Carbon dioxide capture by single droplet using Selexol, Rectisol and water as absorbents: A theoretical approach

Applied Energy 111 (2013) 731–741

Contents lists available at SciVerse ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

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 CO2 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 a similarity method and the technique of separation of variable is employed to approach the liquidphase diffusion. At the interface, a finite difference method is applied to connect the CO2 diffusion between the two phases. The individual capture processes of CO2 by three different absorbents of 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 K, respectively, and they are 30–60 atm and 240–270 K for Rectisol. The analysis indicates that an increase in temperature decreases the CO2 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 CO2 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. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Burning fossil fuels is the main source of carbon dioxide emissions from anthropogenic activities and it accounts for approximately 95% of the total global annual carbon dioxide emissions [1]. Currently carbon capture and storage (CCS) is considered to be technically feasible at commercial scale to reduce anthropogenic carbon dioxide emissions into the atmosphere [2–6]. A number of carbon dioxide separation methods, such as solution absorption, membrane separation, adsorption separation [7,8], and cryogenics [1,9], can be employed. When one is concerned with solution absorption, it can be classified into chemical absorption and physical absorption. Monoethanolamine (MEA), 2-amino-2-methyl-1-propanol (AMP), aqua ammonia, ⇑ Corresponding author. Tel: +886 6 2757575x63600; fax: +886 6 2389940. E-mail address: [email protected] (W.-H. Chen). 0306-2619/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apenergy.2013.05.051

dual-alkali, and the proprietary solvent marketed by Mitsubishi Heavy Industries, KS-1, have been employed as chemical solvents [10] for a variety of applications in industries. With regard to physical absorption, the gas treating solvents of Selexol (dimethylether polyethylene glycol), Rectisol (chilled methanol), Fluor (propylene carbonate), and Purisol (N-methyl-2-pyrollidone) are becoming increasingly popular, especially in the application of coal gasification [11]. When physical absorption is practiced, CO2 is absorbed into a absorbent obeying Henry’s law, and the gas capture amount by the absorbent depends on the partial pressure of CO2 and the temperature of 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 CO2 from metallurgical fuel gases, such as blast furnace gases and Corex gases [13]. The solubility of CO2 in an absorbent is higher at the higher partial

732

W.-H. Chen et al. / Applied Energy 111 (2013) 731–741

Nomenclature c D Dm H 0 H m p pc R r rs t T Ts Tc Tr u x X M Vi

DH

average molar concentration (M) diffusion coefficient (m2 s1) mass diffusion number nondimensional Henry’s law constant Henry’s law constant (M atm1) 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 CO2 capture via absorption in IGCC systems has been reported in some studies. Strube and Manfrida [21] focused on two different CO2 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 CO2 capture was employed. They pointed out that the CO2 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 c g i l qss ss s SL t 1 vp

air diffusive characteristic time gas phase or continuous phase absorbent i liquid phase or discrete phase quasi-saturated state saturated state droplet surface or interface saturated liquid total pressure infinity 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 CO2 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

733

W.-H. Chen et al. / Applied Energy 111 (2013) 731–741

Fig. 1. A schematic of droplet absorption configuration and the equations of two phases in dimensional form.

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 ¼ xð1  ug Þ

and

v l ¼ xul

ð1Þ

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 t ¼ tgct ; sl ¼ R2 t=D ¼ ttlc ; ug ¼ x ¼ Rrd ; sg ¼ R2 =D d

g

d

l

cg ðr;tÞ cg0 ; ul

¼ clcðr;tÞ H; H1 ¼ H0 RT g0

Description

Gas phase

Governing equation

@ug @ sg

Initial condition Boundary conditions

ug ðx; 0Þ ¼ 1;

¼

@ 2 ug @x2

þ

Liquid phase 2 @ug x @x

@ul @ sl

x>1

ug ðx; sg Þ ¼ 1;

ul ðx; 0Þ ¼ 0;

x!1

c

gs ug ð1; sg Þ ¼ cg1 ;

Interface conditions @u

2

l ¼ @@xu2l þ 2x @u @x

l ð @xg = @u Þ ¼ Dm @x x¼1 ugs ¼ uls

sg > 0



@ul  @x x¼0

¼ 0;

06x61

sl > 0 sl > 0

ls ul ð1; sl Þ ¼ ccg1 H;

734

W.-H. Chen et al. / Applied Energy 111 (2013) 731–741

Table 2 A list of diffusion equations as well as initial and boundary conditions (the second transformation). Description

Gas phase

Governing equation

@v g @ sg

Initial condition Boundary conditions

v g ðx; 0Þ ¼ 0; x > 1 v g ðx; sg Þ ¼ 0; x ! 1 v g ð1; sg Þ ¼ 1  cc ¼ 1  ugs ðsg Þ; sg > 0

¼

@2 v g @x2

gs

g1

Description

Liquid phase

Governing equation

@v l @ sl

Initial condition

v l ðx; 0Þ ¼ 0; 0 6 x 6 1 v l ð0; sl Þ ¼ 0; sl > 0 v l ð1; sl Þ ¼ cc H ¼ uls ðsl Þ; sl > 0

Boundary conditions

the interface are invoked to link ug and ul. The mass flux conservation of the dimensionless concentrations is written as

(T1)

   @ug @ul ¼ Dm @x @x x¼1

(T2) (T3) (T4)

where Dm(=Dl/DgH) represents the mass diffusion number [31,32]. Meanwhile, the Henry’s law is converted into the continuity of the dimensionless concentrations. That is

ð11Þ

ugs ¼ uls (T5)

2

¼ @@xv2l

ls

g1

(T6) (T7) (T8)

ð12Þ

At the interface, Eqs. (8) and (10) give

    @ug 1 ¼ ð1  ugs Þ 1 þ pffiffiffiffiffiffiffiffi @x x¼1 psg

ð13Þ

and

x1

g ¼ pffiffiffiffiffi 2 sg

ð2Þ

Eq. (T1) thus becomes an ordinary differential equation and the counterparts of Eqs. (T1)–(T4) are given by 2

d vg dv g þ 2g ¼0 dg2 dg

ð3Þ

v g ð0Þ ¼ 1  ugs

ð4Þ

v g ðgÞ ¼ 0; g ! 1

ð5Þ

The solution of Eqs. (3)–(5) is

vg ¼ A þ B

Z

g

2

en dn

ð6Þ

0

where

A ¼ 1  ugs ;

2 and B ¼ pffiffiffiffi ðugs  1Þ

ð7Þ

p

Therefore, the dimensionless gas-phase concentration ug is obtained as

    1  ugs x1  erfc pffiffiffiffiffi ug ¼ 1  2 sg x

ð8Þ

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 P adopted. Defining v l ¼ 1 n¼1 v n ðsl Þ sinðnpxÞ 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]

Z sl 1 X 2 2 2 2 ð1Þn ðnpÞen p sl sinðnpxÞ  en p k uls ðkÞdk

v l ¼ 2

n¼1

ð9Þ

1 2X 2 2 ð1Þn ðnpÞen p sl sinðnpxÞ  x n¼1

ð14Þ

Theoretically, ugs and uls 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 ugx ugs x1 xs uls ulx xs x2

¼

ugx us D xg us ulx Dxl

¼ Dm

ð15Þ

where ugx is the gaseous concentration at x1(=xs + Dxg) and ulx is the liquid-phase concentration at x2(=xs  Dxl). x1 and x2 designate the grid locations adjacent to the interface in the gas phase and the liquid phase, respectively. With the condition of ugs = uls = us, the interfacial concentration becomes

us ¼

Dxl ugx þ ulx Dm Dxg Dxl þ Dm Dxg

ð16Þ

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 us is obtained, ug and ul 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

0

Hence, the dimensionless liquid-phase concentration is expressed by

ul ¼ 

  Z sl 1 X @ul 2 2 2 2 ¼ 2 ðnpÞ2 en p sl  en p k uls ðkÞdk @x x¼1 0 n¼1

Z sl

2 2 en p k uls ðkÞdk

ð10Þ

0

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 ugs and uls, 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

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]

Dg;CO2 ¼

0:00143T 1:75 pt M 1=2 air;CO2 ½ð

1=3 v Þair

R

þ ðR

1=3 2 v Þco2 

 104 

101:325 100

ð17Þ

where Mair;co2 ¼ 2½ð1=Mair Þ þ ð1=Mco2 Þ1 ; (Rv)air and ðRv Þco2 are the diffusion volumes of air (=19.7  106 m3 mol1) and CO2,

W.-H. Chen et al. / Applied Energy 111 (2013) 731–741

respectively. The values of Mair;co2 and ðRv Þco2 are 17.47 g mol1 and 28.12 m3 mol1, respectively. 2.3.2. Liquid diffusivity The liquid diffusivity of CO2 in a solvent i is evaluated by [34]

Dl;i ¼

7:4  108 ð/Mi Þ1=2 T V 0:6 co2 gi

 104

ð18Þ

where Mi, gi, 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 þ DðDP r =2:118ÞA gSL 1 þ C xDpr

ð19Þ

where Dpr = (p  pvp)/pc; gSL and x are the viscosity of the saturated liquid at vapor pressure (pvp) and the acentric factor, respectively. In Eq. (19), A, C, and D are the functions of Tr and they are expressed as

A ¼ 0:999  ½4:674  104 =ð1:052T 0:03877  1:051Þ r

ð20Þ

D ¼ b0:362=ð1:004  T r2:573 Þ

0:291

ð21Þ

c  0:209

ð22Þ

where Tr = T/Tc and Tc is the critical temperature. The values of pc, Tc, 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

cl ¼ H0 pCO2

ð23Þ

where H0 is the Henry’s law constant and pCO2 stands for the partial pressure of CO2 in the gas phase. The influence of temperature on the constant is estimated by [38]

H0 ¼ H0s  exp

   DH 1 1  R Ts T

R 2p R p R rs cl ¼

0

0

0

cl r2 sin hdrdhdw 4pr 3s =3

ð25Þ

where rs is the droplet radius. In a CO2 capture process, the quasisaturated time (tqss) is identified when the absorption time reaches the moment of cl;qss ¼ 0:99cl;ss where the subscripts qss and ss denote the quasi-saturated state and the saturated state, respectively. Meanwhile, the absorption rate of a droplet per unit volume is defined as cl;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

C ¼ 0:079 þ 2:162T r  13:404T 2r þ 44:171T 3r  84:829T 4r þ 96:121T 5r  59:813T 6r þ 15:672T 7r

735

ð24Þ

H0s means H0 at the standard condition of Ts = 298.15 K. The values of H0s 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 law constant 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 (Dg) 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 law constant 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 CO2 can be captured by the latter at the saturated or steady state.

2.4. Physical scale 3.2. Transient CO2 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 (Tc), and acentric factor (x) [25]. Solvent

pc (atm)

Tc (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 concentration (cl ) in the Selexol droplet at four operating temperatures of 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 CO2 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

736

W.-H. Chen et al. / Applied Energy 111 (2013) 731–741

(a)

(a)

1E-06 9E-07

T=303K T=313K T=323K T=333K

8E-07

T=240K T=250K T=260K T=270K

6E-07

7E-07

5E-07

Dg (m2/s)

Dg (m2 /s)

7E-07

6E-07

4E-07

5E-07 3E-07

4E-07 3E-07 25

30

35

40

45

50

55

60

2E-07

65

P (atm)

30

35

40

45

50

55

60

65

P (atm)

(b) 1.6E-09

(b) 2.2E-09

1.4E-09

2E-09 1.8E-09

D l (m2 /s)

1.2E-09

Dl (m2 /s)

25

1E-09 8E-10

1.6E-09 1.4E-09 1.2E-09

6E-10 4E-10 30

1E-09 35

40

45

50

55

8E-10

60

P (atm)

(c)

0.1

0.09

0.08

0.07

0.06

0.05 300

305

310

315

320

35

40

45

50

55

60

P (atm)

Henry's law constant (M/atm)

Henry's law constant (M/atm)

(c)

30

325

330

335

340

T (K)

0.55 0.5 0.45 0.4 0.35 0.3 0.25 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 CO2 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 CO2 concentration at the quasi-saturated time ðcl;qss ) are shown in Fig. 6a. Upon inspection of the profiles

of cl;qss at the quasi-saturated time shown in Fig. 6a, the value of cl;qss is the function of the operating temperature and pressure. In contrast, the value of tqss 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

737

W.-H. Chen et al. / Applied Energy 111 (2013) 731–741

P t =30atm,

0.5

X g∞, CO = 0.15 2

_ cl,ss =0.419 (M)

0.4

(a) 0.9 0.8 0.7

0.295

cl,qss (M)

0.253

0.5

_

0.2

_

cl (M)

0.3

0.4 0.3

0.1

cl (M)

T=303K T=313K T=323K T=333K

0

0

0.2

0.4

_

0.6 0.5 0.4

0.2 0.1

0.3

0 -0.1

-0.1

P=30atm P=40atm P=50atm P=60atm

0.354

0.6

0

0.05

0.8

1

0.1

t (s)

1.2

0.15

0.2 300

0.2

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,

X g∞, CO = 0.15 2

tqss (s)

0.9 0.8

0.4

0.7

_

cl (M)

0.6

0.3

0.5

0.9 0.8

0.4

0.7

0.2 300

0.6

0.2 0.1 0

0

0.2

0.4

_

P=30atm P=40atm P=50atm P=60atm

cl (M)

0.3

0.5

305

310

315

320

T (K)

0.4 0.3 0.2

(c)

0.1 0 0

0.6

0.05

0.8

0.1 t (s)

0.15

1

2

0.2

1.2

1.8

0.55

Absorption rate (M/s)

t (s)

(b) T=333K, Xg∞,CO = 0.15 2

0.5 0.45 0.4

_

cl (M)

0.35

1.4 1.2 1 0.8

0.3

0.6

0.25

0.6 300

0.5

0.4

305

310

315

320

T (K)

0.3

_

cl (M)

0.2 0.15

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

0.1

0.1

0

0.05 0

1.6

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

738

W.-H. Chen et al. / Applied Energy 111 (2013) 731–741

2

3.5

1.422

cl,qss (M)

0.8

2.5 2

2.5

1.5

2

_

1

0.2

0.5

0.5 0

0

1

1.5

cl (M)

T=240K T=250K T=260K T=270K

0.4

0

3

_

1.2

1.202

0.4

0

0.6

0.05

0.1 t (s)

0.8

0.15

0 235

0.2

1

240

245

250

Fig. 7. Temporal distributions of mean CO2 concentration in Rectisol droplet at the operating pressures of 30 atm.

260

265

270

275

260

265

270

275

260

265

270

275

0.35

0.3

tqss (s)

(a) T=240K, Xg∞,CO2 = 0.15

255

T (K)

(b) 0.4

t (s)

5

P=30atm P=40atm P=50atm P=60atm

4

1.741

1.6

5 4.5

_ cl,ss =2.243 (M)

2

cl (M)

(a)

P t =30atm, Xg∞,CO = 0.15

2.4

0.25 4 0.2 3

cl (M)

5

0.15 235

_

4

_

P=30atm P=40atm P=50atm P=60atm

0

0.2

245

250

3

(c)

2 1 0

255

14 13

0

0.4

0.05

0.1 t (s)

0.6

0.15

0.2

0.8

t (s)

(b) T=270K, X g∞,CO = 0.15 2

2.5

240

T (K)

12

Absorption rate (M/s)

1

0

cl (M)

2

2

11 10 9 8 7 6 5 235

1.5 3

cl (M)

_

250

255

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 1.5

_

cl (M)

245

T (K)

2.5

1

240

1

0.5

0.5 0

0

0.05

0.1 t (s)

0.15

0.2

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.

CO2 capture amount. This is the reason that the absorption rate rises with increasing operating temperature. 3.3. Transient CO2 capture process by Rectisol Fig. 7 displays the temporal distributions of cl 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

739

W.-H. Chen et al. / Applied Energy 111 (2013) 731–741

(a) 0.5

3.9

Selexol Water Selexol/Water

3.8

_

cl,qss (M)

0.4

3.7 3.6

0.3

3.5 3.4

0.2

Ratio (-)

3.3 3.2

0.1

3.1 0 3 295 300 305 310 315 320 325 330 335 340

T (K)

(b) 0.7

3.3

0.6

3.2

tqss (s)

0.5

3.1

0.4 3 0.3

Ratio (-)

in the curves of cl 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 cl 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 cl 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 cl;qss , tqss, and the absorption rate of CO2 by the Rectisol droplet. Within the investigated temperature and pressure ranges, the values of cl;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 CO2 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 CO2 in oxyfuel combustion processes.

2.9

0.2

2.8

0.1

0 2.7 295 300 305 310 315 320 325 330 335 340

T (K)

(c) 1.1

1.5

0.12 Selexol Water

Henry's law constant (M/atm)

0.1

1.4

1

1.3

0.9

1.2 0.8

Ratio (-)

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

Absorption rate (M/s)

3.4. A comparison between Selexol and water

1.1

0.7

1

0.9 0.6 295 300 305 310 315 320 325 330 335 340

T (K) 0.08 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.

0.06

0.04

0.02

0 300

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 cl;qss , tqss, 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 cl;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

740

W.-H. Chen et al. / Applied Energy 111 (2013) 731–741

(a)

1 0.9

3.8

0.8

3.7 3.6

0.6

3.5

0.5

3.4

0.4

Ratio (-)

cl,qss (M)

0.7

_

Table 4 A summary of CO2 capture by Selexol, Rectisol, and water.

3.9

Selexol Water Selexol/Water

3.3

0.3 0.2

3.2

0.1

3.1

3 0 295 300 305 310 315 320 325 330 335 340

T(K)

(b) 0.7

3.3

0.6

3.2 3.1

0.4 3 0.3

Ratio (-)

tqss (s)

0.5

2.9

0.2

2.8

0.1

2.7 0 295 300 305 310 315 320 325 330 335 340

T(K)

(c) 2.1

1.5 1.4

1.9 1.3

1.8

1.2

1.7 1.6

Ratio (-)

Absorption rate (M/s)

2

1.1

1.5 1

1.4 1.3 295

0.9 300 305 310 315 320 325 330 335 340

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. Finally, the physical scales of cl;qss , tqss, and absorption rate using the three absorbents to capture CO2 are summarized in Table 4 for comparison. The value of cl;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

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

water has the shortest absorption period. However, their absorption times are in a comparable state. After simultaneously considering the physical scales of cl;qss and tqss, the absorption rates 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 CO2 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 CO2 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 CO2 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 CO2 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

References [1] Li Y, Liu Y, Zhang H, Liu W. Carbon dioxide capture technology. Energy Procedia 2011;11:2508–15. [2] Gibbins J, Chalmers H. Carbon capture and storage. Energy Policy 2008;36:4317–22. [3] Li H, Yan J, Yan J, Anheden M. Impurity impacts on the purification process in oxy-fuel combustion based CO2 capture and storage system. Appl Energy 2009;86:202–13. [4] Li H, Ditaranto M, Yan J. Carbon capture with low energy penalty: supplementary fired natural gas combined cycles. Appl Energy 2012:164–9. [5] Hu Y, Li H, Yan J. Techno-economic evaluation of the evaporative gas turbine cycle with different CO2 capture options. Appl Energy 2012;89:303–14. [6] Hu Y, Li X, Li H, Yan J. Peak and off-peak operations of the air separation unit in oxy-coal combustion power generation systems. Appl Energy 2013. . [7] Hedin N, Andersson L, Bergström L, Yan J. Adsorbents for the post-combustion capture of CO2 using rapid temperature swing or vacuum swing adsorption. Appl Energy 2013;104:418–33. [8] Cheung O, Bacsik Z, Liu Q, Mace A, Hedin N. Adsorption kinetics for CO2 on highly selective zeolites NaKA and nano-NaKA. Appl Energy 2013. . [9] Figueroa JD, Timothy F, Sean P, Howard M, Srivastava RD. Advances in CO2 capture technology – The US Department of Energy’s Carbon Sequestration Program. Int J Greenhouse Gas Control 2008;2:9–20. [10] Olajire AA. CO2 capture and separation technologies for end-of-pipe applications – a review. Energy 2010;35:2610–28. [11] Burr B, Lyddon L. A comparison of physical solvents for acid gas removal. Bryan Research and Engineering Inc.; 2008. [12] Chen WH, Lu JJ. Microphysics of atmospheric carbon dioxide uptake by a cloud droplet containing a solid nucleus. J Geophys Res-Atmos 2003;108(D15):4470–8. [13] Lampert K, Ziebik A. Comparative analysis of energy requirements of CO2 removal from metallurgical fuel gases. Energy 2007;32:521–7. [14] Breckenridge W, Holiday A, Ong JOY, Sharp C. Use of SelexolÒ process in coke gasification to ammonia project. Laurance Reid Gas Conditioning Conference; 2000. [15] Hackett GA, Gerdes K. Trace species partitioning as affected by cold gas cleanup conditions: a thermodynamic analysis. Natl Energy Tech Lab 2011. [16] Kaneco S, Katsumata H, Suzuki T, Ohta K. Electrochemical reduction of carbon dioxide to ethylene at a copper electrode in methanol using potassium hydroxide and rubidium hydroxide supporting electrolytes. Electrochimica Acta 2006;51:3316–21. [17] Zhou W, Zhu B, Chen D, Zhao F, Fei W. Technoeconomic assessment of China’s indirect coal liquefaction projects with different CO2 capture alternatives. Energy 2011;36:6559–66. [18] Kunze H, Spliethoff H. Assessment of oxy-fuel, pre- and post-combustionbased carbon capture for future IGCC plants. Appl Energy 2012;94:109–16. [19] Martelli E, Kreutz T, Carbo M, Consonni S, Jansen D. Shell coal IGCCS with carbon capture: conventional gas quench vs. innovative configurations. Appl Energy 2011;88:3978–89. [20] Siefert NS, Litster S. Exergy and economic analyses of advanced IGCC–CCS and IGFC–CCS power plants. Appl Energy 2013;107:315–28. [21] Strube R, Manfrida G. CO2 capture in coal-fired power plants – impact on plant performance. Int J Greenhouse Gas Control 2011;5:710–26. [22] Chen C, Rubin ES. CO2 control technology effects on IGCC plant performance and cost. Energy Policy 2009;37:915–24. [23] Li S, Robin S. Rectisol wash process simulation and analysis. J Cleaner Prod 2013;39:321–8.

741

[24] Tippayawong N, Thanompongchart P. Biogas quality upgrade by simultaneous removal of CO2 and H2S in a packed column reactor. Energy 2010;35:4531–5. [25] Lu Y, Ye X, Zhang Z, Khodayari A, Djukadi T. Development of a carbonate absorption-based process for post-combustion CO2 capture: the role of biocatalyst to promote CO2 absorption rate. Energy Procedia 2011;4:1286–93. [26] Li L, Zhao B. Numerical simulation of gas and liquid flow within a vortex spray tower. Energy Procedia 2012;16:1072–7. [27] Chen WH. Air pollutant absorption by single moving droplets with drag force at moderate Reynolds numbers. Chem Eng Sci 2006;61:449–58. [28] Seinfeld JH, Pandis SN. Atmospheric chemistry and physics. New York: Wiley; 1998. [29] Myers GE. Analytical methods in conduction heat transfer. 2nd ed. New York: Genium Pub. Corp; 1987. [30] Strauss WA. Partial differential equations: an introduction. 2nd ed. New York: Wiley; 2008. [31] Chen WH. An analysis of gas absorption by a liquid aerosol in a stationary environment. Atmos Environ 2002;36:3671–83. [32] Chen WH. Scavenging waves and influence distances of gas absorption around single liquid aerosols in clouds. Atmos Environ 2006;40:500–11. [33] Chen WH, Hou YL, Hung CI. A theoretical analysis of the capture of greenhouse gases by single water droplet at atmospheric and elevated pressures. Appl Energy 2011;88:5120–30. [34] Poling BE, Prausnitz JM, O’Connell JP. The properties of gases and liquids. 5th ed. New York: McGraw-Hill; 2001. [35] Li J, Mundhwa M, Henni A. Volumetric properties, viscosities, refractive indices, and surface tensions for aqueous Genosorb 1753 solutions. J Chem Eng Data 2007;52:955–8. [36] Xu Y, Schutte RP, Hepler LG. Solubilities of carbon dioxide, hydrogen sulfide and sulfur dioxide in physical solvents. Can J Chem Eng 1992;70:569–73. [37] Lunsford K, Mcintyre G. Decreasing contactor temperature could increase performance. Bryan Research and Engineering Inc; 2006. [38] Seinfeld JH. Atmospheric chemistry and physics of air pollution. New York: Wiley; 1986. [39] Bouillona BA, Hennes S, Mahieux C. ECO2: Post-combustion or oxyfuel – a comparison between coal power plants with integrated CO2 capture. Energy Procedia 2009;1:4015–22. [40] Sipöcz N, Tobiesen FA, Assadi M. The use of artificial neural network models for CO2 capture plants. Appl Energy 2011;88:2368–76. [41] Mores P, Scenna N, Mussati S. Post-combustion CO2 capture process: equilibrium stage mathematical model of the chemical absorption of CO2 into monoethanolamine (MEA) aqueous solution. Chem Eng Res Des 2011;89:1587–99. [42] Lawal A, Wang M, Stephenson P, Obi O. Demonstrating full-scale postcombustion CO2 capture for coal-fired power plants through dynamic modelling and simulation. Fuel 2012;101:115–28. [43] Chen WH, Chen SM, Hung CI. A theoretical approach of absorption processes of air pollutants in sprays under droplet–droplet interaction. Sci Total Environ 2013;444:336–46. [44] Jordal K, Anheden M, Yan J, StrOmberg L. Oxyfuel combustion for coal-fired power generation with CO2 capture–opportunities and challenges. Greenhouse Gas Control Technol 2005;1:201–9. [45] Saida A, Eloneva S, Fogelholm CJ, Fagerlund J, Nduagu E, Zevenhoven R. Integrated carbon capture and storage for an oxyfuel combustion process by using carbonation of Mg(OH)2 produced from serpentinite rock. Energy Procedia 2011;4:2839–46. [46] Faber R, Yan J, Stark F, Priesnitz S. Flue gas desulphurization for hot recycle oxyfuel combustion: experiences from the 30MWth oxyfuel pilot plant in Schwarze Pumpe. Int J Greenhouse Gas Control 2011;5S:S210–23. [47] Hu Y, Yan J, Li H. Effects of flue gas recycle on oxy-coal power generation systems. Appl Energy 2012;97:255–63.