Upper-bound Efficiency of Spray Towers to Capture CO Using Poly

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Upper-bound Efficiency of Spray Towers to Capture CO2 Using Poly-dispersed NH3 Droplets M.K. Cho, Munkyoung Choi, sookab lee, and Jin W Lee Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03898 • Publication Date (Web): 01 Dec 2017 Downloaded from http://pubs.acs.org on December 3, 2017

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Industrial & Engineering Chemistry Research

Upper-bound Efficiency of Spray Towers to Capture CO2 Using Poly-dispersed NH3 Droplets

MinKi Cho†, Munkyoung Choi‡, Sookab Lee†, J.W. Lee†,* †

Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang,

37673 South Korea ‡

InGineers Inc, Jinae-dong, Gimhae-si, Gyeongnam, 316-11, South Korea

KEYWORDS CO2 capture efficiency, mass exchanger model, poly-dispersed droplets, empirical formula, Eulerian method

ACS Paragon Plus Environment

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ABSTRACT Chemical absorption of CO2 with aqueous NH3 was numerically analyzed in an Eulerian manner for steady 1-D spray towers in which gas velocity and liquid flow were uniform, and the results were formulated into a universal correlation. The capture efficiency η predicted by the proposed correlation is a sort of upper bound, and can be used as a base to evaluate the optimality of each design. Drop-size poly-dispersity was considered; a spray of poly-dispersed droplets was found to be equivalent in η to a spray of mono-dispersed droplets of an equivalent diameter, and a general formula for the equivalent size was attained in terms of mean size and geometric standard deviation. Total mass transfer coefficient was linearly proportional to the gas-liquid flow rate ratio, and the efficiency correlation agreed well with published results.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected].

Tel.: +82-54-279-2170.

Fax: +82-54-279-3199.


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Nomenclature A b C d f H h k L M Mw

droplet surface area (m2) constant used in defining an equivalent drop size, in Eq. (16) mole concentration (mol/m3) droplet diameter (µm) probability or frequency Henry’s law constant mass transfer coefficient (mol/(m2·s·Pa)) reaction rate constant (m3/(mol·s)) effective length or height of absorbing tower (m) mass flow rate of CO2 (kg/s) molecular weight of CO2 (kg/mol)

m ′′g

absorption mass flux into a droplet (kg/(m2·s))

N n Q q R Re T V x y z

number of droplets droplet number density volume flow rate (m3/s) droplet volume (m3) universal gas constant (J/(mol·K)) Reynolds number based on drop diameter and terminal velocity temperature (K) velocity (m/s) mole fraction (mol/mol) mass fraction (kg/kg) height of a unit cell (m)

Greek letters α,β,γ λ η σ ϕ

coefficients used in the empirical formula, Eqs. (12) and (13) margin for the maximum possible absorption ratio, in Eqs. (15) and (16) capture efficiency (%) geometric standard deviation degree of saturation

Subscripts CMD d eqv f g i

count median diameter droplet equivalent falling CO2 gas inlet condition, initial


3


o l SMD T tot

outlet condition liquid, sorbent Sauter mean diameter terminal total

Superscripts ̅ ˙ ´´ ´´´

average per unit time per unit area per unit volume

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1. INTRODUCTION CO2 capture is of increasing importance as a way to mitigate global warming.1 To capture post-combustion CO2, chemical absorption using an aqueous solution of amine or NH3 has the advantages of high capture efficiency and throughput,2-4 simple mechanism and structure, low regeneration temperature, and easy utilization of waste heat.5 Chemical absorption using liquid absorbent is often realized by using spray towers. However, they have relatively low capture efficiency η because the droplets fall so quickly through the tower that they do not become completely saturated with the absorbed gas, and because droplets may be lost by adhesion to the reactor wall and to exiting gas flow. Additional factors such as non-uniformities in spatial droplet distribution, in drop size, and in gas velocity may reduce η to below expectations. These factors originate from the characteristics of common spray nozzles, which generate a conical spray of droplets with a wide size range; the effect of droplet size on its inertia results in non-uniform spatial distribution of droplets in the flow cross section. Small droplets may flow backwards in high-velocity gas fields, and large droplets may adhere to the wall and be lost. All of these factors degrade η; the most factor dominant is the drop-size non-uniformity. The low η of existing spray towers could be increased by optimizing the size and spatial distribution of injected droplets,6 and by controlling operating conditions. A method should be developed to estimate the highest η possible in a spray tower that is operating in ideal conditions, and the degree degradation of η due to various factors that affect it in real conditions.


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η of spray towers that chemically absorb CO2 has never been accurately analyzed with the effect of drop-size poly-dispersity considered. This lack of attention is a consequence of the mathematical difficulty in treating droplets with size-dependent absorption coefficients in an Eulerian manner, because the absorption mass transfer coefficient must be obtained as a function of local gas-liquid conditions.6 Such a model for mass transfer in the presence of chemical reaction has not been developed until recently, and all previous analyses have relied on tracing a single droplet over time or assuming unrealistically that the mass transfer coefficient is constant throughout a reactor.7

η of a spray reactor is determined by the properties of the materials used, and by the primary variables or average conditions, such as gas flow rate, absorbent flow rate, mean drop size and system size. However, empirical formulas obtained from experimental results represent contributions from various secondary effects such as non-uniformities of gas flow, liquid flow, and drop size, and from loss of droplets to the reactor wall. Because empirical formulas are expressed in terms of the primary variables alone, the formulas cannot be used to quantify how secondary effects degrade η, or even to predict the highest possible η. It is thus the aim of this work to develop a model that can estimate the upper-bound of η for a spray tower that uses ammonia droplets to capture CO2. “Upper-bound η” is η expected after elimination of all secondary effects that reduce it. Any deviation from the upper-bound η of a real spray tower results from these secondary effects, which are mostly related to nonuniformities. A most general model to estimate η by multiplying the upper-bound η by degradation factors that represent these secondary effects.


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2. Methods to simulate efficiency of CO2 capture Eulerian analysis was used in this study. This method has become possible due to a recent development of Eulerian mass transfer coefficient,6 and has already been used to develop a potential method to increase η by controlling drop-size poly-dispersity.8

2.1 Model system and simplified conditions for analysis The system for analysis was a vertical channel of constant cross section with a uniform gas flow. Gas mixture containing CO2 was introduced at a uniform velocity from the bottom, and droplets were injected downward uniformly from the top. To facilitate the analysis, some assumptions were introduced. Even when uniform gas flow was introduced at the bottom, a gas velocity profile develops in the direction of flow; but this profile was ignored, because it remains nearly consistent except very near the wall, and because the effect of flow development is should be categorized as a secondary effect. Droplets were assumed to fall at constant terminal speeds relative to the gas flow, and terminal velocity was calculated using an equation that is valid for a droplet with internal circulating flow and when 0.03 ≤ Re ≤ 280.10 Droplet size was assumed to be unchanged by absorption, and the droplet size distribution was uniform all over the reactor space. Droplet loss to the wall was also neglected. Poly-dispersed drop-size distribution was represented by a log-normal distribution with various geometric standard deviations; this distribution is widely used to represent populations of spray droplets.11 Aqueous NH3 was used as the absorbent, and the gas phase was a mixture of N2 and CO2. Gas concentration was uniform at any cross section of the reactor, and average CO2


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concentration on the liquid-side interface was assumed to be proportional to the free stream gas concentration Cg,s ~ H·Cg; this assumption is valid because CO2 diffusion in the gas phase is much faster than the chemical absorption inside the droplet.12 Physical and chemical properties were constant, H was expressed as a function of temperature,13 and reaction rate constant k was borrowed from.14

η[%] =

Heating caused by mass absorption was neglected. η was defined as

Qg,i xg,i −Qg,o xg,o Qg,i xg,i

×100 .

(1)

2.2. Formulas for mass transfer and droplet size distribution To analyze a 1-D mass exchanger in steady state, a reliable formula for the mass transfer coefficient is needed, expressed only in terms of local conditions of flow and concentration, not time. Recently Choi et al. 6 developed an empirical formula for CO2 mass flux into an aqueous NH3 droplet, which is in a proper form needed in this study. The empirical formula was a best-fit formula for numerical data obtained over a wide variation of conditions: gas concentration 1100%, liquid concentration 1-30%, chemical reaction rate constant 1-5000 m2/(mol·s), and Reynolds number 0.01-200 (corresponding drop size 15 ≤ d ≤ 900µm): mg′′ = k

0.48

 2.15 E − 6 1.40 E − 7  Cl ⋅ C g , s ⋅ Cl  +  1 − 0.5 0.3 d  Cl , i  Cl ,i 

  

2.5

 ;  

(2)

it quantifies the absorption mass flux into an absorbent droplet as a function of local and instantaneous gas concentration and absorbent concentration together with droplet size and chemical reaction speed. It is appropriate for η analysis in an Eulerian manner, and when the distribution of gas and liquid are non-uniform. This formula is applicable to any position in the reactor at any instant during the absorption process and for any initial or operating conditions.


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When the size distribution of the droplets generated from a spray nozzle is log-normal with geometric mean or count median diameter dCMD and geometric standard deviation σ.11 If size distribution is represented by a finite number of discrete sizes (d(i); i = 1 ~ imax) and size intervals (∆d(i); i = 1 ~ imax), size frequency or probability f(i) can be approximated as 2    d (i )   ln    dCMD    1  , f (i ) = ⋅ exp  −  2   2π ⋅ d (i ) ⋅ ln σ 2 [ ln σ ]    

(3)

and the number N(i) of d(i)-droplets generated per second can be calculated from the total liquid flow rate Ql as

N(i) = Ntot ⋅ f (i) ⋅∆d (i) =

Ql ⋅[ f (i) ⋅∆d (i)]

∑1 [ q(i) ⋅ f (i) ⋅∆d(i)] imax

,

(4)

where q(i) is the volume of a droplet of diameter d(i). Even when poly-dispersed droplets of a known size distribution at generation are evenly supplied across the reactor cross section, the size distribution and droplet number density in the reactor space are different from those at generation, because droplets fall at velocities that are related to their sizes. Therefore, the number density n´´´(i) of d(i)-droplets in the reactor space is determined by modifying the generation rate by a factor that is inversely proportional to the falling velocity Vf(i) = VT(i) – Vg, in such a way that the generation rate from the nozzle should be equal to the number density multiplied by the falling velocity for each droplet size:

n′′′(i ) =

N (i ) , AC ⋅V f (i )

(5)


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where Ac is the reactor cross sectional area. In a real tower, small droplets for which terminal velocity is lower than the gas velocity are blown out of the top of the tower, so in this model they were removed from the analysis.

2.3 Procedure to analyze capture efficiency of a counter-flow mass exchanger At the start of simulation, reactor height L, gas velocity Vg, liquid flow rate Ql and droplet size distribution were specified, and the reactor space was divided into a sufficient number of unit cells. Once sorbent flow rate and droplet size distribution are given, gas velocity and number density of droplets at each spatial grid point can be determined in advance. Droplets of different sizes were treated separately. The amount of CO2 absorbed by droplets of size d(i) within cell j was calculated as

dM (i, j ) = m′′g (i, j ) ⋅ A(i ) ⋅ [ n′′′(i ) ⋅ z ⋅ AC ] ,

(6)

for each group of droplets of different size, then total amount of CO2 absorbed by all the droplets in cell j was calculated as i

i

1

1

dM ( j ) = ∑ dM (i, j ) = ∑ mg′′ (i, j ) ⋅ {π ⋅ [d (i)]2 } ⋅ [ n′′′(i) ⋅ z ⋅ AC ] .

(7)

Then gas flow rate eg, CO2 concentration Cg in the gas mixture and Ci in the sorbent concentration for each group of droplets were updated as

Qg ( j ) = Qg ( j + 1) − dM ( j ) / ρ g ( j ) ,

(8)


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Cg ( j +1) − Cg ( j) =

Cl ( j) − Cl ( j +1) =

dM ( j) , Mw ⋅ Qg ( j)

dM ( j) , Mw ⋅ Ql

(9)

(10)

where A(i) = πd(i)2 denotes the surface area of a droplet of size d(i), Mw is the molecular weight [kg/mol] of CO2, and z [m] the height of a unit cell. Then mass balance equations for each cell yielded a set of simultaneous equations for the CO2 concentration in the gas mixture, and the number of droplets and sorbent concentrations in droplets of different sizes (Figure 1); the equations were solved iteratively using MATLAB.


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3. RESULTS AND DISCUSSION 3.1. Upper-bound capture efficiency with mono-dispersed droplets Fundamental nature of η was confirmed first for mono-dispersed droplets, and it will correspond to the highest η expected under primary or average operational conditions. η was obtained for lab-scale spray towers obtained with the major primary variables sorbent flow rate Ql, droplet diameter d and tower length L varied over a wide range (Figures 2, 3). Results shown are for just one typical set of conditions for material properties, Henry constant, chemical reaction constant, gas velocity, and concentration conditions at the supply points, but these variables were also varied in the derivation of general formula for η (Section 3.4).

η clearly increases with increase in sorbent flow rate per gas flow rate Ql/Qg (Figure 2), with increase in L (Figure 3, bottom), and with decrease in d (Figure 3, top). Increased sorbent flow increases the surface area for mass transfer, and increased reaction length extends mass transfer time or increases surface area. Decrease in d has several effects, including increased surface area for a given liquid volume, extended falling time due to decrease in terminal velocity, and increased dispersion of absorbed CO2 inside the droplet: all of these effects contribute to increase in capture rate. Among the three variables varied (i.e., Ql, d and L), d affected the capture efficiency most strongly, and the effects of Ql, and L were comparable to each other. L required for a particular high η is almost inversely proportional to Ql/Qg. Even when gas flow rate was varied simultaneously together with one of these three parameters, the effect of varying gas flow appeared only as the ratio Ql/Qg.


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3.2. Capture efficiency for droplets with log-normal poly-dispersed size distribution In conventional spray towers, spray droplets are usually generated by one or two spray nozzles, and the size of the generated droplets is highly poly-dispersed with σ > 2.0.15 Even mono-dispersed droplets generated with mono-dispersed aerosol generators have a size dispersion of about σ ~ 1.2.11 So, to understand the fundamental nature of spray absorbers, the effect of the size poly-dispersity on η must be determined Size distribution was assumed lognormal, but general findings obtained with this particular distribution function are thought to hold good for most of other smooth distribution functions with a single peak and smoothly decreasing away from the peak. When η for poly-dispersed sprays with various size deviations of σ = 1.0, 1.4, 1.7 and 2.0, and for two mean sizes of 250 ≤ dCMD ≤ 600 µm was compared with those for monodispersed sprays of various droplet size, η of poly-dispersed sprays agreed excellently with those of mono-dispersed sprays of equivalent droplet size d eqv = d CMD exp  b ⋅ ln 2 σ  ,

(11)

with b = 1.7 (Figure 4). This result implies that η of a spray tower that uses poly-dispersed spray droplets with dCMD and σ is equivalent to that of a spray tower that uses mono-dispersed spray droplets with deqv. Equivalent diameter as defined in Eq. (11) is close to the diameter of average droplet

volume

(b

=

1.50),

but

smaller

than

the

Sauter

mean

diameter

d SMD = d CMD exp  2.5 ln 2 σ  for the log-normal distribution. This finding contradicts the general

belief that dSMD is the representative diameter in heat or mass transfer with spray droplets. 11


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η results were obtained for several conditions of flow and concentration for gas and liquid. η declined asymptotically as deqv increased Only one condition is illustrated (Figure 4); results for other sets were the same.

3.3 General empirical formula for the capture efficiency In an ideal spray reactor, nine primary variables are associated with η: reactor variable L, droplet variables d and σ, gas variables Vg and xg, sorbent variables Ql/Qg and yl, and reaction constant k, Henry constant H. When sorbent solution is recycled through a regenerator, yl denotes the concentration of NH3 in the droplets supplied to the absorber tower, and the final saturation ϕ is the fraction of NH3 molecules that have been converted to final product in the supply droplets. When η analysis was performed with all related variables varied over a wide range, the results could be condensed well into a single formula

 k 0.43 ⋅ y 0.6 ⋅ L0.9 ⋅ H  V l η0 = 1 − exp −α  T 0.01 β x d ⋅  g eqv  Vf

 Ql    Qg

  , 

(12)

where Vf = VT - Vg is the falling velocity of a droplet of size deqv; β is a coefficient that is partly related to internal dispersion of CO2 within droplets, and is therefore dependent on the drop size; α is a proportionality coefficient, and is dependent on the choice of β. Both e and β vary continuously with drop size, but a very good correlation could be obtained using only two constant values: one for small droplets (120 ≤ d < 200 µm) and one for large droplets (200 ≤ d ≤ 1000 µm) (Table 1).


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Although terminal velocity VT is not an independent variable, it was explicitly included in Eq. (12) to visualize how the velocity ratio affects η. When VT is explicitly expressed as VT ~ dn (n ~ 1.6 for small droplets and n ~ 1.1 for large droplets), Eq. (12) can be rewritten in the final form for the baseline formula to calculate η:

 k 0.43 ⋅ yl0.6 ⋅ L0.9 ⋅ H  Ql η0 = 1 − exp −α 0.01  β −1  xg ⋅ d eqv (deqv − γ ⋅ Vg )  Qg

   ,  

(13)

where α, β and γ are constant coefficients with different values for the two ranges of drop size (Table 1). Equation (13) could predict the simulation results with an excellent correlation coefficient of 0.999 over wide variations of all the involved parameters (Figure 5). Eq. (13) demonstrates that the argument of the exponential is linearly proportional to L, H and Ql/Qg; approximately proportional to the square roots of k and of liquid concentration yl; these results are closely similar to the effects of those variables on local absorption mass flux Eq. (2); and very weakly to proportional to initial gas concentration xg. The weak dependence on xg resulted from the dependence of mass transfer on local liquid concentration: when xg at the inlet is increased, absorption mass flux rises, the decrease in liquid concentration along the droplet path accelerates. If local absorption mass flux were independent of yl, η would be independent of gas concentration, because local mass transfer is linearly proportional to local gas concentration, and because η is defined by the change in gas concentration relative to initial gas concentration. The most dominant factor is d, and the increase gas velocity that results from the change in flow cross section at the same gas flow increases η by reducing the falling velocity of droplets. ηo denotes the upper-bound efficiency with the effect of drop-size poly-dispersity considered; actual η in the presence of various secondary effects can be written as


15


η = η o Fd ,

Page 16 of 27

(14)

where Fd is the degradation factor that expresses the effects of wall loss and non-uniformities in the distribution of gas flow and liquid flow. Fd can be estimated by dividing the observed η by ηo calculated using Eq. (13) and average operational parameter values.

3.4 Comparison with existing models and experimental correlations Theoretical models or formulas for the chemical absorption of CO2 by spray droplets is not available, but a well-known theoretical formula for physical absorption in the absence of chemical reaction exists, and has been updated .9 It considers an acid spray wet scrubber, in which a constant mass transfer coefficient h was assumed and poly-dispersed droplets were represented by mono-dispersed droplets with diameter equal to dSMD. The original formula

Qg   1 − λ  Ql  M ρ  η = 1− ; λ = H w ,l g  M w, g ρl  Q hLH  Ql − λ  − λ g exp α   Ql  V f d SMD  Qg  

(15)

can be simplified to

 hLH  Ql   η = 1 − exp  −α   ; λ 0  V f d SMD  Qg  

(16)

when λQg/Ql is small, which is usually the case in spray towers.


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Equation (16) is quite similar in form to Eq. (12), although (16) does not consider many factors such as internal dispersion of CO2, chemical reaction, and dependence of mass transfer on liquid concentration. Notably, the argument of the exponent is linearly proportional to L, H, Ql/Qg, and Vf. This formula is not of well applicable to chemical absorbers because the mass transfer coefficient h is not explicitly given in terms of operating conditions, and because the characteristics of drop-size poly-dispersity are not properly considered. Furthermore, during chemical absorption of CO2, η is strongly dependent on the concentration of CO2 in the gas mixture and absorbent liquid, and mass transfer across the gas-liquid interface is not determined by the gas-phase transfer coefficient but is dominated by the speed of chemical reaction in the drop. In order to validate the proposed correlation, comparison with experiments was needed, but it was very hard to find a single experiment done under the same conditions used in formulating the correlation – uniform drop size and uniform spatial distribution of liquid and gas. Recent experimental results have reported CO2 capture by a spray tower that is operated under the required uniform conditions,16,17 and with σ ~ 1.2, i.e., drop size distribution very close to mono-dispersed. Experimental results obtained using 300-µm droplets in 1-m and 1.5-m uniform spray towers were in excellent agreement with the predictions of Eq. (13) (Figure 6).


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4. CONCLUSION Chemical absorption of CO2 by aqueous NH3 was numerically analyzed in an Eulerian manner for steady 1-D spray towers in which gas velocity and liquid flow were uniform. A modified upper-bound performance correlation was formulated where the effect of drop-size non-uniformity was explicitly reflected, and it is thought to be applicable to a wide range of operating conditions as shown in the figures. The capture efficiency η predicted by the proposed correlation is an upper bound, and can be used as a standard to evaluate the optimality of each design. A spray of poly-dispersed droplets was shown to be equivalent in η to a spray of monodispersed droplets of an equivalent diameter that is close to the diameter that corresponds to the average mass of a log-normal size distribution. Total mass transfer coefficient was linearly proportional to the gas-liquid flow rate ratio, and the efficiency correlation agreed well with published experimental results.


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Droplets in

Gas out

yl, o

xg, o(assume) j=0

Cg,s(j)=H·Cg(j) Cl(j)

Cg(j)

L

Cl(j+1)

Cg(j+1)

j = Nstep

yl,i Droplets out

xg,i(cal) Gas in

Figure 1. Conditions in the 1-D cell j


19


Capture efficiencty : η [%]

100

80

60 yl=0.1

40

xg=0.2 Vg,i=0.05 m/s

d=150 µm d=300 µm d=600 µm

20

0 0.000

0.002

0.004

L=0.5 m 3 k=300 m /(mol⋅s) 3 H=0.887 Pa⋅m /mol

0.006

0.008

0.010

Ql/Qg 100


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 27

80

60 yl=0.1

40

xg=0.2 Vg,i=0.05 m/s

L=0.25 m L=0.5 m L=1.0 m

20

0 0.000

0.002

0.004

d=300 µm 3 k=300 m /(mol⋅s) 3 H=0.887 Pa⋅m /mol

0.006

0.008

0.010

Ql/Qg Figure 2. Capture efficiency vs. sorbent flow rate Ql/Qg with (top) droplet diameter d and (bottom) tower length L varied.


20

Page 21 of 27

100


Ql/Qg=0.0025 Ql/Qg=0.005

80

Ql/Qg=0.01

60 yl=0.1

40

xg=0.2

20

L=0.5 m 3 k=300 m /(mol⋅s) 3 H=0.887 Pa⋅m /mol

Vg,i=0.05 m/s

0

0

200

400

600

800

1000

d [µm]

100


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


80

60 yl=0.1

40

xg=0.2 Vg,i=0.05 m/s

Ql/Qg=0.0025

20

d=300 µm 3 k=300 m /(mol⋅s) 3 H=0.887 Pa⋅m /mol

Ql/Qg=0.005 Ql/Qg=0.01

0 0.0

0.2

0.4

0.6

0.8

1.0

L [m]

Figure 3. Capture efficiency vs. (top) droplet diameter d and (bottom) tower length L with sorbent flow rate Ql/Qg varied.


21


100 Mono-disperse : σ=1.0 Poly-disperse : dcmd=250 µm, σ=1.0-2.0

Capture efficiency [%]

80

Poly-disperse : dcmd=300 µm, σ=1.0-2.0 Poly-disperse : dcmd=450 µm, σ=1.0-2.0 Poly-disperse : dcmd=500 µm, σ=1.0-2.0

60

Poly-disperse : dcmd=600 µm, σ=1.0-1.7

yl=0.1 xg=0.2

40

Ql/Qg=0.002 Vg=0.326 m/s L=0.5 m 3 k=300 m /(mol⋅s) 3 H=0.887 Pa⋅m /mol

20

0

0

200

400

600

800

1000

1200

deqv [µm] Figure 4. Comparison between poly-dispersed systems (symbols) and their equivalent monodispersed systems (curves), with equivalent diameters for various mean sizes and size deviations.

100

100

dCMD [µm]

dCMD [µm] yl

80

yl

80

xg

xg 3

3

k [m /(mol°s)] L [m] 3 H [Pa°m /mol] Qg [lpm]

60

η [%] : fitting

η [%] : fitting

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 27

Ql [lpm]

40

Vg [m/s]

Ql [lpm]

40

Vg [m/s]

20

20

0

k [m /(mol°s)] L [m] 3 H [Pa°m /mol] Qg [lpm]

60

0

20

40

60

80

100

0

0

20

40

60

80

100

η [%] : simulation

η [%] : simulation

Figure 5. Comparison of the developed correlation with simulation results: (left) small droplets (d=120~200µm) and (right) large droplets (d=200~1000µm). Symbols represent the variables varied.


22

Page 23 of 27

Table 1. Coefficients for the correlation for two different drop-size ranges Range of droplet diameter (µm)

α

β

γ

120 ≤ d < 200

7.87 x 107

2.2

910

200 ≤ d ≤ 1000

3.02 x 107

2.0

270

100

Capture Efficiency [%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


80

60

40 Experiment - L=1.0m Experiment - L=1.5m Simulation - L=1.0m Simulation - L=1.5m

20

0

0

5

10

15

20

25

Mole ratio of NH3 to CO2 [mol/mol] Figure 6. Comparison between experimental results of Cho et al.16 and numerical simulations for tower lengths of 1.0 and 1.5 m: dCMD = 300 µm, σ = 1.2 and k = 10 m3/(mol·s).


23


Page 24 of 27

Acknowledgment This work was supported by Korea Research Foundation (KRF) grants funded by the Korean government (MOE) (No.2013R-1A1A-2057752).


24

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REFERENCES (1).

Wang, M.; Lawal, A.; Stephenson, P.; Sidders, J.; Ramshaw, C., Post-combustion CO2 capture

with chemical absorption: a state-of-the-art review. Chem. Eng. Res. Des. 2011, 89, (9), 1609-1624. (2).

Ma, S.; Zang, B.; Song, H.; Chen, G.; Yang, J., Research on mass transfer of CO2 absorption

using ammonia solution in spray tower. Int. J. Heat Mass Transfer 2013, 67, 696-703. (3).

Hedin, N.; Andersson, L.; Bergström, L.; Yan, J., Adsorbents for the post-combustion capture of

CO 2 using rapid temperature swing or vacuum swing adsorption. Appl Energy 2013, 104, 418-433. (4).

Yan, S.-p.; Fang, M.-X.; Zhang, W.-F.; Wang, S.-Y.; Xu, Z.-K.; Luo, Z.-Y.; Cen, K.-F.,

Experimental study on the separation of CO2 from flue gas using hollow fiber membrane contactors without wetting. Fuel Process. Technol. 2007, 88, (5), 501-511. (5).

Han, K.; Ahn, C. K.; Lee, M. S., Performance of an ammonia-based CO2 capture pilot facility in

iron and steel industry. Int. J. of Greenhouse Gas Control 2014, 27, 239-246. (6).

Choi, M.; Cho, M.; Lee, J., Empirical formula for the mass flux in chemical absorption of CO2

with ammonia droplets. Appl Energy 2016, 164, 1-9. (7).

Bandyopadhyay, A.; Biswas, M. N., Modeling of SO 2 scrubbing in spray towers. Sci. Total

Environ. 2007, 383, (1), 25-40. (8)

Cho, M.; Choi, M.; Lee, J., Possibility of drastically enhancing the capture capability of CO2

with ammonia through the control of droplet size distribution, Proc. Eur. aerosol conf. 2015 (EAC2015) 2015 (9).

Manuzon, R. B.; Zhao, L.; Keener, H. M.; Darr, M. J., A prototype acid spray scrubber for

absorbing ammonia emissions from exhaust fans of animal buildings. Trans. the Am. Soc. Agric. Biol. Eng. 2007, 50, (4), 1395-1407. (10). Beard, K., Terminal velocity and shape of cloud and precipitation drops aloft. J. Atmospheric Sci. 1976, 33, (5), 851-864. (11).

Hinds, W. C., Aerosol technology: properties, behavior, and measurement of airborne particles.

John Wiley & Sons: 2012.


25


(12).

Page 26 of 27

Chen, W.-H.; Tsai, M.-H.; Hung, C.-I., Numerical prediction of CO 2 capture process by a single

droplet in alkaline spray. Appl Energy 2013, 109, 125-134. (13).

Pacheco, M. A. Mass transfer, kinetics and rate-based modeling of reactive absorption.

University of Texas at Austin Austin, TX, 1998. (14).

Pinsent, B.; Pearson, L.; Roughton, F., The kinetics of combination of carbon dioxide with

ammonia. Trans. Faraday Soc. 1956, 52, 1594-1598. (15).

Lim, Y.; Choi, M.; Han, K.; Yi, M.; Lee, J., Performance characteristics of CO2 capture using

aqueous ammonia in a single-nozzle spray tower. Ind. Eng. Chem. Res. 2013, 52, (43), 15131-15137. (16)

Cho, M.; Lee, J., Spray Towers Can Perform Better than Packer Towers in Capturing CO2,

Carbon Manage. Technol. Conf. 2017 (CMTC 2017) 2017 (17)

Cho, M.; Lee, J., Enhancement of Mass Transfer Capacity in Spray Reactors through the

Uniform Injection of Monodisperse Drops, Proc. 4th Int'l Conf. Fluid Flow, Heat Mass Transfer (FFHMT'17) 2017


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654x285mm (96 x 96 DPI)


Upper-bound Efficiency of Spray Towers to Capture CO Using Poly

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