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Modeling phosphorus removal and recovery fromanaerobic digester supernatant through struvitecrystallization in a fluidized bed reactor

Md. Saifur Rahaman a,*, Donald S. Mavinic b, Alexandra Meikleham a,Naoko Ellis c

aDepartment of Building Civil and Environmental Engineering, Concordia University, 1455 de Maisonneuve Blvd,

West, EV-6.139, Montreal, Quebec, Canada H3G 1M8b Pollution Control & Waste Management Group, Department of Civil Engineering, University of British Columbia

(UBC), 2002-6250 Applied Science Lane, Vancouver, BC, Canada V6T 1Z4c Fluidization Research Centre, Department of Chemical & Biological Engineering, University of British Columbia

(UBC), 227-2360 East Mall, Vancouver, BC, Canada V6T 1Z3

a r t i c l e i n f o

Article history:

Received 26 August 2013

Received in revised form

28 November 2013

Accepted 30 November 2013

Available online 13 December 2013

Keywords:

Crystallization

Fluidized bed

Modeling

Phosphorus recovery

Struvite

* Corresponding author. Tel.: þ1 514 848 242E-mail address: saifur.rahaman@concord

0043-1354/$ e see front matter Crown Copyhttp://dx.doi.org/10.1016/j.watres.2013.11.048

a b s t r a c t

The cost associated with the disposal of phosphate-rich sludge, the stringent regulations to

limit phosphate discharge into aquatic environments, and resource shortages resulting

from limited phosphorus rock reserves, have diverted attention to phosphorus recovery in

the form of struvite (MAP: MgNH4PO4$6H2O) crystals, which can essentially be used as a

slow release fertilizer. Fluidized-bed crystallization is one of the most efficient unit pro-

cesses used in struvite crystallization from wastewater. In this study, a comprehensive

mathematical model, incorporating solution thermodynamics, struvite precipitation ki-

netics and reactor hydrodynamics, was developed to illustrate phosphorus depletion

through struvite crystal growth in a continuous, fluidized-bed crystallizer. A thermody-

namic equilibrium model for struvite precipitation was linked to the fluidized-bed reactor

model. While the equilibrium model provided information on supersaturation generation,

the reactor model captured the dynamic behavior of the crystal growth processes, as well

as the effect of the reactor hydrodynamics on the overall process performance. The model

was then used for performance evaluation of the reactor, in terms of removal efficiencies of

struvite constituent species (Mg, NH4 and PO4), and the average product crystal sizes. The

model also determined the variation of species concentration of struvite within the crystal

bed height. The species concentrations at two extreme ends (inlet and outlet) were used to

evaluate the reactor performance. The model predictions provided a reasonably good fit

with the experimental results for PO4eP, NH4eN and Mg removals. Predicated average

crystal sizes also matched fairly well with the experimental observations. Therefore, this

model can be used as a tool for performance evaluation and process optimization of

struvite crystallization in a fluidized-bed reactor.

Crown Copyright ª 2013 Published by Elsevier Ltd. All rights reserved.

4x5058; fax: þ1 514 848 79ia.ca (Md.S. Rahaman).

right ª 2013 Published by

65.

Elsevier Ltd. All rights reserved.

Nomenclature

Symbols

A Cross-sectional area of the bed (column) [m2]

ADH DebyeeHuckel constant

Cd Drag coefficient

Ci Molar concentration of the species (mol/L)

Ci,H Concentration of species i (mol/L) at bed height H

Ci,HþDH Concentration of species i at the height increment,

DH, above H

EC Electrical conductivity (mS cm�1)EC25 Electrical conductivity at 25 �CG Linear growth rate of the struvite crystals (m/s)

I Ionic strength (mol L�1)K Equilibrium reaction rate constants

Ksp Thermodynamic solubility product of struvite

k Struvite crystal growth rate constant

L Struvite crystal diameter (m)

N Number of seed crystals added per unit time

n Expansion index

Q Flow rate (L/s)

R Ideal gas constant (8.314 Jmol�1K�1)Ret Reynolds number

S Relative supersaturation

Ut Terminal settling velocity of struvite crystals (m/s)

y Order of struvite growth kinetics

Zi Valence of ion species i

T Temperature in degree Kelvin

DH Infinitesimal height of the reactor (m)

DH0 Enthalpy of the reaction (Jmol�1)

Greek letters

al Liquid volume fraction (bed voidage)

a Volume factor (for sphere, 4p/3)

b Surface factor (for sphere, 4p)

rl Density of water (kg/m3)

rs Density of struvite crystals (kg/m3)

gi Activity coefficient of ion i

ε Dielectric constant

U Supersaturation ratio

Others

A Harvest zone

B Active zone

C Fine zone

D Seed hopper

{ } Species activity

[ ] Species molar concentration

Abbreviations

ANN Artificial Neural Network

BNR Biological Nutrient Removal

EBPR Enhanced Biological Phosphorus Removal

EDH Extended DebyeeHuckel

MAP Magnesium Ammonium Phosphate

MSE Mean Squared Error

ReZ RichardsoneZaki relation

SSR Supersaturation Ratio

UBC University of British Columbia

wat e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1e1 02

1. Introduction

Phosphorus is a non-renewable, non-interchangeable finite

resource. The simultaneous diminution of natural phos-

phorus reserves available for the phosphate industry and

increasing awareness of pollution problems, such as eutro-

phication due to phosphorus release in wastewater effluents,

have led to research into newprocesses to remove and recover

phosphorus from sewage effluents (Capdevielle et al., 2013).

Therefore, phosphorus recovery fromwastewater is no longer

a possibility, but rather an obvious reality. Several wastewater

treatment facilities have already undertaken initiatives to

adopt new technologies that remove and recover phosphorus

fromwaste streams. Althoughmuch effort has been dedicated

towards the study of the struvite crystallization process itself,

a clear “methodology” to implement the laboratory results to

the design and operations of the plant scale crystallization has

not been reported until now. Struvite crystallization efficiency

depends on a variety of complex processes, such as nucle-

ation, growth, agglomeration and attrition of crystals, fluid

dynamics and mass transfer in the crystallizer (Ali and

Schneider, 2008; Hanhoun et al., 2012; Pastor et al., 2008).

Although some of these mechanisms are not yet fully under-

stood, the design and operation of an industrial scale crys-

tallizer still requires reliable knowledge of the most essential

processes, which has historically been obtained from lab-

scale experiments. This often presents a problem at the

scale-up stage, as lab-based models have historically not

taken into account all of these complex processes (Al-Rashed

et al., 2013).

The University of British Columbia (UBC) Phosphorus Re-

covery Group has developed a novel fluidized bed reactor,

which has been found to be effective in recovering more than

80% of the soluble phosphate fromwaste streams (Adnan et al.,

2003). In order to apply this innovative technology, an effective

design methodology had to be devised. An efficient design of a

fluidized bed reactor relies heavily upon the knowledge of

process kinetics, thermodynamics and systemhydrodynamics.

In order to achieve an effective design, which optimizes reactor

outputs, it was imperative to develop amodel that incorporates

solution thermodynamics, struvite precipitation kinetics and

reactor hydrodynamics e all in one unit.

Multi-pronged models of struvite growth have been

developed from data obtained in a continuous-discrete

reactor system (Ali and Schneider, 2008; Hanhoun et al.,

2012). However, a very limited number of articles can be

traced to the modeling of a fluidized bed crystallizer. In a

fluidized bed crystallizer, the simultaneous progress of fluid-

ization and crystallization yield very complex phenomena. In

order to take into account the segregation and mixing of

particles within the bed, Frances et al. (1994) developed a

model describing the fluidized bed as amultistage crystallizer.

The newmodel provided better prediction of the mean size of

wa t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1e1 0 3

the product crystals over the original model, which was based

on perfect size classification of crystals. However, the growth

rate expression in this model did not include the effect of

crystal size and solid content on crystal growth. Furthermore,

Shiau and Liu (1998) developed a theoretical model for a

continuous fluidized bed crystallizer that assumes the liquid

phase moving upward through the bed in a plug flow, and the

solid phase in the fluidized bed is perfectly classified. The

model describes the variations of crystal size and solute

concentration with respect to vertical position within the

reactor. Later the same investigators, Shiau and Lu (2001)

performed the study on interactive effects of particle mixing

and segregation on the performance characteristics of a batch

fluidized bed crystallizer. In this model, the liquid phase is

again assumed to move upward through the bed in plug flow;

and the solid phase is represented by a series of equal-sized,

ideally-mixed beds of crystals. However, the crystals at

different bed heights are totally segregated. This one param-

eter model can be employed to investigate both the extreme

conditions (completely mixed or segregated) and the inter-

mediate region of mixing. All of the aforementioned studies

dealt only with hydrodynamics and used a simple represen-

tation of crystal growth kinetics.

Recently, several attempts have been taken to model the

struvite crystallization process, in particular to determine the

precipitation potential of struvite from waste streams. Stru-

vite v.3.1, developed by the Water Research Commission,

South Africa, is one of the early models, used for predicting

struvite formation potential (Loewenthal et al., 1994). This

model is used to estimate struvite formation potential from

the ionic concentrations of the reactive species, using the

Extended DebyeeHuckel [EDH] method for activity coefficient

correction. The influence of the partial pressure of CO2, and its

influence on carbonate equilibria, was also considered when

calculating the final pH (Parsons et al., 2001). In several

studies, it has been revealed that, although the model pro-

vides fairly good estimates at lower pH values, it tended to

under-predict struvite formation at pH values >8.5 (Doyle and

Parsons, 2002; Parsons et al., 2001).

A number of chemical equilibrium models such as MINE-

QLþ, MINTEQA2, and PHREEQC have been used to determine

the equilibrium speciation of struvite species constituents.

Each of these models performs an iterative analysis, using an

internal thermodynamic database and user-defined input

concentrations, to calculate the equilibria of all considered

complexes. Since struvite is generally not provided in these

internal databases, the characteristics (Ksp and change in

specific enthalpy, DH�) need to be user-defined as well. Several

studies have used these programs to calculate the solubility

curves of struvite (Ali and Schneider, 2008; Miles and Ellis,

2000; Ohlinger et al., 1998).

Models have also been developed considering the precipi-

tation kinetics of struvite. A three-phase (aqueous, solid, gas)

model, developed by Musvoto et al. (2000) has widely been

used for anaerobic digester liquors, where CO2 stripping by

aeration is used to increase the pH. A more simplified kinetic

model, based only on struvite production rates, has been

developed on several digester liquors in Japan (Yoshino et al.,

2003). More recently, Forrest et al. (2007) used a chemical

equilibrium-based crystallizer model “Crystallizer v.2.0”,

developed in-house by the Struvite Recovery Group at UBC.

The authors also tested an Artificial Neural Network (ANN)

based model, NeuStruvite v.1.0, to predict the struvite crys-

tallization performance of a fluidized bed crystallizer and

claimed that the ANN based model better predicted the pro-

cess performance than the equilibrium-based model, Crys-

tallizer v.20. One large limitation of these equilibrium models

is that they are developed based on thermodynamic chemical

equilibria. The reactions involved in struvite crystallization

processes are generally fast and, hence, can be considered to

have reached the equilibrium state immediately after mixing.

However, crystallization processes, such as nucleation, crys-

tal growth and agglomeration, are relatively slow processes

and hence should be modeled dynamically. Furthermore,

none of the above mentioned models for the struvite crystal-

lization processes have taken reactor hydrodynamics into

account and no information on product quality, in terms of

particle size, can be identified.

Very recently, Rahaman et al. (2008) developed a reactor

model incorporating both struvite precipitation kinetics and

reactor hydrodynamics in one single model. The model uti-

lizes the analytical concentration of struvite constituent spe-

cies and the solution pH as model inputs, and predicts

removal efficiencies of the species, as well as the average

product crystal size. In this model, the conditional solubility

product of struvite is used to determine the crystal growth.

However, the difficulty of using the conditional solubility

product is that it requires supplying the conditional equilib-

rium solubility product (Ksp) of struvite, which heavily de-

pends on the solution pH. The values of conditional Ksp found

in the literature are diverse and; therefore, a reliable value for

a specific system, running at a specific pH is very difficult to

find. One way to overcome this problem is by using the ther-

modynamic (instead of conditional) solubility product of

struvite in its growth rate expression; this requires the activity

based solubility of struvite and, hence, the ionic concentra-

tions need to be determined from the total analytical con-

centration. Thus, in this paper, a chemical speciation model,

based on the solution thermodynamic equilibrium, is devel-

oped and linked to the reactor model, in order to generate a

more generic and robust reactor model.

2. Thermodynamic equilibrium model forstruvite precipitation

In recovering nutrients through struvite crystallization, solu-

tion chemistry plays a vital role in crystal formation, thus

affecting the overall removal/recovery of the nutrients from

wastewater. Magnesium ammonium phosphate hexahydrate

(MgNH4PO4.6H2O), more commonly known as struvite, is a

white crystalline substance, formed by chemical reaction of

free magnesium, ammonium and phosphate, along with six

molecules of water. The simplified form of the reaction

involving the struvite formation is as follows:

Mg2þ þNHþ4 þ PO3�4 þ 6H2O/MgNH4PO4$6H2O

Like any other reactive crystallization processes, struvite

precipitation also depends on solution supersaturation; while,

wat e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1e1 04

the generation of supersaturation depends on the constituent

species concentration, as well as the solution pH and ionic

strength. A reactive solution containing struvite species: Mg,

NH4 and PO4, oncemixed, undergoes chemical transformation

and, based on species concentration and solution pH, can

form different compounds and complexes. In a synthetic

aqueous solution containing Mg, NH4 and PO4, the following

species can be formed: H3PO4(aq), H2PO4

- , HPO42�, PO4

3�,MgH2PO4

þ, MgHPO4(aq), MgPO4- , Mg2þ, MgOHþ, NH4

þ, Hþ, OH-,

NH3(aq).

The formation of the aforementioned species and their

associated equilibrium constants are as follows:

MgOHþ������! ������KMgOHþMg2þ þOH� ; KMgOHþ ¼

gMg2þgOH� ½Mg2þ�½OH��gMgOHþ ½MgOHþ�

(1)

MgHPO4ðaqÞ���! ���KMgHPO4Mg2þ þHPO2�4 ;

KMgHPO4¼

gMg2þgHPO2�4½Mg2þ��HPO2�

4

�hMgHPO4ðaqÞ

i (2)

MgH2POþ4 ��������! ��������K

MgH2POþ4 Mg2þ þH2PO

�4 ;

KMgH2POþ4¼ gMg2þgH2PO

�4½Mg2þ��H2PO

�4

�gMgH2PO

þ4

�MgH2PO

þ4

� (3)

MgPO�4 �������! �������KMgPO�4 Mg2þ þ PO3�

4 ; KMgPO�4 ¼gMg2þgPO3�

4½Mg2þ��PO3�

4

�gMgPO�4

�MgPO�4

�(4)

H3PO4ðaqÞ���! ���KH3PO4Hþ þH2PO�4 ; KH3PO4 ¼

gHþgH2PO�4½Hþ��H2PO

�4

��H3PO4ðaqÞ

�(5)

H2PO�4 �������! �������KH2PO

�4 Hþ þHPO2�

4 ; KH2PO�4¼

gHþgHPO2�4½Hþ��HPO2�

4

�gH2PO

�4

�H2PO

�4

�(6)

HPO2�4 �������! �������K

HPO2�4 Hþ þ PO3�

4 ; KHPO2�4¼

gHþgPO3�4½Hþ��PO3�

4

�gHPO2�

4

�HPO2�

4

� (7)

NHþ4 �����! �����KNHþ

4 NH3 þHþ ; KNHþ4¼ gHþ ½Hþ�½NH3�

gNHþ4

�NHþ4

� (8)

H2O�! �KH2OHþ þOH� ; KH2O ¼gHþgOH� ½Hþ�½OH��

½H2O� (9)

gHþ�Hþ

� ¼ 10�pH (10)

Like any other ionic reactions, once the product of the

species concentration exceeds the solubility product, the

system becomes metastable with respect to the compound

and the substance precipitates. For struvite, the thermody-

namic solubility product, Ksp can be expressed as

Ksp¼�Mg2þ��NHþ4

��PO3�

4

�;where;fgrepresentsspeciesactivity:

Thus, the struvite precipitation reaction can be expressed

as,

MgNH4PO4$6H2OðsÞ�! �KspMg2þ þNHþ4 þ PO3�

4 þ 6H2O;

Ksp ¼gMgþ gNHþ

4gPO3�

4½Mgþ�½NHþ

4 �½PO3�4 �

½MgNH4PO4$6H2O�ðsÞ(11)

where, [ ] shows the molar concentration and gi represents

activity coefficient of species i. The equilibrium constants for

the reactions are taken from Bhuiyan et al. (2007) and

Rahaman et al. (2006).

The activity coefficient of a species depends on the solution

ionic strength (I) and the valence charge of that specific spe-

cies. The Davis equation is the most commonly used expres-

sion for determining species activity coefficients (for I < 0.5).

The equation is as follows:

Loggi ¼ �ADHZ2i

"ðIÞ0:5

1þ ðIÞ0:5#� 0:3I (12)

where,

ADH ¼ 0:486� 6:07� 10�4Tþ 6:43� 10�6T2 (13)

T ¼ Temperature in degrees Kelvin

Now the ionic strength can be calculated from the species

ionic concentrations as,

I ¼ 0:5X

CiZ2i (14)

where, Ci is the molar concentration (mol/L) and Zi is the

valence of species ion i.

The equilibrium constants (K), found in literature, are

usually determined at a standard temperature of 25 �C. Hence,

a temperature correction factor must be introduced, if the

solution temperature is different from the standard one. The

Van’t Hoff equation is used to modify the equilibrium con-

stants based on the reaction temperature as follows:

lnðKÞ ¼ lnðK25Þ � DH0

R

�1T� 1T0

�(15)

where, K25 equilibrium constants at 25 �C, DH0 is the enthalpy

of reaction and R is the gas constant. The value of R is equal to

0.008314 kJ mol-1 deg�1 and DH0 values for different equilib-

rium reactions are taken from Bhuiyan (2007).

Now, the species mole balance, at equilibrium condition,

can be written as:

CTðPO4Þ ¼ H3PO4 þH2PO�4 þHPO2�

4 þ PO3�4 þMgH2PO

þ4

þMgHPO4 þMgPO�4 þ�MgNH4PO4$6H2O

�s

(16)

CTðMgÞ ¼Mg2þ þMgOHþ þMgH2POþ4 þMgHPO4 þMgPO�4

þ �MgNH4PO4$6H2O

�s

(17)

CTðNH3Þ ¼ ½NH3� þ�NHþ4

�þ �MgNH4PO4$6H2O

�ðsÞ (18)

The systemof equations is nowmanipulated to express the

struvite species concentration in terms of the known values:

�Mg2þ� ¼ CT;Mg2þ

aþ b�PO3�

4

� (19)

wa t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1e1 0 5

�PO3�

4

� ¼ CT;PO3�4

cþ b½Mg2þ� (20)

�Mg2þ� ¼ �

�acþ bCT;PO3�

4� bCT;Mg2þ

����

acþ bCT;PO3�4� bCT;Mg2þ

�2

� 4ab � cCT;Mg2þ

��0:52ab

(21)

�NHþ4

� ¼ CT;NHþ4

1þkNHþ

4gNHþ

4

ðgHþ ½Hþ�Þ þgMg2þ gNHþ

4gPO3�

4½Mgþ�½PO3�

4 �Ksp

(22)

where,

1þ kH2OgMg2þ

kMgOH� ðgHþ ½Hþ�Þ¼ a (23)

0BB@ gPO3�

4ðgHþ ½Hþ�Þ2

gMgH2PO�4kMgH2PO

�4kH2PO

�4kHPO2�

4

þgMg2þgPO3�

4ðgHþ ½Hþ�Þ

kMgHPO4kHPO2�

4

þgMg2þgPO3�

4

gMgPO�4kMgPO�4

þgMg2þgNHþ

4gPO3�

4CT;NHþ

4

Ksp

�1þ

KNHþ4gNHþ

4

ðgHþ ½Hþ�Þ�

1CCA ¼ b

(24)

and

0@1þ

gPO3�4ðgHþ ½Hþ�Þ3

kH3PO4kH2PO

�4kHPO2�

4

þgPO3�

4ðgHþ ½Hþ�Þ2

gH2PO�4kH2PO

�4kHPO2�

4

þgPO3�

4ðgHþ ½Hþ�Þ

gHPO2�4kHPO2�

4

1A¼ c

(25)

By solving the equilibrium Equations 19 through 25, the

amount of struvite precipitated, as well as the concentrations

of each individual species are determined at the equilibrium

condition.

3. Reactor modeling

Performing a comprehensive modeling process for struvite

crystallization from wastewater, which is dynamic in nature,

requires the knowledge of thermodynamics, crystallization

kinetics and reactor hydrodynamics, in order to represent the

reactor system completely. In doing so, the reactor model,

which includes crystallization kinetics and the reactor hy-

drodynamics, is linked to the thermodynamic chemical

equilibrium model. The equilibrium model takes care of su-

persaturation generation, while the reactor model determines

the mass deposition of constituent species onto the seed

crystals and subsequently determines the process

performance.

The thermodynamic equilibrium model described in the

earlier section, is used to determine the supersaturation

within the reactor system and the kinetic expression devel-

oped by Bhuiyan et al. (2008) is used for struvite crystal

growth. This kinetic expression is developed from data gath-

ered in the UBC MAP fluidized bed crystallizer. In general, the

type of reactor should not affect the intrinsic kinetic param-

eters; however, the kinetics determined with this reactor type

may be useful, as the mass transfer effect is not explicitly

dealt with in this study. The following assumptions are taken

into consideration during model development.

1. In the struvite crystallization process, the reactions are

rapid; hence, the dynamics of the reactions are ignored and

equilibrium relationships are used to determine the spe-

cies concentrations. However, the crystallization process

involves crystal growth, which is dynamic in nature;

therefore, crystal growth kinetics must be incorporated in

order to determine the species mass deposition onto the

crystals.

2. The system is run at isothermal conditions, i.e., the oper-

ating temperature remained constant throughout an indi-

vidual run.

3. The crystal bed is considered as completely segregated.

This assumption was found to be valid for an identical

system running at lab scale operation (Rahaman, 2009).

Moreover, the numerical investigation of the hydrody-

namics of struvite crystals in a fluidized bed, performed by

Rahaman (2009) also supports this nearly perfect size

classification of struvite crystals.

4. The reactive solution is circulated as a plug flow pattern;

the diffusion/dispersion along the height of the reactor is

considered negligible.

5. Primary nucleation is neglected. Since the in-reactor su-

persaturation is not very high, the generation of primary

nuclei can be neglected. However, secondary nucleation

and agglomeration may still be present in the process. For

simplicity, both secondary nucleation (creation of new

nuclei, attributed either by fluid shear or through the col-

lisions between already existing crystals with either a solid

surface or with other crystals themselves) and agglomer-

ation are lumped into the crystal growth mechanism, to

determine the overall growth and the resulting crystal size

distribution in the reactor. The formation of secondary

nuclei negatively contributes to the crystal growth since

they are generated from the existing crystals. The crystal

growth is also considered to be size independent. Consid-

ering that there is no significant variation in crystal sizes

within a specific computational domain, size independent

crystal growth model is considered in this study.

6. The system is considered as a seeded process. Uniform

sized seed crystals are added in the seed hopper from the

top of the reactor at a specific time interval, and the rate of

addition is averaged over time in order to ensure that the

reactor is run at a steady state condition.

Fig. 2 e A schematic of the model development.

wat e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1e1 06

The basis of developing the reactor model is the same as

described in Rahaman et al. (2008). The only changes are as

follows:

The mole balance for each individual constituent species

(Mg, NH4 and PO4) of struvite is formulated. In the earlier

version (Rahaman et al., 2008), only the mass balance of the

struvite was used, with the species concentration lumped

together into a single equation. In this model, a pilot-scale

reactor is considered and a schematic of the reactor is pre-

sented in Fig. 1. At steady-state operation, all three zones (A, B

and C) are occupied with struvite crystals, which provide

required sites formass deposition through crystal growth. The

seed crystals are added from the seed hopper (section D). In

this study the seed hopper was used only for the addition of

seed crystals, and any processes that may have occurred in

this section are neglected.

A mass/mole balance over an infinitesimal height (DH) of

the reactor (as shown in Fig. 2) is taken. At steady state con-

ditions, the mole balance of struvite constituent species i,

(PO4, Mg, and NH4) on a differential segment, DH can be

expressed as:

Q Ci;H � Ci;HþDH

�� 12ð1� alÞDHAðaL3Þ

bL2

�ðGrsÞ

1MWs

¼ 0 (26)

The first term, in Equation (26), represents the time rate of

disappearance of struvite constituent species ’i’ from the

liquid phase.

Where, Q: flow rate; Ci,H: concentration of species ’i’ (mole/

L) at bed height H; and Ci,HþDH: concentration at the height

increment, DH (m), above H.

The second term representsmole deposition of constituent

species i, onto the suspended crystals in the horizontal slice,

per unit time.

Where, al: liquid volume fraction (bed voidage); A: cross-

sectional area of the reactor; DH: height increment; a:

Fig. 1 e Schematic of the fluidized bed UBC MAP crystallizer. D

dia [ 102 mm, height [ 1549 mm; C: dia [ 152 mm, height [

volume factor; L: crystal diameter; b: surface factor; G (m/s):

linear growth rate of the struvite crystals; rs: density of stuvite

(kg/m3); and MWs: molecular weight of struvite.

By rearranging Equation (26) and taking the limit as DH

approaches zero, the gradient of species concentration ’i’ can

be expressed as,

dCi

dH¼ Abrsð1� alÞ

2aQLMWsG (27)

where, the bed height, H is the only independent variable and

Ci and L are the dependent variables. The bed voidage can be

expressed as a function of liquid velocity and the crystals size,

whereas, the growth rate of struvite, G depends on species

concentrations.

imensions e A: dia [ 76 mm, height [ 749 mm; B:

1270 mm; D: dia [ 381 mm, height [ 457 mm.

wa t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1e1 0 7

The struvite bed expansion characteristics can be explained

by RichardsoneZaki (ReZ) relation (1954) with a newly devel-

oped correlation for expansion index (Rahaman, 2009):

al ¼

QAUt

1n

(28)

where,Ut is the terminal settling velocity of the particles of size

L placed in the column of diameter D. ‘n’ is the expansion index

and differs depending on the range of Reynolds number,

Ret ¼ UtrlL=ml, where, ml for digester supernatant is not found in

the literature and thus it is taken to be the same as for water.

For the range of Ret used in this current study, the expan-

sion index is expressed (Rahaman, 2009) as:

n ¼ 4:7718� Re�0:089t for 26 < Ret < 302 (29)

For spherical particles, the terminal settling velocity (Ut)

can be determined using Newton’s equation as

Ut ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4g3Cd

ðrs � rlÞrl

L

s(30)

where Cd values can be determined using themodified version

of Clift et al. (1978) correlation as

Cd ¼ 24Ret

1þ 0:563Re0:83

t

�(31)

As can be found in Bhuiyan et al. (2008) the growth rate can

be expressed as

G ¼ kSy (32)

where, k and y represents the rate constant and the order of

reaction, respectively and S represents the relative supersat-

uration, which can be represented as

S ¼ U1=3 � 1 (33)

where, U is the supersaturation ratio and can be expressed as

U ¼gMg2þgNHþ

4gPO3�

4½Mg2þ��NHþ4

��PO3�

4

�Ksp

(34)

where, Ksp is the thermodynamic solubility product of struvite.

The second mass balance equates the time rate of mass

increase of growing crystals within the horizontal slice of the

crystallizer, to the time rate of the mass increase in particles,

as calculated by subtracting the particle mass entering the

slice from that exiting the slice:

rsNa L3H � L3HþDH

� ¼ 12

ð1� alÞDHAðaL3Þ

bL2

�ðGrsÞ (35)

By rearranging Equation (35) and taking the limit as DH

approaches zero one obtains:

dLdH¼ �Abð1� alÞ

6Na2L3G (36)

where, N is number of seed crystals added per unit time.

Using different seed sizes is recommended for model

calibration and validation. Two different sizes of seed crystals,

300 and 350 mm, were used. One is for process performance

evaluation and model validation and the other is for model

calibration. All operating conditions and necessary process

parameters were kept the same as those for the experimental

runs. Equations (27) and (36), along with the boundary condi-

tions, (H¼ 0; C]C0 andH¼Ht; L¼ L0), were solved numerically

by using Matlab� to generate struvite concentration and

crystal size as a function of bed height. The boundary condi-

tion for C was considered as C0, which is the concentration of

the struvite species in the inlet (H ¼ 0) and for L, the boundary

condition was considered as the seed crystal size (L0) at the

bed height H¼ Ht. After mass deposition of species on struvite

crystals, the species equilibrium are shifted, causing a change

in ionic strength of the solution. Since the ionic strength has a

profound effect on struvite solubility, and hence the super-

saturation, the equilibrium species activities are updated

based on the existing ionic strength values.

4. Experimental

In order to calibrate and validate the model, the experimental

results acquired from a pilot-scale, struvite crystallizer

(operated in the Lulu Island Wastewater Treatment plant,

Richmond, BC, Canada), are used in this study. The pilot scale

struvite crystallization process is described as follows:

The basic design of the UBC MAP crystallizer follows the

concept of a fluidized bed reactor. As depicted in Fig. 1, the

reactor has four distinct zones depending on the diameter of

the column (Fattah, 2004). The bottom part of the fluidized bed

reactor is called the harvest zone; above that is the active zone,

while the top fluidized section is the ‘fine zone’. There is a

settling zone, also called ‘seed hopper,’ at the top. In the stru-

vite crystallization process, the anaerobic digester supernatant

is fed into the bottom of the reactor, along with the recycle

stream. Magnesium chloride and sodium hydroxide are added

to the reactor through the injection ports, just above the feed

and recycle flows. The digester supernatant contained high

levels of ammonium and phosphate. Therefore, no additional

PO4 and NH4 were added in the reactor. However, due to the

soft nature of Vancouver water, the required (stoichiometric)

amount of magnesium for struvite formation was not found.

Therefore, additional Mg ions in the form of magnesium chlo-

ride (MgCl2) were supplied. Seed crystals are added into the

crystallizer from the seedhopper and are allowed to grow in the

supersaturated solution. The solution velocity is maintained in

such a way that all particles in the crystal bed are fluidized in

the solution. Since the fresh influent is pumped into the bottom

of the reactor, the reactive solution contains the maximum

supersaturation at the bottom of the reactor and the crystals

grow faster than those near the top of the reactor. As a result,

the bigger crystals tend to settle to the bottom and the smaller

crystals rise to the top of the crystallizer. Once the larger

crystals at the bottom reach the desired size, they settle into the

harvest zone and are withdrawn from the bottom.

5. Results and discussion

5.1. Reactor performance evaluation

Using the crystallization kinetics expression presented by

Equation (32), the concentrations of PO4, NH4 and Mg in the

Fig. 4 e Mean crystal size: comparison between model

predictions and experimental results.

wat e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1e1 08

effluent were determined using the model developed in this

study. The model parameters and setting were the same as

the reactor operating conditions listed in Table S1a (see

Appendix). Using the influent and effluent concentrations of

different species, the percent removal of phosphate was

calculated and plotted in Fig. 3. The removal efficiencies of

other constituent species (NH4 and Mg) were also determined

and reported in Figures S1 and S2 (see Appendix).

It was observed that removal efficiencies of phosphate

were over-predicted by the chemical equilibrium model and

under-estimated by the reactor model. These predictions are

logical since the chemical equilibrium model assumes that

thermodynamic equilibrium has been attained with struvite

precipitation, and that the maximum possible conversion has

taken place. In other words, it assumes that the supersatu-

rated species concentrations have been used up completely by

the crystal growth and the remaining SSR in the effluent is 1.

This is the lowest SSR value, below which the precipitation

reaction cannot occur.

On the other hand, the reactor model generated results,

which were significantly lower than the corresponding

experimental values. This was attributed to the kinetic pa-

rameters used in thismodel, estimated by Bhuiyan et al. (2008)

in a lab-scale fluidized bed reactor. Both the reactor configu-

ration and operating parameters were different from the lab

scale set up to the pilot scale reactor. Moreover, the growth

experiments were performed for a range of SSR values, which

belong to the metastable zone. Primary nucleation is insig-

nificant at the metastable zone. However, there could have

been some secondary nucleation due to attrition and fluid

share actions. Both aggregation/attrition and secondary

nucleation effects were lumped into crystal growth in this

model, meaning there was no nucleation assumed (either

primary or secondary). Also, as the reactor hydrodynamics

were different for the two reactor set-ups, the difference in

agglomeration between the particles could be another

possible explanation for the poor model prediction.

This fact ismore evident by the difference found in average

particle size determination between the experimental and the

model predictions (Fig. 4). The predicted particle sizes were

significantly lower than the experimental values. This implies

1 2 3 4 5 6

Run

Fig. 3 e Phosphate removal efficiency: comparison

between model predictions and experimental results.

that, in the pilot scale operation, the governing processes are

different from those occurring in the lab scale reactor. Thus,

the crystal growth mechanism alone does not adequately

represent the actual growth of struvite crystals in the pilot-

scale reactor. Since no previous studies have been per-

formed to identify the exact mechanisms of crystal growth,

this study lumps the kinetics processes into crystal growth.

Hence, in order to improve the predictive capability of the

model, it was necessary to calibrate it for the pilot-scale

operation. This calibration was performed using the experi-

mental data gathered by running the reactor for different time

periods.

5.2. Model calibration

Since the individual kinetic parameters for various probable

processes taking place in the crystallizer are not available in

the literature, the model was calibrated for the kinetic pa-

rameters (K and n) of struvite crystal growth. The model with

calibrated parameters minimizes the Mean Squared Error

(MSE), based on the measurements of effluent Mg, NH4 and

PO4 concentrations. The MSE values used for the model cali-

bration is defined as,

MSE ¼ 1Z

XZj

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1P

XP

i¼1

xmodel;j;i � xdata;j;i

xdata;j;i

2

vuut (37)

where, xj are the values of model output and the measured

data on Z species (Mg, NH4 and PO4) and P is the number of

data points for each j species used in the calibration process.

The experimental conditions for the model calibration are

Table 1 e Estimated parameters for struvitecrystallization kinetics.

Run# K n MSE

7 38 1.45 7.21

8 40 1.46 5.35

9 42 1.5 4.07

10 46 1.48 3.18

11 48 1.5 5.28

12 13 14 15 16 17

Run

19

Fig. 5 e Phosphate removal efficiency: comparison

between model predictions and experimental results for

the validation phase.

wa t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1e1 0 9

presented in Table S2b (see Appendix). The estimated K and n

values, along with the MSE values, are presented in Table 1. It

was observed that, the values of 46 and 1.48 for K and n,

respectively, resulted in the lowest MSE value. Hence, those

values of K and n were taken as the estimated model

parameters.

5.3. Model validation

Themodelwas validated by comparing the predicted values of

process performance with data generated from the pilot scale

operation, for different time periods. The operating conditions

for the validation period are listed in Table S3d (see Appendix).

The model was run with the calibrated kinetics parameters

and the predicted results on process performance were then

compared with those of the experimental results. Fig. 5 rep-

resents the ‘model-predicted’ removal efficiencies of phos-

phate, along with those predicted by the equilibrium model

and the experimental results. Removal efficiencies of other

species (NH4 and Mg) are also reported in Figures S3 and S4

Fig. 6 e Mean crystal size: comparison between model

predictions and experimental results for the validation

phase.

(see Appendix). By comparing the values on these figures

with those estimated before calibration, it is clear that the

predictive capability of the model was improved significantly

(>10%). The predicted removal efficienciesmatched fairly well

with the experimental results, but as seen before, the equi-

librium model still overestimateed the removal efficiencies.

The ‘model-predicted’ mean crystal sizes matched quite well

with experimental observation (Fig. 6) and the predictive

capability increased considerably (around 10%). The struvite

crystallization process in the pilot scale operation involves not

only the crystal growth, but also other processes, such as

nucleation (most possibly the secondary kind), and agglom-

eration. Attrition/breakage may also be present in the reactor.

The crystal segment created by breakagemay also serve as the

seed crystals. Exploring the underlying mechanisms of stru-

vite crystal size enlargement is crucial in facilitating proper

development and unique design methodology for the UBC

MAP crystallizer.

6. Conclusions

The model developed in this work was used to evaluate the

reactor performance based on the removal efficiencies of

struvite constituent species (Mg, NH4 and PO4) and the average

product crystal sizes. The predicted valuesmatched fairly well

with the experimental results, for both the removal effi-

ciencies and the product crystal sizes. Although the product

crystals were found to have some gradation in terms of their

sizes, this mean size estimation provides some prior knowl-

edge concerning the average product crystal size for specific

operating conditions, at a specific treatment site. Although

there is still a significant knowledge gap in exploring the

fundamental mechanisms of struvite crystal formation and

growth in a fluidized bed reactor, this model can be used as a

highly valuable computer-aided design tool. However, due to

the complex nature of the wastewater, use of this model will

not entirely eliminate the pilot testing for a side-stream fa-

cility. The model can also be used as basis for process per-

formance evaluation.

Acknowledgments

The authors would like to thank Natural Science and Engi-

neering Research Council (NSERC) of Canada for providing the

financial support required for conducting this study.

Appendix A. Supplementary data

Supplementary data related to this article can be found at

http://dx.doi.org/10.1016/j.watres.2013.11.048.

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