Numerical simulation for reactive solute transport of arsenic in permeable reactive barrier column including zero-valent iron

Applied Mathematical Modelling 35 (2011) 5198–5207

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Numerical simulation for reactive solute transport of arsenic in permeable reactive barrier column including zero-valent iron Osama Eljamal ⇑, Keiko Sasaki, Tsuyoshi Hirajima Department of Earth Resources Engineering, Kyushu University, 744 Motooka, Fukuoka 819-0395, Japan

a r t i c l e

i n f o

Article history: Received 7 January 2011 Received in revised form 21 April 2011 Accepted 26 April 2011 Available online 1 May 2011 Keywords: Permeable reactive barrier Zero-valent iron Removal of arsenite Groundwater Numerical simulation

a b s t r a c t Numerical modeling was developed in one dimensional solute transport including chemical reaction to simulate the permeable reactive barrier column results, in which arsenite (As(III)) was removed using zero-valent iron (ZVI). Removal principles of As(III) includes oxidation of As(III) to As(V), sorption of As(III) and sorption of As(V) at least. Each kinetic parameter was drawn in preliminary batch tests to integrate the simulation. The column simulation results show that As(V) adsorption rate was faster than the As(III) adsorption rate and that they are affected by the available mass of Fe(III) in the system. The model can be used to design and predict the long term performance of ZVI permeable reactive barriers (PRBs). Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction Arsenic contamination of drinking water is an issue of great concern. Due to its high toxicity to humans, the World Health Organization (WHO) has set a maximum concentration limit of 10 lg L1 for arsenic in drinking water [1]. Natural occurrence of arsenic in groundwater is associated with sedimentary deposits, volcanic deposits, geothermal fields, neotectonic active fault areas and regions near lacustrine or marine deposits [2]. Arsenic contamination in groundwater also occurs due to irresponsible human activity, such as agricultural activities, where arsenic is used for the production of insecticides and herbicides. Areas, which are close to mining activities, have also been found to contain elevated arsenic concentrations [3]. Arsenic is present mainly in inorganic forms in natural waters. As(V) is the predominant species in oxygenated environments, whereas As(III) species is the predominate arsenic form in reducing environments [2]. Inorganic arsenic species are predominantly in molecular form of H3AsO30 and the negatively charged H2AsO4 and HAsO42 at neutral pH values. As(III) is more toxic than As(V) and tends to be more mobile in the environment, but As(III) can be rapidly oxidized to As(V) during the transport of waters and their mixing with shallow oxidized ground waters, rivers or lakes [4]. Several techniques have been proposed for arsenic removal from water. Current technologies include combination of different principles of precipitation, coagulation and filtration, reverse osmosis, ion exchange and adsorption. Zero-valent iron (ZVI) has recently gained attention in removal of arsenic due to its applicability under different geochemical conditions, operational simplicity and low cost maintenance [5]. Recently, the kinetics of arsenic removal by ZVI and the factors affecting arsenic removal by ZVI have been studied extensively [5–11]. As(III) and As(V) removal mechanism by ZVI involves the formation of Fe(II) and Fe(III) corrosion products onto the surface of iron due to oxidation. The formation of corrosion products onto the surface of ZVI results in the increase of ⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (O. Eljamal). 0307-904X/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.apm.2011.04.040

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adsorption places for both As(III) and As(V). The proposed mechanism of arsenic removal is the formation of As(III) and As(V) complexes onto iron corrosion products. Another study proposed that the surface adsorption is the predominant removal process of arsenic by ZVI [10,12]. Su and Puls [13] conducted batch studies to evaluate the effectiveness of four kinds of ZVI granules to remove As(III) and As(V) from water. Their results showed that ZVI is highly effective in removing arsenic from solution and suggests that arsenic forms stronger surface complexes which move into the ZVI structure with increasing time. Farrell et al. [14] investigated electrochemically and spectroscopically the removal of As(V) by ZVI media. They concluded that As(V) removal by ZVI involves surface complexation only and does not involve reduction to metallic form. These studies clearly show arsenic removal by ZVI is a viable method that should be considered as an alternative drinking water treatment method. Hence, both oxidation forms of arsenic can be treated by this method. Lien and Wilkin [11] used the CFITIM program to model arsenic removal from water by columns packed with ZVI using a one dimensional analytical solution to solve non-equilibrium, advection dispersion transport equation with arsenic uptake. Their results showed that the surface precipitates a major mechanism responsible for arsenic remediation by ZVI. Sasaki et al. [15] have reported column performance in removal of As(III) with ZVI using a laboratorial test for two months monitoring oxidation process of As(III) to As(V) in aqueous phase and solid surfaces. In the present work, we propose a modeling approach that attempts to predict the performance of arsenic removal by ZVI for a long term. The model was developed to simulate the immobilization process of arsenic using a one-dimensional advective dispersive equation with chemical reactions. To elucidate kinetics of chemical reactions, additional batch tests were also conducted. 2. Methodology 2.1. Reactive materials The sorbent used in the present work is zero-valent iron (ZVI), which was supplied by Connelly Ltd., Chicago, IL, USA. The Fe content was determined to be 89.82 wt% by XRF. The ZVI grain size rang from 0.25 to 2.0 mm with specific surface area1.8 m2 g1, bulk density 2.4 g cm3 and Hydraulic conductivity 5  102 cm s1. The leaching test results recommended by the Environmental Ministry of Japan (notification No. 46) showed no toxic species released from ZVI above the maximum concentration limit (MCL). 2.2. Batch tests Arsenic solutions were prepared by adding KH2AsO4 for solution as arsenate and adding NaAsO2 for solution as arsenite and the pH controlled at 9.0 using HCl or NaOH solution during the tests. The ZVI was washed with ethanol and acetone to remove the oxidized layer on ZVI. Five grams of ZVI was added into 0.25 L3 of prepared solution in a glass flask. The solution in a flask had been purged with nitrogen gas for about 30 min. The mixtures were shaken at 100 rpm and 25 °C for 120 h. At appropriate intervals solution samples were taken and filtered with a 0.2 lm membrane filter prior to determination of As(III) and As(V) by LC-ICP-MS (Agilent 7500CE, YOKOGAWA, Japan). 2.3. Column experiments The column was made of acrylic with inner diameter of 7.5 cm and height 40 cm with an internal volume of 1.7 L. Three centimetre thick glass bead layers were placed at the top and bottom of the column to provide uniform flow. The rest of the column was filled with material consisting of a mixture by volume of 10% ZVI as reactive material for As(III) immobilization, and the other materials are 20% wood chips, 20% compost leaves, 20% gravel (6.7–16.7 mm in diameter), and 30% glass beads (0.60–0.69 mm in diameter) as inactive materials to maintain the permeability of the column. The ZVI was pre-washed in the same manner described for the batch tests. All the materials were sterilized by autoclaving and then dried prior to filling the column. After packing the column was purged with N2 gas. The pore volume (pv) of the column was gravimetrically measured to be 631.5 mL3, corresponding to 35.8% of porosity. The influent was prepared by modification of actual arsenic contaminated groundwater by spiking arsenite concentration to 20–40 mg L3 as As(III) using NaAsO2. The initial concentration of As(III) was 20 mg L1 until 30 days, then elevated to 40 mg L1 because of better performance than expected, at the same time, other water chemistry of influent was also changed as shown in Table 1. The details of column experimental can be found in Sasaki et al. [15].

Table 1 Chemical compositions of influent solution (mg L1). Time (day)

Na+

K+

Ca2+

Mg2+

Cl

SO42

As

Alkalinity (CaCO3)

Tem. oC

pH

1–35 35–68

1587 1026

296 325

66 23

116 116

1204 1516

1340 442

20 40

360 700

25 17

8.0 8.0

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2.4. Model development 2.4.1. Transport model Arsenic is transported in the column by advection and dispersion processes. Surface adsorption on ZVI and oxidation of As(III) to As(V) were the major As(III) removal mechanisms. The fundamental one-dimensional partial differential equation governing the advective–dispersive solute transport of contaminants with chemical reaction in the porous media can be written as [16]:

  @½C i  @ @½C i  @½C i  ¼ DL  v0 þ Ri @t @y @y @y

ð1Þ

where Ci is the arsenic concentration, DL is the longitudinal dispersion coefficient, v0 is the average pore velocity, t is the time, y is the distance, and Ri is the arsenic reduction rate by chemical reaction. The longitudinal dispersion coefficient DL is described by

DL ¼ aL v 0 þ DM

ð2Þ

where aL is the longitudinal dispersivity, and DM is the molecular diffusion coefficient. 2.4.2. Chemical reactions Based on the results of batch experiments and the proposed mechanisms of arsenic removal, the initial conceptual model of possible chemical reactions was developed. The chemical model was used to simulate the chemical reactions that occurred in the batch experiments. In a subsequent step the column results were simulated with the chemical model, which couples with the solute transport model. The chemical mode describes the rate at which chemical reactions occur in As/ZVI/H2O system. The model takes into account the two main oxidation states of arsenic in natural waters, as As(III) and As(V). The removal processes of As(III) can be described by two mechanisms as follows: (i) adsorption of As(III) on the ZVI, (ii) oxidation of As(III) in aqueous phase to As(V), which is subsequently removed by adsorption on the ZVI. These processes can be described as the reaction mechanism for As(III) oxidation, adsorption and As(V) adsorption by ZVI, possible reactions may include: As(III) oxidation

H2 AsO3 þ 2Fe3þ þ 3OH ! 2Fe2þ þ HAsO2 4 þ 2H 2 O

ð3Þ

As(III) adsorption

H2 AsO3 þ Fe  OH ¼ FeH2 AsO3 þ OH

ð4Þ

As(V) adsorption  þ HAsO2 4 þ Fe  OH þ H ¼ FeHAsO4 þ H 2 O

ð5Þ

The kinetics of reduction from the above two reactions, in general form, can be written as k

As þ Fe  OH ! Fe  As

ð6Þ

where As is the arsenic concentration in the aqueous phase (As(III) and As(V)), FeOH is the available reactive surface, Fe–As is the concentration of arsenic in the solid phase and k is the reaction rate constant. The rate law can then be written as

Ri ¼

d½As ¼ k½Asn ½Fe  Asm dt

ð7Þ

where n and m are the constants representing order(s) of reaction, and t is time. Since the concentration of adsorbent is greater than that of the arsenic, the rate law can be treated as a pseudo-order reaction and simplified as

Ri ¼

d½As ¼ k½Asn dt

ð8Þ

Arsenic(III) oxidation and adsorption are slow processes and were modeled as a first-order-loss reaction [5]. Rate data of our batch test indicate that the kinetics of reduction conform to first-order reaction at different initial concentrations of arsenic(III). Therefore, for all chemical reactions of the arsenic removal a first-order rate expression was implemented, in general form, can be written as [17,18]:

Ri ¼

d½C i  ¼ k½C i  dt

ð9Þ

where Ri is the chemical reduction rate, Ci is the arsenic concentration, k is the reaction rate constant and t is time. The rate of removal of arsenic by ZVI decreases with decrease in surface area of ZVI. The decreases in ZVI surface area are due to As(III) and As(V) adsorption onto ZVI surfaces. A first-order rate equation is used to express the loss of ZVI reactivity, expressed as the loss of ZVI surface area S over time t [19–21]:

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dS ¼ kS dt

ð10Þ

where k is the surface area rate constant. To simulate the loss of ZVI surface area in the chemical model, reaction rate constant parameter k is normalized using the ZVI surface area as follows:

k ¼ ko S

ð11Þ

where k is the reaction rate constant, ko is the specific reaction rate constant and S is the reactive surface area of ZVI. Therefore, the first-order rate expression can be rewritten as:

Ri ¼

d½C i  ¼ ko S½C i  dt

ð12Þ

2.4.3. Coupling of transport and chemical reactions The whole equation describing transport and chemical reactions could be solved simultaneously. The equations are solved numerically using the method of characteristics and finite difference method. However, the sequential procedure is used where first the advective and dispersive transport equations are solved independently for each species. The chemical terms accounting for reactions are taken from the preceding time step. Then the chemical reaction equations are solved with the concentration changes from the transport step. The general procedure performed in advection–dispersion and reaction model for a typical simulation run is illustrated in Fig. 1. 3. Results and discussion 3.1. Model parameter The initial values were increased and decreased by one order of magnitude in order to determine parameter sensitivity. The model parameters are listed in the following tables. Table 2 shows the discretization of the hypothetical column, and the hydraulic parameters used for simulation of advective and dispersive transport. The discretization is chosen such as it meets

Start

Input initial conditions, boundary conditions, constants and

Time and distance calculation of time step and distance

Transport model calculation of advective-dispersive transport term

Chemical reaction model

Calculation of As(III) adsorbed onto the ZVI

Calculation of As(III) oxidized to As(V) Calculation of As(V) adsorbed onto the ZVI Results

Coupling of transport and chemical reactions

Results output results of all grid point

No

next time Yes End Fig. 1. Flow chart of solute transport model with chemical reduction.

Calculation of ZVI surface area

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O. Eljamal et al. / Applied Mathematical Modelling 35 (2011) 5198–5207 Table 2 Discretization and hydraulic parameters for the column simulations. Parameter

Function

Value

L d Dx Dt v

Column length Column diameter Distance between grid points Time step size Pore water velocity Longitudinal dispersivity Molecular diffusion coefficient Porosity

40 cm 7.5 cm 0.5 cm 30 s 5.25  105 cm s1 1.0 cm 2.095  104 cm 35.8%

aL Dm n

Fig. 2. Model and experimental results of Na+ concentration in the column experiment versus time.

Table 3 Chemical parameters for the batch test simulations. ZVI

As(V)

As(III)

S

k

IC

Kd

IC

Kx

Kd

4320 4320 4320

4.05  107 4.05  107 4.05  107

5 20 40

2.3  106 1.1  106 8.8  107

5 20 40

2.0  106 4.5  107 9.2  107

1.6  106 4.2  106 4.6  106

S: initial surface area (m2 L1), k: surface area rate (s1), IC: initial concentration (mg L1), Kx: oxidation rate (s1), Kd: adsorption rate (s1).

numerical stability and accuracy criteria (Courant number = (vDt)/Dx 6 1, grid number = Dx/aL 6 2) [22]. The pore water velocity of the column was calculated based on measured data. The dispersion coefficient parameter was calculated by the column breakthrough curves method [23] using the measured values of Na+ as a tracer were injected into a column (Fig. 2). The chemical parameters used for the simulation of batch test results are displayed in Table 3. The parameters developed from the batch test data were integrated into a reactive transport model to perform column experiment transport predictions. The chemical parameters used for the simulation of column experiment results are displayed in Table 4. 3.2. Batch tests The influence of initial As(V) and As(III) concentrations on arsenic removal was subsequently investigated. The initial concentration range was between 5 and 40 mg L1. The reaction rate constants of arsenic are summarized in Table 3. The As(V) removal rate at various initial concentrations, with the time is shown in Fig. 3, which indicates a rapid initial uptake rate of As(V), followed by a slower removal that gradually approaches an equilibrium condition. For example, about 50%–70% removal of As(V) was achieved within the first 6 h of contact, while only 10%–15% of additional removal occurred in the following 120 h. The slower adsorption is likely because of the decrease in the concentration difference between the solution and the surface, which decelerates transport of the As(V) to the ZVI surface. It is also evident that the rate of decrease of As(V) from the solution is dependent on the initial concentration (highest rate for highest concentration and lower rates for the lower concentrations).

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O. Eljamal et al. / Applied Mathematical Modelling 35 (2011) 5198–5207 Table 4 Chemical parameters for the column simulations. Parameter

Function

Value

Kx Kd Kd k S

Oxidation reaction rate constant for As(III) Adsorption reaction rate constant for As(III) Adsorption reaction rate constant for As(V) Surface area rate constant for ZVI Initial surface area for ZVI

1.38  107 s1 9.2  108 s1 8.8  107 s1 4.05  107 s1 4320 m2 L1

Fig. 3. Model and experimental behaviour of the As(V) in the batch experiment test.

Fig. 4 shows the concentration change of As(III) in aqueous solutions with time. It is important to consider the As(III) in the aqueous phase because As(III) is more toxic than As(V) [24]. Also initial As(III) concentration range was between 5 and 40 mg L1. A fast initial uptake rate of As(III) followed by a slow subsequent removal of arsenic that gradually approaches an equilibrium condition after 120 h of reaction. The results show that 80%–85% of As(III) removal by oxidation or adsorption occurs within 6 h and about 97%–99% of the total arsenic(III) was oxidized or adsorbed at equilibrium.

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Fig. 4. Model and experimental behaviour of the As(III) in the batch experiment test.

Fig. 5. Experimental results and model prediction of arsenic concentration in the column experiment versus time.

These results indicates that the oxidation of As(III) to As(V) could be employed as important role to enhance the reduction of As(III) concentration. The oxidants most likely were Fe(III) components in an oxidized layer on the surface of ZVI [25],

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Fig. 6. Model and experimental results of arsenic vertical profiles in the column experiment at 68 days.

Fig. 7. Model predicted the change in ZVI surface area with time from column experiments.

therefore the soluble arsenic remaining in the aqueous phase is converted to the less toxic and less mobile As(V), thus favouring its immobilization. As(V) concentration achieved the maximum within the first 3 h of contact due to rapid initial oxidation of As(III) followed by As(V) adsorption that gradually approaches an equilibrium condition. The results of As(III) and As(V) removal rate obtained an agreement with several other studies that showed similar time trends for arsenic reduction [26–28]. 3.3. Column experiments The batch experiments enabled us to determine the important reaction parameters needed for developing a model to perform column experiment transport predictions. The parameters developed from batch test into column experiment are summarized in Table 4. To check the validity of the reactive transport model, the experimental observations were compared with model results. The experimental time-dependent results and model simulations of PRB column is presented in Fig. 5. The initial concentration of As(III) was 20 mg L1 for 30 days, after which the concentration was increased to 40 mg L1. The developed model simulated the experimental data very well. Model parameters such as the first-order reaction rate constants were determined through model calibration using initial values from batch test. The first-order reaction rate constants represent the rate of mass of arsenic lost during solute arsenic transport due to oxidation and adsorption of arsenic on surface area of ZVI; a larger number of k indicates faster mass loss. The faster mass loss was the As(V) adsorption process, while a faster mass loss of As(III) was oxidation process. Vertical profiles of dissolved arsenic concentration at 68 days are depicted in Fig. 6. It can be seen arsenic was mostly immobilized within half the length of the column. Intense oxidation of As(III) was observed about 5 cm from the bottom of the column because the dominant species near the bottom of the column was As(III). Afterwards oxidation of As(III) decreases because the dominant species become As(V) due to intense oxidation of As(III) to As(V) in the first 5 cm of the bottom of the column therefore, the main process in the second 5 cm of the column was adsorption of arsenic on surface area of ZVI. The concentration of As(III) decreases again at about 10 cm from the bottom of the column because both oxidation and

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adsorption can occur due to the low concentration of As(III) and As(V). The model considers these variations in concentration along the vertical distance of the column by using different reaction rate constant. The simulated results enable us to predict the long-term performance of ZVI for arsenic removal from groundwater as shown in Fig. 5. The results showed that within the defined experimental conditions, simulations show that ZVI should be able to remove arsenic from groundwater and the arsenic concentration will not exceed the arsenic drinking water standard (0.01 mg L1). By using an initial surface area of ZVI that was estimated from data reported in Section 2.1 the initial surface area of ZVI is 4320 m2 L1. The surface area of the ZVI would decrease to 50% after 20 days and to 1% after 130 days (Fig. 7). However, the relationship between the ZVI surface area and contaminant reduction by chemical reactions is very clear in batch tests results shown in Fig. 3 and Fig. 4, decreasing in the surface area indicates decreasing in arsenic reduction. 4. Conclusions This work studied the oxidation of As(III), adsorption of As(III) and As(V) by ZVI. Batch experiment was conducted to develop the reaction kinetics and adsorption rates for the arsenic on ZVI. The reaction information developed from the batch test was integrated into a reactive transport model to perform column experiment and long-term transport predictions for arsenic removal. More specifically the following conclusions can be drawn: - The present investigation on the removal of arsenic with ZVI suggests that the ZVI can be used as an effective reagent for in situ remediation of groundwater contaminated with arsenic. - Modeling of the solute transport of arsenic in ZVI columns can define the mechanisms of arsenic removal and provide an important tool can be used to design arsenic PRB. - Modeling of arsenic removal by ZVI should be conducted under different geochemical conditions before installing arsenic PRB. - The simulations showed that As(V) sorption rate is faster than the As(III) parameters.

References [1] WHO, 1993. Guidelines for Drinking-Water Quality. vol. 1: Recommendations, second ed. WHO Geneva. [2] K. Fields, A. Chen, L. Wang, Arsenic removal from drinking water by iron removal plants, U.S Environmental Protection Agency Cincinnati. OH (2000) 45268. [3] K. Katsoyiannis, A. Zouboulis, H. Althoff, H. Bartel, As(III) removal from groundwater using fixed-bed upflow bioreactors, Chemosphere 47 (2002) 325– 332. [4] F.W. Pontius, G.K. Brown, J.C. Chien, Health implications of arsenic in drinking water, J. Am. Water Works Assoc. 86 (1994) 52–63. [5] K. Tyrovola, E. Peroulaki, N.P. Nikolaidis, Modeling of arsenic immobilization by zero valent iron, Eur. J. Soil Biol. 43 (2007) 356–367. [6] H.H. Cho, J.W. Park, Sorption and reduction of tetrachloroethylene with zero valent iron and amphiphilic molecules, Chemosphere 64 (2006) 1047– 1052. [7] I. Kouznetsova, P. Bayer, M. Ebert, M. Finkel, Modelling the long-term performance of zero-valent iron using a spatio-temporal approach for iron aging, J. Contam. Hydrol. 90 (2007) 58–80. [8] Y.T. Lin, C.H. Weng, F.Y. Chen, Effective removal of AB24 dye by nano/micro-size zero-valent iron, Sep. Purif. Technol. 64 (2008) 26–30. [9] Y. Mu, H.Q. Yu, J.C. Zheng, S.J. Zhan, G.P. Sheng, Reductive degradation of nitrobenzene in aqueous solution by zero-valent iron, Chemosphere 54 (2004) 789–794. [10] N.P. Nikolaidis, G.M. Dobbs, J.A. Lackovic, Arsenic removal by zero-valent iron: field, laboratory and modeling studies, Water Res. 37 (2003) 1417– 1425. [11] H.L. Lien, R.T. Wilkin, High-level arsenite removal from groundwater by zero-valent iron, Chemosphere 59 (2005) 377–386. [12] J.A. Lackovic, N.P. Nikolaidis, G.M. Dobbs, Inorganic arsenic removal by zero-valent iron, Environ. Eng. Sci. 177 (2009) 29–39. [13] C. Su, R.W. Puls, Arsenate and arsenite removal by zero valent iron: kinetics, redox, transformation, and implications for in situ ground water remediation, Environ Sci Technol. 35 (2001) 1487–1492. [14] J. Farrell, J. Wang, P. O’Day, M. Conklin, Electrochemical and spectroscopic study of arsenate removal from water using zero-valent iron media, Environ Sci. Technol. 35 (2001) 2026–2032. [15] K. Sasaki, H. Nakano, W. Wilopo, Y. Miura, T. Hirajima, Sorption and speciation of arsenic by zero-valent iron, Colloids and surface a: physicochemical and eng. aspects. 347 (2009) 8–17. [16] J. Herzer, W. Kinzelbach, Coupling of transport and chemical processes in numerical transport models, Geoderrna 44 (1989) 115–127. [17] K. Banerjee, G.L. Amy, M. Prevost, S. Nour, M. Jekel, P.M. Gallagher, C.D. Blumenschein, Kinetic and thermodynamic aspects of adsorption of arsenic onto granular ferric hydroxide (GFH), Water Res. 42 (2008) 3371–3378. [18] A. Amirbahman, D.B. Kent, G.P. Curtis, J.A. Davis, Kinetics of sorption and abiotic oxidation of arsenic(III) by aquifer materials, Geochim. Cosmochim. Acta 70 (2006) 533–547. [19] T.L. Johnson, M.M. Scherer, P.G. Tratnyek, Kinetics of halogenated organic compound degradation by iron, Metal. Environ Sci Technol. 30 (1996) 2634– 2640. [20] S. Morrison, Performance evaluation of a permeable reactive barrier using reaction products as tracers, Environ Sci Technol. 37 (2003) 2302–2309. [21] M.C. Shin, H.D. Choi, D.H. Kim, K. Baek, Effect of surfactant on reductive dechlorination of trichloroethylene by zero-valent iron, Desalination 223 (2008) 299–307. [22] D. Schafer, W. Schafer, W. Kinzelbach, Simulation of reactive processes related to biodegradation in aquifers 1. Structure of the three-dimensional reactive transport model, J. Contam. Hydrol. 31 (1998) 167–186. [23] C.A.J. Appelo, D. Postma, Geochemistry, groundwater and pollution, A. A Balkema., 2005. 101–105. [24] S. Banga, M.D. Johnsonb, G.P. Korfiatisa, X. Menga, Chemical reactions between arsenic and zero-valent iron in water, Water Res. 39 (2005) 763–770. [25] K. Sasaki, D.W. Blowes, C.J. Ptacek, Spectroscopic study of precipitates formed during removal of selenium from mine drainage spiked with selenate using permeable reactive materials, Geochem. J. 42 (2008) 283–294. [26] C.C. Fuller, J.A. Davis, G.A. Waychunas, Surface chemistry of ferrihydrite: Part 2 Kinetics of arsenate adsorption and coadsorption, Geochim. Cosmochim. Acta 57 (1993) 2271–2282.

O. Eljamal et al. / Applied Mathematical Modelling 35 (2011) 5198–5207

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[27] P.R. Grossl, M. Eick, D.L. Sparks, S. Goldberg, C.C. Anisworth, Arsenate and chromate retention mechanism on geothite 2. Kinetic evaluation using pressure-jump relaxation technique., Environ Sci. Technol. 31 (1997) 321–326. [28] S.R. Wlckramaslnghe, B. Han, J. Zimbron, Z. Shen, M.N. Karim, Arsenic removal by coagulation and filtration: comparison of groundwaters from the United States and Bangladesh, Desalination 169 (2004) 231–244.