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Modeling phosphorus removal and recovery from anaerobic digester supernatant through struvite crystallization in a fluidized bed reactor Md. Saifur Rahaman a,*, Donald S. Mavinic b, Alexandra Meikleham a, Naoko Ellis c a
Department of Building Civil and Environmental Engineering, Concordia University, 1455 de Maisonneuve Blvd, West, EV-6.139, Montreal, Quebec, Canada H3G 1M8 b Pollution Control & Waste Management Group, Department of Civil Engineering, University of British Columbia (UBC), 2002-6250 Applied Science Lane, Vancouver, BC, Canada V6T 1Z4 c Fluidization Research Centre, Department of Chemical & Biological Engineering, University of British Columbia (UBC), 227-2360 East Mall, Vancouver, BC, Canada V6T 1Z3
article info
abstract
Article history:
The cost associated with the disposal of phosphate-rich sludge, the stringent regulations to
Received 26 August 2013
limit phosphate discharge into aquatic environments, and resource shortages resulting
Received in revised form
from limited phosphorus rock reserves, have diverted attention to phosphorus recovery in
28 November 2013
the form of struvite (MAP: MgNH4PO4$6H2O) crystals, which can essentially be used as a
Accepted 30 November 2013
slow release fertilizer. Fluidized-bed crystallization is one of the most efficient unit pro-
Available online 13 December 2013
cesses used in struvite crystallization from wastewater. In this study, a comprehensive mathematical model, incorporating solution thermodynamics, struvite precipitation ki-
Keywords:
netics and reactor hydrodynamics, was developed to illustrate phosphorus depletion
Crystallization
through struvite crystal growth in a continuous, fluidized-bed crystallizer. A thermody-
Fluidized bed
namic equilibrium model for struvite precipitation was linked to the fluidized-bed reactor
Modeling
model. While the equilibrium model provided information on supersaturation generation,
Phosphorus recovery
the reactor model captured the dynamic behavior of the crystal growth processes, as well
Struvite
as the effect of the reactor hydrodynamics on the overall process performance. The model was then used for performance evaluation of the reactor, in terms of removal efficiencies of struvite constituent species (Mg, NH4 and PO4), and the average product crystal sizes. The model also determined the variation of species concentration of struvite within the crystal bed height. The species concentrations at two extreme ends (inlet and outlet) were used to evaluate the reactor performance. The model predictions provided a reasonably good fit with the experimental results for PO4eP, NH4eN and Mg removals. Predicated average crystal sizes also matched fairly well with the experimental observations. Therefore, this model can be used as a tool for performance evaluation and process optimization of struvite crystallization in a fluidized-bed reactor. Crown Copyright ª 2013 Published by Elsevier Ltd. All rights reserved.
* Corresponding author. Tel.: þ1 514 848 2424x5058; fax: þ1 514 848 7965. E-mail address: [email protected] (Md.S. Rahaman). 0043-1354/$ e see front matter Crown Copyright ª 2013 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.watres.2013.11.048
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DH0
Nomenclature Symbols A ADH Cd Ci Ci,H Ci,HþDH EC EC25 G I K Ksp k L N n Q R Ret S Ut y Zi T DH
1.
2
Cross-sectional area of the bed (column) [m ] DebyeeHu¨ckel constant Drag coefficient Molar concentration of the species (mol/L) Concentration of species i (mol/L) at bed height H Concentration of species i at the height increment, DH, above H Electrical conductivity (mS cm1) Electrical conductivity at 25 C Linear growth rate of the struvite crystals (m/s) Ionic strength (mol L1) Equilibrium reaction rate constants Thermodynamic solubility product of struvite Struvite crystal growth rate constant Struvite crystal diameter (m) Number of seed crystals added per unit time Expansion index Flow rate (L/s) Ideal gas constant (8.314 Jmol1K1) Reynolds number Relative supersaturation Terminal settling velocity of struvite crystals (m/s) Order of struvite growth kinetics Valence of ion species i Temperature in degree Kelvin Infinitesimal height of the reactor (m)
Introduction
Phosphorus is a non-renewable, non-interchangeable finite resource. The simultaneous diminution of natural phosphorus reserves available for the phosphate industry and increasing awareness of pollution problems, such as eutrophication due to phosphorus release in wastewater effluents, have led to research into new processes to remove and recover phosphorus from sewage effluents (Capdevielle et al., 2013). Therefore, phosphorus recovery from wastewater 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 from waste streams. Although much 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 nucleation, 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 understood, the design and operation of an industrial scale crystallizer still requires reliable knowledge of the most essential processes, which has historically been obtained from lab-
Enthalpy of the reaction (Jmol1)
Greek letters Liquid volume fraction (bed voidage) al a Volume factor (for sphere, 4p/3) b Surface factor (for sphere, 4p) Density of water (kg/m3) rl Density of struvite crystals (kg/m3) rs Activity coefficient of ion i gi ε Dielectric constant U Supersaturation ratio Others A B C D {} []
Harvest zone Active zone Fine zone 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
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 Recovery Group has developed a novel fluidized bed reactor, which has been found to be effective in recovering more than 80% of the soluble phosphate from waste 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 system hydrodynamics. In order to achieve an effective design, which optimizes reactor outputs, it was imperative to develop a model 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 fluidization 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 a multistage crystallizer. The new model provided better prediction of the mean size of
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
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 parameter model can be employed to investigate both the extreme conditions (completely mixed or segregated) and the intermediate region of mixing. All of the aforementioned studies dealt only with hydrodynamics and used a simple representation 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. Struvite 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 provides 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 MINEQLþ, 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 precipitation 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”,
3
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 crystallization performance of a fluidized bed crystallizer and claimed that the ANN based model better predicted the process performance than the equilibrium-based model, Crystallizer 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, crystal growth and agglomeration, are relatively slow processes and hence should be modeled dynamically. Furthermore, none of the above mentioned models for the struvite crystallization 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 utilizes the analytical concentration of struvite constituent species 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 equilibrium solubility product (Ksp) of struvite, which heavily depends 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 thermodynamic (instead of conditional) solubility product of struvite in its growth rate expression; this requires the activity based solubility of struvite and, hence, the ionic concentrations need to be determined from the total analytical concentration. Thus, in this paper, a chemical speciation model, based on the solution thermodynamic equilibrium, is developed and linked to the reactor model, in order to generate a more generic and robust reactor model.
2. Thermodynamic equilibrium model for struvite precipitation In recovering nutrients through struvite crystallization, solution 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: 3 Mg2þ þ NHþ 4 þ PO4 þ 6H2 O/MgNH4 PO4 $6H2 O
Like any other reactive crystallization processes, struvite precipitation also depends on solution supersaturation; while,
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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, once mixed, 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 3 species can be formed: H3PO,4(aq) H2PO-4, HPO2 4 , PO4 , 2þ þ þ þ þ MgH2PO4 , MgHPO4(aq), MgPO4, Mg , MgOH , NH4 , H , OH-, NH3(aq). The formation of the aforementioned species and their associated equilibrium constants are as follows: KMgOHþ
MgOHþ ! Mg2þ þ OH ; KMgOHþ ¼
gMg2þ gOH ½Mg2þ ½OH gMgOHþ ½MgOHþ (1)
Thus, the struvite precipitation reaction can be expressed as, Ksp
3 MgNH4 PO4 $6H2 OðsÞ ! Mg2þ þ NHþ 4 þ PO4 þ 6H2 O;
Ksp ¼
gMgþ gNHþ gPO3 ½Mgþ ½NHþ PO3 4 4 ½ 4
Loggi ¼
MgHPO4ðaqÞ ! ; Mg2þ þ HPO2 4 gMg2þ gHPO2 ½Mg2þ HPO2 4 4 h i KMgHPO4 ¼ MgHPO4ðaqÞ
(2)
þ 2 PO4
MgH2 POþ Mg2þ þ H2 PO 4 ! 4 ; 2þ gMg2þ gH2 PO4 ½Mg H2 PO 4 KMgH2 POþ4 ¼ gMgH2 POþ4 MgH2 POþ 4
(3)
gMg2þ gPO3 ½Mg2þ PO3 4 4 ¼ gMgPO4 MgPO 4
MgPO Mg2þ þ PO3 4 ; KMgPO4 4 ! 4
(4) gHþ gH2 PO4 ½Hþ H2 PO 4 H3 PO4ðaqÞ (5) KH2 PO 4 H2 PO Hþ 4 !
þ
HPO2 4
gHþ gHPO2 ½Hþ HPO2 4 4 ¼ gH2 PO4 H2 PO 4
; KH2 PO4
(6) KHPO2
; KHPO2 ¼ HPO2 Hþ þ PO3 4 ! 4 4
4
gHþ gPO3 ½Hþ PO3 4 4 gHPO2 HPO2 4
(7)
4
KNHþ
NHþ NH3 þ Hþ ; KNHþ4 ¼ 4 ! 4
gHþ ½Hþ ½NH3 gNHþ NHþ 4
(8)
4
KH2 O
H2 O! Hþ þ OH ; KH2 O ¼ gHþ Hþ ¼ 10pH
ðIÞ0:5 1 þ ðIÞ0:5
# 0:3I
þ
(12)
where, (13)
T ¼ Temperature in degrees Kelvin Now the ionic strength can be calculated from the species ionic concentrations as, I ¼ 0:5
KMgPO
KH3 PO4
ADH Z2i
ADH ¼ 0:486 6:07 104 T þ 6:43 106 T2
KMgH
H3 PO4ðaqÞ ! Hþ þ H2 PO 4 ; KH3 PO4 ¼
ðsÞ
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 species. The Davis equation is the most commonly used expression for determining species activity coefficients (for I < 0.5). The equation is as follows: "
KMgHPO4
(11)
4
½MgNH4 PO4 $6H2 O
X
Ci Z2i
(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 constants based on the reaction temperature as follows: lnðKÞ ¼ lnðK25 Þ
DH0 1 1 R T T0
(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 deg1 and DH0 values for different equilibrium reactions are taken from Bhuiyan (2007). Now, the species mole balance, at equilibrium condition, can be written as: 2 3 þ CTðPO4 Þ ¼ H3 PO4 þ H2 PO 4 þ HPO4 þ PO4 þ MgH2 PO4 þ MgHPO4 þ MgPO 4 þ MgNH4 PO4 $6H2 O s
(16)
CTðMgÞ ¼ Mg2þ þ MgOHþ þ MgH2 POþ 4 þ MgHPO4 þ MgPO4 þ MgNH4 PO4 $6H2 O s
(17)
CTðNH3 Þ ¼ ½NH3 þ NHþ 4 þ MgNH4 PO4 $6H2 O ðsÞ
(18)
gHþ gOH ½H ½OH ½H2 O
(9)
(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 thermodynamic solubility product, Ksp can be expressed as 3 Ksp ¼ Mg2þ NHþ PO4 ;where;fg represents species activity: 4
The system of equations is now manipulated to express the struvite species concentration in terms of the known values: Mg2þ ¼
CT;Mg2þ a þ b PO3 4
(19)
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3 PO4 ¼
2þ Mg ¼
CT;PO3 4
(20)
c þ b½Mg2þ
4
4
(21)
2ab
CT;NHþ4
1þ
kNHþ gNHþ 4
ðgHþ ½H
þ
þ Þ
4
gMg2þ gNHþ gPO3 ½Mgþ ½PO3 4 4
(22)
kH2 O gMg2þ
¼a
þ
kMgOH ðgHþ ½H Þ
(23)
0 2
gPO3 ðgHþ ½Hþ Þ 4
kMgH2 PO4 MgH2 PO 4
kH2 PO4 kHPO2
þ
4
gMg2þ gPO3 ðgHþ ½Hþ Þ 4
kMgHPO4 kHPO2 4
1 þ
gMg2þ gPO3 4
gMgPO4 kMgPO4
(24)
gMg2þ gNHþ gPO3 CT;NHþ4 C 4 K 4g C þ A¼b NHþ NHþ Ksp 1 þ g 4 ½Hþ 4 ð Hþ Þ
and 0
1 gPO3 ðgHþ ½Hþ Þ 4 4 4 @1 þ A¼c þ þ gHPO2 kHPO2 kH3 PO4 kH2 PO4 kHPO2 gH2 PO4 kH2 PO4 kHPO2 3
gPO3 ðgHþ ½Hþ Þ
2
gPO3 ðgHþ ½Hþ Þ
4
4
4
4
(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.
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.
4 Ksp
where,
B B @g
growth. This kinetic expression is developed from data gathered in the UBC MAP fluidized bed crystallizer. In general, the type of reactor should not affect the intrinsic kinetic parameters; however, the kinetics determined with this reactor type
2
0:5 ac þ bCT;PO3 bCT;Mg2þ ac þ bCT;PO3 bCT;Mg2þ 4ab cCT;Mg2þ
NHþ 4 ¼
1þ
5
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 hydrodynamics, is linked to the thermodynamic chemical equilibrium model. The equilibrium model takes care of supersaturation 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 developed by Bhuiyan et al. (2008) is used for struvite crystal
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 species 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 operating temperature remained constant throughout an individual 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 hydrodynamics 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 supersaturation 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 collisions between already existing crystals with either a solid surface or with other crystals themselves) and agglomeration 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. Considering 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.
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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 presented in Fig. 1. At steady-state operation, all three zones (A, B and C) are occupied with struvite crystals, which provide required sites for mass 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 conditions, the mole balance of struvite constituent species i, (PO4, Mg, and NH4) on a differential segment, DH can be expressed as:
1 ð1 al ÞDHA 2 1 bL Q Ci;H Ci;HþDH Þ ¼0 ðGr s 2 ðaL3 Þ MWs
(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 represents mole deposition of constituent species i, onto the suspended crystals in the horizontal slice, per unit time. Where, al: liquid volume fraction (bed voidage); A: crosssectional area of the reactor; DH: height increment; a:
Fig. 2 e A schematic of the model development.
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 Abrs ð1 al Þ ¼ G 2aQLMWs dH
(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.
Fig. 1 e Schematic of the fluidized bed UBC MAP crystallizer. Dimensions e A: dia [ 76 mm, height [ 749 mm; B: dia [ 102 mm, height [ 1549 mm; C: dia [ 152 mm, height [ 1270 mm; D: dia [ 381 mm, height [ 457 mm.
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The struvite bed expansion characteristics can be explained by RichardsoneZaki (ReZ) relation (1954) with a newly developed correlation for expansion index (Rahaman, 2009): al ¼
Q AUt
n1 (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 Ut rl L=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 expansion index is expressed (Rahaman, 2009) as: n ¼ 4:7718 Re0:089 t
for 26 < Ret < 302
(30)
where Cd values can be determined using the modified version of Clift et al. (1978) correlation as Cd ¼
24 1 þ 0:563Re0:83 t Ret
(31)
As can be found in Bhuiyan et al. (2008) the growth rate can be expressed as G ¼ kS
y
(32)
where, k and y represents the rate constant and the order of reaction, respectively and S represents the relative supersaturation, which can be represented as S ¼ U1=3 1
(33)
where, U is the supersaturation ratio and can be expressed as U¼
3 gMg2þ gNHþ gPO3 ½Mg2þ NHþ PO4 4 4
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: 1 ð1 al ÞDHA 2
bL ðGrs Þ rs Na L3H L3HþDH ¼ ðaL3 Þ 2
(35)
By rearranging Equation (35) and taking the limit as DH approaches zero one obtains: dL Abð1 al Þ ¼ G dH 6Na2 L3
parameters were kept the same as those for the experimental runs. Equations (27) and (36), along with the boundary conditions, (H ¼ 0; C]C0 and H ¼ Ht; L ¼ L0), were solved numerically by using Matlab to generate struvite concentration and crystal size as a function of bed height. The boundary condition 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 H ¼ 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 supersaturation, the equilibrium species activities are updated based on the existing ionic strength values.
(29)
For spherical particles, the terminal settling velocity (Ut) can be determined using Newton’s equation as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4g ðrs rl Þ L Ut ¼ 3Cd rl
7
(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
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 struvite 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 chloride (MgCl2) were supplied. Seed crystals are added into the crystallizer from the seed hopper 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
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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 supersaturated 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 parameters used in this model, estimated by Bhuiyan et al. (2008) in a lab-scale fluidized bed reactor. Both the reactor configuration 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 insignificant 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 is more 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
Fig. 4 e Mean crystal size: 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 pilotscale reactor. Since no previous studies have been performed 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 experimental 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 parameters (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 calibration is defined as, vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u P
Z u X xmodel;j;i xdata;j;i 2 1X t1 MSE ¼ Z j P i¼1 xdata;j;i
(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 struvite crystallization kinetics.
1
2
4
3
5
6
Run
Fig. 3 e Phosphate removal efficiency: comparison between model predictions and experimental results.
Run#
K
n
MSE
7 8 9 10 11
38 40 42 46 48
1.45 1.46 1.5 1.48 1.5
7.21 5.35 4.07 3.18 5.28
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
12
13
14
15
16 Run
17
19
Fig. 5 e Phosphate removal efficiency: comparison between model predictions and experimental results for the validation phase.
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
The model was 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 represents the ‘model-predicted’ removal efficiencies of phosphate, 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
9
(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 efficiencies matched fairly well with the experimental results, but as seen before, the equilibrium 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 agglomeration. Attrition/breakage may also be present in the reactor. The crystal segment created by breakage may also serve as the seed crystals. Exploring the underlying mechanisms of struvite 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 values matched fairly well with the experimental results, for both the removal efficiencies 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 knowledge 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 facility. The model can also be used as basis for process performance evaluation.
Acknowledgments The authors would like to thank Natural Science and Engineering 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.
references Fig. 6 e Mean crystal size: comparison between model predictions and experimental results for the validation phase.
Adnan, A., Mavinic, D.S., Koch, F.A., 2003. Pilot-scale study of phosphorus recovery through struvite crystallization e
10
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
examining the process feasibility. J. Environ. Eng. Sci. 2 (5), 315e324. http://dx.doi.org/10.1139/s03-040. Ali, M.I., Schneider, P.A., 2008. An approach of estimating struvite growth kinetic incorporating thermodynamic and solution chemistry, kinetic and process description. Chem. Eng. Sci. 63 (13), 3514e3525. Al-Rashed, M., Wo´jcik, J., Plewik, R., Synowiec, P., Kus, A., 2013. Multiphase CFD modeling: fluid dynamics aspects in scaleup of a fluidized-bed crystallizer. Chem. Eng. Process.: Process Intens. 63, 7e15. http://dx.doi.org/10.1016/ j.cep.2012.11.001. Bhuiyan, M.I.H., Mavinic, D., Beckie, R., 2008. Nucleation and growth kinetics of struvite in a fluidized bed reactor. J. Cryst. Growth 310 (6), 1187e1194. Bhuiyan, M.I.H., Mavinic, D.S., Beckie, R.D., 2007. A solubility and thermodynamic study of struvite. Environ. Technol. 28 (9), 1015e1026. http://dx.doi.org/10.1080/09593332808618857. Bhuiyan, M.I.H., 2007. Investigation into Struvite Solubility, Growth and Dissolution Kinetics in the Context of Phosphorus Recovery from Wastewater. University of British Columbia, Vancouver. Capdevielle, A., Sy´korova´, E., Biscans, B., Be´line, F., Daumer, M., 2013. Optimization of struvite precipitation in synthetic biologically treated swine wastewatereDetermination of the optimal process parameters. J. Hazard. Mater. 244e245, 357e369. http://dx.doi.org/10.1016/j.jhazmat.2012.11.054. Clift, R., Grace, J.R., Weber, M.E., 1978. Bubbles, Drops, and Particles. Academic Press, New York. Doyle, J.D., Parsons, S.A., 2002. Struvite formation, control and recovery. Water Res. 36 (16), 3925e3940. http://dx.doi.org/ 10.1016/S0043-1354(02)00126-4. Fattah, K.P., 2004. Pilot Scale Struvite Recovery Potential from Centrate at Lulu Island Wastewater Treatment Plant. University of British Columbia, Vancouver. Forrest, A.L., Fattah, K.P., Mavinic, D.S., Koch, F.A., 2007. Application of artificial neural networks to effluent phosphate prediction in struvite recovery. J. Environ. Eng. Sci. 6 (6), 713e725. http://dx.doi.org/10.1139/S07-023. Frances, C., Biscans, B., Laguerie, C., 1994. Modelling of a continuous fluidized-bed crystallizer effects of mixing and segregation on crystal size distribution during the crystallization of tetrahydrate sodium perborate. Chem. Eng. Sci. 49 (19), 3269e3276. http://dx.doi.org/10.1016/0009-2509(94) 00135-9. Hanhoun, M., Montastruc, L., Azzaro-Pantel, C., Biscans, B., Fre`che, M., Pibouleau, L., 2012. Simultaneous determination of nucleation
and crystal growth kinetics of struvite using a thermodynamic modelling approach. Chem. Eng. J. 215e216, 903e912. Loewenthal, R., Kornmuller, U., van Heerden, E., 1994. Modelling struvite precipitation in anaerobic treatment systems. Water Sci. Technol. 30 (12), 107e116. Miles, A., Ellis, T.G., 2000. Struvite precipitation potential for nutrient recovery from anaerobically treated wastes. Water Sci. Technol. 43, 259e266. Musvoto, E.V., Wentzel, M.C., Loewenthal, R.E., Ekama, G.A., 2000. Integrated chemical-physical processes modelling I. Development of a kinetic-based model for mixed weak acid/ base systems. Water Res. 34 (6), 1857e1867. http://dx.doi.org/ 10.1016/S0043-1354(99)00334-6. Ohlinger, K., Young, T., Schroeder, E., 1998. Predicting struvite formation in digestion. Water Res. 32 (12), 3607e3614. Parsons, S., Wall, F., Doyle, J., Oldring, K., Churchley, J., 2001. Assessing the potential for struvite recovery at sewage treatment works. Environ. Technol. 22 (11), 1279e1286. Pastor, L., Mangin, D., Barat, R., Seco, A., 2008. A pilot-scale study of struvite precipitation in a stirred tank reactor: conditions influencing the process. Bioresour.Technol. 99 (14), 6285e6291. Rahaman, M., Mavinic, D., Ellis, N., 2008. Phosphorus recovery from anaerobic digester supernatant by struvite crystallization: model-based evaluation of a fluidized bed reactor. Water Sci. Technol. 58 (6), 1321e1327. Rahaman, M., 2009. Phosphorus Recovery from Wastewater through Struvite Crystallization in a Fluidized Bed Reactor: Kinetics, Hydrodynamics and Performance. University of British Columbia, Vancouver. Rahaman, M., Mavinic, D., Bhuiyan, M., Koch, F., 2006. Exploring the determination of struvite solubility product from analytical results. Environ. Technol. 27 (9), 951e961. Richardson, J.F., Zaki, W.N., 1997. Sedimentation and fluidisation: Part I. Chem. Eng. Res. Des. 75 (Supplement), S82eS100. http:// dx.doi.org/10.1016/S0263-8762(97)80006-8. Shiau, L., Liu, Y., 1998. Simulation of a continuous fluidized bed crystallizer -perfect classified crystallizer model. J. Chinese Inst. Chem. Eng. 29 (6), 445e452. Shiau, L., Lu, T., 2001. Interactive effects of particle mixing and segregation on the performance characteristics of a fluidized bed crystallizer. Ind. Eng. Chem. Res. 40 (2), 707e713. http:// dx.doi.org/10.1021/ie0005250. Yoshino, M., Yao, M., Tsuno, H., Somiya, I., 2003. Removal and recovery of phosphate and ammonium as struvite from supernatant in anaerobic digestion. Water Sci. Technol. 48 (1), 171e178.
Available online at www.sciencedirect.com
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Modeling phosphorus removal and recovery from anaerobic digester supernatant through struvite crystallization in a fluidized bed reactor Md. Saifur Rahaman a,*, Donald S. Mavinic b, Alexandra Meikleham a, Naoko Ellis c a
Department of Building Civil and Environmental Engineering, Concordia University, 1455 de Maisonneuve Blvd, West, EV-6.139, Montreal, Quebec, Canada H3G 1M8 b Pollution Control & Waste Management Group, Department of Civil Engineering, University of British Columbia (UBC), 2002-6250 Applied Science Lane, Vancouver, BC, Canada V6T 1Z4 c Fluidization Research Centre, Department of Chemical & Biological Engineering, University of British Columbia (UBC), 227-2360 East Mall, Vancouver, BC, Canada V6T 1Z3
article info
abstract
Article history:
The cost associated with the disposal of phosphate-rich sludge, the stringent regulations to
Received 26 August 2013
limit phosphate discharge into aquatic environments, and resource shortages resulting
Received in revised form
from limited phosphorus rock reserves, have diverted attention to phosphorus recovery in
28 November 2013
the form of struvite (MAP: MgNH4PO4$6H2O) crystals, which can essentially be used as a
Accepted 30 November 2013
slow release fertilizer. Fluidized-bed crystallization is one of the most efficient unit pro-
Available online 13 December 2013
cesses used in struvite crystallization from wastewater. In this study, a comprehensive mathematical model, incorporating solution thermodynamics, struvite precipitation ki-
Keywords:
netics and reactor hydrodynamics, was developed to illustrate phosphorus depletion
Crystallization
through struvite crystal growth in a continuous, fluidized-bed crystallizer. A thermody-
Fluidized bed
namic equilibrium model for struvite precipitation was linked to the fluidized-bed reactor
Modeling
model. While the equilibrium model provided information on supersaturation generation,
Phosphorus recovery
the reactor model captured the dynamic behavior of the crystal growth processes, as well
Struvite
as the effect of the reactor hydrodynamics on the overall process performance. The model was then used for performance evaluation of the reactor, in terms of removal efficiencies of struvite constituent species (Mg, NH4 and PO4), and the average product crystal sizes. The model also determined the variation of species concentration of struvite within the crystal bed height. The species concentrations at two extreme ends (inlet and outlet) were used to evaluate the reactor performance. The model predictions provided a reasonably good fit with the experimental results for PO4eP, NH4eN and Mg removals. Predicated average crystal sizes also matched fairly well with the experimental observations. Therefore, this model can be used as a tool for performance evaluation and process optimization of struvite crystallization in a fluidized-bed reactor. Crown Copyright ª 2013 Published by Elsevier Ltd. All rights reserved.
* Corresponding author. Tel.: þ1 514 848 2424x5058; fax: þ1 514 848 7965. E-mail address: [email protected] (Md.S. Rahaman). 0043-1354/$ e see front matter Crown Copyright ª 2013 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.watres.2013.11.048
2
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
DH0
Nomenclature Symbols A ADH Cd Ci Ci,H Ci,HþDH EC EC25 G I K Ksp k L N n Q R Ret S Ut y Zi T DH
1.
2
Cross-sectional area of the bed (column) [m ] DebyeeHu¨ckel constant Drag coefficient Molar concentration of the species (mol/L) Concentration of species i (mol/L) at bed height H Concentration of species i at the height increment, DH, above H Electrical conductivity (mS cm1) Electrical conductivity at 25 C Linear growth rate of the struvite crystals (m/s) Ionic strength (mol L1) Equilibrium reaction rate constants Thermodynamic solubility product of struvite Struvite crystal growth rate constant Struvite crystal diameter (m) Number of seed crystals added per unit time Expansion index Flow rate (L/s) Ideal gas constant (8.314 Jmol1K1) Reynolds number Relative supersaturation Terminal settling velocity of struvite crystals (m/s) Order of struvite growth kinetics Valence of ion species i Temperature in degree Kelvin Infinitesimal height of the reactor (m)
Introduction
Phosphorus is a non-renewable, non-interchangeable finite resource. The simultaneous diminution of natural phosphorus reserves available for the phosphate industry and increasing awareness of pollution problems, such as eutrophication due to phosphorus release in wastewater effluents, have led to research into new processes to remove and recover phosphorus from sewage effluents (Capdevielle et al., 2013). Therefore, phosphorus recovery from wastewater 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 from waste streams. Although much 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 nucleation, 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 understood, the design and operation of an industrial scale crystallizer still requires reliable knowledge of the most essential processes, which has historically been obtained from lab-
Enthalpy of the reaction (Jmol1)
Greek letters Liquid volume fraction (bed voidage) al a Volume factor (for sphere, 4p/3) b Surface factor (for sphere, 4p) Density of water (kg/m3) rl Density of struvite crystals (kg/m3) rs Activity coefficient of ion i gi ε Dielectric constant U Supersaturation ratio Others A B C D {} []
Harvest zone Active zone Fine zone 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
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 Recovery Group has developed a novel fluidized bed reactor, which has been found to be effective in recovering more than 80% of the soluble phosphate from waste 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 system hydrodynamics. In order to achieve an effective design, which optimizes reactor outputs, it was imperative to develop a model 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 fluidization 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 a multistage crystallizer. The new model provided better prediction of the mean size of
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
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 parameter model can be employed to investigate both the extreme conditions (completely mixed or segregated) and the intermediate region of mixing. All of the aforementioned studies dealt only with hydrodynamics and used a simple representation 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. Struvite 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 provides 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 MINEQLþ, 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 precipitation 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”,
3
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 crystallization performance of a fluidized bed crystallizer and claimed that the ANN based model better predicted the process performance than the equilibrium-based model, Crystallizer 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, crystal growth and agglomeration, are relatively slow processes and hence should be modeled dynamically. Furthermore, none of the above mentioned models for the struvite crystallization 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 utilizes the analytical concentration of struvite constituent species 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 equilibrium solubility product (Ksp) of struvite, which heavily depends 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 thermodynamic (instead of conditional) solubility product of struvite in its growth rate expression; this requires the activity based solubility of struvite and, hence, the ionic concentrations need to be determined from the total analytical concentration. Thus, in this paper, a chemical speciation model, based on the solution thermodynamic equilibrium, is developed and linked to the reactor model, in order to generate a more generic and robust reactor model.
2. Thermodynamic equilibrium model for struvite precipitation In recovering nutrients through struvite crystallization, solution 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: 3 Mg2þ þ NHþ 4 þ PO4 þ 6H2 O/MgNH4 PO4 $6H2 O
Like any other reactive crystallization processes, struvite precipitation also depends on solution supersaturation; while,
4
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
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, once mixed, 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 3 species can be formed: H3PO,4(aq) H2PO-4, HPO2 4 , PO4 , 2þ þ þ þ þ MgH2PO4 , MgHPO4(aq), MgPO4, Mg , MgOH , NH4 , H , OH-, NH3(aq). The formation of the aforementioned species and their associated equilibrium constants are as follows: KMgOHþ
MgOHþ ! Mg2þ þ OH ; KMgOHþ ¼
gMg2þ gOH ½Mg2þ ½OH gMgOHþ ½MgOHþ (1)
Thus, the struvite precipitation reaction can be expressed as, Ksp
3 MgNH4 PO4 $6H2 OðsÞ ! Mg2þ þ NHþ 4 þ PO4 þ 6H2 O;
Ksp ¼
gMgþ gNHþ gPO3 ½Mgþ ½NHþ PO3 4 4 ½ 4
Loggi ¼
MgHPO4ðaqÞ ! ; Mg2þ þ HPO2 4 gMg2þ gHPO2 ½Mg2þ HPO2 4 4 h i KMgHPO4 ¼ MgHPO4ðaqÞ
(2)
þ 2 PO4
MgH2 POþ Mg2þ þ H2 PO 4 ! 4 ; 2þ gMg2þ gH2 PO4 ½Mg H2 PO 4 KMgH2 POþ4 ¼ gMgH2 POþ4 MgH2 POþ 4
(3)
gMg2þ gPO3 ½Mg2þ PO3 4 4 ¼ gMgPO4 MgPO 4
MgPO Mg2þ þ PO3 4 ; KMgPO4 4 ! 4
(4) gHþ gH2 PO4 ½Hþ H2 PO 4 H3 PO4ðaqÞ (5) KH2 PO 4 H2 PO Hþ 4 !
þ
HPO2 4
gHþ gHPO2 ½Hþ HPO2 4 4 ¼ gH2 PO4 H2 PO 4
; KH2 PO4
(6) KHPO2
; KHPO2 ¼ HPO2 Hþ þ PO3 4 ! 4 4
4
gHþ gPO3 ½Hþ PO3 4 4 gHPO2 HPO2 4
(7)
4
KNHþ
NHþ NH3 þ Hþ ; KNHþ4 ¼ 4 ! 4
gHþ ½Hþ ½NH3 gNHþ NHþ 4
(8)
4
KH2 O
H2 O! Hþ þ OH ; KH2 O ¼ gHþ Hþ ¼ 10pH
ðIÞ0:5 1 þ ðIÞ0:5
# 0:3I
þ
(12)
where, (13)
T ¼ Temperature in degrees Kelvin Now the ionic strength can be calculated from the species ionic concentrations as, I ¼ 0:5
KMgPO
KH3 PO4
ADH Z2i
ADH ¼ 0:486 6:07 104 T þ 6:43 106 T2
KMgH
H3 PO4ðaqÞ ! Hþ þ H2 PO 4 ; KH3 PO4 ¼
ðsÞ
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 species. The Davis equation is the most commonly used expression for determining species activity coefficients (for I < 0.5). The equation is as follows: "
KMgHPO4
(11)
4
½MgNH4 PO4 $6H2 O
X
Ci Z2i
(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 constants based on the reaction temperature as follows: lnðKÞ ¼ lnðK25 Þ
DH0 1 1 R T T0
(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 deg1 and DH0 values for different equilibrium reactions are taken from Bhuiyan (2007). Now, the species mole balance, at equilibrium condition, can be written as: 2 3 þ CTðPO4 Þ ¼ H3 PO4 þ H2 PO 4 þ HPO4 þ PO4 þ MgH2 PO4 þ MgHPO4 þ MgPO 4 þ MgNH4 PO4 $6H2 O s
(16)
CTðMgÞ ¼ Mg2þ þ MgOHþ þ MgH2 POþ 4 þ MgHPO4 þ MgPO4 þ MgNH4 PO4 $6H2 O s
(17)
CTðNH3 Þ ¼ ½NH3 þ NHþ 4 þ MgNH4 PO4 $6H2 O ðsÞ
(18)
gHþ gOH ½H ½OH ½H2 O
(9)
(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 thermodynamic solubility product, Ksp can be expressed as 3 Ksp ¼ Mg2þ NHþ PO4 ;where;fg represents species activity: 4
The system of equations is now manipulated to express the struvite species concentration in terms of the known values: Mg2þ ¼
CT;Mg2þ a þ b PO3 4
(19)
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
3 PO4 ¼
2þ Mg ¼
CT;PO3 4
(20)
c þ b½Mg2þ
4
4
(21)
2ab
CT;NHþ4
1þ
kNHþ gNHþ 4
ðgHþ ½H
þ
þ Þ
4
gMg2þ gNHþ gPO3 ½Mgþ ½PO3 4 4
(22)
kH2 O gMg2þ
¼a
þ
kMgOH ðgHþ ½H Þ
(23)
0 2
gPO3 ðgHþ ½Hþ Þ 4
kMgH2 PO4 MgH2 PO 4
kH2 PO4 kHPO2
þ
4
gMg2þ gPO3 ðgHþ ½Hþ Þ 4
kMgHPO4 kHPO2 4
1 þ
gMg2þ gPO3 4
gMgPO4 kMgPO4
(24)
gMg2þ gNHþ gPO3 CT;NHþ4 C 4 K 4g C þ A¼b NHþ NHþ Ksp 1 þ g 4 ½Hþ 4 ð Hþ Þ
and 0
1 gPO3 ðgHþ ½Hþ Þ 4 4 4 @1 þ A¼c þ þ gHPO2 kHPO2 kH3 PO4 kH2 PO4 kHPO2 gH2 PO4 kH2 PO4 kHPO2 3
gPO3 ðgHþ ½Hþ Þ
2
gPO3 ðgHþ ½Hþ Þ
4
4
4
4
(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.
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.
4 Ksp
where,
B B @g
growth. This kinetic expression is developed from data gathered in the UBC MAP fluidized bed crystallizer. In general, the type of reactor should not affect the intrinsic kinetic parameters; however, the kinetics determined with this reactor type
2
0:5 ac þ bCT;PO3 bCT;Mg2þ ac þ bCT;PO3 bCT;Mg2þ 4ab cCT;Mg2þ
NHþ 4 ¼
1þ
5
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 hydrodynamics, is linked to the thermodynamic chemical equilibrium model. The equilibrium model takes care of supersaturation 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 developed by Bhuiyan et al. (2008) is used for struvite crystal
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 species 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 operating temperature remained constant throughout an individual 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 hydrodynamics 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 supersaturation 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 collisions between already existing crystals with either a solid surface or with other crystals themselves) and agglomeration 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. Considering 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.
6
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
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 presented in Fig. 1. At steady-state operation, all three zones (A, B and C) are occupied with struvite crystals, which provide required sites for mass 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 conditions, the mole balance of struvite constituent species i, (PO4, Mg, and NH4) on a differential segment, DH can be expressed as:
1 ð1 al ÞDHA 2 1 bL Q Ci;H Ci;HþDH Þ ¼0 ðGr s 2 ðaL3 Þ MWs
(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 represents mole deposition of constituent species i, onto the suspended crystals in the horizontal slice, per unit time. Where, al: liquid volume fraction (bed voidage); A: crosssectional area of the reactor; DH: height increment; a:
Fig. 2 e A schematic of the model development.
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 Abrs ð1 al Þ ¼ G 2aQLMWs dH
(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.
Fig. 1 e Schematic of the fluidized bed UBC MAP crystallizer. Dimensions e A: dia [ 76 mm, height [ 749 mm; B: dia [ 102 mm, height [ 1549 mm; C: dia [ 152 mm, height [ 1270 mm; D: dia [ 381 mm, height [ 457 mm.
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
The struvite bed expansion characteristics can be explained by RichardsoneZaki (ReZ) relation (1954) with a newly developed correlation for expansion index (Rahaman, 2009): al ¼
Q AUt
n1 (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 Ut rl L=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 expansion index is expressed (Rahaman, 2009) as: n ¼ 4:7718 Re0:089 t
for 26 < Ret < 302
(30)
where Cd values can be determined using the modified version of Clift et al. (1978) correlation as Cd ¼
24 1 þ 0:563Re0:83 t Ret
(31)
As can be found in Bhuiyan et al. (2008) the growth rate can be expressed as G ¼ kS
y
(32)
where, k and y represents the rate constant and the order of reaction, respectively and S represents the relative supersaturation, which can be represented as S ¼ U1=3 1
(33)
where, U is the supersaturation ratio and can be expressed as U¼
3 gMg2þ gNHþ gPO3 ½Mg2þ NHþ PO4 4 4
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: 1 ð1 al ÞDHA 2
bL ðGrs Þ rs Na L3H L3HþDH ¼ ðaL3 Þ 2
(35)
By rearranging Equation (35) and taking the limit as DH approaches zero one obtains: dL Abð1 al Þ ¼ G dH 6Na2 L3
parameters were kept the same as those for the experimental runs. Equations (27) and (36), along with the boundary conditions, (H ¼ 0; C]C0 and H ¼ Ht; L ¼ L0), were solved numerically by using Matlab to generate struvite concentration and crystal size as a function of bed height. The boundary condition 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 H ¼ 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 supersaturation, the equilibrium species activities are updated based on the existing ionic strength values.
(29)
For spherical particles, the terminal settling velocity (Ut) can be determined using Newton’s equation as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4g ðrs rl Þ L Ut ¼ 3Cd rl
7
(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
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 struvite 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 chloride (MgCl2) were supplied. Seed crystals are added into the crystallizer from the seed hopper 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
8
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
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 supersaturated 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 parameters used in this model, estimated by Bhuiyan et al. (2008) in a lab-scale fluidized bed reactor. Both the reactor configuration 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 insignificant 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 is more 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
Fig. 4 e Mean crystal size: 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 pilotscale reactor. Since no previous studies have been performed 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 experimental 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 parameters (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 calibration is defined as, vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u P
Z u X xmodel;j;i xdata;j;i 2 1X t1 MSE ¼ Z j P i¼1 xdata;j;i
(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 struvite crystallization kinetics.
1
2
4
3
5
6
Run
Fig. 3 e Phosphate removal efficiency: comparison between model predictions and experimental results.
Run#
K
n
MSE
7 8 9 10 11
38 40 42 46 48
1.45 1.46 1.5 1.48 1.5
7.21 5.35 4.07 3.18 5.28
w a t e r r e s e a r c h 5 1 ( 2 0 1 4 ) 1 e1 0
12
13
14
15
16 Run
17
19
Fig. 5 e Phosphate removal efficiency: comparison between model predictions and experimental results for the validation phase.
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
The model was 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 represents the ‘model-predicted’ removal efficiencies of phosphate, 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
9
(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 efficiencies matched fairly well with the experimental results, but as seen before, the equilibrium 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 agglomeration. Attrition/breakage may also be present in the reactor. The crystal segment created by breakage may also serve as the seed crystals. Exploring the underlying mechanisms of struvite 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 values matched fairly well with the experimental results, for both the removal efficiencies 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 knowledge 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 facility. The model can also be used as basis for process performance evaluation.
Acknowledgments The authors would like to thank Natural Science and Engineering 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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