Applied Energy 111 (2013) 731–741
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Applied Energy j o u r n a l h o m e p a g e : : w w w . e l s e v i e r . c o m / l o c a t e / a p e n e r g y
Carbon dioxide capture by single droplet using Selexol, Rectisol and water as absorbents: A theoretical approach Wei-Hsin Chen a, , Shu-Mi Chen b, Chen-I Hung b ⇑
a b
Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan 701, Taiwan, ROC Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan, ROC
h i g h l i g h t s
A theoretical method for carbon dioxide capture is developed. Selexol, Rectisol, and water are taken into account as absorbents. The absorption time is more sensitive to the operating temperature. Rectisol has the highest capacity to capture CO 2 among the three absorbents. The absorption rate of Rectisol is larger than the others by an order of magnitude.
a r t i c l e
i n f o
Article history: Received 12 January 2013 Received in revised form 16 May 2013 Accepted 18 May 2013
Keywords: Greenhouse gas Carbon dioxide (CO2) capture Gas absorption Selexol and Rectisol Theoretical analysis Droplet
a b s t r a c t
A theoretical method is developed to analyze carbon dioxide capture by a stationary single droplet for evaluating the fundamental mass transfer behavior. In the method, the gas-phase diffusion is predicted using using a simila similarit rity y metho method d and the techn techniqu ique e of separa separatio tion n of varia variable ble is emplo employed yed to appro approach ach the liquid liquid-phase phase diffusion. diffusion. At the interface interface,, a finite differenc difference e method method is applied applied to connect connect the CO 2 diffusion between between the two phases. phases. The The individu individual al capture capture processe processess of CO2 by three three differen differentt absorben absorbents ts of Selexol, Selexol, Rectisol and water, are taken into account. The operating pressure and temperature of Selexol and water are in the ranges of 30–60 atm and 303–333 303–333 K, respective respectively, ly, and they are 30–60 atm and 240–270 240–270 K for Rectisol. The analysis indicates that an increase in temperature decreases the CO 2 capture amount and absorption time by Selexol and Rectisol droplets. The absorption time is more sensitive to the operating temperature than the capture amount. As a result, the CO 2 absorption rates by the droplets are increased when the temperature increases. Among the three absorbents, Rectisol has the highest capacity to capture CO2 and its absorption time is in a comparable state to the other two absorbents. This results in that its absorption rate is larger than the others by an order of magnitude. 2013 Elsevier Ltd. All rights reserved.
1. Introduction Burni Burning ng fossil fossil fuels fuels is the main main sourc source e of carbo carbon n diox dioxide ide emiss emissio ions ns from from anthro anthropo poge genic nic activi activitie tiess and and it accoun accounts ts for appr approx oxim imate ately ly 95% 95% of the total total global global annua annuall carbo carbon n dioxid dioxide e emissions [1] [1].. Currently carbon capture and storage (CCS) is considered sidered to be technical technically ly feasible feasible at commer commercial cial scale to reduce reduce anthrop anthropoge ogenic nic carbon carbon dioxide dioxide emissio emissions ns into the atmosp atmosphere here [2–6].. A number [2–6] number of carbon carbon dioxide dioxide separatio separation n method methods, s, such as solution absorption, membrane separation, adsorption separation [7,8],, and cryog [7,8] cryogeni enics cs [1,9], [1,9], can can be emp employe loyed. d. When hen one one is conce concern rned ed with with solut solutio ion n absor absorpti ption on,, it can be classi classifie fied d into into chemical absorption and physical absorption. Monoethanolamine (MEA), (ME A), 2-amin 2-amino-2 o-2-m -methy ethyl-1l-1-pro propan panol ol (AMP), (AMP), aqua ammonia ammonia,, ⇑
Corresponding author. Tel: +886 6 2757575x63600; fax: +886 6 2389940.
[email protected] (W.-H. (W.-H. Chen). E-mail address:
[email protected]
0306-2619/$ - see front matter 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2013.05.051
dual-al dual-alkali kali,, and the propri proprietar etary y solvent solvent markete marketed d by Mitsubis Mitsubishi hi Heavy Industries, KS-1, have been employed as chemical solvents [10] for a variety variety of applica application tionss in industrie industries. s. With With regard regard to physical absorption, the gas treating solvents of Selexol (dimethylether ylether polyethy polyethylene lene glycol), glycol), Rectisol Rectisol (chilled (chilled methano methanol), l), Fluor Fluor (propylene (propylene carbonate), carbonate), and Purisol (N-methyl-2-pyrollid (N-methyl-2-pyrollidone) one) are becomin becoming g increasi increasingly ngly popular popular,, especial especially ly in the applica application tion of coal gasification [11]. [11]. When physical absorption is practiced, CO2 is absorbed into a absorbe absorbent nt obeying obeying Henry’s Henry’s law, and the gas capture capture amount amount by the absorbent depends on the partial pressure of CO 2 and the temperature of absorbent [12] absorbent [12].. In general, CO2 removal using physical absorption allows consuming energy on a reasonable level for its application in large industrial scale. For example, physical absorption may be a suitable process to remove CO 2 from metallurgical fuel gases, such as blast furnace gases and Corex gases [13]. [13]. The solubility of CO2 in an absorbent is higher at the higher partial
W.-H. Chen et al. / Applied Energy 111 (2013) 731–741
732
Nomenclature
c D Dm H 0 H m p pc R r r s t T T s T c T r u x X M V i DH
average molar concentration (M) diffusion coefficient (m2 s1) mass diffusion number nondimensional Henry’s law constant Henry’s law constant (M atm 1) nondimensional solute absorption amount pressure (atm) critical pressure (atm) gas constant (=0.082 atm M1 K1) radial coordinate (m) aerosol radius (m) time (s) temperature (K) temperature at standard condition (=298.15 K) critical temperature (K) reduced temperature nondimensional concentration nondimensional radial coordinate molar fraction molecular weight (g mol1) molar volume of CO2 at its normal boiling temperature (cm3 mol1) enthalpy of solution (atm K1)
pressures of the gas and lower ambient temperatures. The required operating conditions of various absorbents are different. For example, the operating pressure and temperature of Selexol are over 30 atm and approximately at 313 K, respectively [14,15]. The operating pressure and temperature of Rectisol are in the ranges of 30– 80 atm and 213–263 K, respectively [11,16,17]. These conditions reveal that the operating temperature of Rectisol is much lower than that of Selexol. When CO2 captured by Rectisol (chilled methanol) and water are compared with each other, the former has a higher removal capability, especially at low temperatures. Specifically, the CO2 solubility in methanol at a normal temperature is larger than in water by a factor of approximately 5, and 8–15 times when the temperature of methanol is below 273 K [16]. The integrated gasification combined cycle (IGCC) is a crucial system for the application of CCS [18–20] where the synthesis gas (or syngas) and power are generated. If the produced syngas undergoes water gas shift reactions in association with CCS, carbon free fuel can be produced. In this aspect, the research of CO 2 capture via absorption in IGCC systems has been reported in some studies. Strube and Manfrida [21] focused on two different CO 2 capture configurations using Selexol as a physical solvent. In the first configuration CO2 and H2S were individually captured, whereas they were simultaneously captured in the other configuration. They found that the efficiency of CO2 capture was higher in the individual capture system. Chen and Rubin [22] developed a model to analyze the performances and costs of IGCC plants where a GE quench gasifier along with water gas shift reactors in the presence/absence of a Selexol system for CO 2 capture was employed. They pointed out that the CO 2 avoidance cost was lowest when the total CO2 removal efficiency was approximately 90%, indicating that it was the optimal CO2 capture efficiency for the designed plant. In respect of the application of Rectisol, Li and Robin [23] used Rectisol as an absorbent to study CO2 removal from syngas in a polygeneration system. Two configurations, including a singlestage wash process and a two-stage wash process, were analyzed
Greek letters g viscosity (cP) h polar angle Rv diffusion volume (m3 mol1) s nondimensional time / association factor w azimuthal angle x acentric factor Subscript air air c diffusive characteristic time g gas phase or continuous phase i absorbent i l liquid phase or discrete phase qss quasi-saturated state ss saturated state s droplet surface or interface SL saturated liquid t total pressure 1 infinity vp vapor phase
and simulated in Aspen Plus for the process comparison. They reported that the two configurations could fulfill CO2 separation, but they were different in the aspect of process power and energy demand. Another application of CO 2 removal using Rectisol is the indirect coal liquefaction (ICL). Zhou et al. [17] analyzed CO2 removal in an ICL process utilizing three absorbents of dimethyl carbonate (DMC), MEA, and Rectisol. They discovered that Rectisol was the most economic option for capturing CO2 in the ICL process. Although many studies have been published on CO2 capture by physical solvents, such as Selexol and Rectisol, the theoretical analyses of CO2 capture by these absorbents are still absent so far. In industry, a variety of devices, such as Venturi scrubbers, spray towers, stirred tanks, packed columns, and bubble columns, have been adopted to remove CO2 from flue gases [24–26]. When one is concerned with spray towers, the basic mass transfer unit is CO2 uptake by single liquid droplets [27]. To evaluate the capture characteristics of CO2 in spray towers through physical absorption, the mass transfer behavior of CO2 by three different absorbents, Selexol, Rectisol, and water, in the form of droplet will be explored theoretically. The absorption processes at various operating temperatures and pressures will be examined. Finally, the difference in the capture phenomena of the three absorbents will be addressed.
2. Mathematical formulation 2.1. Physical description This study focuses on CO2 capture by a single droplet and three absorbents of Selexol, Rectisol, and water are considered. A theoretical method is developed and the following assumptions are adopted to simplify the physical problem: (1) the droplet is in a quiescent environment; (2) the droplet and its surrounding are isothermal so that no vaporization or condensation occurs; (3) the fluid properties such as the densities and diffusivities of the gas and liquid phases are constant; (4) phase equilibrium prevails at
W.-H. Chen et al./ Applied Energy 111 (2013) 731–741
733
Fig. 1. A schematic of droplet absorption configuration and the equations of two phases in dimensional form.
¼ xð1 u Þ
the interface and the absorption obeys Henry’s law; and (5) mass diffusion in the two phases abides by Fick’s law. Carbon dioxide absorption by droplet is related to the mass transfer between the gas phase and the liquid phase. The mass diffusion equations in the two phases as well as the initial and boundary conditions are shown in Fig. 1. A two-stage transformation is developed to solve the equations. In the first stage, the equations shown in Fig. 1 are nondimensionalized in terms of a set of nondimensional parameters. The nondimensionalized parameters and equations are tabulated in Table 1. In the second stage, two parameters of
v g
g
and
¼ xu
v l
ð1Þ
l
are defined and substituted into the equations in Table 1. The diffusion equation as well as the initial and boundary conditions of the gas phase and the liquid phase are given in Table 2.
2.2. Theoretical approach 2.2.1. Gas phase To solve the gas-phase equation shown in Table 2, a similarity parameter [28] is defined as
Table 1
A list of dimensionless parameters, diffusion equations as well as initial and boundary conditions (the first transformation). Dimensionless parameters
x ¼
r Rd
; s g ¼
t R2d =D g
t ¼ t gc ; sl ¼
Description
t R2d =Dl
;t Þ ¼ t t lc ; u g ¼ c g c g 0t ; ul ¼ c lc ðr H ; 1H ¼ H 0 RT g 0 ðr ; Þ
Gas phase
Governing equation
@ u g @ s g
Initial condition Boundary conditions
u g ð x; 0Þ ¼ 1;
¼
2
@ u g @ x2
þ 2 x
Liquid phase @ u g @ x
u g x; s g u g 1; s g
ð ð
@ ul @ sl
x > 1
ul ð x; 0Þ ¼ 0;
Þ ¼ 1; x ! 1 Þ ¼ 1 ; s > 0 c gs c g
g
Interface conditions
ð
@ u g @ ul = @ x x 1 @ x
u gs
¼ u
Þ ¼ ¼ D
ls
2
@ ul ¼ @ @ xu2l þ 2 x @ x
m
0 6 x 6 1
@ ul @ x x 0
¼ 0; ¼
ul 1; sl
ð
Þ¼
c ls c g 1
sl > 0 H ; sl > 0
W.-H. Chen et al. / Applied Energy 111 (2013) 731–741
734 Table 2
A list of diffusion equations as well as initial and boundary conditions (the second transformation). Description
@ v g @ s g
¼
(T1)
2
@ v g @ x2
ð x; 0Þ ¼ 0; x > 1 x ! 1 v g ð x; s g Þ ¼ 0 ;
Initial condition Boundary conditions
v g
ð1; s g Þ ¼ 1 c c g gs1 ¼ 1 u gs ðs g Þ;
v g
Description
Liquid phase
Governing equation
@ v l @ sl
Initial condition
v l
s g > 0
(T2) (T3) (T4)
l
@ x
@ x
(T6) (T7) (T8)
¼ u
x 1 2 s g
ffiffi ffi p
ð2Þ
Eq. (T1) thus becomes an ordinary differential equation and the counterparts of Eqs. (T1)–(T4) are given by 2
d v g dg2
þ 2g ddg ¼ 0
ð3Þ
ð0Þ ¼ 1 u ðgÞ ¼ 0; g ! 1
ð4Þ ð5Þ
v g
v g
gs
v g
The solution of Eqs. (3)–(5) is g
¼ A þ B
v g
Z
2
en dn
ð6Þ
0
where
A
¼ 1 u
gs ;
and B
¼ p ffi2pffi ffi ðu 1Þ
ð7Þ
gs
Therefore, the dimensionless gas-phase concentration u g is obtained as
1 u x 1 u ¼ 1 erfc 2p ffisffi ffi x gs
ð8Þ
g
g
In the above equation, erfc is the complimentary error function [29].
2.2.2. Liquid phase For the liquid phase, the technique of separation of variable is P1 adopted. Defining v l ¼ n¼1 v n ðsl Þ sinðnp xÞ and substituting it into Eq. (T5) shown in Table 2, the solution of Eq. (T5) in conjunction with the conditions of Eqs. (T6) and (T7) is given by [30]
X1
n
n2 p2 sl
¼ 2 ð1Þ ðnpÞe
v l
n 1
¼
sin np x
ð Þ
Z
sl
2
en
p2 k
uls k dk
0
ðÞ
ð9Þ
Hence, the dimensionless liquid-phase concentration is expressed by
ul
X1
¼ x2 ð1Þ ðnpÞe n 1
¼
n
n2 p2 sl
sin np x
ð
sl
Þ
Z 0
en
2 p2 k
uls k dk
ðÞ
ð10Þ
2.2.3. Interface An exact solution and an analytical one in the gas phase and the liquid phase are obtained, respectively. The dimensionless concentrations of the gas phase and the liquid phase are expressed in terms of the interfacial concentrations u gs and u ls, respectively, as shown in Eqs. 8 and 10. When the two-phase solutions are simultaneously solved, the mass flux conservation and Henry’s law at
¼
¼ D
ð11Þ
m
ð12Þ
ls
At the interface, Eqs. (8) and (10) give
@ u g
@ x
@ u
gs
l
@ x
1
¼ ð1 u Þ 1 þ p ffips ffiffiffiffi ¼
x 1
and
g ¼
x 1
where D m(=Dl/D g H ) represents the mass diffusion number [31,32]. Meanwhile, the Henry’s law is converted into the continuity of the dimensionless concentrations. That is
u gs (T5)
2 ¼ @ @ xv 2l
ð x; 0Þ ¼ 0; 0 6 x 6 1 sl > 0 v l ð0; sl Þ ¼ 0 ; c ls 0 v l ð1; sl Þ ¼ c g 1 H ¼ u ls ðsl Þ; sl >
Boundary conditions
@ u @ u g
Gas phase
Governing equation
the interface are invoked to link u g and u l. The mass flux conservation of the dimensionless concentrations is written as
x 1
¼
X1
ð13Þ
g
2
¼ 2 ðnpÞ e
n2 p2 sl
n 1
¼
sl
Z
2 p2 k
en
uls k dk
ð14Þ
ðÞ
0
Theoretically, u gs and u ls can be obtained when Eqs. (12)–(14) are substituted into Eq. (11). However, ul shown in Eq. (10) is piecewise continuous so that one is unable to differentiate it term by term [30], as shown in Eq. (14). In other words, a fully analytical solution is impossible [31]. Instead, a semi-analytical method is developed to resolve the difficulty encountered. At the gas–liquid interface, Eq. (11) is discretized as the following u gx x1 uls xs
u gs xs ulx x2
u gx us D x g us ulx D xl
¼
¼ D
ð15Þ
m
where u gx is the gaseous concentration at x 1(= xs + D x g ) and ulx is the liquid-phase concentration at x 2(= xs D xl). x1 and x 2 designate the grid locations adjacent to the interface in the gas phase and the liquid phase, respectively. With the condition of u gs = uls = us, the interfacial concentration becomes
þ u ¼ D xDu x þ D
us
l gx l
lx Dm D x g
ð16Þ
m D x g
Seeing that the interfacial concentrations of the two phases are the function of time, an iterative procedure is required to find us. As long as u s is obtained, u g and u l can be obtained. The criterion of convergence is 108. That is, when the relative errors of the interfacial concentrations are less than the aforementioned value, the next time step calculation proceeds. The spatial and temporal concentration distributions of CO2 in the gas phase and in a water droplet in terms of the theoretical analysis have been compared to the numerical predictions in a previous study [33]. The theoretical results were in good agreement with the numerical predictions, ascertaining the validity of the conducted method.
2.3. Properties The phenomena of gaseous carbon dioxide uptake by single water droplets at various environmental pressures and temperatures are considered, hence the variations of gaseous mass diffusivity, aqueous mass diffusivity and Henry’s law constant at various conditions are taken into account.
2.3.1. Gas diffusivity The gas diffusivity of CO2 in air is estimated by [34]
D g ;CO2
¼
0:00143T 1:75 pt M 1=2 air;CO2
1=3 air
4
½ðR Þ þ ðR Þ v
10 101:325 100
v
ð17Þ
1=3 2 co2
1
where M air;co2 ¼ 2½ð1=M airÞ þ ð1=M co2 Þ ; (Rv)air and ðR Þco2 are the diffusion volumes of air (=19.7 106 m3 mol1) and CO2, v
W.-H. Chen et al./ Applied Energy 111 (2013) 731–741
respectively. The values of M air;co2 and ðR Þco2 are 17.47 g mol1 and v
3
1
28.12 m mol
, respectively.
2.3.2. Liquid diffusivity The liquid diffusivity of CO 2 in a solvent i is evaluated by [34] 8
¼ 7:4 10V ðg/M Þ
Dl;i
i
0:6 co2
1=2
T
i
10
4
ð18Þ
where M i, g i, and / are the molecular weight, viscosity, and association factor, respectively, and the value of V co2 is 37.34 cm3 mol1. The association factor of water and Rectisol are 2.6 and 1.9, respectively. Because Selexol is unassociated, its association factor is 1.0 [34].
2.3.3. Viscosity The viscosities of water and Rectisol are calculated by [34]
gi ¼
1
A
þ DðDP =2:118Þ 1 þ C xD p r
r
gSL
ð19Þ
where D pr = ( p p vp)/ pc ; gSL and x are the viscosity of the saturated liquidat vapor pressure ( pvp) and the acentric factor, respectively. In Eq. (19), A , C, and D are the functions of T r and they are expressed as 4
0:03877
¼ 0:999 ½4:674 10 =ð1:052T
A
r
C
2 r
1:051Þ 3 r
ð20Þ
r
5 r
6 r
2:573 0:291 r
D
¼ b0:362=ð1:004 T Þ
7 r
c 0:209
ð21Þ ð22Þ
where T r = T /T c and T c is the critical temperature. The values of pc , T c , and x of Rectisol and water are listed in Table 3. The viscosity of Selexol is obtained from the work of Li et al. [35].
2.3.4. Henry’s law constants The Henry’s law constants for CO2 absorbed by Selexol and Rectisol at various temperatures can be found in the studies of Xu et al. [36] and Lunsford and Mcintyre [37], respectively. With regard to CO2 in water, it can be predicted by the Henry’s law as the following
¼ H 0 p
c l
ð23Þ
CO2
where H 0 is the Henry’s law constant and p CO2 stands for the partial pressure of CO2 in the gas phase. The influence of temperature on the constant is estimated by [38]
H 0
¼ H 0 exp s
H 1 1 D
R
T s
ð24Þ
T
¼
p
r s 0
2
R R R c r sin drd d 0
l
h
h w
4pr 3s =3
ð25Þ
where r s is the droplet radius. In a CO2 capture process, the quasisaturated time (t qss) is identified when the absorption time reaches c l;ss where the subscripts qss and ss dethe moment of c l;qss ¼ 0:99 note the quasi-saturated state and the saturated state, respectively. Meanwhile, the absorption rate of a droplet per unit volume is defined as c l;qss =t qss .
3. Results and discussion Three different absorbents of Selexol, Rectisol, and water in the form of single droplet for capturing carbon dioxide are adopted. According to the practical applications of Selexol and Rectisol, their operating pressure ranges from 30 to 60 atm [11,14–17]; the absorbing temperatures of Selexol and Rectisol are in the ranges of 303–333 K and 240–270 K, respectively. To provide a comparison with Selexol, the operating temperature of water is between 303 and 333 K. The CO2 concentration in the flue gas is generally between 4 and 24 vol% [39–42] and the droplet radius in a spray is in the range of approximately 6–60 lm [43]; hence the CO2 concentration of 15 vol% and the droplet radius of 30 lm serve as the basis of this work.
3.1. Properties of absorbents
4 r
¼ 0:079 þ 2:162T 13:404T þ 44:171T 84:829T þ 96:121T 59:813T þ 15:672T
c l
2p 0
735
H 0s means H 0 at the standard condition of T s = 298.15 K. The values of H 0s and DH /R for CO2 in water are 3.4 102 M atm1 and 2400 K, respectively.
The properties of an absorbent play an important role in determining the CO2 capture process and the absorption amount. For instance, the CO2 flux from the gas phase into an droplet is proportional to the gas diffusivity and the liquid diffusivity, and the final or saturated absorption amount of the solute in the droplet depends on the Henry’s law constant. Because of this, the values of gas diffusivity, liquid diffusivity, and Henry’s lawconstant of Selexol and Rectisol are displayed in Figs. 2 and 3, respectively. For the two absorbents, Figs. 2a and 3a suggest that their gas diffusivities (D g ) are sensitive to the operating pressure and they increase as the operating pressure decreases. On the other hand, an increase in operating temperature raises the gas diffusivity, regardless of which solvent is utilized. In contrast, their liquid diffusivities ( Dl) are independent of the operating pressure, but they increase when the operating temperature rises, as shown in Figs. 2b and 3b. The Henry’s lawconstant is the function of temperature alone. The constant decreases from 0.093 to 0.056 M atm1 for Selexol [36] when the operating temperature increases from 303 and 333 K (Fig. 2c); it also decreases from 0.267 to 0.499 M atm1 for Rectisol [37] as the operating temperature is lifted from 240 to 270 K (Fig. 3c). From the curves shown in Figs. 2 and 3, the CO2 capture process and amount can be preliminarily figured out and a higher temperature lessens the CO2 absorption amount by the two absorbents. The Henry’s law constant of Selexol is lower than that of Rectisol within their temperature ranges, implying that more CO 2 can be captured by the latter at the saturated or steady state.
2.4. Physical scale 3.2. Transient CO 2 capture process by Selexol In the following discussion, the mean CO2 concentration in a droplet is defined by
Table 3
Values of critical pressure ( pc ), critical temperature (T c ), and acentric factor ( x) [25]. Solvent
pc (atm)
T c (K)
x (–)
Rectisol Water
79.91 217.75
512.46 647.14
0.656 0.344
Fig. 4 shows the temporal distributions of mean CO2 concentrac l ) in the Selexol droplet at four operating temperatures of tion ( 303, 313, 323, and 333 K and the operating (total) pressure of 30 atm. Corresponding to the operating temperatures of 303, 313, 323, and 333 K, the final CO2 concentrations in the droplet are 0.419, 0.354, 0.295, and 0.253 M, respectively. This reflects that a lower temperature renders a higher final CO 2 concentration at the saturated state. The influence of operating pressure on CO2 capture process is examined in Fig. 5 where two operating temperatures of 303 (Fig. 5a) and 333 K (Fig. 5b) are considered. Contrary
W.-H. Chen et al. / Applied Energy 111 (2013) 731–741
736
(a)
(a)
1E-06
7E-07
9E-07
T=303K T=313K T=323K T=333K
8E-07
) s /
T=240K T=250K T=260K T=270K
6E-07
5E-07
) s /
7E-07
2
2
m (
m ( g D
g 6E-07
D
4E-07
5E-07 3E-07 4E-07
3E-07 25
30
35
40
45
50
55
60
2E-07
65
25
30
35
40
P (atm)
55
60
65
(b) 2.2E-09 2E-09
1.4E-09
1.8E-09
1.2E-09
) s / m ( l D
50
P (atm)
(b) 1.6E-09
2
45
) s /
1E-09
1.6E-09
2
m ( l 1.4E-09 D 8E-10 1.2E-09 6E-10 1E-09
4E-10 30
35
40
45
50
55
8E-10
60
30
35
40
P (atm)
(c)
50
55
60
P (atm)
(c)
0.1
0.55
) 0.5 m t a / 0.45 M ( t n a 0.4 t s n o c 0.35 w a l s ' 0.3 y r n e H 0.25
) 0.09 m t a / M ( t 0.08 n a t s n o c 0.07 w a l s ' y r 0.06 n e H 0.05 300
45
305
310
315
320
325
330
335
340
T (K)
0.2 235
240
245
250
255
260
265
270
275
T (K)
Fig. 2. Distributions of (a) gas diffusivity, (b) liquid diffusivity, and (c) Henry’s law constant for Selexol absorption.
Fig. 3. Distributions of (a) gas diffusivity, (b) liquid diffusivity, and (c) Henry’s law constant for Rectisol absorption.
to the impact of temperature, a higher operating pressure intensifies the CO2 capture process, as a result of higher final CO 2 concentration. In the initial period, the mean concentration of CO2 grows faster at a higher operating pressure and a lower temperature. It follows that the absorption rate of CO2 by the droplet is higher at the aforementioned conditions. The profiles of mean CO 2 concentration at the quasi-saturated c l;qss ) are shown in Fig. 6a. Upon inspection of the profiles time ð
of c l;qss at the quasi-saturated time shown in Fig. 6a, the value of c l;qss is the function of the operating temperature and pressure. In contrast, the value of t qss is hardly affected by the operating pressure, as shown in Fig. 6b. This can be explained by the independence of liquid diffusivity from the operating pressure (Fig. 2b). By examining the absorption rate of the droplet, Fig. 6c depicts that the environment with higher operating temperature and pressure
W.-H. Chen et al./ Applied Energy 111 (2013) 731–741
P t =30atm,
Xg
= 0.15
, CO2
∞
0.5
_ cl,ss =0.419 (M)
737
(a) 0.9 0.8
0.4
P=30atm P=40atm P=50atm P=60atm
0.354 0.7
0.295 0.3
) 0.6 M (
) M 0.2 ( l _ c
0.253
s s q , l
0.5
_ c
0.4
0.5
0.3
0.1
T=303K T=313K T=323K T=333K
0
0.4
) M0.2 ( l _ c 0.1
0.3
0
-0.1
0
0.05
0.1
0.15
0.2 300
0.2
t (s)
-0.1 0
0.2
0.4
0.6
0.8
1
1.2
305
310
315
1.4
320
325
330
335
340
325
330
335
340
325
330
335
340
T (K)
t (s) Fig. 4. Temporal distributions of mean CO2 concentration in Selexol droplet at the operating pressures of 30 atm.
(b) 0.6
0.5
(a) T=303K, 0.9
Xg
, CO2
∞
= 0.15 ) s (
0.8
s s
0.4
t q 0.7 0.6 0.3
) M ( l _ c
0.5 0.9 0.8
0.4
0.7
0.2 300
0.6
) 0.5 M ( l _ c 0.4
0.3
P=30atm P=40atm P=50atm P=60atm
0.2 0.1
305
310
315
320
T (K)
0.3 0.2
(c)
0.1 0 0
0.05
0.1
0.15
0.2
2
t (s)
0 0
0.2
0.4
0.6
0.8
1
1.2
1.8
t (s)
(b) T=333K, Xg
) s 1.6 / M ( e 1.4 t a r n o 1.2 i t p r o s 1 b A
= 0.15
,CO2
∞
0.55 0.5 0.45 0.4 0.35
0.8
) 0.3 M ( l 0.25 _ c
0.6
0.6 300
0.5
0.4
0.2
305
310
315
320
T (K)
) M0.3 ( l
_ c
0.15 0.1
0.1
0
0.05 0
Fig. 6. Profiles of (a) the mean CO2 concentration in the liquid phase at the quasisaturated time, (b) the quasi-saturated time, and (c) the absorption rate of the Selexol droplet.
0.2
0
0.05
0.1
0.15
0.2
t (s)
0
0.2
0.4
0.6
t (s) Fig. 5. Temporal distributions of mean CO2 concentration in Selexol droplet at the operating temperatures of (a) 303 and (b) 333 K.
enhances the CO2 capture process. A higher operating temperature lowers the mean CO2 concentration (Fig. 6a) and, thereby, the CO2 capture amount, but it intensifies the gas and liquid diffusivities so as to reduce the quasi-saturated time (Fig. 2a and b). The role played by the diffusivities in the absorption rate prevails over the
W.-H. Chen et al. / Applied Energy 111 (2013) 731–741
738
P t =30atm, Xg
,CO2
∞
2.4
= 0.15
(a)
5 4.5
_ cl,ss =2.243 (M)
2
1.741
3.5
1.422
1.6
) M ( s s q , l
) 1.2 M ( l c
3 2.5
_ c 1.202 T=240K T=250K T=260K T=270K
0.4
2
2.5
1.5
2
0.8
P=30atm P=40atm P=50atm P=60atm
4
) 1.5 M (
l _ c
1
1
0.5 0.5
0 235
0 0
0.05
0.1
0.15
0.2
t (s)
240
245
250
0 0
0.2
0.4
0.6
0.8
(b)
Fig. 7. Temporal distributions of mean CO2 concentration in Rectisol droplet at the operating pressures of 30 atm.
, CO2
∞
260
265
270
275
260
265
270
275
260
265
270
275
T (K)
1
t (s)
(a) T=240K, Xg
255
0.35
) s (
= 0.15
0.4
0.3
s s
5
t q 0.25
4 0.2 3
) M ( l _ c
5
0.15 235
240
245
250
255
4
T (K)
2 ) M ( l _ c
P=30atm P=40atm P=50atm P=60atm
1
3
(c)
2
1
13
0 0
0.05
0.1
0.15
0.2
t (s)
0.2
0.4
0.6
0.8
t (s)
(b) T=270K, X g
n o i t p r o s b A
= 0.15
,CO2
∞
12
) s / 11 M ( e t 10 a r
0 0
14
2.5
2
9 8 7 6 5 235
240
245
250
255
1.5
) M (
T (K)
3
l _ c
2.5
1
Fig. 9. Profiles of (a) the mean CO2 concentration in the liquid phase at the quasisaturated time, (b) the quasi-saturated time, and (c) the absorption rate of the Rectisol droplet.
2
) M1.5 ( l
_ c
1
0.5
0.5
0 0
0.05
0.1
0.15
0.2
CO2 capture amount. This is the reason that the absorption rate rises with increasing operating temperature.
t (s)
0 0
0.1
0.2
0.3
0.4
t (s) Fig. 8. Temporal distributions of mean CO2 concentration in Rectisol droplet at the operating temperatures of (a) 303 and (b) 333 K.
3.3. Transient CO 2 capture process by Rectisol Fig. 7 displays the temporal distributions of c l in the Rectisol droplet at four operating temperatures of 240, 250, 260, and 270 K and the operating pressure of 30 atm. As a whole, the trend
W.-H. Chen et al./ Applied Energy 111 (2013) 731–741
in the curves of c l shown in Fig. 7 is similar to that in Fig. 4. However, the distributions of the curves shown in Fig. 7 are higher than those in Fig. 4, stemming from the larger Henry’s law constant of Rectisol (Fig. 3c) when compared to that of Selexol ( Fig. 2c). For example, the value of c l at the saturated state shown in Fig. 7 is in the range of 1.202–2.243 M, whereas it is between 0.253 and 0.419 M in Fig. 4. It is thus recognized that the CO2 capture amount by Rectisol is higher than that by Selexol. When the temporal distributions of c l at various operating pressures under the temperatures of 240 (Fig. 8a) and 270 K (Fig. 8b) are examined, it is not surprising that a higher operating pressure or a lower operating temperature is conducive to the CO2 capture process. Fig. 9 shows the distributions of c l;qss , t qss, and the absorption rate of CO2 by the Rectisol droplet. Within the investigated temperature and pressure ranges, the values of c l;qss in the Selexol and Rectisol droplets are in the ranges of 0.25–0.83 M (Fig. 6a) and 1.19– 4.44 M (Fig. 9a), respectively. This reveals that the Rectisol droplet provides a higher capacity for capturing CO2 than the Selexol droplet. For the Rectisol droplet, the CO 2 capture process is achieved within 0.4 s (Fig. 9b). A higher operating temperature leads to a shorter absorption time. Similar to the Selexol droplet, increasing temperature or pressure facilitates the absorption rate (Fig. 9c). However, the influence of operating temperature on the absorption rate of the Rectisol droplet is not as significant as that of the Selexol droplet (Fig. 6c). A comparison to the Selexol droplet (Fig. 6), both the CO2 absorption amount and the absorption rate of the Rectisol droplet (Fig. 9) are higher the Selexol droplet to a certain extent. The CO2 concentration in the flue gas from oxyfuel combustion typically ranges from 63 to 87 vol% [39,44–47]. Seeing that the CO2 partial pressure has a pronounced influence on the CO2 capture amount and absorption rate (Figs. 6 and 9), the performance of CO2 absorption by Selexol or Rectisol droplets can be further improved if they are employed to capture CO 2 in oxyfuel combustion processes.
(a) 0.5
739
3.9 Selexol Water Selexol/Water
3.8
0.4
3.7 3.6
) 0.3 M (
3.5
s s q , l
3.4
_ c 0.2
R a t i o ( )
3.3 3.2
0.1
3.1 0 295
300
305
310
315
320
325
330
335
3 340
T (K)
(b) 0.7
3.3
0.6
3.2
0.5 3.1
) 0.4 s (
3
s s
R a t i o ( )
t q0.3 2.9 0.2 2.8
0.1
0 295
300
305
310
315
320
325
330
335
2.7 340
T (K)
(c) 1.1
1.5
3.4. A comparison between Selexol and water Water is a common absorbent to capture gas solutes. To give an insight into the difference of CO2 capture between a Selexol droplet and a water droplet with the radius of 30 lm, their Henry’s law constants are presented in Fig. 10. For the operating temperature range of 303–333 K, the Henry’s law constant of Selexol is by far
0.12
Selexol Water
0.1
) m t a / M ( 0.08 t n a t s n 0.06 o c w a l s 0.04 ' y r n e H 0.02
0 300
1.4
1
) s / M ( e 0.9 t a r n o i t 0.8 p r o s b A0.7
0.6 295
1.3
1.2
R a t i o ( )
1.1
1
300
305
310
315
320
325
330
335
0.9 340
T (K) Fig. 11. Profiles of (a) the mean CO2 concentration in the liquid phase at the quasisaturated time, (b) the quasi-saturated time, and (c) the absorption rate of the Selexol and water droplets and their ratios at the operating pressure of 30 atm.
310
320
330
340
T (K) Fig. 10. A comparison of the Henry’s law constants of Selexol and water at various operating temperatures.
larger than that of water. This means that Selexol used for CO2 capture is more feasible that water. The profiles of c l;qss , t qss , and the absorption rate of the Selexol droplet and the water droplet at the operating pressures of 30 and 60 atm are shown in Figs. 11 and 12, respectively. It can be seen that the value of c l;qss in the Selexol droplet at the quasi-saturated state is larger than in the water droplet by factors of 3.12–3.84 (Figs. 11a and 12a). Alternatively, the time required for the Selexol droplet reaching the quasi-saturated state is also longer than the water droplet by factors of 2.7–3.3 (Figs. 11b and 12b). It is of interest that the trend in the absorption rate of the Selexol droplet is different from that of the water droplet (Figs. 11c and 12c). Specifically, increasing
W.-H. Chen et al. / Applied Energy 111 (2013) 731–741
740
(a)
1 0.9
3.7
0.7
3.6
R 3.5 a t i o
0.6
s s 0.5 q , l
_ c
3.4 ( -
0.4
3.3
0.3
)
3.1
0.1
300
305
310
315
320
325
330
335
3 340
T(K)
(b) 0.7
3.3
0.6
3.2
0.5 3.1
) s (
0.4 3
s s
t q
0.3 2.9
R a t i o ( )
0.2 2.8
0.1
0 295
300
305
310
315
320
325
330
335
2.7 340
T(K)
(c) 2.1
1.5
2 1.4
) s / M ( e t a r n o i t p r o s b A
1.9 1.3 1.8
R a t i 1.2 o ( )
1.7 1.6
1.1 1.5 1 1.4 1.3 295
Absorbent
Selexol
Rectisol
Water
Molar fraction of CO2 Operating pressure (atm) Operating temperature (K) Mean CO2 quasi-saturated concentration (M) Quasi-saturated time (s) Absorption rate (M s1)
0.15 30–60 303–333 0.250–0.830
240–270 1.190–4.442
303–333 0.065–0.266
0.255–0.561 0.742–1.951
0.182–0.370 6.066–12.946
0.092–0.175 0.707–1.521
3.2
0.2
0 295
A summary of CO2 capture by Selexol, Rectisol, and water.
3.8
0.8
) M (
Table 4
3.9 Selexol Water Selexol/Water
300
305
310
315
320
325
330
335
0.9 340
T (K) Fig. 12. Profiles of (a) the mean CO2 concentration in the liquid phase at the quasisaturated time, (b) the quasi-saturated time, and (c) the absorption rate of the Selexol and water droplets and their ratios at the operating pressure of 60 atm.
temperature raises the absorption rate of the Selexol droplet, but it slightly diminishes the absorption rate of the water droplet. As a result, an increase in operating temperature significantly enlarges the absorption rate ratio between the Selexol droplet and the water one. However, for the operating temperature of 303 K, the absorption rate of the former is lower than that of the latter, regardless of the operating pressure of 30 or 60 atm. c l;qss , t qss, and absorption rate using Finally, the physical scales of the three absorbents to capture CO2 are summarized in Table 4 for comparison. The value of c l;qss in water is the lowest among the three absorbents, whereas it is the highest in Rectisol. The capture process of Selexol is longer than the other two absorbents, whereas
water has the shortest absorption period. However, their absorption times are in a comparable state. After simultaneously considc l;qss and t qss, the absorption rates of ering the physical scales of water and Selexol are in the same order of magnitude, as shown in Figs. 11c and 12c. In contrast, the absorption rate of Rectisol is larger than the other two by an order of magnitude (Table 4). This reflects that using Rectisol gives the best performance of CO 2 capture among the three absorbents. However, it should be mentioned that the implementation of CO2 capture by Rectisol is based on low temperature operation. This needs to refrigerate the solvent, thereby resulting in high capital and operating costs of the plant [10].
4. Conclusions The capture process of carbon dioxide by a single droplet has been analyzed through a theoretical approach where three different absorbents of Selexol (dimethylether polyethylene glycol), Rectisol (chilled methanol), and water have been regarded. In the method, the CO2 diffusion in gas phase is solved through a similarity method, whereas the diffusion in the liquid phase is predicted by use of the technique of separation of variable. The theoretical difficulty encountered at the interface is overcome using the finite difference scheme. From the obtained results, it is found that increasing temperature decreases both the CO2 capture amount by a droplet and its absorption time, regardless of which absorbent is employed. The influence of varying temperature on the absorption time is beyond on the CO2 capture amount; this results in the growth of the absorption rates of CO 2 by the droplets when the temperature increases. The variation of operating pressure almost plays no part in determining the absorption time; this leads to a pronounced growth in the absorption rate as the operating pressure is raised. When the absorption behavior of the three absorbents is compared with each other, more CO 2 can be captured by Rectisol than by the other two absorbents. Meanwhile, the absorption times of the three solvents are in a comparable state. As a consequence, the absorption rate of the Rectisol droplet is larger than the other two by an order of magnitude. If the partial pressure of CO2 in a flue gas is lifted, say, from oxyfuel combustion, the efficiency of CO2 capture by a droplet can be further improved. The present study has provided a fundamental insight into the application of sprays for CO 2 capture using Selexol, Rectisol, and water as solvents. If a droplet is in motion, the Ranz–Marshall correlation can be employed to describe the influence of convective flow on the mass transfer. On the other hand, if the droplet is in a non-isothermal environment, the energy equations in the gas phase and the liquid phase should be included in the governing equations, and the Clausius–Clapeyron equation has to be utilized to link the vaporization or condensation process at the interface. This topic deserves further investigation in the future.
Acknowledgment The authors gratefully acknowledge the financial support of the National Science Council, Taiwan, ROC, for this study.
W.-H. Chen et al./ Applied Energy 111 (2013) 731–741
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