an overview: reaction mechanisms and modelling …mineral-water) reactions, such as...

Aerosol and Air Quality Research, 18: 829–848, 2018 Copyright © Taiwan Association for Aerosol Research ISSN: 1680-8584 print / 2071-1409 online doi: 10.4209/aaqr.2018.03.0093

Review

An Overview: Reaction Mechanisms and Modelling of CO2 Utilization via Mineralization Shu-Yuan Pan1**, Tung-Chai Ling2, Ah-Hyung Alissa Park3,4, Pen-Chi Chiang1,5* 1 Carbon Cycle Research Center, National Taiwan University, Taipei 10672, Taiwan 2 Key Laboratory for Green and Advanced Civil Engineering Materials and Application Technology of Hunan Province, College of Civil Engineering, Hunan University, Changsha 410082, China 3 Department of Chemical Engineering; Department of Earth and Environmental Engineering, Columbia University, New York, NY 10027, USA 4 Lenfest Center for Sustainable Energy, Columbia University, New York, NY 10027, USA 5 Graduate Institute of Environmental Engineering, National Taiwan University, Taipei 10673, Taiwan ABSTRACT

Accelerated carbonation using alkaline solid wastes has been considered an effective approach to mineralizing flue gas CO2 from industries or power plants. Despite its recent progress, mechanistic understanding and modelling at interface levels are still needed to control the reactivity and equilibrium of the reaction system. This review focuses on several phenomenological models for accelerated carbonation that look at the solid-fluid interface. We first illustrate the principles of kinetic and mass transfer driven reactions for CO2-mineral-water systems. Then, we provide an overview into the reaction mechanisms and modelling for CO2 mineralization including leaching-precipitation model, shrinking core model and surface coverage model. Advanced models considering multiple mechanisms, such as two-layer diffusion model, are also discussed. Finally, the perspectives and prospects are provided to shine a light on future directions, including incorporation of structural and physical properties in phenomenological models, identification of dynamic speciation by in-situ high-resolution equipment, and integration of heat transfer in reaction modelling for system optimization. Keywords: Mechanism; Diffusion; Kinetics; Shrinking core model; Surface coverage model. INTRODUCTION

Numerous approaches to carbon capture, storage and utilization have been evaluated to mitigate rapid anthropogenic CO2 emissions in the atmosphere, such as adsorption on modified carbon surfaces (Adelodun et al., 2017) or carbon aerogels (Xie et al., 2017), accelerated carbonation (Gadikota and Park, 2014), biological fixation (Su et al., 2017), chemical looping (Ku et al., 2017), assimilation by vegetation (Yu et al., 2017), and geological storage (Jean et al., 2016; Jen et al., 2017). Accelerated carbonation using alkaline solid wastes has been considered an effective approach to mineralizing flue gas CO2 from * Corresponding author.

Tel.: 886-2-2362-2510; Fax: 886-2-2366-1642 E-mail address: [email protected]

** Corresponding author. Tel.: 886-2-3366-9324; Fax: 886-2-2366-1642 E-mail address: [email protected]

industries or power plants (Li et al., 2016). Accelerated carbonation, originally proposed by Seifritz (1990), mimics and accelerates natural weathering to a timescale less than a few hours. It involves gaseous CO2 reacting with metal-oxide bearing materials (mostly calcium and/or magnesium oxides) in the presence of moisture to form stable and insoluble carbonate precipitates. From the viewpoint of water chemistry, the affinity of metal oxides to form carbonate precipitates replies on (i) chemisorption strength to carbonate ions (or gaseous CO2) at the fluid-solid interface, (ii) number of active basic sites at the surface of the particle, and (iii) solubility product constant (Ksp) in the case of aqueous carbonation. In general, CaO and MgO are the most favourable metal oxides in reacting with CO2 (Pan et al., 2012).

Alkaline solid wastes are suitable feedstock for CO2 mineralization via accelerated carbonation. These solid wastes are usually produced in a large amount from nearby CO2 emission sources. Some examples of alkaline solid wastes as feedstock for CO2 mineralization include blast furnace slag (Ukwattage et al., 2017), converter slag (Said et al., 2013), electric arc furnace slag (Pan et al., 2017),

Pan et al., Aerosol and Air Quality Research, 18: 829–848, 2018 830

ladle furnace slag (Araizi et al., 2016), municipal solid waste incinerator bottom ash (Um and Ahn, 2017), red gypsum (Azdarpour et al., 2017), circular fluidized bed fly ash (Pan et al., 2016a), construction and demolition wastes (Ben Ghacham et al., 2017; Kaliyavaradhan and Ling, 2017), and mine tailings (Entezari Zarandi et al., 2017; Mouedhen et al., 2017). Several innovative approaches such as pH swing (Zhao et al., 2013) are also developed to increase the leaching rate of reactive phases from solid matrix into the solution. In general, calcium-bearing minerals, such as CaO, Ca(OH)2 and CaSiO3, are the major phases participating in the accelerated carbonation reaction using alkaline solid wastes.

Despite recent progress on developing various types of processes for CO2 mineralization, mechanistic understanding is still needed to unlock CO2 mineralization at interface levels for controlling reaction pathways and rates. In this article, we review the reaction mechanism and coupled modelling for CO2 mineralization via accelerated carbonation that are looking at the solid-fluid interfaces. We first illustrate the principles of kinetic and mass transfer driven reactions for CO2-mineral-water systems, and then provide an overview into the reaction mechanisms and modelling for CO2 mineralization. We review the progress of several commonly used classical models for the heterogeneous (CO2-mineral-water) reactions, such as leaching-precipitation model, shrinking core model and surface coverage model. Several advanced models considering multiple mechanisms, such as two-layer diffusion model, are also discussed. KINETIC AND MASS TRANSFER DRIVEN REACTIONS FOR CO2-MINERAL-WATER SYSTEMS

The effect of key operating parameters on the performance of reaction kinetics and mass transfer for CO2 mineralization is strategically important for system optimization. In general, CO2 mineralization using alkaline solid wastes can be simply described by three simultaneous steps of reactions: (i) dissolution of gaseous CO2 into a liquid phase; (ii) hydration and leaching of CO2-reactive components from a solid phase; (iii) nucleation and growth of carbonate precipitates. In this section, we illustrate the theoretical considerations of kinetic and mass transfer driven reactions for CO2-mineral-water systems. Tools for Modelling Equilibrium and Mechanisms

The equilibrium of the heterogeneous (CO2-mineral-water) reaction system depends on numerous factors and parameters, such as temperature, pressure, pH of the solution, and the mixing extent. The thermodynamic modelling can assess the saturation state of system, pH changes, and reaction rate with a complex chemistry and varying solid-fluid interfaces. A sophisticated numerical simulation on thermodynamics can be performed by a variety of codes, such as PHREEQC (Swanson et al., 2014; Mun et al., 2017), GEMS (Azad et al., 2016), Outokumpu HSC (Teir et al., 2007), and TOUGHREACT (André et al., 2015), to determine the equilibrium parameters of reaction system

and thus improve the understanding of reaction mechanism. Thermal analyses are commonly used as rapid methods

for the quantification of the carbonate products, e.g., carbonation conversion, in the reacted samples. Due to the chemical complexity of alkaline wastes and various ways to interpret thermogravimetric curves, it is difficult to evaluate the carbonation conversion and capacity of different solid wastes in the literature on the same basis. Pan et al. (2016b) proposed an integrated thermal analysis for determining carbonation parameters (i.e., CO2 uptake and carbonation conversion) in alkaline solid wastes based on thermogravimetric, derivative thermogravimetric, and differential scanning calorimetry. They modified the interpretation of thermal analysis by considering the consecutive weight loss of specimen between 200 and 900°C, which was attributed to the decomposition of hydrated compounds. This proposed methodology can effectively evaluate the CO2 fixation capacity of alkaline solid wastes, thereby providing more accurate and precise data for subsequent system modelling and process assessment.

Advanced techniques on mineral solids, such as in-situ X-ray diffraction (Cizer et al., 2012), carbon (δ13C) and oxygen (δ18O) isotope (Gras et al., 2017), and nuclear magnetic resonance (Ashraf and Olek, 2018), can assist in characterizing the changes in physico-chemical properties during the reactions. Gras et al. (2017) performed an isotopic analysis for elucidating the mechanisms of in-situ natural weathering using waste rocks and mining tailings from the Dumont Nickel Project at Quebec. They proposed three major steps that control the rate of CO2 uptake, as shown in Fig. 1: (i) diffusion of gaseous CO2 into unsaturated phases such as the porous medium, (ii) dissolution of gaseous CO2 in interstitial water, and (iii) precipitation of metal carbonates from the interstitial water. In general, natural weathering is controlled by diffusion of atmospheric CO2 toward the center of the minerals due to low CO2 concentration and moisture in the atmosphere, as well as insufficient advection Gras et al. (2017).

Similar finding was also found that the rate-limiting step in passive carbonation should be the dissolution of atmospheric CO2 into interstitial water (Wilson et al., 2010). Other potential mechanisms influencing the compositions of interstitial water may include evaporation, bedrock carbonate dissolution, and microbial activities such as photosynthesis reactions (Gras et al., 2017). Liang et al. (2017) gave an intensive review on four major mechanisms that trap CO2 in the pores of subsurface, namely (i) structural trapping, (ii) residual trapping, (iii) dissolution trapping, and (iv) mineral trapping, for modelling the CO2-solid-fluid wettability. Both the structural and residual trappings are considered to be dominated by capillary action, and control by wettability in the porous media. In a well mixing system, the reaction with calcium should be the rate-limiting step (Mitchell et al., 2009). Molecular Diffusion at Interface Levels

The non-catalytic heterogeneous reaction with porous particles is a complex system, which involves a number of physical (e.g., mass transfer and diffusion through interfaces)


Fig. 1. A process-based conceptual model for carbonation reaction using waste rocks and mineral processing tailings with the isotope fractionation. Field experiments were conducted at the Dumont Nickel Project (Abitibi, Quebec) site. Adapted from the literature (Gras et al., 2017).

and chemical (e.g., reaction) phenomena. Although the porous network could be complex, Benedetti (2014) suggests that the pore size distribution of particles during reaction should be considered in determining the reaction kinetics. It may also be necessary to consider the effects of heat transfer (e.g., exothermic or endothermic reactions) in the surrounding fluid or in the interior of the porous particle. For aqueous carbonation using alkaline solid wastes, there are four major resistances to molecular diffusion (Fig. 2): Bulk diffusion: mass transfer of CO2 from the bulk

flow (i.e., the gas phase) to the liquid film Inter-particle diffusion: the CO2-related species diffuse

within the liquid film through molecular diffusion among each particle

Intra-particle diffusion: the CO2-related species diffuse inside the pore network of the particle

Product layer diffusion: during the reaction, a layer of carbonate products is formed on the surface of particles. Afterwards, the CO2-related species much be adsorbed on and then diffuse through the product layer to reach the surface of unreacted solid matrix.

One of the technical challenges in CO2 mineralization is the slow dissolution rate of gaseous CO2 into the liquid phase (Pei et al., 2017). Therefore, sufficient mass transfer among phases is a strategical key to effective carbonation for CO2 mineralization. Accelerated carbonation is usually regarded as a diffusion controlled reaction (Chang et al., 2012b; Pan et al., 2012). Mattila et al. (2012) found that effective mixing would significantly reduce the reaction time to reach equilibrium. In most cases of carbonation, the resistance of the product layer increases with the thickness of the product layer on the surface of the particle.

Due to the inherent properties of the carbonation reaction, a well-designed reactor with efficient mass transfer between the gas and liquid phases are required to achieve cost effectiveness. AN OVERVIEW INTO REACTION MECHANISM AND MODELING FOR CO2 MINERALIZATION

Prior to the process scale-up and optimization, it is imperative to obtain the key process data for reactor design, such as reaction kinetics, diffusivity of the reactant and mass transfer coefficient. Kinetic analyses can effectively characterize the mechanistic factors that control the reactivity and equilibrium of the reaction system. For the sake of simplicity, a number of reasonable assumptions is typically considered to avoid complicated calculations. Benedetti (2014) reviewed the kinetic models for non-catalytic fluid-solid reactions, including the grain model (i.e., assuming non-porous spherical grains) and the random pore model (i.e., considering particle porosity). In the grain model, it is assumed that the solid particle consists of a matrix of dense and porous grains with shapes of a sphere, a cylinder or a flat plate. In contrast, the pore model describes the pore network by a collection of capillaries with a cylindrical shape, which may overlap in the course of reaction. Several studies have applied the classical (theoretical) models (e.g., random pore model (Bhatia and Perlmutter, 1983), surface coverage model (Pan et al., 2014)) and/or the grain models (e.g., crackling core model (Farhang et al., 2017) and shrinking core model (Lekakh et al., 2008; Chang et al., 2012a)), for evaluating the performance of leaching and/or carbonation steps for CO2


Fig. 2. Types of resistances for molecular diffusion in aqueous carbonation, including bulk diffusion, inter-particle diffusion, intra-particle diffusion, and product layer diffusion.

mineralization. Several advanced computational approaches, such as saturation state model (Zeebe and Westbroek, 2003), dissolution-precipitation model (Lagasa, 1995), and moving-sharp-interface model (Muntean et al., 2011), have also been developed for determining the kinetics of CO2 mineralization. In this section, we illustrate two theoretical approaches to evaluating reaction kinetics, including solid-state-reaction approach and transition-state-theory approach. Solid-State-Reaction Approach

CO2 mineralization using alkaline solid wastes via accelerated carbonation is a heterogeneous and irreversible fluid-particle reaction. CO2-bearing compounds diffused from the bulk fluid phase and then either (i) permeated into the mineral matrix through micropores and reacted with reactive components, or (ii) directly reacted with reactive components leached out from the mineral matrix at water (fluid)-mineral (solid) interfaces. In this case, the external mass transfer from bulk gas phase was neglected. The reaction kinetics of a general solid-state reaction can be described by the law of mass action, as shown in Eq. (1), associated with Arrhenius theory.

dXk f X

dt (1)

where X is the carbonation conversion of solid wastes (-), t is the reaction time (s), k is the reaction rate constant, and f(X) is an algebraic function determined by reaction mechanisms. The reaction rate constant (k) is dependent on the reaction temperature according to the Arrhenius’s equation (Eq. (2)): k = A·exp((–Ea)⁄RT) (2) where A, known as the pre-exponential factor, represents the frequency of collisions in the correct orientation (s–1), Ea is the apparent activation energy for the reaction (kJ mol–1), T is the reaction temperature (K), and R is the universal gas constant (i.e., 8.314 J K–1 mol–1).

The function f(X) can be generally expressed by Eq. (3): f(X) = C·Xm (1 – X)n [–ln(1 – X)]p (3) where m, n, and p are empirically obtained exponent factors depending on the reaction mechanism, and one of them should always be zero. Eq. (1) can be solved and expressed by Eq. (4), in terms of an algebraic function of g(X). g(X) = kt (4)

Table 1 summarizes several commonly employed functions of solid-state reactions with their associated mechanisms. Several studies on mineral carbonation have applied the classic solid-state reactions to describe the reaction behaviours, such as wet carbonation (Um and Ahn, 2017) and carbonation curing (Wang et al., 2017). For instance, the experimental data of accelerated carbonation can fit the theoretical functions derived from Eq. (5). By taking the logarithmic form, the obtained equation shows a linear relationship of ln [(1 – (1 – X)1/3] and ln t, as indicated by Eq. (6). When the n value equals one, the chemical reaction at the phase boundary (such as the unreacted core surface) is the rate-limiting step. Whereas the n value equals two, the diffusion through the product layer of the particle becomes the rate-determining step. [1 – (1 – X)1⁄3]n = k·t (5)

1/3 1 1ln 1 1 X ln lnt k

n n

(6)

Um and Ahn (2017) applied the theoretical functions to

evaluate the kinetics of wet carbonation reaction for bottom ash. They found that, during the initial 20 min of carbonation, the rate-limiting step should be the phase-boundary reaction controlled mechanism at the interfaces of water film and the surface of bottom ash. As the reaction proceeded, the rate-limiting step switched to the diffusion-controlled mechanism through the product layer.


Tab

le 1

. Kin

etic

Fun

ctio

ns o

f S

olid

-Sta

te R

eact

ions

and

thei

r A

ssoc

iate

d M

echa

nism

.

Con

trol

led

step

M

echa

nism

Sy

mbo

l F

unct

ion

f(α)

in E

q. (

1) a

g(α)

= k

t in

Eq.

(2)

a

Rem

arks

R

ando

m n

ucle

atio

n an

d nu

clei

gro

wth

F

irst

ord

er r

ando

m n

ucle

atio

n F

1, A

1 (1

– X

) –

ln (

1 –

X)

R

ando

m n

ucle

atio

n A

3/2

(3/2

) (1

– X

) [–

ln (

1 –

X)]

1/3

(– ln

(1

– X

))2/

3 A

vram

i-E

rofe

v eq

. B

i-di

men

sion

al n

ucle

atio

n A

2 2

(1 –

X)

[– ln

(1

– X

)]1/

2 (–

ln (

1 –

X))

1/2

Avr

ami-

Ero

fev

eq.

Thr

ee-d

imen

sion

al n

ucle

atio

n A

3 3

(1 –

X)

[– ln

(1

– X

)]2/

3 (–

ln (

1 –

X))

1/3

Avr

ami-

Ero

fev

eq.

Bra

nchi

ng n

ucle

i A

u X

(1

– X

) ln

(X

/ (1

– X

))

Pro

ut-T

omki

ns e

q.

Che

mic

al r

eact

ion

One

and

a h

alf

orde

r F

3/2

2(1

– X

)3/2

(1 –

X)–1

/2 –

1

S

econ

d-or

der

rand

om n

ucle

atio

n F

2 (1

– X

)2 (1

– X

)–1

T

hird

-ord

er r

ando

m n

ucle

atio

n F

3 (1

/2)(

1 –

X)3

(1 –

X)–2

Nuc

leat

ion

(Acc

eler

ated

X-t

cur

ve)

Nuc

leat

ion

E1

X

ln X

E

xpon

entia

l law

N

ucle

atio

n P

3/2

(2/3

)X–1

/2

X3/

2 M

ampe

l Pow

er la

w

Nuc

leat

ion

P1/

2 2X

1/2

X1/

2 M

ampe

l Pow

er la

w

Nuc

leat

ion

P1/

3 3X

2/3

X1/

3 M

ampe

l Pow

er la

w

Pha

se b

ound

ary

(sur

face

rea

ctio

n)

Con

trac

ting

disk

R

1 (P

1, F

0)

(1 –

X)0

X

Pow

er la

w

Con

trac

ting

cylin

der

R

2 2(

1 –

X)1/

2 1

– (1

– X

)1/2

Pow

er la

w

Con

trac

ting

sphe

re

R3

(F2/

3)

3(1

– X

)2/3

1 –

(1 –

X)1/

3 Po

wer

law

D

iffu

sion

(D

ecel

erat

ory

X-t

cur

ve)

One

-dim

ensi

onal

dif

fusi

on

D1

(1/2

)X

X2

Par

abol

a eq

. T

wo-

dim

ensi

onal

dif

fusi

on

D2

[– ln

(1

– X

)]–1

X

+ (

1 –

X)

ln (

1 –

X)

Val

ensi

eq.

T

hree

-dim

ensi

onal

dif

fusi

on

D3

(3/2

) (1

– X

)2/3 [1

– (

1 –

X)1/

3 ]–1

[1 –

(1

– X

)1/3 ]2

Jand

er e

q.

a The

term

X r

epre

sent

s th

e ca

rbon

atio

n co

nver

sion

of

alka

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id w

aste

s, ty

pica

lly

dete

rmin

ed b

y th

erm

ogra

vim

etri

c an

alys

is.


Transition-State-Theory Derived Approach Transition-state-theory, known as activated-complex

theory, provides an approach to describing the concentration dependence of the kinetic rate law for elementary chemical reactions. The theory assumes a quasi-equilibrium between reactants and activated transition state complexes. Using a simplified form of the general transition-state-theory derived model is a common approach to modelling the kinetics of both leaching and precipitation reactions. It is assumed that the heterogeneous leaching-precipitation reactions occur at the surface of a particle (Lagasa, 1995). The governing equation of the reaction kinetics (r, mol s–1) is shown as follows:

exp H in nas i RH

i

Er k A a a f G g I

RT

(7)

where k+ is the rate constant of the forward reaction (mol m–2 s–1), As is the reactive surface area of the particle (m2), aH+

nH is the pH dependence of the rate for the reaction, and ai

ni represents catalytic or inhibitory effects due to the presence of other solutions. The terms f(∆GR) and g(I) denote the dependence of the rate on the thermodynamic driving force and ionic strength (I) of the aqueous solution, respectively. The thermodynamic driving force, f(∆GR), can be simplified to Eq. (8):

1 expRT

RR

Gf G

(8)

where ∆GR is the free energy of the reaction. The transition-state-theory approach can well describe the reaction system when it is below saturation. To better evaluate the mineral formation rates, Pham et al. (2011) combined the Burton-Cabrera-Frank growth equation with a simplified form of the classical nucleation theory. This integrated model was successfully applied to assess the supersaturation reaction system, while the transition-state-theory approach was used for states below saturation levels. LEACHING-PRECIPITATION MODEL

Accelerated carbonation reaction is a heterogeneous system containing two dynamic interfaces, i.e., the gas-liquid interface and the liquid-solid interface. The overall reaction can be generally simplified into three simultaneous steps: (1) dissolution of CO2 in bulk solution through the gas-liquid interface, (2) leaching of reactive components (e.g., Ca2+) from solid matrix into solution which typically occurs at the liquid-solid interface, and (3) precipitation of carbonate (e.g., CaCO3) crystals in the bulk liquid phase or at the liquid-solid interface. Gaseous CO2 dissolution is usually considered as a diffusion-limited step, where the mass transfer between the gas and liquid phases plays an important role on reaction kinetics. Several simulation models on evaluating the dissolution behaviors of gaseous CO2 into the aqueous phase are available (Legendre and

Zevenhoven, 2016, 2017). For instance, Legendre and Zevenhoven (2016) established a numerical model by incorporating mass transfer boundary layer with bubble force. This model was developed by the mass time derivative of the dissolving bubbles as the function of local dimensionless numbers such as Re, Sc and Sh. However, if we look at the solid-fluid interfaces by neglecting the external mass transfer of gaseous CO2 dissolution, several kinetic models regarding the leaching and precipitation reactions can be applied for accelerated carbonation. Leaching Kinetics

In CO2 mineralization, leaching is the process of dissolving and releasing metal ions from the solid matrix (e.g., steel slag or fly ash) to the aqueous solution. The rate of metal ion leaching depends on the mineralogy of metal oxides in the solid matrix and their affinity to the solution speciation and pore water. A simple kinetic formulation for weathering of natural ores, such as wollastonite and serpentine, can be applied to describe the leaching rate of certain components (ri) from alkaline solid wastes (De Windt et al., 2011), as indicated by Eq. (9).

1Ω 1 1i

i i i i i i ii

Qdr M k A k A

dt K

(9)

where Mi stands for the mineral phase that contributes to leaching, ki is the intrinsic rate constant, Ai is the mineral surface area, Ωi is the saturation state of solution with respect to the mineral phase i, Qi is the ion activity product, and Ki is the thermodynamic formation constant. The thermodynamic equilibrium constant of calcite (Ca2+ + HCO3

– → CaCO3 + H+) at 25°C is approximately 10–1.85 (De Windt et al., 2011). When Ωi equals to one, the solution is exactly in equilibrium or saturation with respect to the mineral phase, i.e., the term (Qi/Ki

–1 – 1) becomes zero and the mineral phase i does not dissolve afterwards.

A mass conservation approach is also commonly applied to determine the leaching kinetics of metal ions in solution. The metal ions are usually leached out rapidly in the beginning, and then gradually approach a maximum concentration in solution (Ci, max). By the mass-loss based approach, the kinetics of the leaching reaction can be described in Eq. (10):

,in

i i i i max i

dr C k C C

dt (10)

where Ci is the leaching concentration of metal ions, and ni is the order of the leaching reaction. The values of Ci,max

and ki constants should generally increase as the particle size of solid waste decreases. Eq. (10) can be integrated into Eq. (11a) in the case of n = 1, or Eq. (11b) in the case of n ≠ 1.

, 1 , for 1ik ti max iC C e n (11a)

1 1/(1 ), ,[ (1 ) ] , for 1n n

i max i max i iC C C n k t n (11b)


Pan et al. (2013) found that the leaching of Ca, Na and K ions from steel slags were more sensitive to the concentration driving force in comparison to other ions. In most curriculum, the release of Mg ions from steel slag was quite low compared to Ca release (Chang et al., 2012a). Several factors could increase the leaching concentration of calcium ions from the solid matrix (Park et al., 2003; Iizuka et al., 2004; Alexander et al., 2005): (i) high porosity and fine particle size of alkaline solid wastes; (ii) high temperature and low pH value in solution; and (iii) sufficient mixing between the solid and liquid phases to avoid severe agglomeration. The leaching of calcium ions is probably determined by the diffusion through the Ca-depleted silicate rim inside the solid matrix (O'Connor et al., 2002; Santos et al., 2009), rather than by the surface reaction at the phase boundary (i.e., the solid-liquid interface) which usually is the rate-limiting step in the beginning of aqueous carbonation.

Aside from the conventional mass conservation method, several approaches are developed for evaluating the leaching behaviors of solid particles. For example, Hariharan et al. (2014a) developed a non-steady state dissolution kinetic model for lizardite particles by considering the dynamics of the pH value during the reaction. This model can accurately describe the non-stoichiometric concentration profiles of magnesium and silica ions in the solution. Similar approaches have also been applied for other solid particles, such as thermally activated serpentine (Hariharan et al., 2014b). Precipitation Kinetics

Contact between calcium and carbonate ions would lead to the formation of calcium carbonate precipitates. Calcium carbonate is almost insoluble in water at the pH above 9 (Chiang and Pan, 2017b). The reaction of calcium ions with carbonate ions is fast and usually related to the carbonate ion concentration in the liquid phase. Ishida and Maekawa (2000) suggested that the precipitation of calcium carbonates should be a first-order reaction with respect to the concentrations of Ca2+ and CO3

2– ions, as described by Eq. (12):

2 23 3i

dr CaCO k Ca CO

dt (12)

The formation of calcium carbonate precipitates occurs

when the precipitation kinetics is not equal to dissolution kinetics (i.e., not equilibrium). The balance between leaching and precipitation reactions depends on their reaction kinetics and solubility of the feedstock and reaction products (e.g., the solubility of CaCO3 is about 0.15 mmol L–1 at 298 K). As the calcium ions in solution are consumed to form precipitates, more calcium-bearing components in the solid phase dissolve to equalize the difference in calcium ion concentration. Applications in CO2 Mineralization

CO2 mineralization via accelerated carbonation proceeds

via dissolution and precipitation reactions in which the aqueous solution plays a critical role on reaction kinetics. Gadikota et al. (2014c) developed a systematic framework on experimental design and data analysis for accurate evaluation of dissolution and carbonation behaviors. Harrison et al. (2017) applied the transmitted light and backscattered electron micrographs to evaluate the mechanism of brucite [Mg(OH)2] carbonation at the pore scale. They found that brucite in dry pores remained visibly unreacted, whereas hydrated carbonate precipitates (e.g., nesquehonite [MgCO3·3H2O]) were abundant in water filled pores, as shown in Figs. 3(a)–3(b). This reveals that the gas-mineral interface is relatively unreactive. As the reaction proceeds, the magnitude of the solid-fluid interfaces is significantly dynamic due to the water loss and the entrainment of reactive minerals by the moving gas-water interfaces, as illustrated by Figs. 3(c)–3(e).

Cizer et al. (2012) evaluated the reaction mechanisms of carbonation of lime pastes with an in-situ X-ray diffraction determining the dynamic changes in mineralogy including portlandite and calcite. The results revealed that the reaction first was chemically controlled at the exposed surface with a strong CO2 diffusion resistance, and then followed by a transition to a CO2-diffusion controlled regime through the carbonate product layer (Cizer et al., 2012). Ashraf and Olek (2018) conducted a multi-technique approach to elucidating accelerated carbonation products of calcium silicates, as shown in Fig. 3(f). They found that the presence of agglomerations of silica gel clusters on the surfaces of amorphous calcium carbonate would result in a lower inter-cluster porosity for carbonated matrixes. The small portion of gel pores in carbonated matrix of monocalcium silicate (CaO·SiO2) may be formed between the partial agglomerates of silica gel clusters. SHRINKING CORE MODEL

For the noncatalytic reaction of solids with surrounding fluid (i.e., heterogeneous reactions), the shrinking core model can be used to determine its reaction kinetics and rate-determining step. The features of the shrinking core model include (Benedetti, 2014): Applicable to each grain, but not to the particle as a

whole Suitable for explaining data where the conversion is

less than 100% There is a non-porous passivated product layer around

the grain reactive surfaces In the shrinking core model, it is assumed that an

unreacted core of material always exists before complete conversion of particle to product. The reaction occurs at the surface of the unreacted core (i.e., typically a sharp interface for non-porous grains) and then proceeds into the inside of the core, leaving behind the reacted rims (known as an ash layer). In other words, the size of the unreacted core gradually shrinks during the reaction. Shrinking core model exhibits inherent limitations to the reactions with a porous particle. Ahn and Choi (2017) indicated that the shrinking core model for a porous pellet would become


valid only when the reaction was controlled by inward diffusion (i.e., the reaction proceeded with the core-shell structure). Governing Equations

According to the definition of a fluid-solid reaction in shrinking core model, accelerated carbonation can be simply expressed by Eq. (13):

CO2(fluid) + b CaO(solid) → CaCO3(s) (13)

where b is the stoichiometric coefficient for carbonation reaction (-). For this reaction, three possible rate-determining steps can be considered in the shrinking core model (Fig. 4): fluid-film diffusion (F-mechanism), ash-layer diffusion (D-mechanism), and chemical reaction at the unreacted core surface (C-mechanism).

In the classic shrinking core model, it is assumed that the particle size (R) remains constant during the reaction. The characteristic time (τ) for complete conversion of particle to product with respect to three rate-determining steps can be obtained via the governing equations: Fluid-film Diffusion (F-mechanism)

When the diffusion of the carbonate ions through the boundary layer at the fluid–particle interfaces is the rate-determining step, the carbonation conversion of solid particles (X, dimensionless) can be described as the function of reaction time (t, sec) by Eq. (14): kF·t = X (14) where kF is the apparent reaction rate constant (s–1) for the fluid-film diffusion control mechanism. The characteristic time for the fluid-film diffusion control mechanism (τF) can be determined by Eq. (15):

1

3B

FF e Ag

R

k bk C

(15)

where ρB is the molar density of the particles, R is the radius of the particles, ke is the mass-transfer coefficient, and CAg is the molar concentration of CO2 in the bulk fluid. Ash-layer Diffusion (D-mechanism)

When the diffusion of the carbonate ions through the ash layer is the rate-determining step, the governing equation can be described by Eq. (16): kD·t = [1 – 3(1 – X)2⁄3 + 2(1 – X)] (16) where kD is the apparent reaction rate constant (s–1) for the ash-layer diffusion control mechanism. The characteristic time for the ash-layer diffusion control mechanism (τD) is shown as Eq. (17):

21

6B

DD e Ag

R

k bD C

(17)

where De is the effective diffusivity of carbonate ions through the ash layer. Chemical Reaction at the Unreacted Core Surface (C-mechanism)

When the chemical reaction at the phase boundary (such as the unreacted core surface) is the rate-determining step, the carbonation conversion of solid particles can be expressed by Eq. (18):

kc·t = [1 – (1 – X)1⁄3] (18)

where kc is the apparent reaction rate constant (s–1) for the

Fig. 4. Profiles of reagent concentrations at solid-fluid interfaces based on shrinking core model. Adapted from the literature (Chiang and Pan, 2017a).


reaction control mechanism. The characteristic time for the reaction control mechanism (τc) is shown as Eq. (19):

1 Bc

c Ag

R

k bk C

(19)

where k’ is the first-order rate constant for the surface reaction. Combination of Mechanisms

In actuality, the relative importance of the above single mechanism varies as the reaction proceeds due to the dynamical changes in several factors such as mineralogical compositions, particle size, and pore blockage. To consider the simultaneous action of the above three mechanisms, the time to reach any stage of conversion (τtotal) can be determined by the sum of the times needed if each resistance acted alone, as shown in Eq. (20): τtotal = τF + τD + τc (20)

Farhang et al. (2017) applied the crackling core model, which is an extension to the shrinking core model by involving two parameters of step reactions (τcc and τgp), to evaluate the dissolution kinetics of magnesium ions from serpentine. τcc and τgp are the characteristic times for being completely converted to grainy porous solid and for complete conversion of a grain, respectively. They found the formation of meso-pores in the particles along the leaching process (Farhang et al., 2017). For accelerated carbonation, initial operating parameters such as liquid-to-solid ratios will result in different buffering capacities and reactant concentrations (CAg) in solution (Pan et al., 2016c). Also, the release of reaction heat from accelerated carbonation may cause local temperature gradients within the particles or between particle and the bulk fluid. The heat transfer phenomena would affect the importance of the chemical reaction control mechanism at the unreacted core surface. One of the technical challenge in CO2 mineralization is to accelerate the reaction while exploiting the heat of reaction to minimize the energy use (Bobicki et al., 2012).

Carbonation fronts at the solid-fluid interface are dynamic during the reaction. The changing solid-fluid interface is dependent on the rate of dissolution/precipitation at the mineral surface (i.e., the reaction-controlled mechanism) and the rate of reactant/product transport (i.e., the transport-controlled mechanism). The Damköhler (Da) number has been typically used to distinguish between the regimes of mechanisms in mineral systems (Steefel and Maher, 2009; Deng et al., 2018). The Da number represents the ratio of the characteristic time of transport (τD) to that of reaction (τR), as shown in Eq. (21):

advD

eqc

MW

tDa

S

k I

(21)

where tadv is the advection time (or residence time) of the bulk fluid, k is the dissolution rate constant (mol s–1 m–2 mineral), Seq is the solubility of the mineral phase (mol m–3 fluid), and IMW is the solid-fluid interfacial area in units of m2 mineral per m3 fluid.

Harrison et al. (2017) suggest that the particle movement could shift the overall control of the carbonation since Da number is proportional to the solid-fluid interfacial area (IMW). In general, a Da value less than one indicates a kinetics-limited system, while a Da value higher than one refers to mixing-limited conditions. Deng et al. (2018) proposed a multireaction Da number to evaluate multimineral systems with differing reactivity of minerals. However, they still mentioned several limitations for this framework, e.g., the mineral spatial heterogeneity was not considered. Considering Particle Size Changes with Reaction

In practice, the particle size would change in the course of reaction due to the formation of ash and/or product layers. This would affect the diffusivity of the reactant in the ash and/or product layers. It is observed that the thickness of the product layer (precipitated calcium carbonate) on the surface of the steel slag ranges from 1 to 3 µm (Chang et al., 2012a). To consider the effect of particle size distribution, several factors can be included to modify the relationship between the carbonation conversion and reaction time. Z Factor

A “Z factor” (Sohn, 2004) can be introduced to modify the governing equation for ash layer diffusion control in the classic shrinking core model, as shown in Eq. (22):

2/3

2/31 13 1

1 / 3D

Z Z Z Xt X

Z

(22)

where the Z factor represents the ratio of the volume of product solid to the volume of original solid (both including pore volumes). A Z value of one indicates the volume of the product solid remains the same as that of the original solid reactant, i.e., the particle size is unchanged in the course of reaction. In this case, Eq. (22) can be simplified to Eq. (16) by applying L’ Hospital’s rule. λ Factor

Li et al. (2015) applied fractal geometry principles, i.e., a “λ factor”, for considering the changes in the surface area and volume of the solid particles during the liquid-solid reaction between acid and minerals. In the shrinking core model, the λ factor can be used to modify the conversion (X) with the changes of particle size (R) in the course of reaction, as shown in Eq. (23):

0,?

1

η

η

η Dη D

η

λ

λ

1max

D

R

t

tR

X f R dRR

(23)


where the term D represents the fractal dimension of the external surface area of a particle. The value of η is defined as Eq. (24): η = (4D – 2)⁄D (24)

For a spherical particle, the D and η values can be assigned to be two and three, respectively. It is noted that this modification factor can be used for determining the reaction kinetics of acid extraction for solid wastes that is controlled at the surface reaction stage. Applications in Leaching and Carbonation Reactions for CO2 Mineralization

Shrinking core model has been commonly applied in evaluating the unit processes and reactions for accelerate carbonation, such as the dissolution of Mg(OH)2 (Bharadwaj et al., 2013), the extraction of calcium ions by dicarboxylic acids (Baldyga et al., 2011), and calcium leaching from steel slags (Lekakh et al., 2008). The leaching of calcium ions from the solid particles by aqueous carbonation is much faster compared to that by natural weathering (Costa, 2009). However, Daval et al. (2009) noticed that the calcium leaching should be the primary rate-limiting step with respect to the entire accelerated carbonation reaction. The leaching of calcium and/or magnesium ions would result in a metal-depleted rim (e.g., SiO2) around the surface of the unreacted core (Park and Fan, 2004). In particular, the rate-determining step for the initial stage of calcium leaching from steel slags (i.e., < 30% conversion) should be reaction controlled mechanism, while the later stage was controlled by molecular diffusion (Lekakh et al., 2008).

If we consider both the leaching and carbonation steps as a whole reaction, the ash-diffusion mechanism is found to be the rate-limiting step. Table 2 summarizes the effective diffusivity (De) of reactant for CO2 minerlization via accelerated carbonation based on shrinking core model. The diffusivity varies remarkably among the types of feedstock and reactors, and operating conditions. In general, the effective diffusivity is highly dependent on the reaction temperatures, i.e., it increases as the temperature increases. Therefore, at similar levels of operating temperatures, the diffusivities in a slurry reactor and in a rotating packed bed were found to be at the similar magnitude of ~10–6 cm2 s–1. Fricker and Park (2014) found that reaction temperature also was the dominant parameter driving the formation of specific carbonate phases (e.g., needle-like crystals at a lower temperature while rhombohedral shapes at a higher one). Aside from the reaction temperature, both the porosity and pore volume of the particles were significantly changed as the reaction proceeded (Fernandez Bertos et al., 2004; Gadikota et al., 2014b; Pan et al., 2016c). This was attributed to the formation of carbonate products, such as calcite (CaCO3), deposited on the surface of the solid particles. In some cases, the pores surrounded by Si-rich phases were opened as the solid particle dissolved, and then carbonate products would precipitate within the pores, thereby reducing the available pore space for further reaction (Gadikota et al., 2014a). The protective product (or ash) layer around

Tab

le 2

. Com

pari

son

of d

iffu

sivi

ty f

or C

O2

min

erli

zati

on v

ia a

ccel

erat

ed c

arbo

nati

on b

ased

on

shri

nkin

g co

re m

odel

.

Rea

ctor

a

CO

2 st

ream

b

Sol

id w

aste

c

Liq

uid

agen

t d

Ope

ratin

g ti

me

(s)

Tem

pera

ture

(K

) D

iffu

sivi

ty

(10–7

cm

2 s–1

) R

efer

ence

C

oncn

P

Q

g T

ype

Dp

Ct

Typ

e Q

s L

/S

RP

B

(HiG

Car

b)

~99%

~1

-

BO

FS

22

.9

0.31

D

W

1.2

20

1200

29

8 4.

82−9

.18

(Cha

ng e

t al.,

20

12a)

31

8 5.

47−1

1.0

338

12.2−1

4.9

SR

~1

0%

~1

2.5

BH

C

20.6

0.

42

CR

W

- 20

72

00

298

1.72

(C

hang

et a

l.,

2012

b)

338

16.6

S

R

~99%

~1

0.

1 B

OF

S

53.0

0.

40

DW

-

20

7200

30

3 28

.2

(Pan

et a

l.,

2016

c)

313

52.9

32

3 67

.9

333

102.

0 34

3 10

3.0

SR

~9

9%

~1

- M

SWI-

BA

17

5.8

0.11

C

RW

-

10

7200

29

8 10−

290

(Cha

ng e

t al.,

20

15)

a RP

B:

rota

ting

pac

ked

bed;

SR

: sl

urry

rea

ctor

. b C

oncn

.: C

O2

conc

entr

atio

n in

the

fee

d st

ream

(%

); P

: pr

essu

re (

bar)

; Qg:

gas

flo

w r

ate

(L m

in–1

). c B

OF

S:

basi

c ox

ygen

fu

rnac

e sl

ag; B

HC

: ble

nded

hyd

raul

ic c

emen

t sla

g; M

SWI-

BA

: mun

icip

al s

olid

was

te in

cine

rato

r bo

ttom

ash

; Dp:

mea

n di

amet

er (μm

); C

t: th

eore

tical

max

imum

cap

acit

y of

sol

id w

aste

bas

ed o

n S

tein

our

equa

tion

(kg

CO

2 pe

r kg

was

te).

d CR

W:

cold

-rol

ling

was

tew

ater

; D

W:

deio

nize

d w

ater

; Q

s: sl

urry

flo

w r

ate

(L m

in–1

); L

/S:

liqu

id-t

o-so

lid

rati

o (m

L g

–1).


the surface of the unreacted core would limit further diffusion of the reactants from inside the solid matrix into solution, thereby resulting in a dynamic equilibrium. The effect of the coverage of the product layer on the reaction kinetics is considered in the surface coverage model, which is illustrated in the next section. SURFACE COVERAGE MODEL

The surface coverage model was first developed by Shih et al. (1999) for evaluating the kinetics of carbonation and desulfurization of hydrated lime (Ca(OH)2) at low temperatures. Because of the similar behaviors to these heterogeneous reactions, the surface coverage model has been utilized to evaluate the kinetics of accelerated carbonation for alkaline solid wastes (Chang et al., 2011b, 2013b). Governing Equations

In the surface coverage model, the reaction occurs only at the unreacted sites of surface that is not covered by any reaction product (Φ). Then the product is coated on the particle surface (mono-layer coverage) at the solid-fluid interface. As the reaction proceeds, the solid particle will reach a maximum carbonation conversion (Xmax). It is assumed that the surface of the reactant particle is homogeneous and all sites are equivalent. In the surface coverage model, the governing equation of carbonation reaction rate per initial surface area of particles (rs, mole min–1 m–2) can be described by Eq. (25):

1 XΦs s

g

dr k

S M dt (25)

where ks (mole min–1 m–2) is the apparent reaction rate constant, Φ (-) represents the fraction of the active surface sites without being covered by reaction products, Sg (m

2 g–1) is the initial specific surface area of particles, M (g mol–1) is the weight of solid particles per mole of calcium oxide, X (-) is the carbonation conversion of particles, and t (min) is the reaction time. It is noted that, in the above governing equation, only the calcium-bearing components are considered to be the major reactive species for accelerated carbonation.

The fraction of the active surface sites (Φ) should gradually reduce with the progress of the reaction depending on the reaction rate, which can be illustrated by Eq. (26):

1 nΦΦ Φn

p s p s

dk r k k

dt (26)

where kp (m

2 mol–1) represents a coefficient indicating the availability of the active surface sites. Shih et al. (1999) found that the n value of 1.7 was the best fitting value for the carbonation of Ca(OH)2.

We can simplify the above kinetic rate constants by designating the terms k1 (min–1) and k2 (-), as shown in Eqs. (27) and (28), respectively:

k1 = ks·SgM (27) k2 = kp/(SgM) (28)

By assigning the n value to be one for simplicity, the

carbonation conversion of the particle (X), in terms of k1 and k2, can be expressed by Eq. (29): X = [1 – exp(–k1 k2 t)]/k2 (29)

In the model, the reactant particles would eventually

reach a maximum carbonation conversion (Xmax) when the system is under the equilibrium conditions. Thus, we can convert Eq. (29) to be Eq. (30) in terms of Xmax: X = Xmax[1 – exp(–kS kp t)] (30) where Xmax equals to the value of the reciprocal of k2. Applications in CO2 Mineralization

In the surface coverage model, the reaction products continuously deposit on the active surface of solid particles in the course of carbonation. The surface structure of the reacted particles also changes with the reaction. Due to the formation of the product layer, the diffusion of reactants from the inside unreacted particles through the product layer would be the rate-determining step as the reaction proceeds. This would hinder the solid particles from further reaction, thereby reaching a maximum conversion. Hariharan and Mazzotti (2017) found that the passivation behaviors by amorphous silica precipitation on the dissolving particle increased with temperature (30–60°C). The inhibitory effect would significantly reduce the rates of the magnesium ion release from the solid matrix.

Table 3 summarizes the kinetic parameters of accelerated carbonation determined by the surface coverage model. A higher ks value indicates a more rapid carbonation reaction rate with a higher carbonation conversion. As shown in Table 3, the rate of the carbonation reaction using inorganic wastewater (such as cold-rolling wastewater) is found to be generally higher than that using pure-water (such as deionized water). The maximum carbonation conversion (Xmax) in the high-gravity carbonation process is generally greater than that in the autoclave reactor and the slurry reactor. However, a high ks value would also lead to a large quantity of reaction product deposited on the surface of particles at the beginning of the reaction. This might inhibit further leaching of reactive species from the inside unreacted particles into the bulk solution (Pan et al., 2014). Therefore, in addition to the ks value, the kp value is another important kinetic parameter in reactor design. A higher kp value implies that the product would cover the active surface of particles more uniformly. The fresh solid particle usually has a smooth morphology before the reaction, while exhibiting characteristic precipitates (e.g., in the shapes of needle-like, rhombohedral, or cubic crystals) on the surface of particles after the reaction (Pan et al., 2014).

The limitation of the surface coverage model is that only a single layer of the diffusion-limited rim around the


Tab

le 3

. Com

pari

son

of k

inet

ic p

aram

eter

s fo

r C

O2

min

erli

zatio

n vi

a ac

cele

rate

d ca

rbon

atio

n ba

sed

on s

urfa

ce c

over

age

mod

el.

Rea

ctor

a

Sol

id w

aste

b

Liq

uid

agen

t c

Exp

erim

enta

l dat

a d

Mod

el p

aram

eter

s (m

ean

valu

e)

Ref

eren

ce

XC

aO (

-)

T (

K)

M

S g

k 1 (m

in–1

) k 2

(-)

k s·k

p (m

in–1

) A

R

BH

C

DW

0.

68

433

106.

0 0.

12

0.03

3 1.

67

0.05

5 (C

hang

et a

l., 2

011b

) F

AS

0.

35

433

144.

3 0.

24

0.02

7 3.

12

0.08

4 U

FS

0.

38

433

132.

0 0.

15

0.01

9 2.

90

0.05

5 S

R

BO

FS

D

W

0.80

29

8 13

6.1

3.20

0.

227

1.45

7 0.

331

(Cha

ng e

t al.,

201

3b)

EW

0.

78

298

136.

1 3.

20

0.12

3 1.

322

0.16

3 C

RW

0.

89

298

136.

1 3.

20

0.30

3 1.

304

0.39

5 R

PB

B

OF

S

TW

0.

52

303

130.

0 0.

67

0.03

0 1.

933

0.05

8 (C

hen

et a

l., 2

016)

0.

58

333

130.

0 0.

67

0.03

4 1.

724

0.05

9 C

RW

0.

87

298

130.

0 0.

67

0.69

0 1.

146

0.79

1 0.

95

338

130.

0 0.

67

0.22

0 1.

055

0.23

2 R

PB

B

OF

S

DW

0.

86

298

117.

8 9.

36

0.69

0 1.

146

0.79

0 (P

an e

t al.,

201

4)

0.92

33

8 11

7.8

9.36

0.

220

1.05

5 0.

234

RP

B

EA

FS

D

W

0.30

29

3 95

.0

0.89

0.

014

3.31

2 0.

046

(Pan

et a

l., 2

018)

0.

61

333

95.0

0.

89

0.02

7 1.

629

0.04

4 A

R

FA

D

W

0.31

31

3 89

.0

30.2

9 0.

406

0.03

2 0.

013

(Ji e

t al.,

201

8)

0.23

34

3 89

.0

30.2

9 0.

351

0.04

3 0.

015

a AR

: aut

ocla

ve r

eact

or; R

PB

: rot

atin

g pa

cked

bed

; SR

: slu

rry

reac

tor.

b FA

S: f

ly-a

sh s

lag;

UF

S: u

ltra

-fin

e sl

ag; B

OF

S: b

asic

oxy

gen

furn

ace

slag

; EA

FS

: ele

ctri

c ar

c fu

rnac

e sl

ag; F

A: f

ly a

sh. c D

W: d

eion

ized

wat

er; T

W: t

ap w

ater

; EW

: eff

luen

t wat

er f

rom

was

tew

ater

trea

tmen

t pla

nt; C

RW

: col

d-ro

llin

g w

aste

wat

er.

d XC

aO: c

arbo

natio

n co

nver

sion

det

erm

ined

by

ther

mog

ravi

met

ric

anal

ysis

(-)

; T: t

empe

ratu

re (

K);

M (

g m

ol–1

); S

g (m

2 g–1

)


particle is considered. In real circumstances, the coverage at the solid-fluid interface may not always be a mono-layer. Also, the product layer and the reactive-species-depleted layer (i.e., the ash layer in the shrinking core model) may co-exist during the carbonation. Therefore, the determined parameters of modelling should be seen as the apparent (global) reaction rate, which can not clearly distinguish the effect of the aforementioned mechanisms. In any case, by applying the surface coverage model, preliminary information on the order of reaction rate can be obtained for evaluating various types of processes and/or feedstocks. ADVANCED MODELS CONSIDERING MULTIPLE MECHANISMS

Classical kinetic models are usually developed based on a single resistance for the sake of simplicity. In real situations, the interplay among various resistances on the reaction kinetics is complex due to the dynamical changes in chemical (e.g., mineralogy of solid reactants and alkalinity of bulk solution) and physical (e.g., particle size and pore volume) properties. This section provides an overview on several advanced models that consider multiple mechanisms in evaluating the reaction kinetics of accelerated carbonation, including integrated reaction-diffusion model, two-layer diffusion model and integrated transport-reaction model. Integrated Reaction-diffusion Model

Lee and Koon (2009) coupled the chemical reaction mechanism in the shrinking core model with diffusion mechanism to predict the kinetics of the desulfurization reaction. The concept of desulfurization (if a dry process) is introducing CaO-based sorbents into the flue gas, where the flue gas SO2 would react with CaO in the sorbents to form CaSO4 precipitates. This is basically a non-catalytic solid-gas (solid-fluid) reaction at low temperature. As a result, the phenominalogical kinetic model of desulfurization could be applicable to accelerated carbonation. The rate of the desulfaration reaction was normally considered to be controlled by particle pore diffusion and product layer diffusion (Han et al., 2005). In other cases, Christopher-Chia et al. (2005) presumed that the non-catalytic reaction between gaseous SO2 and solid reactants is either a reaction-controlled or diffusion-controlled mechanism. They developed a global reaction rate model with the aim to incorporate both the reaction and diffusion controlling step for the desulfurization reaction.

Considering both chemical reaction and diffusion as the rate-determining step, the change of conversion (X) in the solid phase with time (t) is shown in Eq. (31). A surface coverage effect, i.e., f(θ), is included in the original shrinking core model with chemical reaction mechanism.

2/331

p

X b C Yf k X

t r

(31)

where b is the stoichiometric coefficient (the molar ratio of solid reactant to gas reactant), Y is the dimensionless

concentration of reacting gas (e.g., CO2) with a function of time, C is the initial reacting gas concentration (mol m–3), ρp is the density of the particle (mol m–3), and r is the radius of unreacted core (m). The surface coverage effect, i.e., f(θ), can be expressed by conversion of the solid phase, as shown in Eq. (32):

f(θ) = α·ea·T·Cc·(1 – bX)d (32)

where α is the pre-exponential constant (-), T is the reaction temperature (K), and a, c and d are the order for the effect of the respective operating parameters on the surface coverage. Two-layer Diffusion Model

In the classic shrinking core model, the product layer diffusion is not considered in the ash-diffusion controlled mechanism. In real circumstances, three distinguishable layers in a solid particle may exist during the carbonation: (i) the unreacted core, (ii) the ash layer containing the calcium-depleted zones, and (iii) the product layer with carbonate precipitates such as calcite. Several studies applied the shrinking core model and identified that the ash-layer diffusion is the rate limiting step for accelerated carbonation (Lekakh et al., 2008; Chang et al., 2011a). In other cases, the resistance from the product layer may also be the rate-determining step for the carbonation reaction. For instance, Min et al. (2017) observed a layer of amorphous silica and calcite products surrounded the solid particles after aqueous carbonation with supercritical CO2, where the product layer could act as a diffusion barrier to the reaction. In other words, the diffusion resistances from both the ash and product layers are perhaps considerably important.

Gopinath and Mehra (2016) modified the classic shrinking core model and proposed a novel two-layer diffusion model. As shown in Fig. 5, the kinetic model simultaneously considers two layers outside the unreacted core of a solid particle, i.e., the ash layer (calcium-depleted rim) and the product layer (calcium carbonate product). Thus, it describes the aqueous carbonation reaction with two moving boundaries, i.e., the product-ash interface (ro) and the ash-core layer (rc). The kinetic resistance of calcium leaching from alkaline solid wastes is also incorporated into the model.

It is assumed that (i) the calcium oxide forms carbonate instantaneously, and (ii) the carbonation reaction results in little CaCO3 precipitates within the pores of the ash layer. The kinetics of carbonation with respect to the carbonation boundary (rc) are expressed in Eq. (33):

0

00 1

cc

pc

a a p p c

q Hdrr A

dt r rr r

D A D A kA

(33)

where ρc is the molar density of reactive calcium species in the fresh solid particle, A0 is the superficial specific area of cross section, Aa is the total cross area of the pores in the ash layer, Ap is the specific surface area of the product layer, Ac is the initial surface area of the core, r0 is the


Fig. 5. Schematic of a carbonated particle by considering two diffusion layers, i.e., ash layer and product layer, in dynamic modelling. It is assumed that the carbonation reaction occurs at the surface of unreacted core (i.e., the interface of the unreacted core and the ash layer).

radius of the original particle, rp is the radius of the reacted particle, q is the stoichiometry of the evaluated reaction, Da is the effective diffusivity of hydrogen ions in the ash layer, Dp is the diffusivity of protons in the product layer, and Φ is the fraction of active pores in the ash layer.

Gopinath and Mehra (2016) applied the modified model to the experimental data from the literature, and found that the Da and Dp for accelerated carbonation of steel slag in DI water in a slurry reactor (i.e., CO2 pressure ~0.1 MPa at 293–343 K) were 2.67 × 10–5 and 8.99 × 10–5 cm2 s–1, respectively. Similarly, the Da and Dp for accelerated carbonation of steel slag in an autoclave reactor (i.e., pressure of CO2 0.1–3.0 MPa at 298–498 K) were 1.78 × 10–5 and 8.97 × 10–5 cm2 s–1, respectively. These results reveal that the diffusion through the ash layer should be the dominant rate-limiting step in comparison to the diffusion through the product layer. Incorporated Mass Transfer with Reaction Kinetics

To include the effect of mass transport, the kinetics of the carbonation reaction can be developed based on the classical mass transfer model such as two-film theory. The diffusion control mechanism implies the relative importance of mass transfer phenomena, which involves the movement of a single mass molecular from one phase into another phase. In the carbonation reaction, the mass transfer of CO2 between the gas and liquid phases should be significant. Chang et al. (2013a) developed an apparent kinetic model of aqueous carbonation based on a shell mass balance, as shown in Eq. (34). The CO2 (gas phase) is characterized by convection behaviors between the inlet and outlet streams. It is also assumed that the mass transfer between the liquid and solid phases can be neglected.

2

2 2 2 2

COg g

g g,i CO ,i g,o CO L p l CO CO TIC

dC ρ V

dt

ρ (Q C Q C ) k a V P H C

(34)

where ρg (mol cm–3) is the density of CO2 gas, Vg (cm3) and Vl (cm3) are the volume of gas and liquid, CCO2 (-) is the CO2 concentration in exhaust gas, kL (cm s–1) represents the mass transfer coefficient on the liquid side, ap (cm2 cm–3) is the specific surface area of packing materials, HCO2 (mol cm–3 atm–1) refers to the Henry’s law constant of gaseous CO2 in water, and CTIC (mol cm–3) is total inorganic carbon in the bulk liquid solution.

For the bulk liquid, the rate of total inorganic carbon consumption during the reaction can be described by Eq. (35). Assuming the carbonation reaction is at the steady-state conditions, the concentration of total inorganic carbon would remain relatively unchanged during the carbonation.

2 2

TICl

L p l CO CO TIC c TIC l S S,0

dC V

dt

k a V P H C k C V C C 0

(35)

where kc (cm3 mol–1 s–1) is the reaction rate constant, and Cs (mol cm–3) is the CaO concentration of solid particles. Similarly, the rate of the solid concentration can be expressed by Eq. (36):

ss c TIC s l

dCV k C C V

dt (36)

where the term Cs and Vl can be substituted by Eqs. (37) and (38), respectively. Cs = Cs0(1 – XCaO) (37)

l s s

LV V

S (38)

where Cs0 (mol cm–3) is the initial solid concentration. Thus, the liquid-phase mass transfer coefficient can be thus calculated by Eq. (39).

2 2

0 CO CO(1 exp )s c TIC

Lk C t

Sc TIC s L p TICk C C k a P H C

(39)

Chang et al. (2013a) found that the kLa value for the

carbonation reaction using wastewater with steel slag was about 9.23 × 10–4 s–1, while the corresponding kc value was ~216.9 cm3 mol–1 s–1. It was also noted that the reaction rate using wastewater (188–217 cm3 mol–1 s–1) was higher than that using DI water (160–195 cm3 mol–1 s–1). PERSPECTIVES AND PROSPECTS

This article provides an overview on the phenomenological modelling at the solid-fluid interfaces for CO2 mineralization via accelerated carbonation. To improve the understanding of CO2 mineralization at interface levels, three priority research directions, including (1) incorporation of structural and physical properties in phenomenological models, (2)


identification of dynamic speciation by in-situ high-resolution equipment, and (3) integration of heat transfer in reaction modelling for system optimization, should be focused. Incorporation of Structural and Physical Properties in Phenomenological Models

For CO2 mineralization, transport phenomena such as carbonate- and calcium-ions diffusion to/from reaction sites are normally found to be the rate-limiting steps. Boundary layers would directly affect the reaction rate and CO2 fixation capacity of accelerated carbonation, such as diffusion across precipitate coatings on particles, pore blockage in the ash layer, or dissolution of reactive components from solid matrix at the particle surface. Especially for the non-catalytic systems, the pore structure of the solid particle changes during the reaction. Therefore, in addition to the chemical reaction at the interface, the phenomenological models should consider the reaction dynamics in terms of structural and physical properties, e.g., the pore size and surface area (both internal and external) of particles, the thickness of product layer, and the extent of pore overlapping. Identification of Dynamic Speciation by in-situ High-resolution Equipment

Determining the dynamic speciation and product properties in the heterogeneous system (i.e., CO2 gas, liquid, and solid particles) plays a key role in controlling reaction pathways and rates. This requires the development and application of in-situ high-resolution investigative equipment for measuring local mass transfer and identifying phase characteristics at the molecular level. For different types of processes and/or feedstocks, broad-spectrum collection of thermodynamic and kinetic information, especially focusing on mass transfer and reaction rate at the solid-fluid interfaces, should be the priority research directions. Integration of Heat transfer in Reaction Modelling for System Optimization

In practice, process heat integration is a necessary component for system optimization. It would also provide opportunities on increasing process energy efficiency that is required for achieving the positive carbon fixation. Björklöf and Zevenhoven (2012) suggest that a thermodynamic efficiency analysis from the perspective of exergy should be conducted to evaluate the overall thermal/energy efficiency of CO2 mineralization processes. CO2 mineralization by accelerated carbonation is an exothermic reaction, where the heat of reaction could be utilized as a source of energy input. From the viewpoint of a plant, the actual reaction temperature is related to the heat of carbonation reaction, the heat loss from reactors, and the energy recovered in heat exchangers. To realize the system optimization, the heat transfer at interface levels should be considered in the phenomenological models. CONCLUSIONS

CO2 mineralization using alkaline solid wastes has been considered one of the most promising potential technologies

to combat anthropogenic CO2 emissions. Classical models such as shrinking core model and surface coverage model can provide a rapid assessment on the reaction kinetics. However, in practice, multiple mechanisms should be considered in evaluating the reaction kinetics of CO2 mineralization due to the dynamical changes in chemical (e.g., mineralogy of solid reactants) and physical (e.g., particle size and pore volume of reactant particles) properties. Future priority research directions on phenomenological modelling include incorporation of structural and physical properties, identification of dynamic speciation by in-situ high-resolution equipment, and integration of heat transfer for system optimization. ACKNOWLEDGMENTS

This study was supported by the Ministry of Science and Technology (MOST), Taiwan (ROC) under Grant No. MOST-107-3113-E-007-002 and 107-2917-I-564-043. We also thank Dr. Mengyao Gao from Department of Chemical Engineering, National Taiwan University for her technical assistance on preparing figures. REFERENCES Adelodun, A.A., Ngila, J.C., Kim, D.G. and Jo, Y.M.

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Received for review, March 14, 2018 Revised, March 20, 2018

Accepted, March 20, 2018

an overview: reaction mechanisms and modelling …mineral-water) reactions, such as...

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