A statistical shrinking core model to estimate the

Chemical Engineering Science 167 (2017) 191–203

Contents lists available at ScienceDirect

Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces

A statistical shrinking core model to estimate the overall dechlorination rate of PCE by an assemblage of zero-valent iron nanoparticles Christos D. Tsakiroglou a,⇑, Kata Hajdu a, Katerina Terzi a,b, Christos Aggelopoulos a, Maria Theodoropoulou c a

Foundation for Research and Technology Hellas – Institute of Chemical Engineering Sciences, Stadiou Street, Platani, 26504 Patras, Greece Department of Chemical Engineering, University of Patras, 26504 Patras, Greece c Department of Mechanical Engineering, Technological Educational Institute of Western Greece, M. Alexandrou 1, Koukouli, 26334 Patras, Greece b

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


A shrinking-core model is developed

for nanoparticles/dissolved pollutant reactions.
The overall reaction rate is expressed as function of transport/reaction parameters.
The statistics of particle size distribution is incorporated into the model.
Batch tests of dissolved PCE remediation by nZVI are used for parameter estimation.
For the system nZVI/PCE, the parameter values are estimated with inverse modeling.

CLRb CLRs CLR

a r t i c l e

a b s t r a c t

i n f o

Article history: Received 1 September 2016 Received in revised form 4 April 2017 Accepted 6 April 2017 Available online 8 April 2017 Keywords: Zero-valent iron Nanoparticles Shrinking core model Reaction rate Mass transfer Particle size distribution

SR rc rs

r

Reactant SR Product SP

CLRc 0

0

A parametric shrinking-core model is used to quantify the dechlorination rate of chlorinated pollutants dissolved in water by zero-valent iron nanoparticles (nZVI). The mass-transfer processes are coupled with the instantaneous reaction occurring in the solid/liquid interface to compute the transient changes of dissolved pollutant concentration in bulk and suspended nZVI concentration. A sensitivity analysis is carried out to identify the dominant parameters governing the overall reaction rate for a system of uniform nanoparticles. The model is extended to assemblages of non-uniform ZVI nanoparticles with sizes following a distribution function. The statistical shrinking-core model is used to estimate the PCE dechlorination kinetic parameters along with the mass-transfer coefficients with inverse modeling of batch experiments. The observed discrepancy between numerical predictions and experimental datasets may be attributed to uncertainties associated with the nZVI oxidation by other species, and PCE adsorbed on oxidized iron. An approximate analysis of model equations allows the development of an analytic phenomenological model providing the overall reaction rate as a function of dissolved PCE concentration. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Zero-valent iron (ZVI) has widely been used in various environmental applications for a long time as an excellent reducing agent, ⇑ Corresponding author. E-mail address: [email protected] (C.D. Tsakiroglou). http://dx.doi.org/10.1016/j.ces.2017.04.007 0009-2509/Ó 2017 Elsevier Ltd. All rights reserved.

Liquid boundary layer

depending on its inexpensive and nontoxic characteristics (Tratnyek and Johnson, 2006; Crane and Scott, 2012; Mueller et al., 2012). Microscopic and spectroscopic studies have revealed that zero-valent iron nanoparticles (nZVI) in the aqueous environment consists mainly of a zero-valent iron core covered by a surface layer of iron oxide (Nurmi et al., 2005; Ji, 2014), which is a mixture of Fe(II)/Fe(III) oxides near the interface with Fe0 and

192

C.D. Tsakiroglou et al. / Chemical Engineering Science 167 (2017) 191–203

mostly Fe(III) oxide near the oxide/water interface (Wang et al., 2009). This core-shell structure has important implications for the chemical properties of nZVI. The disordered nature of the oxide shell renders it potentially more reactive than a simple passive oxide layer formed on bulk iron materials (Yan et al., 2010). It seems that the core-shell structure is a highly important aspect to consider when studying the reactivity of nZVI for various remediation processes. The measurement of zero-valent iron reactivity and the identification of the reaction pathways for specific pollutants is commonly carried out with tests on batch reactors filled with aqueous solutions of halogenated hydrocarbons mixed with nZVI suspensions (Orth and Gillham, 1996; Campbell et al., 1997; Arnold and Roberts, 2000; Liu et al., 2005; Schmid et al., 2015). The progress of pollutant dehalogenation is commonly monitored by measuring the concentration of initial and intermediate pollutants through combining a variety of sampling approaches and spectroscopic analysis techniques. For instance, the PCE dechlorination by nZVI has been monitored by combining gas phase head space with Gas Chromatography – Flame Ionization Detector (GC-FID) (Fagerlund et al., 2012), liquid phase micro-extraction (LPME) with Gas Chromatography – Electron Capture Detector (GC-ECD) (He et al., 2010), and High Performance Liquid Chromatography (HPLC) (Chen et al., 2014). Depending on the nanoparticle chemistry (e.g. bare nZVI, carboxymethylcellulose--coated nZVI, Pt/Fe bimetallic nanoparticles), aqueous solution composition (e.g. pH), nanoparticle morphology, and particle-size statistics, very different reaction rates (orders of magnitude) can be measured for the same pollutant (Petersen et al., 2012; Fagerlund et al., 2012; Gunawardana et al., 2012; Zhang et al., 2012; Chen et al., 2014). In spite of the numerous studies combining batch and/or column tests with macroscopic transport and reaction models to quantify the rate of reductive dehalogenation of halogenated hydrocarbons by nZVI (Taghavy et al., 2010; O’Carroll et al., 2013; Yan et al., 2013), a little attention has been paid on the analysis of experiments in terms of a core-shell reaction model at nanoparticle-scale, and the subsequent development of a relevant, true-to-mechanism phenomenological kinetic model. In the present work, first, a shrinking core – growing shell model, coupling the transport with reactive processes, is developed to calculate the overall reaction rate at the scale of a single nanoparticle. Then, the model is generalized for an assemblage of particles with sizes following a distribution function. The model is fitted to experimental results of batch tests of PCE dechlorination by carboxymethylcellulose (CMC)-coated nZVI (Tsakiroglou et al., 2016) to estimate the reaction kinetic constant. Finally, a phenomenological kinetic model is suggested to describe the kinetics of dissolved PCE remediation by nZVI in aqueous phase. 2. Synthesis of nZVI and reactivity tests 2.1. Synthesis and characterization of zero-valent iron nanoparticles Aqueous solutions of carboxyl-methyl-cellulose (CMC) were prepared by dissolving 20 g of CMC (molecular weight: MWCMC = 90,000 g/mol) in 200 mL of deionized water under stirring for a period of 3 days. Then, the solution was purified with a membrane of 30 kDa and condensed by freeze drying for 48 h (Bokias et al., 2001). Aqueous suspensions of nZVI were prepared in a three-neck flask by the common borohydride technique (He and Zhao, 2007). The NaBH4 solution was added in an aqueous solution of FeSO47H2O pre-grafted with the solution of CMC which acts as stabilizing coating. The mixing was done under the continuous injection of N2 to ensure anoxic conditions and prevent the

fast nZVI oxidation. The entire system was placed inside a thermos-statted bath to keep a low temperature close to 4 °C. More details of the synthesis procedure are reported elsewhere (Tsakiroglou et al., 2016). Stock nZVI suspensions were prepared at three concentrations: 1.0, 0.1, 0.01 g/L, and used to perform the full set of batch tests at various initial PCE concentrations as described below. The number- and volume-based particle size distributions were measured with dynamic light scattering in a f-Nano-sizer (MALVERN). 2.2. Tests in batch reactors A stock PCE solution of concentration 100 ppm was prepared in deionized and degased water. The stock PCE solution was diluted at concentrations 100, 75, 50, 20, 10, 5 ppm. With the aid of a syringe, 1 mL of each PCE solution was mixed with 1 mL of a stock nZVI suspension in extraction bottles without opening them. The bottles were filled with N2 gas on the top to prevent the oxidation of the iron particles, placed in a rotator, and rotated for a variable period (2 min–2 h) which specifies the reaction time. The PCE extraction from the aqueous phase into hexane was performed by (1) mixing 400 lL of the PCE solution/nZVI suspension with 4 mL of hexane in extraction bottles, and (2) shaking the mixture for 20 min at 20 Hz. After the extraction has been completed, the polar and non-polar phases were separated. Liquid samples were collected for chemical analyses from the (upper) hexane phase, and the residual PCE concentration was detected with a Shimadzu GC-2010 gas chromatograph, equipped with an Electron Capture Detector (ECD) and auto-sampler (Tsakiroglou et al., 2016). 3. Mathematical model 3.1. Reaction pathways Complicated mechanistic reaction networks have been suggested to describe the dechlorination of chlorinated hydrocarbons by nZVI, with the most dominant ones being the following (Liu et al., 2005; O’Carroll et al., 2013; Yan et al., 2013): (a) The hydrogenolysis where chlorine atoms are progressively substituted by hydrogen atoms with the production of ethylene as final product. (b) The b-elimination where two chlorine atoms are removed with the simultaneous creation of an additional bond and the subsequent substitution of chlorine atoms by hydrogen atoms resulting in the production of acetylene as final product. By overlooking the intermediate and final products, we assume that the ratecontrolling step is the initial step of hydrocarbon dechlorination. The metallic core of nZVI is covered by an oxide layer (shell) which consists of a mixed Fe(II)/Fe(III) phase, whereas the Fe(III) oxide phase prevails on the surface of the nanoparticles (Wang et al., 2009). The surface of the oxide contains hydroxide groups after exposure to water media, resulting in an apparent surface stoichiometry close to iron oxy-hydroxy oxide (FeOOH) (Baer et al., 2010) which is also associated with the generation of hydrogen (Chen et al., 2011). These surface groups may function as reactive sites to bind with contaminants in the solution, in a mode similar to surface adsorption on iron oxyhydroxy oxide (Yan et al., 2010). Therefore, the irreversible reduction of tetrachloro-ethylene (PCE) to trichloro-ethylene (TCE) by solid nZVI according to hydrogenolysis mechanism can be described by the following simple equation 

Fe0 ðsÞ þ C2 Cl4 ðlÞ þ 2H2 O ! FeOOHðsÞ þ C2 HCl3 ðlÞ þ Cl þ 2Hþ ð1aÞ Then, the TCE is transformed to dichloro-ethylene (DCE) which is converted to vinyl-chloride (VC) and finally ethylene (C2H4) is obtained as final product.

193

C.D. Tsakiroglou et al. / Chemical Engineering Science 167 (2017) 191–203

Respectively, the PCE reduction according to the b-elimination mechanism is described by the simple equation 

Fe0 ðsÞ þ C2 Cl4 ðlÞ þ 2H2 O ! FeOOHðsÞ þ C2 Cl2 ðlÞ þ 2Cl þ 3Hþ ð1bÞ To simplify the problem, we assume that the reduction of PCE either to trichloro-ethylene, Eq. (1a), or dichloro-acetylene, Eq. (1b), is the step controlling the overall dechlorination rate. On the other hand, it might be of key importance to identify the role of nZVI characteristics (e.g. particle-size distribution) and masstransfer mechanisms (e.g. diffusion) at particle-scale on the overall process dynamics. 3.2. Shrinking core model for uniform particles When a compound of a fluid reacts irreversibly with suspended solid particles, the global reaction rate at the particle-scale is commonly governed by three (3) fundamental mechanisms: (1) mass transfer from the bulk phase to the external surface of particles; (2) diffusion in the interior of particle; (3) intrinsic reaction on the solid/liquid interface. To determine the nZVI reaction rate as a function of PCE concentration in liquid bulk phase, we will analyse the mass transfer-reaction processes at the scale of a single iron particle by considering a general reaction between the liquid reactant LR, and the solid reactant SR, which transit to a liquid, LP, and solid, SP, products (Smith, 1981):

LRðlÞ þ bSRðsÞ ! LPðlÞ þ SPðsÞ

ð2Þ

Given that initially, the iron nanoparticles, SR, are not porous, the reaction will occur on their external surface. According to the shrinking core model (Huang et al., 2007; Lopez-Fonseca et al., 2009), this surface retracts with the extent of reaction and time (Fig. 1). As the reaction proceeds, a porous layer of product, SP (iron oxyhydroxy oxide), is generated around the core of the particle that has yet not reacted. The basic feature of this model is that the reaction always occurs on the interface separating the nonreacted core from the surrounding solid product (Fig. 1). A spherical particle SR (nZVI) of initial radius rs is suspended in an aqueous solution where the bulk concentration of compound LR (e.g. PCE) is CLRb. As the reaction proceeds, a layer (shell) of product SP (e.g. FeOOH) is created around the non-reacted core of SR. We assume that this layer is porous so that the compound LR may diffuse through SP to react with SR on the SR/SP interface (Fig. 2). The radial distribution of the concentration of LR on the region bounded by the liquid phase and reacting surface will resemble that shown in Fig. 2. In order to calculate the global reaction rate in a single particle, the following assumptions are adopted (Smith, 1981): (1) the

nanoparticle retains its spherical shape during reaction. (2) the density of produced porous iron oxide and reacting nZVI are identical, so that the particle radius does not change with time; (3) no liquid region is inserted between the unreacted core, SR, and produced layer, SP; (4) the velocity of reaction interface at the radial distance r = rc, drc/dt, is sufficiently low, compared to the diffusion rate of LR through the porous oxide layer, SP, so that pseudosteady-state is considered; (5) the reaction rate on the interface is proportional to its area. Based on assumption (4), the mass-transfer rate of LR through the boundary layer of liquid phase surrounding the particle, the diffusion rate of LR through the porous layer SP, and the reaction rate on the interface are equal. The three aforementioned rates, expressed in moles of LR consumed per unit time per particle dNLR =dt are given by the following equations:



dNLR ¼ 4pr 2s km ðC LRb  C LRs Þ dt

ð3aÞ




 dNLR dC LR ¼ 4pr 2c De dt dr r¼rc

ð3bÞ



dNLR n ¼ 4pr 2c kC LRc dt

ð3cÞ

In the foregoing equations, km is the mass-transfer coefficient from the bulk liquid phase to the external particle surface, De is the effective diffusion coefficient of LR through the produced porous iron oxide, and k is the kinetic constant of the irreversible nth order reaction on the interface.

SR rc rs

Reactant SR

CLRb CLRs CLR

Product SP

CLRc 0

0

Fig. 2. Radial distribution of compound LR concentration across a spherical particle.

Inial reacng nanoparcle

Shrinking core nanoparcle

SR

SR

SP

r

Liquid boundary layer

Final product

SP

Fig. 1. Schematic diagram of reacting nanoparticle consumption according to the shrinking core model.

194

C.D. Tsakiroglou et al. / Chemical Engineering Science 167 (2017) 191–203

Considering pseudo-steady-state in a spherical shell between the radial positions r and r + Dr within the layer of the porous product, SP, the mass balance for the diffusion of LR is written

ðNLR Þr  ðN LR ÞrþDr



 dC LR dC LR ¼ 0 ) pr 2 De  pr 2 De ¼0 dr r dr rþDr ð4Þ

Taking the limit as Dr ! 0 it is obtained


 d dC LR r 2 De ¼0 dr dr

ð5Þ

which, in conjunction with the boundary conditions r ¼ rs , C LR ¼ C LRs & r ¼ r c , C LR ¼ C LRc , and after two integrations yields

C LR


 1  rc =r ¼ C LRc þ ðC LRs  C LRc Þ 1  r c =rs

ð6Þ

From Eq. (6), the concentration gradient of reactant is calculated at the radial position r = rc


 dC LR C LRs  C LRc ¼ dr r¼rc rc ð1  r c =r s Þ

dNLR C LRs  C LRc ¼ 4pr2c De dt rc ð1  r c =rs Þ

ð14Þ

where CSR0 is the initial concentration of SR in terms of moles per volume unit. In a batch reactor, the variation of the concentration of reacting compound LR is associated with its reaction with SR, and the mass balance is written

Rp qSR þ

dC LRb ¼0 dt

ð15Þ

Replacement of Eq. (10) and (14) in Eq. (15) yields

dC LRb 3M SR kðr c =r s Þ2 C SR0 C nLRc ¼ dt qs r s

ð16Þ

The effective diffusion coefficient in porous solid SP, De, is closely related with the molecular diffusion coefficient, Dm, through the general relation

/Dm d

De ¼

ð8Þ

where / is the porosity and d is the tortuosity of the porous shell of iron oxide, SP. By introducing the parameter, k ¼ /=d, Eq. (17) is written

By combining Eqs. (3a) and (3c) with Eq. (8), it is obtained

C nLRc ½ðr c =r s Þ2 ðk=km Þ þ ðkrc =De Þð1  r c =r s Þ þ C LRc  C LRb ¼ 0

C SR0 M SR qs 43 pr3s

qSR ¼

ð7Þ

By substituting Eq. (7) in Eq. (3b) we get



The concentration of particles of identical size, rs, per mass unit of the suspension, qSR, is given by the relation

ð9aÞ

st

De ¼ kDm ;

ð17Þ

k 1:0) the model predicts that the quantity of nZVI is not sufficient for the reduction of all PCE (Fig. 11a and b), while in the other two cases (a < 1:0), the model predicts the PCE depletion without the consumption of nZVI (Fig. 11c–f). However, there is a significant discrepancy between the model predictions and experimental datasets, particularly with reference to the residual PCE concentration (Fig. 11a, c, and e). The non-zero PCE concentration measured at the end of each test, even for high nZVI concentrations, might be attributed to the adsorption of PCE on the oxidized iron particles. During the extraction of residual dissolved PCE to n-hexane, the adsorbed and not reacted PCE is also desorbed and included in the residual concentration. Therefore, in order to improve the predictability of the statistical shrinking-core model, some mechanism of PCE adsorption on the porous layer of iron oxide should be taken into account. On the other hand, nZVI may

be oxidized, before and during reaction, by other (except of chlorinated hydrocarbons) species, even under anaerobic conditions (Filip et al., 2014), whereas PCE adsorbed on porous iron oxide surfaces may be reduced to other chlorinated substances. Subsequently, a high uncertainty is embedded in both the initial radius of non-oxidized core, and adsorbed PCE mass that has not reacted and desorbs in organic solvent. This uncertainty may explain the non-monotonic changes of measured PCE concentrations (Fig. 11a, c, and e). With differentiation of Eq. (33) and use of Eq. (29) it is obtained

!Z  1 2 dC SR 3L2 bMSR C nLRb0 k C n LRc r c f ðr s Þdr s ¼ Dm qs ds rs 0

ð39Þ

From Eqs. (39) and (29) we get  dC SR  dC LRb

¼ a ) C SR ¼ aC LRb þ 1  a ) C SR ¼ 1  að1  C LRb Þ

ð40Þ

which coincides to Eq. (25b) for mono-disperse nanoparticles. If Eq. (29) is combined with Eq. (31a) we get !Z  1 dC LRb 3L2 M SR C SR0 k ðC LRb  C LRc Þr 2 c f ðr s Þ ¼ dr s 2 ðk=k Þ þ r  ð1  r  Þðkr Þ=ðkD Þ Dm qs r ds ½r s c m s m 0 c c

ð41aÞ For n = 1, Eq. (41a) is converted to

199

C.D. Tsakiroglou et al. / Chemical Engineering Science 167 (2017) 191–203 100

100

10-1

10-2 10-8

Dimensionless bulk conc., CLRb*

Dimensionless core radius, rc*

(a) a=0.1 a=0.2 a=0.5 a=1.0 a=2.0 a=10.0

10-7

10-6

10-5

(b) a=0.1 a=0.2 a=0.5 a=1.0 a=2.0 a=10.0

10-1

10-8

10-4

10-7

Dimensionless interfacial conc., CLRc*

10-5

10-4

Dimensionless time, τ

Dimensionless time, τ 100

10-6

(c) a=0.1 a=0.2 a=0.5 a=1.0 a=2.0 a=10.0

10-1

10-2 10-8

10-7

10-6

10-5

10-4

Dimensionless time, τ Fig. 6. Transient response of the dimensionless (a) particle core radius, (b) reactant (LR) concentration in bulk liquid, (c) reactant (LR) concentration in unreacted core/reacted shell interface, as a function of molar ratio a for: Da = 0.1, Sh = 0.1, k = 0.1, n = 1.0, rs = 50 nm.

! Z 1  dC LRb 3L2 M SR C SR0 k  r2 c f ðr s Þ dr s ¼ C LRb 2 D m qs rs ½rc ðk=km Þ þ rc ð1  rc Þðkr s Þ=ðkDm Þ ds 0 ð41bÞ

Based on Eq. (33), the last term of Eq. (41b) can be regarded as a function of the concentration of SR (nZVI) through an approximation of the form

Z 0

1

r 2 c f ðr s Þ dr s ¼  ð1  r  Þðkr Þ=ðkD Þ r s ½r 2 ðk=k Þ þ r m s m c c c




C SR

l

ms ð42Þ

5. Conclusions

where ms is an adjustable exponent. For mono-disperse particle distribution, it is obtained ms ffi 2=3. Eq. (41) in conjunction with Eq. (42) yields

!  dC LRb 3L2 MSR C SR0 k  ms C LRb C SR ¼ Dm qs lms ds

ð43Þ

and accounting for Eq. (40), we finally get

!  dC LRb 3L2 MSR C SR0 k  m C LRb ½1  að1  C LRb Þ s ¼ Dm qs lms ds

constant, k, and the exponent ms. By fixing the kinetic constant to the values of Table 4, the exponents ms was estimated by fitting the experimental datasets to Eq. (44) by (Table 5). The exponent ms specifies the dependency of the overall reaction rate on the nZVI concentration. In which cases, nZVI is available in excess, ms tends to the limiting value 2/3 (Table 5). In contrast, the value of ms increases and approaches unity when nZVI is insufficient for the reduction of PCE (Table 5).

ð44Þ

Eqs. (44) and (40) comprise an approximate phenomenological model from which the SR (nZVI) core radius has been eliminated. Unknown parameters to estimate are: the surface reaction kinetic

To calculate the overall reaction rate of uniform spherical solid nanoparticles with liquid compounds in batch reactors, the classical shrinking core model (Smith, 1981) is generalized for nth order surface reactions, and used to analyze the effect of dimensionless parameters (Da, Sh, n, a, k) on the transient variation of the concentration of reactants. A statistical shrinking core model is developed to compute the overall reaction rate for non-uniform particle distributions, and used to estimate the reaction kinetic parameters and mass-transfer coefficients for the PCE dechlorination by nZVI, with inverse modeling of experimental datasets of batch experiments (Tsakiroglou et al., 2016). Based on the results of analysis, a true-to-the mechanism phenomenological parametric model is suggested to describe analytically the dechlorination rate of PCE as a function of PCE and nZVI concentrations.

200

C.D. Tsakiroglou et al. / Chemical Engineering Science 167 (2017) 191–203 100

(a) 10-1

10-2

n=0.25 n=0.5 n=0.75 n=1.0 n=1.5 n=3.0

10-3

10-4 10-7

10-6

(b)

Dimensionless bulk conc., CLRb*

Dimensionless core radius, rc*

100

10-5

10-4

10-3

10-2

10-1

n=0.25 n=0.5 n=0.75 n=1.0 n=1.5 n=3.0

10-2 10-3 10-4 10-5 10-6 10-7 10-7

10-1

10-6

10-4

10-3

10-2

10-1

Dimensionless time, τ

Dimensionless time, τ

Dimensionless interfacial conc., CLRc*

10-5

100 10-1

(c)

10-2

n=0.25 n=0.5 n=0.75 n=1.0 n=1.5 n=3.0

10-3 10-4 10-5 10-6 10-7 10-7

10-6

10-5

10-4

10-3

10-2

10-1

Dimensionless time, τ Fig. 7. Transient response of the dimensionless (a) particle core radius, (b) reactant (LR) concentration in bulk liquid, (c) reactant (LR) concentration in unreacted core/reacted shell interface, as a function of reaction order n for: Da = 0.1, Sh = 0.1, k = 0.1, a = 1.0, rs = 50 nm.

100

10-1

10-2

10-3 10-6

Dimensionless bulk conc., CLRb

Dimensionless bulk conc., CLRb*

*

100

μ=25.0 μ=50.0 μ=75.0 μ=100.0 μ=200.0 μ=500.0 σ/μ=0.4

10-5

10-4

10-3

10-2

Dimensionless time, τ

10-1

10-2

10-3 10-6

σ=0.0 nm σ=5.0 nm σ=10.0 nm σ=40.0 nm σ=80.0 nm σ=150.0 nm μ=100 nm

10-5

10-4

10-3

10-2

Dimensionless time, τ

Fig. 8. Effect of the mean value of the log-normal particle size distribution on the transient response of the of the reactant concentration (LR) in bulk liquid for: k = 0.1 m s1, km = 104 m s1, k = 0.1, n = 1.0, a = 1.0.

Fig. 9. Effect of the standard deviation of the log-normal particle size distribution on the transient response of the reactant concentration (LR) in bulk liquid for: k = 0.1 m s1, km = 104 m s1, k = 0.1, n = 1.0, a = 1.0.

The statistical shrinking core model enables us to interpret nZVI reactivity tests in terms of the particle-size distribution and parameters quantifying the reaction and mass-transfer processes at particle-scale. In addition, it allows us to suggest true-to-the physics phenomenological models for the PCE

dechlorination rate to be built-in macroscopic numerical simulators of PCE remediation. However, the model predictability is still weak because of uncertainties associated with PCE adsorption on oxidized particles and anaerobic oxidation of nZVI.

201

C.D. Tsakiroglou et al. / Chemical Engineering Science 167 (2017) 191–203 Table 2 Physicochemical properties of nZVI suspensions. pH

Eh (mV)

Size (nm)

PDI

Zeta Potential (mV)

Conductivity (mS/cm)

Quality result

Concentration (g/L)

8.35 8.45 9.61

500 500 568

177.2 31.84 405.3

0.351 0.461 0.333

58.1 43.1 52.5

0.0653 0.107 0.563

Good Good Good

0.9087 0.091975 0.0104

1.2

(a) CFe =0.46 g/L 0

1.4

Probability density, dF/d(lnDs)

Probability density, dF/d(lnDs)

1.6

Number-based PSDs

1.2

PSD1 PSD2 PSD3

1.0 0.8 0.6 0.4 0.2 0.0 100

101

102

103

104

(b) CFe =0.46 g/L 0

1.0 0.8

Volume-based PSDs PSD1 PSD2 PSD3

0.6 0.4 0.2 0.0 100

101

Particle diameter, Ds (nm)

CFe =0.046 g/L 0

1.4 1.2

Number-based PSDs

1.0

PSD1 PSD2 PSD3

0.8 0.6 0.4 0.2 101

102

103

104

(d)

CFe =0.046 g/L 0

1.0 Volume-based PSDs

0.8

PSD1 PSD2 PSD3

0.6 0.4 0.2 0.0 100

101

103

104

1.2

1.6

(e) CFe =0.005 g/L

Probability desnity, dF/d(lnDs)

Probability desnity, dF/d(lnDs)

102

Particle diameter, Ds (nm)

Particle diameter, Ds (nm)

0

1.4

104

1.2

(c)

0.0 100

103

Particle diameter, Ds (nm)

Probability density, dF/d(lnDs)

Probability density, dF/d(lnDs)

1.6

102

Number-based PSDs 1.2

PSD1 PSD2 PSD3

1.0 0.8 0.6 0.4 0.2 0.0 100

101

102

103

104

(f)

CFe =0.005 g/L 0

1.0 0.8 Volume-based PSDs 0.6

PSD1 PSD2 PSD3

0.4 0.2 0.0 100

101

102

103

104

Particle diameter, Ds (nm)

Particle diameter, Ds (nm)

Fig. 10. Measured number- and volume-based particle diameter distributions. Table 3 Statistical moments of measured number- & volume-based nZVI diameter distributions. Fe conc. (g/L)

l1 (nm)

r1 (nm)

l2 (nm)

r2 (nm)

l (nm)

r (nm)

Number-based distribution

0.46 0.046 0.005

88.3 7.9 305

25.5 2.35 116.4

67.7 11.4 270.4

21.5 2.84 96.6

78.0 9.6 287.7

23.6 2.6 106.5

Volume-based distribution

0.46 0.046 0.005

192.7 13.4 542.9

139.7 7.1 261.5

211.4 15.5 487.2

196.4 6.2 261.3

202 14.5 515

168.1 6.6 261.4

202

C.D. Tsakiroglou et al. / Chemical Engineering Science 167 (2017) 191–203

Table 4 Parameter values of the statistical shrinking-core model estimated from experimental measurements of batch tests by using the volume-based log-normal particle size distributions of nZVI (Table 3). Fe conc. (g/L)

0.46

0.046

k [m s1 (m3/kmol)n1 ]

1:395 103 5:62 104

1:10 103 1:32 105

3

n km (m s1)

0:93 5:93 102

1:65 9:9 10

9:62 103 4:63 103

6:87 104 7:87 106

1:78 10

5:62 104 1:00 104

3

1:51 3:4 10 4

k

0.005

3:48 10

5

1:75 10

4

4:97 10

4:3 104 3:25 105

5

8:78 102 6:2 103

(a)

CSR0=0.005 g/L

1.0

0.8

0.6

0.4

Exper. Predicted CLRb0=50.0 ppm CLRb0=37.5 ppm

0.2

CLRb0=25.0 ppm CLRb0=10.0 ppm

0.0 10-5

10-4

10-3

10-2

10-1

Dimensionless nZVI conc., CSR*

Dimensionless PCE conc., CLRb*

1.0

(b) 0.8

0.6 CLRb0=50.0 ppm

0.4

CLRb0=37.5 ppm CLRb0=25.0 ppm CLRb0=10.0 ppm

0.2

0.0 10-5

10-4

Dimensionless time, τ

10-1

1.0 Exper. Predicted

(c)

CLRb0=50.0 ppm CLRb0=37.5 ppm

0.8

0.6

CLRb0=25.0 ppm CLRb0=10.0 ppm

CSR0=0.046 g/L

CLRb0=5.0 ppm CLRb0=2.5 ppm

0.4

0.2

0.0 10-5

10-4

10-3

10-2

Dimensionless nZVI conc., CSR*

Dimensionless PCE conc., CLRb*

10-2

Dimensionless time, τ

1.0

10-1

(d) 0.9

0.8 CLRb0=50.0 ppm

0.7

CLRb0=37.5 ppm CLRb0=25.0 ppm CLRb0=10.0 ppm

0.6

CLRb0=5.0 ppm CLRb0=2.5 ppm

0.5 10-5

10-4

Dimensionless time, τ

Exper. Predicted CLRb0=50.0 ppm CLRb0=37.5 ppm

(e)

CLRb0=25.0 ppm

0.6

CLRb0=10.0 ppm CLRb0=5.0 ppm

0.4

CLRb0=2.5 ppm

0.2

0.0 10-5

10-4

10-3

10-2

10-1

1.00

CSR0=0.46 g/L

0.8

10-3

Dimensionless time, τ

10-2

10-1

Dimensionless time, τ

Dimensionless nZVI conc., CSR*

1.0

Dimensionless PCE conc., CLRb*

10-3

0.99

CLRb0=50.0 ppm

(f)

CLRb0=37.5 ppm CLRb0=25.0 ppm

0.98

CLRb0=10.0 ppm CLRb0=5.0 ppm

0.97

CLRb0=2.5 ppm

0.96

0.95 10-5

10-4

10-3

10-2

10-1

Dimensionless time, τ

Fig. 11. (a, c, e) Comparison of experimentally measured with numerically predicted transient responses of the concentration of dissolved compound LR (PCE) for various initial concentrations of solid particles SR (nZVI) in the suspension. (b, d, f) Numerical prediction of the transient response of nZVI concentration.

Acknowledgements

Table 5 Estimated values of the exponent ms in Eq. (44). Fe conc. (g/L)

ms volume-based PSD

0.46 0.046 0.005

0:684 0:0265 0:662 0:021 1:004 0:102

The research is co-financed by the European Union (European Social Fund-ESF) and Greek national funds in the context of the action ‘‘EXCELLENCE II” of the Operational Program ‘‘Education and Lifelong Learning”, project no 4118 (project title: ‘‘Optimizing the properties of nanofluids for the efficient in situ soil

C.D. Tsakiroglou et al. / Chemical Engineering Science 167 (2017) 191–203

remediation-SOILREM”). Also, the financial support of the project ‘‘Monitoring and Modeling of Natural Environment and Natural Resources” (General Secretariat for Research and Technology/ Siemens) is acknowledged.

References Arnold, W.A., Roberts, A.L., 2000. Pathways and kinetics of chlorinated ethylene and chlorinated acetylene reaction with Fe(0) particles. Envrion. Sci. Technol. 34, 1794–1805. Baer, D.R., Gaspar, D.J., Nachimuthu, P., Techane, S.D., Castner, D.G., 2010. Application of surface chemical analysis tools for characterization of nanoparticles. Anal. Bioanal. Chem. 396 (3), 983–1002. Bokias, G., Mylonas, Y., Staikos, G., Bumbu, G.G., Vasile, C., 2001. Synthesis and aqueous solution properties of novel thermoresponsive graft copolymers based on a carboxymethylcellulose backbone. Macromolecules 34, 4958–4964. Campbell, T.J., Burris, D.R., Roberts, A.L., Wells, J.R., 1997. Trichloethylene and tetrachloroethylene reduction in a metallic iron-water-vapor batch system. Environ. Toxicol. Chem. 16 (4), 625–630. Chen, K.-F., Li, S., Zhang, W.-X., 2011. Renewable hydrogen generation by bimetallic zero valent iron nanoparticles. Chem. Eng. J. 170, 562–567. Chen, S.-S., Huang, Y.-C., Lin, J.-Y., Lin, M.-H., 2014. Dechlorination of tetrachloroethylene in water using stabilized nanoscale iron and palladized iron particles. Desalination Water Treat. 52, 702–711. Crane, R.A., Scott, T.B., 2012. Nanoscale zero-valent iron: future prospects for an emerging water treatment technology. J. Hazard. Mater. 211–212, 112–125. Fagerlund, F., Illangaserake, T.H., Phenrat, T., Kim, H.-J., Lowry, G.V., 2012. PCE dissolution and simultaneous dechlorination by nanoscale zero-valent iron particles in a DNAPL source zone. J. Contam. Hydrol. 131, 9–28. Filip, J., Karlicky, F., Marusak, Z., Lazar, P., Cernik, M., Otyepka, M., Zboril, R., 2014. Anaerobic reaction of nanoscale zerovalent iron with water: mechanism and kinetics. J. Phys. Chem. C 118, 13817–13825. Gbor, P.K., Jia, C.Q., 2004. Critical evaluation of coupling particle size distribution with the shrinking core model. Chem. Eng. Sci. 59, 1979–1987. Gunawardana, B., Singhal, N., Swedlund, P., 2012. Dechlorination of pentachlorophenol by zero valent iron and bimetals: effect of surface characteristics and bimetal preparation processes. In: Proc. of the Ann. Intern. Conf. on Soils, Sediments, Water, and Energy, vol. 17, Article 8. He, F., Zhao, D., 2007. Manipulating the size and dispersibility of zerovalent iron nano particles by use of carboxymethyl cellulose stabilizers. Environ. Sci. Technol. 41, 6216–6221. He, F., Zhao, D., Paul, C., 2010. Field assessment of carboxymethyl cellulose stabilized iron nanoparticles for in situ destruction of chlorinated solvents in source zones. Water Res. 44, 2360–2370. Huang, H., Kobayashi, N., Hasatani, M., Matsuyama, K., Sasaki, T., 2007. Reaction kinetics analysis of dechlorination process of PCB by sodium dispersion process. Chem. Eng. Sci. 62, 5144–5149.

203

Ji, Y., 2014. Ions removal by iron nanoparticles: a study on solid–water interface with zeta potential. Coll. Surfaces A: Physicochem. Eng. Aspects 444, 1–8. Liu, Y., Majetich, S.A., Tilton, R.D., Sholl, D.S., Lowry, G.V., 2005. TCE dechlorination rates, pathways, and efficiency of nanoscale iron particles with different properties. Environ. Sci. Technol. 39 (5), 1338–1345. Lopez-Fonseca, R., Gonzalez-Velasco, J.R., Gutierez-Ortiz, J.I., 2009. A shrinking core model for the alkaline hydrolysis of PET assisted by tributylhexadecylphosphonium bromide. Chem. Eng. J. 146, 287–294. Mueller, N.C., Braun, J., Bruns, J., Cernik, M., Rissing, P., Rickerby, D., Nowack, B., 2012. Application of nanoscale zero valent iron (NZVI) for groundwater remediation in Europe. Environ. Sci. Pollut. Res. 19, 550–558. Nurmi, J.T., Tratnyek, P.G., Sarathy, V., Baer, D.R., Amonette, J.E., Pecher, K., Wang, C. M., Linehan, J.C., Matson, D.W., Penn, R.L., Driessen, M.D., 2005. Characterization and properties of metallic iron nanoparticles: spectroscopy, electrochemistry, and kinetics. Environ. Sci. Technol. 39, 1221–1230. O’Carroll, D.M., Sleep, B., Krol, M., Boparai, H., Kocur, C., 2013. Nanoscale zerovalent iron and bimetallic particles for contaminated site remediation. Adv. Water Resour. 51, 104–122. Orth, W.S., Gillham, R.W., 1996. Dechlorination of trichloroethylene in aqueous solution using Fe(0). Environ. Sci. Technol. 30, 66–71. Petersen, E.J., Pinto, R.A., Shi, X., Huang, Q., 2012. Impact of size and sorption on degradation of trichloroethylene and polychlorinated biphenyls by nano-scale zerovalent iron. J. Hazard. Mater. 243, 73–79. Schmid, D., Micic, V., Laumann, S., Hofmann, T., 2015. Measuring the reactivity of commercially available zero-valent iron nanoparticles used for environmental remediation with iopromide. J. Contam. Hydrol. 181, 36–45. Smith, J.M., 1981. Chemical Engineering Kinetics. McGraw-Hill. Stewart, W.E., Caracotsios, M., 2008. Computer-Aided Modeling of Reactive Systems. Wiley. Taghavy, A., Costanza, J., Pennell, K.D., Abriola, L.M., 2010. Effectiveness of nanoscale zero-valent iron for treatment of a PCE-DNAPL source zone. J. Contam. Hydrol. 118, 128–142. Tratnyek, P.G., Johnson, R.L., 2006. Nanotechnologies for environmental cleanup. Nano Today 1, 44–48. Tsakiroglou, C., Terzi, K., Sikinioti-Lock, A., Hajdu, K., Aggelopoulos, C., 2016. Αssessing the capacity of zero valent iron nanofluids to remediate NAPLpolluted porous media. Sci. Tot. Environ. 563–564, 866–878. Wang, C.M., Baer, D.R., Amonette, J.E., Engelhard, M.H., Antony, J., Qiang, Y., 2009. Morphology and electronic structure of the oxide shell on the surface of iron nanoparticles. J. Am. Chem. Soc. 131, 8824–8832. Yan, W., Herzing, A.A., Kiely, C.J., Zhang, W.-X., 2010. Nanoscale zero-valent iron (nZVI): aspects of the core-shell structure and reactions with inorganic species in water. J. Contam. Hydrol. 118, 96–104. Yan, W., Lien, H.-L., Koel, B.E., Zhang, W.-X., 2013. Iron nanoparticles for environmental clean-up: recent developments and future outlook. Environ. Sci. Process. Impacts 15, 63–77. Zhang, Z.-Y., Lu, M., Zhang, Z.-Z., Xiao, M., Zhang, M., 2012. Dechlorination of short chain chlorinated paraffins by nanoscale zero-valent iron. J. Hazard. Mater. 243, 105–111.