Adsorption Using Lime-Iron Sludge–Encapsulated Calcium Alginate Beads for Phosphate Recovery with ANN- and RSM-Optimized Encapsulation

Chittoo, Beverly S.; Sutherland, Clint

doi:10.1061/(ASCE)EE.1943-7870.0001519

Open access

Technical Papers

Mar 12, 2019

Adsorption Using Lime-Iron Sludge–Encapsulated Calcium Alginate Beads for Phosphate Recovery with ANN- and RSM-Optimized Encapsulation

Authors: Beverly S. Chittoo, Aff.M.ASCE [email protected], and Clint Sutherland, Ph.D., A.M.ASCE https://orcid.org/0000-0002-5569-325X [email protected]Author Affiliations

Publication: Journal of Environmental Engineering

Volume 145, Issue 5

https://doi.org/10.1061/(ASCE)EE.1943-7870.0001519

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Abstract

Excessive discharge of phosphates in municipal and industrial effluents into water bodies continues to amplify the rate and extent of eutrophication that is impairing aquatic ecosystems throughout the world. Consequently, research into technologies to combat the problem of eutrophication continues unabated. This study aimed to develop a protocol to encapsulate dewatered lime-iron sludge in calcium alginate beads and assess and optimize its phosphate adsorption performance. Response surface methodology (RSM) and artificial neural network (ANN) were used to optimize the encapsulation process through parameter variation. RSM was superior in capturing the nonlinear behavior of the process. Numerical optimization in RSM revealed that maximum adsorption could be obtained from beads prepared using 0.25 g sodium alginate and 0.5 g lime-iron sludge in 25 mL of distilled water to produce a homogeneous mixture and added dropwise into a solution of 0.31 g

{CaCl}_{2}

in 25 mL of distilled water. The accuracy of the RSM prediction was subsequently validated by laboratory experiments that revealed a residual error of 2.9% and thus highlights the applicability of the model. Batch experiments were conducted and modeled to expound the mechanisms of adsorption. Kinetic data were best simulated using the pseudo-second order model while equilibrium data followed the Langmuir isotherm at room temperature and the Sips isotherm at higher temperatures. Physisorption, hydrogen bonding, dipole interaction, and ligand exchange were the dominant attachment mechanisms while film and intraparticle diffusion were the pertinent transport mechanisms. The beads exhibited a maximum monolayer adsorption capacity of

8.3 mg / g

that compared well to other phosphate-targeting adsorbents reported in the literature.

Introduction

Anthropogenic activities have accelerated the rate and extent of eutrophication through the discharge of excessive nutrients such as phosphate in municipal and industrial effluents into aquatic ecosystems (Yang et al. 2008). This frequently stimulates the extraordinary growth of blue-green algae, destroys aquatic life, disrupts the natural food chain, and leads to deterioration of water quality (Chislock et al. 2013). The problem of eutrophication is of growing concern and affects several regions (Nixon et al. 1986). The estimated cost of damages due to freshwater eutrophication in England and Wales alone is estimated to be US$105–160 million per annum (Pretty et al. 2003) while the cost of damages due to eutrophication in the United States is estimated to be US$2.2 billion per annum (Dodds et al. 2008). It is also reported that approximated 30% of the channel lengths of Irish rivers are polluted mainly from eutrophication (Walsh 2005). The removal of phosphate from wastewater before its discharge into water bodies is critical to curbing the problem of eutrophication (Akpor 2011).

Removal of phosphate from water bodies can be accomplished through various treatment processes including ion exchange, dissolved air floatation, membrane filtration, high-rate sedimentation, and adsorption (Mohammed and Rashid 2012). Among these treatment techniques adsorption is drawing increasing attention and becoming an attractive technology because of its simplicity of design and operation, insensitivity to toxic pollutants, and its potential to remove contaminants present in water even at low concentrations to produce a high quality treated effluent (Chen et al. 2013). However, the search for efficient and low-cost adsorbents that are readily available remains a crucial issue of current research interest (Gadd 2009).

The efficiency of adsorbents for phosphate removal is controlled by the method of adsorption. According to Loganathan et al. (2014) there are five methods of phosphate sorption: ion exchange (outer-sphere surface complexation), ligand exchange (inner-sphere surface complexation), hydrogen bonding, surface precipitation, and diffusion into the interior structure of the adsorbent. The authors went on to explain that ligand exchange is advantageous because of its ability to remove large proportions of anions even from solutions of very low concentrations of target anions and in the presence of competing anions of lower selectivity. In ligand exchange, covalent bonds form between anions such as phosphate and metallic cations on the surface of the adsorbent. It would, therefore, be advantageous to use metal oxide adsorbents for removing phosphates from wastewater.

Commercial adsorbents such as granular ferric oxide and activated aluminum oxide have been reported by several authors including Genz et al. (2004), Zhao et al. (2015), and Xie et al. (2015). However, a major drawback for the large-scale application of these commercial adsorbents is its high cost. An attractive alternative is the use of low-cost value-added adsorbents generated from waste materials. Industrial by-products are a striking option owing to their high oxide content, availability, and low cost. Its reuse for phosphate removal not only aids in curbing the problem of eutrophication but is beneficial toward mitigating existing waste disposal issues. Low-cost materials such as blast furnace slag (Johansson and Gustafsson 2000), iron oxide tailings (Zeng et al. 2004), fly ash (Ugurlu and Salman 1998), and lime-iron sludge (Chittoo and Sutherland 2017) have been reported to efficiently adsorb phosphate from aqueous solutions. The adsorption capacities of these materials were reported to be influenced by its mineral composition, and the most effective were those with a high content of metal oxides such as aluminum hydroxide, iron oxide, and calcium oxide. However, use of these low-cost adsorbents in powdered form may not be practical for large-scale applications due to the difficulty of separation from water, ultimate disposal, and its potential reuse. It would, therefore, be worthwhile to encapsulate the adsorbent while at the same time maintaining its high adsorption capacity.

Alginate, a polysaccharide biopolymer composed of (

1 \to 4

) linked

α

-L-guluronate and

β

-D-manuronate has attracted much attention for encapsulating materials due to its low cost and ability to form stable hydrogels in the presence of divalent ions such as

{Ba}^{2 +}

,

{Ca}^{2 +}

, and

{Fe}^{2 +}

by cross linking (Lee and Mooney 2012). The resulting porous hydrogels allow solutes to diffuse in and out consequently making contact with the encapsulated material. Additionally, encapsulation using alginate is advantageous because it is nontoxic and biodegradable [A. Bezbaruah, T. B. Almeelbi, and M. Quamme, US Patent No. 15/147,437 (2014)]. While entrapment of adsorbents using alginate beads has been extensively investigated for the uptake of various metals (Wang et al. 2017), few studies have focused on the uptake of phosphate from solution. Sujitha and Ravindhranath (2017) reported an exceptionally high phosphate adsorption capacity of

133.3 mg / g

by calcium alginate beads doped with active carbon derived from the Achyranthes aspera plant. However, activated carbon is expensive to produce and may not be the most viable option. Mahmood et al. (2015) studied the use of alginate calcium-carbonate beads for phosphate adsorption but reported a low phosphate adsorption capacity of only

0.62 mg / g

. This study aims to encapsulate lime-iron sludge, a waste material, in calcium alginate beads as a low-cost adsorbent and at the same time maintain a high adsorption capacity. Lime-iron sludge encapsulated alginate beads for phosphate adsorption is unreported. Further, the extraordinarily high iron content of lime-iron sludge obtained from central Trinidad makes this material an excellent candidate for investigating its encapsulation for phosphate removal.

The process of encapsulation involves numerous variables that can affect the adsorptive performance of the adsorbent. It is therefore important to select a suitable experimental technique that will evaluate the effects of significant variables along with possible interactions (Bhunia and Ghangrekar 2008). Response surface methodology (RSM) and artificial neural network (ANN) have both been used to optimize and model processes such as adsorption (Shojaeimehr et al. 2014), fermentation (Desai et al. 2008), and air drying (Karimi et al. 2012).

RSM is a collection of mathematical and statistical techniques that use specific experimental designs to develop mathematical models to improve and optimize processes (Yeniay 2014). According to Ferreira et al. (2007), the Box-Behnken design is most efficient in RSM mainly because it requires few experiments (three levels per factor) and therefore saves time and resources. It has been successfully used to optimize encapsulation of several materials including L-Asparaginase (Bahraman and Alemzadeh 2017), peat (Vecino et al. 2013), and

α

-Amylase (Dey et al. 2003) in calcium alginate beads.

ANN is a computational technique that attempts to simulate human intuition in making decisions and drawing conclusions given complex, irrelevant, and partial information (Saeh and Khairuddin 2009). It has been successfully used to optimize encapsulation of various materials including papain (Sankalia et al. 2005) and drugs (Derakhshandeh et al. 2012) in calcium alginate beads.

Adsorption from the aqueous phase onto the solid phase usually involves three steps: (1) boundary layer mass transfer across the liquid film surrounding the particle as film diffusion; (2) internal diffusion/mass transport within the particle boundary as pore and/or solid diffusion; and (3) adsorption within the particle and on the external surface (Poots et al. 1976). The slowest of these steps will be rate limiting and therefore determines the rate of the reaction (Girish and Murty 2016). Consequently, knowledge of the mechanisms involved in the adsorption process is critical to understanding the suitability of the adsorbent as well as improving the efficiency of the adsorption process (Sutherland and Venkobachar 2013).

The objectives of this investigation are: (1) to develop a protocol and optimize the encapsulation of lime-iron sludge in calcium alginate beads using RSM and ANN; (2) to develop an empirical model to predict the phosphate adsorption capacity for different encapsulation conditions; and (3) to optimize the adsorption process by varying operational parameters and by elucidating the transport and attachment mechanisms through batch kinetic, equilibrium, thermodynamic, and mass transfer studies.

Materials and Methods

Chemicals and Adsorbents

Preparation of Adsorbent

Lime-iron sludge used in this study was obtained from a water treatment plant located in central Trinidad. After collection, the sludge was heated in an oven (ELE78-1215/01, ELE International, UK) at 378 K for 24 h and then cooled to room temperature for 72 h. It was then pulverized using a mortar and pestle and sieved to pass through a 710-µm sieve.

The sludge was encapsulated in calcium alginate beads using the ionic cross-linking technique previously reported by Mahmood et al. (2015) with slight modification. Commercial grade sodium alginate [laboratory reagent (LR) grade, Breckland Scientific Supplies, UK] was first dissolved in double distilled water and stirred to obtain a gel-like consistency. Varying masses of prepared sludge were then added to the polymer solution and mixed thoroughly to achieve a homogeneous mixture. The suspension was subsequently injected dropwise into a calcium chloride (

{CaCl}_{2}

, anhydrous granular, LR, Som Datt Finance Corporation, New Delhi, India) bath using a 30-mL syringe. After gelation, the beads were rinsed three times and kept in a double distilled water bath. All experiments were carried out in duplicate.

Detailed screening experiments were carried out to determine the most optimal range of adsorbent, sodium alginate, and

{CaCl}_{2}

for encapsulation. The selected ranges were 0.5%–5% (w/v) adsorbent, equivalent to 0.125–1.25 g of adsorbent per 25 mL of distilled water, 0.5%–5% (w/v) sodium alginate, equivalent to 0.125–1.25 g of sodium alginate per 25 mL of distilled water, and 0.5–5% (w/v)

{CaCl}_{2}

, equivalent to 0.125–1.25 g of

{CaCl}_{2}

per 25 mL of distilled water. Similar ranges for sodium alginate and

{CaCl}_{2}

were suggested for encapsulation by cross linking [A. Bezbaruah, T. B. Almeelbi, and M. Quamme, US Patent No. 15/147,437 (2014)]. Other researchers including Ociński et al. (2016), Derakhshandeh et al. (2012), and Mahmood et al. (2015) also experimented successfully within these ranges.

Preparation of Adsorbate

Phosphate stock solution was prepared by dissolving preweighed amounts of potassium dihydrogen phosphate (

{KH}_{2} {PO}_{4}

, J.T Baker, Mexico) in double distilled water.

Characterization of Adsorbent

The morphological structure of the adsorbent was characterized using a Hitachi S-3000N scanning electron microscope (SEM) (Hitachi, Tokyo), and the elemental composition was determined using an energy dispersive spectroscopy (EDS) analyzer (IXRF Systems, Austin, Texas) at a voltage of 20 kV. The particle size was determined using a Vernier caliper and calculated as the average value of the diameter of 100 beads.

Adsorption Studies

Kinetic Studies

Batch studies were conducted using the parallel method according to the EPA Office of Prevention, Pesticides and Toxic Substances (OPPTS) method 835.1230 (USEPA 2008). Experiments were carried out in duplicate with 0.5 g of sludge encapsulated in calcium alginate beads and spiked with 100 mL of synthetic phosphate solution (

10 mg / L

). Adsorbent masses were accurate to

\pm 0.001 g

and solution volumes to

\pm 0.5 m L

. The effect of pH was studied in the range 4–10 and kept constant using appropriate amounts of acetate buffers and sodium bicarbonate buffers and measured using a HACH multiparameter meter (HQ430d, HACH, Loveland, Colorado). Identical reaction mixtures were prepared for each time interval, agitated to maintain complete mixed conditions on a mechanical shaker (SK-330-Pro Orbital Digital Shaker, Scilogex, Rocky Hill, Connecticut) and removed at predetermined time intervals (Weber and Miller 1988). The adsorbent was separated by vacuum filtration using a Buchner funnel and Whatman No. 3 qualitative filter paper. The concentration of phosphate in the filtrate was estimated by the molybdate/ascorbic acid method with single reagent (Method 365.2) using an ultraviolet spectrophotometer (UV-1800 Recording Spectrophotometer, Shimadzu Scientific Instruments, Toyko).

Equilibrium Studies

The effect of initial phosphate concentration was studied by equilibrating 0.5 g of lime-iron sludge encapsulated in calcium alginate beads and 100 mL of synthetic phosphate solution of varying concentrations (

10

–

100 mg / L

). The effect of temperature was examined by agitating reaction mixtures in a shaking water bath (Julabo SW23, Julabo GmbH, Seelbach, Germany) at temperatures varying from

300 \pm 2 K

to

328 \pm 2 K

. Experiments were carried out in duplicate.

Point of Zero Charge

The point of zero charge (

{pH}_{PZC}

) was evaluated using the solid addition method described by Lee et al. (2012). Adsorbents were contacted with

{100 mL KNO}_{3}

solution (

50 mg / L

) at various pH solutions. The graph of ΔpH versus the initial pH was plotted, and the

{pH}_{PZC}

was taken as the intersection of the initial pH with ΔpH.

Adsorption Yield

The adsorption yield was calculated using Eq. (1)

% A d s o r p t i o n = \frac{C_{o} - C_{t}}{C_{o}} \times 100

(1)

where

C_{o}

= initial adsorbate concentration in solution (

mg / L

); and

C_{t}

= adsorbate concentration in solution (

mg / L

) at time

t

.

Adsorption Capacity

The adsorption capacity was determined using Eq. (2)

q_{e} = \frac{(C_{o} - C_{e})}{M} \times V

(2)

where

q_{e}

= mg of adsorbate adsorbed/g of adsorbent at equilibrium (

mg / g

);

C_{e}

= equilibrium adsorbate concentration (

mg / L

);

V

= volume of adsorbate solution (L); and

M

= mass of adsorbent (g).

Kinetic Models

Lagergren Model

Lagergren [as cited in Ho and McKay (1998a)], developed a first-order rate equation to describe the kinetic process of oxalic acid and malonic acid onto charcoal. Ho and McKay (Ho and McKay 1998a), described the equation as pseudo-first order

q_{t} = q_{e} (1 - \exp^{- K_{P F O} t})

(3)

where

K_{P F O}

= pseudo-first order rate constant (

h^{- 1}

); and

q_{t}

= mg of adsorbate adsorbed/g of adsorbent at time, t (

mg / g

).

Pseudo-Second Order Model

The pseudo-second order equation was developed for the adsorption of divalent metal ions onto peat moss (Ho and McKay 1998b). The model is based on pseudo-second order chemical reaction kinetics (Ho and McKay 1999) and is expressed as

q_{t} = \frac{K_{P S O} q_{e}^{2} t}{1 + K_{P S O} q_{e} t}

(4)

h = (K_{P S O}) q_{e}^{2}

(5)

where

K_{P S O}

= pseudo-second order rate constant (

g / mg \cdot h

); and

h

= initial rate of adsorption (

mg / g \cdot h

).

Intraparticle Diffusion Model

The intraparticle diffusion model (Weber and Morris 1963) assumes that the rate of intraparticle diffusion varies proportionally with the half power of time. The model has the following form:

q_{t} = K_{i d} (t^{1 / 2})

(6)

where

K_{i d}

= rate constant of intraparticle transport (

mg / g \cdot h^{1 / 2}

).

Diffusion-Chemisorption Model

The diffusion-chemisorption model (Sutherland and Venkobachar 2010) was developed to simulate biosorption of heavy metals onto heterogeneous media. The model can be represented as follows:

q_{t} = \frac{1}{\frac{1}{q_{e}} + \frac{1}{K_{D C} \times t^{0.5}}}

(7)

k_{i} = \frac{K_{D C}^{2}}{q_{e}}

(8)

where

K_{D C}

= diffusion-chemisorption constant (

mg / g \cdot h^{1 / 2}

); and

k_{i}

= initial adsorption (

mg / g \cdot h

).

Mass Transfer Studies

External Diffusion Model

The external diffusion model assumes that during the initial stages of adsorption, intraparticle resistance is negligible and transport is mainly due to film diffusion (Aksu and Isoglu 2006). It was derived from an application of Fick’s second law and expresses the concentration of solute in the solution as a function of the difference in concentration of the solute in the solution,

C

, and at the particle surface,

C_{i}

, according to the following equation (Jansson-Charrier et al. 1996):

\frac{d q}{d t} = - k_{f} S_{o} (C - C_{i})

(9)

where

q

= average solute concentration in the solid (

mg / g

);

C

= concentration of the solute in the bulk of the liquid (

mg / L

);

C_{i}

= concentration of the solute in the liquid at the particle/liquid interface (

mg / L

);

k_{f}

= external mass transfer coefficient (

m / s

); and

S_{o}

= surface area for mass transfer (

{c m}^{- 1}

).

Since

C_{i}

approaches zero and

C

approaches

C_{o}

, as

t \to 0

, Eq. (9) could be simplified [Eq. (10)] and

k_{f}

can be determined from the slope of the curve

C / C_{o}

versus

t

{[\frac{d (C / C_{o})}{d t}]}_{t = o} = - k_{f} S_{o}

(10)

Assuming the particles are spherical, the surface area for mass transfer,

S_{o}

, can be obtained by the following equation (Furusawa and Smith 1973):

S_{o} = \frac{6 m_{s}}{d_{p} ρ (1 - ε_{p})}

(11)

where

m_{s}

= mass of adsorbent particles per unit volume (

g / {c m}^{3}

);

d_{p}

= average particle diameter (cm);

ρ

= adsorbent density (

g / {c m}^{3}

); and

ε_{p}

= adsorbent porosity.

Homogeneous Particle Diffusion Model

The homogeneous particle diffusion model (HPDM) assumes that the rate controlling step of adsorption could be described by either film or particle diffusion (El-Naggar et al. 2012). Particle diffusion was described by Boyd et al. (1947) as follows:

X (t) = 1 - \frac{6}{π^{2}} \sum_{Z = 1}^{\infty} \frac{1}{Z^{2}} \exp [\frac{- Z^{2} π^{2} D_{e} t}{r^{2}}]

(12)

where

X (t)

= fractional attainment of equilibrium at time,

t

;

D_{e}

= effective diffusion coefficient of adsorbate in the sorbent phase (

m^{2} / s

);

r

= radius of the adsorbent particle assumed to be spherical (m); and

z

= integer number.

X (t)

values could be determined as follows:

X (t) = \frac{q_{t}}{q_{e}}

(13)

Vermeulen (1953) approximation of Eq. (12) fits the whole range

0 < X (t) < 1

X (t) = {[1 - \exp [- \frac{π^{2} D_{e}^{2} t}{r^{2}}]]}^{\frac{1}{2}}

(14)

This equation could be further simplified to the following expression (Lao-Luque et al. 2014):

- \ln (1 - X^{2} (t)) = 2 K t

(15)

where

K = \frac{π^{2} D_{e}}{r^{2}}

(16)

A linear plot of

- \ln (1 - X^{2} (t))

versus

t

with an intercept of zero would suggest particle diffusion was the controlling step. If film diffusion controls the rate of adsorption, the following analogous expression can be used:

X (t) = 1 - \exp [\frac{3 D_{e} C_{e}}{r δ C_{s}}]

(17)

or

- \ln (1 - X (t)) = k_{f} t

(18)

where

k_{f} = \frac{3 D_{e} C_{e}}{r δ C_{s}}

(19)

where

C_{s}

= equilibrium concentration of adsorbate in the solid phase (

mg / L

); and

δ

= thickness of liquid film.

A linear plot of

- \ln (1 - X (t))

versus

t

with an intercept of zero would suggest film diffusion was the controlling step.

Particle Diffusion Model

The model assumes that particle diffusion is rate controlling and that Vermeulen’s approximation for particle diffusion [Eq. (14)] could be simplified to cover most of the data points for calculating effective particle diffusivity as follows (Vermeulen 1953):

\ln (1 - X^{2} (t)) = \frac{π^{2}}{r^{2}} D_{e} t

(20)

X (t) = \frac{q_{t}}{q_{e}}

(21)

Biot Number

The Biot number,

B i

, indicates the predominance of internal diffusion against external diffusion (Subash and Krishna Prasad 2016)

B i = \frac{k_{f} r}{D_{e}}

(22)

Equilibrium Models

Langmuir Isotherm

The Langmuir isotherm (Langmuir 1916) assumes that adsorption sites on the adsorbent possess an equal affinity for molecules and that each site is capable of adsorbing one molecule thereby forming a monolayer. The model is expressed as

q_{e} = \frac{q_{m} K_{L} C_{e}}{1 + K_{L} C_{e}}

(23)

where

K_{L}

= Langmuir equilibrium constant (

L / mg

); and

q_{m}

= maximum adsorption capacity (

mg / g

).

Freundlich Isotherm

Firth [as cited in Swan and Urquhart (1927)], explained that the equation of the form

x = k c^{1 / n}

was first applied to adsorption of gases by De Saussure in 1814. Its application was further extended to solutions by Boedecker in 1859 (Swan and Urquhart 1927). In 1906, Freundlich described the adsorption isotherm mathematically as a special case for nonideal and reversible adsorption (Freundlich 1906). This equation is presented as

q_{e} = K_{F} {(C_{e})}^{1 / n_{F}}

(24)

where

K_{F}

= Freundlich constant related to adsorption affinity [

(mg / g)

{(L / mg)}^{1 / n}

]; and

n_{F}

= Freundlich constant related to heterogeneity.

Redlich-Peterson Isotherm

The Redlich-Peterson isotherm (Redlich and Peterson 1959) is a hybrid isotherm that incorporates the features of the Langmuir and the Freundlich isotherms. It is represented by

q_{e} = \frac{K_{R P} C_{e}}{1 + α_{R P} C_{e}^{g_{R P}}}

(25)

where

K_{R P}

= Redlich-Peterson equilibrium constant;

g_{R P}

= Redlich-Peterson exponent; and

α_{R P}

= Redlich-Peterson constant.

Sips Isotherm

The Sips isotherm (Sips 1948) is a combined form of the Langmuir and Freundlich isotherms developed for predicting heterogeneous adsorption systems and bypassing the limitation of the rising adsorbate concentration associated with Freundlich isotherm model. It is expressed as

q_{e} = \frac{q_{S} {(α_{S} C_{e})}^{n_{S}}}{1 + {(α_{S} C_{e})}^{n_{S}}}

(26)

where

q_{S}

= Sips maximum adsorption capacity (

mg / g

);

α_{s}

= Sips affinity constant; and

n_{s}

= Sips index of heterogeneity.

Thermodynamic Equations

Gibbs free energy change

Δ G °

is given by the following equation (Nollet et al. 2003):

Δ G ° = - R T {l n K}_{L}

(27)

According to Eq. (28) the slope and intercept obtained from linear plots of

Δ G °

versus temperature,

T

, represents entropy change,

Δ S °

, and enthalpy change,

Δ H °

, respectively

Δ G ° = Δ H ° - T Δ S °

(28)

Activation energy

E_{a}

and sticking probability

S^{*}

can be estimated using a modified Arrhenius-type equation related to surface coverage as

S^{*} = (1 - θ) \exp (- E_{a} / R T)

(29)

The linearized form is given as

\ln (1 - θ) = \ln S^{*} + E_{a} / R T

(30)

where

θ

is the surface coverage expressed as

θ = (1 - C_{e} / C_{o})

(31)

According to Eq. (30),

S^{*}

and

E_{a}

can be determined from a plot of

l n (1 - θ)

versus

1 / T

(Nollet et al. 2003).

Error Analysis

The goodness of fit by the various kinetic, isotherm, mass transfer, and predictive models to the experimental data were evaluated using the coefficient of determination (

R^{2}

), the Relative Percent Error (RPE), the Root Mean Square Error (RMSE), Marquardt’s Percent Standard Deviation (MPSD), the Hybrid Error Function (HYBRID), the Mean Square Error (MSE), and the Chi-square function (

χ^{2}

) presented as follows:

R^{2} = \frac{\sum_{i = 1}^{N} {({(q e_{i})}_{\exp} - q e_{\exp, m e a n})}^{2} - \sum_{i = 1}^{N} {({(q e_{i})}_{\exp} - {(q e_{i})}_{p r e d})}^{2}}{\sum_{i = 1}^{N} {({(q e_{i})}_{\exp} - {(q e_{i})}_{p r e d})}^{2}}

(32)

R P E % = \frac{1}{N} \sum_{i = 1}^{N} \frac{[| {(q e_{i})}_{p r e d} - {(q e_{i})}_{\exp} |]}{{(q e_{i})}_{\exp}} * 100

(33)

R M S E = \sqrt{\frac{1}{N} \sum_{i = 1}^{N} {({(q_{e_{i}})}_{\exp} - {(q_{e_{i}})}_{p r e d})}^{2}}

(34)

M P S D = 100 {\sqrt{\frac{1}{N - P} \sum_{i = 1} [\frac{{(q_{e i})}_{\exp} - {(q_{e i})}_{p r e d}}{{(q_{e i})}_{\exp}}]}}^{2}

(35)

H Y B R I D = \frac{100}{N - P} \sum_{i = 1}^{N} [\frac{{({(q_{e i})}_{\exp} - {(q_{e i})}_{p r e d})}^{2}}{{(q_{e i})}_{p r e d}}]

(36)

M S E = (\frac{1}{N} \sum_{i = 1}^{N} {[{(q_{e_{i}})}_{\exp} - {(q_{e_{i}})}_{p r e d}]}^{2})

(37)

χ^{2} = \sum_{i = 1}^{N} \frac{{({(q_{e_{i}})}_{p r e d} - {(q_{e_{i}})}_{\exp})}^{2}}{{(q_{e_{i}})}_{p r e d}}

(38)

where

N

= number of experimental points; and

P

= number of parameters in the model.

Experimental Design and Procedure

Response Surface Methodology

A three-level three-factor Box-Behnken experimental design in RSM was generated using Design-Expert version 9.0 software (Minneapolis, Minnesota) to determine the optimum conditions for encapsulation of lime-iron sludge. Similar designs were used by Chen et al. (2016) for optimizing microencapsulation of Bifidobacterium bifidum BB01, Narsaiah et al. (2014), for optimizing microencapsulation of nisin with sodium alginate and guar gum and Ismail and Madhavan Nampoothiri (2010) for optimizing the encapsulation of probiotic Lactobacillus plantarum in calcium alginate beads. A total of 17 runs were carried out to optimize the chosen variables, namely, sodium alginate dose,

{CaCl}_{2}

dose, and lime-iron sludge dose. For statistical computations, the three independent variables were denoted as

X 1

,

X 2

, and

X 3

, respectively. The ranges as determined by screening experiments and the levels of each variable are given in Table 1. Phosphate adsorption capacity was taken as the response of the system. The optimum parameter values were obtained by numeric optimization and by analyzing the response surface 3D plots.

Table 1. Coded and actual values of variables for the Box-Behnken design

Variable	w/v ratio (%)	Code	Coded levels of variables
Variable	w/v ratio (%)	Code	$- 1$	0	1
Sodium alginate ( $g / 25 m L$ )	1–2	X1	0.25	0.38	0.5
${CaCl}_{2}$ ( $g / 25 m L$ )	1–2	X2	0.25	0.38	0.5
Lime-iron sludge ( $g / 25 m L$ )	1–2	X3	0.25	0.38	0.5

Pareto Analysis

The Pareto analysis was carried out to check the percentage effect (

P_{i}

) of each variable on the response (Khuri and Cornell 1996)

P_{i} = (\frac{β_{i}^{2}}{\sum β_{i}^{2}}) \times 100 (i \neq 0)

(39)

where

β_{i}

= regression coefficient of individual process variables.

Artificial Neural Network

The neural network toolbox of MATLAB version 7.14.0 (R2012a) was used to develop a three-layer feed forward ANN model for predicting phosphate adsorption capacity. Sodium alginate dose,

{CaCl}_{2}

dose, and lime-iron sludge dose were used as inputs to the network, and the corresponding adsorption capacity was used as the target. The data were first normalized in the range

- 1

to 1 using the following equation:

X n o r m = 2 [\frac{X_{i} - X_{\min}}{X_{\max} - X_{\min}}] - 1

(40)

where

X_{i}

= input or output variable

X

;

X_{m i n}

= minimum value of variable

X

; and

X_{m a x}

= maximum value of variable

X

.

The data set was divided whereby 70% of the data was applied to training the network, 15% for validation, and 15% for testing the accuracy of the model and its prediction. The tangent sigmoid transfer function (tansig) [Eq. (41)] and the linear transfer function (purelin) [Eq. (42)] were used at the hidden and outer layers, respectively.

Tansig

f (n) = [2 / (1 + e x p (- 2 * n))] - 1

(41)

Purelin

f (n) = n

(42)

Relative Importance Index

The relative importance of the input variables on the adsorption capacity was determined by sensitivity analysis using the weight method proposed by Garson (Garson 1991) and is presented as Eq. (43)

I j = \frac{\sum_{m = 1}^{m = N h} ((| W_{j m}^{i h} | / \sum_{k = 1}^{N i} | W_{k m}^{i h} |) \times | W_{m n}^{h o} |)}{\sum_{k = 1}^{k = N i} {\sum_{m = 1}^{m = N h} (| W_{k m}^{i h} | / \sum_{k = 1}^{N i} | W_{k m}^{i h} |) \times | W_{m n}^{h o} |}}

(43)

where

I_{j}

= relative importance of the

j

th input variable on the output variable;

N_{i}

= number of input neurons;

N_{h}

= number of hidden neurons; and

W

= connection weight. The superscripts ‘

i

’, ‘

h

’, and ‘

o

’ refer to input, hidden, and output layers, respectively, and subscripts ‘

k

’, ‘

m

’, and ‘

n

’ refers to input, hidden, and output neurons, respectively.

Results and Discussion

Protocol for Encapsulation of Lime-Iron Sludge Beads

Preliminary experiments were conducted to determine suitable ranges for different variables to optimize the encapsulation of lime-iron sludge. In all instances, the syringe was held approximately 6.0 cm above the

{CaCl}_{2}

bath as it was observed that the beads flattened on contact with the

{CaCl}_{2}

if the syringe was held less than 6.0 cm above the bath. This may be attributed to the inability of the droplet viscosity and surface tension forces to overcome the surface tension exerted by the

{CaCl}_{2}

solution (Chan et al. 2006). Additionally, beads were left in the

{CaCl}_{2}

for 30 min after which they were rinsed and stored in a distilled water bath. Beads isolated from

{CaCl}_{2}

in less than 15 min were not completely gelled. Longer curing time significantly improved the gelation and reduced bead diameter. However, beads cured for more than 24 h were easily disintegrated when agitated.

Determination of Optimum Range of Lime-Iron Sludge for Encapsulation

Increase of sludge content in calcium alginate beads from 0.125 to 0.5 g resulted in 91% increase in adsorption capacity due to the increased number of available adsorption sites. However, increase in sludge dose beyond 0.5 g resulted in only marginal increments in adsorption (Fig. 1). This behavior may be due to the binding of almost all phosphate anions to the sludge and the establishment of equilibrium. Similar results were reported by Rezaei et al. (2017) for dye adsorption using

{Fe}_{3} O_{4}

nanoparticles encapsulated in calcium alginate beads and Fiol et al. (2004) for chromium uptake using grape stalk waste encapsulated in calcium alginate beads.

Fig. 1. Effect of lime-iron sludge content of encapsulated calcium alginate beads on phosphate adsorption capacity.

Determination of Optimum Range of ${CaCl}_{2}$ for Encapsulation of Lime-Iron Sludge

Increase in

{CaCl}_{2}

dose from 0.125 to 0.38 g resulted in 151% increase in adsorption. This increase may be attributed to the increased porosity of the beads. According to Barde (2015) the pore size of calcium alginate beads depends on the amount of calcium ions present. The authors found that increasing the concentrations of

{CaCl}_{2}

resulted in increased pore diameter. However, it was observed that increase in

{CaCl}_{2}

beyond 0.5 g had an insignificant effect on the adsorption capacity (Fig. 2). This may be attributed to the possible saturation of calcium binding sites in the guluronic acid chains of the sodium alginate as a result of which no additional cross linking could occur with higher

{CaCl}_{2}

dosages (El-Kamel et al. 2003).

Fig. 2. Effect of ${CaCl}_{2}$ content of encapsulated calcium alginate beads on phosphate adsorption capacity.

Determination of Optimum Range of Sodium Alginate for Encapsulation of Lime-Iron Sludge

Uniform-sized spherical beads were produced using 0.25–0.5 g of sodium alginate [Figs. 3(c and d)]. Sodium alginate doses less than 0.25 g resulted in flattened beads [Figs. 3(a and b)]. According to Senuma et al. (2000) this was due to the impact of the less viscous droplets against the surface of the

{CaCl}_{2}

bath. Doses more than 0.5 g [Figs. 3(e and f)] resulted in larger deformed beads due to its high viscosity and denser matrix structure (Fundueanu et al. 1999). The selected parameter ranges for encapsulation are presented in Table 2.

Fig. 3. Images of alginate beads formed using varying masses of sodium alginate: (a) 0.125 g; (b) 0.2 g; (c) 0.25 g; (d) 0.5 g; (e) 0.75 g; and (f) 1.0 g.

Table 2. Parameter ranges used for encapsulation

Parameter	Range
Height of syringe above ${CaCl}_{2}$ bath	6 cm
Gelation time	30 mins
Sludge dose ( $/ 25 m L$ )	0.25–0.5 g
${CaCl}_{2}$ dose ( $/ 25 m L$ )	0.25–0.5 g
Sodium alginate dose ( $/ 25 m L$ )	0.25–0.5 g

Determination of Optimum Combination of Parameters for Encapsulation

The optimum ranges of individual parameters were used to construct a Box-Behnken design in RSM to determine the optimum combination of parameters for lime-iron sludge encapsulation. The impact of parameter variation on the adsorption capacity for each run performed according to the Box-Behnken design is given in Table 3. By applying multiple regression analysis, the following quadratic polynomial equation in coded terms was obtained:

Y = 1.70078 - 0.064994 X_{1} + 0.0365795 X_{2} + 0.105731 X_{3} + 0.0285035 X_{1} X_{2} + 0.013836 X_{1} X_{3} - 0.019121 X_{2} X_{3} - 0.0162616 X_{1}^{2} - 0.0105021 X_{2}^{2} - 0.052366 X_{3}^{2}

(44)

where

Y

is the adsorption capacity and

X_{1}

,

X_{2}

, and

X_{3}

represent the sodium alginate,

{CaCl}_{2}

, and lime-iron sludge dose, respectively. The accuracy of the model was assessed by comparing the predicted

q_{e}

to the experimental

q_{e}

. The results presented in Fig. 4 reveal a significantly high correlation (

R^{2} = 0.9985

) and highlight the accuracy of the RSM prediction.

Table 3. Box-Behnken experimental and predicted adsorption capacities

Run	Coded values			$q_{e}$ ( $mg / g$ )
Run	$X 1$	$X 2$	$X 3$	Experimental	Predicted
1	$- 1$	0	$- 1$	1.6060	1.6053
2	1	0	$- 1$	1.4506	1.4477
3	0	$- 1$	$- 1$	1.4791	1.4765
4	0	0	0	1.7057	1.7008
5	$- 1$	$- 1$	0	1.7276	1.7309
6	0	$- 1$	1	1.7326	1.7262
7	1	0	1	1.6860	1.6868
8	1	$- 1$	0	1.5383	1.5440
9	0	0	0	1.6981	1.7008
10	0	0	0	1.6990	1.7008
11	0	1	$- 1$	1.5815	1.5879
12	1	1	0	1.6775	1.6742
13	0	1	1	1.7585	1.7611
14	0	0	0	1.6998	1.7008
15	$- 1$	1	0	1.7528	1.7471
16	0	0	0	1.7012	1.7008
17	$- 1$	0	1	1.7860	1.7891

Fig. 4. Comparison of experimental and RSM model predictions.

The analysis of variance (ANOVA) was conducted to test the significance and adequacy of the quadratic equation, and the results are presented in Table 4. The calculated

F

-value (502.30) was greater than the tabulated

F

-value (3.68) at 95% significance and therefore confirms the adequacy of the model fits. The

p

-value was

< 0.0001

, which confirms that the model was statistically significant. Additionally, all the model terms were statistically significant (

p < 0.05

) at the 95% confidence interval.

Table 4. ANOVA results for response surface quadratic model

Source	Sum of squares	Degrees of freedom	Mean square	$F$ value	$p$ -value $Prob > F$
Model	0.1500	9	0.0170	502.3000	$< 0.0001$
A-Sodium alginate	0.0340	1	0.0340	996.2400	$< 0.0001$
B-Calcium chloride	0.0110	1	0.0110	315.5700	$< 0.0001$
C-Lime-iron sludge	0.0890	1	0.0890	2636.4500	$< 0.0001$
AB	0.0033	1	0.0033	95.8000	$< 0.0001$
AC	0.0008	1	0.0008	22.5700	0.0021
BC	0.0015	1	0.0015	43.1100	0.0003
$A^{2}$	0.0001	1	0.0011	32.8200	0.0007
$B^{2}$	0.0005	1	0.0005	13.6900	0.0077
$C^{2}$	0.0120	1	0.0120	340.3800	<0.0001
Residual	0.0002	7	0.0000	—	—
Pure error	0.0000	4	0.0000	—	—
Cor total	0.1500	16	—	—	—
Std. dev.	0.0058
Mean	1.6600
C.V. %	0.3500
PRESS	0.0033
R-squared	0.9985
Adj R-squared	0.9965
Pred R-squared	0.9786
Adeq precision	76.4390

The percentage effect of each independent variable on the adsorption capacity was determined by Pareto analysis using Eq. (39). The results shown in Fig. 5 indicate that sludge dose was the most influential parameter in the process, followed by sodium alginate, and finally

{CaCl}_{2}

dose.

Effect of Varying Bead Encapsulation Parameters

Three-dimensional (3D) surface plots were analyzed to gain insight into the main and interactive effects of the independent variables on phosphate adsorption capacity. Figs. 6(a and b) show that an increase in sludge dose resulted in a significant increase in adsorption. This increase may be attributed to the availability of more surface area and accessibility to more adsorption sites (Ociński et al. 2016). An increase in sodium alginate dose resulted in a reduction in adsorption capacity [Figs. 6(b and c)]. This may be due to the high viscosity of the beads, which decreases the pore size, and consequently, impedes the diffusion of adsorbate into the alginate matrix (Singh et al. 2012). Adinarayana et al. (2004) added that an increase in sodium alginate dose also reduces the porosity of the beads. Increase in

{CaCl}_{2}

concentration increased adsorption capacity [Figs. 6(a and c)]. According to Saha and Ray (2013), increase in

{CaCl}_{2}

concentration increases the porosity of the beads. Analysis of the plots corroborates that lime-iron sludge was the most influential variable, which is in agreement with the results of the Pareto analysis.

Fig. 6. Surface plots for phosphate adsorption at (a) constant ${CaCl}_{2}$ ; (b) constant sodium alginate; and (c) constant lime-iron sludge.

Artificial Neural Network

A three-layer feedforward ANN was developed to predict the adsorption capacity of the sludge encapsulated beads. The number of hidden neurons was varied from 1 to 15 and its impact on performance assessed using the MSE. Using the Levenberg–Marquardt algorithm to train the network with the tansig and purelin transfer functions at the hidden and output layer, respectively, a minimum MSE value of 0.000245 was obtained using three hidden neurons. A comparison of the ANN predicted and the experimental

q_{e}

(Fig. 7), reveals a high correlation (

R^{2} = 0.9405

).

Fig. 7. Comparison of experimental and ANN predictions.

ANN Empirical Equation

An empirical equation correlating the inputs was developed to predict adsorption capacity without having to run the ANN software (Shahryari et al. 2013). The equation derived using the weights (

W_{i}

) and biases (

b_{i}

) of the optimized network (Table 5) is presented as follows:

q_{t pred} = 0.17028 F_{1} - 0.5279 F_{2} + 0.37552 F_{3} + 0.4983

(45)

where

F_{i}

is the tansig activation function used in the hidden layer and is given as

F i = \frac{2}{[1 + \exp (- 2 * E i)]} - 1; i = 1 : 3

(46)

Table 5. ANN weight and bias values

$I$	$W_{i 1}$	$W_{i 2}$	$W_{i 3}$	$b_{i}$
1	$- 1.5598$	4.0395	0.51599	$- 2.6509$
2	2.3435	$- 0.85485$	$- 4.4497$	$- 2.014$
3	$- 0.9159$	$- 1.5009$	0.44498	$- 2.4417$

E_{i}

is the weighted sum of the input,

I

, defined as

E_{i} = W_{i 1} \times Sodium alginate + W_{i 2} \times {CaCl}_{2} + W_{i 3} \times Sludge dose + b_{i}

(47)

ANN Relative Importance Index

The relative importance of the input variables on the adsorption capacity was determined using the Garson’s equation [Eq. (43)]. Lime-iron sludge dose was found to be the most influential parameter with a relative importance of 35.38%. This was followed by

{CaCl}_{2}

(34.31%) and finally sodium alginate dose (30.30%).

Comparison of RSM and ANN

The predictive accuracy of the RSM and ANN models was assessed using

R^{2}

,

χ^{2}

, RMSE, and RPE functions. The results presented in Table 6 indicate that the RSM model produced a higher

R^{2}

and significantly lower

χ^{2}

, RMSE, and RPE and was, therefore, superior to the ANN model.

Table 6. Comparison of predictive accuracy of RSM and ANN models

Parameter	Model
Parameter	RSM	ANN
$R^{2}$	0.9985	0.9405
$χ^{2}$	0.0001	0.0079
RMSE	0.0037	0.0273
RPE	0.1930	0.9611

Optimization Analysis

Numerical optimization in RSM was used to determine the optimum parameters for bead preparation. The results revealed that maximum adsorption could be achieved using beads prepared with 0.25 g of sodium alginate and 0.5 g of lime-iron sludge in 25 mL of distilled water to produce a homogeneous mixture and added dropwise into a solution of 0.31 g

{CaCl}_{2}

in 25 mL of distilled water. Laboratory experiments were subsequently conducted to validate these findings. The resulting adsorption capacity was

1.8285 mg / g

producing a residual error of 2.9%, and thus confirms the validity of the model.

Characterization of Adsorbent

Optimization of the encapsulation process produced beads that were spherical with the sludge dispersed throughout the calcium alginate matrix and had an average diameter of

4.0 \pm 1.0 mm

[Fig. 8(a)]. SEM images illustrated in Figs. 8(b–d) were used to examine the surface morphology of the beads. SEM image of the lime-iron sludge prior to encapsulation revealed a rough surface and particles appeared amorphous, with irregular flocs. After encapsulation, there was a reduction in roughness; however, an abundant amount of protuberance was observed that according to Soni et al. (2012) may have resulted due to the agglomeration of the encapsulated material. The SEM image after adsorption appears stable in morphology. The EDS was used to assess the change in elemental composition before and after encapsulation as well as before and after adsorption. The spectrum [Fig. 9(a)] reveals that Fe, Ca, and O were the dominant elements present before encapsulation. Following encapsulation Fe, Ca, C, and O were the dominant elements present both before and after adsorption [Figs. 9(b and c)]. It was noted that after encapsulation the Fe and Ca peaks (particularly the Fe peak) diminished significantly. This was attributed to the finite mass of sludge (approximately 0.002 g per bead) encapsulated. A further significant reduction in the Fe and Ca peaks was observed following adsorption [Fig. 9(c)]. These findings, therefore, suggest that Fe and Ca were the main components for phosphate removal. According to Chen et al. (2007), the presence of Fe-OH functional groups may result in adsorption of phosphate via ligand exchange. The authors further explained that phosphate removal by Ca components might have occurred by Ca orthophosphate precipitation resulting in

{CaHPO}_{4}

. The EDS exposes the presence of small concentrations of phosphate before adsorption. The increased phosphate peak after adsorption confirms that phosphate was successfully adsorbed. The high presence of oxygen shown presumes its occurrence in the oxide and oxo-hydroxide form (Ociński et al. 2016).

Fig. 8. (a) Diameter of encapsulated lime-iron sludge bead; (b) SEM of lime-iron sludge before encapsulation at 1,000×; (c) SEM before adsorption of phosphate at 500×; and (d) SEM after adsorption of phosphate at 500×.

Fig. 9. EDS of (a) lime-iron sludge before encapsulation; (b) encapsulated lime-iron sludge before adsorption of phosphate; and (c) encapsulated lime-iron sludge after adsorption of phosphate.

Kinetic Modeling

Modeling the Effects of Agitation

Kinetic data were fitted to four models: Lagergren model; pseudo-second order model; Weber and Morris intraparticle diffusion model, and the diffusion-chemisorption model. The goodness of fit was assessed using the RPE, MPSD, and HYBRID error functions presented as Eqs. (33), (35), and (36), respectively. The results of nonlinear regression presented in Table 7 show the pseudo-second order model produced the best simulation of the data.

Table 7. Analysis of kinetic models using nonlinear regression

RPM	Model	Constants		Error functions
RPM	Model	$K_{P S O}$	$h$	RPE	MPSD	HYBRID
150	Pseudo-first order	—	—	4.1135	6.5949	0.4555
	Pseudo-second order	0.2593	1.2468	1.1841	1.971	0.0511
	Intraparticle diffusion	—	—	18.0584	24.3061	8.1625
	Diffusion-chemisorption	—	—	5.953	8.9449	0.8511
250	Pseudo-first order	—	—	4.5018	7.3306	0.5714
	Pseudo-second order	0.2776	1.3879	1.7276	2.5991	0.0842
	Intraparticle diffusion	—	—	19.7641	26.4275	9.6994
	Diffusion-chemisorption	—	—	5.1932	7.6453	0.7079
350	Pseudo-first order	—	—	5.1326	7.9981	0.8571
	Pseudo-second order	0.374	1.9657	1.7431	2.6507	0.0983
	Intraparticle diffusion	—	—	23.2589	31.4809	14.9196
	Diffusion-chemisorption	—	—	3.281	4.7816	0.3588

According to the pseudo-second order model, the increase in agitation speed resulted in an increase in both the initial and overall adsorption rate. This may have occurred because increased agitation reduces the thickness of the liquid boundary layer and as a consequence reduces the mass transfer resistance. Additionally, it increases the turbulence of the bulk liquid and therefore promotes greater collision of adsorbate onto adsorption sites (Patil et al. 2011).

For all agitation speeds tested, adsorption occurred rapidly and then slowed as equilibrium approached. This may be attributed to the availability of a significant number of unoccupied adsorption sites early in the reaction, however, after a certain time, the available sites become occupied by adsorbate and consequently create a repulsive force between the adsorbate on the adsorbent surface and in bulk solution (Banerjee and Chattopadhyaya 2013). Equilibrium was reached after 16 h of agitation. Makris et al. (2005) explained that relatively slow phosphate uptake might be due to intraparticle diffusion within the micropores of an adsorbent.

Effect of pH on Adsorption

The effect of solution pH was studied at an initial phosphate concentration of

10 mg / L

and is presented in Fig. 10. Adsorption capacity increased with increase in pH and reached a maximum at a value of pH 7.5. Further increase in pH resulted in a significant decrease in adsorption. Fig. 11 shows the

{pH}_{PZC}

to occur at pH 8.9. Despite the surface being positively charged below the

{pH}_{PZC}

, adsorption decreased significantly with decreasing pH. This may be attributed to the presence of different phosphate species. At pH 3 the dominant species is

H_{3} {PO}_{4}

, however, as pH increases

H_{2} {PO}_{4}^{-}

and

{HPO}_{4}^{2 -}

become the dominating, both of which are more easily adsorbed according to Liu et al. (2002). At pH 12,

{PO}_{4}^{3 -}

is the dominant species and phosphate adsorption reduces possibly due to competition between

{PO}_{4}^{3 -}

and

{O H}^{-}

for active sites on the adsorbent. Additionally, the negatively charged carboxylic groups in calcium alginate may impede the diffusion of anions into the beads, therefore contributing to the decrease in adsorption capacity at pH above the

{pH}_{PZC}

(Ociński et al. 2016).

Fig. 10. Effect of pH on phosphate uptake.

Fig. 11. ${pH}_{PZC}$ for encapsulated beads.

Equilibrium Modeling

Nonlinear Regression of Isotherm Data

Equilibrium data were fitted to the two-parameter Langmuir and Freundlich isotherms as well as the three-parameter Sips and Redlich-Peterson isotherms. The goodness of fit was assessed using the RPE, MPSD, and HYBRID error functions presented as Eqs. (33), (35), and (36), respectively. The results of nonlinear regression (Table 8) showed the Langmuir isotherm was the best performing two-parameter model. However, beyond room temperature, a more robust simulation was observed by the three-parameter Sips isotherm. It is postulated that at room temperature there was no transmigration of the adsorbate in the plane of the surface (Foo and Hameed 2010). At higher temperatures, the increased kinetic energy of the adsorbate anions increases its collision onto adsorption sites and may have influenced transmigration of the adsorbate. The Sips index of heterogeneity,

n_{S}

, deviated widely from unity indicating some degree of heterogeneity of the surface of the adsorbent.

Table 8. Analysis of isotherm models using nonlinear regression

Temperature (K)	Model	Constants	Error functions
Temperature (K)	Model	Constants	RPE	MPSD	HYBRID
300.15	Langmuir	$q_{m} = 8.3116$ ; $K_{L} = 0.2688$	34.9966	59.9874	69.5136
	Freundlich	$K_{F} = 3.2127$ ; $n_{F} = 4.509$	49.7344	87.6678	143.1319
	Sips	$α_{S} = 0.3417$ ; $q_{S} = 7.4404$ ; $n_{S} = 4.6424$	61.1378	84.7882	497.5884
	Redlich-Peterson	$α_{R P} = 0.0204$ ; $K_{R P} = 1.2433$ ; $g_{R P} = 1.1581$	84.648	114.0732	601.5185
308.15	Langmuir	$q_{m} = 10.942$ ; $K_{L} = 0.307$	35.5465	62.0614	85.5195
	Freundlich	$K_{F} = 4.1639$ ; $n_{F} = 4.2207$	53.9349	97.0906	196.8808
	Sips	$α_{S} = 0.3445$ ; $q_{S} = 9.7485$ ; $n_{S} = 3.0483$	10.4284	17.6354	8.1528
	Redlich-Peterson	$α_{R P} = 0.0294$ ; $K_{R P} = 1.8954$ ; $g_{R P} = 1.4851$	21.1128	37.7606	30.4237
318.15	Langmuir	$q_{m} = 14.584$ ; $K_{L} = 0.2364$	32.5097	64.253	69.7454
	Freundlich	$K_{F} = 3.8719$ ; $n_{F} = 2.8553$	58.942	117.4239	215.6085
	Sips	$α_{S} = 0.3272$ ; $q_{S} = 12.664$ ; $n_{S} = 1.984$	15.8939	28.6884	20.9149
	Redlich-Peterson	$α_{R P} = 0.0552$ ; $K_{R P} = 2.4541$ ; $g_{R P} = 1.3151$	29.1539	55.9125	55.5898
328.15	Langmuir	$q_{m} = 17.2209$ ; $K_{L} = 0.5074$	47.0785	97.5448	145.036
	Freundlich	$K_{F} = 6.0827$ ; $n_{F} = 3.007$	70.2111	144.1451	319.1363
	Sips	$α_{S} = 0.7765$ ; $q_{S} = 14.5938$ ; $n_{S} = 2.3109$	13.9427	22.6276	14.0724
	Redlich-Peterson	$α_{R P} = 0.2598$ ; $K_{R P} = 7.0637$ ; $g_{R P} = 1.1576$	42.1666	85.1678	113.1317

According to the Langmuir isotherm, lime-iron sludge encapsulated beads produced a maximum phosphate adsorption capacity of

8.31 mg / g

. This was compared to that of other adsorbents reported in the literature (Table 9). The reduction in adsorption capacity when compared to that of powdered lime-iron sludge,

15.30 mg / g

, as reported by Chittoo and Sutherland (2017) may be attributed to the presence of the polymer matrix that creates a diffusional barrier to adsorption sites on the lime-iron sludge. However, the presence of the polymer matrix provides beneficial properties that allow its recovery and reuse. Additionally, its adsorptive performance compares well to several adsorbents reported in the literature; this further suggests its effectiveness as an adsorbent.

Table 9. Comparison of the phosphate adsorption capacity by various adsorbents reported in the literature

Adsorbent	Adsorbent dose (g)	pH	Temperature (K)	Adsorption capacity, $q_{e}$ ( $mg / g$ )	Reference
Iron oxide tailings	2	6.7	266	7	Zeng et al. (2004)
Dolomite	10	9.5	266	4.76	Yuan et al. (2015)
Arundo donax reeds	0.1	6.5	269	16.4	Abdelhay et al. (2018)
Lime-iron sludge	0.5	8	298	15.30	Chittoo and Sutherland (2017)
Alginate calcium carbonate composite beads	1.5	10	298	0.62	Mahmood et al. (2015)
Lime-iron sludge encapsulated calcium alginate beads	0.5	7.5	300	8.31	This study

Effect of Initial Phosphate Concentration on Adsorption

The effect of initial phosphate concentration was studied at room temperature using a constant sludge dose of 0.5 g. The results presented in Fig. 12 reveal a decrease in removal from 90% to 61% as the concentration increased from

8

to

105 mg / L

. At lower concentrations, most phosphate anions could interact with an adsorption site on the adsorbent. However, as adsorbate concentration increases the number of available adsorption sites becomes relatively insufficient therefore reducing the percentage adsorption.

Fig. 12. Effects of initial phosphate concentration.

The results also show an increase in uptake capacity as the phosphate concentration increased. Steeper concentration gradients generate a greater driving force sufficient enough to overcome the mass transfer resistance between the solid and liquid phases. Hence the unit mass saturation of the adsorbent will increase with higher initial concentration (Banerjee and Chattopadhyaya 2013). Minimum change in adsorption capacity was obtained for phosphate concentrations beyond

77 mg / L

possibly due to the filling of most of the adsorptions sites.

Thermodynamic Analysis

The thermodynamic effect of phosphate adsorption was investigated at four different temperatures (300, 308, 318, and 328 K) and the results are presented in Table 10.

Δ G °

values between 0 and

- 20 kJ / mol

indicate that the adsorption process is controlled by physisorption, whereas values within the range of

- 80

to

- 400 kJ / mol

indicate that the process is controlled by chemisorption (Yu et al. 2001). In this study

Δ G °

varied from

- 8.0847

to

- 10.5722 kJ / mol

indicating that physisorption was the dominant mechanism. For all temperatures studied,

Δ G °

was negative, indicating that the process was spontaneous. The positive value of

Δ H °

suggests that the process was endothermic with the presence of an energy barrier. According to Fu et al. (2012),

Δ H °

for Van der Waals interactions, hydrogen bond, ligand exchange, dipole interaction, and chemical bond is 4–10, 2–40,

\approx 40

, 2–29, and

> 60 kJ / mol

, respectively. In this study,

Δ H °

was

19.585 kJ / mol

and therefore involves hydrogen bonding and dipole interaction. The positive

Δ S °

reflects the high affinity of lime-iron sludge beads for phosphate anions. This may be due to the opening of pores of the alginate matrix, overcoming the activation energy barrier and enhancing the rate of intraparticle diffusion (Aravindhan et al. 2007).

Table 10. Thermodynamic parameters

Temperature (K)	$K_{a}$ ( $L / mol$ )	$Δ G °$ ( $kJ / mol$ )	$Δ S$ ( $kJ / mol$ )	$Δ H$ ( $kJ / mol$ )	$E_{a}$ ( $kJ / mol$ )	$S *$
300	25.5280	$- 8.0847$	0.092	19.585	37.5826	$1.978 \times 10^{- 7}$
308	29.1558	$- 8.6406$
318	40.7611	$- 9.8073$
328	48.1878	$- 10.5722$

The

E_{a}

value was found to be

37.5826 kJ / mol

. According to Nollet et al. (2003), low

E_{a}

values (

5 - 40 kJ / mol

) denote physisorption and suggest that the energy barrier existing between the reactants is relatively low. The low value of the sticking probability (

S * < 1

) indicates favorable sticking of adsorbate to the adsorbent and further highlights physisorption as the dominant attachment mechanism.

Mechanisms

External Diffusion Model

Kinetic data were first analyzed using the external diffusion model, and the results are presented in Table 11. A slight increase in

k_{f}

was obtained as agitation increased from 150 to 250 rpm. Further increase in agitation resulted in a marginal decrease in

k_{f}

. Increase in agitation decreases the external film resistance allowing the adsorbate to reach the adsorbent more rapidly and thus increases

k_{f}

. At higher agitation, the overall rate of adsorbate uptake may cause blocking of the pores due to adsorbate ions competing for available adsorption sites and as a result reduces

k_{f}

(Allen et al. 2005).

R^{2}

obtained for all agitation speeds was well below 0.95 and therefore implies that external mass transfer may not be rate controlling for the entire reaction.

Table 11. Mass transfer coefficients and biot numbers

Agitation RPM	External diffusion model		Particle diffusion model		$B i$
Agitation RPM	$k_{f}$ ( $m / s$ )	$R^{2}$	$D_{e}$ ( $m^{2} / s$ )	$R^{2}$	$B i$
150	${5.08 \times 10}^{- 4}$	0.7116	${9.3 \times 10}^{- 8}$	0.9953	21.8404
250	${5.25 \times 10}^{- 4}$	0.7316	${9.4 \times 10}^{- 8}$	0.9911	22.3532
350	${4.57 \times 10}^{- 4}$	0.7196	${1.08 \times 10}^{- 8}$	0.9343	16.9263

Weber and Morris Intraparticle Diffusion Model

The data were then assessed using the Weber and Morris intraparticle diffusion model to determine if intraparticle diffusion was rate controlling. The plots of

q_{t}

versus

t^{1 / 2}

(Fig. 13) reveal two distinct linear phases during the adsorption process. The first linear phase may be attributed to intraparticle diffusion. The second linear phase represents the slowing down of intraparticle diffusion possibly due to low solute concentration in the solution (Aksu and Kabasakal 2005). According to Nethajia et al. (2010), the intercept

c

is proportional to the boundary layer thickness and the larger the intercept, the greater is the boundary layer effect. Patil et al. (2011) explained that increasing the agitation speed increases turbulence, which reduces the film boundary thickness. However, in this instance, an increase in intercept

c

, was observed with increased agitation. Similar observations were reported by McKay et al. (1983) and Sağ and Aktay (2000). The authors attributed such effects to systems in which surface mass transfer was not significant.

Fig. 13. Intraparticle diffusion model for various agitation speed.

Homogeneous Particle Diffusion Model

Kinetic data were further analyzed using the HPDM to determine the relative impact of film and intraparticle diffusion. The data were fitted to the two model equations [Eqs. (15) and (18)] by plotting−(

\ln (1 - X^{2} (t))

versus

t

and

- \ln (1 - X (t))

versus

t

, respectively. The straight lines obtained in Fig. 14(a) do not pass through the origin, indicating that film diffusion is not the rate-limiting step in the adsorption process. It was noted as agitation speed increased the plots move further from the origin. The straight lines obtained in the plot of Fig. 14(b) passed through the origin for all agitation speeds tested indicating that intraparticle diffusion is the dominant transport mechanism.

Fig. 14. HPDM plot for (a) film diffusion; and (b) intraparticle diffusion.

Particle Diffusion Model

The predominance of intraparticle diffusion was further assessed using the particle diffusion model. The results (Table 11) show an increase in

D_{e}

with increasing agitation. According to Ha et al. (2008), as agitation increases the diffusion barrier would decrease as particles move further apart thereby increasing the diffusion coefficient. According to Walker and Weatherley (1999), the magnitude of the diffusion coefficient is directly related to the nature of the adsorption process. For physical adsorption,

D_{e}

ranges from

10^{- 6}

to

10^{- 9} m^{2} / s

and for chemical adsorption process

D_{e}

ranges from

1 0^{- 9}

to

10^{- 17} m^{2} / s

. In this study,

D_{e}

was in the order

10^{- 8} m^{2} / s

suggesting that physisorption was the dominant attachment mechanism.

R^{2}

values were well above 0.95 indicating that particle diffusion may be the rate controlling step in the process.

Biot Number

B i

was determined using

k_{f}

and

D_{e}

values presented in Table 11. Crittenden et al. (2012) explained that for

B_{i}

values

< 1.0

, external mass transfer dominates while for

B_{i} > 30

, surface diffusion controls and for values between 1 and 30, both external and intraparticle mass transfer contribute to the adsorption rate. The results (Table 11) therefore indicate that both external and intraparticle mass transfer contributes to the reaction rate.

Design of Batch Adsorption System from Isotherm Data

Laboratory-scale equilibrium studies are used to predict batch adsorber size and performance. Fig. 15 shows the schematic of a single-stage batch adsorber with a solution volume of

V

(L) and an initial phosphate concentration,

C_{o}

(

mg / L

), which is reduced to

C_{t}

(

mg / L

) as the reaction proceeds. The phosphate loading on the adsorbent in the reactor of mass

M

(g), changes from

q_{o}

to

q_{t}

with increased reaction time. The mass balance for the reactor is given by the following equation (McKay et al. 1985):

V (C_{0} - C_{t}) = M (q_{t} - q_{0}) = M q_{t}

(48)

Fig. 15. Design of single-stage batch system.

The adsorption process at 300 K was best represented by the Langmuir isotherm. Therefore, the mass balance under equilibrium condition (

C_{t} \to C_{e}

and

q_{t} \to q_{e}

) is arranged as follows:

\frac{M}{V} = \frac{C_{o} - C_{e}}{q_{e}} = \frac{C_{o} - C_{e}}{q_{m} K_{L} C_{e} / (1 + K_{L} C_{e})}

(49)

Fig. 16 illustrates a series of plots of the predicted values of

M

(g) versus

V

(L) for 60%, 70%, 80%, and 90% phosphate ion removal at the initial concentration of

15 mg / L

and 300 K. For example, the mass of adsorbent required for the 70% phosphate removal from aqueous solution was 2.3, 11.5, and 18.5 g, for phosphate solution volumes of 1, 5, and 8 L, respectively. This evaluation becomes relevant for pilot-batch system design as well as large-scale batch applications. Following adsorption saturation, the spent adsorbent may be considered for agricultural applications as a fertilizer. According to A. Bezbaruah, T. B. Almeelbi, and M. Quamme [US Patent No. 15/147,437 (2014)], alginate is biodegradable, and so phosphate saturated beads can be used directly as fertilizer, without the need to desorb or extract the phosphate. Robalds et al. (2016) highlighted the importance of ensuring that the concentrations of heavy metals are within safe limits if the spent adsorbent is to be used for land application. Elemental analysis before and after adsorption did not indicate the presence of heavy metals and therefore underscores its potential for agricultural applications.

Fig. 16. Adsorbent mass ( $M$ ) versus volume of phosphate solution treated ( $V$ ).

Conclusion

A protocol for encapsulating lime-iron sludge in calcium alginate beads was successfully developed. RSM was found to be more accurate than ANN in optimizing the encapsulation process. An empirical model was developed, and numeric optimization indicated that maximum adsorption capacity could be obtained from beads prepared using 0.25 g of sodium alginate and 0.5 g of lime-iron sludge in 25 mL of distilled water to produce a homogeneous mixture and added dropwise into a solution of

{0.31 g CaCl}_{2}

in 25 mL of distilled water. The accuracy of the RSM prediction was subsequently validated by laboratory studies that revealed a residual error of 2.9%.

The beads exhibited a maximum phosphate adsorption capacity of

8.3 mg / g

that compared well to other reported adsorbents in the literature. EDS and thermodynamic analysis indicated that physisorption, ligand exchange, hydrogen bonding, and dipole interaction were the dominant attachment mechanisms. Mass transfer studies indicated that film diffusion was present; however, the reaction was dominated by intraparticle diffusion.

At the given operational parameters, the solution pH influenced the speciation of phosphate that in turn had a significant effect on the adsorption process. Kinetic data were best simulated using the pseudo-second order model while equilibrium data followed the Langmuir isotherm at room temperature and the Sips isotherm at higher temperatures.

The findings of this study reveal that due to the high iron content, this encapsulated waste material may be used as a novel adsorbent to remove phosphate (a limiting nonrenewable resource) from wastewater. It has a high adsorption capacity with the ability to reduce synthetic phosphate concentrations from

45 mg / L

to a final value of

4.5 mg / L

(

1.5 mg / L

phosphorous) with an adsorbent dosage of

8.9 g / L

. This makes it a promising adsorbent considering the limit value of

< 2.0 mg / L

phosphorus set by most regulatory agencies for the discharge of treated effluents into sensitive waters.

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Journal of Environmental Engineering

Volume 145 • Issue 5 • May 2019

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This work is made available under the terms of the Creative Commons Attribution 4.0 International license, http://creativecommons.org/licenses/by/4.0/.

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Received: Jul 6, 2018

Accepted: Oct 23, 2018

Published online: Mar 12, 2019

Published in print: May 1, 2019

Discussion open until: Aug 12, 2019

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Beverly S. Chittoo, Aff.M.ASCE [email protected]

Instructor, Project Management and Civil Infrastructure Systems, Univ. of Trinidad and Tobago, San Fernando Campus, Tarouba Link Rd., San Fernando, Trinidad and Tobago. Email: [email protected]

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Clint Sutherland, Ph.D., A.M.ASCE https://orcid.org/0000-0002-5569-325X [email protected]

Assistant Professor, Project Management and Civil Infrastructure Systems, Univ. of Trinidad and Tobago, San Fernando Campus, Tarouba Link Rd., San Fernando, Trinidad and Tobago (corresponding author). ORCID: https://orcid.org/0000-0002-5569-325X. Email: [email protected]

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Abstract

Introduction

Materials and Methods

Chemicals and Adsorbents

Preparation of Adsorbent

Preparation of Adsorbate

Characterization of Adsorbent

Adsorption Studies

Kinetic Studies

Equilibrium Studies

Point of Zero Charge

Adsorption Yield

Adsorption Capacity

Kinetic Models

Lagergren Model

Pseudo-Second Order Model

Intraparticle Diffusion Model

Diffusion-Chemisorption Model

Mass Transfer Studies

External Diffusion Model

Homogeneous Particle Diffusion Model

Particle Diffusion Model

Biot Number

Equilibrium Models

Langmuir Isotherm

Freundlich Isotherm

Redlich-Peterson Isotherm

Sips Isotherm

Thermodynamic Equations

Error Analysis

Experimental Design and Procedure

Response Surface Methodology

Pareto Analysis

Artificial Neural Network

Relative Importance Index

Results and Discussion

Protocol for Encapsulation of Lime-Iron Sludge Beads

Determination of Optimum Range of Lime-Iron Sludge for Encapsulation

Determination of Optimum Range of CaCl2 for Encapsulation of Lime-Iron Sludge

Determination of Optimum Range of Sodium Alginate for Encapsulation of Lime-Iron Sludge

Determination of Optimum Combination of Parameters for Encapsulation

Effect of Varying Bead Encapsulation Parameters

Artificial Neural Network

ANN Empirical Equation

ANN Relative Importance Index

Comparison of RSM and ANN

Optimization Analysis

Characterization of Adsorbent

Kinetic Modeling

Modeling the Effects of Agitation

Effect of pH on Adsorption

Equilibrium Modeling

Nonlinear Regression of Isotherm Data

Effect of Initial Phosphate Concentration on Adsorption

Thermodynamic Analysis

Mechanisms

External Diffusion Model

Weber and Morris Intraparticle Diffusion Model

Homogeneous Particle Diffusion Model

Particle Diffusion Model

Biot Number

Design of Batch Adsorption System from Isotherm Data

Conclusion

References

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Determination of Optimum Range of ${CaCl}_{2}$ for Encapsulation of Lime-Iron Sludge