petroleum engineering

T

Y a

T b

1

a

A R R A A

K C N M M

1

p m i C i m c r H i P u o h t p c i p

h 1

International Journal of Greenhouse Gas Control 50 (2016) 49–56

Contents lists available at ScienceDirect

International Journal of Greenhouse Gas Control

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 / i j g g c

he use of TiO2 nanoparticles to enhance CO2 absorption

u Zhang a, Bo Zhao a,∗, Jiazong Jiang b, Yuqun Zhuo a, Shujuan Wang a

Key laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory of CO2 Utilization and Reduction Technology, singhua University, Beijing 100084, China Key Laboratory of Condition Monitoring and Control for Power Plant Equipment, Ministry of Education, North China Electric Power University, Beijing 02206, China

r t i c l e i n f o

rticle history: eceived 29 September 2015 eceived in revised form 8 April 2016 ccepted 11 April 2016 vailable online 23 April 2016

a b s t r a c t

The enhancement of absorption of CO2 by propylene carbonate in the presence of TiO2 nanoparticles was investigated. The influences of solids loading and particle size of TiO2 nanoparticles on the absorption rate were studied experimentally. The results show that the gas absorption rate can be enhanced significantly in the presence of TiO2 nanoparticles. The CO2 absorption enhancement factor firstly increases and then decreases with the increases of solids loadings, which proves the existence of optimal solids loading. The

eywords: O2 absorption anofluid ass transfer enhancement ass transfer model

particle size is also a main factor, which affects CO2 absorption enhancement factor. As the particle size increases, the optimal solids loading gradually increases. A three-dimensional instantaneous numerous- particle di-mechanism model based on the shuttle mechanism as well as a micro-convection mechanism was developed. The results calculated by the model are close to the experimental results, which showed the model can predict experimental data very well.

© 2016 Elsevier Ltd. All rights reserved.

. Introduction

The global climate change has seriously affected the security and rosperity of human beings. Scientific research shows that the cli- ate change has an undeniable connection with the increase of CO2

n the atmosphere. So, it is crucial to control the CO2 concentration. urrent methods of CO2 sequestration can be divided into phys-

cal methods, chemical methods, physical-chemical absorption ethods, membrane methods, and biological methods based on

apturing principles. In physical methods, water-washing method, ectisol method, and propylene carbonate method are common. owever, water-washing method is limited by the low solubil-

ty of CO2 and rectisol method leads to high energy consumption. ropylene carbonate method is widely used because of the high sol- bility of CO2 in propylene carbonate, the low energy consumption f regeneration and low corrosion to steel. Propylene carbonate as other excellent properties, so it can be used in some indus- rial sector. For example, propylene carbonate can be applied on etrochemical industry to extract petroleum fraction. Propylene

arbonate method was first developed by Fluor Company in Amer- ca and then applied to natural gas purification, ammonia feed gas urification, hydrogen production, and other industrial sectors. In

∗ Corresponding author. E-mail address: [email protected] (B. Zhao).

ttp://dx.doi.org/10.1016/j.ijggc.2016.04.014 750-5836/© 2016 Elsevier Ltd. All rights reserved.

1978, propylene carbonate method was introduced into China to retrofit water-washing process of old synthetic ammonia plants, and then spread to soda plants, city gas, natural gas, methanol syn- thesis, and other sectors which needed gas decarbonization within the following few years. Propylene carbonate method is used to remove CO2 in synthetic ammonia plants operated at 0.98∼2.7 MPa now in China (Jianbin Huang, 2002).

The absorption of CO2 with propylene carbonate is a diffu- sion process. The resistance of liquid to mass transfer is the main resistance. Because of the low mass transfer coefficient of CO2 in propylene carbonate, the absorption tower should be very large—this leads to a high initial cost. To absorb CO2 sufficiently and reduce initial costs, it is necessary to enhance gas-liquid mass transfer.

Many studies (Ma et al., 2009a; Krishnamurthy et al., 2006; Kim et al., 2006a; Quicker et al., 1989; Alper and Ozturk, 1986) have shown that adding tiny particles to the liquid phase can accelerate the rate of gas-liquid mass transfer. G. Quicker et al. (Quicker et al., 1987) studied CO2 was absorbed from gas mixtures of CO2/N2 into 0.5 M Na2CO3/0.5 M NaHCO3 solutions containing various amounts of arsenite, in the absence and presence of finely powdered acti- vated carbon and kieselguhr. He found that gas absorption rates were increased measurably by the addition of fine activated car-

bon, while they were affected negligibly when fine kieselguhr particles were added.M.V. Dagaonkar et al. (Dagaonkar and Heeres et al., 2003) used a stirring reactor to study CO2 absorption in

50 Y. Zhang et al. / International Journal of Greenhouse Gas Control 50 (2016) 49–56

Nomenclature

As Surface area of nanoparticle, (m2) cA Gas concentration (mol/m

3) cL Gas concentration in the liquid bulk in the presence

of nanoparticles, (mol/m3) Cp Solids loading, (kg/m3) c∗ Gas concentration at the gas-liquid interface in the

presence of nanoparticles, (mol/m3) c∗A Concentration of gas A at the gas-liquid interface in

the presence of nanoparticles, (mol/m3) D Diffusion coefficient in nanofluid, (m2/s) D0 Diffusion coefficient in pure fluid, (m2/s) ds Particle diameter, (m) E Enhancement factor E∗ Simulated enhancement factor H Henry’s constant h Heat transfer coefficient, (W/m2 K) hm Convective mass transfer coefficient, (m/s) k Non-dimensional coefficient, k = Vg /HRTVl kf Thermal conductivity of fluid, (W/m·K) kL Mass transfer coefficient in the presence of nanopar-

ticles, (m/s) kL0 Mass transfer coefficient in the absence of nanopar-

ticles, (m/s) kq Absorption coefficient of the gas, (m/s) ms Mass of nanoparticle, (kg) Nu Nusselt number nA Mole number of gas, (mol) → n The normal vector Pe Berkeley number Pr Prandtl number pA End pressure of gas in the presence of nanoparticles,

(pa) pA

′ End pressure of gas in the absence of nanoparticles, (pa)

pA0 Initial pressure in the presence of nanoparticles, (pa) pA0

′ Initial pressure in the absence of nanoparticles, (pa)

q The adsorption amount of gas per unit mass of the nanoparticles, (mol/kg)

qm The maximum adsorption amount, (mol/kg) R Ideal gas constant r The distance from the center of the nanoparticle, (m) rs Particle radius, (m) S Gas-liquid interfacial area, (m2) Sc Schmidt number T Thermodynamic temperature, (K) t Absorption time, (s) Vg Volume of gas, (m3) Vl Volume of liquid, (m

3) Vs Volume of nanoparticle, (m3) � Velocity of nanoparticles, (m/s)

Greek symbols v Kinematic viscosity of liquid with nanoparticles,

(m2/s) v0 Kinematic viscosity of liquid without nanoparticles,

(m2/s) � Dynamic viscosity of nanofluid, (mPa s) �0 Dynamic viscosity of pure fluid, (mPa s)

� The interaction coefficient

� The residence time in the presence of nanoparticles,

(s)

�0 The residence time in the absence of nanoparticles, (s)

˚A Mass flux in the presence of nanoparticles, (mol/s)

hexadecane of TiO2 nanoparticles and found that the absorp- tion rate of CO2 reached 1.9 times that of pure hexadecane’s when solids loading of TiO2 nanoparticles was 10 kg/m3. Jiazong Jiang et al. (Jiang and Zhao et al., 2014) adopted a bubble reactor to study the effect of Al2O3 nanoparticles on CO2/MEA mass transfer and found that the mass transfer coefficient of CO2-MEA increased to 1.04-fold that of pure MEA’s at 0.6 kg/m3 solids loading. Israel Torres Pineda et al. (Pineda et al., 2012) studied the absorption of CO2 bubble in methyl alcohol in the presence of SiO2 nanoparticles and found that the enhancement factor reached to 1.10 when the volume fraction of SiO2 nanoparticles was 0.05%. Seyf et al. (Seyf and Nikaaein, 2012) studied the effects of particle size and the particle Brownian motion on the thermal performance of nanofluid flow in a micro-channel heat sink. However, there are few explanations for these results (Kim et al., 2006b; Ma et al., 2009b), and further investigation is urgently needed.

Many scholars have studied the fine particles enhancement of gas-liquid mass transfer. The current generally accepted mechanisms are the shuttle mechanism, the mechanism of mixed boundary layer, preventing bubble coalescence mecha- nism, and micro-convection mechanism. For example, Demmink et al. (Demmink et al., 2002) used fresh S particles as a dis- persed phase to study the absorption of C2H4, H2S and so on and formulated a surface renewal particle-to-interface adhesion model (SRPIA model) based on Danckwerts’ (unsteady state) surface renewal model. Brilman et al. (Brilman et al., 1998) established a heterogeneous, unsteady, multidimensional, many- particle model based on shuttle mechanism that is suitable for gas-liquid-solid three-phase systems. Zhang Dan (2006) proposed a three-dimensional instationary, heterogeneous, and irregu- larly distributed numerous-particle di-mechanism (TIHIND) model based on both the shuttle mechanism and hydrodynamic inter- actions. Many researchers have established the micro-convection model to explain the enhancement of thermal conductivity of nanofluids—this was shown to agree excellently with a wide range of experimental data (Patel et al., 2005; Ravi Prasher et al., 2006). Recently, Sheikholeslami et al. (Sheikholeslami et al., 2015; Sheikholeslami and Abelman, 2015; Sheikholeslami et al., 2014) adopted advanced simulation methods to investigate nanofluid flow and heat transfer—this will help study mass transfer.

In this paper, a stirred, self-designed cell was used to study the influence of solids loading and particle size of TiO2 nanoparticles on the absorption of CO2 in propylene carbonate. A three-dimensional instationary numerous-particle di-mechanism model was used to explain the data and predict the relationship between enhance- ment factor and solids loading.

2. Experiment

2.1. Experimental system

The experiment was conducted in a stirred cell and the schematic of the experimental system is shown in Fig. 1, which consisted of a stirred autoclave with pipes for feeding and discharg- ing the gas and liquid. In autoclave, the upper was gas zone and the lower was liquid zone. There was no agitation in absorption

process. The temperature could be controlled through circulating water system and the control precision was ±0.2 ◦C. The pressure and temperature in the stirred cells were measured by sensors and

Y. Zhang et al. / International Journal of Greenhouse Gas Control 50 (2016) 49–56 51

Fig. 1. Schematic of the experimental system: (1) Reaction autoclave, (2) Liquid stirrer, (3) Gas storage cylinder, (4) (5) Valves, (6) (10) Circulating water, (7) Tem- perature sensor, (8) Pressure sensor, (9) Electric motor, and (11) Computer.

Table 1 The parameters of the stirred cell.

The inside diameter of the vessel 82.22 mm The total vessel volume 1171 mL The gas-liquid interfacial area 5089.82 mm2

Table 2 Experimental operating conditions.

Parameters Values

Volume of propylene carbonate 500 mL Initial pressure of CO2 200 kPa Types of particles TiO2 Solids loading levels 0–1.6 kg/m3

Particle diameters 10, 20, 50 nm

r T

2

p a T b a a t w e

i g m i i s t a E

0 10 20 30 40 50 60 70

160

170

180

190

200

210

P re

ss ur

e (k

P a)

Time (min)

0 kg/m3

0.6 kg/m3

0.8 kg/m3

1.0 kg/m3

1.2 kg/m3

1.4 kg/m3

Fig. 2. The Pressure of Carbon dioxide with time for different TiO2 loadings with 10 nm nanoparticles at 25◦ C.

0 10 20 30 40 50 60

160

170

180

190

200 P

re ss

ur e

(k P

a)

Time (min)

10 nm 20 nm 50 nm

nanoparticle size is 10 nm. The conclusions above are not complicated that are obtained

Stirring speeds 0 r/min Temperature 25 ◦ C

ecorded digitally. The parameters of the stirred cell are listed in able 1.

.2. Experimental testing

TiO2 nanoparticles were purchased from Aladdin Industrial Cor- oration with 99.8% purity and a particle diameter of 10 nm, 20 nm, nd 50 nm. Propylene carbonate was purchased from Hong Ye ian Cheng Technology Ltd with 99.5% purity. The purity of car- on dioxide was over 99%. The experimental operating conditions re listed in Table 2. To produce the nanofluid, nanoparticles were dded to propylene carbonate. The solutions were then subjected o 60 min of ultrasonic vibration. Before the experiment, the vessel as air-tight. After confirming that the stirred cell did not leak, the

xperiments were performed. When the experiments began, the prepared nanofluid was fed

nto the stirred cell, and the vacuum pump was started to make the as dissolved in propylene carbonate discharge. When the vacuum et the requirement, the vacuum pump was closed and the heat-

ng system was started. When the temperature of the nanofluid ncreased to the desired temperature, CO2 was fed into the ves- el until the CO2 fixed pressure was 200 kPa. The pressure of CO2 hen decreased continuously as the absorption proceeded, and the

bsorption rate was calculated by measuring the pressure drop. ach set of experiment took 60 min and was repeated three times.

Fig. 3. The Pressure of Carbon dioxide with time for different TiO2 particle sizes at 1.0 kg/m3 solids loading, 25◦ C.

2.3. Data analysis

The pressure of CO2 removed with time for different solids load- ings is shown in Fig. 2. We take 10 nm nanoparticles as an example. From the figure, we can see that nanoparticles do increase the pressure decreasing rates and the decreasing rates are different at different solids loadings. We also find that the decreasing rates in the first two minutes are larger than that in the rest of time, which may be caused by the pressure fluctuation. What’s more, the aver- age decreasing rate reaches a maximum value at 1 kg/m3 solids loading.

The pressure of CO2 removed with time for different particle sizes is shown in Fig. 3. We take 1.0 kg/m3 solids loading as an example. From the figure, we can see that the average pressure decreasing rates are different at different particle sizes. What’s more, the decreasing rate reaches a maximum value when TiO2

from intuitive experimental data. Next, the indirect conclusions can be got through analyzing the data.

5 of Greenhouse Gas Control 50 (2016) 49–56

e d t

p

W o n c

t

i f

˚

W c t b a

a

c

W

p

c

W i

d

f

I e

H t

u

˚

E

2 Y. Zhang et al. / International Journal

CO2 can be regarded as an ideal gas because the pressure of the xperiments was low and the temperature was close to the stan- ard conditions. The following equation was achieved according to he ideal gas equation:

A = nART

Vg (1)

here pA is the pressure of CO2 in the stirred cell in the presence f nanoparticles, nA is the mole number of gas in the presence of anoparticles, T is the thermodynamic temperature in the stirred ell, Vg is volume of gas, and R is the universal gas constant.

Taking the derivative of both sides of Eq. (1) with respect to time , the following formula results:

d(nA) dt

= Vg RT

d(pA) dt

(2)

The mass flux ˚A that component A transfers to liquid phase n unit time in the presence of nanoparticles can be expressed as ollows according to Henry’s law:

A = kL S(c∗ − cL ) (3)

here kL is mass transfer coefficient in the presence of nanoparti- les, c∗ is molar concentration of component A at phase interface in he presence of nanoparticles, cL is molar concentration in the liquid ulk in the presence of nanoparticles, and S is gas-liquid interfacial rea.

At the gas-liquid interface, the following equation can be chieved according to Henry’s law:

∗ = HpA (4)

here H is Henry’s constant. At the same time, we assume that gas A dissolved in a liquid

hase is uniform, and cL results from the following equation:

L = Vg

RTVl (pA0 − pA) (5)

here Vl is the volume of liquid in the stirred cell and pA0 is the nitial pressure of gasA in the presence of nanoparticles.

According to the equations above, the following formula can be erived:

d(nA) dt

= Vg RT

d(pA) dt

= −˚A = −kL S(c∗ − cL ) (6)

Combining formula (4) and (5) into formula (6), results in the ollowing differential equation:

Vg RT

d(pA) dt

= −kL S[HpA − Vg

RTVl (pA0 − pA)] (7)

n accordance with the initial condition: t = 0, pA = pA0, the differ- ntial equation can be solved.

k

1 + k ln pA0

(1 + k)pA − kpA0 = kL

S

Vl t (8)

ere, k = VgHRTVl . Thus, the mass transfer coefficient kL can be got hrough Eq. (8).

The mass flux ˚Athat component A transfers to liquid phase in nit time can also be expressed below:

A = − Vg RT

d(pA) dt

(9)

The enhancement factor E can be defined as:

= gasabsorptionfluxinthepresenceofnanoparticles gasabsorptionfluxintheabsenceofnanoparticles

(10)

Fig. 4. The schematic diagram of mass transfer.

According to the equation above, the enhancement factor E can be expressed below:

E = (pA0 − pA)Vg /RTt (pA0

′ − pA′ )Vg /RTt = pA0 − pA

pA0 ′ − pA′

(11)

Where pA0 ′ and pA

′ are initial and end pressure of gas in the absence

of nanoparticles. The enhancement factor E can be easily and correctly got

through Eq. (11).

3. Theoretical model

Since nanofluids were first described, they have been studied extensively by many scholars. Some possible mechanisms have also been proposed. In this paper, we pay attention to the shuttle mechanism and micro-convection mechanism.

(1) Shuttle mechanism

As the shuttle mechanism describes, when the mass transfer starts, nanoparticles will move to the gas-liquid interface. Nanopar- ticles will absorb the gas and return to the liquid bulk to desorb. In this way, nanoparticles regenerate. Because nanoparticles move between gas-liquid interfaces and liquid bulk circularly, the gas- liquid mass transfer can be enhanced.

(2) Micro-convection mechanism

As the micro-convection mechanism describes, nanoparticles may cause fluctuation of liquid around because of Brownian move- ment. Thus, in the liquid bulk, there is convective mass transfer that enhances the gas-liquid mass transfer.

In this paper, a new model was pointed out based on the two above mechanisms.

3.1. Mass transfer differential equation

For nanoparticles with adsorptive characteristics, the shuttle mechanism and micro-convection mechanism should be consid- ered simultaneously. A schematic diagram of mass transfer using only one particle as an example is shown in Fig. 4. As Fig. 4 describes, when mass transfer begins, the nanoparticles will move to the gas- liquid interface. Nanoparticles will absorb the gas and return to liquid bulk to desorb. Nanoparticles may cause fluctuation of liquid

because of Brownian movement. Thus, we think that the process of desorption is convective mass transfer. The mass transfer coeffi- cient can be achieved through analogy between heat transfer and mass transfer.

Y. Zhang et al. / International Journal of Gree

w T d d n n a c c

( s fi e t t b t ı m s

c s

W fi e

D

W d d

t

a

W o d

J0 = −D0 |x=0dAdt (24)

Fig. 5. The diagram of the model.

Because the actual conditions of mass transfer are complicated, e should simplify them and make the following assumptions: 1)

he gas-liquid interface is flat; 2) The solids and gas phases have no irect contact; 3) Nanoparticles near gas-liquid interface are evenly istributed; 4) Multiple particles affect the mass transfer; 5) Every anoparticle is spherical and wrapped by liquid layer whose thick- ess is ıc . 6) Convective mass transfer developed between liquid nd nanoparticle in this liquid layer and the mass transfer coeffi- ient is hm; and 7) The mass transfer resistance inside nanoparticles an be ignored because the particle size is small.

With these assumptions, and similar to the analysis of Nagy et al. Nagy et al., 2007), the computational domain can be chosen as hown in Fig. 5. We use only one nanoparticle as an example in the gure for convenience. According to Nagy et al. (Sheikholeslami t al., 2014), the distance, L, between the first nanoparticles and he gas-liquid interface can change between 0 and �x, where �x is he distance between two nanoparticles which can be determined y �x = d

( 1/ϕ1/3 − 1

) , where ϕ is the nanoparticle volume frac-

ion. In these simulations, L can be chose as �x/2 and the values of y, ız can be chosen as �x + ds. What’s more, ıx is the distance of ass transfer in the residence time � which can be determined by

imulation. In region 1—the continuous phase—the mass transfer equation

an be derived according to Fick’s second law of molecular diffu- ion:

∂cA ∂t

= D( ∂ 2 cA

∂x2 + ∂

2 cA

∂y2 + ∂

2 cA

∂z2 ) (12)

here cA is gas concentration in region 1 and D is the diffusion coef- cient of gas in nanofluid that can be determined by the following quation:

= D0 �0 �

(13)

here D0 is the diffusion coefficient of gas in pure fluid, � is the ynamic viscosity of nanofluid that can be got from experimental ata, and �0 is the dynamic viscosity of pure fluid.

In region 2—the region of convective mass transfer—the mass ransfer equation can be written as follows:

∂cA,d ∂t

= D( ∂ 2 cA,d

∂x2 + ∂

2 cA,d

∂y2 + ∂

2 cA,d

∂z2 ) − hmas(cA,d − cA,s) (14)

s = As Vs

= 4 ( ds2 )

2

4 3 (

ds 2 )

3 = 6

ds (15)

here cA,d is gas concentration in region 2, As is the surface area of ne nanoparticle, Vs is the volume of one nanoparticle,ds is particle iameter, and hm is convective mass transfer coefficient.

nhouse Gas Control 50 (2016) 49–56 53

In region 3, according to conservation of mass, the following equation can be achieved:

ms ∂q ∂t

= hmAs(cA,d − cA,s) (16)

Where ms is the mass of one nanoparticle, cA,s is gas concentration in region 3, and q is the adsorption amount of gas per unit mass of the nanoparticles that is described by a Langmuir-type adsorption isotherm.

q = qm kqcA,s

1 + kqcA,s (17)

Here, qm is maximum adsorption amount, kq is absorption coeffi- cient of the gas.

The necessary initial condition is:

t = 0, x ≥ 0, cA = 0 (18)

The necessary boundary conditions are:

t > 0, x = 0, cA = c∗A x = ıx, cA = 0

y = 0/ıy, ∂cA ∂y

= 0

z = 0/ız , ∂cA ∂z

= 0

(19)

Where c∗ A

is concentration of gas A at the gas-liquid interface. On the interface between region 1 and region 2, the boundary

conditions are:

→ n · (−D∇cA,d) = hm(cA,d − cA,s) (20) cA,d = cA (21)

Where → n is the normal vector that points to region 2. The complex mass transfer differential equations and boundary

conditions were solved numerically. The equations were solved by finite element method to obtain concentration distribution at any time and any place. After getting the concentration distribution, the total mass flux JA in the presence of nanoparticles can be achieved below:

JA = ∫

�

∫ S

−D ∂cA ∂x

|x=0dAdt (22)

The time-averaged flux follows from:

JA = 1 �

∫ �

∫ S

−D ∂cA ∂x

|x=0dAdt (23)

Where S is gas-liquid interface area and � is residence time in the presence of nanoparticles.

According to Lamont and Scott (Lamont and Scott, 1970), the

residence time � can be expressed as: � = �0 (

/ 0 )1/2

, where 0 is kinematic viscosity of pure liquid, is the kinematic viscosity of nanofluid, and �0 is residence time of an infinitesimal liquid element without nanoparticles which can be obtained from Hig- bie penetration theory as:�0 = 4D0/

( kL0

2 )

, where kL0 is the mass transfer coefficient of gas in pure liquid.

The total mass flux J0 in the absence of nanoparticles can be expressed below:∫ ∫

∂c

�0 S ∂x

Where c is gas concentration in pure liquid which can be easily got through solving basic mass transfer differential equations.

5 of Greenhouse Gas Control 50 (2016) 49–56

J

E

3

s

v S i �

W fl

t l

W

t b

a

ı

F s b e u m s ( h

N

H t ( b

N

f S

S

4 Y. Zhang et al. / International Journal

The time-averaged flux can be expressed:

0 = 1 �0

∫ �0

∫ S

−D0 ∂c ∂x

|x=0dAdt (25)

So, the simulated enhancement factor E∗ can be obtained:

∗ = JA J0

(26)

.2. Model parameters

The relevant parameters in the model should be determined to olve the model.

We first determined the thickness ıc of the liquid layer. The elocity of nanoparticle because of Brownian motion is very small. o, the flow around nanoparticle is a creeping flow whose velocity s a function of distance r from the center of the particle and angle . The function relationship is as follows:

�r = � cos �(1 − 3 2

rs r

+ 1 2

rs 3

r3 )

�� = −� sin �(1 − 3 4

rs r

− 1 4

rs 3

r3 )

(27)

hen � is 90◦ and �� is equal to 0.99�, we get: r = 75rs. Thus, the ow-boundary-layer thickness ı is equal to 74rs.

According to the results of fluid flowing across isothermal plate, he ratio of flow-boundary-layer thickness and thermal-boundary- ayer thickness is:

ı

ıt ∼= Pr1/3 (28)

here ıt is thermal-boundary-layer thickness. According to the similarity of heat transfer with mass transfer,

he ratio of flow-boundary-layer thickness and mass-transfer- oundary-layer thickness can be obtained:

ı

ıc ∼= Sc1/3 (29)

Thus, the mass-transfer-boundary-layer thickness can be chieved from the following equation:

c = ı

Sc1/3 = 75rs − rs

( D ) 1/3

(30)

We then determine the convective mass transfer coefficient hm. irstly, we consider the heat convection whose corresponding Nus- elt number can be calculated through the equation Nu = hds/kf etween the fluid and one nanoparticle immersed in a fluid. In this quation, h is the heat transfer coefficient between sphere and liq- id, and kf is the thermal conductivity of fluid. Because Brownian ovement of the nanoparticle is extremely weak and the corre-

ponding Reynolds number Re is much lower than 1, Acrivos et al. Acrivos and Taylor, 1962) gave the Nusselt number of convective eat transfer between sphere and liquid:

u = 2 + 0.5Pe + 0.25Pe2 ln Pe + 0.0334Pe2 + · · · (31) ere, Pe = RePr. Because the velocity of the nanoparticle is so small

hat Pe is far lower than 1, every term after the second term of Eq. 31) can be ignored. The Nusselt number of convective heat transfer etween nanoparticle and liquid can be simplified as:

u = 2 + 0.5RePr (32)

According to the similarity of heat transfer with mass trans-

er, Nu is in analogy with Sh, and Pr is analogous to Sc. Here, h = hmds/D, Sc = /D. Thus, the equation can be transformed: h = 2 + 0.5ReSc (33)

Fig. 6. The viscosity of the nanofluid for various TiO2 nanoparticle loadings with 10 nm nanoparticles.

Because there are lots of nanoparticles in nanofluids that inter- act with each other all the time, the interaction coefficient� is introduced. Thus, the equation is transformed to be:

Sh = 2 + 0.5�ReSc (34)

hm = (2 + 0.5�ReSc) · D

ds (35)

Here, � can be determined by fitted curves of experimental data. Terms k and qm can be determined by the least squares method.

4. Results and analysis

4.1. The effects of solids loading on viscosity

The variation in fluid viscosity as a function of solids loading at 25◦C is shown in Fig. 6. In this figure, the particle size is 10 nm. From the figure, we can see that the viscosity of the nanofluid increases as the solids loading increases. Furthermore, the increasing range is not large. Thus, pipes will not be blocked, if a nanofluid is used in engineering applications.

4.2. Effects of solids loading on enhancement factor E and mass transfer coefficient kL

The effects of solids loading were studied via experiments with different nanoparticle loadings (0.6-1.4 kg/m3) at 25 ◦C and 10 nm nanoparticles. The variations in enhancement factor and mass transfer coefficient are presented in Figs. 7 and 8 with various solids loading levels for TiO2 nanoparticles. The carbon dioxide absorp- tion enhancement factor increases as a function of solids loading levels up to a plateau and then decreases. Thus, there is an optimal solids loading.

This phenomenon can be explained by the following mech- anism. When the solids loading level is small and suboptimal, there are more nanoparticles transporting the gas, and the micro- convection caused by Brownian motion becomes more severe as the loading of solids increases. Thus, the enhancement factor will gradually increase. When the solids loading is large and higher than

optimal, the viscosity of the nanofluid increases and the interac- tion between nanoparticles becomes stronger with increases in the solids loading levels. Thus, the enhancement factor will gradually decrease.

Y. Zhang et al. / International Journal of Greenhouse Gas Control 50 (2016) 49–56 55

0.6 0.8 1.0 1.2 1.4

1.35

1.40

1.45

1.50

1.55

1.60

1.65 E

Cp (kg/m3)

Fig. 7. Carbon dioxide absorption enhancement factor for various TiO2 nanoparticle loadings with 10 nm nanoparticles at 25 ◦ C.

F n

c p

4

t 1 a f l p f s r f q i

0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

E

Cp (kg/m3)

10 nm 20 nm 50 nm

Fig. 9. Carbon dioxide absorption enhancement factor for various TiO2 nanoparticle loadings levels at 25 ◦ C.

0.6 0. 8 1.0 1. 2 1. 4

1.35

1.40

1.45

1.50

1.55

1.60

1.65

E

Cp (kg/m3)

Experimental Calculated

Fig. 10. Comparisons of numerical and experimental results for various solids load- ings of 10 nm TiO2 particles at 25 ◦ C.

Table 3 Simulation parameters.

experimental results

ig. 8. Mass transfer coefficient of carbon dioxide absorption for various TiO2 anoparticle loadings with 10 nm nanoparticles at 25 ◦ C.

Fig. 8 shows that the variation trend of the mass transfer oefficient is similar to the enhancement factor. Of course, this henomenon can be explained by the above-mentioned reasons.

.3. Effects of particle size on enhancement factor E

Fig. 9 shows the change in the enhancement factor with a par- icle size of TiO2 for a temperature of 25 ◦C and particle sizes of 0 nm, 20 nm, and 50 nm. When the solids loading level is small nd consistent, the enhancement factor gradually decreases as a unction of increasing particle size. When the solids loading level is arge and consistent, the enhancement factor gradually increases as article size increases. This phenomenon can be explained by the ollowing mechanism. When the loading is small and consistent, maller particles result in more nanoparticles transferring the gas esulting in more severe micro-convection. Thus, the enhancement

actor will be larger. When the loading is large and consistent, the uantity of nanoparticles in the nanofluid is lower and the viscos-

ty of the nanofluid decreases as particle size increases. Thus, the

D0 /m 2 · s−1 kq /m3 · mol−1 qm /mol · kg−1 c∗A /mol · m−3 �0 /s �

8.25 × 10−10 5.6 × 10−4 5.94 292.69 0.1 0.1

enhancement factor is larger. In addition, the particle size cannot be very large or else it will precipitate.

From the figure, we see that the optimal loading gradually increases with increases in particle size. This is because the smaller the particle size is, the larger the viscosity of the nanofluid is—this gives slower rates of gas-liquid absorption. We assume that the viscosity of nanofluid was similar at optimal loading. Here, larger particles give larger loading levels of the corresponding solids.

4.4. Comparisons of the numerical predictions with the

Numerical simulation was made using the parameters listed in Table 3.

56 Y. Zhang et al. / International Journal of Gree

0.8 1. 0 1.2 1. 4 1.6 1. 8 1.0

1.1

1.2

1.3

1.4

1.5

1.6

E

Cp (kg/m3)

Experimental Calculated

Fig. 11. Comparisons of numerical and experimental results for various solids load- ings of 20 nm TiO2 particles at 25 ◦ C.

0.8 1.0 1.2 1.4 1.6 1.8 1.1

1.2

1.3

1.4

1.5

1.6

1.7

E

Cp (kg/m3)

Experimental Calculated

F i

l i a w

l m

5

e i i o t i t i

simulation of magnetohydrodynamic natural convection heat transfer of al2O3-water nanofluid in a horizontal cylindrical enclosure with an inner triangular cylinder. Int. J. Heat Mass Transf. 80, 16–25.

Zhang Dan, 2006. Study on Mechanism and Model of Gas-Liquid Mass Transfer Enhancement by Dispersed Particles[D]. Tianjin University, Tianjin.

ig. 12. Comparisons of numerical and experimental results for various solids load- ngs of 50 nm TiO2 particles at 25 ◦ C.

The numerical predictions on the influence of the solids loading evels on the enhancement factor are compared with the exper- mental data in Figs. 10–12. We also find that the carbon dioxide bsorption enhancement factor firstly increases and then decreases ith the increases of solids loadings through numerical simulation.

The results in Figs. 10–12 have average errors between the calcu- ated and experimental results of less than 10%, indicating that the

odel is reliable and can predict the experiments to some extent.

. Conclusions

The effects of nanoparticles (TiO2) on the CO2 absorption nhancement were experimentally studied for various work- ng conditions. The results show that the viscosity of nanofluid ncreases with the increases in solids loading levels. There is an ptimal nanoparticle loading. When the loading is lower than

he optimal loading, the enhancement factor increases with the ncreases of loading levels. When the loading is higher than he optimal loading, the enhancement factor decreases with the ncreases of loading levels. Particle size is also one of the most

nhouse Gas Control 50 (2016) 49–56

important factors which affect CO2 absorption rate. When the solids loading is at low level, smaller nanoparticles result in larger enhancement factors. When the solids loading is at high level, larger nanoparticles create larger enhancement factors. The opti- mal solids loading level increases with the increase of particle size. The calculation data are close to the experimental results. The model can predict the experiments well.

Acknowledgement

This work was supported by the National Natural Science Foun- dation of China (No. 51376108).

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