the graph appear to show a small influence of the viscosity on the interfacial area, with a slight decreasing tendency despite the huge difference in the value of the viscosity. The difference between the values obtained does not exceed 10% with the pure water case as the reference. If the 30 wt.% MEA solution is compared to pure water, only a 1.5% is found in the associated values of the interfacial area. In light of these results, it can be concluded that increasing the contents of monoethanolamine in the solution has practically no impact on the interfacial area. This fact, combined to the increase in the reaction rate reported in the literature, gives place to an overall beneficial impact on the process performance. 3.5. Effect of the contact angle on the interfacial area Fig. 8 depicts the effect of the contact angle on the interfacial area. These cases were run at a liquid load of 180 m3 /m2 /h for

a 30 wt.% MEA solution. The contact angles considered were 10◦ , 40◦ and 70◦ , which cover different adhesion intensity conditions. Constant contact angles have been considered in the present simulations, being 70◦ a common value for water on metallic surfaces. It is found that higher values of the interfacial area appear for lower contact angles. Low values of the contact angle suggest better wetting conditions by virtue of the prevalence of adhesion forces over the cohesion of the liquid phase. Previous studies have stated that the spreading of the liquid over the surface of the metallic plate is a consequence of the preponderance of the distortive forces (i.e. inertia) over the surface tension, the latter tending to reduce the interfacial area. Therefore, the analysis of the liquid spreading over the metallic plate is usually carried out in terms of the Weber number, which is the ratio between both the inertia and surface tension forces. It was already suggested in our previous work that not only the inertia of the liquid translates into a better liquid spreading. Also a good adhesion of the liquid to the solid surface of the packing (i.e. contact angles below 90◦ ) can increase the amount of wetted area (Sebastia-Saez et al., 2014). The same tendency between the contact angle and the amount of area available for mass transfer has been established in the literature (Haroun et al., 2014; Qi et al., 2014; Basden, 2014). The influence of the contact angle can be appointed as significant from the values observed in the graph. As a matter of fact, the wetting conditions obtained with a contact angle of 10◦ double the interfacial area with respect to the 70◦ contact angle case. These results highlight the importance of the selection of the material used to manufacture the structured packing sheets.

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397

Fig. 7. Effect of the MEA wt. percentage on the interfacial area.

However, it is worth to mention that a substantial research effort should be done, especially about the influence of dynamic contact angles during the wetting process. As the influence of the contact angle has been proven not to be negligible, huge variations from the static values due to advancing or receding liquid fronts can also have an effect on the final interfacial area characterization of the packing.

3.6. Mass transfer performance characteristics After the analysis of the liquid hold-up and the interfacial area, the next step in order to complete the model is the inclusion of source terms to describe the absorption of gas into the liquid phase. For this study, the oxygen–water system was considered for two different liquid loads. In order to reduce the computational time, instead of adding the mass transfer source terms by means of a userdefined function, constant values based on Higbie’s penetration theory from the previous micro-scale simulations have been incorporated to the present simulations. The non-reactive mass transfer for the oxygen–water system was validated in our previous work at micro-scale (Sebastia-Saez et al., 2013). The oxygen mass source term added to the present simulations is equal to 0.015 kg/m3 /s. Table 1 summarizes the values of the liquid load, the interfacial area, and the oxygen concentration considering the entire liquid volume. The data in Table 1 shows a considerable improvement in

Table 1 Mass transfer parameters. Liquid load (m3 /m2 /h)

Interfacial area (m2 /m3 )

Liquid hold-up (–)

Oxygen concentration (mg/l)

180 265

116 146

0.23 0.30

360 1220

the oxygen concentration when the liquid load increases whereas the increment in the liquid hold-up is not especially dramatic. Fig. 9 presents the results for the mass fraction of oxygen in the liquid phase for two values of the liquid load. It can be seen that the mass transfer increases with the liquid load. Thus, the tendency is coherent with the mass transfer results obtained at micro-scale. The absorption rate increases by virtue of the higher amount of interfacial area available for mass transfer when an increment in the liquid load takes place. It was reported in our previous work that, at micro-scale, this behavior happens until the full film flow is reached. Beyond that point the interfacial area does not augment and the contact time between the phases diminishes, which consequently causes a diminution in the mass transfer rate. As it has been observed, the full film flow regime is never reached at meso-scale. Therefore, the mass absorption rate has necessarily to increase with the liquid load, which is in agreement with the results obtained in this work. Thus, the present model can be able to reproduce with actual commercial geometries, the tendency already reported in the

Fig. 8. Effect of the contact angle on the interfacial area.

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Fig. 9. Oxygen mass fraction vs. liquid load.

literature by which the mass transfer performance improves with the liquid load by virtue of the enhanced interfacial area. The model could be further improved to simulate reactive mass transfer for post-combustion CCS. 4. Conclusions In this work, the multiphase flow within structured packings is reproduced for various liquid loads, which cover both experimental and industrial ranges. A meso-scale model based on REUs of structured packings has been developed to account for the liquid hold up and the interfacial area in addition to the dry pressure drop per unit length of the system. The present meso-scale model has been proven to be able to predict the trends reported in the literature for the hydrodynamics (e.g. pressure drop, liquid hold up and interfacial area) and non-reactive mass transfer. According to this, the dry pressure drop increases exponentially with the inertia of the gas phase. The liquid hold-up and the interfacial area predicted from the simulations also present the same tendency observed in the literature. Both parameters increase with the amount of liquid injected into the domain but their rate of change diminishes for high values of the liquid load. The mass transfer performance has been carried out based on previous micro-scale predictions. The results on mass transfer show that higher interfacial area enhances the total mass transfer rate, which has been represented by the mass fraction of oxygen in the liquid volume. The main novelty of this work is thus the fact that the meso-scale modeling (i.e. focused on a limited number of REUs), is able to predict, not only the dry pressure drop of the packing, but also important hydrodynamic characteristics such as liquid holdup and interfacial area. These parameters directly affect the wet pressure drop and the mass transfer performance of the packing, respectively. The present model could be further investigated and utilized for geometry optimization purposes to improve the hydrodynamic and mass transfer characteristics of structured packed columns. Acknowledgements The authors gratefully acknowledge the financial support for this work by the UK Engineering and Physical Sciences Research Council (EPSRC) project grant: EP/J020184/1 and FP7 Marie Curie iComFluid project grant: 312261.

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