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Mathematical modeling of arsenic(V) adsorption onto iron oxyhydroxides in an adsorption-submerged membrane hybrid system

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The adsorption of arsenic (V), As(V), on two porous iron oxyhydroxide-based adsorbents, namely, micro-sized tetravalent manganese feroxyhyte (µTMF) and granular ferric hydroxide (µGFH), applied in a submerged microfiltration membrane hybrid system has been investigated and modeled. Batch adsorption tests were carried out to determine adsorption equilibrium and kinetics parameters of As(V) in a bench-scale slurry reactor setup. A mathematical model has been developed to describe the kinetic data as well as to predict the As(V) breakthrough curves in the hybrid system based on the homogeneous surface diffusion model (HSDM) and the corresponding solute mass balance equation. The kinetic parameters describing the mass transfer resistance due to intraparticle surface diffusion (Ds) involved in the HSDM was determined. The fitted Ds values for the smaller (1 - 63 μm) and larger (1 - 250 μm) diameter particles of µGFH and μTMF were estimated to be 1.09 × 10-18 m2/s and 1.53 × 10-16 m2/s, and 2.26 × 10-18 m2/s and 1.01 × 10-16 m2/s, respectively. The estimated values of mass transfer coefficient/ kinetic parameters are then applied in the developed model to predict the As(V) concentration profiles in the effluent of the hybrid membrane system. The predicted results were compared with experimental data for As(V) removal and showed an excellent agreement. After validation at varying adsorbent doses and membrane fluxes, the developed mathematical model was used to predict the influence of different operation conditions on As(V) effluent concentration profile. The model simulations also exhibit that the hybrid system benefits from increasing the amount of adsorbent initially dosed and from decreasing the membrane flux (increasing the contact time).
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Preprint: Usman et al .2020.
Mathematical modeling of arsenic(V) adsorption onto iron
oxyhydroxides in an adsorption-submerged membrane hybrid system
Muhammad Usmana,*, Mohsen Zarebanadkoukib, Muhammad Waseema, Ioannis A.
Katsoyiannisc and Mathias Ernsta,*
aInstitute for Water Resources and Water Supply, Hamburg University of Technology, Am Schwarzenberg-
Campus 3, 20173 Hamburg, Germany
bChair of Soil Physics, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
cLaboratory of Chemical and Environmental Technology, Department of Chemistry, Aristotle University of
Thessaloniki, 54124 Thessaloniki, Greece
* Correspondence: (M.U.); (M.E.);
The adsorption of arsenic (V), As(V), on two porous iron oxyhydroxide-based adsorbents, namely, micro-sized
tetravalent manganese feroxyhyte TMF) and granular ferric hydroxide (µGFH), applied in a submerged
microfiltration membrane hybrid system has been investigated and modeled. Batch adsorption tests were carried
out to determine adsorption equilibrium and kinetics parameters of As(V) in a bench-scale slurry reactor setup. A
mathematical model has been developed to describe the kinetic data as well as to predict the As(V) breakthrough
curves in the hybrid system based on the homogeneous surface diffusion model (HSDM) and the corresponding
solute mass balance equation. The kinetic parameters describing the mass transfer resistance due to intraparticle
surface diffusion () involved in the HSDM was determined. The fitted values for the smaller (1 - 63 μm) and
larger (1 - 250 μm) diameter particles of µGFH and μTMF were estimated to be 1.09 x 10-18 m2/s and 1.53 x 10-16
m2/s, and 2.26 x 10-18 m2/s and 1.01 x 10-16 m2/s, respectively. The estimated values of mass transfer coefficient/
kinetic parameters are then applied in the developed model to predict the As(V) concentration profiles in the
effluent of the hybrid membrane system. The predicted results were compared with experimental data for As(V)
removal and showed an excellent agreement. After validation at varying adsorbent doses and membrane fluxes, the
developed mathematical model was used to predict the influence of different operation conditions on As(V) effluent
concentration profile. The model simulations also exhibit that the hybrid system benefits from increasing the
amount of adsorbent initially dosed and from decreasing the membrane flux (increasing the contact time).
Keywords: Arsenic, adsorption, granular ferric hydroxide, tetravalent manganese feroxyhyte, waste utilization,
hybrid membrane process, modeling, mass transfer coefficients
The two most commonly applied technologies for As(V) removal from groundwaters are coagulation with iron /
aluminum-based salts and adsorption onto iron hydroxides / activated alumina (Hering et al. 2017). In particular,
iron (oxy)hydroxides packed fixed-bed adsorption filters have been extensively studied for As(V) removal
(Katsoyiannis and Zouboulis 2002, Pal 2001, Westerhoff et al. 2005) and the most widely applied commercially
available iron oxide based adsorbents are granular ferric hydroxide (GFH) and Bayoxide, E33, (Driehaus 2002,
Katsoyiannis et al. 2015, Tresintsi et al. 2013b). Tresintsi et al. (2013a) developed a novel iron oxyhydroxidebased
adsorbent, tetravalent manganese feroxyhyte (TMF), which has shown high adsorption capacities for As(V) and
has already been in use for arsenic removal in community drinking water treatment systems in Greece (Katsoyiannis
et al. 2015).
Under oxidizing conditions and at pH values relevant to drinking water treatment, As(V) exists as an oxyanion
of H3AsO4 in the form of H3AsO4- and /or H2AsO42-. Adsorption of As(V) species (H3AsO4- / H2AsO42-) onto porous
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iron oxyhydroxides is known to take place via Coulombic and/or Lewis acidbase interactions (ligand exchange
reactions) and to form monodentate and bidentate inner sphere complexes (Zhang and Stanforth 2005, Banerjee et
al. 2008). Generally, it is believed that the porous nature of iron (oxy)hydroxides leads to As(V) adsorption at
internal iron complexation sites (Sinha et al. 2002, Badruzzaman et al. 2004).
During the industrial production of iron oxyhydroxides, a powdered micro-sized fraction is generated as a by-
product, which cannot be employed in fixed-bed adsorption filters because of high clogging potential. However,
those fractions have a high adsorption potential for As(III) and As(V). For instance, the micro-sized granular ferric
hydroxide (µGFH) have shown higher As(III) and As(V) adsorption capacities than conventional GFH.
Furthermore, µGFH is at least five times cheaper than conventional GFH (Usman et al. 2018). According to Wang
et al. (2011), the major part of the total cost of an adsorption filtration system (>80%) arises from adsorbent’s price.
Accordingly, the use of the powdered micro-sized fraction of the low-cost iron oxyhydroxide-based adsorbents in
water treatment would not only lower the overall costs of arsenic treatment systems but would also increase the
sustainable footprint of the production process as a waste product will be used. One of the possible solutions to
remove As(V) in potable water treatment systems is to combine adsorption using micro-sized iron oxyhydroxides
with the lowpressure membrane process such as microfiltration (MF) as indicated by Hilbrandt et al. (2019) and
Usman et al. (2020). In such systems, MF is an absolute barrier for arsenic loaded adsorbent particles, while arsenic
adsorption onto the small adsorbent particles is particularly effective.
The membranes may be placed either outside of the adsorption reactor (A) or submerged directly into the reactor
(B). In the A configured hybrid system, the membrane unit can be operated in either crossflow or dead-end filtration
mode (Jia et al. 2009a). In system B, the membrane is integrated into the reactor as the submerged membrane. The
adsorbent is added into the reactor and permeate is drawn through the membrane by a suction pump. The submerged
membrane system is preferred over the external membrane system in potable water systems because it allows
operation under conditions higher solid adsorbent concentration (Kalaruban et al. 2018a). Independently of the
various integration options of the membranes in the hybrid system, As(V) removal is mainly achieved by adsorption
onto iron oxyhydroxides. However, adsorption performance of iron oxyhydroxides in a hybrid treatment system
may not be effective if not properly designed. The currently available mathematical model to simulate the
breakthrough of inorganic and organic pollutants in fixed-bed adsorbers cannot be applied to adsorption-membrane
hybrid systems where adsorption occurs in a slurry reactor. In contrast to fixed-bed adsorbers where adsorption
process proceeds successively, layer by layer, from the filter inlet to the filter outlet, adsorption in a slurry reactor
simulates continuous stirred tank reactor conditions.
The proper design of the hybrid system requires the proper selection of the following variables: type and particle
size distribution of adsorbent, membrane water flux corresponding to the residence time of adsorbent in the reactor
and mass of initially dosed adsorbent (Mad) into the reactor. The required information might be obtained by carrying
out lab-scale investigations, which are time-consuming and expensive. The prediction of the process performance
and the selection of the optimal process parameters require the use of a mathematical models, which are currently
not existing for such process design.
In previous studies, the homogenous surface diffusion model (HSDM) based on Fick’s law of diffusion has
proven to be an adequate model to describe the adsorption kinetics of organics and inorganics water constituents
onto activated carbon, GFH and anion exchange resin (Badruzzaman et al. 2004, Jia et al. 2009b, Sperlich et al.
2008, Piazzoli and Antonelli 2018, Kalaruban et al. 2018b). The HSDM combines the adsorption equilibrium data
with mass transport mechanisms. If equilibrium and kinetic adsorption input parameters under changed water
quality conditions are available (have been derived), the mathematical model based on the HSDM can be applied
to simulate the influence of water chemistry (e.g., pH and water matrix) on arsenic adsorption filtration systems..
However, the main obstacle in using the HSDM is that it requires two mass transfer coefficients, i.e., surface
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diffusion coefficient () and liquid film mass transfer coefficient () that can only be obtained through a number
of bench-scale adsorption kinetic experiments. Values of mass transfer coefficients from the literature cannot be
used because they are a function of liquid and solid-phase adsorbate concentration (Sontheimer 1988). Moreover,
strongly depends on the pH value of water and adsorbent particle size (Badruzzaman et al. 2004, Sontheimer
1988), whereas depends on the mixing intensities in the adsorption reactor (Jia et al. 2009a).
The main aim of this work is to develop a mathematical model based on the HSDM to predict the breakthrough
behavior of As(V) adsorption onto suspended micro-sized fractions of porous oxyhydroxides in a continuous flow
submerged membrane hybrid system. Specific objectives of this paper include: (i) estimation of kinetic parameters
describing As(V) adsorption onto micro-sized oxyhydroxides; (ii) validation of the developed model with
experimentally derived As(V) breakthrough curves using the parameters obtained from bench-scale equilibrium
and kinetic tests; (iii) investigation of the effect of iron oxyhydroxide-based adsorbent and mean particle size on
effluent quality of hybrid membrane system; and (iv) finally investigation of the effects of process parameters on
As(V) removal to understand the boundaries of the hybrid membrane system. To the best of our knowledge, this is
the first study on mathematically predicting the performance of adsorption in a slurry reactor employing
microporous materials (such as µGFH or µTMF) for arsenic removal.
Modelling approach and parameter estimation
2.1 Quantification of As(V) adsorption in a continuous flow adsorption-submerged membrane hybrid
For a continuous flow adsorption-submerged membrane system, with initially dosed adsorbent, the change in
effluent concentration is based on the solute overall mass balance for steady operation can be quantified from:
  
 (1)
where is the volumetric flow rate, is liquid volume in the reactor,  is the influent adsorbate concentration
flowing into the slurry reactor,  is the mass of adsorbent initially dosed into the reactor. Assuming a spherical
particle then the  can be expressed as:
  
where is adsorbent particle diameter,  is the radial distance, and  is the solid phase adsorbate
concentration with time at any distance from the center of the adsorbent particle during adsorption.
In general, the adsorption kinetic process of adsorbate onto porous adsorbent can be characterized by four
consecutive steps: (1) transport of adsorbate from the bulk solution to stagnant boundary layer (2) diffusion through
the boundary layer to the external surface of a particle, termed liquid film mass transfer or external film diffusion
(3) diffusion in the adsorbed state along the internal surface of a particle, termed intraparticle surface diffusion (4)
adsorption between the adsorbate molecules and adsorption sites in the pores. Since first and the fourth step are
very fast, and the total rate of the adsorption process is determined by either external film diffusion (step 2) or
intraparticle surface diffusion (step 3). One of them could be the rate-limiting process for adsorbate adsorption by
porous adsorbents as the film diffusion and surface diffusion act in series (Worch 2012, Jia et al. 2009a, Traegner
and Suidan 1989).
The HSDM incorporates both film and surface diffusion and envisages an adsorbent particle as a sphere
surrounded by a stagnant liquid boundary layer. The HSDM assumes that the mass transfer occurs in the adsorbed
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state along the internal surface of the adsorbent particle as represented by Eq. (3). Here, the gradient of the solid-
phase concentration within the particle acts as a driving force for the transport.
  
 (3)
where donates the adsorbate radial concentration within the particle over time, is the intraparticle
diffusion along the inner adsorbent surface. The initial and boundary conditions of Eq. (3) are provided in
supplementary information.
The Biot number (), which is a ratio of mass transport processes (Eq. 4), has been used to determine the
relative importance of film diffusion mass transfer to intraparticle surface diffusion.
 (4)
where is particle density, denotes liquid film mass transfer coefficient, is initial liquid phase in batch
slurry reactor, and is adsorbed phase adsorbate concentrations at which are correlated based on the
Freundlich isotherm. According to (Sontheimer 1988) intraparticle surface diffusion is the overall adsorption
process controlling step, when Bi > 30. In this study the batch adsorption tests were operated with the goal of
achieving this limit.
2.2 Model implementation and parameterization
The set of derived equations based on the HSDM were solved numerically using a fully implicit finite difference
method. First, both differential Eqs (1) and (2) were substituted by their finite difference expressions based on the
backward finite difference method (fully implicit) for temporal derivatives and backward finite difference method
for spatial derivatives. The details of finite difference discretization are given in Zheng et al. (2016). Then the
resulting sets of ordinary differential equations were solved simultaneously in MATLAB (R2015b) using an
iterative method with regards to their initial and boundary conditions. The procedure allowed us to calculate the
profile of , , and adsorbate concentration in the bulk solution (.
To predict the concentration profiles of adsorbate in the permeate of the hybrid membrane system, the model
input parameters were classified into three categories: (1) readily available (geometrical and mass related) model
parameters which include the mass of adsorbent added initially added into the reactor, liquid volume in the reactor,
the influent concentration of adsorbate, volumetric flow rate which governs the membrane water flux, particle size,
and particle density, (2) equilibrium adsorption constants () which are determined by fitting the equilibrium
isotherm’s data, (3) Mass transfer (adsorption kinetic) coefficients () which cannot be measured directly. To
determine the mass transfer coefficients simultaneously, the HSDM is first solved using initial estimates of and
, and then these values were inversely adjusted to best reproduce the data collected from batch adsorption kinetic
experiments. To do so, we used pattern search minimizer in MATLAB to minimize sum of squares of error (SSE)
 
 (5)
whereis the experimental data points, is the modeling output data and m denotes the number
of data points in time.
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Materials and methods
3.1 Materials and test solution
Micro-sized granular ferric hydroxide (µGFH) and micro-sized tetravalent manganese tetravalent (µTMF) were
used as representative iron oxyhydroxide-based adsorbents in this study. As(V) was selected as the target
contaminant to represent the adsorption efficiency of chosen iron oxyhydroxides towards the main pollutant for
which these iron oxyhydroxides are generally applied for. The commercially available µGFH was delivered by
GEH Wasserchemie GmbH & Co, Osnabrück, Germany, and µTMF was kindly provided by Manassis Mitrakas
from Aristotle University of Thessaloniki (Tresintsi et al. 2013a). Table 1 summarizes the physicochemical
properties of iron oxyhydroxides under investigation.
Table 1. Material characterisation of used adsorbent media (Usman et al. 2020).
content (%)
Fe content
(wt %)
BET surface
area (m2/g)
point (IEP)
~ 50 ± 2
283 ± 3
7.8 ± 0.2
~ 5
178 ± 8
7.2 ± 0.1
µGFH (mean dp= 1 - 250 µm) contains ~ 50% moisture content. It is produced from a ferric chloride solution by
neutralization and precipitation with sodium hydroxide. The preparation of TMF involves the co-precipitation of
FeSO4 and KMnO4 (Tresintsi et al. 2013a). TMF (as received) was sieved, in order to obtain two size fractions, for
application in the bench-scale experiments. The smaller fraction of TMF (1 63 µm) was obtained by passing
through a 230-mesh sieve (= 63 µm), while the larger fraction of TMF (1 250 µm) was separated by a 60-mesh
sieve (= 250 µm). The smaller and larger particle fractions of TMF are termed as µTMF (1 63 µm) and µTMF (1
250 µm), respectively. The grain size of the µGFH obtained from the manufacturer ranged between 1 and 250
µm, termed as µGFH (1- 250 µm). A smaller fraction of µGFH (1 - 63 µm) was separated from air-dried µGFH by
passing a sieve with mesh size 63 µm. All results presented on a dry mass basis after drying at 105°C for 24 h and
subsequent storage in a desiccator.
For batch adsorption and continuous flow adsorption-submerged membrane tests, As(V) test solution was
prepared using As(V) standard solution (Merck Chemicals GmbH, Darmstadt, Germany, Product code: 119773).
To facilitate the constant pH conditions, 2 mM of a buffer (N,N-Bis(2-hydroxyethyl)-2-aminoethanesulfonic acid
(BES) were added to the test solution (Carl Roth GmbH + Co. KG, Karlsruhe, Germany). Prior to batch adsorption
experiments and continuous flow adsorption-submerged membrane experiments, pH was adjusted to 8 ± 0.1 by
adding either NaOH or HCl.
3.2 Batch equilibrium isotherm tests
Adsorption equilibrium isotherms were derived using powdered fractions µGFH (1- 63 µm) and µTMF (1 63
µm) in ultrapure deionized (DI) water for 7 days at temperature of 20 °C. Upon equilibration, samples from each
flask were filtered (0.45µm syringe filter) to remove the adsorbent particles and the filtrates were stored in
refrigerator at 4 C prior to the measurement. Controls without adsorbent media were carried out also, no As(V)
loss was recorded in 7 days. All experiments were conducted at least in duplicate.
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3.3 Batch kinetic tests
The slurry reactor was applied for kinetic tests to determine the mass transfer coefficients for the adsorption process
(Worch 2012, Dotto et al. 2017). To ensure that film mass diffusion mass would not be the rate-limiting step for
the overall adsorption process (Bi > 30) high mixing at 150 rpm using electrical stirrer (Heidolph Instruments
GmbH & Co. KG) in the batch slurry reactor setup was provided. The adsorbent media mass of 40 mg/L was
brought in contact with test solution. This media mass was calculated from the batch adsorption isotherm data to
ensure that batch kinetic tests were carried out in the presence of limited adsorption sites for accurate determination
of adsorption mass transfer rates through kinetic data. In the slurry reactor setup, aforementioned amount of
adsorbent media was carefully added into a 2 L glass beaker containing ultrapure water spiked with As(V). The
stirrer did not impact the particle size distribution of the media, which was proofed by measurements (Fig. 1 of
supplementary information’s)
The mixing was continuously maintained during sampling in order to avoid changes in adsorbent media
concentration. The pH value of the test solutions in the slurry reactor were monitored intermittently. Sample
aliquots of ~ 5 mL were collected at predefined time intervals in each test. The same volume of test solution without
As(V) was then injected back into the flask. The collected sample aliquots were stored for further analysis.
3.4 Continuous flow adsorption-submerged membrane experiments
The adsorption-submerged membrane experiments employed a self-assembled MF membrane module which was
made with hollow fiber outside-in PVDF-type membrane (Microza microfilter, Pall membrane) to retain the As(V)
loaded adsorbent particles. The nominal pore size of the MF membrane is 0.1 µm. A transparent slurry reactor
made of polyvinylchloride (PVC) was used for adsorption-submerged membrane tests. A sintered glass diffuser
(VitraPOR® ROBU Glasfilter Geräte GmbH) with a pore diameter of 10 -16 µm was fixed at the bottom of the
slurry reactor. Air was transported from a purified air cylinder by PVC tubing to a sintered glass diffuser to generate
fine air bubbles. The air bubbles keep the adsorption particles in suspension. The bubbling rate was adjusted using
an air flowmeter installed between the glass diffuser and the gas cylinder to 2 L/min. For a continuous flow slurry
reactor setup, air bubbling rate of 2 Lair/(min.Lslurry) was necessary to reach optimum mass transfer for As(V)
adsorption onto micro-sized iron oxyhydroxides (Usman et al. 2020).
The MF membrane module was positioned in the middle of the reactor. Adsorption-submerged membrane tests
were carried in continuous feeding/influent mode for 7h with adsorbent initially dosed mode. In this mode of
operation, the total amount of adsorbent was added into the reactor at the beginning of the experiment. The amount
of adsorbed initially dosed was varied from 1 to 3 g/L. The system was operated at constant membrane flux in a
dead-end mode. The permeate port was located on the topside of the MF module. The liquid volume in the reactor
was 1 L. A multi-channel peristaltic pump was employed and it was operated in such a way that the feed solution
was pumped into the reactor at the same volumetric flow rate as the permeate. Prior to the adsorbent addition, the
peristaltic pump for feed and permeate was operated for at least 5 min to precondition the system. After the addition
of the adsorbent, the samples were collected from the permeate side at predefined time intervals. The membrane
flux was maintained constant at 100 and 200 L/(m2.h) and the influent concentration of As(V) was constant during
the course of the continuous flow experiments. The transmembrane pressure was measured by a signal conditioned
precision vacuum pressure transducer (423SC15D-PCB, Sensortechnics). The data were collected automatically
by a data logger.
A Perkin-Elmer atomic absorption spectrometer with a Graphite Furnace Tube atomizer was used to measure
the arsenic concentrations (Model 4100 ZL).
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Results and discussion
At the beginning As(V) adsorption isotherm tests were carried out using the powdered fractions of
adsorbents to determine the equilibrium parameters. Later adsorption kinetics of As(V) on two different
particle size fraction of each adsorbent were determined experimentally to estimate mass transfer
coefficients. The mass transfer coefficients were calculated simultaneously by fitting the experimental
data with the model solution. Finally, As(V) breakthrough curves determined experimentally were
modelled using the mathematical approach discussed in section 2.1.
4.1 Equilibrium parameters for As(V) adsorption
The Freundlich isotherm was used to determine the adsorption equilibrium parameters. The mathematical
expression of the Freundlich isotherm is given by Eq. 6.
 
where and are the liquid phase and solid phase equilibrium concentration of As(V). The Freundlich isotherm
fit to the adsorption equilibrium isotherm data is shown in Fig. 1 (> 0.99).
Fig. 1. Freundlich isotherms for µGFH and µTMF developed using fine particle fractions (1 - 63 µm).
Freundlich adsorption equilibrium parameters of GFH, µGFH and µTMF from different studies are summarized
in Table 2. The adsorption capacity of µGFH is 1.4 times higher than that of µTMF for the same particle size
fraction and identical experimental conditions. This difference in adsorption capacities might be explained by
higher BET surface area of µGFH (283 m2/g vs. 178 m2/g) and by the higher isoelectric point of µGFH
(specification of arsenic species).
Table 2. Adsorption equilibrium parameters for As(V) removal by iron oxyhydroxides at pH 8 ± 0.1. Literature and present
data are also displayed
Q10 (µg/mg)
at Ce = 10
Data source
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500 -
DI water
(Saldaña-Robles et al.
105 - 250
DI water
(Badruzzaman et al.
1 - 63
DI water
100 - 800
This work
1 - 63
DI water
100 - 800
This work
1 - 63
DI water
200 - 2000
(Tresintsi et al. 2013a)
Note: Ce is the liquid phase As(V) equilibrium concentration.
Table 2 exhibits differences in KF values, whereas the values of n are comparable with the literature data. GFH is
a commercial adsorbent media and has constant BET surface area of ~ 300 m2/g. The adsorption capacities in a
similar magnitude are generally expected at equilibrium for different grain sizes of adsorbent media. For instance,
Badruzzaman et al. (2004) reported similar magnitudes of KF and n for GFH (grain size: 105 - 250 µm) after an
equilibration time of 18 days. However, (Saldaña-Robles et al. 2017) obtained for GFH a lower value of KF than
this study after an equilibration time of 1 day, despite the fact that the former study was conducted at lower pH.
This divergence in results might be attributable to the fact that equilibrium for As(V) onto GFH was not fully
reached after a contact time of 1 day due to large-sized grains of iron oxyhydroxides. This was shown by Westerhoff
et al. (2005) where equilibrium was not fully accomplished for GFH (grain size: 600 - 2000 µm) even after 7 days
of contact time. Similar results were also observed in the current study through batch kinetic tests.
4.2 Determination of mass transfer coefficients for As(V) adsorption
The developed model was also adopted to determine the mass transfer coefficients from batch adsorption kinetics
experiments. When experimental conditions are comparable (Q = 0). In this case, Eq. (1) reduces to:
   
 (7)
Eq. (7) describes the overall mass balance in a batch adsorption test. The right-hand and left-hand side of Eq. (7)
represents the sum of mass change of As(V) that adsorbed onto adsorbent and that remains in the reactor (in the
liquid phase) over time.
As(V) adsorption kinetics for µGFH (1 - 63 µm) and µTMF (1 - 63 µm) are shown in Fig. 2(A). The results
indicate a fast initial As(V) adsorption onto both iron oxyhydroxides followed by a slower removal which gradually
approaches an equilibrium plateau. The faster kinetics of µTMF may be due to smaller mean particle size compared
to µGFH as well as due to its large pore volume (Table 2). The best fit values of for the two-particle size fractions
of each adsorbent along with values of sum of the square of the error (SSE) and determination coefficients () are
reported in Table 3. Best fit value for µGFH (1 - 250 µm) at pH 8 is 1.53 x 10-16 m2/s with R2 > 0.99 and SEE <
2.8 x 10-2. The fitted value is similar in magnitude to that reported for the adsorption of As(V) on GFH (18
250 µm) in differential column batch reactor (DCBR) at pH 7 in DI water spiked with 100 μg As(V)/L
(Badruzzaman et al. 2004).
Representative best-fit model simulations together with kinetic data for two-particle size fractions of µTMF are
shown in Fig. 2(B). As anticipated based on Fick’s second law of diffusion, the adsorption rate is faster with the
smaller particles of the same adsorbent. The HSDM is based on Fick’s law, which states that the adsorption rate is
inversely proportional to the square of the radius of the particle. After 7 days of contact time, the residual
concentration of As(V) in the solution for smaller and larger particle size fractions of µTMF is almost the same.
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Fig. 2. Model fit to the batch kinetic tests data at Mad = 40 mg/L; (A) for small particle size fractions ( 1 63 µm) of iron
oxyhydroxides, μGFH and μTMF; (B) for effect of particle size on As(V) adsorption rate for μTMF.
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Table 3. Values of intraparticle diffusion coefficient (), sum of square of error (SSE) and determination coefficients ()
estimated by fitting kinetic data by the HSDM.
Particle size
Mean particle
(x 10-2)
Data source
1 - 63
1.09 x 10-18
This work
1 - 250
1.53 x 10-16
This work
18 - 250
5.42 x 10-16
(Badruzzaman et al.
250 - 600
1.12 x 10-15
800 - 1000
3.0 x 10-15
(Sperlich et al. 2008)
1 - 63
2.26 x 10-18
This work
1 - 250
1.01 x 10-16
This work
4.3 Model verification
In this section, verification of the developed model has been carried out by comparing the results predicted by
model with experimental data points for As(V) normalized permeate concentrations. Fig. 3 shows experimentally
determined As(V) breakthrough curves along with the model predictions for the two particle size fractions of
µGFH, employed in adsorption-submerged MF membrane system, expressed as C/Cin over the operation time. The
amount of adsorbent dosed into the reactor was kept at 1, 2 and 3 g/L, while the membrane flux was maintained at
200 L/(m2 h). An excellent agreement between the experimentally and simulated breakthrough curves of As(V) is
calculated with SSE < 1 x 10-2 and the corresponding R2 value is > 0.956 (R2 and SSE are reported in supplementary
information’s, Table. 1 for all cases). However, for larger size fraction of µGFH (1 250 µm) of 1 g/L deviation
of experimental data points from the model predicted values were noticed. D value depends strongly on the particle
size as indicated by the adsorption kinetic data and the particle size distribution of larger sized µGFH (1 250 µm)
varies over a wider range (particle size distribution for smaller and larger fractions of both adsorbents are reported
in the supplementary information). It is highly possible that the mean particle size of larger sized µGFH might be
smaller than that is used in simulations. Due to which internal particle diffusion coefficient which is adsorbate
diffusion along the inner surface of the adsorbent (illustrated in Fig. 1 of supplementary information’s) would have
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Fig. 3. Model verification for continuous-flow adsorption-submerged membrane hybrid system at Cin = 380 µg/L, pH = 8
and membrane water flux = 200  using (A) µGFH (1 250 μm) (B) µGFH (1 – 63 μm).
been changed and accordingly model tends to slightly underpredict the normalized As(V) concentrations in the
permeate from beginning of the experiment to operation time of 7 h.
To check the correctness of the model solution at varying membrane fluxes which determines the hydraulic
residence time of As(V) in the slurry reactor, the adsorption-submerged membrane tests were also carried out at
two membrane fluxes of 100 and 200 L/(m2.h) for the larger and small fraction of each adsorbent media. The
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adsorbent dosage was kept at 1 g/L to monitor a sharp increase in normalized As(V) permeate concentrations. Fig.
4 shows the experimentally observed concentration profiles along with model solution at corresponding membrane
flux for larger and smaller particle size fractions of µGFH. The As(V) breakthrough curves for adsorption onto
µTMF in an adsorption-submerged membrane hybrid system are shown in supplementary information. The model
predictions exhibit that the experimentally determined As(V) breakthrough curves for µTMF fit well.
Fig. 4. Model verification for continuous-flow adsorption-submerged membrane hybrid system at Cin = 380 µg/L, pH = 8
and membrane water flux = 100  using: (A) µGFH (1 250 µm); (B) µGFH (1 63 µm).
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4.4 Model predictions
After the model has been developed and validated, it will be applied in the following section to derive information
on possible technical variations of type of adsorbent, adsorbent mean particle size, along with the process
parameters and conditions such as adsorbent dosage and membrane water flux (hydraulic residence time) on As(V)
adsorption in an submerged membrane hybrid system. By this approach we transfer the mathematical model into a
convectional planning tool for the evaluation of process design boundary conditions.
4.4.1 Influence of adsorbent type
Fig. 5 shows the predicted breakthrough curves of As(V) adsorption for µGFH (1 250 µm) and respective particle
size fraction for µTMF at an adsorbent dosage of 3 g/L and at 100 L/(m2.h). To better understand the influence of
adsorbent type on As(V) breakthrough curves, five zones of the breakthrough curve, as defined by Sontheimer
(1988) are taken into consideration (Fig. 10 in suppl. information)
Zone A (immediate breakthrough): Adsorbate concentration drops to the minimum effluent concentration
after the starting up the filtration.
Zone B (higher adsorption efficiency): After the sudden adsorbate breakthrough, a time span occurs in
which the adsorbate effluent concentration stays at a nearly constant level. In this paper, this zone is until
the breakthrough point of 0.1 and is termed as a working zone.
Zone C (decreasing adsorption efficiency): This zone indicates the asymptotic shape of the breakthrough
curve. In this zone, the adsorbate concentration changes rapidly and consequently, represents the main zone
of the curve.
Zone D (low adsorption efficiency): During this phase of the breakthrough curve, only a small part of the
adsorbate is removed over time.
Zone E (constant removal efficiency): In this zone, adsorption does not occur, and effluent concentration
is almost the same as the influent level of the adsorbate.
An immediate decrease in adsorbate concentration in permeate was caused by the addition of micro-particles of
iron oxyhydroxides. This immediate reduction in As(V) concentration was not only due to presence of large excess
of adsorption sites but also due to the presence of high As(V) concentration gradient between the bulk solution and
external surface adsorption sites of the adsorbent. The lowest As(V) concentration was achieved in the hybrid
system using µTMF (1 250 µm) despite the adsorption capacity of µTMF for As(V) calculated through isotherm
experiments was lower compared to µGFH. This might be explained by almost the same magnitude of value for
µTMF even though its mean particle size is almost half of µGFH mean particle size.
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Fig. 5. Simulated breakthrough curves for As(V) removal using iron oxyhydroxides in hybrid system at membrane flux =
100 L/(m2.h) and adsorbent dose= 3 g/L. Dashed line in inset of figure reflects the working zone (B).
In the working zone (B), µTMF gives rise to longer times of higher adsorbate removal (inset Fig. 5). In the zone
(C) the steep increase in C/Cin can be seen for both adsorbents. This phase of the breakthrough curve suggests a
decreasing intraparticle surface diffusion with time and represents an extremely slower rate of adsorption capacity
for both adsorbents (Sperlich et al., 2005). However, the decrease in adsorption capacity of µTMF is faster in zone
(C) and therefore, favourable for As(V) adsorption in hybrid membrane system. In general, the adsorption
efficiency of the adsorbent decreases as the breakthrough curve becomes flatter.
Taken into account the complete breakthrough curve for As(V) in adsorption-submerged membrane hybrid
system, Sperlich et al., (2008) categorized this type of breakthrough curve with surface diffusion-controlled mass
transfer limitations (Bi > 30) and this type of breakthrough curve propounds an extremely slow intraparticle
diffusion. Similar shape of breakthrough curves has been observed during adsorption of As(V) onto GFH in fixed-
bed adsorbers (Sperlich et al. 2005, Westerhoff et al. 2005, Sperlich et al. 2008, Saldaña-Robles et al. 2018).
Hilbrandt et al. (2018) also reported the similar trend of breakthrough curve for phosphate removal in fixed-bed
filters packed with GFH and fine fraction of GFH, termed as µGFH in this paper.
4.4.2 Influence of adsorbent size
Fig. 5 also displays the model predictions for the As(V) removal using the two different particle size fractions of
each adsorbent media. The smaller particle size fractions of both absorbents have prolonged the working zone of
the breakthrough curve. It can be seen that hybrid system resulted in longer times of higher As(V) removal using
smaller particle size fractions (3.1 and 3.2 times for µTMF and µGFH, respectively). If water utility is interested
in 90% As(V) removal (i.e., C/Cin = 0.1), more volumes of water can be treated by smaller particle size fraction of
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iron oxyhydroxides. Moreover, 1.3 times more volume of water can be filtered by smaller fraction of µTMF in this
hybrid membrane process than that of µGFH with same particle size fraction. In case of small particle size fractions
of iron oxyhydroxides, steepness of the zone C (decreasing adsorption efficiency zone) of the breakthrough curve
has been increased and also the compete As(V) breakthrough has been achieved earlier than larger diameter iron
oxyhydroxides. At the end of 720 h operation, the adsorption sites of µGFH (1 63 µm) and µTMF (1 63 µm)
were fully covered (full surface coverage), while the adsorption sites of µGFH (1 250 µm) were around 98%
A decrease in length of zone C and D of breakthrough curve following an elongated operating zone (B) indicates
a less dependence on the surface diffusion of As(V) into the adsorbent media. In case of µTMF (1 - 63µm), the
length of zone C and D has been shortened significantly and therefore favourable. This type of breakthrough curve
does not vary too much from ideal s-shaped breakthrough curve and thus favourable. Therefore, it was concluded
that hybrid membrane system show significance of using powdered micro-sized fractions (1 63 µm) of the
commercial adsorbents.
4.4.3 Influence of membrane water flux
The influence of membrane flux was studied by varying the flux in the range of 20 - 200 L/(m2h) at a fixed adsorbent
dosage of 5 g/L for each flux (Fig. 6). The model simulations show that the membrane flux affects the immediate
breakthrough of As(V) after the addition of the adsorbent. For instance, the lowest normalized As(V) permeate
concentration after the addition of adsorbent was 0.04 at the highest membrane flux (200 L/m2.h). This normalized
As(V) concentration in the permeate has been reduced to almost zero immediately after adsorbent’s addition at a
membrane flux of 20 L/(m2h). This is because the amount of As(V) entering the slurry reactor per unit time has
been reduced by 10 times. This allows diffusion of As(V) along the inner surface within the adsorbent media,
adsorption at binding sites, decreasing the As(V) concentration in the stagnant layer around the adsorbent particle
and consequently, results in a larger concentration gradient between the bulk solution and the external adsorbent’s
For a better comparison, volume of water treated per unit mass of adsorbent was considered to study the effect
of membrane flux on the breakthrough curve. The model simulations exhibit that membrane flux can substantially
alter the behavior of breakthrough curves for As(V) onto iron oxyhydroxides. For instance, more volumes of treated
water can be generated with decreasing membrane flux. This is explained by the higher hydraulic retention times
(HRT = V/Q) of slurry reactor at lower membrane fluxes. At the lowest membrane water flux of 20 L/(m2h), the
corresponding As(V) retention time was increased from 17 min at 200 L/(m2.h) to 170 min.
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Fig. 6. Model prediction for As(V) removal at different membrane fluxes at adsorbent dose = 5 g/L using; (A) µGFH (1
250 μm); (B) µGFH (1 63 μm).
With the smaller particle size fraction of µGFH (1 - 63 μm), 1.8 times more water could be treated at 100 L/(m2.h)
with C/Cin = 0.1 in comparison to 200 L/(m2.h). This increase rises to 3.1 times when the hybrid system operation
was set at 20 L/(m2.h). With the larger diameter of µGFH particles, lower membrane flux of 20 L/(m2.h), with HRT
of 170 min, provided an increment of almost 7 times to lower normalized As(V) permeate concentration. When
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both fractions of µGFH are compared in terms of volume of water treated until C/Cin = 0.1, the increase in volume
of treated water has been shrank to 29% at 20 L/(m2.h) from 70% at 200 L/(m2.h). It is found the lowest membrane
flux of 20 L/(m2.h) is favourable in terms of more volume of treated water per unit mass of iron oxyhydroxide but
the amount of product water generated per unit time until C/Cin reaches to 0.1 has been decreased by 10 times. To
overcome the matter in discussion the operation of the hybrid system in cyclical on-off modes could be adopted in
future studies as suggested by Westerhoff et al. (2005) for the operation of GFH packed columns for As(V) removal
at higher influent flow rates. Upon restarting the operation of the hybrid system, a higher concentration gradient
exists between the bulk solution and iron oxyhydroxides surface because of adsorption at the internal adsorption
sites which reduces the adsorbent concentration in the stagnant layer around the adsorbent particle. The large
concentration gradient facilitates the rapid removal of adsorbate from the solution as indicated by the initial plot of
adsorption kinetic data.
The adsorption capacity of the adsorbent in the hybrid system was calculated by integrating the breakthrough
curve until C/Cin = 1 with varying membrane fluxes. The calculated adsorption capacities recorded through
continuous flow hybrid system along with adsorption capacities observed through batch isotherm experiments are
summarized in Table 4. It can be seen that adsorption capacities recorded through two different experiment set ups
at As(V) concentration of 380 µg/L are the same.
Table 4. As(V) adsorption capacities (Q) of iron oxyhydroxides under investigation with influent As(V) = 380 µg/L.
Particle size fraction
range (µm)
Q (µg/mg)
at C/Cin = 1
Data source
1 250
Integrating breakthrough curve
1 63
Isotherm experiments from the present study
1 63
Integrating breakthrough curve
1 - 250
Integrating breakthrough curve
1 63
Integrating breakthrough curve
1 63
Isotherm experiments from the present study
4.4.4 Influence of absorbent dosage
The influence of iron oxyhydroxides was studied by varying the adsorbent dosage in the range of 3 8 g/L and
membrane flux was fixed at 100 L/(m2.h) (Fig. 7A). As(V) contaminated water flows continuously to the reactor
containing a comparatively large amount of iron oxyhydroxides. The abundant amount of adsorbent initially dosed
into the reactor affects not only the immediate breakthrough and working zone but also the later zones of the
breakthrough curve. With increasing adsorbent dosage, the immediate breakthrough not only occurs faster but also
achieves the lowest As(V) concentration in the reactor (~99.9%). It can be seen in Fig 7(A) that the increasing
adsorbent dosage has elongated the length of the working zone. For instance, when Mad was doubled (from 4 to 8
g/L) the time taken to reach C/Cin= 0.1 was delayed by more than twice. This implies that adding more adsorbent
at the start of the experiment is beneficial for longer time operations so that the time interval to supplement fresh
or to start regeneration process can be prolonged. Using higher adsorbent dose in hybrid membrane system is also
favourable in term of regeneration of adsorbent. It is generally expected that time taken to regenerate the different
amounts of adsorbent under strong alkaline conditions are the same (Verbinnen et al. 2015) .
To investigate the combined effect of adsorbent dosage and hydraulic retention time of adsorbate, a parameter
so-called “adsorbent load” has been defined (Eq. 8). This parameter represents the ratio of the total amount of
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adsorbent in the slurry reactor to the influent flow rate.
  
Fig. 7(B) shows the simulated effect of the adsorbent load on the breakthrough time to reach As(V) removal
efficiency of 90% (C/Cin = 0.1). The results are shown as a function of membrane flux, for values 200 and 100
L/(m2.h), corresponding HRT of 17 and 34 min. The influence of the operating parameters such as residence time
and adsorbent dosage was similar for both adsorbents in the hybrid membrane system.
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Fig. 7. (A) Model prediction for As(V) removal using µGFH (1 63 μm) at adsorbent dosage at membrane flux = 100 L/(m2.h);
(B) Simulated effect of adsorbent load on breakthrough time of 0.1 for two particle size fractions of µGFH and µTMF. Small
filled solid symbols represents the results at 200 L/(m2.h), whereas large unfilled solid symbols at 100 L/(m2.h).
The model simulations show a linear relationship between the breakthrough time and adsorbent load. This
relationship is almost indistinguishable for the hybrid membrane system at varying retention times and iron
oxyhydroxides dose. This implies that with a same particle size fraction, longer times of higher As(V) removal
(90%) can be achieved either at a higher adsorbent dose with smaller residence times or at lower adsorbent dosages
with larger residence times. A minimum of one adsorbent load is necessary to achieve 90% removal using iron
oxyhydroxides in the hybrid system.
In this study, As(V) adsorption onto porous micro-scaled oxyhydroxides, namely micro tetravalent manganese
feroxyhyte (µTMF and micro granular ferric hydroxide (µGFH), has been investigated through batch adsorption
tests and continuous flow adsorption-submerged membrane hybrid system with the aim to develop a mathematical
model based on the HSDM to simulate the As(V) removal. The key findings are:
As(V) adsorption capacities recorded through batch isotherm tests in ultrapure water with equilibration
time of 7 days were larger for µGFH than for µTMF (As(V) loadings of 22.4 µg/mg for µGFH vs. 15.4
µg/mg for µTMF at 380 µg/L). The lower adsorption capacity of µTMF is associated to smaller BET
surface area and a lower isoelectric point.
Two particles size fractions of µGFH and µTMF were employed in batch kinetic tests. The smaller particle
size fraction (1 63 µm) of both iron oxyhydroxides have shown profound effect on As(V) adsorption
Results have shown that the developed mathematical model can be used to describe the As(V) adsorption
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by suspended iron oxyhydroxides in a continuous flow adsorption-submerged membrane hybrid system
with complete mixing by air bubbling (simulating continuous stirred tank reactor conditions) when
adsorption equilibrium data is described by Freundlich isotherm and instantaneous adsorption occurs on
active sites.
The breakthrough curves for As(V) onto oxyhydroxides were different significantly from ideal s-shaped
breakthrough due to surface diffusion-controlled mass transfer limitations.
As(V) adsorption rate in membrane hybrid system using smaller diameter iron oxyhydroxides (1 - 63 µm)
was faster than larger iron diameter oxyhydroxides. When comparing the performance of both iron
oxyhydroxides in the hybrid system, µTMF elongated the time taken to breakthrough point of 0.1 (90%
As(V) removal) by 1.3 times than that of µGFH. The achieved As(V) loadings in batch equilibrium tests
and the adsorption-submerged membrane tests are the same for the both particle size fractions of iron
Effect of intraparticle diffusion limitations can be reduced at lower membrane fluxes. A membrane flux of
20 L/(m2.h) at As(V) residence time of ~ 3 h found to be the most beneficial.
The model simulations have shown that a parameter so-called adsorbent load is an important process
parameter that could be used to help in the selection of process design parameters for full-scale arsenic
treatment systems. Based on the studied conditions, it was found that the hybrid membrane system benefits
from higher iron oxyhydroxides dosage. Adsorbent dosage of 8 g/L is optimum that could be applied for
real applications in advanced water treatment.
The developed model can be used for description of similar experimental set up approaches, even if
porous iron oxyhydroxides are replaced by other types of porous adsorbents.
Acknowledgments: The authors are grateful to the German Academic Exchange Service (DAAD) for fellowship
and the Technische Universität Hamburg for resources. The authors gratefully acknowledge Manassis Mitrakas,
Department of Chemical Engineering, Aristotle University of Thessaloniki, Greece for delivering tetravalent
manganese feroxyhyte and GEH Wasserchemie GmbH & Co, Osnabrück, Germany for micro-sized granular ferric
hydroxide media.
Conflicts of Interest: The authors declare that they have no conflict of interest.
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... Through fixing the optimal operative parameters, the adsorption can be better controlled than in the case of in situ methods. However, the mass transfer of arsenic from the groundwater to adsorbents such as GFH in a column is limited [17][18][19], and the competitive effects of some oxyanions present in the water could be an additional problem [1,9,20,21], giving an early breakthrough of arsenic. Long-term clogging effects in the column could also decrease the effectiveness of arsenic removal [16]. ...
... To improve the arsenic adsorption, some references have shown that micro-sized iron hydroxide particles can increase the adsorption capacity [19,22,23] and that processes operated using these small particles in stirred systems increase the arsenic-adsorbent masstransfer [17,19,22] when compared to the GFH in columns. In the case of iron-based NMs, several reports have shown that the maximum adsorption capacity is clearly increased in stirred batch systems by reducing the particle size within the nanometer range [10,13,14]. ...
... In the case of iron-based NMs, several reports have shown that the maximum adsorption capacity is clearly increased in stirred batch systems by reducing the particle size within the nanometer range [10,13,14]. These small sizes are easily operated in stirred batch processes and are an alternative that could also be combined in hybrid methods [3,9,17,24,25] for better arsenic removal. ...
Full-text available
The remediation of groundwater containing arsenic is a problem that has been addressed using adsorption processes with granulated materials in columns, but the remediation itself could be improved by using micro-sized adsorbents in stirred systems. In this study, arsenate (As(V)) batch adsorption experiments were performed using granular ferric hydroxide (GFH) and two derived micro-sized materials. Reduced-size adsorbents were produced by energetic ball milling, giving final sizes of 0.1–2 µm (OF-M samples) and ultra-sonication, producing final sizes of 2–50 µm (OF-U samples). Equilibrium isotherm studies showed that the Langmuir model was a good fit for the three sorbents, with the highest maximum adsorption capacity (qmax) for OF-U and the lowest for OF-M. The adsorption of the two groundwater samples occurred according to the obtained equilibrium isotherms and indicated the absence of interfering agents for the three adsorbents. Batch kinetics tests in stirred beakers followed a pseudo second-order model and indicated that the kinetics of the OF-U sorbent was faster than the kinetics of the GFH sorbent. The tests also showed an increase in the qe values for the reduced-size sorbent. The application of ultrasonication to the GFH produced an increase of 23% in the qmax and b term and an increase of 34-fold for the kinetic constant (k2) in the stirred batch systems tested. These results suggest that this new approach, based on ultra-sonication, has the potential for improving the adsorption of arsenic in groundwater.
... Mathematical models have been widely used to estimate the dynamics of the operation of a GAC column. Specifically, Homogeneous Surface Diffusion Model (HSDM), which has been applied in studies with several pollutants providing reliable information that reproduces the operation of a column of Full-scale [31][32][33][34][35][36]. The model considers the adsorption process occurring in two sequential diffusion steps, namely: diffusion through the stationary fluid layer surrounding the adsorbent particle (film diffusion) and diffusion through the internal pores of the adsorbent (surface diffusion). ...
... The model considers the adsorption process occurring in two sequential diffusion steps, namely: diffusion through the stationary fluid layer surrounding the adsorbent particle (film diffusion) and diffusion through the internal pores of the adsorbent (surface diffusion) as depicted in Figure 4. Adapted from Usman et al., 2021 [35] The following conditions are considered in the model: 1-The dispersion of the pollutant through the bed occurs according to a plug-flow system 2-The applied hydraulic load is constant. 3-Internal diffusion is the predominant mechanism in mass transport and is independent of the pollutant concentration. ...
... The equations that describe the HSDM are presented in Table 2. Adapted from Usman et al., 2021 [35] The following conditions are considered in the model: ...
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Climate change and the increase in the availability of nutrients in aquatic environments have increased the occurrence of cyanobacterial blooms which can produce cyanotoxins such as cylindrospermopsin (CYN). Activated carbon adsorption have been proved to be efficient for CYN removal. In the present study, a carbon with high CYN adsorption capacity was identified between two granular activated carbons. For this carbon was estimated the operating time of a full-scale granular activated carbon column under different empty bed contact times (EBCT). The fixed-bed breakthrough was estimated using the Homogeneous Surface Diffusion Model (HSDM). Wood carbon showed greater capacity to remove CYN. The experimental equilibrium data best fitted Langmuir isotherm model, in which wood carbon had a maximum adsorption capacity of 3.67 μg/mg and Langmuir adsorption constant of 0.2791 L/μg. The methodology produced satisfactory results where the HSDM simulated the fixed-bed breakthrough with a coefficient of determination of 0.89, to the film diffusion coefficient (Kf) of 9 × 10−6 m/s and surface diffusion coefficient (Ds) of 3 × 10−16 m2/s. It was observed that the increase in EBCT promotes a reduction in the carbon use rate. The best carbon use rate found was 0.43 kg/m3 for a EBCT of 10 min and breakthrough time of 183.6 h
... Using adsorption technology for environmental remediation minimizes environmental impacts and waste production [20]. The commonly employed adsorbents for removing As from aqueous solutions are iron oxyhydroxides [21], iron oxide-modified adsorbents [22], activated alumina [23], and iron-modified activated carbon [24]. ...
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Aluminum-impregnated food waste was selected as a filter medium for removing As(III) from aqueous solutions. The modification of food waste and its carbonization conditions were optimized using the Box–Behnken model in the response surface methodology. Pyrolysis temperature and Al content significantly influenced the As(III) adsorption capacity of aluminum-modified food waste biochar (Al-FWB), but the pyrolysis time was insignificant. Several factors affecting the adsorption capacity of the Al-FWB, including the pH, contact time, dosage, competitive anions, and reaction temperature, were studied. The low solution pH and the presence of HCO3−, SO42−, and PO43− reduced the As(III) adsorption onto Al-FWB. The pseudo-second order model showed a better fit for the experimental data, indicating the dominance of the chemisorption process for As(III) adsorption. Langmuir and Freundlich isotherm models fit the adsorption data, but the Langmuir model with a higher (R2) value showed a better fit. Hence, As(Ⅲ) was adsorbed onto Al-FWB as a monolayer, and the maximum As(Ⅲ) adsorption capacity of Al-FWB was 52.2 mg/g, which is a good value compared with the other porous adsorbents. Thus, Al-FWB is a promising low-cost adsorbent for removing As(III) from aqueous solutions and managing food waste.
... The results obtained show that K d increased almost linearly with an increase in adsorbent dose (R 2 of the linear regression line equal to 0.75): the values were 0.9, 2.6 and 2.7 g/L, respectively. This may suggest the heterogeneous nature of the adsorbent surface as also reported by [40]. By contrast, it is referred that for the homogeneous surface, the K d value should not change with the adsorbent dose. ...
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The fluoride removal capability of six different adsorbents (four commercial, i.e., titanium dioxide-TiO2, ArsenXPnp-A33E, granular activated carbon (GAC) and granular ferric hydroxide (GFH), and two laboratory media, i.e., nano-fine media and nano-granular media) was determined under batch conditions using synthetic and real contaminated water containing arsenic and vanadium. The kinetic and equilibrium characteristics of the adsorption process under different operating conditions (pH value, initial fluoride concentration, adsorbent dosage, water composition) were obtained. Among the tested adsorbents, TiO2 showed the highest adsorption capacity; it was also capable of reducing fluoride concentration below the limit set for drinking water without pH control. TiO2 still remained the best adsorbent in the treatment of real contaminated groundwater, where it was also capable of efficiently removing both arsenic and vanadium. The other adsorbents were capable of achieving the same fluoride reduction, although only for acid pH. The nano-sized laboratory media showed an adsorption removal efficiency below that of TiO2 but superior to that of A33E, GAC and GFH. Among the investigated parameters, the removal efficiency was mainly affected by adsorbent dosage and pH. The pseudo-second order model best fitted the kinetic experimental data of all the media. The maximum adsorption capacity predicted by this model was in the following decreasing order: TiO2 > A33E > GAC > GFH. The removal capability of all the media drastically decreased due to the presence of competitive ions and unfavorable pH conditions. The best isotherm model changed depending on the type of adsorbent and pH conditions.
... The adsorption phenomena of MO can be studied from a kinetic point of view; the experimental data concerning the adsorbed quantity of the pollutant as a function of the contact time variation are important because they provide us additional information on mass transfer resistance. During biosorption, the transfer of adsorbing metal ions takes place from the fluid phase to the active sites of the biosorbents take place in four chronological phases (Worch 2012;Usman et al. 2020bUsman et al. , 2021 as illustrated in Fig. 10. These four chronological phases of adsorption kinetic are a) Transport of metal ion from the solution to the stagnant (boundary) layer enveloping the discrete particle of the biomaterial b) Transfer of metal ions across the boundary layer to the biosorbent's surface. ...
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The increasing demand for using competent and inexpensive methods based on biomaterials, like adsorption and biosorption, has given rise to low-priced alternative biosorbents. In the past few years, Moringa oleifera (MO) has emerged as a green and low-priced biosorbent for the treatment of contaminated waters with heavy metals and dyes, and given its availability, we can create another generation of effective biosorbents based on different parts of this plant. In this review paper, we have briefed on the application of MO as a miraculous biosorbent for water purification. Moreover, the primary and cutting-edge methods for the purification and modification of MO to improve its adsorption are discussed. It was found that MO has abundant availability in the regions where it is grown, and simple chemical treatments increase the effectiveness of this plant in the treatment of some toxic contaminants. The different parts of this miraculous plant’s “seeds, leaves, or even husks” in their natural form also possess appreciable sorption capacities, high efficiency for treating low metal concentrations, and rapid adsorption kinetics. Thus, the advantages and disadvantages of different parts of MO as biosorbent, the conditions favorable to this biosorption, also, the proposal of a logical mechanism, which can justify the high efficiency of this plant, are discussed in this review. Finally, several conclusions have been drawn from some important works and which are examined in this review, and future suggestions are proposed.
... Iron-based oxide/hydroxides [10] and ozone [8] are used by oxidizing agents, and electrocoagulation is a selective method [11] for removing As (III). Particularly, porous membranes, hybrid membranes processes, electrocoagulation, and adsorption assisted membrane systems have proven to be effective for arsenate adsorption in addition to iron oxyhydroxides adsorption [12][13][14][15]. However, due to the additional energy required to filter coagulants rich in As to purify water, it is not practical for use in developing nations [8,9]. ...
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In recent decades, the removal of hazardous chemicals that have entered wastewater and groundwater as a result of industrial and consumer activities has become an issue of concern. Specifically, removing arsenic (III) from groundwater is critical and equally crucial in the use of low-cost, efficient adsorbent materials. One purpose of this study was to develop a low-cost hydroxyapatite adsorbent (Ca5(PO4)3OH) by reacting the Ca component of calcined dolomite with phosphorus, and another was to apply the developed adsorbent to remove arsenic (III) from well water in developing countries. In this study, phosphorus adsorption was performed on thermally calcined dolomite, and the adsorption isotherm of the phosphorus study was investigated on selected calcined dolomite. The maximum amount of phosphorus on the selected calcined dolomite was 194.03 mg-P/g, and the Langmuir isotherm model was fitted. Arsenic (III) adsorption was investigated in a wide pH range (pH 2~12) using the new adsorbent. The amount of arsenic (III) adsorbed was 4.3 mg/g. The new absorbent could be effective in removing arsenic (III) and become an affordable material.
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Heavy metal pollution represents an urgent worldwide problem due to the increasing number of its sources; it derives both from industrial, e.g., mining, metallurgical, incineration, etc., and agricultural sources, e.g., pesticide and fertilizer use. Features of membrane technology are the absence of phase change or chemical additives, modularity and easy scale-up, simplicity in concept and operation, energy efficiency, and small process footprint. Therefore, if membrane technology is coupled to adsorption technology, one of the most effective treatment strategies to remove heavy metals, namely, Adsorptive Membrane Technology, many typical disadvantages of traditional processes to remove heavy metals, such as low-quality treated water, excessive toxic sludge production, which requires further treatment, can be overcome. In this review, after a broad introduction on the relevance of heavy metal removal and the methods used, a thorough analysis of adsorptive membrane technology is given in terms of strategies to immobilize the adsorbents onto/into membranes and materials used. Regarding this latter aspect, the impressive number of papers present in the literature on the topic has been categorized into five types of adsorptive membranes, i.e., bio-based, bio-inspired, inorganic, functionalized, and MMMs.
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Arsenic (As(V)), a highly toxic metalloid, is known to contaminate wastewater and groundwater and is difficult to degrade in nature. However, the development of highly efficient adsorbents, at a low cost for use in practical applications, remains highly challenging. Thus, to investigate the As(V) adsorption mechanism, a novel porous α-Fe2O3/Fe3O4/C composite (PC-Fe/C-B) was prepared, using bamboo side shoots as a bio-template, and the breakthrough performance of the PC-Fe/C-B composite-packed fixed-bed column in As(V) removal was evaluated, using simulated wastewater. The PC-Fe/C-B material accurately retained the hierarchical porous microstructure of the bamboo bio-templates, and the results demonstrated the great potential of PC-Fe/C-B composite, as an effective adsorbent for removing As(V) from wastewater, under the optimal experimental conditions of: influent flow 5.136 mL/min, pH 3, As(V) concentration 20 mg/L, adsorbent particle size < 0.149 mm, adsorption temperature 35 °C, PC-Fe/C-B dose 0.5 g, and breakthrough time 50 min (184 BV), with qe,exp of 21.0 mg/g in the fixed-bed-column system. The CD-MUSIC model was effectively coupled with the transport model, using PHREEQC software, to simulate the reactive transportation of As(V) in the fixed-bed column and to predict the breakthrough curve for column adsorption.
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A green ZnO@polynaniline/bentonite composite (G.Zn@PN/BE) was synthesized as an enhanced adsorbent for As (V) ions. Its adsorption properties were assessed in comparison with the integrated components of bentonite (BE) and polyaniline/bentonite (PN/BE) composites. The G.Zn@PN/BE composite achieved an As (V) retention capacity (213 mg/g) higher than BE (72.7 mg/g) and PN/BE (119.8 mg/g). The enhanced capacity of G.Zn@PN/BE was studied using classic (Langmuir) and advanced equilibrium (monolayer model of one energy) models. Considering the steric properties, the structure of G.Zn@PN/BE demonstrated a higher density of active sites (Nm = 109.8 (20 °C), 108.9 (30 °C), and 67.8 mg/g (40 °C)) than BE and PN/BE. This declared the effect of the integration process in inducing the retention capacity by increasing the quantities of the active sites. The number of adsorbed As (V) ions per site (1.76 up to 2.13) signifies the retention of two or three ions per site by a multi-ionic mechanism. The adsorption energies (from −3.07 to −3.26 kJ/mol) suggested physical retention mechanisms (hydrogen bonding and dipole bonding forces). The adsorption energy, internal energy, and free enthalpy reflected the exothermic, feasible, and spontaneous nature of the retention process. The structure is of significant As (V) uptake capacity in the existence of competitive anions or metal ions.
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Owing to environmental pollution and increasingly strict regulations, heavy metals have attracted the attention of many researchers in various disciplines. Alginate and chitosan derivatives have gained popularity as biosorbents for water treatment. An increase in the number of publications on modified biosorbents for the biosorption of toxic compounds reveals widespread interest in examining the requirements and positive contribution of each modification type. This paper reviews the advantages and disadvantages of using alginate and chitosan for adsorption. Well-known modifications based on chitosan and alginate, namely, grafting, functionalization, copolymerization and cross-linking, as well as applications in the field of adsorption processes, especially amino acid functionalization, are reviewed. The selection criteria for the best biosorbents and their effectiveness and proposed mechanism of adsorption are discussed critically. In the conclusion, the question of why these adsorbents need modification before use is addressed.
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Arsenic is among the major drinking water contaminants affecting populations in many countries because it causes serious health problems on long-term exposure. Two low-cost micro-sized iron oxyhydroxide-based adsorbents (which are by-products of the industrial production process of granular adsorbents), namely, micro granular ferric hydroxide (μGFH) and micro tetravalent manganese feroxyhyte (μTMF), were applied in batch adsorption kinetic tests and submerged microfiltration membrane adsorption hybrid system (SMAHS) to remove pentavalent arsenic (As(V)) from modeled drinking water. The adsorbents media were characterized in terms of iron content, BET surface area, pore volume, and particle size. The results of adsorption kinetics show that initial adsorption rate of As(V) by μTMF is faster than μGFH. The SMAHS results revealed that hydraulic residence time of As(V) in the slurry reactor plays a critical role. At longer residence time, the achieved adsorption capacities at As(V) permeate concentration of 10 μg/L (WHO guideline value) are 0.95 and 1.04 μg/mg for μGFH and μTMF, respectively. At shorter residence time of ~ 3 h, μTMF was able to treat 1.4 times more volumes of arsenic-polluted water than μGFH under the optimized experimental conditions due to its fast kinetic behavior. The outcomes of this study confirm that micro-sized iron oyxhydroxides, by-products of conventional adsorbent production processes, can successfully be employed in the proposed hybrid water treatment system to achieve drinking water guideline value for arsenic, without considerable fouling of the porous membrane. Graphical abstract
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The fine fraction of granular ferric hydroxide (µGFH, <0.3 mm) is a promising adsorbent for the removal of heavy metals and phosphate, but properties of µGFH were hitherto not known. The present study aimed at characterizing µGFH regarding its physical and chemical properties and at evaluating methods for the conditioning of fixed-bed filters in order to develop a process that combines filtration and adsorption. Conditioning was done at different pH levels and for different particle sizes. Anthracite, coke, pumice and sand were studied as potential carrier materials. A method for the evaluation of the homogeneity of the iron hydroxide particle distribution on pumice filter grains using picture analysis was developed. Pre-washed pumice (pH 8.5) proved to lead to high embedment and a homogeneous distribution of µGFH. Filter runs with phosphate (2 mg/L P) showed similar breakthrough curves for the embedded fine fraction adsorbent and for conventional GFH.
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The small sized powdered ferric oxy-hydroxide, termed Dust Ferric Hydroxide (DFH), was applied in batch adsorption experiments to remove arsenic species from water. The DFH was characterized in terms of zero point charge, zeta potential, surface charge density, particle size and moisture content. Batch adsorption isotherm experiments indicated that the Freundlich model described the isothermal adsorption behavior of arsenic species notably well. The results indicated that the adsorption capacity of DFH in deionized ultrapure water, applying a residual equilibrium concentration of 10 µg/L at the equilibrium pH value of 7.9 ± 0.1, with a contact time of 24 h (i.e., Q10), was 6.9 and 3.5 µg/mg for As(V) and As(III), respectively, whereas the measured adsorption capacity of the conventionally used Granular Ferric Hydroxide (GFH), under similar conditions, was found to be 2.1 and 1.4 µg/mg for As(V) and As(III), respectively. Furthermore, the adsorption of arsenic species onto DFH in a Hamburg tap water matrix, as well as in an NSF challenge water matrix, was found to be significantly lower. The lowest recorded adsorption capacity at the same equilibrium concentration was 3.2 µg As(V)/mg and 1.1 µg As(III)/mg for the NSF water. Batch adsorption kinetics experiments were also conducted to study the impact of a water matrix on the behavior of removal kinetics for As(V) and As(III) species by DFH, and the respective data were best fitted to the second order kinetic model. The outcomes of this study confirm that the small sized iron oxide-based material, being a by-product of the production process of GFH adsorbent, has significant potential to be used for the adsorptive removal of arsenic species from water, especially when this material can be combined with the subsequent application of low-pressure membrane filtration/separation in a hybrid water treatment process.
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Excessive concentrations of nitrate in ground water are known to cause human health hazards. A submerged membrane adsorption hybrid system that includes a microfilter membrane and four different adsorbents (Dowex 21K XLT ion exchange resin (Dowex), Fe-coated Dowex, amine-grafted (AG) corn cob and AG coconut copra) operated at four different fluxes was used to continuously remove nitrate. The experimental data obtained in this study was simulated mathematically with a homogeneous surface diffusion model that incorporated membrane packing density and membrane correlation coefficient, and applied the concept of continuous flow stirred tank reactor. The model fit with experimental data was good. The surface diffusion coefficient was constant for all adsorbents and for all fluxes. The mass transfer coefficient increased with flux for all adsorbents and generally increased with the adsorption capacity of the adsorbents.
Adsorption processes have played a central role in water treatment for many years but their importance is on the rise with the continuous discoveries of new micropollutants in the water cycle (pharmaceuticals for example). In addition to the classical application in drinking water treatment, other application fields are attracting increasing interest, such as wastewater treatment, groundwater remediation, treatment of landfill leachate, and so on. Based on the author's long-term experience in adsorption research, the scientific monograph treats the theoretical fundamentals of adsorption technology for water treatment from a practical perspective. It presents all the basics needed for experimental adsorption studies as well as for process modelling and adsorber design. Topics discussed in the monograph include: introduction into basic concepts and practical applications of adsorption processes; adsorbents and their characterisation, single and multi-solute adsorption equilibria, adsorption kinetics, adsorption dynamics in fixed-bed adsorbers and fixed-bed adsorber design, regeneration and reactivation of adsorbents, introduction into geosorption processes in bank filtration and groundwater recharge. According to the increasing importance of micropollutants in the water cycle, particular attention is paid to their competitive adsorption in presence of background organic matter. Clear illustrations, extensive literature references and a useful index make this work indispensible for both scientists and technicians involved in water treatment. © 2021 Walter de Gruyter GmbH, Berlin/Boston. All rights reserved.
The use of micro-sized iron hydroxide adsorbents in mixed reactors is a promising technique for the removal of inorganic contaminants from wastewater within minutes of contact time. This study focusses on phosphate adsorption onto fine fraction granular ferric hydroxide (μGFH) and iron oxy(hydr)oxide agglomerates (IOAs) in a reactor with submerged ultrafiltration (UF) membrane. The performance of the hybrid adsorption/UF membrane system was evaluated for various adsorbents and phosphate concentrations, residence times and concentrations of co-existing ions. The membrane was not fouled at the experimental conditions used (up to 6.3 g/L adsorbent). Phosphate loadings of 20 and 60 mg P/g Fe (36.1 and 108.3 mol P/mol Fe) were reached for μGFH and IOAs, respectively (C0(P)=4.5 mg/L, deionized water at pH 8, C(Fe)=0.6 g/L). A shortened residence time of 15 min in the reactor led to a decrease in final loading of 6 mg/g compared to 30 min residence time (54 mg/g compared to 60 mg/g). An extension to 60 min did not result in higher loadings. An increase in adsorbent (IOA) concentration from 0.1 to 0.3 mg/L resulted in an increase of phosphate removal (27 to 35%). Simultaneously, loadings decreased from 50 to 35 mg/g. The application of the developed process for the treatment of artificial secondary effluent resulted in an increase of 87 and 60% in treated volumes until breakthrough (50%) for μGFH and IOAs, respectively, compared to deionized water. Thus, the combined process of adsorption and particle separation using a submerged membrane can be well adjusted according to water composition, initial pollutant concentrations and desired removals.
Homogeneous Surface Diffusion Model (HSDM) has been widely used to simulate the breakthrough of organic micropollutants in fixed-bed adsorbers, but its practical applicability in real-scale conditions is not fully established. In this study we proposed a validated methodology to support the assessment of full-scale GAC adsorbers, providing a sound framework for a sustainable management. Specifically, we predicted the breakthrough of volatile organic compounds by the HSDM applied to full-scale granular activated carbon (GAC) adsorbers treating a complex groundwater matrix. Isotherm and short bed adsorber (SBA) tests were conducted to obtain equilibrium and mass-transfer coefficients for two contaminants (chloroform and perchloroethylene, PCE) and two GACs. Isotherm data were well described by Freundlich and Langmuir models, showing that single-component isotherms can be also used in complex water matrices, indirectly taking into account competition phenomena into the estimated parameters. The fitting of SBA data by HSDM was effective for chloroform, while PCE results were not well described, indicating that the combination of isotherm and SBA experiments to estimate HSDM parameters is not always effective, but it can depend on the characteristics of the adsorbate. Breakthrough data from the monitoring of two full-scale adsorbers were finally used to validate HSDM parameters for chloroform: its breakthrough was effectively simulated, without introducing any competition effect in HSDM equations. The model well reproduced also the release of the contaminant (resulting in chromatographic effect) by considering the variation of its influent concentration over time.
Arsenic is a natural contaminant present in groundwater mantles which, in high concentrations, causes severe health and environmental problems such as the degradation of human health and the contamination of land used for agriculture during irrigation. Understanding the process of arsenic removal from water contributes to the sustainability of regions where this problem is present. This work presents an experimental study complemented with numerical predictions of the adsorption of arsenic (As(V)) in mini-columns using Granular Ferric Hydroxide (GFH) as adsorbent. The work focuses on the effects of the presence of organic matter, i.e., humic (HA) and fulvic (FA) acids, in a water inflow that is contaminated with As(V). The treatments contain the same concentration of organic matter, the same initial concentration of As(V) of 0.8 mg L⁻¹, and the same amount of GFH of 2 g for the filters. Results show that the samples containing organic matter (HA and FA) show a lower adsorption capacity, a lower breakthrough volume, a lower pH, and a non uniform saturation of the GFH filter. The results suggest the need to include the effects of organic matter in all subsequent analyses of arsenic removal from water because organic matter is always present in real life scenarios. Also, this work provides useful information to solve the problematic of the presence of high concentrations of As(V) (greater than 50 μg L⁻¹) in the water mantles of the Bajio region of Mexico.
Adsorption is one of the most widely applied unit operations to separate molecules that are present in a fluid phase using a solid surface. Adsorption kinetic aspects should be evaluated in order to know more details about its mechanisms, characteristics, and possibilities of application. These data can determine the residence time to reach the required concentration of the adsorbate, making possible the design and operation of an adsorption equipment and defining the performance in batch and continuous systems. This chapter presents the particularities of adsorption kinetics in liquid phase. Batch and fixed-bed systems are considered. For discontinuous batch systems, diffusional mass transfer models and adsorption reaction models are discussed. For fixed-bed systems, the shape of breakthrough curves is studied on the basis of mass balance equations and empirical models. Furthermore, the design and scale up of fixed-bed columns are detailed according to the length of unused bed (LUB) and bed depth service time (BDST) concepts. Several numerical methods are presented in order to solve the required models for batch and fixed-bed systems. Some parameter estimation techniques are discussed in order to obtain the fundamental parameters for adsorption purposes, like mass transfer coefficients and empirical parameters.
This work studied the impact of humic and fulvic acids on the removal kinetics of arsenic (V) by granular ferric hydroxide (GFH) and the adsorption capacity of arsenic (V) onto GFH at equilibrium. The Freundlich and DubininRadushkevich models describe the arsenic (V) adsorption behavior onto GFH reasonably well ( ). The removal kinetics were studied by fitting the experimental data to both first-order and second-order models. The lowest adsorption capacity was observed in the presence of fulvic acids (FA), and conversely, the adsorption capacity in the presence of humic acids (HA) was lower than that without humic substances (WHS). The removal kinetics of arsenic (V) were well defined for the second-order model, with correlation coefficients ranging from 0.951 to 0.977. This study suggests that the presence of humic substances negatively impacts the removal of arsenic from water.