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energies Article

3D Numerical Study of Multiphase Counter-Current Flow within a Packed Bed for Post Combustion Carbon Dioxide Capture Li Yang 1,2 , Fang Liu 2 , Zhengchang Song 2, *, Kunlei Liu 3 and Kozo Saito 3, * 1 2 3

*

Key Laboratory of Coal-Based CO2 Capture and Geological Storage, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China; [email protected] School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China; [email protected] Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USA; [email protected] Correspondence: [email protected] (Z.S.); [email protected] (K.S.); Tel.: +86-139-5220-3069 (Z.S.); +1-859-312-7273 (K.S.)

Received: 11 May 2018; Accepted: 1 June 2018; Published: 4 June 2018

Abstract: The hydrodynamics within counter-current flow packed beds is of vital importance to provide insight into the design and operational parameters that may impact reactor and reaction efficiencies in processes used for post combustion CO2 capture. However, the multiphase counter-current flows in random packing used in these processes are complicated to visualize. Hence, this work aimed at developing a computational fluid dynamics (CFD) model to study more precisely the complex details of flow inside a packed bed. The simulation results clearly demonstrated the development of, and changes in, liquid distributions, wetted areas, and film thickness under various gas and liquid flow rates. An increase in values of the We number led to a more uniform liquid distribution, and the flow patterns changed from droplet flow to film flow and trickle flow as the We number was increased. In contrast, an increase in gas flow rate had no significant effect on the wetted areas and liquid holdup. It was also determined that the number of liquid inlets affected flow behavior, and the liquid surface tension had an insignificant influence on pressure drop or liquid holdup; however, lower surface tension provided a larger wetted area and a thinner film. An experimental study, performed to enable comparisons between experimentally measured pressure drops and simulation-determined pressure drops, showed close correspondence and similar trends between the experimental data and the simulation data; hence, it was concluded that the simulation model was validated and could reasonably predict flow dynamics within a counter-current flow packed bed. Keywords: post combustion CO2 capture; computational fluid dynamics (CFD); multiphase counter-current flow; flow characteristics

1. Introduction Global warming and climate change attract much attention worldwide, and a large amount of the anthropogenic CO2 emission is reported to be responsible for it [1]. Statistics have pointed to a 40% increase in atmospheric CO2 concentrations since preindustrial times, and this increase is primarily due to fossil fuel combustion [2]. Hence, if the deleterious effects of rising CO2 concentrations are to be averted, an imperative need exists to reduce the extent to which it is emitted into the atmosphere [3]. Currently, technologies are under development for capturing and sequestering CO2 , with a primary focus on power generation; these include pre-combustion, post combustion, oxy-fuel combustion, and Energies 2018, 11, 1441; doi:10.3390/en11061441

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chemical looping combustion scenarios. Among them, post combustion capture removes CO2 from the flue gas, a stage when fuel has already been combusted. Solvent-based CO suitable Energies 2018, 11, x FOR PEER REVIEW is one of the most promising approaches and is particularly 2 of 14 2 absorption for post combustion processing [4]. A diagram of a post combustion CO2 capture, presented in Figure 1, combustion, oxy-fuel combustion, and chemical looping combustion scenarios. Among them, post includes two reactors that are, respectively, an absorber and a stripper. An aqueous solution, usually combustion capture removes CO2 from the flue gas, a stage when fuel has already been combusted. amine-based,Solvent-based is circulated the two reactors to produce a flow of highly concentrated CO2 CObetween 2 absorption is one of the most promising approaches and is particularly from the relatively lowcombustion CO2 concentration flueofgas. Incombustion the absorber, gas and liquid reactants suitable for post processing [4].in A the diagram a post CO2 capture, presented in Figure 1, includes two reactors that are, respectively, an absorber and a stripper. An aqueous flow counter-currently through a packed bed containing packing material consisting of hollow tubes, solution, usually amine-based, is circulated between the two reactors to produce a flow of highly pipes, or other types of vessels. The packing greatly increases the contacting area between the fluids; concentrated CO2 from the relatively low CO2 concentration in the flue gas. In the absorber, gas and this contact area is where reaction or mass transfer [5]. Increasing the contact liquid reactants flow counter-currently through a packedoccurs bed containing packing material consistingarea is one hollow tubes, pipes, or other types of vessels. The packing greatly increases the contacting area importantofpathway recognized to enhance mass transfer and chemical reactions. Therefore, the use between the fluids; this contact area is whereadvantages reaction or mass transfer occurs [5]. Increasing the of a packed bed promotes reactor and reaction such as high capacity, high efficiency and, contact area is one important pathway recognized to enhance mass transfer and chemical reactions. if designed appropriately, low pressure drop. Therefore, the use of a packed bed promotes reactor and reaction advantages such as high capacity, The packing is usually stationary and contributes to drop. complex interactions between the gas and high efficiency and, if designed appropriately, low pressure The packing is usually can stationary and contributes to complex interactions between the can gas and liquid flows. These interactions be manifested under different flow regimes and cause distinct liquid flows. These interactions can be manifested under different flow regimes and can cause distinct gas and liquid distributions in packed beds [6]. Hence, it is imperative to understand the hydrodynamic gas and liquid distributions in packed beds [6]. Hence, it is imperative to understand the flow regimes, pressure drops, liquid holdups, wetted areas, liquid distributions, and the packing hydrodynamic flow regimes, pressure drops, liquid holdups, wetted areas, liquid distributions, and arrangement if optimized reactor and reaction performance are to bearerealized. the packing arrangement if optimized reactor and reaction performance to be realized. CO2 Depleted Flue Gas

CO2

EHX Absorber

Stripper

Heat

Flue Gas

Figure 1. Diagram of a post combustion solvent-based CO2 capture process. Figure 1. Diagram of a post combustion solvent-based CO2 capture process.

Gamma Gamma and X-ray tomography, resonance imaging, radioactive particle tracking, and X-ray tomography,magnetic magnetic resonance imaging, radioactive particle tracking, electrical capacitance tomography, and positron emission tomography have been used to investigate electrical capacitance tomography, and positron emission tomography have been used to investigate liquid distributions [7–10]. Li et al. [11] investigated two-phase flow in a packed bed experimentally, liquid distributions [7–10]. Li et al. [11] investigated two-phase flow in a packed bed experimentally, proposing a method to predict pressure drops of two-phase flow through packed beds with coarse proposingparticles. a method to predict drops two-phase flow through packed beds with coarse Ali Toukan et al.pressure [12] studied flow of regimes in a cocurrent, gas–liquid, upflow-moving particles. packed Ali Toukan et using al. [12] studied flow regimes in athe cocurrent, bed reactor gamma ray densitometry, and found flow regimegas–liquid, as bubbly andupflow-moving pulse flow. However, eachgamma of these experimental approaches hadfound limitations in the regime spatial and packed bed reactor using ray densitometry, and the flow as temporal bubbly and pulse resolution that could be accomplished, and the results are especially difficult to scale when flow. However, each of these experimental approaches had limitations in the spatial and temporal considering large reactors [13]. Experimental studies of packed bed reactors are also very time resolutionconsuming that could beexpensive, accomplished, results areimpossible, especially scale when and and it is and very the difficult, if not to difficult accuratelyto measure the veryconsidering large reactors [13]. Experimental studies of packed bed reactors are also consuming and complex geometry of some packed bed materials, especially when limited spacevery exists time between the Furthermore, is impracticaltotoaccurately insert measuring devices packed beds geometry expensive,packing and itcomponents. is very difficult, if not itimpossible, measure theinto very complex because their presence may disturb or alter liquid and gas flow patterns. of some packed bed materials, especially when limited space exists between the packing components. The ever-increasing computational power of computers and the development of computational Furthermore, is impractical to allowed insert measuring devices into packedsimulations beds because presence may fluid it dynamics (CFD) have promising applications of numerical to the their modeling disturb or alter liquid and gas flow patterns. The ever-increasing computational power of computers and the development of computational fluid dynamics (CFD) have allowed promising applications of numerical simulations to the modeling of multiphase flow in packed bed reactors [14–18]. Hence, CFD simulations on spherical particle packing may help to study and understand complex fluid flow regimes and establish a reliable database for

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analyzing and interpreting the macroscopic phenomenon and results. As examples, Bednarz et al. [19] Energies 2018, 11, x FOR PEER REVIEW 3 of 14 developed a 2D model for a multiphase counter-current loop reactor and demonstrated the flow characteristics in a packed et al. [20] developed 3D modelontospherical study particle counter-current of multiphase flow in bed; packedZhao bed reactors [14–18]. Hence, CFDa simulations packing to study and complex fluid flow regimes and establish a reliable multiphase flow,may but help the packing wasunderstand simplified to porous media, different than the actual, existing database for analyzing the macroscopic phenomenon and results.model, As examples, forms of packing; Tong et al. and [21]interpreting built a meso-scale 2D cocurrent, two-phase and described Bednarz et al. [19] developed a 2D model for a multiphase counter-current loop reactor and detailed flow patterns within corrugated structures. In general, a packed bed is not symmetrical; rather, demonstrated the flow characteristics in a packed bed; Zhao et al. [20] developed a 3D model to study it may have a complicated packing configuration thetouse of amedia, 2D model isthan inappropriate. counter-current multiphase flow, but the packing for waswhich simplified porous different the actual, existing forms of packing; Tong et al. [21] built a meso-scale 2D cocurrent, two-phase model, The development and use of 3D models could create more usable data for the study of and described detailed flow patterns within bed corrugated structures. In general, a packed bednumber is not counter-current, multiphase flows in packed reactors; however, a very limited of such symmetrical; rather, it may have a complicated packing configuration for which the use of a 2D model 3D studiesisare available in the open literature. Therefore, the objective of this work was to develop a inappropriate. comprehensive 3D CFD model study multiphase flows at a microscopic The development andto use of 3D gas–liquid, models could counter-current create more usable data for the study of countermultiphase in packed bedflow reactors; however, a very limited number such 3Dholdups, studies level, andcurrent, to elaborate on flows film formation, distributions, pressure drops,ofliquid wetted in the open literature. Therefore, the objective of this work was to develop a areas, andare theavailable interactions between phases. The 3D modeling focused on the relationships between comprehensive 3D CFD model to study gas–liquid, counter-current multiphase flows at a the characteristics of the liquid film in a packed bed and the concomitant capturing efficiency of microscopic level, and to elaborate on film formation, flow distributions, pressure drops, liquid gaseous CO . To validate thisand model, experimental data wereThe also3D acquired holdups, wetted areas, the interactions between phases. modelingfollowing focused onthe the technique 2 relationships between the characteristics of the liquid film in a packed bed and the concomitant recommended by Saito and Williams [22] and practiced by Liu et al. [23]. capturing efficiency of gaseous CO2. To validate this model, experimental data were also acquired followingMethods the technique recommended by Saito and Williams [22] and practiced by Liu et al. [23]. 2. Experimental 2. Experimental A schematic of the Methods experimental setup is shown in Figure 2. The height of packed volume was 550 A spheres schematicwith of theaexperimental is shown in uniformly Figure 2. Thepacked height ofinpacked volume mm and plastic diameter ofsetup 9.5 mm were the bed. Thewas void fraction 550 mm and plastic with CO a diameter ofrate 9.5 mm were uniformly by packed in the bed. The void of the packed volume wasspheres 0.4. The flow was controlled a mass-flow controller (MFC) 2 fraction of the packed volume was 0.4. The CO2 flow rate was controlled by a mass-flow controller (Aalborg, Orangeburg, NY, USA), and the water flow rate was controlled by a peristaltic pump (Longer, (MFC) (Aalborg, Orangeburg, NY, USA), and the water flow rate was controlled by a peristaltic pump Boonton, NJ, USA). The CO entered the2 entered column itsfrom bottom and and waswas contacted (Longer, Boonton, NJ, 2USA). The CO thefrom column its bottom contacted counter-currently countercurrently withentered the waterfrom whichthe entered top. Thedrop pressure dropthe along the packing bed was with the water which top.from Thethe pressure along packing bed was measured by measured by the inclined manometer. A Labview system was applied for flow rate adjustment and the inclined manometer. A Labview system was applied for flow rate adjustment and data recording. data recording.

Gas Outlet

Periodic Pump

△P

MFC Controller

MFC

Gas Cylinder Water Container

(a)

(b)

Figure 2. Experiment Setup, (a) Schematic diagram of the experiment setup; (b) Image of plastic

Figure 2. spheres. Experiment Setup, (a) Schematic diagram of the experiment setup; (b) Image of plastic spheres.

3. Development of the Numerical Model 3.1. Mesh Generation As depicted in Figure 3, the packed bed was modeled as a rectangular container filled with spherical balls having the same size and void fraction as used in the experimentation. The size of

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Energies 2018,3.11,Development 1441 of the Numerical Model

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3.1. Mesh Generation

the rectangle domain wasin 19.2 ×3,19.2 × 52 mm, with a 0.1 mm gap between eachfilled nearby As depicted Figure the packed bed was modeled as a rectangular container withsphere to spherical balls having the same size andAvoid fraction used in of thespheres experimentation. The size of thealong the facilitate meshing on the sphere surfaces. total of sixaslayers were constructed domain was 19.2 × 19.2 × 52 mm, four with aspheres, 0.1 mm gap between each nearby sphere facilitate packed bedrectangle domain. The first layer included and the second layer hadtoone whole-sphere meshing on the sphere surfaces. A total of six layers of spheres were constructed along the packed in the center with four half-spheres on the sides and four 1/4 spheres at the four corners of the layer. bed domain. The first layer included four spheres, and the second layer had one whole-sphere in the The remaining were arrangedonfollowing thisfour same sequence and arrangement centerlayers with four half-spheres the sides and ¼ spheres at the fourcreated corners an of the layer. The having remaining layers were sequence and created arrangement having the same 0.4 void fraction overarranged the sixfollowing layers asthis insame the experimental tests.anLiquid entered from the top the same void fraction the the six layers as in the tests.the Liquid entered from the top out from of the domain and0.4 flowed downover from bottom; gasexperimental entered from bottom and flowed of the domain and flowed down from the bottom; gas entered from the bottom and flowed out from the top. the top.

Gas Outlet

Liquid Inlet

Symmetric Wall

Z

X

Gas Inlet

Liquid Outlet

Y

Figure 3. 3D geometry and meshed model. Figure 3. 3D geometry and meshed model.

3.2. Governing Equation in the VOF Model

3.2. Governing Equation in the VOF Model Commercial CFD software ANSYS FLUENT (V12.1, ANSYS, Canonsburg, PA, USA) was used for this study. A phasic volume of fraction (VOF) multiphase model was applied to track the interface Commercial CFD software ANSYS FLUENT (V12.1, ANSYS, Canonsburg, PA, USA) was used for between the gas and liquid to capture the effect of surface tension on the flow behavior of two this study. immiscible A phasicphases volume of fraction (VOF) multiphase model was to track the interface in mini-channels. The mass transfer terms between theapplied two immiscible phases between the gas and liquid to capture the effect of surface tension on the flow behavior of two were neglected. The VOF model solves the single equation through the domain theimmiscible volume of phases immiscible phases in mini-channels. Themomentum mass transfer terms between theand two each phase is tracked in grid cell. The governing equations of two phase flow are expressed as follows: were neglected. Continuity equation The VOF model solves the single momentum equation through the domain and the volume of ∂ρ (1) as follows: +equations ∇ ∙ (ρ v ⃑ ) = 0 of two phase flow are expressed each phase is tracked in grid cell. The governing ∂t ContinuityMomentum equationequation → ∂ρ + ∇· ρ v = 0 ⃑⃑⃑⃑T (1) ∂ (2) (ρv ⃑ ) + ∇(ρv ⃑∂t ⃑ ) = −∇p + ∇ [μ (∇v v ⃑ + ∇v )] + ρg⃑ + ⃑F ∂t a ρ v +a ρ v Momentum equation ⃑⃑ is the drag force. where v = 1 1 1 2 2 2 , F ρ

Each phase’s volume fraction is a k , where: ∂ → →→

∂t

ρv + ∇ ρv v

→ → → → = −∇p + ∇ µ ∇ v + ∇vT + ρg + F

(2)

→

a 2 ρ 2 v2 where v = a1 ρ1 v1 + , F is the drag force. ρ Each phase’s volume fraction is ak , where: n

∑ ak = 1

(3)

ρ = a2 ρl + (1 − a2 )ρg

(4)

µ = a2 µl + (1 − a2 )µg

(5)

k=1

For a two-phase system:

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where ak ranges from 0 to 1; a zero corresponds to a cell filled with gas phase and a value of one corresponds to a cell filled with the liquid phase. Intermediate values correspond to interfaces between phases. Also, the drag force term in Equation (2) considered only surface tension and gravity effects. The surface tension model can be expressed by: →

F =σ

ρk∇ak 0.5 ρl + ρg

where k is the free surface curvature, which is defined as 1 n ˆ k = ∇·n = ·∇ |n| − (∇·n) |n| |n|

(6)

(7)

The symbol nˆ is a unit normal vector, and n = ∇ak . 3.3. Turbulence Model In fluid dynamics, turbulent flow is characterized by chaotic property changes. These changes include low momentum diffusion, high momentum convection, and rapid variation of pressure and flow velocity in space and time. Multiphase flows in packed beds are often characterized as laminar flow but several studies have reported them to be turbulent [24]. A Dybbs et al. [25] used laser anemometry and flow visualization technology to investigate liquid flow regimes in hexagonal packing of spheres and rods, and classified four flow regimes for different ranges of Reynolds number. For 1 < Re, the flow was dominated by viscous force; for 1 < Re < 150, the flow was a steady laminar inertial flow; for 150 ≤ Re ≤ 300, the laminar inertial flow was unsteady; and, for Re > 300, the flow was highly unsteady, chaotic, and qualitatively resembled turbulent flow. The Reynolds number has been calculated as: Re =

ρvd µ

(8)

where the characteristic length d is the thickness of the phase inlet, ρ is the density of the fluid (kg/m3 ), v is its velocity (m/s), and µ is the viscosity (kg/m/s). Therefore, since the Reynolds numbers for both liquid and gas phases (min: 180, max: 1100) are within the range of turbulent flow, a turbulence model was applied. For turbulent flow, several different models have been developed, such as large eddy simulation (LES), k-ε model, and k-omega. The k-ε model is only valid for fully turbulent and nonseparated flows. The k-omega model is a two-transport-equation model solving for kinetic energy, k, and turbulent frequency, ω; it allows for more accuracy near walls and for a low Reynolds numbers (ANSYS help). The LES model is also popular for turbulent flow simulation, and it emphasizes the interactions between phases. Labourasse [26] successfully applied the LES model to resolve two-phase flow problems and accounted for the complex interactions between turbulence and interfaces. Vincent [27] also applied the LES model for phase separation, and Christensen [28] adopted a standard LES model coupled with a VOF free surface approach in a wave break simulation study. Therefore, the LES turbulent model will be used in the simulation of the plastic sphere, packed bed. 3.4. Model Parameters and Boundary Conditions The rectangular domain was part of a packed bed; the side wall boundary was set as the symmetric wall because the cuboid domain represented only part of the total packed bed that was used experimentally. The contact angle at the wall was calculated and therefore set at 70◦ . One liquid inlet was placed at the top and one liquid outlet was placed at the bottom; each had a diameter of 7.2 mm. Because of counter-flow, gas entered the bottom hole around which liquid flowed outward

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and then gas exited the top outlet around which liquid entered. Side wall boundaries were set as symmetric boundaries instead of solid wall boundaries. The fluids were assumed to be Newtonian, isothermal, and incompressible. The boundary conditions are listed in Table 1. Table 1. Boundary Conditions. Boundary

Materials

Type

Value

Liquid inlet Gas inlet Liquid outlet Gas outlet

Water Air

Mass flow rate Mass flow rate Pressure-outlet Pressure-outlet

100–1200 mL/min 5–25 L/min 0 Pa 0 Pa

Velocity (m/s)

Reynolds Number

0.012–0.147 0.076–0.382

180–1100 99–500

We Number 0.014–2.2

The Geo-reconstruct algorithm method was used for interface reconstruction of the volume fraction, a simple scheme for which was the pressure-velocity coupling. For spatial discretization, the Least Squares Cell Based was used for the gradient in the spatial discretization set up, the Presto method was used for pressure, the Second Order Upwind method was used for the momentum equation, and the First Order Implicit method was used for the transient formulation. The simulation used a transient state to observe the growth of the liquid film and the development of gas–liquid interactions. The time step size for this model was 0.00005 s while solving a maximum 30 iterations per time step. 4. Results and Discussions 4.1. Model Validation The results of CFD assessments of gas–liquid flows are generally validated by comparing pressure drops obtained from modeling and experimentation. Experiments were conducted in which both gas and liquid flow rates were changed, as listed in Table 2. In the 1st group of tests, liquid flow rates were held constant at 200 mL/min while gas flow rates were varied. In the 2nd group of tests, gas flow rates remained constant at 10 L/min and the liquid flow rates were varied. Pressure drops, measured at each experimental condition, are also displayed in Table 2; they increased with the increment of either liquid or gas flow rates, but were more sensitive to gas flow rate variations than to liquid flow variations. Table 2. Experimental matrix and gas side pressure drops. Cases

Gas Phase Mass Flow Rate (L/min)

Liquid Phase Mass Flow Rate (mL/min)

Gas Side Pressure Drop (Pa/m)

1 1 1 2 2 2

5 10 15 10 10 10

200 200 200 100 200 300

23.64 65.45 105.45 54.55 65.45 72.73

Pressure drops were also obtained during the CFD simulations using the conditions listed in Table 1. A comparison of pressure drops obtained from the simulations and experimental measurements are shown in Figure 4. In general, the trends in pressure drops from CFD and the experiments mirrored each other; their differences were less than 30%. These comparisons established a validation of the 3D CFD model for use in modeling a packed bed reactor during gas–liquid, counter current flow operation.


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experiments mirrored each other; their differences were less than 30%. These comparisons established Energies 2018, 11, 1441 a validation of the 3D CFD model for use in modeling a packed bed reactor during gas–

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liquid, counter current flow operation. Energies 2018, 11, x FOR PEER REVIEW

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120

80

60 120 40

20

Experiment Simulation

80 0 60 4

6

8

10

12

Gas Mass Flow Rate / L min 40

50 40 80 30 70

-1

100

Pressure Drop / Pa m Pressure Drop / Pa m-1

-1 Pressure Drop / Pa m Pressure Drop / Pa m-1

experiments mirrored each other; their differences 70were less than 30%. These comparisons 100 established a validation of the 3D CFD model for use in modeling a packed bed reactor during gas– 60 80 liquid, counter current flow operation.

14

16

-1

(a)

20


20 60 10 50 50 40 30

100

150

200

250

300

350

Liquid Mass Flow Rate / mL min-1

(b)

Experiment Figure 4. Pressure drops obtained from experiments and simulation using six differen t conditions.


20

Simulation Figure 4. drops and liquid simulation using differen t conditions. (a)Pressure Pressure drop as obtained a function from of gas experiments flow rate at a fixed flow rate of Vsix L = 200 mL/min; (b) 0 10 4 6 8 10 12 14 16 50 100 150 200 250 300 350 (a) Pressure drop asasa afunction ofliquid gas flow rateatata fixed a fixed flow VL = 200 mL/min; (b) pressure drop function of flow rate gas liquid flow rate of Vgrate = 10 of L/min. -1 Liquid Mass Flow Rate / mL min-1 Gas Mass Flow Rate / L min pressure drop as a function of liquid flow rate at a fixed gas flow rate of Vg = 10 L/min.

(a) 4.2. Liquid Distribution Characterization

(b)

Figure 4. Pressure drops obtained from experiments and simulation using six differen t conditions. The evolution of liquid distributions within the reactor as a function of liquid flow rates was also 4.2. Liquid Distribution Characterization (a) Pressure drop as a function of gas flow rate at a fixed liquid flow rate of V L = 200 mL/min; (b)

studied. However, Weber numbers (We), which are a measure of the relative importance of a fluid’s pressure drop as a function of liquid flow rate atthe a fixed gas flow of Vg = 10 of L/min. Theinertia evolution of liquid distributions within as rate a of function liquid ratesorwas also compared to its surface tension, were used asreactor the variable interest rather thanflow the liquid studied.gas However, which flow rates.Weber The Wenumbers values are(We), expressed as: are a measure of the relative importance of a fluid’s 4.2. Liquid Distribution Characterization inertia compared to its surface tension, were We used as the variable of interest rather than the liquid or = (ρv2 l)/σ (9) The evolution of liquid distributions within the reactor as a function of liquid flow rates was also gas flow rates. The We values are expressed as: 3), v is are studied. Weber (We), which measure of the relative importance of a length, fluid’s where ρHowever, is the density of numbers the fluid (kg/m the afluid velocity (m/s), l is its characteristic (N/m). variable inertia compared to its surface(N/m) tension, were used as2the of interest ratherthat thanWe thevalues liquidare or and σ is the surface tension of the liquid It is generally accepted = inρv l /σ (9) gas flow rates. The We values are expressed as: valuable for analyzing multiphase fluidWe flows which an interface exists between the fluids and especially when strongly curved surfaces are present2 [24]. We = (ρv l)/σ (9) 3 ), v results Figures 5 andof6 the display the(kg/m simulation for flow distributions and wetted surface areas, length, where ρ is the density fluid is the fluid velocity (m/s), l is its characteristic 3), v is the fluid velocity (m/s), l is its characteristic length, ρ is the density of the fluid respectively, attension a fixed gas flow rate where Reynolds number = 199, and different liquid and σ iswhere the surface (N/m) of(kg/m the liquid (N/m). It Re is ggenerally accepted thatflow Werates values are and σ is the surface tension (N/m) of the liquid (N/m).state It is condition. generally accepted that We the values as represented by We; each figure represents the steady Figure 7 displays VOFare of valuable for analyzing multiphase fluid flows in which an interface exists between the fluids and valuable for liquid analyzing multiphase fluidrepresents flows in which an % interface exists between the fluids and the gas and in which a red color 100 vol. liquid and blue represents 100 vol. % especially when strongly curved surfaces are present [24]. especially when strongly curved surfaces are present [24]. gas. FiguresFigures 5 and56and display thethe simulation forflow flowdistributions distributions wetted 6 display simulationresults results for and and wetted surfacesurface areas, areas, respectively, at a fixed gas flow where Reynolds number number ReRe g = 199, andand different liquid liquid flow rates respectively, at a fixed gas flow raterate where Reynolds different flow rates g = 199, as represented byeach We; each figure representsthe the steady steady state Figure 7 displays the VOF of VOF of as represented by We; figure represents statecondition. condition. Figure 7 displays the the gas and liquid in which a red color represents 100 vol. % liquid and blue represents 100 vol. % the gas and liquid in which a red color represents 100 vol. % liquid and blue represents 100 vol. % gas. gas.

(a) We = 0.014

(b) We = 0.062

(a) We = 0.014

(b) We = 0.062

Figure 5. Cont.

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(c) We = 0.137

(d) We = 0.240

(e) We = 0.547

(f) We = 0.958

(g) We = 1.51

(h) We = 2.16

Figure 5. Flow distribution of iso-surface 0 at different liquid We from 0.014 to 2.16 at fixed Reg = 199.

Figure 5. Flow distribution of iso-surface 0 at different liquid We from 0.014 to 2.16 at fixed Reg = 199.


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We = 0.014

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We = 0.062

We = 0.137

We = 0.240

We = 0.014

We = 0.062

We = 0.137

We = 0.240

= 0.547 We = We 0.547

We = 0.958 We = 0.958

We = 1.51

We = 2.16

We = 1.51

We = 2.16

Figure 6. Liquid flow regime and wetted area at different liquid We numbers from 0.014 to 2.16 at Liquid area at at different liquid We We numbers fromfrom 0.0140.014 to 2.16 fixed Figure 6. Liquid flow flowregime regimeand andwetted wetted area different liquid numbers to at 2.16 at fixed Reg = 199.

Reg = Re 199. fixed g = 199.

0.4

Liquid Holdup / %

Liquid Holdup / %

0.4

0.3

0.3

0.2 Re =1056 L

Re =704

0.2

L

0.1

Re =352 L

Re =1056 L

100

200

0.1

300

500 ReL=704

400

Re =352

Reg

L

Figure 7. Influence of gas velocity with fixed liquid velocities on liquid hold up. 100

200

300

400

500

Reg Figure 7. Influence of gas velocity with fixed liquid velocities on liquid hold up. Figure 7. Influence of gas velocity with fixed liquid velocities on liquid hold up.

The liquid distributions became mostly uniform after the first layer of the packing material, indicating that almost fully-developed flow was established rapidly within the bed; also, more liquid

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The liquid distributions became mostly uniform after the first layer of the packing material, indicating that almost fully-developed flow was withinonly the bed; also, more liquid was distributed throughout the bed at higher Weestablished values. Asrapidly examples, a quarter of the domain was distributed throughout thewas bed0.014, at higher We values. examples, onlywas a quarter of the domain was filled with liquid when We whereas, theAs whole domain completely filled with filled Wevalue was 0.014, whereas, the whole domain was completely filled with of liquidwas when Wewith wasliquid 2.16. when The We also had an impact on flow patterns and the development liquid when We was 2.16. The We value also had an impact on flow patterns and the development droplets or film flow. At We = 0.014, liquid flow was not continuous and contained droplets; at of such a droplets or film flow. At We = 0.014, liquid flow was not continuous and contained droplets; at such low We number, the liquid surface tension was considered a dominant influence on flow, which may a low We number, the liquid surface tension was considered a dominant influence on flow, which result in the formation of droplets. After We was increased to 0.547, droplet flow was greatly weakened may result in the formation of droplets. After We was increased to 0.547, droplet flow was greatly and most of the flow was connected, as shown as in shown Figurein5e, indicating a pattern expected for film weakened and most of the flow was connected, Figure 5e, indicating a pattern expected flow. for Although surface tension maytension still dominate higher at We, the formation of film flow beneficially film flow. Although surface may still at dominate higher We, the formation of film flow increased the amount of interfacial wetted area, as wetted shownarea, in Figure 6e. With further of We to beneficially increased the amount of interfacial as shown in Figure 6e.increases With further increases of We to 1.51, engulfed trickle flow gradually engulfedand the the whole domain and the wetted domain 1.51, trickle flow gradually the whole domain wetted domain continued to increase. continued increase. areas and liquid holdups were also modeled, and are presented in Figures 7 The wettedtointerfacial The wetted interfacial areas holdups were also modeled, andflow are presented Figuresareas and 8, respectively, as a function of and the liquid Reynolds number, Re. At fixed gas rates, theinwetted 7 and 8, respectively, as a function of the Reynolds number, Re. At fixed gas flow rates, the wetted and liquid holdups increased with an increase in Re. However, an increase in the gas flow rate had no areas and liquid holdups increased with an increase in Re. However, an increase in the gas flow rate significant effect on the wetted areas and liquid holdups. These outcomes are distinct from the results had no significant effect on the wetted areas and liquid holdups. These outcomes are distinct from of cocurrent flow modeling analyses in which both wetted areas and liquid holdups decreased with the results of cocurrent flow modeling analyses in which both wetted areas and liquid holdups increased gas flow [29].gas flow rates [29]. decreased with rates increased 0.30

Wetted Area / %

0.25 0.20 0.15 0.10

Re =1056 L Re =704 L Re =352 L

0.05 0.00 100

200

300

400

500

Reg

Figure 8. Influence of gas velocity with fixed liquid velocities on wetted area.

Figure 8. Influence of gas velocity with fixed liquid velocities on wetted area. 4.3. Gas–Liquid Interactions

4.3. Gas–Liquid Interactions

Because of limited free space within a packed bed, the gas and liquid are in a competitive relation

Because of limited space within aimpact packed gas and liquid in a competitive relation with respect to flow;free hence, a significant onbed, fluidthe distributions may beare expected as Re is varied. Figure 9to shows gas and liquid velocity vectors in the packed bed may whenbe Reexpected g = 199, and was with respect flow;the hence, a significant impact on fluid distributions as Re ReL is varied. varied between 180 and 884; upward vectors depict gas velocities and downward vectors depict Figure 9 shows the gas and liquid velocity vectors in the packed bed when Reg = 199, and ReL was velocities. At Re L = 180, gas phase flow dominated the flow region and the interactions between variedliquid between 180 and 884; upward vectors depict gas velocities and downward vectors depict liquid the gas and liquid occurred mainly on the top and bottom of the spherical balls. The gas flow velocity velocities. At ReL = 180, gas phase flow dominated the flow region and the interactions between the also displayed a shearing effect on the liquid that was expected to lead to the formation of droplets. gas and liquid occurred mainly on the top and bottom of the spherical balls. The gas flow velocity When ReL was increased to 884, as indicated in Figure 9b, the region near the middle section of the also displayed a shearing effect the liquid was flowing expected to lead to the formation of droplets. balls was filled with both liquidon and gas, with that the liquid along the ball surfaces; this condition Whenled ReLtowas increased increase to 884, asinindicated in Figure 9b, the region the middle sectionduring of the balls a significant the wetted area. These effects arenear considered important was filled with both liquid and gas, with the liquid flowing along the ball surfaces; this condition interactions between the gas and liquid on the packing surfaces because increased interactions will led to a significant the wetted Theseaeffects important during interactions enhance theincrease chemicalinadsorption of area. CO2 within packedare bedconsidered reactor. between the gas and liquid on the packing surfaces because increased interactions will enhance the chemical adsorption of CO2 within a packed bed reactor.

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(a) Reg = 199 and ReL = 180

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(b) Reg = 199 and ReL = 884

Figure 9. Gas and liquid velocity vectors. 9. Gas and liquid velocity vectors. (a) Reg = 199 and ReFigure L = 180 (b) Reg = 199 and ReL = 884

4.4. Effect of the Number of Liquid Inlets Figure 9. Gas and liquid velocity vectors. 4.4. Effect of the Number of Liquid Inlets As noted in the results of Figures 5 and 6, the effect of having only one liquid inlet was to cause 4.4.As Effect of the of Liquid Inlets 5 and 6, the effect of having only one liquid inlet was to noted inNumber the results of Figures somewhat poorly distributed liquid throughout the modeled domain. These results point to the cause somewhat poorly distributed liquidand throughout theofmodeled domain. Theseinlet results to the As noted in the results of Figures 6, the effect having only one liquid waspoint to cause importance of the design of liquid inlets5 for the reactor because flows which are initially developed importance of the design of liquid inlets for the reactor because flows which are initially developed somewhat poorly distributed liquid throughout the modeled domain. These results point to affect the may be expected to depend on flow injection geometries; in addition, distribution changes will may be expected to depend onliquid flow inlets injection geometries; in addition, distribution changes will affect importance of the design of for the reactor because flows which are initially developed flow hydrodynamics [6,30]. Hence, CFD models having a different number of liquid inlets were flow hydrodynamics [6,30]. on Hence, injection CFD models having different number ofchanges liquid will inlets were may be expected to their depend geometries; in aaddition, distribution affect constructed to study effectsflow on flow. Figure 10 shows the geometric models when the number constructed to study their effects on flow. Figure 10 shows the geometric models when the number flow hydrodynamics CFD having a different number liquid inlets were of inlets was varied from[6,30]. 1 to 4Hence, to 13. As themodels number of inlets were varied theirofrespective diameters of constructed inlets was varied from 1 to 4 to 13. As theFigure number of inlets were variedmodels their respective diameters to study their effects on flow. 10 shows the geometric when the number were also varied from 0.0072 m with one inlet, to 0.0036 m with four inlets, and 0.002 m with 13 inlets; were also varied from from 0.0072 m 4with one to 0.0036 with fourvaried inlets,their and respective 0.002 m with 13 inlets; of inlets was varied 1 to to 13. Asinlet, the number of m inlets were diameters these values of the inlet diameters enabled the total liquid inlet area to be constant and, therefore, the were also varied from 0.0072 m with one inlet, to 0.0036 m with four inlets, and 0.002 m with 13 inlets; these values of the inlet diameters enabled the total liquid inlet area to be constant and, therefore, overall inlet liquid velocity remained constant. All three inlet configurations were simulated using values the inlet diameters enabled the totalAll liquid inlet area to be constantwere and,simulated therefore, the thethese overall inletofliquid velocity remained constant. three inlet configurations using identical operation conditions. overalloperation inlet liquid velocity remained constant. All three inlet configurations were simulated using identical conditions. Figure 11 demonstrates the influence of the number of inlets on wetted areas, liquid hold ups, identical conditions. Figureoperation 11 demonstrates the influence of the number of inlets on wetted areas, liquid hold ups, and pressure drops. The configuration withoffour inlets had the highest wetted arealiquid and liquidups, hold Figure 11 demonstrates the influence the number of inlets on wetted areas, and pressure drops. The configuration with four inlets had the highest wetted area and hold liquid hold up;and in contrast, pressure drops continuously increased as the number of inlets was increased to 13. pressure drops. Thedrops configuration with four inlets had thenumber highest wetted area and liquid hold up; in contrast, pressure continuously increased as the of inlets was increased to 13. This may bepressure a consequence of the ease increased with which liquid was of distributed small droplets up;result in contrast, drops continuously as the number inlets was as increased to 13. This result may be a consequence of the ease with which liquid was distributed as small droplets when 13 inlets were used as compared to when four inlets were used. An increased ease forming This result may be a consequence of the ease with which liquid was distributed as smallof droplets when 13 inlets were used as compared to when four inlets were used. An increased ease of forming small droplets would be as beneficial to to liquid film development. Among these three configurations, when 13 inlets werenot used compared when four inlets were used. An increased ease of forming small droplets would not be beneficial to liquid film development. Among these three configurations, thesmall best choice a point view of to mass transfer efficiency was the use ofthree four configurations, inlets because it dropletsfrom would not beofbeneficial liquid film development. Among these the best choice from a point of view of mass transfer efficiency was the use of four inlets because it produced highest hold ups and wetted areasefficiency with lower drops. the bestthe choice fromliquid a point of view of mass transfer waspressure the use of four inlets because it produced the highest liquid hold ups and wetted areas with lower pressure drops. produced the highest liquid hold ups and wetted areas with lower pressure drops.

Figure 10.10.CFD of liquid liquid inlet. Figure CFDmodel modelwith withdifferent different numbers numbers Figure 10. CFD model with different numbersof of liquidinlet. inlet.

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0.4 0.2

600

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500

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600 400

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0.3 0.1

0.10 0.20 0.05 0.15

0.2 0.0

1

0.1

0.00 0.10

13

4 Number of Inlets

500 300 400 200 300 100 0200 100

0.05

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0.35

Hold Up / Hold % Up / %

Wetted Wetted Area / % Area / %

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0.00 Figure 11. 0.0 Influence of liquid inlet numbers on wetted area, liquid hold up, and 0pressure drop.

1 inlet numbers 13 liquid hold up, and pressure drop. 4 on wetted area, Figure 11. Influence of liquid Number of Inlets

4.5. Effect of Liquid Surface Tension

Figure 11. Influence of liquid inlet numbers on wetted area, liquid hold up, and pressure drop. 4.5. Effect of Liquid Surface Tension

During operation of a commercial CO2 absorption process using a packed bed, the temperature

During operation ofand a commercial COchange process a packed bed, the the absorber temperature of MEA solvent adsorbent depending uponusing their location within 4.5.the Effect of Liquid Surface Tension will 2 absorption column [31]; this temperature change will affect solvent surface tension. Accordingly, the effects of of the MEA solvent and adsorbent will change depending upon their location within the absorber During operation of a commercial CO2 absorption process using a packed bed, the temperature surface tension on the hydrodynamics in packed beds were explored. Modeling was accomplished column [31]; this temperature change will affect solvent surface tension. Accordingly, the effects of of the MEA solvent and adsorbent will change depending upon their location within the absorber in which water washydrodynamics used as the liquid and its surface tension was changed between 0.005–0.07 N/m surface tension onthis the packed were explored. Modeling was accomplished column [31]; temperature changeinwill affectbeds solvent surface tension. Accordingly, the effects of in to mimic expected variations that would occur in a large-scale reactor. whichsurface watertension was used as the liquid and its tension changed between N/m to on the hydrodynamics in surface packed beds werewas explored. Modeling was0.005–0.07 accomplished The effects of surface tension on pressure drops, liquid holdups, wetted area, and liquid film mimicinexpected variations that would occur in surface a large-scale which water was used as the liquid and its tensionreactor. was changed between 0.005–0.07 N/m thicknesses are shown in Figure 12. The value of the surface tension had an insignificant influence on to mimic expected variations thaton would occur in a large-scale reactor. The effects of surface tension pressure drops, liquid increased holdups,wetted wetted area, and liquid film pressure drops and liquid holdups, but lower surface tensions areas and decreased The effects of surface tension on pressure drops, liquid holdups, wetted area, and liquid film on thicknesses are shown inexpected Figure 12. value of the surface tension had when an insignificant influence film thicknesses. It is thatThe thicker films are more difficult to form surface tensions are thicknesses are shown in Figure 12. The value of the surface tension had an insignificant influence on pressure drops and liquid but lower surface tensions increased wetted areas andwetted decreased small because the liquidholdups, is more highly influenced by gas flow than by surface tension. Larger pressure drops and liquid holdups, but lower surface tensions increased wetted areas and decreased film thicknesses. It is expected thicker are more difficult to aform when surface areas and thinner films are that preferred in films a chemical reaction; hence, solvent with lower tensions surface are film thicknesses. It is expected that thicker films are more difficult to form when surface tensions are would be preferred. smalltension because the liquid is more highly influenced by gas flow than by surface tension. Larger wetted small because the liquid is more highly influenced by gas flow than by surface tension. Larger wetted areas areas and thinner filmsfilms are preferred in a chemical reaction; hence, a solvent withwith lower surface tension and350thinner are preferred in a chemical reaction; hence, a solvent lower surface 0.35 wouldtension be preferred. would be preferred. 300

Water Re=704 Water Re=180

150 250 100 200


50 150 0 100 0.00

0.01

0.02

0 0.00

0.03

0.04

0.05

0.06

0.07

0.08

Surface Tension / N m-1

50

(a) Pressure Drop 0.01

0.02

0.03

0.04

0.05

0.06


0.4

(a) Pressure Drop Area % Wetted AreaWetted %

Liquid Liquid Holdup / % Holdup / %

200 300

0.07


0.3 Water Re=704 Water Re=180

0.4 0.2 0.3 0.1 0.2 0.0 0.10.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Surface Tension / N m-1 0.0 0.00

0.02

0.03

0.04

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0.30 Water Re=704 Water Re=180

0.20 0.25 0.15


0.20 0.10 0.00 0.15

0.01

0.06

0.07

0.08

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.06

0.07

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(b) Liquid Holdup 0.01

0.02

0.03

0.04

0.05


2.2

(b) Liquid Holdup

2.0 2.4 1.8 2.2 1.6 2.0 1.4 1.8 1.2 1.6 1.0


1.4 0.8 1.2 0.6 1.00.00

0.01

0.6 0.00

0.02

0.03

0.04

0.05

0.06

-1 Surface Tension / N m

0.8

(c) Wetted Area 0.01

0.35 0.25

0.10 2.4 0.00

0.08

Film/ mm Thickness / mm Film Thickness

-1

Pressure Pressure Drop / Pa m Drop / Pa m

-1

0.30

250 350

0.01

(d) Film Thickness 0.02

0.03

0.04

0.05

0.07

0.08

Water Re=704 Water Re=180 0.06

0.07

0.08

-1 Figure 12. Influence of surface wetted area,/ Nand Surface Tension tension / N m-1 on pressure drop, liquid holdup,Surface Tension m film thickness.

(c) Wetted Area

(d) Film Thickness

Figure 12. Influence of surface tension on pressure drop, liquid holdup, wetted area, and film thickness.

Figure 12. Influence of surface tension on pressure drop, liquid holdup, wetted area, and film thickness.

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5. Conclusions The characteristics of the liquid flow for CO2 capture in a packed bed reactor with spherical balls were investigated experimentally and computationally. Pressure drops were determined experimentally under six different test conditions. A comprehensive 3D CFD model for counter-current multiphase flow was developed and validated by favorable comparisons of its predicted pressure drops with those from the experiments. Because of model validation, the hydrodynamics of a packed bed reactor with plastic spheres of a specific size and geometry were investigated under various operational conditions. The key findings of these studies were (1) An increase of We values led to more uniform liquid distributions. The flow regimes with spherical packing were film flow when We was greater than 0.547; at values of We between 0.547–1.57, more trickle flow areas were observed; (2) Liquid holdups and wetted areas increased linearly with increasing liquid flow rates, while gas flow rates had no significant effect on either liquid holdup or wetted area; (3) The number of liquid inlets significantly affected flow behavior; however, increasing the number of inlets did not always enhance wetted areas or liquid holdups. Instead, the highest wetted areas and liquid holdups occurred for four inlets rather than 13; (4) Surface tension had an insignificant influence on pressure drops and liquid holdups; however, lower surface tension provided larger wetted areas and thinner films. Author Contributions: L.Y. built the model and wrote most of the paper; F.L. performed the experimental study; K.S. and K.L. contributed to results analysis and validation; Z.S. optimized the mathematical model. Funding: This research was funded by the Key Laboratory of Coal-based CO2 Capture and Geological Storage, Jiangsu Province (China University of Mining and Technology) (NO: 2016B05). Acknowledgments: John Stencel provided valuable comments that helped to improve this paper. Conflicts of Interest: The authors declare no conflicts of interest.

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