UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Phosphorus recovery from wastewater through struvite crystallization in a fluidized bed reactor : kinetics,… Rahaman, Md. Saifur 2009

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2010_spring_rahaman_md_saifur.PDF [ 4.38MB ]
Metadata
JSON: 24-1.0072391.json
JSON-LD: 24-1.0072391-ld.json
RDF/XML (Pretty): 24-1.0072391-rdf.xml
RDF/JSON: 24-1.0072391-rdf.json
Turtle: 24-1.0072391-turtle.txt
N-Triples: 24-1.0072391-rdf-ntriples.txt
Original Record: 24-1.0072391-source.json
Full Text
24-1.0072391-fulltext.txt
Citation
24-1.0072391.ris

Full Text

PHOSPHORUS RECOVERY FROM WASTEWATER THROUGH STRUVITE CRYSTALLIZATION IN A FLUIDIZED BED REACTOR: KINETICS, HYDRODYNAMICS AND PERFORMANCE by  MD. SAIFUR RAHAMAN B.Sc. (Eng.), Bangladesh University of Engineering and Technology (BUET), 2000 M.A.Sc., Dathousie University, 2003  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in  THE FACULTY OF GRADUATE STUDIES  (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  December 2009  © Md. Saifur Rahaman, 2009  Abstract Struvite crystallization from wastewater, using a novel fluidized bed reactor developed at UBC, offers a significant reduction (80—90%) of soluble phosphate from waste streams and generates a product that can be reused as a slow release fertilizer. To implement this green technology at a plant scale, a reactor model that incorporates process kinetics, thermodynamics and the system hydrodynamics, is required. Therefore, the main objectives of this dissertation were to study the struvite precipitation kinetics, thermodynamics, and fluidization characteristics of the struvite crystals bed, and finally, develop a model based on this information. Both dissolution and precipitation experiments were carried out in a jar test apparatus to study the solubility and precipitation kinetics of struvite. The struvite solubility product, pK values were found to vary from 13.43—14.10, for different water and wastewater samples tested at 20 °C. Also, a correlation was developed to estimate struvite solubility at different temperatures. In struvite precipitation experiments, the operating conditions of supersaturation, pH, Mg:P ratio, mixing and seeding conditions were varied to identify the effect of those process parameters on the precipitation kinetics. The kinetic rate constant increases with increasing both the supersaturation and Mg:P ratios. Both the mixing energy and seeding rate were found to have minimal effect on ortho-P removal. Detailed experimental and numerical investigations of the fluidization characteristics of struvite crystals were performed. The bed expansion behaviour of mono-sized struvite crystals can be represented reasonably well by the Richardson-Zaki relation and the expansion characteristics of poly-dispersed struvite crystals bed can be predicted by the ‘serial model’. The CFD simulated bed expansion behaviour of the crystals bed was found to  11  be consistent with the experimental results. Also, CFD simulations were capable of capturing the mixing/segregation behavior of a fluidized-bed of multi-particle stnivite crystals. Finally, a mathematical model was developed by assuming a complete segregation of the bed crystals and liquid movement as plug flow in the reactor. The model predictions provided a reasonably good fit with the experimental results for both 4 P0 P and NH -N 4 removal. The model predicted mean size of product crystals matched reasonably well with pilot scale experimental results.  111  Table of Contents  Abstract Table of Contents List of Tables List of Figures Preface Acknowledgements Co-Authorship Statement Chapter 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Chapter 2  2.1 2.2 2.2.1 2.2.2 2.3 2.4 2.5  Chapter 3  3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3  Introduction  ii iv vii ix xiii xv xvi 1  Preface Struvite formation kinetics Hydrodynamics Development of a reactor model Computational fluid dynamics (CFD) simulation Research objectives Thesis outline References  1 3 4 6 8 10 10 14  Exploring the determination of struvite solubility product from analytical results  16  Introduction Materials and methods Treatment of data Calculation of the molar concentrations of [Mg ] and [NH 3 4 j, [P0 2 ] 4 Results and discussion Conclusions References  16 20 21 23 24 30 40  Effects of various process parameters on struvite precipitation kinetics and subsequent determination of rate constants 43 Introduction Materials and methods Synthetic liquor preparation Methods Analytical techniques Treatment of data Results and discussion  43 45 45 46 47 47 48 iv  3.3.1 3.3.2 3.3.3 3.3.4 3.4 3.5 Chapter 4  4.1 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6 4.4 4.5  Chapter 5  5.1 5.2 5.2.1 5.2.2 5.3 5.4 5.5 5.5.1 5.5.2 5.5.3 5.5.4 5.5.4.1 5.5.4.2 5.5.4.3 5.6 5.7  Influence of supersaturation ratio and pH on struvite precipitation Effect of Mg:P ratio Effect of degree of mixing Effect of seeding Conclusions References  48 49 51 52 53 62  Fluidization characteristics of struvite crystals produced from wastewater treatment plants  63  Introduction Materials and methods Density determination Size Determination of terminal settling velocity Fluidization column Results and discussion Size and shape of struvite crystals Terminal settling velocity (Ui) Minimum fluidization velocity (Umj) Bed expansion behaviour of monosized struvite crystals Minimum fluidization velocity for multiparticle systems Bed expansion behaviour of multiparticle systems Conclusions References  63 65 65 67 67 68 69 69 72 75 80 83 85 88 109  Numerical simulation of liquid-solid fluidized bed of mono and polydisperse struvite crystals  112  Introduction Model development Governing equations Constitutive parameters Boundary conditions Reactor geometry and model configuration Results and discussion Sensitivity analysis Drag laws Simulation of liquid-solid fluidized bed of mono size struvite crystals Mixing and segregation of struvite crystals in multi-particle fluidized bed MS particle group ML particle group MC particle group Conclusions References  112 115 115 117 123 124 126 126 127 128 131 131 135 137 139 178 v  Chapter 6  6.1 6.2 6.3 6.4 6.5 6.6 6.7  Chapter 7  7.1 7.2 7.3 7.4 7.5 7.5.1 7.5.2 7.5.3 7.5.4 7.6 7.7  Chapter 8 8.1 8.2 8.3 8.4 8.5  Phosphorus recovery from anaerobic digester supernatant by struvite crystallization: Model-based evaluation of a fluidized bed reactor...181 Introduction Process description Mathematical model development Experimental Results and discussion Conclusions References  181 184 185 188 189 192 201  Phosphorus recovery from anaerobic digester supernatant by struvite crystallization: Modeling of a fluidized bed reactor incorporating thermodynamics, kinetics and reactor hydrodynamics 202 Introduction Model development Reactor modeling Experimental Results and discussion Sensitivity analysis Reactor performance evaluation Model calibration Model validation Conclusions References  202 207 213 218 220 220 221 222 223 223 244  General conclusions and direction for future research  246  Introduction Overall conclusions Practical implications for wastewater industries Future work References  246 249 252 254 256  vi  List of Tables Table 2.1  Reported experimental values for the K 3 of struvite at 25 °C  32  Table 2.2  Reported equilibrium constants  33  Table 2.3  Summary of the average solubility product in various solvents  34  Table 3.1  Operational conditions for various experimental runs  55  Table 4.1  Fluidized bed experimental conditions  93  Table 4.2  Charateristics of struvite crystals  94  Table 4.3  Terminal settling velocities for different size classes  95  Table 4.4  Predicted and experimental minimum fluidization velocity  96  Table 4.5  Parameters of Richardson-Zaki equation  97  Table 4.6  Minimum fluidization velocities for multi-particle system  98  Table 5.1  Properties of different size classes of struvite crystals and experimental conditions  144  Table 5.2  Summary of simulation settings (model parameters)  145  Table 5.3  Comparison of bed pressure drop and voidage estimated using different grid size 146  Table 5.4  Comparison of bed pressure drop and voidage estimated using different Drag models 147  Table 5.5  Size ratios and hypothetical binary combinations of different size classes  Table 6.1  Operating conditions and basic physicochemical properties of struvite crystals and the reaction solution 195  Table 7.1  Equilibrium constants and the enthalpies of the reactions involved in struvite precipitation (Rahaman, et al., 2006; Bhuiyan, 2007) 227  Table 7.2  Dimension of the pilot scale fluidized bed UBC MAP crystallizer in relation to Figure 7.1 228  ....  148  vii  Table 7.3  Reactor operating conditions at pilot scale for process evaluation phase (Source: Fattah, 2004) 229  Table 7.4  Reactor operating conditions (pilot-scale) for the reactor calibration phase (Source: Fattah, 2004)  230  Table 7.5  Estimated parameters for struvite crystallization kinetics  231  Table 7.6  Reactor operating conditions (pilot-scale) for the reactor validation phase (Source: Fattah, 2004)  232  viii  List of Figures Figure 2.1  pH versus pK values for different water and wastewaters at 20 °C  35  Figure 2.2  Variation of pK with ionic strength  36  Figure 2.3  pH versus pK of Annacis WWTP anaerobic digester supernatant at different temperatures (10 °C, 15 °C and 20 °C) 37  Figure 2.4  Variation of pK with temperature  38  Figure 2.5  Conductivity versus ionic strength at 20 °C  39  Figure 3.1  Variation of ortho-P concentrations with the reaction time  56  Figure 3.2  Linear form of the first order kinetic of struvite precipitation with different SSR values 57  Figure 3.3  Variation of ortho-P concentration with the reaction time for different Mg:P ratios 58  Figure 3.4  Linear form of the first order kinetic of ortho-P removal for different Mg:P ratios  —  59  Figure 3.5  Variation of ortho-P concentration with the reaction time for different stirrer speeds 60  Figure 3.6  Variation of ortho-P concentration with the reaction time for seeded and unseeded conditions  61  Figure 4.1  Experimental set-up; a) schematic and b) photograph  99  Figure 4.2  Pressure drop (experimental and predicted by Ergun equation) vs. superficial liquid velocity for the packed bed condition of the different size classes of struvite crystals 100  Figure 4.3  Correlations between terminal velocities determined experimentally and estimated using Clift et al. (1978) correlations  101  Figure 4.4  Pressure drop vs. upflow liquid velocity for determining minimum fluidization velocity 102  Figure 4.5  Voidage (a!) vs. upflow liquid velocity (U) relationship found in experimental bed expansion tests 103 ix  Figure 4.6  Comparison between ‘n’ values determined experimentally and estimated using the correlation 104  Figure 4.7  Pressure drop vs. upflow liquid velocity for determining minimum fluidization velocities (Ubf, Ua and Utf) for a multi-particle system (ML) 105  Figure 4.8  Comparisons of bed expansion characteristics for the multi-particle systems (Run#MS) 106  Figure 4.9  Comparisons of bed expansion characteristics for the multi-particle systems (Run#ML) 107  Figure 4.10 Comparisons of bed expansion characteristics for the multi-particle systems (Run#MC) 108 Figure 5.1  Schematic of the a) the experimental set-up; and b) the computation domain 149  Figure 5.2  (a) Snapshot of solid volume fractions of struvite particles (group D) at different time intervals, fluidized at a superficial velocity of 24.67 mm/s. (b) comparison of overall liquid volume fraction with experimental result 151  Figure 5.3  Bed expansion characteristics: comparison between experimental results, CFD and Richardson-Zaki predictions for (a) struvite size class A, (b) struvite size class B, (c) struvite size class C, (d) struvite size class D, and (e) struvite size class F 153  Figure 5.4  Comparison of the time-averaged liquid volume fraction, on radial positions, for the simulated and experimental results for struvite particles (group B), fluidized at a superficial velocity of 24.67 mm/s 158  Figure 5.5  Comparison of the time mean area weighted liquid volume fraction at a bed height of 0.184 m, (both simulated and experimental results) with the overall CFD predicted voidage, for struvite particles (group D) 159  Figure 5.6  Time average pressure profiles along the bed height at different upflow velocities for the mixture group of MS  160  Figure 5.7  Time average liquid volume fractions along the bed height at different upflow velocities for the mixture group MS 161  Figure 5.8  Simulated time average mean crystal diameter along the bed height at two different upflow velocities for the mixture group of MS  162  Simulated time average bulk density along the bed height at different two different upflow velocities for the mixture group of MS  163  Figure 5.9  x  Figure 5.10 Comparison between experimentally determined bed expansion behaviour of MS group and CFD and serial model predictions 164 Figure 5.11 Time average pressure profiles along the bed height at different upflow velocities for the mixture group of ML  165  Figure 5.12 Time average liquid volume fractions along the bed height at different upflow velocities for the mixture group ML 166 Figure 5.13 Simulated time average mean crystals diameter along the bed height at different two different upflow velocities for the mixture group of ML 167 Figure 5.14 Simulated time average bulk density along the bed height at different two different upflow velocities for the mixture group of ML  168  Figure 5.15 Comparison between experimentally determined bed expansion behaviour of ML group and CFD and serial model predictions 169 Figure 5.16 Snapshot of solid volume fractions of struvite particles for MC groups at different time intervals, fluidized at a superficial velocity of 26.77 mm/s  170  Figure 5.17 Simulated time average solids and liquid volume fractions for MC group particle mixture fluidized at upflow velocity of 26.77 mm/s  174  Figure 5.18 Time average liquid volume fractions along the bed height at different upflow velocities for the mixture group MC 175 Figure 5.19 Time average pressure profiles along the bed height at different upflow velocities for the mixture group of MC  176  Figure 5.20 Comparison of between experimentally determined bed expansion behaviour of MC group and CFD and serial model predictions 177 Figure 6.1  Schematic of the fluidized bed UBC MAP crystallizer and the model development  196  Figure 6.2  P0 4 P and NH -N concentrations along the bed height 4  197  Figure 6.3  Removal of P0 -P and NH 4 -N 4  198  Figure 6.4  Variation of crystal sizes along the bed height  199  Figure 6.5  Variation of bed voidage along the bed height  200  Figure 7.1  Schematic diagram of the fluidized bed UBC MAP crystallizer  233  xi  Figure 7.2  A schematic of the model development  Figure 7.3  Variation of supersaturation ratio (SSR) with pH, estimated using different correlations. ([Mg]T =60 mg/L; [NH4]T=450 mg/L; [PO4]T= O mg/L; 5 Conductivity =6.5mS) 235  Figure 7.4  Phosphate removal efficiency: comparison between model predictions and experimental results 236  Figure 7.5  Ammonium removal efficiency: comparison between model predictions and experimental results 237  Figure 7.6  Magnesium removal efficiency: comparison between model predictions and experimental results 238  Figure 7.7  Mean crystal size: comparison between model predictions and experimental results 239  Figure 7.8  Phosphate removal efficiency: comparison between model predictions and experimental results for the validation phase 240  Figure 7.9  Ammonium removal efficiency: comparison between model predictions and experimental results for the validation phase 241  234  Figure 7.10 Magnesium removal efficiency: comparison between model predictions and experimental results for the validation phase 242 Figure 7.11 Mean crystal size: comparison between model predictions and experimental results for the validation phase 243  xii  Preface The present Ph.D. thesis has been prepared in a manuscript-based format. A manuscript thesis, as described by the Faculty of Graduate Studies at The University of British Columbia, is a collection of published, in-press, accepted, submitted or draft manuscripts. The body of this thesis has been separated into eight main chapters. Chapter 1 is an introductory chapter presenting the background of the engineering problem and the main objectives of the thesis. The results of the research program are presented in Chapters 2 through 7. Chapter 8 relates the manuscript chapters to each others, outlines the engineering significance of the research work, and provides directions for future research. The following is a list of the manuscripts submitted and in preparation that pertain to this thesis. 1. Rahaman, M.S., Mavinic, D.S, Bhuiyan, M.I.H., Koch, F.A. (2006) Exploring the determination of struvite solubiity product from analytical results. Environ. Technol. 27, 95 1-961. 2. Rahaman, M.S., Ellis, N., and Mavinic, D.S. (2008) Effects of various process parameters on struvite precipitation kinetics and subsequent determination of rate constants. Water Sci. Technol. 57(5), 647-654. 3. Rahaman, M.S., Mavinic, D.S. and Ellis, N. (2009) Fluidization characteristics of struvite crystals produced from wastewater treatment plants. In preparation. 4. Rahaman, M.S., Mavinic, D.S., Ellis, N., and Taghipour, F. (2009) Numerical simulation of liquid-solid fluidized bed of mono and poly-dispersed struvite crystals. In preparation.  xiii  5. Rahaman, M.S., Mavinic, D.S., and 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), 132 1-1327. 6. Rahaman, M.S., Mavinic, D.S., and Ellis, N. (2009) Phosphorus recovery from anaerobic digester supematant through struvite crystallization: Modeling of a fluidized  bed  reactor  incorporating  thermodynamics,  kinetics  and  reactor  hydrodynamics. In preparation.  xiv  Acknowledgements First of all, I wish to express my sincere gratitude and profound indebtedness to my supervisors Dr. Donald S. Mavinic and Dr. Naoko Ellis for their continued encouragement, support and expert advice throughout the course of this thesis work, without which this research would not have been possible. I would like to express my heartiest thanks and gratefulness to my committee members, Dr. Fariborz Taghipour and Dr. Victor Lo for their review and comments on the thesis. Dr. Fariborz Taghipour also provided much appreciated support by allowing me to use one of his Fluent Licenses. Appreciation goes to Ms. Susan Harper and Ms. Paula Parkinson of the Environmental Engineering laboratory at UBC for providing enthusiastic assistance throughout the research period. I would also like to thank Doug Hudniuk and John Wong of the Machine shop, Civil Engineering Department at UBC for building the reactor for me. I am also grateful to Fred Koch, Parvez Fattah and Dr. Iqbal H. Bhuiyan for their support and suggestions during the course of this research. Special thanks is extended to my beloved wife, Sormin Sultana who provided endless support and encouragement over the past six-years. Finally, I would like to thank NSERC for providing the financial assistance required for conducting this research.  xv  Co-Authorship Statement Collaborations with several parties have provided valuable support for this thesis research. The published papers and manuscripts in preparation of this thesis have been strengthened by inputs given by my supervisor Dr. Donald S. Mavinic, coauthors, scientific colleagues and anonymous reviewers. Below is a summary of the contributions of coauthors to each chapter. Chapter 2 Struvite solubility lab tests were performed by previous three graduate students, Ahren Britton, All Adnan and Hui Huang. However, I was the key researcher and took the role in analysing data and preparing the draft manuscriprt. However, many issues and controversy regarding the reported values were fmally resolved with the help of other coauthors. Chapters 3 and 4 As a very important and integral part of my thesis research, I had several important discussions with my co-supervisor, Dr. Naoko Ellis of Department of Chemical and Biological Engineering at UBC. Dr. Ellis helped me a lot in setting up the procees parameters for the struvite kinetics study and guided me during the investigation of the hydrodynamics of a liquid-solid fluidized bed of struvite crystals. Her valuable suggestions provided useful insights on the research activities and manuscript content. She also contributed to the critical review of the manucripts. Chapter 5 The CFD analysis in this study was perfomed using a commercial CED software, Fluent 6.3. Prof. Fariborz Taghipour of the Department of Chemical and Biological xvi  Engineering at University of British Columbia (UBC) provided me access to one of his Fluent Licenses. He has helped me learn the simulation techniques used in this study, and provided guidance and suggestions throughout the simulation run. Dr. Naoko Ellis allowed me to use the optical probes, which belong to the Fludization Research Centre at UBC, and also taught me how to use the optical probes to determine the local solid concentration. Both Dr. Taghipour and Dr. Ellis contributed with a critical review of the manuscript. Chapters 6 and 7 I have had several long discussions with Dr. Naoko Ellis on developing a reactor model for the fluidized bed crystallizer and she provided knowledge on many aspects of advanced reactor design and modeling. She also provided helpful suggestions on the revision of the manuscript.  xvii  Chapter 1  1.1  Introduction  Preface The various forms of naturally occurred calcium phosphate, collectively known as  “Phosphate rock”, is the main commercial source of phosphorus, commonly used by the fertilizer, detergent and the insecticide industries (Steen, 2004). Around 38 million tons of phosphate (expressed as P ) is extracted each year (Driver et al., 1999) in the United States, 5 0 2 alone. Globally, that figure is about 140 million tons (Mavinic, Personal communication, 2009). Although phosphate rock is present throughout the earth’s crust, most deposits are low in phosphate content. Over the last twenty years, the highest grade deposits have been heavily exploited and are being rapidly depleted. Moreover, the known reserves of highquality phosphate rock are limited and the intensive exploitation of this resource may cause stock depletion in 25—30 years (Cordell and Mavinic, Personal communication, 2009). The quality of this mined phosphate rock is also decreasing as lower grade ore deposits are used; this contain less phosphorus and more contaminants such as cadmium, uranium, nickel, chromium, copper and zinc (Driver et al., 1999). For these reasons, the processing of mined phosphate rock is becoming more expensive and therefore, the phosphate industry is now searching for more sustainable sources of high purity raw material. At the same time, in the wastewater industry, significant levels of phosphates are released in the secondary digestion phase of the biological nutrient removal (BNR) process. Therefore, the recovery of phosphates from wastewater is one such potential source that, not only has economic merit, but also makes the wastewater treatment industry more sustainable. A secondary benefit of 1  exploiting this resource is to remove phosphates from the treatment process. Over the last few years, the University of British Columbia (UBC) Phosphate Recovery Team has developed a novel reactor design that converts soluble phosphates into crystalline struvite. With the application of UBC MAP (magnesium ammonium phosphate hexahydrate, struvite) fluidized bed crystallizer, more than 80% of phosphate present in the anaerobic digester supernatant was recovered during pilot scale studies (Adnan et al., 2003). This led directly to the development and application of full-scale reactors by Ostara Corporation, a UBC spin-off company (http://www.ostara.com!). Fluidization is the preferred mode of operation for many physical or chemical processes. This method provides several advantages over the other methods of operation such as good solids mixing (thus providing uniform temperature throughout the reactor), high mass and heat transfer and easy solids handling. Fluidized state of a fluid-solid system is achieved when the solid particles weight is entirely balanced by the solid-fluid interaction forces. This complete support is obtained for a fluid velocity greater than a certain value: the minimum fluidization velocity, U. Depending on the fluid velocity, the system can be operated as a homogeneous fluidized condition or in the heterogeneous state. Crystal growth in a liquid fluidized bed is one long standing and industrially well established process. The system involves liquid fluidization of seeded crystal growth by moderately supersaturated (metastable) solution to the solute to be precipitated. In fluidized bed crystallizers, the larger particles remain in the bed are not circulated with the mother liquor. Therefore, they undergo considerably less attrition and breakage than in circulating suspensions crystallizers. This type of crystallizer is thus, well suited for the crystallization of large crystals. The most common type of crystallizer of this kind is Krystal (Oslo or  2  Jerimiassen) crystallizer (Perry et al., 1984). Mullin and his coworkers have extensively studied the operating conditions of this type of system (Mullin, 2001). Recently, Tai et al. (1999) have also studied the same system. Most studies involve the crystallization of inorganic salts from aqueous solutions. However, Glasby and Ridgway (1968) reported the crystallization of acetylsalicylic (aspirin) from the absolute alcohol. Most recently, the UBC Environmental Engineering Group has introduced a pilot scale Magnesium Ammonium Phosphate (MAP) fluidized bed crystallizer to recover phosphate from the anaerobic digester supernatant by formation of struvite 0 2 P (MgNH . 4 H O ) crystals (Adnan et al., 2003). In order to implement this flourishing technique in the plant scale operations, an efficient scaling up is required which mostly relies on the process kinetics and hydrodynamics of the system. Information on the hydrodynamics, mass transfer, kinetics and contacting pattern is essential for the optimum analysis, design and operation of the UBC MAP fluidized bed crystallizer. This calls for the understanding and quantification of kinetics, hydrodynamics and flow pattern that should provide the guidelines about design and scale-up to industrial scale systems. Therefore, both the kinetics and the hydrodynamics were studied in this PhD dissertation.  1.2  Struvite formation kinetics In the precipitation crystallization reactions, the primary processes involved are firstly,  the nucleation, which determines the initial formation of the particles and secondly, their subsequent growth. The growth determines the size of the crystals. Other secondary processes such as agglomeration and breakage of the particles are also likely to take place in the crystallization processes. Agglomeration is a process for particle enlargement, in which  3  fine particles, rather than ions or molecules, are joined in an assembly, resulting in rapid size enlargement. On the other hand, the particle breakage (attrition) is the process by which the existing particles are broken down into a larger number of smaller fragments. Several texts have been dedicated to discuss the nucleation and the growth process during the crystallization (Mullin, 2001; Jones, 2002; Tavare, 1995). The kinetics of all these processes are very important to understand in order to design and analyze the crystallizers. Nucleation and struvite growth kinetics of struvite crystallization have recently been studied by Bhuiyan (2007). However, only the precipitation kinetics has been studied in this dissertation.  1.3  Hydrodynamics Fluidized bed crystallization possesses a very complex hydrodynamic behaviour since  a wide range of particles are employed and the liquid upflow velocity has to be such that the fines do not leave the reactor; at the same time, the larger particles must be kept suspended for growth, to yield the desired size crystals. To maintain such conditions within the reactor, the UBC MAP crystallizer has been devised applying a varying reactor cross-section. Although the fluidized bed consists of only the struvite crystals, the varying size of the seed and the product crystal make the hydrodynamic behaviour more complex in the case of the MAP fluidized bed crystallizer. Under fluidized bed conditions, particles tend to segregate according to their size/density in a multi-particle system. For particles denser than the fluidizing medium, larger/heavier particles populate at the bottom of the reactor and the smaller/lighter particles accumulate near the top of the bed (Al-Dibouni and Garside, 1979). This principle has been used in many other industrial processes like particle classification, mineral dressing and coal beneficiation and expanded bed adsorbers.  4  In a fluidized bed crystallizer, the simultaneous progress of two processes, fluidization  and  crystallization,  yield  very  complex  phenomena  which  requires  comprehensive experimentation of the process hydrodynamics, to help design an efficient reactor. As the supersaturated solution flows upward through a fluidized bed crystallizer, the liquor contacting the bed relieves its supersaturation on the growing crystals and subsequently the supersaturation decreases along the upward direction. As a result, crystals near the bottom grow faster than those near the top of the crystallizer. Such behaviour results in the variation of particle size with height. When the bed is composed of particles of different sizes, the particle size distribution is influenced by two opposite phenomenon: classification and dispersion (Tavare et al., 1990). Classification results from the movement of particles of different weights; a large particle among the smaller one tends to reach the bottom part of the bed, whereas a smaller particle, between larger ones, rises. At the same time, dispersion is induced by irregular motions of the solid. Perfect classification and perfect mixing of the solid in fluidized bed are the two extreme situations. More often, a mixing zone is created between the two layers of classification particles, allowing partial classification within the bed. For simplicity, design methods for fluidized bed crystallizers are generally based on the perfect size classification (Mullin and Nyvlt, 1970). Due to the complex hydrodynamic behaviour of the particle mixtures, the reported studies on the fluidization of multiparticle systems are only limited to very simple situation, like fluidization of binary systems with particle differing in size or density. Al-Dibouni and Garside (1979) measured the particle size distribution at various heights within the bed and came to a conclusion that classification dominates in a bed having the ratio of the largest to  5  the smallest particle diameter greater than 2.2. The variation of size distribution with height could be accurately predicted by assuming perfect classification of the particles in bed. With the variation of particle sizes with height, bed voidages also vary along the height of the reactor. Bed expansion is an important parameter required for sizing the reactor, which is a significant factor affecting the total cost of the process. In the literature, the Richardson-Zaki (1954) correlation was found to be effective in predicting the bed expansion characteristics of a fluidized bed of mono-sized spherical particles. It is worth noting that the Richardson-Zaki equation was developed for the spherical and single size particle expansion. Therefore, in this study the applicability of the relationships found in the literature was investigated for the fluidized bed struvite crystallization process. Application of liquid-solid fluidized bed crystallizer for recovering phosphorus from wastewater has several advantages, such as the production of larger size particle and better process control. However, some key technical issues need to be better understood and resolved in order to enable design and optimization of the UBC MAP crystallizer. This involves fundamental hydrodynamic studies, including the determination of design parameters such as the minimum fluidization velocity, bed expansion, and segregation and mixing characteristics, as a function of various operating conditions. Therefore, these hydrodynamics aspects have also been studied in this research project.  1.4  Development of a reactor model Although a large amount of work have been done on developing mechanistic model  for the industrial crystallizers (stirred tank reactor), very few researchers have attempted to develop such models for a fluidized bed crystallizer. This may be due to the complex nature  6  of the fluidized bed reactor and the limited application of this type of reactor for the crystallization process. Frances et al. (1994) developed a model for a continuous fluidized bed crystallizer. In order to take into account the segregation and particles mixing within the bed, the model was developed based on the description of the fluidized bed as a multistage crystallizer. The model provided better prediction of the mean size of the product. Influences of various parameters on ammonium sulphate crystallization in a fluidized bed crystallizer were simulated by Belcu and Turtoi (1996). The model was developed based on a phenomenological approach and the results found strong influence of the equipment geometry. Shiau et a!. (1999) developed a theoretical model for a continuous fluidized bed crystallizer, assuming that the liquid phase moves upward through the bed in 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 vertical position within the reactor and also allows one to study the effects of various operating parameters, such as the feed rate and height/diameter ratio, on the performance of a continuous fluidized bed crystallizer. Later, the same investigators (Shiau and Lu, 2001) performed a study on the 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 ideal mixed beds of crystals. However, the crystals in different beds are totally segregated. This one parameter model can be employed to investigate both extreme conditions, i.e., completely mixed and segregated, and also for the intermediate region of mixing. In performing a complete process modeling for struvite crystallization, which is dynamic in nature, requires both thermodynamics, reaction kinetics and the hydrodynamics  7  to represent the reactor system completely. Therefore, in this research, the reactor model (which includes crystallization kinetics and the reactor hydrodynamics) is linked to the chemical speciation model for the reactions involved in the creation of super-saturation, with respect to struvite. The equilibrium model takes care of the supersaturation generation, while, the reactor model determines the mass deposition of constituent species onto the seed crystals and subsequently determines the process performance.  1.5  Computational fluid dynamics (CFD) simulation Computational fluid dynamics (CFD) is becoming an important tool for studying the  hydrodynamic behaviour of crystallization process. This technique allows the prediction of flow patterns, local solids concentration and local kinetic energy values, taking into account the reactor shape. It has been used to assess the effect of mixing variables and system geometry on mixing performance. CFD has been successfully applied to describe local concentrations in a conventional crystallizer; however, new developments are needed to better describe the distributed micro-mixing behaviour in precipitators. Examining some of the successful CFD work on crystallization that has been reported, each model has significant limitations to its applicability. For instance, several researchers have modeled precipitation, using the assumption that, since the particles are present at a small size and low concentration, they do not significantly affect the fluid flow (Garside and Tavare, 1985). Others have had a more limited initial goal, such as predicting only the flow field or the flow fields and distribution of solids (Wojcik and Plewik, 2007). Still others have used greatly simplified hydrodynamic models to examine the effect of other aspects of the process, such as using Poiseuille flow and examining the effect on aggregation. Since struvite crystallization is a  8  multi-particle system, in this research, CFD simulation for different size classes of struvite crystals was performed. Numerical models of particulate multiphase flows usually employ Eulerian continuum descriptions of the phases (Gidaspow, 1994), or a Lagrangian descriptions of the particulate phase, and an Eulerian continuum description of the fluid phase (Hu, 1996; Patankar and Joseph, 2001). The latter approach employs the lagrangian tracking method for calculating the behaviour of individual particles, and thus it is capable of simulating phase interaction with high spatial resolution. However, this technique is limited by the total number of particles employed in the multiphase systems. On the other hand, the Eulerian continuum approach considers the particulate phase to be a continuous  ‘fluid’  interpenetrating and interacting with the fluid phase. Dense particulate systems are commonly modeled using this approach. Continuum models allow for the modeling of particle-particle stresses using spatial gradients of the volume fraction and velocities (Gidaspow, 1994). However, introduction of more than one solid phase significantly complicates the formulation and requires the introduction of additional equations to represent the interaction among the different solid phases and the dynamics of the solid phases. Eulerian-Eulerian models are especially useful and computationally effective, when the volume fractions of the phases are comparable, or body forces act to separate the phases or the interactions within and among the phases plays a significant role in determining the hydrodynamics of the system. In this Ph.D. dissertation, the Eulerian-Eulerian multiphase model was employed to simulate the liquid-solid fluidized bed reactor.  9  1.6  Research objectives The overall objective of this proposed research is to address the knowledge gap from  the point of view of kinetics and hydrodynamics of the struvite crystallization in a fluidized bed reactor, and then to develop a complete model for struvite crystallization based on obtained information. The specific objectives of this study were as follows: 1) determination of solubility constant of struvite crystals; 2) experimental investigation and modeling of precipitation kinetics of struvite; 3) experimental study of hydrodynamics in a liquid-solid fluidized bed crystallizer, including determination of the minimum fluidization velocity and the bed expansion, and mixing and segregation behaviour in the reactor; 4) computational fluid dynamics (CFD) simulation of the liquid-solid fluidization of struvite crystals; and 5) development of a mechanistic model for the UBC MAP fluidized bed crystallizer.  1.7  Thesis outline As indicated in the preface, the thesis is presented in a manuscript-based format. The  individual papers (manuscript-chapter) are presented in a logical manner that directs the reader towards the development of the crystallization process model, while addressing the individual objectives. The three major parts of my dissertation are briefly summarized below: 1. Solubility and kinetics of struvite precipitation: In order to achieve better control of struvite recovery systems, an appropriate knowledge of the solubility of struvite is required. A widely varied value has been reported in the literature for struvite solubility  10  product and the use of an incorrect value yields erroneous information about the level of saturation of an effluent sample. Therefore, in this doctoral dissertation (Chapter 2), the struvite solubility products are determined from the analytical results of the solubility, performed for a wide variety of wastewaters. These values will eventually be utilized for designing and controlling the struvite recovery, through the fluidized bed crystallizer. A proper estimation of the process kinetic parameters can help in design of the reactor and establish optimum process conditions. But adequate information in terms of struvite precipitation kinetics is lacking in the literature. It can be cited from the literature that various process parameters, such as supersaturation ratio, pH, Mg:P ratio, degree of mixing, temperature and seeding conditions, are likely to affect the struvite precipitation process. In this dissertation, the struvite precipitation kinetics is studied at different operating conditions and the rate constants are determined by fitting data into an appropriate kinetic model (Chapter 3). 2. Reactor hydrodynamics: Hydrodynamics play a key role in the crystallization process, especially having a critical effect on mixing and mass transfer within the system; this affects the growth rate and quality of the crystals, in terms of size and shape. In this dissertation, both experimental (Chapter 4) and numerical investigations (Chapter 5) of the hydrodynamics in the liquid-solid fluidized bed of struvite crystals are performed. Commercial Computational Fluid Dynamics (CFD) software, Fluent 6.3 is used for numerical investigations and a reactor setup, equipped with pressure manometers and an optical fiber probe, was used for experimental tasks. The findings of this study provide insight into the actual hydrodynamics of the reactor which will finally contribute to the development of an overall, improved reactor model.  11  3. Reactor modeling: Based on the information obtained from both the kinetics and hydrodynamics study, a mathematical model has been developed by assuming a complete segregation of the bed crystals and liquid movement as plug flow in the reactor. The model is tested for the reactor performance evaluation at different operating conditions and its predictions provide a reasonable fit with the experimental results (Chapters 6 and 7). Therefore, the model can be used as a tool for early evaluation of performance of a fluidized bed crystallizer. This can be extended to optimize the struvite crystallization process in the UBC MAP Crystallizer, to ensure efficient reactor design. This chapter (Chapter 1) has provided an introduction to the theme and objectives of the study with some background literature review, while Chapter 8 concludes the research findings with identification of overall significance of the thesis research to the field of the study; it also provides specific recommendations for future research.  12  Nomenclature Symbols U  =  Minimum fluidization velocity  Abbreviations BNR CFD MAP Mg:P UBC  = = = = =  Biological Nutrient Removal Computational Fluid Dynamics Magnesium Ammonium Phosphate Magnesium to Phosphorus ratio University of British Columbia  13  1.8  References  Adnan, A., Mavinic, D.S., and Koch, F.A. (2003) Pilot-scale study of phosphorus recovery through struvite crystallization examining the process feasibility. J. Environ. Eng. Sci. 2 (5), 315-324. -  Al-Dibouni, M.R., and Garside, J. (1979) Particle classification and mixing in liquid fluidized beds. Trans. IChemE, 57, 94-103. Belcu, M., and Turtoi, D. (1996) Simulation of the fluidized bed crystallizers (I) influences of parameters, Cryst. Res. Technol. 31, 1015-1023. Bhuiyan, M.I.H. (2007) Investigation into struvite solubility, growth and dissolution kinetics in the context of phosphorus recovery from wastewater. Ph.D. Thesis, Department of Civil Engineering, University of British Columbia. Driver, J., Lijmbach, D., and Steen, I. (1999) Why recover phosphorus for recycling, and how? Environ. Technol. 20, 65 1-662. Frances, C., Biscans, B., and Laguerie, C. (1994) Modeling of a continuous fluidized-bed crystallizer. Chem. Eng. Sci. 49, 3269-3276. Garside, 3., and Tavare, N.S. (1985) Mixing, reaction and precipitation: limits of micromixing in an MSMPR crystallizer. Chem. Eng. Sci. 40, 1485-1493. Gidaspow, D. (1994) Multiphase Flow and Fluidization Continuum and Kinetic Theory Descriptions, Academic Press, Boston, MA. Glasby, J., and Ridgway, K. (1968) The crystallization of aspirin from ethanol. J. Pharm. Pharmacol. 20 (suppl.), 94S-103S. Hu, H.H. (1996) Direct simulation of flows of solid-liquid mixtures. 22, 335-352.  mt. J. Multiphase flow,  Jones, A.G. (2002) Crystallization Process Systems, Butterworth Heinemann, Oxford. Mullin, J.W. (2001) Crystallization,  4 t h  edition. Butterworth-Heinemann, Oxford.  Mullin, J.W., and Nyvit, J. (1970) Design of classifying crystallizers, Trans. IChemE, 48, T7T14. Patankar, N.A., and Joseph, D.D. (2001) Modeling and numerical simulation of particle flows by Eulerian-Lagrangian approach. mt. .1. Multiphase flow, 27, 1659-1684. Perry, R.H., Green, D.W., and Maloney, 3.0. (1984) Perry’s Chemical Engineers’ Handbook, edition, McGraw-Hill, New York.  6 t h  14  Richardson, J.F., and Zaki, W.N. (1954) Sedimentation and fluidization. Part I. Trans. IChemE, 32, 35-53. Shiau, L-D., Cheng, S-H., and Liu, Y-C. (1999) Modeling of a fluidized bed crystallizer operated in a batch mode. Chem. Eng. Sci. 54, 865-87 1. Shiau, L-D., and Lu, T-S. (2001) Interactive effects of particle mixing and segregation on the performance characteristics of fluidized bed crystallizer. md. Eng. Chem. Res. 40, 707-713. Steen, I. (2004) Phosphorus recovery in the context of industrial use. In: Phosphorus in Environmental Technologies, principles and applications, Valsami-Jones, E. (Ed.), pp. 339354, IWA publishing. Tai, C.Y., Chien, W.-C., and Chen, C.-Y. (1999) Crystal growth kinetics of calcite in a dense fluidized bed crystallizer. AIChE J. 45, 1605-16 14. Tavare, N.S., Matsuoka, M., and Garside, J. (1990) Modelling a continuous column crystallizer: dispersion and growth characteristics of a cooling section. J. Ciyst. Growth, 99, 1151- 1155. Tavare, N.S. (1995) Industrial Crystallization Plenum Press, New York.  —  Process Simulation Analysis and Design,  15  Chapter 2  Exploring the determination of struvite solubility product from analytical results 1  2.1  Introduction Magnesium ammonium phosphate hexahydrate 0 2 P (MgNH . 4 6H ), more commonly O  known as struvite, is a white crystalline substance consisting of equal molar amount of magnesium, ammonium and phosphate, as well as six water of hydration. The simplified form of the reaction involving the struvite formation is as follows (Abbona et al., 1984): 2 Mg  +  4 NH  +  4 PO  +  0 2 6H  —  2 P MgNH . 4 0 6H O  (2.1)  However, the precipitation of struvite produces a rapid decrease in pH of the solution, as observed in crystallization experiments, suggesting that  2 4 HP0  would participate in the  reaction, rather than P0 3 (Schuiling and Andrade, 2001). This view is supported by other 4 researchers (Tsuno et al., 1991; Yoshino et al., 2003), where the struvite equilibrium equation is written as: 2 Mg  +  4 NH  +  2 4 HP0  +  0H  +  0 2 5H  —*  2 P MgNH . 4 0 6H O  (2.2)  Struvite precipitation is a well recognized problem in anaerobic sludge digesters, where it precipitates in digester supematant recycle lines, especially at the elbows and the suction side of pumps. It has also been observed in the sludges derived from the anaerobic digestion of animal farming liquid wastes and agricultural wastes (Booram et al., 1975). The  ‘A  version of this chapter has been published:  Rahaman, M.S.; Mavinic, D.S.; Bhuiyan, M.I.H. and Koch, F.A. (2006) Exploring the determination of struvite solubility product from analytical results. Environ. Technol. 27, 951-961.  16  engineering solution for this struvite precipitation is to recover struvite by crystallization, a process that has been well documented (Tsuno et al., 1991; Yoshino et al., 2003). In order to achieve control of struvite recovery systems, a better understanding of struvite chemistry is required, whereby an exact knowledge of the solubility of struvite becomes essential.  Generally speaking, for any precipitation reaction to take place, the  thermodynamic solubility product (K ) has to be exceeded. The solubility product (K 3 ) 3 represents the product of the activities of the particular species involved in the equilibrium. For the case of struvite, the following relation can be expressed: =  +}[Po 4 {Mg2+}fNH 3 }  (2.3)  Furthermore, the definition of the actual species in solution is required for equilibrium characterization. In the case of struvite, all three of the reacting ions exhibit complex equilibria in aqueous solutions. Therefore, a complete speciation is the prime consideration in determining the struvite solubility product, precisely. Extensive studies, involving the calculation of the solubility product 5 (K , ,) value for struvite, have been conducted by several researchers. A summary of values reported in the literature are shown in Table 2.1. These values of 5 K , , range from 4.37x10’ 4 to 3.89x10’° p from 9.41 to 13.36] and differ by as much as four orders of magnitude. Widely varying 5 [pK  experimental methodologies and conditions, with respect to pH, temperature and ionic strength, account for much of the discrepancies that exist between these reported values. However, the most commonly used value in environmental engineering is 12.6 (Snoeyirik and Jenkins, 1980). The conventional technique for determination of K ,, value of a particular 5 reaction involves either the formation of precipitate, or the dissolution of a previously formed salt in distilled water. However, other techniques have also been employed. For instance, the  17  values for struvite have been determined using the radioisotope 32 P as a tracer over a wide range of temperatures (Aage et al., 1997). The determined values from this technique were found to be slightly lower than values derived using traditional techniques (Wu and Bishop, 2004). Another important factor for the wide discrepancies in the reported values is that various computational methods, with different thermodynamic databases, have been used to calculate the K values. In addition, in many earlier studies, the effect of ionic strength was neglected in determining the struvite solubility product. In reality, ionic strength may vary depending on the concentration and the ions present in the solution. In fairness to the authors, it should also be pointed out that, in certain instances (Borgerding, 1972; Abbona et al., 1982), alternative forms of the equilibrium equations were used; however, even if one excludes these values, a wide range of  values is apparent. Finally, the inherent limitations,  which lead to calculation of dispersed values, can be related to some of the following reasons (Schuiling and Andrade, 2001). •  the solubility product may be derived using approximate solution equilibria  •  the effects of ionic strength are often neglected  •  mass balance and electro neutrality equations are not always used  •  different chemical species are selected for calculations  •  the thermodynamic  value determinations are not extrapolated for zero ionic  strength The presence of both organic and inorganic complexes, as well as the dissolved species formed between the principal constituents of struvite, may also lead to the variation in the values of its thermodynamic solubility product. Also, the reported  values are not the true  thermodynamic solubility product, since they are not determined at zero ionic strength.  18  The use of an incorrect value yields erroneous information about the level of saturation of an effluent sample, with respect to struvite. Therefore, the first objective was to determine the solubility product from analytical results of the solubility tests from a wide variety of water and wastewaters. A fairly complete speciation of the constituent ions of struvite was also employed, to minimize the error in struvite solubility determination. The ionic strength of a solution directly affects the activity of each ion and thus affects the solubility. A wide variety of values for the average ionic strength in wastewater can be found in the literature (Snoeyink and Jenkins, 1980). However, it is advisable to estimate the true ionic strength, when dealing with a specific water or wastewater. Due to the complexity in the determination of ionic strength for complex solutions like wastewater or anaerobic digester supernatantlfilter press centrate, it is prudent to use an approximation of ionic strength, derived from a correlation with electrical conductivity. There are several correlations relating ionic strength to conductivity found in the literature, of which some are widely reported (Ponnamperuma et a!., 1966; Griffin and Jurinak, 1973; Russell, 1976). Recently, Reluy et al. (2004) have developed linear equations to relate total equivalent concentration, total dissolved solids and ionic strength to electrical conductivity (EC) in natural aqueous systems, from low to medium level salt content (from the theory of EC in aqueous solutions). However, none of the correlations has been derived particularly for wastewater or anaerobic digester supematant or from the filter press centrate. A second objective was to develop a correlation between the conductivity data obtained during the struvite solubility tests and the ionic strength calculated during the determination of the solubility product. This correlation is also compared with existing correlations, in further data interpretation.  19  2.2  Materials and methods The apparatus used for determining the solubility of struvite was a six-station paddle  stirrer (Phipps and B irdTM). Square jars, containing 1.5 liters of the solution being tested, were immersed in a constant temperature bath (10 to 20 °C). A sufficient mass of struvite crystals harvested earlier from an on-site, pilot—scale crystallizer, were placed in each jar, to ensure that some solid phase struvite remained at equilibrium. Equilibrium was assumed to be reached within 24 hours after conditions were changed in each jar (Burn and Finlayson, 1982). The pH in each jar was adjusted using dilute hydrochloric acid and sodium hydroxide solutions, in order to determine the solubility of struvite over the reported operating pH range (7 to 9) of struvite crystallization (Schuiling and Andrade, 2001). In the first phase, two sets of tests were conducted: one using distilled water and another using digester supematant from the City of Penticton, B.C., Canada, Advanced Wastewater Treatment Plant (AWWTP) (Britton, 2002). For each test, each jar was filled with 1.5 liters of either distilled water or supematant. Struvite crystals were added to the jar and mixed in. For the tests using supernatant, a reagent grade magnesium chloride solution was dosed into the supematant, to create in an initial molar Mg:P ratio of 1.3:1, as used in the on-going, pilot-scale experiments. The pH of each jar was then adjusted as desired and the apparatus was left to equilibrate for 24 hours. At the end of the 24-hour period, the pH and conductivity in each jar were measured and the samples of the equilibrated solution were filtered through 0.45gm size filter paper. The filtered samples were then analyzed for magnesium, calcium, ammonia and ortho-phosphate. Analyses for ortho-phosphate and  ammonia were done using flow the injection method on a LaChat QuikChem 8000 instrument.  Magnesium  analysis  was  performed  by  flame  atomic  absorption  20  spectrophotometry, using a Varian Inc. SpectrAA22O Fast Sequential Atomic Absorption Spectrophotometer. pH measurements were performed using a Beckman D44 pH meter, equipped with an Oakton pH probe and the conductivity was measured using a Hanna Instruments H19033 multi range conductivity meter, for the struvite solubility tests. In the second phase, an additional two sets of experiments were conducted to determine the struvite equilibrium conditions in tap water and synthetic supematant at 10 °C and 20 °C (Adnan, 2002). Since the struvite solubility is temperature dependent, the tests were conducted at different temperatures. Finally, in the third phase, three additional sets of experiments were conducted; one to determine the struvite solubility product in the synthetic supernatant and the other to determine the struvite  values in anaerobic digester  supernatants from the Annacis Island and Lulu Island Wastewater treatment plants (WWTP), in Vancouver, B.C, Canada (Huang, 2003).  2.2.1  Treatment of data The estimation of thermodynamic solubility products of struvite has been made from  the total initial molar concentration of magnesium, ammonia, phosphate, and measured equilibrium pH. In the calculations, the equilibrium of the following twelve species was taken into account: , 4 P 2 H 0 HP0 , 4 2 4 P0 , , 3 4 P 2 MgH O MgHPO , MgPO 0 4 , Mg 4 , MgOH, 2 , H, OH and NH 4 NH 3 (aq). In a system exposed to atmospheric carbon dioxide and higher pH, carbonate species can help create a sink for magnesium, through the formation of magnesium carbonate, thus making the struvite much more soluble. In a real supematant, the presence of metals such as calcium, iron and aluminum can make the calculations much more difficult. For an accurate  21  prediction of the solubility of struvite, consideration of their contributions may be useful. Since analytical determinations of magnesium, ammonia and phosphate provide the total concentrations of these species in solution, it is necessary to calculate ion activities, by making use of the appropriate activity coefficients and dissociation constants. The values of equilibrium constants at 25 °C were obtained from the literature and are presented along with the corresponding equilibrium relationships in Table 2.2. Equilibrium constants for other temperatures were then estimated, based on the thermodynamic relationship. Individual ion activity coefficients (y) have been calculated from the GUntelberg approximation of the Debye-Huckel limiting law, which is valid for solutions with ionic strength  < 10  [Stumm  and Morgan, 1970], Log  =  _ADHZI2[l ()5  (2.4)  Where A is the Debye-Huckel constant dependent on temperature and calculated as ADH  6 =  (eT)’ 6 =1.82x10 ; 5  dielectric constant and T= temperature in degree Kelvin.  And I is the ionic strength calculated using the following equation proposed by Lewis and Randall [Lewis and Randall, 1921] 2 Z 1 I=0.5C  (2.5)  Where, C = molar concentration of species i and Z 1 = valence of ion i. In this way, it was possible to calculate the activities of all aforementioned species.  22  2.2.2  Calculation of the molar concentrations of [Mg ], [P0 2 ] and [NH] 3 4 The analytical measurements of magnesium, ammonium and phosphates provide the  total concentrations of those species in the original sample. However, the solubility determination requires the molar concentration of those ionic species. Therefore, the molar concentrations for all aqueous species were determined for each solubility test, using the following equations and the equilibrium relationships presented in Table 2.2. Depending on the pH of the solution, the following species are considered to be present at various extents and are included in the determination of the total magnesium. Therefore, the total concentration of magnesium CT(Mg) =  2 Mg  (CT(Mg))  is:  + MgOH + 4 PO + MgHPO° + MgPO 2 MgH 4  (2.6)  The following species of P0 3 would be present in the solution at different extent and are 4 considered for the determination of the total phosphate. Therefore, the total concentration of phosphate CT(po) =  4 P 3 H 0  +  4 P 2 H 0  +  2 4 HP0  +  3 4 P0  (CT(pQ))  is:  +4 PO + MgHP° + MgPO 2 MgH  (2.7)  Similarly, the total concentration of ammonia (CT(NH )) in the solution is determined as, ) 113 CT(N  =  3 [NH  j 4 1+ {NH  (2.8)  After mathematical manipulation of the above equations, with the aid of the  equilibrium relationships of different species (as mentioned in Table 2.2), the following expressions were developed to determine the molar concentrations of magnesium 2 ([Mg ] ), ammonium 4 ([NH ] ) and the phosphate 4 ([P0 7 3 ). 1  1  [Mg ] 2 =  CTM  a+b[P0 3 4  1  ]  (2.9)  23  04 CT(P [po 4 j= c+b[Mg2+j  [Mg2+j=  4 —(ac+bCF(P ) O  -  4 _bCT(Mg))± ) kac+bCF(po  bCr(Mg))  C T(NH)  [NH i 4 =  r(Mg))i°  (2.10)  -(2.11)  (2.12)  [irJ Where a, b and c can be defined as follows:  (11+ I  II  k I=a, kMgoH[H+1)  [ii  3 k 1 k k  1+  [H÷f  3 2 1 k  +  [H]  [H÷  3 2 k  I=b  J 3 kMg  3 k 2 kMg  +  1  +  +  [Hi 3 k  and  =  These molar concentrations have been corrected for activity, by using the Guntelberg approximation, as described earlier.  2.3  Results and discussion The equilibrium molar concentrations of P0 , Mg 3 4 2 and 4 NH for the samples ,  collected during all the solubility tests, were calculated from the analytical results, using Equations (2.10), (2.11) and (2.12), respectively. Using the Equation (2.5), ionic strengths of these solutions, under different pH and temperature conditions, were determined. The activity coefficients (y) were then calculated, using the Guntelberg approximation, by making use of  24  these ionic strengths. Finally, the molar concentrations were corrected for activities, to estimate the solubility products. A summary of the average solubility product, in different samples, is provided in Table 2.3. Figure 2.1 represents the variation of solubility product with pH, for different water and wastewaters for 20 °C, only. As a general trend, K 3 increased with increasing pH values in all the cases. Thermodynamically, there should be a single value of the struvite solubility product applicable for all solutions. Solubility of struvite varies as a function of multitude of parameters, many of which are dynamic in a precipitating and or dissolving solution, which make the experimental determination of struvite  values very challenging.  Moreover, it is quite difficult to determine the complete speciation of the compounds present in wastewater, as well their corresponding activities. Therefore, the presented  values  differ significantly for the range of pH studied in this paper. As shown in Figure 2.1, the pK 5 values at a specific pH, for different supematants, also differed considerably.  It can be  observed that the Ks,, values for Annacis supematant were the highest, while the values for distilled water were the lowest. This may be attributed to the higher ionic strength of the Annacis supematant, thus increasing the struvite solubility (since the electrostatic interaction of the ions in solution will reduce their real activities or effectiveness). Another possible explanation of the higher values of K for Annacis supernatant may be due to the presence of other chemical material, such as carbonate, which could inhibit the precipitation of struvite and increase the solubility significantly. The effect of ionic strength of the medium is very important, particularly in the case of struvite crystallization. If the solution contains an ion that is the same as one of the constituent ions of struvite, then the struvite solubility will be lower than that of pure water.  25  On the other hand, the solubility will often be increased in the presence of ions other than the constituent ions. In the present study, the ionic strength was not varied by adding any external salt, rather than by changing the pH value of the solution. The ionic strength was estimated using the Equation (2.5) as presented earlier. Figure 2.2 displays the variation of pK values with ionic strength for the synthetic supernatant and anaerobic digester supernatants for the three wastewater treatment plants. In all four cases, an increase in the pK values was observed with increasing ionic strength of the solution. The greater the ionic strength, the higher the number and/or amount of charges in the ionic atmosphere, where an anion is surrounded by more cations than anions and vice versa. Each ion-plus-atmosphere contains less net charge, so there is less attraction between any particular cation and anion. Since no external salt was added into the system to increase the ionic strength of the solution, any increase may be attributed to the change in the speciation of the constituents, with varying pH values. It has been reported (Burns and Finlayson, 1982) that the decrease in struvite solubility in an alkaline medium (with higher ionic strength) is a consequence of the common-ion-effect. The working range of pH in the current study was 6—9. In this pH range, the speciation of NH P0 and Mg are subjected to ,4 4 possible changes; this might stimulate the common ion effect of the solution, thereby decreasing the solubility of struvite. Although the curves in Figure 2.2 apparently show two different slopes in the range of ionic strengths tested in the current study, regression analysis with the data sets for each water and wastewater samples provide a relationship that corresponds to straight lines with good correlation coefficients. For the chemical species (e.g. Mg, NH 2 and P0 4 ) present in the test sample, it is observed that activities decrease with 4 increasing ionic strengths (Harris, 1998) and thus pK values increase (K values decrease)  26  with increasing ionic strength. Hence, for the ionic strength range of this study, a linear relationship between pK values and ionic strengths is most likely to hold. Temperature is another important factor affecting the solubility of struvite. A study showed that a steady increase in solubility with increasing temperature up to 50 °C, followed by a steady decline in solubility at higher temperatures (Aage et al., 1997; Doyle, 2002). The change in the structure of struvite crystals with increasing temperature is believed to be the possible reason for variation of solubility in the specified temperature range (Doyle, 2002). Another group of researchers (Bums and Finlayson, 1982) determined the  values at  different temperatures and also found the similar trend of increased K , 8 1 values with increasing temperature, in the range of 25 to 45 °C. The enthalpy is an important parameter for predicting the K 8 values at different temperatures. The calculated enthalpy of the struvite formation was 24.23 Kjmor’ (Bums and Finlayson, 1982), which indicates that the struvite formation in a solution is endothermic. Figure 2.3 shows the pK 8 values of the anaerobic digester supernatant of the Annacis Island WWTP, with varying pH values, at temperatures of 10, 15 and 20 °C. Although the changes were not pronounced in the lower range of pH values (5.5—7), struvite solubility did increase at higher pH values with increasing temperature in the studied range (10—20 °C). The results were found to be identical for other wastewater samples as well (not published). There is much debate regarding the change in struvite solubility with temperature in the literature. Most of the reported pK, values were determined in the temperature range of 25— 45 °C, while only a small group of researchers (Aage et al., 1997) reported the pK 3 values in the range of 10—65 °C. In the latter case, radioisotope 32 P was used as tracer to determine the solubility and higher values of pK 8 were observed than those determined by conventional  27  techniques (such as formation or dissolution). For the present study, since the working temperature was lower than 25 °C, it became necessary to determine the pK values in these lower ranges of temperature. The unknown enthalpy of the equilibrium reaction can be calculated using Equation (2.13) (Snoeyink and Jenkins, 1980):  (2.13)  =  Where, T 1 and T 2 are temperatures in degrees Kelvin 41-1° is the enthalpy of the reaction (JmoU’) R is the ideal gas constant (8.3 14 Jmol’K’) and pkj and pk 2 are the solubility constants at T 1 and T , respectively. 2 Using the above equation, the estimated enthalpy for Annacis and Lulu Island WWTP supematants were found to be 57.62 and 44.79 KJmo[ , respectively. These values are higher 1 than the reported values of 24.23 KJmor’ (Burns and Finlayson, 1982) and of 34.48 KJmo[ 1 (Aage et al., 1997) in the literature, as well as the text book value of struvite’s enthalpy of formation, 29.29 KJmo[’ (Faure, 1991; Lide, 2004). Therefore, an attempt was made to estimate the variation of pK , with temperature, by developing a correlation between these 3 two parameters using a linear regression analysis.  In order to include a wider range of  temperatures (10—45 °C) and because the determination of struvite solubility in this study was only performed between 10—20 °C, the values of pK 3 for other temperatures were taken from the literature (Bums and Finlayson, 1982; Ohlinger, 1999). The results are shown in Figure 2.4. Here, the error bars represent the standard deviation associated with each point. After regression analysis, the data yields a linear relationship as follows: 28  pK  =  —0.02658+13.972  -(2.14)  with an R 2 value of 0.806, where, 0 is the temperature in degree Celsius. However, increasing the number of data points across the entire temperature spectrum would probably make this correlation even more reliable. The conductivity of various waters and wastewaters, at different pH values, was also measured during the solubility tests. Since the ionic strength is a measure of the intensity of the electrical field in an electrolyte solution, correction of the analytical concentrations used to compute the ionic strength for neutral ion pair species and ion-pairs of reduced charge are necessary to provide an accurate measure of the ionic strength-electrical conductance relation. However, as mentioned earlier, the ionic strengths of these solutions have been calculated by using the Equation (2.5). The species considered in calculating the ionic strength include, , MgOH 2 Mg , 4 4 , MgPO 4 PO NH, P0 2 MgH , , HP0 3 4 P0 H 2 H , 4 2 4 4 and OW. Detailed calculations were done in Excel spreadsheet and the results are presented in Figure 2.5. In general, the conductivity increases with an increase in ionic strength. A correlation was developed using the linear regression analysis and the following equation was found to best fit the data set: I  =  5x10 E 6 C  with an R 2  =  (2.15)  0.8523, where, EC is the electrical conductivity in (i.tScm’).  The regression coefficient found in this study is smaller than that of the existing correlations. Therefore, the correlation proposed in this study estimates values of ionic strength lower than those estimated by other existing correlations for the same electrical conductivity. This may be due to the fact that, in the present study, all of the ionic species might not be accounted for  29  in calculation of the ionic strength of the solution. Also, temperature dependence of the conductivity was not considered.  2.4  Conclusions The following preliminary conclusions can be drawn, based on the experimental  evidence accumulated so far: 1) The solubility product of struvite, determined in different water and wastewater samples, varies significantly with pH, as well amongst each other, due to the difficulty of controlling and measuring the influencing parameters. The average pK values, thus determined, varied from 13.43—14.10, for different solutions, at a temperature of 20 °C. 2) In the range of ionic strength tested in the current study, a linear relationship with good correlation coefficients was found between pK and ionic strength (1). 3) Discrepancies with the literature and text book values of enthalpy of formation of struvite were noted. However, a correlation (pK  =  —0.02650+13.972, with an  value of 0.806) was developed to find the K 3 values with varying temperature. 4) A possible correlation between ionic strength and conductivity (I an R 2  =  =  5E O6EC, with —  0.8523) was developed using different solution matrices; it was found to yield  lower values of ionic strength than those predicted by the existing correlations for the same electrical conductivity.  30  Nomenclature Symbols Debye-HUckel constant Constants used in Equations 2.9 -2.11 and defined in text Molar concentration of species i (molIL) Total analytical concentration of magnesium species (mol/L) Total analytical concentration of ammonia species (molfL)  ADH  a, b & c C, CT(Mg) CT(NH) CT(po)  =  EC I k  Total analytical concentration of phosphate species (mol/L)  [Mg ] 2 ] 4 [NH pH pK 37 4 [P0 R T  Electrical conductivity (iS cm’) Ionic strength (mol U’) Equilibrium constants for specific reactions Thermodynamic solubility product of struvite Molar concentrations of magnesium (molJL) Molar concentrations of ammonium (molIL) -log[yHI-fl -log[K] Molar concentrations of phosphate (molJL) Ideal gas constant (8.3 14 Jmor’K’) Temperature (K)  zlR°  Valence of the ion i Enthalpy of the reaction (Jmo[’)  Greek letters = =  0  =  Activity coefficient of ion i Dielectric constant Temperature (°C)  Abbreviations AWWTP MAP Mg:P WWTP  = = = =  Advanced Wastewater Treatment Plant Magnesium Ammonium Phosphate Magnesium to Phosphorus ratio Wastewater Treatment Plant  31  Table 2.1  Reported experimental values for the Ks,, of struvite at 25 °C  pK 9.41  Reference 3.89 x 1010  (Borgerding, 1972)  1010  (Abbona et al., 1982)  11.84  1.44 x 1042  (Booram et al., 1975)  12.60  2.51 x i0’ 3  (Snoeyink and Jenkins, 1980)  13.00  1.00 x i0’ 3  (Mamais et a!., 1994)  13.12  7.58 x i0’  (Bums and Finlayson, 1982)  13.15  7.08 x i0’  (Buchanan et al., 1994)  13.26  5.50 x i0’ 4  (Ohlinger et a!., 1998)  13.36  4 4.37x10’  (Babic-Ivancici et al., 2002)  1.15  32  33  4 ] 2 [Mg 3 [HPO i/[MgHPO 1 4 ][PO i/[MgPO 2 [Mg 3 4 1 4 ][Hj/[NH 3 [NH ] 4 O] 2 [H][OHh/[H  2 [H][H ] 4 P 3 ] /[H O i/[H [H][HPO P 2 i 4 O 3 i/[HP0 4 [H’i[P0 1 2 4 9[OHh/[MgOH] 2 [Mg 4[g [Mg P / p 2 ] 4 ][H Q o  Constant pk (25 °C) [Ref] 1 k 2.148 [Smith and Martell, 1989] 2 k 7.198 [Smith and Martell, 1989] 12.375 [Smith and Martell, 1989] 2.56 [Morel and Hering, 1993] kMgoH 1.207 [Childs, 1970] kMgl 2.428 [Childs, 1970] kMg2 4.92 [Childs, 1970] kMg3 9.24 [Bouropoulos and Koutsoukos, 2000] kb 13.997 [Smith and Martell, 1989] k  Reported equilibrium constants  Equilibrium  Table 2.2 pk (20 °C) 2.11 7.21 12.27 2.46 0.45 2.77 4.8 9.71 14.38  pk (15 °C) 2.09 7.23 12.43 2.46 0.36 2.83 4.72 9.62 14.34  pk (10 °C) 2.07 7.25 12.49 2.46 0.32 2.91 4.68 9.78 14.52  Table 2.3  Summary of the average solubility product in various solvents  Solvent  Temperature (°C)  Annacis Island WWTPAnaerobic digester supernatant  10 15 20  Lulu Island WWTPAnaerobic digester supematant Penticton AWWTPAnaerobic digester supernatant Distilled water Synthetic supematant  10 20  Mean K  Mean pK  5.97—9.09  4 3.71x10’  13.53 (±0.34)  5.98—9.06  4 5.23x10’  13.43 (±0.41)  5.62—8.77  4 5.75x10’  13.55 (±0.54)  5.94—9.05  4 3.51x10’  13.68 (±0.4)  5.89—9.02  4 6.18x10’  13.53 (±0.45)  6.45—8.97  4 4.80x10’  13.45 (±0.37)  7.01—9.52  8.52x 10  14.10 (±0.16)  6.62—9.31  4 4.42x10’  13.61 (±0.51)  6.68—9.69  4 8.52x10’  13.51 (±0.56)  6.59—9.44  4 2.04x10’  13.96 (±0.41)  6.64—9.43  4 2.76x10’  13.73 (±0.3 5)  20  20 10 20  Tap water  pH range  10 20  34  • Synthetic  I Penticton  C Distilled water  A Tap water  0 Annacis  Lulu  15  I  14.5  14  %a  oé  o  •.  AA  AAC A  C  C C  A  135  A  13  •%  0  I  A  0  12.5  12  I  5  5.5  6  I  6.5  7  7.5  8  8.5  I  I  9  9.5  10  pH Figure 2.1  pH versus pK values for different water and wastewaters at 20 °C  35  • Penticton  • Synthetic  OAnnacis  Lu1u  A Tap water  0 Distifled water  14.5 00 A  14  11  0 0 o0 0  13.5  0 0  13  A. 0  12.5  . 12 0  0.02  0.04  0.06  0.08  0.1  0.12  0.14  Ionic strength (moles F’)  Figure 2.2  Variation of pK with ionic strength  36  D20°C  A15°C  010°C  14.50  1010 A 14.00 CD  0 Q  13.5O  0  A° C  A0  A  13.00  0  C  A C  12.50  12.00  5  5.5  6  6.5  7  7.5  8  8.5  9  9.5  pH  Figure 2.3  pH versus pK of Annacis WWTP anaerobic digester supernatant at different temperatures (10 °C, 15 °C and 20 °C) —  37  14.6 14.4  • Supernatant_Synthetic Supernantant_Annacis • Burns & Finlayson (1982) C Distilled water  A Tap water • Supernatant_Penticton Supernantant_Lulu Ohlinger (1999)  -  0  -  14.2 1413.8 13.6 13.413.213-  -  12.8 12.6 0  5  I  I  10  15  20  I  I  I  I  25  30  35  40  45  50  Temperature (°C)  Figure 2.4  Variation of pK with temperature  38  • Penticton AWWTP  0.08  0 Distilled Water  0  o  0.07 ATap Water  o o  0  0.06 • Synthetic Supernatant  0.05  0  0 Annacis WWTP  0 0  0.04  •  á Lulu WWTP 0.03 0.02  •  •  A  0.01.  1  0 0  •  p I  2000  4000  6000  8000  10000  12000  14000  Conductivity (iScm ) 1  Figure 2.5  Conductivity versus ionic strength at 20 °C  39  2.5  References  Aage, H.K., Anderson, B.L., Blom, A., and Jensen, I. (1997) The solubility of struvite. J. Radio. Anal. Nuclear Chem. 223, 213-215. Abbona, F., Madsen, H.E.L., and Boistelle, R. (1982) Crystallization of two magnesium phosphates, struvite and newberyite: Effects of pH and concentration. J. Cryst. Growth, 57, 6-14. Abbona, F., Caleni, M., and Ivaldi, G. (1984) Synthetic struvite, 2 P MgNH . 4 0 6H O ; correct polarity and surface features of some complementary forms. Acta Crystallogr. Sect. B:Struct. Sci. 40, 223-227. Adnan, A. (2002) Pilot scale study of phosphorus recovery through struvite crystallization. M.A.Sc. Thesis, Department of Civil Engineering, University of British Columbia. Babic-Ivancici, V., Kontrec, J., Kralj, D., and Brecvic, L. (2002) Precipitation diagrams of struvite and dissolution kinetics of different struvite morphologies. Croat. Chem. Acta, 75, 89-106. Booram, C.V., Smith, R.J., and Hazen, T.E. (1975) Crystalline phosphate precipitation from anaerobic animal waste treatment lagoon liquors. Trans. ASAE, 18, 340-343. Borgerding, J. (1972) Phosphate deposits in digestion systems. J. Water Pollut. Control Fed. 44, 813-819. Bouropoulos, N.Ch., and Koutsou.kos, P.G. (2000) Spontaneous precipitation of struvite from aqueous solutions. J. Cryst. Growth, 213. 381—388. Britton, A.T. (2002) Pilot scale struvite recovery trials from a full-scale digester supematant at the city of Penticton advanced wastewater treatment plant. M.A.Sc. Thesis, Department of Civil Engineering, University of British Columbia. Buchanan, 3., Mote, C., and Robinson, R. (1994) Thermodynamics of struvite formation. Trans. ASAE, 37, 617-621. Bums, I., and Finlayson, B. (1982) Solubility product of magnesium ammonium phosphate hexahydrate at various temperatures. J. Urol. 128, 426-428. Childs, C.W. (1970) A potentiometric study of equilibria in aqueous divalent metal orthophosphate solutions. Inorg. Qiem. 9, 2465—2469. Doyle, J.D. (2002) Struvite formation, control and recovery. Water Res. 36, 3925-3940. Faure, G. (1991) Principles and Applications of Inorganic Geochemistry. Macmillan Publishing Company, New York, USA. 40  Griffin, R.A., and Jurinak, J.J. (1973) Estimation of activity coefficients from the electrical conductivity of natural aquatic systems and soil extracts. Soil Sci. 116, 26-30. Harris, D.C. (1998) Quantitative Chemical Analysis,  th 5  ed. W H Freeman & Co, New York.  Huang, H. (2003) Pilot scale phosphorus recovery from anaerobic digester supernatant. M.A.Sc. Thesis, Department of Civil Engineering, University of British Columbia. Lewis, G.N., and Randall, M. (1921) The activity coefficient of strong electrolytes. J. Am. Chem. Soc. 43, 1112-1154. Lide, D.R. (2004) CRC Handbook of Chemistry and Physics, 85th ed. CRC Press, Cleveland, Ohio. Mamais, D., Pitt, P., Cheng, Y., Loiacono, J., and Jenkins, D. (1994) Determination of ferric chloride dose to control struvite precipitation in anaerobic sludge digesters. Water Environ. Res. 66, 912-918. Morel, F.M., and Hering, J.G. (1993) Principles and Applications qfAquaric Chemistry. John Wiley and Sons, Inc., NY. Ohlinger, K.N., Young, T.M., and Schroeder, E.D. (1998) Predicting struvite formation in digestion. Water Res. 32, 3607-36 14. Ohlinger, K.N. (1999) Struvite controls in anaerobic digestion and post-digestion wastewater treatment processes. Ph.D. Thesis, Department of Civil and Environmental Engineering, University of California, Davis, CA, USA. Ponnamperuma, F.N., Tianco, E.M., and Loy, T.A. (1966) Ionic strengths of the solutions of flooded soils and other natural aqueous solutions from specific conductance. Soil Sci. 102, 408-413. Reluy, F.V., Becares, J.M.D., Hernandez, J.D.Z., and Diaz, J.S. (2004) Development of an equation to relate electrical conductivity to soil and water salinity in a Mediterranean agricultural environment. Aust. J. Soil Res. 42, 38 1-388. Russell, L. (1976) Chemical aspects of groundwater recharge with wastewaters. Ph.D. Thesis. Department of Civil and Environmental Engineering, University of California, Barkley. Schuiling R.D. and Andrade, A. (2001) The chemistry of struvite crystallization. Mineral Jourl. (Ukraine), 23, 37-46. Smith, R.M., and Martell, A.E. (1989) Critical Stability New York.  (‘onstants,  Vol. 6, Plenum Press,  Snoeyink, V., and Jenkins, D. (1980) Water Chemistry. John Wiley & Sons, New York. 41  Stumm, W., and Morgan, JJ. (1970) Aquatic Chemistry: An Introduction Emphasizing Chemical Equilibria in Natural Waters. Willey-Intersceince. New York. Tsuno, H., Somiya, I., and Yoshino, M. (1991) Production of struvite from phosphate and ammonium in supernatant of anaerobic digestion. Journal of Japan Sewage Works Association, 28, 68-77 (in Japanese). Wu, Q., and Bishop, P.L. (2004) Enhancing struvite crystallization from anaerobic supernatant. .1. Environ. Eng. Sci. 3, 2 1-29. Yoshino, M., Tsuno, H., and Somiya, I. (2003) Removal and recovery of phosphate and ammonium as struvite from supematant in anaerobic digestion. Water Sci. Technol. 48, 171178.  42  Chapter 3  Effects of various process parameters on struvite precipitation kinetics and subsequent determination of rate constants 2  3.1  Introduction Magnesium ammonium phosphate hexahydrate 0 2 P (MgNH . 4 6H O ), more commonly  known as struvite, is a white crystalline substance consisting of equal molar amount of magnesium, ammonium and phosphate, as well as six water of hydration. The simplified form of the reaction involving the struvite formation is as follows: 2 + NH Mg 4+  +  0 2 6H  —>  2 P MgNH . 4 0 6H O  (3.1)  Struvite precipitation is a well recognized problem in anaerobic sludge digesters, where it precipitates in digester supematant recycle lines, especially at the elbows and the suction side of pumps. It has also been observed in the sludge derived from the anaerobic digestion of animal farming liquid wastes and agricultural wastes (Booram et al., 1975). In recent years, extensive research has been conducted by several researchers with respect to recovering phosphorus from wastewater through struvite 0 2 P (MgNH . 4 6H O ) crystallization. The UBC fluidized bed MAP (Magnesium Ammonium Phosphate) crystallizer, is found to be very effective in recovering phosphorus (80—90% recovery) from anaerobic digester supernatant (Adnan et a!., 2003). In order to implement this process in the plant scale operation, an  2  A version of this chapter has been published:  Rahaman, M.S., Ellis, N., and Mavinic, D.S. (2008) Effects of various process parameters on struvite precipitation kinetics and subsequent determination of rate constants. Water Sci. Technol. 57 (5), 647—654.  43  efficient design and scale-up method has to be developed. A good estimation of process kinetics can help design the reactor and establish optimum process conditions. Several articles have been published with regards to the effectiveness of the struvite crystallization process in recovering phosphorus from wastewaters. However, adequate information in terms of kinetics of struvite precipitation is still lacking in the literature. Ohlinger et al. (1999) studied the kinetic effects on preferential struvite accumulation in wastewater. The authors found struvite nucleation as a reaction controlled process and thus strongly dependent on the degree of supersaturation level. At the same time, crystal growth rate was found to be transport-limited and depended heavily on the mixing strength. In further research, the same group of researchers found that the first order kinetic relationship suited well to the disappearance of ortho-phosphate from bulk solutions with a rate constant estimated as 4.2 h’, by fitting the first order kinetic model (Ohlinger et al., 2000). Nelson et al. (2003) studied the effect of pH in the range of 7.5 to 9.5 and Mg:P ratios between 1:1 and 1.6:1 on struvite precipitation in anaerobic swine lagoon liquid. For all Mg:P ratios, the minimum concentrations of P0 -P occurred between pH 8.9 and 9.25. The authors described 4 the rate of ortho-P decrease by a first-order kinetic model, and estimated rate constants as 3.7, 7.9 and 12.3 W 1 at pH 8.4, 8.7 and 9.0, respectively. On the other hand, Bouropolouos and Koutsoukos (2000) studied the kinetics of spontaneous precipitation of struvite in aqueous solutions supersaturated with respect to struvite species concentrations and reported kinetics following a second-order dependence on the solution supersaturation, implying a surface controlled mechanism. Ven Rensburg et al. (2003) investigated the reaction kinetics and design parameters of struvite production, using a draft-tube type reactor. The authors devised an equation in order to estimate the struvite production rate and found that rate constant  44  increased with increasing struvite concentration and mixing intensity in the reactor. Quintana et al. (2005) studied the kinetics of phosphorus removal and struvite formation by the utilization of by-product of magnesium oxide production from both synthetic and real anaerobic digester liquor. The authors have demonstrated that a first-order kinetic model adequately represented the rate of phosphorus removal and found an increase in reaction rate constant (k) and a decrease in the equilibrium concentration (Ceq) with increasing Mg:P molar ratio. It was also observed that the kinetic constants for real wastewater were higher (0.018—0.024 min’) than those obtained for synthetic liquor (0.0009—0.017 min’). Yoshino et al. (2003) observed that the reaction kinetic was influenced by the mixing intensity and constituent species concentrations of struvite in bulk solutions. As can be found in the literature, various process parameter such as supersaturation ratio, pH, Mg:P ratio, degree of mixing, temperature and seeding conditions are likely to affect the struvite precipitation process. Therefore, in this chapter, struvite precipitation kinetics were studied at different operating conditions, to determine the rate constants by comparing the experimental data with a suitable kinetic model.  3.2  Materials and methods  3.2.1  Synthetic liquor preparation In this study synthetic supernatant containing the constituent ions of struvite was used.  The reagent salts used to prepare the synthetic liquor were commercial grade magnesium chloride hexahydrate 0 .6H 2 (MgC1 ), diammonium hydrogen phosphate J E-1P0 and 2 ) 4 [(NH ammonium chloride (NH C1). Commercial grade sodium hydroxide (NaOH) was used for pH 4  45  adjustment. Bulk solutions were adjusted over a range of P0 4 concentration to reflect typical low strength anaerobic digester supernatant (< 40 mg/L).  3.2.2  Methods A six-station Phipps and BirdTht jar tester was used to investigate the struvite  formation kinetics. Three sets of experiment were run for this current study. In the first set of experiments four replicate runs, each having identical initial concentrations of 4 P0 P, Mg and 4 NH N were conducted. Among all these four replicates, the only parameter varied was the supersaturation ratio (SSR) and the changes in SSR were done by adjusting the solution pH values. In the second set three replicate runs of experiment, each having same SSR were carried out. Among these three, the first two runs were identical in terms of all the process variables, except 10 g of struvite seed crystals were added in the second run. In third run ion species concentrations, with respect to those in the first ones were varied to get different Mg:P ratio. In the last set of experiments only two replicate runs were carried out with two different Mg:P ratio and a constant stirrer speed of 70 rpm was maintained. The experimental conditions for all nine runs are shown in Table 3.1. In each experimental run, 1.5 L of synthetic supematant was transformed into a 2 L jar. The solution pH was adjusted accordingly to ensure desired supersaturation ratio with a constant Mg:P ratio. All the experimental runs were performed in a temperature controlled room set at 20 °C. The pH in each jar was raised to a desired value by adding 6M sodium hydroxide (NaOH) solution. The solution in each jar was then stirred for 240 mm and the samples were collected at every 15 mm for the first 60 mm, and at 30 mill interval for the rest of the period. Samples were  46  filtered immediately through a 0.45 pm mixed cellulose ester membrane filter and preserved for chemical analysis.  3.2.3  Analytical techniques The filtered samples were analyzed for magnesium, ammonia and ortho-phosphate.  Analyses for ortho-phosphate and ammonia were performed using flow injection method on a LaChat QuikChem 8000 instrument. Magnesium analysis was performed by flame atomic absorption spectrophotometry, using a Varian Inc. SpectrAA22O Fast Sequential Atomic Absorption Spectrophotometer. pH measurements were performed using a Beckman (1)44 pH meter, equipped with an Oakton pH probe.  3.2.4  Treatment of data As demonstrated in the literature, first order kinetic model represents the struvite  formation in aqueous solutions. In this present study, the kinetic data were fitted to a slightlymodified, first-order kinetic model, as proposed by Nelson et a!. (2003). The model expresses the relationship between the disappearance of a reactant (-dC/dt) and its instantaneous concentration above the equilibrium value (Equation 3.2). A constant of proportionally, k, referred as the rate constant, is introduced. By mathematical manipulation of Equation 3.2 and integration, it generates the linear form of the first-order reaction kinetics (Equation 3.3). As described by the first order reaction kinetics, a plot of ln(C-Ceq) against time generates a straight line with slope —k. -dC/dt  k(C-Ceq)  (3.2)  ln(C-Ceq)=-kt +ln(Co-Ceq)  (3.3)  =  47  3.3  Results and discussion  3.3.1  Influence of supersaturation ratio and pH on struvite precipitation Supersaturation ratio (SSR) is defined as the ratio of conditional solubility product  (Ps) to the equilibrium conditional solubility product  (PSeq).  Conditional solubility product  represents the solubility product in actual conditions and equilibrium counterpart means its value at equilibrium state. Therefore, SSR Ps/Pseq  (3.4)  And the conditional solubility product is expressed as PS[CTMg][CmH3][CTpo4]  PSeq  (3.5)  is highly pH dependent as found by various researchers (Ohlinger et al., 1998). With an  increase in pH value, the concentration of phosphate ion increases, while the concentrations of Mg and NH 4 decrease; thus establishing a range of solubility limits. An increase in the concentrations of the any constituent ions would increase the conditional solubility product, whereas at a higher pH, the values of PSeq would decrease. Thus, the prevailing SSR in the process fluid can be increased by increasing the concentration of struvite constituent ions or by increasing the pH of the bulk solutions. In this study, the SSR of the reaction solutions were changed by adjusting the pH value. To investigate the effects of SSR on the formation of struvite, the disappearance of the ortho-P ions were monitored during the experimental run. As shown in Figure 3.1, the results clearly indicate that SSR plays an important role in the struvite precipitation kinetics. With increasing SSR, the removal of P0 4 increases with the equilibrium being achieved faster for the SSR ranging from 9.64 to 1.13. The desired SSR values were achieved by adjusting solution pH values (from 7.6 to 8.5). Therefore, it can also be inferred that the higher phosphorus removal efficiency could be achieved by increasing 48  pH values from 7.6 to 8.5. Subsequently, the reaction rate constants were estimated by fitting the experimental data in the modified first-order kinetic model (Figure 3.2). The estimated rate constants were 2.034, 1.7 16 and 0.69 hr’ for supersaturation ratio of 9.64, 4.83, and 2.44, respectively. A similar trend in the variation of rate constants with respect to pH (means SSR) was observed by Nelson et al. (2003). They estimated the rate constants 3.7, 7.9 and 12.3 h’ for the pH values of 8.4, 8.7 and 9.0. The rate constant reported by the group, 3.7 h 1 at pH 8.4 is higher than the calculated rate constant (2.034 h’) at pH 8.5 in the present work. The lower rate constant reported in the present study may be due to the difference in initial concentrations of the constituent ions, which, in turn affects the SSR. Also, the rate constant in this current study was determined for synthetic liquor whereas Nelson et al. (2003) performed their experiments with real swine liquor. It has also been observed by Quintana et al. (2005) that the k values in real liquor were higher than those obtained with the synthetic liquor.  3.3.2  Effect of Mg:P ratio Magnesium is another important constituent ion for struvite precipitation. Hence, it  also affects the supersaturation level and the progress of precipitation process. In many cases of strtuvite formation from anaerobic digester supernatant, the addition of magnesium from an external source is necessary as struvite forms in a theoretical Mg:N:P molar ratio of 1:1:1 and many domestic wastewaters do not contain Mg ions required to fulfill the stoichiometric requirements for struvite formation. Although unwanted struvite can be formed at any Mg:P molar ratio, for intentional struvite crystallization the Mg:P ratio should be at least unity. Higher magnesium can increase the P-removal from reaction solutions. At a given pH, any  49  increase in the Mg:P ratio would increase the degree of saturation with respect to struvite formation, which, in turn, would enhance the phosphorus removal (Adnan et al., 2004). In this current study, Mg:P ratio in the range of 1.00 to 1.60 is investigated and results for phosphorus removal, with respect to time, is illustrated in Figure 3.3. It was found that better removal of phosphorus was achieved with higher Mg:P ratio in the range of studied ratios. A similar trend was observed by many other researchers (Adnan, et al., 2004; Nelson et al., 2003). In general, Mg:P ratio of 1.1—1.6 was considered as optimum in most of the cases of investigation (Adnan, et a!., 2004). As can be observed in Figure 3.3, a rapid decrease in 4 P0 P concentration was observed during the first 50 minutes for Mg:P ratios of 1.3 and 1.6. However, a gradual decrease in 4 P0 P concentration was observed in case of Mg:P ratio of 1.0. Thus, the molar ratio had a strong influence on the decrease of phosphorus concentration. However, the difference in the reduction between Mg:P ratios of 1.3 and 1.6 was minimal. Data were plotted as ln(C-Ceq) versus time in order to obtain the kinetic values. As can be seen in Figure 3.4, a plot of ln(C-Ceq) versus time generates straight lines with different slopes. This means that the rate of reaction with different Mg:P ratios varied and the straight lines suggest the proposed first order kinetic model fit reasonably well with the experimental observations. Kinetic parameters were also evaluated for different Mg:P ratio (1.0, 1.3 and 1.6) and the results showed that the higher the ratio, the better the phosphorus removal efficiency for the range of Mg:P ratio investigated. The rate constants, from Figure 3.4, are found to be 0.942, 2.034 and 2.712hr’ for Mg:P ratios of 1.0, 1.3 and 1.6, respectively.  50  3.3.3  Effect of degree of mixing Figure 3.5 shows the residual phosphorus concentration with respect to time for two  different mixing speeds (100 and 70 rpm). The experimental observations clearly indicated that mixing intensity had little effect on the intrinsic kinetics of struvite precipitation for the range of mixing speed tested. In the precipitation process, crystal formation is taken place in two different stages: nucleation and growth. At the optimum pH, the induction time is affected by the process fluid turbulence (Ohlinger et al., 1999). Therefore, the induction time decreases as the stirring speed increases and the nucleation of struvite becomes rapid. Once the nuclei are formed, struvite crystal growth on the existing nucleation sites is primarily controlled by the mixing energy. The reason for the insignificant influence of mixing strength in this current study may be due to fact that the mixing energy might be in excess of the optimum value for the set process parameters in the experiment. As excessive mixing strength may cause the break down of the crystals and thus the settalibilty and the removal of phosphorus is decreased. Findings in this experiment make sense as Wang et al. (2006) reported that the optimum mixing strength (G value) was 76  1  for unseeded synthetic animal  lagoon wastewater and no significant increase in phosphorus removal were obtained when mixing strength was greater than 76 s . In this study, the different mixing strength (G values) 1 used was 97 and 165 s , both of which were greater than the optimum mixing strength found 1 by Wang et al. (2006). Subsequently rate constants were determined by fitting the experimental results with modified first-order kinetic model. The precipitation rate constants were estimated as 2.034 and 1.902 hr’ for 100 and 70 rpm, respectively.  51  3.3.4  Effect of seeding Kinetic experiments were also conducted to reveal the effect of seeding with struvite  seed crystals (initial size range of 250 to 500pm) in the reactive solutions and it was found that the seeding had very little effect on the intrinsic kinetics of struvite precipitation. The effects of seeding have been studied by several investigators to enhance the struvite crystallization and postulated that the seeding material should pose sufficient size and crystal structure that mimic the precipitating substances. Seeding is considered to enhance the struvite crystallization by providing the adequate reaction surface. Therefore, specific surface area of the seed could be one of the factors influencing the ortho-P removal (Ohlinger et al., 1999). A seed with larger specific surface area and therefore, a smaller size could promote P removal. However, as seen in Figure 3.6, the difference in P removal between seeded and unseeded condition was not significant. A similar observation was reported by Adnan et al. (2004). The reason behind this phenomena could be that the reaction equilibrium was reached very fast and nuclei were formed which had much greater surface area than the seed crystals, since seed crystals are of much bigger size and the amount added was small (10 g of 250-500 pm struvite crystal). It is very likely that the surface area provided by the seed crystals might be very small in comparison to that of the fresh produced nuclei. Seeding would obviously influence the precipitation process. But for the species concentrations of struvite in this current study, equilibrium reached before the growth could be taken place on the surface of the seed particles.  52  3.4  Conclusions The experimental results reveal that supersaturation plays an important role in the  struvite precipitation kinetics. Since the desired SSR of bulk solutions was achieved by adjusting the pH values, it can be inferred that pH is also important factor influencing the precipitation reaction kinetics. The rate of disappearance of optho-P in the bulk solutions increases with increasing SSR values. The estimated rate constants are 2.034, 1.7 16 and 0.69 h’ for supersaturation ratios of 9.64, 4.83 and 2.44, respectively, with a constant Mg:P ratio of 1.3 at 20 °C. The results for struvite precipitation kinetics with varying Mg:P ratio reveal that the higher the ratio (in the range of 1.0—1.6), the better is the ortho-P removal efficiency. The rate constants are found to be 0.942, 2.034 and 2.712 W 1 for Mg:P ratios of 1.0, 1.3 and 1.6, respectively. The experimental observations for kinetics of struvite precipitation with different stirrer speeds clearly show that the mixing intensity used in this study had little effect on the intrinsic rate constants; k values found to be 2.034 and 1.902 h 4 for 100 and 70 rpm, respectively. Seeding, with 250—500 urn of seed crystals, during the struvite precipitation kinetics test was found to have very little effect on ortho-P removal.  53  Nomenclature Symbols C Co Ceq dC/dt G k N pH P  = = = = = = = = =  Ps  Concentration of P0 3 (mgIL) 4 Initial concentration of P0 4 (mg/L) Equilibrium concentration of P0 (mg/L) 3 4 Disappearance of P0 3 (mg/Us) 4 Mixing strength (s’) Reaction rate constant (time’) Nitrogen -log[yHffi Phosphorus Conditional solubility product Equilibrium conditional solubility product Time (s)  PSeq t  Abbreviations MAP Mg Mg:P Mg:N: P rpm  = = = = =  Magnesium Ammonium Phosphate Magnesium Magnesium to Phosphorus ratio Magnesium:Nitrogen:Phosphorus molar ratio revolution per minute  SSR  =  Supersaturation Ratio =Ps/Pseq  54  55  *  600 1.3 8.51 9.64 100 20  Initial NH -N Cone. (mgIL) 4  Mg:P molar ratio  pH  Supersaturation ratio (SSR)  Stirrer speed (rpm)  Temperature (°C)  In run # 6, lOg of struvite  31  Initial Mg Cone. (mgfL)  20  100  2.44  7.91  1.3  600  31  20  100  1.13  7.6  1.3  600  31  30.5  20  100  9.97  8.51  1.6  500  38  30.5  Run#4 Run#5  seed crystal in the size range of 250—500 jim was added  20  100  4.83  8.2  1.3  600  31  30.5  30.5  Initial P0 -P Cone. (mg/L) 4 30.5  Run#1 Run#2 Run#3  Operational conditions for various experimental runs  Process parameters  Table 3.1  20  100  9.97  8.51  1.6  500  38  30.5  *Run#6  20  100  9.91  8.51  1.0  760  24  30.5  20  70  9.97  8.51  1.6  500  38  30.5  Run#7 Run#8  20  70  9.64  8.51  1.3  600  31  30.5  Run#9  -.--SSR=9.64  35  -—SSR=4.83  —--SSR=2.44  —e—SSR= 1.13  30 25 20 15  j  10 5 0 0  50  100  150  200  250  Time (mm)  Figure 3.1  Variation of ortho-P concentrations with the reaction time  56  4  -  —  3  SSR = 9.64 Linear (SSR = 2.44)  • -  -  -  SSR = 4.83 Linear (SSR = 4.83)  —  —  SSR = 2,44 Linear (SSR = 9.64)  --  y=-0.0115x+2.4861 =0.9649 2 R  -  2  %%  1  0%. 4  y  4  4  -  -  -0.0339x + 2.863 1 = 0.9796  =  -0.0286x + 3.3429 2 = 0.9677 R  -2 -3  . 0  —4  -4-  -4 -5 0  50  100  150  200  Time (mm)  Figure 3.2  Linear form of the first order kinetic of struvite precipitation with different SSR values  57  —e—Mg:P=1.0  35  -A--Mg:P=1.3  -e—Mg:P=1.6  30 25 20 15 0  110 0 0  50  100  150  200  250  Time (mm)  Figure 3.3  Variation of ortho-P concentration with the reaction time for different Mg:P ratios  58  Mg:P=1.O  0  4  —  3.  -  A  Linear(Mg:P=1.O)  -  -  Mg:P=1.3 -  0  Linear(Mg:P=1.3)  —  Mg:P=1.6 —Linear(Mg:P=1.6)  %. —.  c  2  y=-0.0157x+3.291 2 = 0.986 R  -  %s4  1•  %  o  y=-0.0452x+3.161 1  =0.9717 2 R  .  %..  A. y = -0.0339x  —  +  2.863 1  2 = 0.9796 R  -2 0  -3  A A  -4. 5. 0  I  I  50  100  150  200  Time (mm)  Figure 3.4  Linear form of the first order kinetic of ortho-P removal for different Mg:P ratios  59  ——Mg:P=1.3;RPM=1OO  40  -  O  Mg:P=1.3;RPM=70  35  I  30 25  0  20  0  15  I  0  10 •0  5 0 0  50  100  150 Time  Figure 3.5  200  250  (mm)  Variation of ortho-P concentration with the reaction time for different stirrer speeds  60  40  -  Unseeded  Seeded  35 30  25 0  20 I  0 -‘  15  0  S  10  5 0 0  50  100  150  200  250  Time (mm)  Figure 3.6  Variation of ortho-P concentration with the reaction time for seeded and unseeded conditions  61  3.5  References  Adnan, A., Mavinic, D.S., and Koch, F.A. (2003). Pilot-scale study of phosphorus recovery through struvite crystallization examining the process feasibility. J. Environ. Eng. Sci. 2, 315-324. —  Adnan, A., Dastur, M., Mavinic, D.S., and Koch, F.A. (2004). Preliminary investigation into factors affecting controlled struvite crystallization at the bench scale. J. Environ. Eng. Sci. 3, 195-202. Booram, C. V., Smith, R.J. and Hazen, T.E. (1975). Crystalline phosphate precipitation from anaerobic animal waste treatment lagoon liquors. Trans. ASAE, 18, 340-343. Bouropoulos, N.Ch., and Koutsoukos, P.G. (2000). Spontaneous precipitation of struvite from aqueous solutions. J. Crvst. Growth, 213, 381—388. Nelson, N.O., Mikkelsen, R.L., and Hesterberg, D.L. (2003). Struvite precipitation in anaerobic swine lagoon liquid: effect of pH and Mg:P ratio and determination of rate constants. Bioresour. Technol. 89, 229-236. Ohlinger, K.N., Young, T.M., and Schroeder, E.D. (1998). Predicting struvite formation in digestion. Water Res. 32, 3607-36 14. Ohlinger, K.N., Young, T.M., and Schroeder, E.D. (1999). Kinetic effects on preferential struvite accumulation in wastewater. J. Environ. Eng. 125, 730-737. Ohlinger, K.N., Young, T.M., and Schroeder, E.D. (2000). Post digestion struvite precipitation using a fluidized bed reactor. J. Environ. Eng. 126, 36 1-368. Quintana, M., Sanchez, E., Colmenarejo, J., Barrera, J., Garcia, G., and Borja, R. (2005). Kinetics of phosphorus removal and struvite formation by the utilization of by-product of magnesium oxide production. Chem. Eng. Jour. 111,45-52. Ven Rensburg, P.E., Musvoto, V., Wentzel, M.C., and Ekama, G.A. (2003). Modeling multiple mineral precipitation in anaerobic digester liquor. Water Res. 37, 3087-3097. Wang, J., Burken, J.G., and Zhang, X. J. (2006). Effect of seeding materials and mixing strength on struvite precipitation. Water Environ. Res. 78(2), 125-132. Yoshino, M., Tsuno, H., and Somiya, I. (2003). Removal and recovery of phosphate and ammonium as struvite from supernatant in anaerobic digestion. Water Sci. Technol. 48, 171178.  62  Chapter 4  Fluidization characteristics of struvite crystals produced from wastewater treatment plants 3  4.1  Introduction The expenditures associated with the disposal of additional phosphate sludge, the  stringent regulations to limit phosphate discharge to the aquatic environments and resource shortages due to limited phosphorus rock reserves have diverted attention to phosphorus recovery from wastewater, leading to production of a high-value slow release fertilizer called struvite (Yoshino et al., 2003). The species composed of magnesium, ammonium and phosphate ions detected in wastewater bind together to form a crystal called struvite or simply MAP [Magnesium Ammonium Phosphate] 0 2 . (Mg.NH . 4 6H P0 ). The struvite crystals can readily be used for vegetable gardening, golf courses and as supplements for salmon hatcheries. Considering the crystallization process as a viable option for recovering nutrients from wastewater, different types of crystallizers have been proposed and tested by different research groups. Today, two main types of reactors are being used for recovering phosphorus from wastewater: mechanically agitated reactors; and fluidized bed crystallizers. Although stirred tank reactors are abundantly used in the field of industrial crystallization, the fluidized bed reactors have been frequently used for the production of large sized uniform crystals by seeded crystal growth in a bed and fluidized by a moderately supersaturated solution of the solute, which needs to be precipitated.  A version of this chapter will be submitted for publication. Rahaman, M.S., Mavinic, D.S., and Ellis, N. (2009). Fluidization characteristics of struvite crystals produced from wastewater treatment plants. In preparation.  63  In recovering phosphorus from wastewater, the fluidized bed reactor, FBR, configuration is often selected because a fluidized bed crystallizer can conveniently produce uniform sized large crystals. These crystals processed from fluidized bed acquire spheroidal shape with relatively rough substrate morphology. Along with the physical chemical properties, the knowledge of liquid-solid fluidization characteristics of struvite particles is essential in designing and operating an FBR. Although citations on liquid-solid fluidization is not extensive, if compared to the gas-solid systems, numerous studies are found to be applicable on liquid-solid fluidized bed with ideal systems primarily composed of spherical particles and water. In reality, processes such as crystallization may produce nonspherical and irregular shaped crystals in a fluid phase of saturated solution other than an aqueous medium. Hence, the various relationships relating liquid solids dynamics (reported in the literature), must be adjusted for the cases that deviate from ideal conditions. Despite the very promising future of struvite crystals production from wastewater in a fluidized bed reactor, no data exist in the literature associated with fluidization characteristics of struvite crystals. Therefore, in this study, struvite particle characterization and fluidization behaviour is analyzed extensively. In order to characterize the struvite particles, several intrinsic static parameters such as particle density, size, shape and morphology are studied; as well, terminal settling velocity, drag coefficient, minimum fluidization velocity and the bed expansion characteristics are important parameters to be determined. Furthermore, the applicability of existing correlations for liquid-solid fluidized bed hydrodynamics is examined for the case of fluidized bed struvite crystallization systems. Information obtained from this work is expected to become a useful reference for efficient design and operation of the fluidized bed crystallizer for recovering phosphorus through struvite crystallization.  64  4.2  Materials and methods Struvite crystallization in a fluidized bed reactor results in various crystal sizes in the  reactor. Thus, fluidization characteristics have been studied for a wide range of sizes of struvite crystals produced in wastewater treatment plants. The struvite crystals produced in the Edmond full scale phosphorus recovery plant were categorized into six different classes according to their sizes (A, B, C, D, E & F; size decreases from A to F). Even though the struvite crystals are sparingly soluble in water, to avoid any growth or dissolution in the mother liquor, saturated solutions in terms of struvite were prepared and used for all fluidization experimental tests. Initially, different sizes of crystals were characterized in terms of their size, shape and density and then significant basic hydrodynamic characteristics, such as terminal setting velocity, minimum fluidization velocity and bed expansion behaviour were studied with respect to specific size class of struvite crystals. In order to reveal the bed expansion characteristics, some combination of different size class were also reported.  4.2.1  Density determination Pure struvite crystals have an established cited density value of 1730 kg/rn . However, 3  during the crystallization processes, due to occurrence of different simultaneous phenomena, such as nucleation, growth and agglomeration, the density of product crystals may differ from those of pure struvite crystals. Therefore, the density of each different size class of struvite crystals was determined in this current study. The struvite crystals mentioned in this study were produced from the Edmonton full-scale P-recovery plant, run by OSTARA Nutrient Recovery Technologies Inc., Vancouver, BC, Canada. Crystals were classified as  65  different size classes by performing sieve analyses using standard sieves. The density of each size class was then determined by a displacement technique. In order to determine the apparent wet density of struvite particles, saturated surface dry condition (SSD) of struvite crystals was maintained. The term SSD is used to describe the condition of wet particles with no water on the outer surface. The SSD condition was approximated by soaking the particles and then drying them by spreading for 15 minutes on a paper towel. The following procedure was used to determine the densities of struvite crystals at SSD and dry conditions. 1) The struvite particles were soaked in water for 5 to 10 minutes in order to fill their pores with water. 2) An empty weighing dish was weighed and the mass was recorded as  Mdjh  3) A graduated cylinder was filled with 50 (±0.1) ml of water and mass recorded as . 50 M 4) The graduated cylinder was emptied and the struvite crystals were placed in it and then the cylinder was refilled with water up to the 50-ml (±0.1) mark. The weight was recorded as 50 M . 5) The water was carefully decanted and the struvite particles were spread on the paper towel to remove water from the outer surface 6) Saturated Surface Dry (SSD) struvite particles were transferred to the weighing dish and their weight was recorded as MssD+djh 7) In order to determine the dry density, the particles were allowed to dry at room temperature until the mass was constant with time (typically 3 to 4 days). The dry weight was then recorded as Md+djh  66  8) The density is then calculated as follows: MssD, in =MssD+djsh  50 MSSD, in water = M  —  —  Mdh  M 5 0  Vparticies = (MssD, in air MSSD, in water) Ip i —  Ps,ssd = MssD, in air’ Vparticies  Md = Md,+djh  —  Mdjh  Ps,dry = Mdry/ Vparticies  where, Pt and Ps are the density of liquid and solid struvite crystal, respectively.  4.2.2  Size Initial screening of struvite particles was performed using standard sieves. The  standard sieves used in this cunent study were # 8, 10, 18, 20, 30, 35, 60, 120 and the size ranges from 500 urn to 2.36 mm. For each size class, representative fractions of struvite crystals were taken and analyzed using a microscope to determine the size in terms of Martin’s diameter, which was the average of the four different diameters taken at 0, 45, 90 and 135 degree angles. These diameters were taken as the distance from one edge to another, passing though the center of gravity of the particles.  4.2.3  Determination of terminal settling velocity Terminal settling velocity of struvite particles was measured in a 0.7 m high circular  column of diameter 0.1 m, filled with water. Five to ten particles from same size group were introduced into the water column from the top and the terminal velocity was measured by obtaining time taken for the particles to drop a measured distance through the fluid (water,  67  with density of 998.2 kg/rn ) of a known viscosity value of 0.001003 Pa.s. In order to 3 determine the time taken by the particles to travel a known distance freely, a computer model was developed to capture the initial time and the moment at which the particles cross the final line. The enter key on the keyboard was pressed every time the particles cross the set end line. In order to avoid errors in the measurements, initial time was computed when the particles attained their terminal velocities. Also, in determining the terminal velocity, particle collisions were considered negligible. An identical assumption was considered by Ellis et al. (1996), in determining the free-fall terminal velocity for biobone particles.  4.2.4  Fluidization column The fluidized-bed column was built of Plexiglas and had an inner diameter of 0.10 m  and a height of 1.118 m. An expanded section, having a diameter of 0.191 m and a height of 0.254 m, was placed on top of the reactor, and was used as a seed hopper. The liquid, used in this study, was a saturated solution of struvite and the solids were struvite crystals. The liquid was pumped from a storage tank and distributed into the bed through a 3-mm thick perforated grid with 130 holes of 2 mm dia on 7-mm pitch. The distributor was used to ensure uniform longitudinal (axial) liquid velocity distribution above the distributor and was confirmed by the fact that the grid pressure drop was always greater than 20% of the total fluidized bed pressure drop. Jackson (1985) found that the ratio of distributor to fluidized-bed pressure drop should exceed 0.2 in order to suppress the convective instabilities in a large diameter (1 m) bed, while lower values of this ratio should be sufficient for smaller bed diameters. A calming section, having plastic balls, was also introduced just before the distributor, to ensure uniform flow distribution. The liquid flow rate was measured with a  68  calibrated rotameter. The reactor was filled with struvite crystals of different mono-sizes in different experimental conditions, with varying maximum packed bed heights. A complete list of experimental conditions is given in Table 4.1. The experiments were run in a controlled room at a temperature of 20 °C. The reactor was equipped with 13 pressure ports connected to the L-shaped liquid manometers. A schematic of the experimental set-up is presented in Figure 4.1. The ranges of upflow velocities associated with the fluidization experiments were such that uniform homogenous fluidization behaviour prevailed. The bed height could be determined visually and the overall solids volume fraction was calculated from bed height and initial volume of the struvite crystals used. The overall liquid volume fraction can be estimated from the pressure drop data obtained through manometer readings.  4.3  Results and discussion In the first part of this study, a wide range of sizes of struvite crystals were  characterized in terms of their size, shape and density. The fundamental characteristics parameters for different sizes of crystals are discussed below.  4.3.1  Size and shape of struvite crystals Crystal characterization, in terms of size and shape, is important in all aspects of  crystal production, manufacturing, handling, processing and applications. Therefore, a complete characterization of solid particles is the foremost task in any crystallization processes. In this current study, six groups of struvite crystals were categorized according to their sizes (see Table 4.1), and were carefully sieved in a close size range from a batch lot of  69  struvite crystals, produced from the Edmonton full scale P-recovery plant. The crystals of each specific size class were then studied under the microscope and characterized by the following different characteristic dimensions. 1) Martin’s diameter: the average of the four “diameters” taken at angles of 0, 45, 90 and 135 degree (a ‘diameter’ goes from edge to edge, through the center of the projected outline of the particle). Martin’s diameter was determined by image analysis. 2) The diameter of the sphere having the same volume as the particles, d, was determined by weighing more than 100 crystals from each specific size classes. The volume equivalent diameter (dy) was then calculated by using the following relationship,  d  =  /  6M  (4.2)  2 Ps,ci,y  where, M is the total mass of z number of particles. 3) Spherical diameter is the diameter of a sphere having the same projected area of the particle when it sits on the plane of the greatest stability and was determined using image analysis. 4) Feret’s diameter is the greatest distance possible between any two points along the periphery of a particle. 5) Aspect ratio: Defined as the ratio of the particle’s smallest diameter to its largest diameter. 6) Circularity is the ratio of the circumference of circle having same projected area as the particle to the actual perimeter of the projected area of particle. All the above mentioned characteristic dimensions, along with the density of each struvite size groups, are summarized in Table 4.2. A feature very transparent from the data set is that for all size groups (except particles D [1—i .18 mmj), both the average values of 70  Martin’s and projected area diameters are higher than the top screen sizes. This implies that the struvite particles studied in this paper were not ideally spherical. More than 50% of the crystals of the size classes A [2—2.2 mm] and B [1.68—1.98 1 mm], were observed to have the smallest diameter greater than the top screen size used in the sieve analysis. It reveals that the thickness of the particles of those size classes is probably lower than any Feret’ s diameters that are determined at their most stable orientations. This allows a significant portion of struvite crystals classified to the size classes A and B to pass through the top screen. This can only be happened if the largest dimension of the particles is lower than the diagonal of the opening of a particular sieve. Noting the shape factors (aspect ratio and circularity), it can be inferred that the larger particles are closer to the circular shape, whereas the smaller ones E [0.6—0.833 mm] and F [0.5—0.6 mm] deviate more from the circular geometry and resemble an elliptical shape. The reason for this difference in shape between smaller and larger crystals may be due to the fact that different mechanisms were in place during the crystal enlargements of different sizes of crystals. Although both the aspect ratio and the circularity factors for most of the larger particles approach close proximation to the spherical shape, the small sized particles are not considered as completely spherical, rather they could be approximated as ellipsoids. The sphericity of each size group was determined by measuring pressure drops due to flow of water through a fixed bed of struvite crystals and the data obtained were then interpreted using well established Ergun equation as follows (Ergun, 1952): =  150  (1— cx 1 ,u 2 ) U  +1.75  2 (1— a U 1 p ) 1 3 1 ia  (43)  71  where:  AP is the pressure drop across the bed, H is the static bed height (height at fixed bed  condition), P1 is the viscosity of the liquid, U is the upflow superficial liquid velocity, d is the volume equivalent spherical diameter of particles,  0 is the sphericity and at is the liquid  volume fraction (voidage) of the bed. Sphericity was estimated by plotting pressure gradients against upflow liquid velocities, and best fitting the Ergun equation with the experimental results for each size groups. Figure 4.2 displays the measured pressure drop over a fixed bed length for the different struvite crystal size classes as a function of liquid superficial velocity. The pressure drop pattern follows the general trends shown by the fixed bed pressure drop experiments, i.e., pressure gradient increases with increasing upflow velocity and particles with smaller diameter exhibiting higher pressure drop at the same upflow velocity.  However, the  calculated values of pressure gradients, using Ergun equation, are lower (10 to 30%) than the experimental ones for all the size classes of struvite crystals studied in this chapter. The reason for this inconsistency between estimated and the experimental results is due to the fact that in estimating the pressure drop using Ergun equation the struvite particles are considered as spherical  (0 =1), though the particles were found to possesses a spheroidal shape. This  requires determination of sphericity of struvite crystals and the estimated sphericity values for struvite particles range from 0.811 to 0.9 154 [reported in Table 4.2].  4.3.2  Terminal settling velocity (Ui) Terminal settling velocity is a significant parameter in design and operation of a  fluidized bed reactor. The terminal settling velocity is the highest velocity at which the bed crystals can be fluidized, without any wash away or entrainment effects. Beyond this velocity 72  the fluid bed becomes a diffused zone and is considered within the fast fluidization regime. A handful of crystals from each size group were taken and tested for the terminal settling velocity. The calculated average and median values of the terminal settling velocities are reported in Table 4.3. It is observed in Table 4.3 that the mean and median values are very close to each other for all size classes, which implies that the crystal size distribution within each size groups, studied in this work, is normally distributed. However, a significant standard deviation ranging from 0.225 to 0.659 cmls, occurred in each series of experiments owing to non-uniformity of struvite crystal sizes within each size group. Both the fluidization and terminal settling velocity determinations were performed in the same size (diameter of 10 cm) of column. However, for comparing the experimental results with those estimated using the correlations available in the literature, the wall effect should be considered and hence the terminal velocities determined experimentally are corrected using the correlation provided by Landenburg (1907). The correlation is as follows: U = Urexp[1 +  (4.4)  where, U is the terminal settling velocity corrected for wall effects, Ut(exp) is the experimentally determined terminal settling velocity (with wall effect), and D is the diameter of the column. The terminal settling velocities corrected for wall effects are presented in Table 4.3. In order to compare the experimental results found in this study, terminal velocities for each size group were also estimated using five different correlations and the values are presented in Table 4.3. One noticeable feature is that the correlation by Fair and Geyer (1954), generally used for settling velocity calculation in environmental engineering design, yields the largest deviation (23-42%) from the experimental terminal settling velocities of struvite, so does the direct method by Turton and Clark (1987). Among all the 73  correlations considered in this study, Clift et al. (1978), Turton and Levenspiel (1986) and Haider and Levenspiel (1989) are found to estimate near identical values for a particular size group (as shown in Table 4.3). However, each of the existing models does overestimate the terminal velocities for the size ranges of the particles studied in this paper. It is noteworthy that the estimated terminal settling velocities of particle size groups A, B and C are considerably higher than the experimental values after corrected with the wall effects: the average deviation for these 3 classes of particles is more than 27%. The deviations for the smaller particle size groups (D, E and F) are relatively low.  This higher deviation for the  larger particle groups may be attributed to the fact that though the particles resemble spheroid shapes in their stable orientation, the thickness is significantly lower than any dimensions at its stable orientation. It can also be observed from the sphericity factors, that these values are lower for larger particles than proportionately smaller ones. It is worth mentioning that in all the calculations, using different correlations, the volume equivalent diameter is used as the representative average particle size. The volume equivalent diameter was selected as the characteristic dimension. This is based on the assumption that the struvite crystals are spheroidal in shape and during their fall, the crystals revolve, thus presenting different section perpendicular to the vertical direction. These two facts make it reasonable to consider volume equivalent diameter as the characteristic dimension. Since none of the existing correlations tested in this study estimates close enough terminal settling velocity for the size groups of struvite crystals, determination of terminal settling velocity using any of those correlations will generate erroneous values. As the terminal settling velocity is one of the very important design criteria for the fluidized bed crystallizer, the values should either be determined experimentally or a new correlation  74  developed to accurately estimate the terminal velocity of struvite crystals. The reactor should be operated at an upflow velocity, lower than the terminal settling velocities of the particles, in order to avoid any wash away or entrainments problems. The values of terminal settling velocities generated, using Clift et a!. (1978) correlations, are consistent with the average experimental terminal velocities (corrected for wall effects). Figure 4.3 displays a linear correlation between those two terminal settling velocities for the range of particle sizes studied in this work. As such, the terminal settling velocity, for any size of struvite crystals, can be determined by using this correlation, once the terminal velocities are estimated using the correlations provided by Clift et al. (1978). The difference in terminal settling velocity arises due to the usage of various drag laws at different correlations. The drag laws define the correlation for the drag coefficients (Cd) and link the Cd value with Reynolds number, at the particle settling velocity.  4.3.3  Minimum fluidization velocity (Umf) The minimum fluidization velocity is another essential parameter in designing a  fluidized bed crystallizer. This corresponds to the minimum upflow velocity at which the bed can be considered as a fluidized bed. The minimum fluidization velocities for different size classes of struvite are determined experimentally and the values are compared with the predicted minimum fluidization velocities, estimated using different existing correlations found in the literature. Experiments were performed by increasing the upflow velocities and determining the pressure drop. The same thing was reversed by decreasing the upflow velocity from the complete fluidized condition. The upflow velocities at which pressure drop is slated to be the maximum, is called the “minimum fluidization velocity”. Minimum  75  fluidization velocity is determined by plotting pressure gradient versus upflow velocity both for increasing and decreasing water flow rate. A typical plot for the particle size groups of C and D is shown in Figure 4.4. It is very clear from the Figure 4.4 that the pressure drop increases with increasing upflow velocity and reaches a constant value at two different upflow velocities for the size groups C and D. By increasing the liquid velocity from a fixed bed, the bed pressure drop reaches a maximum, due to the partial bridging of the interlocked particles resulting in the frictional forces exerted by the walls, before dropping down to the theoretical value (Richardson, 1971). Therefore, in order to obtain reproducible fluidization data, the general consensus is to use the pressure drop data with decreasing upflow velocity. As presented in Figure 4.4, the minimum fluidization velocities were found to be 6.8 mm/s and 3.37 mm/s for C and D particles, respectively. Experimental values for Umj of different sizes of struvite crystals are summarized in Table 4.4. The minimum fluidization velocity can also be estimated using the expression for pressure drop in a fixed bed extendable up to minimum fluidization velocity. The most general form of expression for the pressure drop through a fixed bed of particulate solids can be written as:  H  =  f  p 6(1— a 2 U 1 ) 1 2  where, the bed friction factor  (45) ) and the particle Reynolds 1 (t) is a function of bed voidage (a  number at terminal settlmg velocity, Re  dUp =  and can be expressed by the equation,  proposed by Ergun (1952) as follows:  76  = 150(1 a ) 1 +1.75 ØRe, —  -(4.6).  At the minimum fluidization condition, taking  = (Pd  —  1 )O p  —  almf  )g, the Equation  4.5 becomes 1  Ar =  Re  2  f  (4.7)  where, . 111 is the bed voidage at minimum fluidization velocity (Urnf), g is the acceleration a due to gravity (9.81 2 mIs ) , Rernf is the Reynolds number at minimum fluidization velocity, Umf 1 p dV 11 = Re,,  (4.8)  /11  and Ar is the Archimedes number, Ar  =1 p ( 3 d p1 —p ) g  (4.9).  1 p Combining Equations 4.6 and 4.7 at Urnf condition and rearranging: 1.75 1 fta  + 2150 2 Re  (1— aln)Remf  0  =  Ar  (4.10)  The Equation 4.10 is of quadratic nature and can be solved as Re,, = (C Ar) 2 C 1 + 112  where C 1 =  —  1 150(1—a 20(1.75)  1 C  )  (4.11)  = 42.86  1 (1—a  )  (4.12)  = and C 2  = 0.5714Øa,,, 3  (4.13)  The values of C 1 and C 2 depend on both sphericity and the voidage at minimum fluidization condition. If the values for both  0  and al,flf are precisely known, the C 1 and C 2 values can be  calculated using Equation 4.12 and 4.13 and the Rernf and hence, the Urnf can be calculated 77  using Equation 4.10. Based on the experimental results, different researchers proposed different sets of values for C 1 and C . Among them the values provided by Wen and Yu 2 (1966) are commonly used. Taking C 1 and C 2 values of Wen and Yu (1966), the Equation 4.11 becomes, Re,  [(33•7)2  If  is not known but a reasonable estimate of  2 —33.7 +0.0408Ar]”  (4.14)  0  is available, then Epstein (2003)  recommends that C 1 and C 2 be chosen from the values found by Lucas et al. (1986), as follows: 1 C  =  29.5; C 2  =  0.0357, for Round granular particles (0.8<0<1)  1 C  =  32.1; C 2  =  0.0571, for sharp jagged particles (0.5<0<0.8)  1 C  =  25.2; C 2  =  0.0672, for other particles, e.g. rings, (0.1<0<0.5)  All the size classes of particles used in this study possess sphericity values greater than 0.8. Hence taking C 1 Re,flf  =  =  [(29.5)2 +  29.5 and C 2  2 0.0357Arj”  =  —  0.357, Equation 4.11 becomes, 29.5  (4.15)  The voidage at minimum fluidization, a can be determined experimentally by fluidizing the struvite particles with water in the column and shutting off the liquid flow quickly. The ratio of particle volume and the collapsed bed volume represents (1—  The al,?!I. values  for different size classes of struvite used in this study are reported in Table 4.4. The experimental values for  are then compared with the correlations provided by  Wen and Yu (1966) and Chen (1987). Wen and Yu (1966) provided two different  78  correlations covering a wide range of particle size (50 pm to 50 mm), as well as a large voidage (0.385—0.935) and sphericity range (0.136—1). The correlations are as follows: 1 1-a  0  ‘  2  =11  (4.16)  14  (4.17)  =  0alflf  Therefore, both the correlation values were compared with the experimental results in order to test the applicability of those correlations for the case of struvite crystals. Another correlations provided by Chen (1987) is, (4.18).  =  Both Umf and a ,, values, determined through experimental works as well as estimated using 1 aforementioned correlations are summarized in Table 4.4. The minimum fluidization velocity can also be estimated using different empirical correlations developed for more restrictive conditions. Riba et al. (1978) proposed a correlation by fitting data for a wide variety of experimental conditions in the Remf range 101000. The correlation is as follows: O.O4  Re,,  =  0.0154Ar0661 Ps,ssd Pt  —  “1  (4.19)  )  A comparison of voidage at minimum fluidization velocity, a 111 is presented in Table 4.4. It is found that the correlation proposed by Chen (1987) [Eq. 4.18] and Wen and Yu (1966) [Eq. 4.16] result in very close values of  and those values are in good agreement with the  values determined experimentally (average deviation 5%). The deviation was highest for the values determined using the correlation provided by Wen and Yu (1966) [Eq. 4.17]. 79  The minimum fluidization velocities for different size classes were estimated using the pressure drop method, taking the parameters values from Wen and Yu (1966) and Lucas et al. (1986). Both the correlations overestimate the Umf for all the size classes except F [0.5— 0.6 mm]. Since the sphericities of all size group fall between 0.8—0.9, the prediction using the Lucas et al. (1986) reported closer estimation to the experimental values. The deviations from the experimental values are still high (around 20%). From the particles characteristics such as circularity, aspect ratio and the sphericity, it is obvious that struvite particle shapes closely resemble a spheroid. Hence, the use of Riba et al. (1978) correlation provides very useful data on Urnf and is in close agreement with this experimental data. As is the case for other correlations, the estimation by Riba et al. (1978) also overestimates the U values for all size ranges. However, the deviation is higher for medium size particles tested in this study. Therefore, care should be taken while estimating the Umf, especially for the case of smaller particles. As Riba et a!. (1978) provides conservative values of Umf for all size groups, it is recommended that this correlation could be utilized for design purposes, if the Umf is not experimentally evaluated. However, for particle size less than 1mm, both Wen and Yu (1966) and Lucas et a!. (1986) provide reasonable agreement with the experimental values.  4.3.4  Bed expansion behaviour of monosized struvite crystals A quantitative knowledge of bed expansion as a function of the liquid superficial  velocity is essential for efficient design of a fluidized bed reactor. Due to the lack of a theoretical model capable of identifying the dependencies on the physical parameters, empiricism has remained the preferred approach.  A number of researchers, including  Richardson and Zaki (1954), Wen and Yu (1966) and Riba and Couderc (1977), have worked  80  to develop correlations between the expansion of liquid-solid fluidized beds of spherical single particles and the liquid superficial velocity. Among all these correlations, the Richardson and Zaki (1954) correlation has been most extensively used to predict the expansion of single component beds. The correlation provided by Richardson and Zaki (1954) is as follows, =  ” 1 a  (4.20)  where, the bed expansion index, n is solely a function of the particle Reynolds number (Ret) at terminal settling velocity and following correlations were recommended based on the experimental data of the bed expansion. n=4.65  Re < 1 O.2  n  =  3 4.4xRe°°  0.2<Re<1  n  =  01 4.4xRe,  1<Re < 1 500  n=2.4  (4.21)  50O<Re  Rowe (1987), using the same data, proposed a single relationship applicable to the entire flow range: —  n—2.35  =  0.175 Re° 75  (4.22)  Khan and Richardson (1989) repeated the same exercise and fitted the data with the Galileo number as follows: 4.8 n—2.4 —  =  57 0.043Ga°  (4.23)  where, Ga is the Galileo number.  81  Garside and Al-Dibouni (1977) proposed the following correlation for estimating n, which generates values of n some 10% greater than that of the corresponding Richardson and Zaki correlation. 5.1—n 9 =0.lRe° n—2.7  (4.24)  Five sets of bed expansion tests were performed with reference to the crystals size classes reported in Table 4.1. The results obtained in terms of logarithmic velocity-voidage are well fitted by straight lines (Fig. 4.5), in agreement with the Richardson-Zaki relationship. The values of correlation coefficient of the straight lines always exceed 97%, as reported in Table 4.5. The parameters of the fitting curves are also tabulated in Table 4.5. By comparing the values of fitting parameters U (in Table 4.5) with the corresponding experimental settling velocities (in Table 4.3), it is apparent that the estimated parameter U is always higher than the terminal settling velocity experimentally determined in this study. As the voidage converges to unity, the superficial velocity should approach the terminal settling velocity, but the extrapolation generates higher velocity values. The average ratio between Ut(exp) and the U is about 0.9. The observed expansion behaviour is characterized by two different regimes. The initial region of bed expansion characteristic can be well represented by the Richardson-Zaki equation. However, the variance in slope is observed at higher voidage values and this corresponds to the slope decrease with increase in voidage. The data sets presented in this Chapter do not display the second regime. The experiments at higher voidage were intentionally excluded because the bed height can not be accurately determined at higher voidage. Various researchers’ works could be mentioned as evidence of the existence of this behaviour. To name a few, Richardson and Zaki (1954) with reference to data of Lewis et al. 82  (1949), Chong et al. (1979) and Fan et al. (1985) works are highly relevant. The observed change in the slope is noted to be a function of the Galileo number (Ga) and varies from 0.85 to 0.70, as Ga increases. The expansion index ‘n’ for all the size classes were also calculated using some well established correlations (mentioned in the earlier section) and are reported in Table 4.5. The experimental values of the expansion index for all crystals sizes are higher than those estimated using the existing correlations. However, the correlation provided by Garside and Al-Dibouni (1977) generates the lowest deviations. The same observation was reported by Fan et al. (1985) for a similar type of expansion behaviour observed in this study. As none of the existing correlations for expansion index provides approximate values for the struvite crystals, an attempt was made to modify the existing Richardson-Zaki correlation, for the range of particle sizes studied in this paper. This was done by fitting the experimentally determined terminal settling velocities and the expansion index on the well-established Richardson-Zaki relationship, which modifies the existing correlation as follows. n = 4.7718xRe°° 89  for 26< Re <302  (4.25)  Figure 4.6 compares the n values determined experimentally and calculated using the above correlation. A close agreement between the values can be found.  4.3.5  Minimum fluidization velocity for multiparticle systems As the fluidized bed crystallizer is usually considered as a classifying crystallizer,  particle sizes ranging from the seed size to the product crystals size are likely to be present in the crystal bed. Unlike single particle fluidized beds, for which there is a well-defined single minimum fluidization velocity, there is a range of velocities over which the fixed and  83  fluidized bed behaviour exists simultaneously for multi-particle systems (Epstein, 1984; Kwauk, 1992). This is because different particle sizes have different minimum fluidization velocities. In this study, three different mixtures of particles with different size ranges are tested for the minimum fluidization velocity. Particles sizes and their combination in the three different mixtures are presented in Table 4.1, in methods and materials section. The group ‘MS’ represents the mixture of 3 smaller size classes (D, E and F), used in the fluidization study of mono-dispersed crystals; group ‘ML’ represents a mixture of the three larger sizes of crystals (A, C and D) and finally group ‘MC’ represents the complete mixture of 6 different size classes (A, B, C, D, E and F), used in the earlier study of mono-component fluidized bed. For multi-particle systems, the sharp transition from the fixed bed to fluidized state (as in the case of Fig 4.4) no longer exists in the pressure drop-upflow liquid velocity curve. Rather, a gradual transition from the fully fixed bed to fully fluidized bed is observed with increasing superficial liquid velocity, especially when the fixed bed condition attained is from the fluidized state by decreasing the liquid superficial velocity. This phenomenon is evident in Figure 4.7. Similar behaviour is reported in the literature (Couderc, 1985). In this situation, three different velocities are observed with the transition from the fixed bed to the fluidized bed state. First, the velocity at which the initial deviation (point X) from the fixed bed line occurs is defined as the velocity for initiation of fluidization, Ubf. Other velocities are the ones at which the deviation merges (point Z) with the constant pressure drop line, known as velocity for total fluidization, Uc and the velocity at the intersection (point Y) of the extrapolated fixed bed line and the fluidized bed line, is known as the apparent minimum fluidization velocity, Umfa (Obata et al., 1982). The correlations for predicting the minimum  84  fluidization velocity for single particle system can still be used for calculating the Ubf and Ur approximately, with d taken as the smallest and the largest particle size, respectively. The same equation can also be used to estimate Umfa, by taking the d as the Sauter or reciprocal mean diameter (Jean and Fan, 1998), d =  1 N  (4.26)  (x / d) Where, x 1 is the volume fraction of size group i, d 1 is the diameter of size group i and N is the total number of size classes. The three different fluidization velocities corresponding to the three different mixtures are experimentally determined. The values are tabulated in Table 4.6. For all the three cases, Urf is determined to be almost identical to the minimum fluidization velocity for the largest particle present in a particular mixture of struvite crystals. However, the onset of the fluidized condition was observed at slightly lower upflow velocities than the values noted for the corresponding smallest particle sizes isolated in that particular group of mixed particles.  4.3.6  Bed expansion behaviour of multiparticle systems An accurate prediction of the bed expansion is especially important for this current  study. The bed height is critical for liquid solid fluidized bed crystallizer design and particle volume fraction prediction. For multi-particle fluidized bed systems, particles may segregate completely according to species, segregate incompletely or mix completely. Generally, if the particles characteristics are fairly even: with identical density and close enough sizes, an averaging model, which assumes that the mixed bed behaves as the equivalent of a single component bed by applying some average of particle size and density, can be used to predict  85  the overall expansion. This is termed as the “average model” (Kunii and Levenspiel, 1969; Epstein et al., 1981). A generalized version of Richardson-Zaki correlation was used by Asif (1998) for prediction of expansion behaviour of liquid fluidization of the binary solids. The author used average particle size and the density for determining the U, and n for the Richardson-Zaki correlation. In this study, the same averaging approach was used and the method was extended for the multi-particle system (more than 2 components). With the approach used by Asif (1998) the average diameter and density were evaluated as d  1 =  N  xi  1=1  v  (4.27)  (4.28) =  where, x is the volume fraction of size group i, defined as xi = NCI  (4.29)  c,  where, C 1 represents the volumetric concentration of particle species i and  is the density  of struvite class i at SSD condition. If the size and density of the particle species differ significantly, particle segregation phenomena can occur in the fluidized bed. In this case, the pseudo-single species approach is no longer suitable for predicting overall bed expansion (As if, 2001; Bhattacharya and Dutta, 2002). Wen and Yu (1966) suggested that for the binary mixture of the particles of the same density, the average model is not appropriate when the size ratio is greater than about 1.3. A relative velocity model is used by Lockett and Al-Habbooby (1973) to measure the bed expansion of a mixture in a continuous fluidized bed. Later, Yu and Shi (1985) displayed that 86  the relative velocity model was not applicable for steady-state batch operations. It has been reported by Lewis and Bowerman (1952) and Richardson and Zaki (1954), that the serial model can be used to predict the expansion of the mixtures. The model assumes that the overall bed expands as if it were simply the sum of the n individual species, each acting independently of the other. For the mixture of N species,  1- a 1 =  [‘ 1  (4.30) —,  where, a 1 is the voidage when species i is fluidized alone at the same superficial liquid velocity as the mixture. Similarly, the bed height of mixtures can be estimated by the serial model as follows: H  = i1  M 1 A(1  —  1) a  (4.31)  where, H 1 is the total expanded bed height of a mixture, M 1 is the mass of species i charged to the bed, A is the cross sectional area of the bed. In predicting the bed expansion characteristics, the first approach is used for a completely mixed situation and the second one is used for the case of complete segregation. But neither approach is conceptually appropriate for the intermediate situations, since the degree of mixing is not considered in either case. In this current study, both the average and serial models were exploited to predict the bed expansion of the three different mixtures of multi-particle systems. The predicted bed expansion characteristics, voidage and the expanded bed heights for the mixtures, are compared in Figures 4.8, 4.9 and 4.10. It is evident that the experimental results match reasonably well with the serial model. In relation to the fluidization run of MS and MC, both the expanded bed height and the overall bed  87  voidage were determined using the serial model. It matched very closely with the experimental results, with an average deviation of only 1%. The similar observation was reported by Epstein et al. (1981) and Howley and Glasser (2002). The prediction by either model deviates significantly in the case of the ML group. The reason may be due to presence of larger struvite crystals in this size group. The upflow velocity employed for this case was not sufficient enough to rearrange the crystals in accordance to their size classes. Therefore, significant amount of smaller crystals may be entrapped within the larger crystals, which prevented the bed from expanding at its ultimate values. For a smaller crystal group (MS), it becomes very difficult to accurately determine the expanded bed height visually. The tiniest crystals diffuse into the bed and generate a much diluted bed. Therefore, in case of very high upflow liquid velocity conditions, the experimental results for the MS group of mixture are observed to vary significantly from the values predicted by either models (Fig. 4.8).  4.4  Conclusions A comprehensive characterization of the struvite crystals produced from wastewater  in the Edmonton full scale P-recovery plant is discussed in this section. The characterization of struvite particles include the determination of intrinsic static parameters such as size, density, shape and morphology, as well as determination of their dynamic behaviour in relation to liquid flow, such as terminal settling velocity, minimum fluidization velocity and the bed expansion characteristics for both mono-sized and the multi-particle systems. Based on this extensive study, the following conclusions can be drawn. •  The different sizes of struvite crystals possess almost the same dry densities and a spheroidal shape. For most of the size ranges of particles, the Martin’s diameter and  88  the projected diameter are found to be higher than the top screen size of that particular size group. However the volume equivalent diameter was found to represent the particle dimension more accurately, as the average values of volume equivalent diameter fall within the range of sieve diameter. Therefore, in all subsequent calculations related to particle dynamics, the volume equivalent diameter was considered as both the representative and characteristic dimension of a particular size group. •  None of the well-established correlations were capable of correctly estimating the terminal velocities of struvite particles. However, the correlations provided by Clift et a!. (1978) were found to generate more consistent values than other correlations. Hence the experimental terminal settling velocities are correlated with those values predicted by Clift et al. (1978). A very good correlation between average experimental terminal velocities and those predicted by Clift et al. (1978) was found. A linear relationship with a correlation coefficient of 0.9846 was determined to effectively validate the experimental results with the values estimated by Clift et al. (1986). The proposed correlation is as follows. U  •  =  0.7306 x  +  0.0081  Minimum fluidization velocities for the struvite crystals studied in this paper range from 0.0026 to 0.0111 mIs. As in the case of terminal settling velocity determination, none of the existing correlations provides proximate estimation of minimum fluidization velocity for struvite crystals. However, the correlation by Riba et al. (1979) was found to provide conservative values of Umf for all size groups with an average deviation of 10% and hence this correlation could be used for any  89  conservative design of fluidized bed crystallizer used for phosphate recovery from wastewater. Expansion characteristics of mono-dispersed struvite crystals bed are well represented by the Richardson-Zaki relationships. However, the successful usage of the Richardson-Zaki relationship for struvite crystals requires modification of the expansion index. The expansion index for the struvite crystals can be correlated with the particle Reynolds number at terminal settling velocity by the following expression: n  =  4.7718 x Re°° 89  for 26< Re <302  This expression was later utilized for the multi-particle struvite crystal systems and was found to be successful in predicting bed expansion characteristics of struvite crystals. •  For a multi-particle system, the bed expansion behaviour for struvite crystals was better predicted by the serial model, than the average model.  90  Nomenclature Symbols A  =  Cross sectional area of the bed (m ) 2  Ar  =  Archimedes number (Ar =  CD 1 C 1 C 2 C D d  =  Drag coefficient Volumetric concentration of particle species i Constants, defined by equation 4.12 Constants, defined by equation 4.13 Diameter of the colunm (m) Volume equivalent spherical diameter of particles (m) Diameter of size group i (m) Bed friction factor Acceleration due to the gravity (9.8 lmls ) 2 Galileo number Static bed height (m) Total expanded bed height of a mixture (m) Total mass of struvite crystals (kg) Bed expansion index Reynolds number under terminal settling conditions for the multi dUp, particle system (Re = V t )  f g Ga H,, H, M n Re,  pldV ( 3 pSSSd  —p,)g  )  ‘UI  1 Rem  =  Reynolds number at minimum fluidization velocity = dvUmjPi (Re,, ‘U’  U Umf  = =  Ubf  =  U Uma U, Ut(exp)  = = = = =  X,Y & Z  = =  z Al’  = =  Upflow superficial liquid velocity (mis) Minimum fluidization velocity (mis) Velocity for initiation of fluidization (mis) Velocity for total fluidization (mis) Apparent minimum fluidization velocity (mis) Terminal settling velocity of particles, corrected for wall effects (mis) Experimentally determined terminal settling velocity (with wall effect) (mis) Terminal settling velocity estimated using Clift et al. (1978) relation Points showing three different minimum fluidization velocity for multi-particle system Volume fraction of size group i (or fluid-free fractional volumetric concentration of particle species i) Number of struvite particles Pressure drop across the bed (Pascal)  91  Greek letters 1 a  =  Liquid volume fraction (voidage) of the bed  1 a  = =  Voidage when species i is fluidized alone at the same superficial liquid velocity as the mixture Bed voidage at minimum fluidization velocity (Umf)  ‘Ii  =  Liquid viscosity (Pa.s)  1 p  =  Density of liquid (kg/rn ) and i 3 ’s solid phase t  Ps,ssd  = =  Density of struvite at SSD condition (kg/rn ) 3 Density of struvite class i at SSD condition (kg/m ) 3  = =  Density of struvite at dry condition (kg/rn ) 3 Sphericity of particles  =  Crystal size classes with decreasing diameter  Ps,ssd, Ps,dry  0 Others A, B, C, D, E,&F MS, ML & MC  Mixture of different size classes  Abbreviations BC FBR MAP P SSD  = = = = =  British Columbia Fluidized Bed Reactor Magnesium Ammoniurn Phosphate Phosphorus Saturated Surface Dry  92  Table 4.1 Run  Fluidized bed experimental conditions Struvite size group  Sieving range (mm)  Range of upflow velocity (mmls) for Bed 1 Urn determination expansion 1 A 2—2.2 1.83—13.12 11.10—26.93 2 1.68—1.98 B 1.31—16.28 12.21—25.53 3 1.41—1.68 C 1.02—13.60 9.25—23.07 4 D 1.0—1.18 0.47—6.17 5.55—24.67 5 F 0.5—0.6 0.90—8.02 8.02—16.28 ML* [A, C and [2—2.2; 1.41—1.68; 1.83—14.43 15.66—28.68 D] 1.0—1.18] MS* [D, E and [1.0—1.18; 0.6—0.83; 0.95—6.72 13.07—27.50 F] 0.5—0.6] MC* [A, B, C, [2—2.2; 1.68—1.98; 0.90—13.81 14.60—26.77 D, E and 1.41—1.68; 1.0—1.18; F] 0.6—0.83; 0.5—0.61 ML: Mixture of larger struvite crystal size classes A, C and D  Fixed bed height (mm) 109 220 111 192 79 209 225 216  MS: Mixture of smaller struvite crystal size classes D, E and F MC: Mixture of complete struvite crystal size classes A, B, C, D, E and F  93  94  1700  1700  1670  1650  C  D  E  F 1600  1650  1677  1687  1687  0.60  0.80  1.16  1.69  1.97  Experimenta11y determined using Equation 4.3 4 N ot determined  1700  B  Martin’s diameter (mm) Mean Median (±a) 2.42 2.43 (0.16) 2.08 2.12 (0.12) 1.69 1.69 (0.07) 1.10 1.09 (0.04) 0.87 0.86 (0.07) 0.66 0.66 (0.05)  Charateristics of struvite crystals  Particles Density Volume size ) 3 (kg/rn diameter group Dry SSD [dr] (mm) A 1700 1687 2.23  Table 4.2 Projected diameter (mm) Mean Median Sauter mean (±a) 2.48 2.50 2.50 (0.15) 2.12 2.16 2.14 (0.13) 1.71 1.71 1.70 (0.07) 1.14 1.15 1.14 (0.04) 0.88 0.87 0.89 (0.07) 0.67 0.68 0.67 (0.05) 0.76  0.75  0.86  0.88  0.92  0.92  0.93  0.94  0.94  0.94  0.88 0.87  Circularity  Aspect ratio  0.92  +  0.80  0.89  0.84  0.81  Spheri city*  95  A B C D E F  2.23 1.97 1.69 1.16 0.80 0.60 12.89 12.37 11.50 8.95 6.01 4.37  Average terminal settling velocity [ Uf(exp)] (cmls) 0.41 0.51 0.66 0.62 0.22 0.53  (cmls)  Standard deviation ] 1 [U  12.82 12.44 11.48 9.05 6.19 4.44  Median [ Ut(exp)] (cmls)  13.58 12.96 11.97 9.20 6.13 4.43  Corrected for wall effects, U (cmls)  Terminal settling velocities for different size classes  Struvite Average crystal diameter group [volume equivalent dia, d] (mm)  Table 4.3  19.31 17.68 15.73 11.53 7.92 5.46  U by Fair & Geyer (1954) (cmls)  18.52 16.80 14.72 10.19 6.76 4.63  U by Clift et al. (1978) (cmls)  18.22 16.45 14.39 10.22 6.92 4.80  U by Haider & Levenspiel (1989) (cmls)  18.25 16.48 14.42 10.24 6.93 4.89  U by Turton & Levenspiel (1986) (cmls)  U by Direct method of Turton & Clark (1987) (cmls) 19.30 17.74 15.85 11.67 7.98 5.43  Table 4.4 Size group  A B C D E F  Predicted and experimental minimum fluidization velocity 1/1inimum fluidization velocity, Umf (mmls) Wen Lucas Riba & Yu et al. et al. Experi(1966) (1986) (1978) mental 13.94 13.48 11.23 11.1 11.82 11.49 9.95 9.8 9.29 9.08 8.45 6.8 5.02 4.96 5.87 3.37 2.52 2.51 3.97 1.44 1.44 2.83 2.6 —  Liquid volume fraction (voidage) at Umf ] 1 [a Wen & Yu [Eq. 4.16] 0.43 0.42 0.41 0.43  Wen & Yu [Eq. 4.17] 0.45 0.44 0.43 0.45  —  —  0.40  0.43  Chen Experi (1987) mental 0.46 0.46 0.45 0.45 0.44 0.43 0.46 0.42 0.47 0.43 0.47 —  96  Table 4.5 Particle group  A B C D E F  Parameters of Richardson-Zaki equation U (cmls)  16.55 13.44 11.96 11.36 —  5.02  Correlation n (Experimental) coefficient  2.90 2.92 2.96 3.12 —  3.58  98.44 97.88 98.12 98.73 —  97.82  n (Richardson & Zaki, 1954)  n (Rowe, 1961)  2.49 2.53 2.59 2.76 2.98 3.17  2.52 2.54 2.58 2.70 2.90 3.12  n (Garside & AlDibouni, 1977) 2.83 2.85 2.89 3.01 3.26 3.52  97  Table 4.6  Minimum fluidization velocities for multi-particle system  Mixture group  Ubf (mmls)  Uamf (mm/s)  Utf (mmls)  MS ML MC  1.80 3.30 1.80  1.95 5.10 3.20  3.40 10.90 11.00  98  (a)  (b)  iH1flT1TTT  Pump  Figure 4.1  Experimental set-up; a) schematic and b) photograph  99  4500  4000 A  3500  I  D  0  A  3000  0  2500  0  A  •  --  2000  / 0  1500  /  —  —  0  .tj 0  A  /  1000  / 0/  500  .;  0  0 0  1  2  3  4  5  6  7  8  Superficial liquid velocity (minis)  Figure 4.2  Pressure drop (experimental and predicted by Ergun equation) vs. superficial liquid velocity for the packed bed condition of the different size classes of struvite crystals  100  0.16 0.14 0.12 .  y=O.7306x+O.0081 =O.9846 2 R  0.1 ...  .>l  i  0.06  >.  0.04 0.02 .  x  Lii  0  I  I  0.05  0.1  0.15  0.2  Terminal settling velocity (mis) by Clift et al. (1978)  Figure 4.3  Correlations between terminal velocities determined experimentally and estimated using Clift et al. (1978) correlations  101  • D_Increasing  0  D_Decreasing  A  C_Increasing  CI  C_Decreasing  4500 4000  c3  •  Ce  LI  •  II  0  I  0  3000  9  CI A  2500 2000  0  • 1500  a  A  0  1000-  . 500 i  0—  0  1  2  I  I  3  4  5  I  I  I  I  I  I  6  7  8  9  10  11  12  13  14  15  16  Upflow superficial liquid velocity (minis) Figure 4.4  Pressure drop vs. upflow liquid velocity for determining minimum fluidization velocity  102  •A  AB  GD  •C  •F  0.5 0.4  A  D  . D  0.3H • A  0.2  A  0.1  D  C  0]  . C  -0.1 -0.2 C  -0.3  —r—  -0.45  -0.4  -0.35  -0.3  -0.25  -0.2  -0.15  -0.1  Log (a!)  Figure 4.5  Voidage (as) vs. upflow liquid velocity (Li) relationship found in experimental bed expansion tests  103  4 p  3.5 0’  —‘  2.5  1.5  0.5  o O  0.5  1  1.5  2  2.5  3  3.5  4  Experimental ‘n’ values  Figure 4.6  Comparison between ‘n’ values determined experimentally and estimated using the correlation  104  —  4500  ML_Increasing  — —  ML_Decreasing  z  Y  4000 —  1  3500  x  3000 2500 2000 1500 1000 500 0 0  2  Uhf  4  Umfa  6  8  10  Utf  12  14  16  Superficial liquid velocity (minis)  Figure 4.7  Pressure drop vs. upflow liquid velocity for determining minimum fluidization velocities (Ubf, Umfa and Uff) for a multi-particle system (ML)  105  0 — —  —  MS_ExperimentalVoidage MS_MixtureModel_Voidage MS_BedHeight_SeriaI  -  -  -  0 —  -  MS_SerialModel_Voidage MS_BedHeight_Experimental MS_Bedlleight_Mixture  0.9  0.9 0  E  ::j 0  ‘  .-.  0.5  0.5-  ‘.  0.3  _,.#.  0.3  0.2 0.01  ,  0.2 0.015  0.02  0.025  0.03  Superficial liquid velocity (mis)  Figure 4.8  Comparisons of bed expansion characteristics for the multi-particle systems (Run# MS)  106  o ML_Voidage_Experimental .  0.75  —  —  ML_Voidage_Mixture ML_BedHeight_Serial  —  0 ci  ML_Voidage_Serial ML_BedHeight_Experimental ML_BedHeight_Mixture  0.7 0.65  0.65 —  —  —  0.61 0  E:  0  —  0  0.55 0  0.45 0  0.35  0.35  0.3 0  0.25  0  0.25  0.2 0.15 0.012  0.15 0.014  0.016  0.018  0.02  0.022  0.024  0.026  0.028  0.03  Superficial liquid velocity (mis)  Figure 4.9  Comparisons of bed expansion characteristics for the multi-particle systems (Run# ML)  107  Voidagesjj 0 — -  08  -  -  06  -  —  —  —  —  —  ::  I  0.3  0.3j  0.2  0.21 0.l If 0 . 0  1  0.012  0 0.014  0.016  0.018  0.02  0.022  0.024  0.026  0.028  Superficial liquid velocity (mis)  Figure 4.10  Comparisons of bed expansion characteristics for the muItj.partjcje systems (Run# MC)  108  4.5  References  Asif, M. (1998) Generalized Richardson-Zaki correlation for liquid fluidization of binary solids. Chem. Eng. Technol. 21,77-82. Asif, M. (2001) Expansion behaviour of a binary-solid liquid fluidized bed with large size difference. Chem. Eng. Tech. 24, 1019-1024. Bhattacharya, S., and Dutta, B.K. (2002) Effective voidage model of a binary solid-liquid fluidized bed: Application to solid layer inversion. md. Eng. Chem. Res. 41, 5098-5108. Chen, J.J.J. (1987) Comments on improved equation for the calculation of minimum fluidization velocity. md. Eng. Chem. Res. 26, 633-634. Clift, R., Grace, J.R., and Weber, M.E. (1978) Bubbles, Drops, and Particles. New York: Academic Press, pp 114. Chong, Y.S., Ratkowsky, D.A., and Epstein, N. (1979) Effect of particle shape on hindered settling in creeping flow. Powder Technol. 23, 55-66. Couderc, 3-P. (1985) Incipient fluidization and particulate systems. In: Davidson JF, Clift R, Harrison D, eds. Fluidization. 2d ed. London: Academic Press, pp 1-46. Ellis, N., Margaritis, A., Briens, C.L., and Bergougnou, M.A. (1996) Fluidization characteristics of biobone particle used for biocatalysts. AIChE Journal, 42 (1), 87-95. Epstein, N., Leclair, B.P., and Pruden, B.B. (1981) Liquid fludization of binary mixture. I Overall bed expansion. Chem. Eng. Sci. 36, 1803-1809. Epstein, N. (1984) Comments on a unified model for particulate expansion of fluidized beds and flow in fixed porous media. Chem. Eng. Sci. 39, 1533-1534. Epstein, N. (2003) Liquid-solids fluidization. In: Yang, W-C. ed. Handbook of Fluidization and Fluid-particle Systems, Marcel Dekker, New York. Fair, G., and Geyer, 3. (1954) Water supply and waste disposal, Wiley, New York. Fan, L.-S., Kawamura, T., Chitester, D.C., and Komosky, R.M. (1985) Experimental observation of nonhomogeneity in a liquid-solid fluidized bed of small particles. Chem. Eng. Commun. 37, 141-157. Garside, 3., and Al-Dibouni, M.R. (1977) Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems. md. Eng. Chem. Process Des. Dev. 16, 206-2 13.  109  Haider, A., and Levenspiel, 0. (1989) Drag coefficient and terminal velocity of spherical and nonspherical particles. Powder Technol. 58, 63-70. Howley, M.A. and Glasser, B.J. (2002), Hydrodynamics of a uniform liquid-fluidized bed containing a binary mixture of particles. Chem. Eng. Sci. 57,4209-4226. Jean, R.H., and Fan, L.S. (1998) Multiphase flow: liquid/solid fluidized bed systems. In: Johnson R.W., ed. Handbook of Fluid Dynamics. Boca Raton, FL: CRC Press, pp 19-1 1925. -  Khan, A.R., and Richardson, J.F. (1989) Fluid-particle interactions and flow characteristics of fluidized beds and settling suspensions of spherical particles. Chem. Eng. Commun. 78, 111-130. Kunii, D., and Levenspiel, 0. (1969) Fluidization Engineering, John Wiley and Sons Inc., New York. Kwauk, M. (1992) Particulate fluidization: an overview. Adv. Chem. Eng. 17, 207-360. Lewis, W. K., Gilliland, E. R., and Bauer, W. (1949) Characteristics of fluidized particles. md. Eng. Chem. 41, 1104-1117. Lewis, E. W., and Bowerman, E. W. (1952) Fluidization of solid particles in liquids. Chem. Eng. Prog. 48, 603-11. Lockett, M.J. and Al-Habbooby, H.M. (1973) Differential settling by size of two particle species in a liquid. Trans Instn Chem Engrs. 51, 281-292. Lucas, A., Arnaldos, J., Casal, J., and Puigjaner, L. (1986) Improved equation for the calculation of minimum fluidization velocity. md Eng Chem Process Des Dev. 25,416-429. Obata, E., Watanabe, H., and Endo, N. (1982) Measurement of size and size distribution of particles by fluidization. J. Chem. Eng. Jpn. 15, 23-28. Richardson, J.F., and Zaki, W.N. (1954) Sedimentation and fluidization: Part I. Trans Instn Chem Engrs. 32, 35-53. Riba, J.P., and Couderc, J.P. (1977) Expansion de couches fluidisees par des liquids. Can. J. Chem. Eng. 55, 118-121. Riba, J.P., Routie, R., and Couderc, J.P. (1978) Conditions minimales de mise en fluidisation par un liquide. Can. J. Chem. Eng. 56, 26-30. Rowe, P.N. (1987) A convenient empirical equation for estimation of the Richardson-Zaki exponent. Chem. Eng. Sci. 42, 2795-2796.  110  Turton, R., and Levenspiel, 0. (1986) A short note on drag correlation for spheres. Powder Technol. 47, 83-86. Turton, R., and Clark, N.N., (1987) An explicit relationship to predict spherical particle terminal velocity. Powder Technol. 53, 127-129. Wen, C.Y., and Yu, Y.H. (1966) Mechanics of fluidization. Chem. Engng Prog. Symp. Ser. 62, 100-111 Yoshino, M., Tsuno, H., and Somiya, I. (2003) Removal and recovery of phosphate and ammonium as struvite from supematant in anaerobic digestion. Water Sci. Technol. 48, 171178. Yu, H., and Shi, Y. (1985) Characteristics of fluidization of binary particle mixtures. Fluidization’ 85 Science and Technology, Beijing, China, 250.  ill  Chapter 5  Numerical simulation of liquid-solid fluidized bed of mono and polydisperse struvite crystals 4  5.1  Introduction A significant amount of ortho-phosphate is released in the secondary anaerobic  digestion phase of the biological nutrient removal (BNR) process. Under favourable conditions, this high level of phosphates in anaerobic digester supernatant causes struvite P MgNH • 4 0 6H O ) precipitation in the digester line. This is extremely prevalent in (MAP: 2 the elbows and the suction side of pumps. Struvite precipitation is also a very common phenomenon in the sludge derived from the anaerobic digestion of animal farming liquid wastes and agricultural wastes (Booram el. al., 1975). One way to solve this struvite precipitation problem, in the BNR plants, is to recovering phosphorus intentionally from the supernatant, through struvite crystallization. This process not only alleviates the formation of unwanted struvite deposits in the digester piping and supematant overflow and (or) return lines, but also provides an environmentally benign and renewable nutrient source to the agricultural industries (Yoshino et al., 2003). Thus, the recovery of nutrients from biological wastewater treatment plants, through struvite crystallization, provides an innovative and sustainable approach for treating municipal wastewater. In recent years, a substantial number of studies have been conducted by several researchers with respect to recovering phosphorus from wastewater, through struvite crystallization. The studies include process identification and the performance evaluation of  A  version of this chapter will be submitted for publication.  Rahaman, M.S., Mavinic, D.S., Ellis, N., and Taghipour F. (2009). Numerical simulation of liquid-solid fluidized bed of mono and polydisperse struvite crystals. In preparation.  112  the struvite crystallization process, in both bench and pilot scale operations. The technology has also been validated in some full-scale wastewater treatment plants, operating in different parts of the world. The largest ones are operated in Japan: Shimane Prefecture (500m /day), 3 Fukuoka Prefecture (1 70m /day); and at Osaka South Ace Center (266m 3 1day) (Parsons et al., 3 2001). The Shimane Prefecture reactor has been found to remove 90% of ortho-P from the treated supematant. A full-scale, struvite crystallization plant has also been installed in Italy to remove ortho-P from anaerobic digester supematant (Battistoni et al., 2001). Being a part of this diverse research community, the Environmental Engineering Group, at the University of British Columbia (UBC), has been conducting research on P-recovery since 1999 and has developed a novel fluidized bed reactor configuration that converts 80 to 90% of soluble phosphates into crystalline struvite (Adnan et al., 2003). More recently, the Ostara Nutrient Recovery Technologies Inc. (a spin-off company of the UBC P-recovery group) has installed a full scale demonstration nutrient recovery plant in Edmonton, AB, Canada, as well as three full-scale reactors in Portland, Oregon, USA. In order to optimize the process, a handful of research has been performed concerning the chemistry of struvite formation and growth (Rahaman et al., 2006; Rahaman et al., 2008a); however, very little initiative has been taken to look into the hydrodynamics of the liquid-solid fluidized bed of struvite crystals. In a fluidized bed crystallizer, the simultaneous progress of two processes fluidization and crystallization yield very complex phenomena, which require comprehensive studies of the process hydrodynamics to help design an efficient reactor. As the supersaturated solution flows upward through a fluidized bed crystallizer, the liquor contacting the bed relieves its supersaturation on the growing crystals and subsequently the supersaturation decreases along the upward direction. As a result, crystals near the bottom  113  grow faster than those near the top of the crystallizer. Such behaviour results in the variation of particle size along the height of the reactor. When the bed is composed of particles of different sizes, the particle size distribution is influenced by two opposite phenomenon: classification and dispersion. Classification results from the movement of particles of different weights; larger particles tends to reach the bottom of the reactor, whereas smaller particles rise. Simultaneously, dispersion is induced by irregular motions of the solid particles. Perfect classification and perfect mixing of the solids in fluidized bed are the two extreme situations. More often, a mixing zone is created between the two layers of classification particles, allowing partial classification within the bed. Accurate knowledge of mixing behaviour of the particles is essential in modeling and design optimizing the multiparticle fluidized bed crystallizers. For simplicity, design methods for fluidized bed crystallizers are generally based on the perfect size classification (Mullin and Nyvlt, 1970). Also in most of the modeling efforts for liquid fluidized bed crystallizer (Shiau and Lu, 2001; Rahaman et al., 2008b), a complete segregation of particles is considered. However, the majority of actual crystallizer systems exhibit some degree of mixing of solid crystals within the bed. Therefore, in designing the fluidized bed crystallizers, containing a wide range of particles, a better knowledge of bed expansion and particle mixing/segregation is required. Computational Fluid Dynamics (CFD) is becoming an important tool for studying the hydrodynamic behaviour of the conventional industrial crystallization processes. This technique allows the prediction of flow patterns, local solids concentration and local kinetic energy values, taking into account the reactor shape. However, to the authors’ knowledge, none of the studies has dealt with the fluidized bed crystallizers, which involve multi-particle systems. In this current project, a numerical investigation of the hydrodynamics of the liquid  114  solid fluidized bed of both mono and poly-disperse struvite crystals, was performed, using the commercial CFD package, Fluent 6.3 (Fluent, 2006). The simulation results are then evaluated by comparing with the experimental investigation, performed using a lab-scale reactor.  5.2  Model development  The governing and constitutive equations, the boundary and initial conditions, as well as the numerical procedure used in the CFD modeling are described in this section.  5.2.1  Governing equations In this study, a multi-fluid Eulerian-Eulerian granular model of Fluent 6.3 was used to  simulate the hydrodynamics of a liquid-solid fluidized bed of struvite crystals. In an Eulerian-Eulerian Granular model, the primary (liquid) and secondary (solid) phases are treated mathematically as interpenetrating continua and conservation laws for mass and momentum of each phase are used to obtain a set of governing equations. These equations are closed by providing constitutive relations which are obtained from empirical information or theoretical assumptions. In addition to the mass and momentum conservation equations for the solid phase, a fluctuation kinetic energy equation is also used to account for the conservation of solid fluctuation energy through the implementation of the kinetic theory of granular flow. In the case of multi-particle fluidized bed systems, each individual solid phase (classified according to their size) is considered as a separate secondary phase and an equivalent number of additional continuum and momentum equations are included to  115  represent the additional phases. Also, additional closure expressions for interactions with the phases, and the stresses are introduced to the continuum and momentum equations. The governing equations for the liquid and  ith  solid phases are as follows:  Continuity; For liquid phase, ) =0 ã p 1 ) + V.(a  (5.1)  and for “i” th solid phase,  ) + V.(a p ü ) = 0  (5.2)  where, a 1 and a 5 are the volume fraction of liquid and are the density of liquid and for liquid and  ith  th 1  ith  solid phase, respectively; p 1 and  solid phase, respectively; 11 and  115  are the velocity vetor  solid phase, respectively.  Momentum: For liquid phase, i1 p V.Qx 1 1 ) 1 = —a VP + Va+ a 1 p+a 1 p 1  +  —  ü)  (5.3)  For “i” th solid phase, (a ) p l ) 5 V +V.(a =—a P—V i +V.r+a p 5 51 , 5 K , (ü  —  11  p +K 5 +a 1 —ü)+ (11 15  )  in=1; ini  (5.4) where, (a 1  +  5 =1); P is the static pressure shared by all phases; a  tensors for the liquid and the  ith  solid phase, respectively;  Ti  and v are the stress  is the acceleration due to 116  gravity;  and F 5 are the external body force applied to liquid and  respectively; K 15 phase;  ith  solid phase,  51 is the momentum exchange coefficient between liquid and K (= )  ith  solid  is the momentum exchange coefficient between solid phases m and i; and F is  the solids pressure. Kinetic energy of solid phases: The kinetic energy equation for the solid phase employs the granular temperature,  O, which is proportional to the kinetic energy of the random motion of particles (Ding and Gidaspow, 1990). 5 Oslis)] = (—F 1+ v) : VU 5 5a ) + V.(P +V.(kVe ) 5 — 75.  (55)  +ølsi  The first term of the right hand side of the expression [(—Ps I + ‘r ) : ViJ represents the 5 generation of energy by the solid stress tensor, where I is the unit tensor; kVe 5 is the diffusion of energy, which describes the diffusive flux of granular energy, where k is the diffusion coefficient for solid phase energy fluctuation; y, the collisional dissipation of the energy, represents the rate of energy dissipation within the solid phases due to collisions between particles; and  5.2.2  is the energy exchange between the liquid and the solid phases.  Constitutive parameters Several closure models, based on the kinetic theory of granular flow, have been  proposed to define the appropriate constitutive equations for multi-phase flow. The constitutive equations provide relations for the stress tensor (r) of different phases, solid 117  pressure 3 (F ) , the parameters for the kinetic energy equation and the momentum exchange between solid-liquid (K ) and different solid-solid phases (K 13 3  ). The following are the  constitutive relations used in the current study. i) Stress and pressure: The stress tensor for both the liquid and the solid phases has the form: =  u(Vii + \7ü )+ a(2 ..p)V.ñI, T —  (5.6)  where, p =(ps, Mi) and 2=(,l, 2) are the shear and bulk viscosity of the phases, respectively and I is the unit tensor. The solid shear viscosity, p is composed of three different parts. The first part is the contribution from collisions, which is significant in dense flows. The second one is the kinetic term, which is dominates in dilute flow. The last one is the frictional viscosity. Thus the solid share viscosity can be written as (Gidaspow, 1994): Ms  +J sfr t  +  Ps,coi  (5.7)  where, collisional viscosity is expressed as  ,‘s,Col  =  5 e L 2 5 )°5 035 d p 5 a (1 g + )(.  (5.8)  with d the diameter of particles, e 55 the restitution coefficient due to particle collisions, €) the granular temperature, and  33 go,  the radial distribution function expressed by Ding and  Gidaspow, (1990) as  5 , 0 g  3 =  /  ‘1I3  iaI  1  (5.9)  —  \f’’s,max)  118  where,  is the maximum solids volume fraction (or packing) in the bed. According to  Ding and Gidaspow (1990), a value of 0.63 for £Ls,max is used. The kinetic viscosity is given as = Ps,kin  l0dp 96a (1 + )g 0  [1+ga(1+e)12  (5.10)  5  and the frictional viscosity is given as P sine Ps,fr =  (5.11)  JjE  where, P is the solids pressure, t is the angle of internal friction, defined as the angle measured between the normal force and resultant force that is attained when failure just occurs in response to a shearing stress, finally,  ‘2D  is the second invariant of the deviatoric  stress tensor. The solid pressure is given by: =  + 2p (1 +  The solid bulk viscosity  O 03 )ag  (5.12)  (,) is the resistance of the granular particles to compression and  expansion and is given by (Lun et al., 1984): 2  (5.13)  ii) Parameters for the kinetic energy equation: The diffusion coefficient for the energy fluctuations of a solid phase (kr) is given by (Drew and Lahey, 1993):  k  12 150pdJiE 6 [1 + g a (1 + ess)] 0 384(1± e 5 )g , 0 —  =  +  2  0 (1 + 2a pdg  0 )(......)0.5  (5.14)  The collisional dissipation of energy (7s) can be expressed by (Drew, 1983): 119  =  12(1—e  2  0 )g ‘‘  dq  2 PaO’  -(5.15)  The dissipation of energy fluctuations due to the transfer of the kinetic energy of random fluctuations in the particle velocity from the solid phases to the liquid phase is given by (Schaeffer, 1987): øls  (5.16)  G 1 —3K  iii) Momentum exchange coefficients: There are several drag laws, such as Wen & Yu (1966), Gidaspow (1986) and Syamlal O’Brien (1988), which can explain momentum exchange between the solid and liquid phases. All the drag laws mentioned here are empirical and hence, their appropriateness for a particular system should be checked. In this study, all three aforementioned drag models were examined. Wen & Yu (1966) model: This model is an extension of Richardson and Zaki (1954) to high void fraction (a 1 ? 0.8). 1 K  =  24  1 [1+O.15(a  4a R 1 e  Res)0687j  d  (5.17)  where, Re  =  dV  1  —i S  1  (5.18)  1  Gidaspow (1986) model: Proposing a model to cover the whole range of void fraction, Gidaspow (1986) employed the Ergun (1952) equation in conjunction with the Wen and Yu (1966) model: For a > 0.8, the Wen & Yu (1966) model (Equation 5.17) is used, and 1  120  for 1 a < 0.8,  1 K  (1—  = 150  1 )p  d 1 a  +  1.75  PIaS  —  u  -(5.19)  d  Syamlal O’Brien Model (1988): Based on the measurement of the terminal velocity of particles in fluidized or settling beds, Syamlal and O’Brien (1988) proposed the following drag correlation: 15 K  3CD  =  pi  u  —  ui 1[Resaa  d  4 U rs  (5.20)  Ur,s,)  2  where, CD  0.63  =  +  4.8  (5.21) Urs  and  is the terminal velocity correlation for the solid phase and can be calculated using the  Ur,s  voidage—velocity correlation proposed by Garside and Al-Dibouni (1977) as follows: Urs =  0.5(X  —  0.306 Re 5 + j(0.06 Re) 2  +  0.012 Re 5 (2Y  —  X) + X 2  (5.22)  with X  Y  =  =  a  Ia a‘ ‘  (5.23) 0.85  1 <0.85 28 a qa,’  (5.24)  Here, the Syamlal O’Brien drag law was calibrated for p and q values in Equation 5.24, using experimental minimum fluidization velocities of struvite particles. The calibration of the Syamlal O’Brien drag law was performed as follows. The p and q values were adjusted based on the minimum fluidization velocity and the voidage at the incipient fluidization condition. As described by Vejahati et al. (2009), the parameter p can be estimated by changing its values in order to meet the following criteria: 121  Objective function:  U7ta1  —  Re  a p 1 j 1 dp  Minimized  0  -(5.25)  Where, Ret, is the Reynolds number under terminal settling conditions for the multi-particle system, and expressed as Re  = Urs  (5.26)  5 Re  Re is the Reynolds number at particles’ terminal settling velocity for a single particle system and can be expressed as =[u123.04 + 2.52%J4Ar/3  5 Re  _4.8]  (5.27)  where, Ar =  —  )dp 1 p g  (5.28)  Ii Ur,s  is given by =  Urs  X +0.06YRe 3 5 1+O.O6Re,  (5.29)  Finally the parameter, q can be related to p as follows: q  =  1.28+log(p)/log(0.85)  (5.30)  The adjusted drag model was incorporated in the simulations presented here through Fluent User Defined Function (UDF) capabilities. The solid-solid momentum exchange coefficient  K  = .  3(1 + e 55 )( + Cfr )a 5P , Ps,. (d 5 2 8 5 d + p, d ) 2r(p ,,  +  d  )2  has the form:  0 g iis  —1.I  (5.31)  122  where, Cfr is the coefficient of friction between solid phases m and i, and  is the  restitution coefficient due to collisions between solid phases m and i. The restitution coefficient takes into account the change of kinetic energy of particles when they collide with each other. A restitution coefficient of 1 means that no energy is lost during collision (perfect elastic collision), while a value of 0 would mean that all kinetic energy is dissipated into heat during the collision. Rahaman and Mavinic (2009) tested three different restitution coefficients (0.5, 0.9 and 0.95) for simulation of the hydrodynamics of a liquid-solid fluidized bed of struvite crystals and no variation in CFD predicted voidage was noticed. Therefore, in this current study, a particle-particle restitution,  5.3  0.9 was used.  Boundary conditions A schematic diagram of the computational domain is provided in Figure 5.1 (b). The  inlet boundary is set at the inlet section, from where liquid is continuously injected into the reactor, and the liquid upflow (superficial) velocities were taken as the axial liquid velocity (along the height of the column) as the inflow boundary condition. Although a discrete distributor was used at the inlet of the reactor, a uniform distribution of the upflow velocity is assumed in the entire set of simulations. Cornelissen et al. (2007) studied the effect of a distributor on a CFD simulation of a liquid-solid fluidized bed reactor of similar dimensions and no significant effect on simulation results was found. Hence, for simplicity, in this study, the upflow velocity is assumed to be uniformly distributed over the entire cross-section at the inlet boundary of the reactor. The outlet boundary condition was held constant at atmospheric pressure. Zero normal and tangential (ie. no-slip) velocities for lthe iquid phase are assumed at all wall boundaries. Also the solid velocity normal to the walls is set at zero. However, the 123  tangential velocity and granular temperature were determined using correlations developed by Johnson and Jackson (1987). The slip velocity between particles and the wall was obtained by equating the tangential force exerted on the boundary and the particle shear stress close to the wall. The granular temperature at the wall was obtained by equating the granular temperature flux at the wall to the inelastic dissipation of energy, and to generation of granular energy due to slip in the wall region.  5.4  Reactor geometry and model configuration The same reactor, as used in the experimental investigation, was used for numerical  simulation. As mentioned in Chapter 4, the reactor was built of Plexiglas and had a diameter of 0.10 m and a height of 1.392 m. The liquid used in this study was a saturated solution of struvite and the solids were struvite crystals. The liquid was pumped from a tank to the reactor. A flow meter was installed to measure the inflow rate of the liquid. The reactor was filled with struvite crystals of different sizes and their mixtures. The properties of the different sizes of struvite crystals are listed in Table 5.1. The experiment was run at about 20 °C in a temperature controlled room. The reactor was equipped with several pressure ports on one side and ports for optical probes on the other side. Pressure ports were connected to the L-shaped manometers. For the numerical investigation, a simulated two-dimensional (Cartesian) domain (2D), representing a vertical section through the diameter of the fluidized bed column [Figure 5.1(b)] was created using Gambit 2.3.16 (Fluent, 2006). The extent of the domain in the radial and axial directions was identical to those of the actual colunm used in experimental apparatus, 0.10 m and 1.39 m, respectively. The domain was meshed with the grid sizes of  124  2x2 mm. However, in the horizontal direction, a cell growth factor of 1.035 was applied to the computational cells to create a somewhat finer mesh approaching both wall sides, (with a maximum cell size of 2 mm at the center) in order to capture the complex flow behavior in this region. Several other meshes were generated with different grid sizes, in order to study grid dependency of the CFD simulation. The governing equations explained earlier, are discretized, using the finite volume approach with an implicit second order upwind differencing scheme. The discretized sets of equations, along with the appropriate initial and boundary conditions are solved using Fluent 6.3 in double precision mode. This identical model setup was used to simulate fluidization behaviour of all different size classes of struvite crystals. The properties of struvite crystals used in this study are listed in Table 5.1. The liquid phase used for all the simulation was water with a density of 998.2 kg/m 3 and viscosity of 0.001003 Pa s. Simulation were run for all six size classes of struvite particles. In order to mimic the multi-particle crystallization process, the hydrodynamic simulations of the mixtures of different size classes of struvite were also performed. For a multi-particle system, each size class was represented as an individual secondary phase and the liquid is considered as the only primary phase. Each size class and the combinations of different size groups were run for different upflow liquid (superficial) velocities to simulate the bed expansion characteristics and also the solid mixing and segregation behaviour in case of multi-particle systems. Most of the simulations were run for 120 s with a time step of 0.00 1 s. A summary of model settings can be found in Table 5.2. The SIMPLE algorithm (SIMPLE-PC) (Fluent 6.3, 2006) is used for pressure-velocity coupling. The convergence criterion was set at i0 for all the equations and the convergences were achieved within a maximum number of iterations (100) per time step. The simulations were performed on a 64 bit machine with two  125  Zeon processors in parallel, with a clock speed of 2.2 GHz, and 4GB RAM. The results were analyzed both qualitatively and quantitatively for the solids volume fractions, phase velocities and the overall bed expansion.  5.5  Results and discussion  5.5.1  Sensitivity analysis In order to set up the appropriate model parameters, sensitivity analyses for different  parameters, such as mesh size and time step were performed, by varying a particular parameter and keeping the other parameters constant. The results of the sensitivity analysis are presented below: Grid size. For a CFD modeling, it is important to achieve results independent of the mesh size and structure. Therefore, in this current study, four different grid sizes (lx 1, 2x2, 3x3 and 4x4 mm) were chosen to check mesh dependency. Since simulations were performed for different sizes of struvite crystals and for their mixture, the grid dependency for both the smallest and the largest particle size classes, used in this study, were performed. Simulated bed pressure drop and time average bed voidage are tabulated in Table 5.3 along with the corresponding experimental values. As reported in Table 5.3, the deviations in both overall pressure drop and bed voidage are not significant for the grid sizes of [lxi], [2x2] and [3x3], indicating mesh independency is achieved for 3x3 mm and fmer grid size. The simulation with the finest grid size of [lxi mm] took more than a week to complete a simulation of 120 s of real time run. The computational time required for this fme mesh, is significantly higher than the time needed for simulation with other mesh sizes. Hence, in this study, a [2x2] mm 126  grid size was chosen for the rest of the simulations. The selections of the mesh size also support the rule of thumb previously proposed by several authors (Syamlal and O’Brien, 2003; Zimmerman and Taghipour, 2005; and Taghipour et al., 2005) that the mesh size for fluidized bed CFD simulation is expected to be less than or equal to ten times the particle size used in the simulation. Time step: For better convergence and capturing the local hydrodynamics of the liquid solid fluidized bed more accurately, time step selection has significant effects on simulation results. In a preliminary investigation, three different time steps were tested such as 0.001, 0.002 and 0.005 s. All three time steps were found to generate almost identical overall bed voidage (not reported here). However, a time step of 0.001 s was found to more accurately capture the local voidage characteristics as per earlier studies on hydrodynamics of the UBC MAP fluidized bed crystallizer (Rahaman and Mavinic, 2009). Hence, in all the simulations performed in this study, a time step of 0.00 is was chosen.  5.5.2  Drag laws In order to calculate the liquid-solid momentum exchange coefficient, several drag  models including Wen & Yu (1966), Gidaspow (1986) and the calibrated Syamlal and O’Brien (1988) (Section 5.2. ii) were compared. Tables 5.4 summarize the overall bed voidage estimated, using different drag laws, and compared with their experimental counterparts. It is obvious that Wen and Yu (1966) correlations works best for this current study and generates almost identical values for both pressure drop and overall bed voidage, to those of the experimental values. The overall bed voidage and the total pressure drop  127  values, predicted by the Gidaspow (1986) model were also close to the experimental results. However, the calibrated Syamlal O’Brien drag model overpredicts (more 15%) both the overall bed voidage and the pressure drop data. Therefore, Wen and Yu (1966) drag laws are used further on for the simulation of mono sized struvite systems. However, for multiparticle systems, the Gidaspow drag law was used, as this drag law covers the whole range of voidage and expected to be the best suited for the poly disperse fluidized bed systems.  55.3  Simulation of liquid-solid fluidized bed of mono size struvite crystals A typical qualitative result of the simulation, along with the quantitative transient  behaviour (variation with respect to time) of bed expansion of struvite size class D, fluidized at a superficial liquid velocity of 24.67 mm/s, is plotted in Figure 5.2. It is observed that bed crystals get randomly distributed in the liquid phase and reach a steady state condition after 60 s, with a total expanded bed height of 33.2 cm [Figure 5.2(a)]. As can be seen from Figure 5.2(b) simulated overall bed voidage reproduced steady state experimental values extremely well. In a similar fashion, the steady state bed expansion for each different size class of struvite particles, at different upflow velocities, was determined from the simulation results. These values are then compared with the experimental results obtained in earlier studies (presented in Chapter 4). The well-established Richardson-Zaki (1954) relationship with expansion index, calculated using the conelation developed in the Chapter 4, was also compared with both the experimental and CFD simulation results. Figure 5.3 represents the expansion behaviour of five different size classes of struvite crystals studied in this paper. For all five crystal groups, the average voidage is found to increase with increasing superficial liquid velocity. Quite interestingly, the simulated time  128  average overall bed voidage profiles for different size groups, match quite well with the experimental voidage-velocity profiles. The average deviation is less than 5% among all the 5 cases, studied and the highest deviation was observed with the struvite size class of B. It is also worth pointing out that the CFD predicted values are closer to the observed values than those predicted by the Richardson-Zaki relation. This implies that the applicability of CFD model for predicting the hydrodynamics of liquid-solid fluidized bed, under the conditions studied here is sound. Similar observations were reported by several other researchers on CFD simulation of liquid solid fluidized bed [e.g. Reddy and Joshi (2009), Comelissen et al. (2007), Cheng and Thu (2005), Lettieri et a!., (2006)]. However, in all of the previous studies, spherical solid particles were used and a spherical diameter was considered as the characteristic dimension of the particles. The struvite crystals used in this current study were not exactly spherical in shape. Although the crystals show very good circularity in their stable orientations, the elliptical shape is sharply evident along the plane perpendicular to the plane of its most stable orientation at rest. This makes it difficult to characterize the struvite crystals with respect to its dimension. Chapter 4 dealt with characterizing the struvite crystals in terms of size and shape and the volume equivalent diameter was suggested to be used for any calculation related to the dynamics of fluid-particle interaction. Hence, in all the CFD simulations, performed in this work, the “volume equivalent” diameter was considered as the characteristic dimension for a specific struvite size group. Comparing all the simulation predictions with the experimental results, it is obvious that the struvite crystal can best be represented by its “volume equivalent” diameter. Other diameters, such as sieve diameter, as well as the Martin’s and Feret’ s diameter were also tested. But all of these diameters generate  129  results that deviate more than 10% from the corresponding experimental values (not presented here). Thus, for any fluid-solid dynamics representation of struvite crystals, the volume equivalent diameter should be taken as the characteristics dimension. These results can also be extended to other non-spherical particles with sphericity greater than 0.8, and the CFD simulation for these types of particles can be performed effectively by taking “volume equivalent” diameters as the characteristic dimension. In order to compare the simulation predictions with the experimental results, a fiber optic voidage probe was used to measure the radial distribution of solids volume fraction. Both emissive and reflective optical measurement systems can be used to deduce the solid volume concentration. However, emission is not suitable for dense suspensions (Werther, 1999). Therefore, in this current study, a reflective type optical probe was used. Reflective optical probes work on the principle that a small volume of particles is illuminated and the reflected light intensity is correlated to the volumetric concentration within a local measuring volume at the tip of the probe. Solid volume fraction measurements, using optical probes, are slightly invasive, yet they provide insight into the physical phenomena of the fluidized bed. In order to get the radial distribution of solids volume fraction along the diameter, at a bed height of 0.184 m, the probe was inserted into the reactor through the port located at the side wall of the reactor. The experimental results are then plotted and compared with the simulation predictions in Figure 5.4. Both the experimental and simulation results exhibit only minor variation of bed voidage in the radial direction. However, the measured voidage along the radial positions were found to be slightly lower than the values predicted by the CFD simulation.  130  The CUD predicted time-mean area-weighted average voidage for a specific bed height of 0.184 m (from the bottom) are also compared with values determined by the optical probe, for different upflow velocities (Figure 5.5). The simulated results match fairly well the experimental findings for the range of superficial velocities except for the highest velocity of 26 mm/s. The reason for reduced liquid volume fraction, determined by the optical probe at upflow liquid velocity of 26 mm/s, may be due to fact that local voidage does vary from overall voidage due to the change in particle size distribution at that high upflow velocity. As expected, the overall bed voidage, (estimated from the CUD predicted total bed height), was higher than both the simulated and experimentally determined (using optical fibre probe) local area-weighted voidage.  5.5.4  Mixing and segregation of struvite crystals in multi-particle fluidized bed In order to study the mixing and segregation behaviour of struvite crystals in multi-  particle fluidized bed systems, three different sets of mixtures were prepared. The first two sets consisted of 3 different size classes, where “ML” represents mixture of three larger size classes (A, B and D) and “MS” represents the mixture of three smaller size classes (D, E and F). Finally, the 3rd mixture, which is represented by “MC”, consisted of all 6 different size classes studied in this work. The details of the multi-particle combinations can be found in Table 5.1.  5.5.4.1 MS particle group As mentioned earlier, the “MS” mixture contained three different size classes (D, E and F) of struvite crystals, having characteristics dimensions of 1164, 804, and 602 rim,  131  respectively. CFD simulations were performed for this mixture, with 4 different superficial liquid velocities (MS1: 13.08 mmls; MS2: 18.5 mmls; MS3: 22.17 mmls; and MS4: 27.51 mni’s). Each of the simulation runs was started with an initial condition of particles being at rest and completely mixed. Hence, once the fluidization began, they start moving randomly and finally, reached a steady state with a stable particle size distribution. It is commonly observed that, once a multi-particle system is fluidized, particles experience both classification, due to gravitational force, and dispersion, due to irregular motions of particles being fluidized (Epstein, 2003). Therefore, complete segregation and well mixed are the two extreme conditions usually observed in the fluidized bed with multi-particle systems. Since only the pressure drop data for the MS mixture were determined experimentally, the CFD simulated pressure profiles are compared with the experimental results in order to validate the CFD simulation for the MS mixture. Both the experimental and simulated pressure profiles along the bed height are plotted in Figure 5.6. As can be seen, the simulation results agree quite well with the experimental pressure profile, except for the run M52, in which the simulated pressure profile deviates considerably from the experimental results at higher bed heights. For the “MS” mixture, a steady state condition in terms of particle size distribution was achieved after 60 s of run. The time average bed properties are, therefore, calculated by averaging the properties over the remaining time period of a particular simulation run. The time-averaged bed voidage (liquid volume fraction) for different superficial liquid velocities are plotted in Figure 5.7. Sharp (step wise) changes in the simulated liquid volume fractions along the bed height are observed for all the cases, except for run MS2. These sharp changes imply almost complete segregation of particles in the fluid bed. In multi-particle system,  132  when the particles differ only in size, the larger particle will always separate to some degree below the smaller one, unless the size difference is small enough and/or complicating factors such as bulk circulation or hydrodynamic instability are large enough to mix the two particle species completely (Epstein, 2003). The axial distribution of particles in multi-particle system can also be described based on stability considerations: the compositions of different layers adjust themselves in order to minimize the potential energy of the suspension (Gibilaro, et al., 1986). This condition is satisfied when the slurry density at the bottom layer is the maximum. It was also found by previous researchers (Hoffman et al., 1960) that complete segregation took place when the size ratio greater or equal to 1.58. In this current study the particle diameter ratios of the size pairs D-E and E-F are 1.45 and 1.34, respectively, which implies that some intermixing between groups D and E and between E and F is expected. However, the determination of the extent of mixing between two different size classes of particles requires further experimentation and its complete theoretical analyses, which has not been performed in this preliminary work on mixing/segregation behaviour of multiparticle struvite crystals. In simulation MS2, the bed was divided into three layers, with gradual changes in the solids volume fraction in the middle section. This implies that struvite crystals are being partially mixed in the middle layer. In order to compare the CFD prediction of time averaged liquid volume fraction along the bed height, the liquid volume fraction was calculated from the pressure drop data between two consecutive pressure ports as,  =  (P  —  1 )(1 P  —  a, )g  (5.32)  where, H is the distance between two consecutive pressure ports. The calculated value of liquid volume fraction is considered as the average value between two pressure ports and presented as the area-weighted average voidage at the midpoint of two 133  consecutive pressure ports. Most of the calculated bed voidage were found to differ from those of the simulation results. One of the reasons for this deviation is that the calculated values represent average voidage of a particular section between two pressure ports, but in Figure 5.7, the values are presented for specific bed heights (midpoints of two consecutive ports). Also, it may be possible that one pressure port falls in one layer of particles and the next one falls into the region of next size group of crystals. This segregation of particles is further backed by the simulation results presented in Figures 5.8 and 5.9 on the average diameter and bulk density of the slurry along the bed height, respectively. However, these limited experimental results do not necessarily validate the CFD simulation completely; rather represent some basic trends of mixing/segregation patterns. The total simulated expanded bed height was composed of three different segments with different identical sets of simulated average particle diameter and bulk density of the slurry. A close look at Figure 5.8 reveals that the bottom portion contained particles with an average diameter of 1164 pm, which represents the particle size class of D. The middle portion contained particles of average diameter 804 pm, which is the characteristic dimension of particle group E. Finally, the top section of the expanded bed held particles of an average diameter of 602 pm (Group F). A close look at Figures 5.8 and 5.9 reveals that both simulated average diameter and the bulk density of the slurry varies gradually in the middle section of the bed, with two different slopes for run MS2, implying that the lower portion of the middle section is composed of particles D and E and the upper portion is occupied by a mixture of particles E and F. Figure 5.10 displays time average expanded bed heights for the mixture MS, at different upflow liquid superficial velocities. As expected, the bed height increases with  134  increasing upflow velocities. The bed expansion characteristics are also determined using the serial model, as described in Chapter 4. A good agreement of the experimental results is observed with the values predicted by both the CFD and serial model. This implies that the CFD simulation can estimate the overall bed characteristics quite well. However, in order to validate the CFD simulation for the local bed characteristics a detailed experimental investigation is warranted.  5.5.4.2 ML particle group The ML mixture was prepared by combining three different size classes of struvite crystals chosen from the larger sizes (A, C, and D), with characteristic dimensions of 2233, 1687, and 1164 Jim, respectively. As with the study performed for the mixture of smaller size classes (MS), four different CFD simulation runs were carried out for the ML mixture for different superficial upflow liquid velocities (ML1: 18.26 mmls; ML2: 22.7 mmls; ML3: 25.29 mnVs; MM: 28.68 mmls). As was the case in MS group, the particles were considered to be completely mixed initially. Usually, a steady state condition in terms of particle size distribution was achieved within 80 s of simulation for the ML mixture. Thus, the time average bed properties, presented in this section, represent the average values found during the time period of steady state operation. In order to validate the simulation results for ML mixture, the experimental pressure profiles for different runs are compared with the simulation results. The pressure profiles for different upflow liquid velocities are plotted in Figure 5.11. As can be seen, the simulation results reproduce the basic trends of experimental pressure drop along the bed height. However, the simulation results are found to deviate from the experimental values more and  135  more as the simulation progresses from inlet to the farthest end point the total bed height. A close look at Figure 5.11, the simulated profiles exhibit curvatures representing the transition from one zone to another. This phenomena is more pronounced in case of run MM (running at the highest upflow velocity). The existence of curvature in the pressure profiles reflects the gradual variation of particle volume fraction. The simulated, time-averaged bed voidage (liquid volume fraction) for different superficial liquid velocities are plotted in Figure 5.12, where the crystal bed is found to be separated into 3 layers in each simulation run. This means that the three size classes were segregated, with the largest particles occupying the bottom of the column, the smaller particles concentrated in the upper part and the middle section was occupied by the medium size group of particles. However, instead of a sharp (step wise) change as found in the case of simulation of MS group, gradual changes in the simulated liquid volume fractions are observed between two successive layers of particles, which means that a thin mixing zone may developed between two successive, completely-segregated layers of particles. The mixing zone is clearly evident between the top and middle section of the crystal bed, especially at a higher superficial liquid velocity (ML4), from the simulation results. The simulated time-averaged liquid volume fraction data are also compared with the values calculated from the experimental pressure drop data, shown in Figure 5.11. The simulated voidage profiles are found to follow the general trends observed in the experimental results. The gradual changes in the simulated average particle sizes (Fig. 5.13) and bulk density of the slurries (Fig. 5.14) also support the above observation. Figure 5.15 displays time-average expanded bed heights for the mixture ML at different upflow velocities. As expected, the bed height increases with increasing upflow  136  liquid velocities. A reasonably good agreement of experimental data is observed with the values predicted by the CFD simulation, with some deviation at higher upflow velocities. The serial model, described in Chapter 4, is found to overpredict the expanded bed heights for the range of upflow liquid velocities studied in this paper, as the serial model assumes complete segregation of the particles being fluidized and hence estimate the maximum likely bed height.  5.5.4.3 MC particle group The MC group of mixture represents a combination of all 6 individual size classes of struvite particles (A, B, C, D, E and F) studied in this work. An identical amount (weight) of struvite crystals from each size class was taken and was mixed to produce the MC group of particles. The characteristics dimension of the individual species components are 2233, 1975, 1687, 1164, 804, and 602 jim for A, B, C, D, E and F, respectively. The fluidization characteristics of this mixture of struvite crystals were studied for three different upflow velocities (MC 1: 16.84 mmls; MC2: 22.02 mm/s; MC3: 26.77 mm/s). The snapshots of simulated volume fraction of different solid crystals at 4 different time intervals (15, 30, 50 and 120 s), for run MC3 are shown in Figure 5.16. Initially, the bed was completely mixed with respect to particle sizes. As time progressed, crystals became mixed and/or segregated and finally orientated in a stable crystals size distribution in the crystal bed. At time 15 s, the crystal bed was found to be expanded but still remains completely mixed, with respect to particle size distribution. At time 30 s, the size groups started segregating according to their sizes. Although the largest and the smallest crystals were found to concentrate in the bottom and the top of the reactor, respectively, a considerable portion of them still remained in the mixture. At 50 s, the particle groups 137  segregated according to their sizes, leaving mixing zones in between the segregated sections. As depicted from Figure 5.16, at time 120 s, all 6 size classes are found to be classified according to their sizes, with the largest ones at the bottom and the smallest ones at the top. At any particular bed height, the average solid volume fractions can be calculated by taking the mean of the volume fractions across the bed cross-sectional area. Figure 5.17 shows the time mean area-weighted average solid volume fractions of different size classes of struvite crystal along with the liquid volume fractions, with respect to bed height. It is observed from Figure 5.17 that the entire bed became divided into six clearly defmed segments, with some intermixing between successive layers. This is also realized from the very steep changes in liquid volume fraction along the bed height. Perfect size classification of particles are usually found in the case of binary particles, having size ratio greater or equal to 1.58 and partial segregation is observed for the range of size ratio between 1.24 to 1.58 (Hoffman et al., 1960). In this study, we have 6 different sizes of crystals with increasing sizes from F to A. The size ratios between different possible combinations of binary particles are reported in Table 5.5. Based on the size ratios the maximum mixedness should appear in combinations of AB and BC. The result shows that those two binary mixtures (AB and BC) are found to be partially mixed at their interface but not completely. As expected, the combinations CD, DE and EF were found to be segregated with partial intermixing at their interfaces and no mixing between the combinations of AD, AE, AF, BD, BE and BF were observed. Figure 5.18 displays the simulated liquid volume fraction profiles along the bed height for three different upflow velocities. As already shown, crystals were segregated according to their sizes with some intermixing between successive size classes. The mixing  138  zones were found to expand with increasing upflow velocity and observed to be the maximum at the highest upflow velocity of 26.77 mm/s. The simulated pressure profiles for the MC mixture are compared with the experimental data in Figure 5.19. It can be observed that the simulated pressure profiles are in good agreement with the experimental results. The existence of curvature in the simulated pressure profiles, especially for run MC3, is evident; this reflects the gradual variation of solid volume fraction, indicating some intermixing between particles. As performed with other mixture groups (MS and ML), the expanded bed heights determined experimentally, are compared with the values predicted by CFD and a serial model. The CFD predictions closely match with the experimental results (Fig. 5.20). The highest deviation of 8% was found for the case of MC2. The predictions by using the serial model also match quite well with the experimental results. The serial model was found to predict a somewhat higher expansion, as this model assumes complete segregation of the particles being fluidized and hence estimate the maximum likely bed height.  5.6  Conclusions An Eulerian-Eulerian granular multi-fluid CFD model was employed for the  simulation of both mono and poly-dispersed fluidized bed of struvite crystals. The simulated bed expansion behaviour of different sizes of struvite crystals was found to be consistent with the experimental results. A meaningful CFD simulation of a liquid-solid fluidized bed of struvite crystals is possible, using “volume equivalent” diameter as the characteristic dimension of a particular crystal group. The mixing and segregation characteristics of liquid solid fluidized bed of different sizes of struvite crystals, captured by the CFD simulations  139  were found follow the basic principle of particle segregation: at steady-state all six size classes of struvite were found to be classified according to their sizes, with the largest ones at the bottom and the smallest one at the top of the bed. And a very limited intermixing between two successive layers of particle classes was observed. However, further detail experimental investigation is warranted in order to validate the simulation results. The CFD simulated overall bed characteristics were found to be consistent with the established correlations found in the literature.  140  Nomenclature Symbols Ar CD Cfr d  Archimedes number defined by equation 5.28 Drag coefficient Coefficient of friction between solid phases m and i Volume equivalent diameter of particles (m) Restitution coefficient for particle collisions Restitution coefficient due to collisions between solid phases m andi External body force applied to liquid phase  p  External body force applied to the  go,ss H  Acceleration due to the gravity (9.81 m/s ) 2 Radial distribution function of solids Distance between two consecutive pressure ports (m) Unit tensor  7 ‘2D  k 1 K 1 = K K 1  P P p q Re Re Re  us  X Y  t1 h  solid phase  Second invariant of the deviatoric stress tensor Diffusion coefficient for solid phase energy fluctuation Momentum exchange between solid-liquid phases Momentum exchange coefficient between liquid and ith solid phases Momentum exchange coefficient between solid phases m and i Static pressure shared by all phases Solid pressure Solid pressure for th solid phase Coefficient in Equation 5.24 Coefficient in Equation 5.24 Reynolds number Reynolds number under terminal settling conditions for the multi-particle system Reynolds number at particles’ terminal settling velocity for a single particle system Velocity vector for liquid phase (mis) Velocity vector for th solid phase (mis) Velocity vector for mth solid phase (mis) Terminal velocity correlation for the solid phase (mis) Coefficient in Equation 5.22 Coefficient in Equation 5.22  141  Greek letters 1 a  Volume fraction of liquid phase Volume fraction of solid phase Volume fraction of ith solid phase Maximum solid volume fraction (or packing) in the bed Collisional dissipation of the energy  2=(,, A ) 1 P =(Ps, P1) ,u1  Bulk viscosity of the phases Solid bulk viscosity Shear viscosity of the phases Solid shear viscosity Solid shear viscosity  11 r’s,co1  Solid collisional shear viscosity  rs,kin  I’  Solid kinetic shear viscosity  fls,f  Solid frictional shear viscosity  1 p  Density of liquid 3 (kg/rn and ith solid phase ) Density of th solid phase (kg/m ) 3 Angle of internal friction Energy exchange between the liquid and the  ith  solid phases  Stress tensor of different phases Stress tensors for the liquid phase Stress tensors for the  ith  solid phase  granular temperature for solid phase granular temperature for the th solid phase Others A, B, C, D, E,&F EXP/Exp MS, ML & MC R R-Z  Crystal size classes with decreasing diameter Experimental values Mixture of different size classes Size ratio of two different size classes of particles Richardson-Zaki relation  Abbreviations 2-D BNR CFD  Two Dimensional Biological Nutrient Removal Computational Fluid Dynamics 142  Fluent RAM UBC UDF  CFD software written and distributed by Fluent Inc Random Access Memory University of British Columbia User Defined Function  143  Table 5.1  Properties of different size classes of struvite crystals and experimental conditions  Struvite Size Sieving Group Range (mm) A B C D E F  2—2.2 1.68—1.98 1.41—1.68 1.0—1.18 0.6—0.833 0.5—0.6  Density Volume equivalent (kg/m3) diameter (pm) 2233 1687 1974 1687 1687 1687 1677 1164 804 1650 602 1600  ML[A,C and D]  2—2.2 1.41—1.68 1.0—1.18  2233 1687 1164  1687 1687 1677  209  0.205 0.205 0.205  15.66—28.68  MS[D,E and F]  1.0—1.18 0.6—0.833 0.5—0.6  1164 804 602  1677 1650 1600  225  0.189 0.192 0.198  13.07—27.50  MC[A,B,C, D,EandF]  2—2.2 1.68—1.98 1.41—1.68 1.0—1.18 0.6—0.833 0.5—0.6  2233 1974 1687 1164 804 602  1687 1687 1687 1677 1650 1600  216  0.099 0.099 0.099 0.099 0.101 0.102  14.60—26.77  Initial bed height (mm) 110 220 111 192  Packed bed solid volume fraction 0.62 0.637 0.635 0.624  Range of upflow velocity (mmls) 11.10—26.93 12.21—25.53 9.25—23.07 5.55—24.67  —  —  —  79  0.541  8.02—16.28  144  Table 5.2  Summary of simulation settings (model parameters)  Model parameters Total reactor height Reactor width Inlet boundary condition Outlet boundary condition Wall boundary condition Mesh resolution Discretization method Convergence criteria Time step Maximum iterations per time step Coefficient of restitution of particle and wall  Values 1392 mm 100 mm Uniform velocity inlet Pressure outlet No slip condition 2x2 mm Second order upwind i0 0.00 1 S 100 0.9  145  Table 5.3  Comparison of bed pressure drop and voidage estimated using different grid size  Struvite crystal group A  Mesh sizes (mm) lxi 2x2 3x3 4x4  F  2x2 3x3 4x4  Total bed pressure drop (Pa) Simulation Experimental 264.0 265.0 266.0 266.0 261.0 161.3 162.0 170.0  160.0  Voidage  Simulation time (h)  Simulation 0.55 0.55 0.56 0.55  Experimental 0.55  0.68 0.68 0.69  0.68  168.0 60.0 20.0 15.0 22.7 10.5 9.0  146  Table 5.4  Comparison of bed pressure drop and voidage estimated using different Drag models  Struvite Drag laws used crystal group Wen&Yu(1966) Gidaspow (1986) F Modified Syamlal O’Brien (1988)  Pressure drop Voidage Simulated Experimental Simulated Experimental 161.30 166.00 189.20  160.00  0.68 0.70  0.68  0.78  147  Table 5.5 Size group  Size ratios and hypothetical binary combinations of different size classes  A A B C D E F  2233.40 1973.76 1686.80 1164.33 803.79 602.45  Hypothetical combinations with size ratio (R)  Size ratio between  Diameter (im)  I  1.00 1.13 1.32] 1.92 2.78 3.71  B  1.00 1.17 1.70 2.46 3.28  C  D  E  1.00 2.10 2.80  1.00 1.45 1.93  1.00 1.33  1.24<R R>1.58 <1.58 AD AC AE CD DE AF EF BF BD 1.00 BE, BF F  R<1.24 AB BC  148  Figure 5.1  Schematic of the a) the experimental set-up; and b) the computation domain  (a)  J ank 1  Fluidized bed Optical fiber probes Manometers  Flow meter  Pump  149  (b)  Liquid Outlet Pout: 1 atm  100mm  H H Upflow liquid velocity  150  Figure 5.2  (a) Snapshot of solid volume fractions of struvite particles (group D) at different time intervals, fluidized at a superficial velocity of 24.67 mm/s. (b) comparison of overall liquid volume fraction with experimental result (a)  I  .29e-01 5.Q8e-0I  -1300  5.06.-Ol  -1200  5.35.-UI 5.03.-UI  -1100  4.72*-Ol  -1000  4..-01 4.0G.-Ui  -900  3.77.-Ui  -800  3.46.-Ol 3.15.-Ol  -700  2.83.-UI 2.52.-UI  -600  2.20e-0I  -500  I .89.-UI I .57.-Ol  400  I .26.-UI  -300  Q.44-02 6.29 .02  -200  3.15.-02  -100  0.00e4O0  1)  (c)  I Os  5s  lOs  15s  20s  25s  30s  40s  I SOs  -0  I 60s  120s  151  (b)  0  Simulated  —  —  Experimental  0.7 —  0.6 j 5 O. 0  0.3 1  E 0.1 0 0  10  20  30  40  50  60  70  80  90  100  110  120  Time (s)  152  Figure 5.3  Bed expansion characteristics: comparison between experimental results, CFD and Richardson-Zaki predictions for (a) struvite size class A, (b) struvite size class B, (c) struvite size class C, (d) struvite size class D, and (e) struvite size class F.  (a)  ACFD  OEXP  —-R-Z  0.6  0.55 0 -  0  0.5  a  2  o  0.45  a 0  0  I  04’  0  0.3 10  12  14  16  18  20  22  24  26  28  Upflow superficial liquid velocity (mm/s)  153  (b)  A  0.6  1  CFD  0  EXP  —  -  R-Z  0.55 0 A  0 A  0.5  0 A  0  0.45  0.4  0.35  0.3  -—--F——.  10  12  14  16  18  20  22  24  26  28  Upflow superficial liquid velocity (mmls)  154  (c)  ACFD  OEXP  —-R-Z  16  18  0  0.6  I  0.4  0.35  0.3 8  10  12  14  20  22  24  Upflow superficial liquid velocity (mm/s)  155  (d)  ACFD  OEXP  —-R-Z  0.7  —  0.6 -A  -  e  0  0.55  C  -  0.45 0.4--  0.35 0.3  --—  3  ---  -  8  -  -——-  13  18  23  Upflow superficial liquid velocity (mmls)  156  (e) 0.8  A  CFD  0  Exp  —  -  R-Z  A 0 —.  ?  a 0 -  a  a .  A 0  ‘J.v  0.5 6  8  10  12  14  16  18  Upflow superficial liquid velocity (mmls)  157  OCFD  •Exp  0.55 -  0.54w  0  0  0  0  00  0.0 15  0.02  0  00000  OOOOOOoO  OO  0.5  0.47 0.46  -  0  0.005  0.01  0.025  0.03  0.035  0.04  0.045  0.05  Radial position (m) Figure 5.4  Comparison of the time-averaged liquid volume fraction, on radial positions, for the simulated and experimental results for struvite particles (group B), fluidized at a superficial velocity of 24.67 mm/s.  158  A  Area-weighted Average_CFD  0  Overall_CFD  D  Area-weighted Average_Exp  0.56 0.541  2 2  0.44 0.42 i 0.4  T  15  17  19  21  23  25  27  Upflow superficial liquid velocity (mm/s)  Figure 5.5  Comparison of the time mean area weighted liquid volume fraction at a bed height of 0.184 m, (both simulated and experimental results) with the overall CFD predicted voidage, for struvite particles (group D).  159  e  800  Exp_MS1  — CFD_MS 1  X — -  Exp_MS2  t  Exp..MS3  o  Exp_MS4  CFD_MS2  — —  CFD_MS3  - - -  CFD_MS4  700 600 ,  500..1 400 .  .0  300 •  •••  200 ‘ •  100  x  0  -..  4%  0  4.-  •  0 0  0.1  0.2  0.3  0.4  0.5  0.6  Bed height (m)  Figure 5.6  Time average pressure profiles along the bed height at different upflow velocities for the mixture group of MS  160  0 —  Exp_MSI CFD_MS 1  X Exp_MS2 CFD_MS2  —  —  Exp_MS3 CFD_MS3  0 —  Exp_MS4 CFD_MS4  1.1  1  0.9 0  c.e  0.8  a 0  0  0.7  0.6  0.5 0  0.1  0.2  0.3  0.4  0.5  0.6  Bed height (m)  Figure 5.7  Time average liquid volume fractions along the bed height at different upflow velocities for the mixture group MS  161  —  0.6  Average_Dia_MS2  -  -  -  Average_Dia_MS3  0.5  0.4  0.1  0  0.4  0.5  0.6  0.7  0.8  0.9  1  1.1  1.2  1.3  Average diameter (mm)  Figure 5.8  Simulated time average mean crystal diameter along the bed height at two different upflow velocities for the mixture group of MS  162  —  Bulk density_MS2  -  -  -  Bulk density_MS3  0.6  0.5  0.4 S  I:  S  I’  S S  —  0.1  0  900  950  1000  1050  1100  1150  1200  1250  1300  1350  Bulk density (kg/m3)  Figure 5.9  Simulated time average bulk density along the bed height at different two different upflow velocities for the mixture group of MS  163  A  0.7  Experimental  0  CFD  —  —  Serial model  0.65  A  /  0.45  /  /  /  /0  -  0.4 0.35 0.3  -  0.01  -  0.012  0.014  0.016  0.018  0.02  0.022  0.024  0.026  0.028  Upflow superficial liquid velocity (mis) Figure 5.10  Comparison between experimentally determined bed expansion behaviour of MS group and CFD and serial model predictions  164  ‘  800  Exp_ML1  —CFD_ML1  -  o Exp_ML4  Exp_ML3  Exp_ML2  X —  CFD_ML2  — —  CFD_ML3  -  -  -  CFD_ML4  700  600 500 400 4 4 4  300  4  4  200 4 4  4  100 0. 0  0.05  0.1  0.15  0.2  0.25  0.3  0.35  0.4  0.45  0.5  Bed height (m) Figure 5.11  Time average pressure profiles along the bed height at different upflow velocities for the mixture group of ML  165  0  1.1 —  I  Exp_MLI  X Exp_ML2  CFD_ML1  —  CFD_ML2  Exp_ML3 —  CFD_ML3  0 —  Exp_ML4 CFD_ML4  1  0.9 0.8 0.7  E 0.6 0.5 0.4  0.3 0  0.05  0.1  0.15  0.2  0.25  0.3  0.35  0.4  Bed height (m)  Figure 5.12  Time average liquid volume fractions along the bed height at different upflow velocities for the mixture group ML  166  —ML1  0.4  -  -  -  ML2  —  —ML3  —  -  ML4  0.35 0.3  O.15  0.1  -.  0.05  0 1  1.2  1.4  1.6  1.8  2  2.2  2.4  Average particle diameter (mm)  Figure 5.13  Simulated time average mean crystals diameter along the bed height at different two different upflow velocities for the mixture group of ML  167  -  -MLI  —ML2  -  —  ML3  -  -  -  ML4  0.4 0.35 I  0.3  j  0.25 S  ) I  1 1  0.15  I Ii  0.1  -I  J 1  0.05 0  900  1000  1100  1200  1300  1400  1500  Bulk density (kglm3)  Figure 5.14  Simulated time average bulk density along the bed height at different two different upflow velocities for the mixture group of ML  168  0  CFD  A  Experimental  —  —  Serial model  0.38 0.36 0 A  0.32 ‘  0 A  03  0.28  -  A  0.26 A  0.24 0.22 0.2 0.012  0.014  0.016  0.018  0.02  0.022  0.024  0.026  0.028  0.03  Upflow superficial liquid velocity (mis)  Figure 5.15  Comparison between experimentally determined bed expansion behaviour of ML group and CFD and serial model predictions  169  Figure 5.16  Snapshot of solid volume fractions of struvite particles for MC groups at different time intervals, fluidized at a superficial velocity of 26.77 mm/s (a) at 15s  170  (b) at 30s  171  (c) at 50s  172  (d) at 120s  173  —  0.5  —  0.45  —Solid_A Solid_E  —  Solid_B —Solid_F —  —  —  —Solid_C Total voidage  — —  Solid_D  —  1  0.4  0.35  1 0.3  I  I  0.25  )  0.2  / 1  0.15  —I--.-.-  0.1  -=-  —  —  —  0.05  —  —  . —-=-  0  0.1  0.2  0.3  0.4  1  0.5  0.6  0.7  0.8  0.9  1  Volume fraction of the phases  Figure 5.17  Simulated time average solids and liquid volume fractions for MC group particle mixture fluidized at upflow velocity of 26.77 mm/s  174  0  1.1  X Exp_MC2  Exp_MCI  —CFD_MC1  0  —CFD_MC2  Exp_MC3  —CFD_MC3  1 0.9 0 C  0.8  0  0.7  EC C  0.6  C  0.5 0.4 0  0.05  0.1  0.15  0.2  0.25  0.3  035  0.4  0.45  0.5  Bed height (m)  Figure 5.18  Time average liquid volume fractions along the bed height at different upflow velocities for the mixture group MC  175  ‘  800  —  Exp_MC1 CFD_MC 1  Exp_MC2 —  —  Exp_MC3  0  CFD_MC2  -  -  -  CFD_MC3  700  600 500 400 300 200 100  0 0  0 0  0.1  0.2  0.3  0.4  0.5  0.6  Bed height (m)  Figure 5.19  Time average pressure profiles along the bed height at different upflow velocities for the mixture group of MC  176  A  Exp  0  CFD  —  —  Serial model  0.55 0.5 0.45  —•  A  !0.4 0 A  0.35 0  0.3 0.25 0.2 0.012  -  0.014  0.016  0.018  0.02  0.022  0.024  0.026  0.028  Upflow superficial liquid velocity (mis)  Figure 5.20  Comparison of between experimentally determined bed expansion behaviour of MC group and CFD and serial model predictions  177  5.7  References  Adnan, A., Mavinic, D.S., and Koch, F.A. (2003). Pilot-scale study of phosphorus recovery through struvite crystallization examining the process feasibility. J. Environ. Eng. Sci. 2, 315-324. —  Battistoni, P., De Angelis, A., Pavan, P., Prisciandaro, M., and Cecchi, F. (2001) Phosphorus removal from a real anaerobic supematant by struvite crystallization. Water Res. 35 (9), 2167-2178. Booram, C.V., Smith, R.J., and Hazen, T.E. (1975). Crystalline phosphate precipitation from anaerobic animal waste treatment lagoon liquors. Trans. ASAE, 18, 340-343. Cheng, Y., and Thu, J. (2005) CFD modeling and simulation of hydrodynamics in liquidsolid circulating fluidized beds. Can. J. Chem. Eng. 38, 6 10-620. Cornelissen, J.T., Taghipour, F., Escudie, R., Ellis, N., and Grace, J.R. (2007) CFD modeling of liquid-solid fluidized bed. Chem. Eng. Sci. 62, 6334-6348. Ding, J., and Gidaspow, D. (1990) A bubbling fluidization model using kinetic theory of granular flow. AIChE J. 36, 523-53 8. Drew, D. (1983) Mathematical modeling of two-phase flow. A Rev. Fluid Mech. 15, 261-291. Drew, D.A., and Lahey, R.T. (1993) Particulate two-phase flow, Butterworth-Heinemarm, Boston, MA. Epstein, N. (2003) Liquid-solids fluidization. In: Yang, W-C. ed. Handbook of Fluidization and Fluid-particle Systems, Marcel Dekker, New York. Ergun, 5. (1952) Fluid flow through packed columns. Chem. Eng. Prog. 4, 89-94. Fluent (2006) Fluent User’s Guide, Fluent Inc., Lebanon, NH, USA. Garside, J., and Al-Dibouni, M.R. (1977) Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems. md. Engng Chem. Process Des. Dev. 16, 206-2 13. Gidaspow, D. (1994) Multiphase Flow and Fluidization Continuum and Kinetic Theory Descriptions, Academic Press, Boston, MA. Johnson, P.C., and Jackson, R. (1987) Frictional-collisional constitutive relations for granular materials with application to plane shearing. J. Fluid Mech. 176, 67-93. Lettieri, P., Di Felice, R., Racciani, R., and Owoyemi, 0. (2006) CFD modeling of liquid fluidized beds in slugging mode. Powder Technol. 167, 94-103.  178  Lun, C.K.K., Savage, S.B., Jeffrey, D.J., and Chepumiy, N., (1984) Kinetic theories for granular flow: inelastic particle in Couette flow and slightly inelastic particles in a general flow field. J Fluid Mech., 140, 223-256. Mullin, J.W., and Nyvlt, J. (1970). Design of classifying crystallizers, Trans. Instn. Chem. Engrs. 48, T7-T14. Parsons, S.A., Wall, F., Doyle, J., Oldring, K., and Churchley, J. (2001) Assessing the potential for struvite recovery at sewage treatment works. Env. Tech. 22, 1279-1286. Rahaman, M.S., and Mavinic, D.S. (2009) Recovering nutrients from wastewater treatment plants through struvite crystallization: CFD modelling of the hydrodynamics of UBC MAP fluidized-bed crystallizer. Water Sci. Technol. 59 (10), 1887-1892. Rahaman, M.S., Ellis, N., and Mavinic, D.S. (2008a) Effects of various process parameters on struvite precipitation kinetics and subsequent determination of rate constants. Water Sci. Technol. 57 (5), 647-654. Rahaman, M.S., Mavinic, D.S., and Ellis, N. (2008b). Phosphorus recovery from anaerobic digester supernatant by struvite crystallization: model-based evaluation of a fluidized bed reactor. Water Sci. Technol. 58 (6), 1321-1327. Rahaman, M.S., Mavinic, D.S., Bhuiyan, M.I.H., and Koch, F.A. (2006). Exploring the determination of struvite solubility product from analytical results. Env. Tech. 27, 951-961. Reddy, R.K., and Joshi, J.B. (2009) CFD modeling of solid-liquid fluidized beds of mono and binary particle mixtures. Chem. Eng. Sci. 64 (16), 3641-3658. Richardson, J.F., and Zaki, W.N. (1954) Sedimentation and fluidization: Part I. Trans Instn Chem Engrs. 32, 35-53. Schaeffer, D.G. (1987) Instability in the evolution equations describing incompressible granular flow. J. Duff Eq. 66, 19-50. Syamlal, M., and O’Brien, T.J. (1988) Simulation of granular layer inversion in liquid fluidized beds. mt. J. Multiphase Flow, 14(4), 473-48 1. Syamlal, M., and O’Brien, T.J. (2003) Fluid dynamic simulation of 03 decomposition in a bubbling fluidized bed. AIChE J. 49, 2793-280 1. Shiau, L.D., and Lu, T.S. (2001) Interactive effects of particle mixing and segregation on the performance characteristics of fluidized bed crystallizer. md. Eng. Chem. Res. 40, 707-713. Taghipour, F., Ellis, N., and Wong, C. (2005) Experimental and computational study of gassolid fluidized bed hydrodynamics. Chem. Eng. Sci. 60, 6857-6867.  179  Vejahati, F., Mahinpey, N., Ellis, N., and Nikoo, N.B. (2009) CFD simulation of gas-solid bubbling fluidized bed: A new method for adjusting drag law. Can. J. Chem. Eng. 87(1), 1930. Wen, C. Y., and Yu, Y. H. (1966) Mechanics of fluidization. Chem. Eng. Prog. Symp. Ser. 62, 100-111. Werther, J. (1999) Measurement techniques in fluidized bed. Powder Technol. 102, 15-36. Yoshino, M., Tsuno, H., and Somiya, I. (2003) Removal and recovery of phosphate and ammonium as struvite from supernatant in anaerobic digestion. Water Sci. Technol. 48, 171178. Zimmerman, S., and Taghipour, F. (2005) CFD modeling of the hydrodynamics and reaction kinetics of FCC fluidized-bed reactors. md. Eng. Chem. Res. 44, 98 18-9827.  180  Chapter 6  Phosphorus recovery from anaerobic digester supernatant by struvite crystallization: Modelbased evaluation of a fluidized bed reactor 5  6.1  Introduction In the wastewater treatment industries, significant levels of phosphates are released in  the secondary anaerobic digestion phase of the biological nutrient removal (BNR) process. Under favorable conditions, this high level of phosphates in anaerobic digester supernatant causes struvite (MAP: 0 2 P MgNH . 4 6H ) precipitation in the digester line, especially in the O elbows and the suction side of pumps. Struvite precipitation is also a very common phenomenon in the sludge derived from the anaerobic digestion of animal farming liquid wastes and agricultural wastes (Booram el. al., 1975). One way to solve this precipitation problem, in BNR plants, is to recover phosphorus from the supematant through struvite crystallization before it forms and accumulates on the equipment. This process not only alleviates the formation of unwanted struvite deposits, but also provides an environmentally benign and renewable nutrient source to the agricultural industry (Yoshino et al., 2003). In recent years, a number of studies have been conducted by various researchers, with respect to recovering phosphorus from wastewater through struvite crystallization. The studies include process identification and the performance evaluation in both bench and pilot scale operations. The technology has also been validated in some full-scale wastewater A  version of this chapter has been published:  Rahaman, M.S.; Mavinic, D.S. & 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), 132 11327.  181  treatment plants, operating in different parts of the world. The largest ones are operated in Japan: Shimane Prefecture (500 m /day), Fukuoka Prefecture (170 m 3 lday); and at Osaka 3 South Ace Center (266 m /day) (Parsons et al., 2001). The Shimane Prefecture reactor has 3 been found to remove 90% of P0 -P from the treated supernatant. A full scale struvite 4 crystallization plant has also been installed in Italy to remove 4 P0 P from anaerobic digester supematant (Battistoni et al., 2001). In most of these cases, the reactor configuration was considered as a fluidized bed system; due to the fact that the fluidized bed crystallizer suitably produce uniform sized large crystals. The Environmental Engineering Group in the Department of Civil Engineering at the University of British Columbia (UBC), has been performing scientific studies on phosphorus recovery from domestic wastewater since 1999 and has developed a novel reactor design that converts soluble phosphates into crystalline struvite. The basic design of the lab and pilotscale UBC MAP (Magnesium Ammonium Phosphate) crystallizer is based on a fluidized bed system. Experimental data reveals that the UBC MAP fluidized bed crystallizer is effective in recovering phosphorus (80—90% recovery) from both synthetic and real supematants (Adnan et al., 2003). However, in designing a reactor for the plant scale operations, various operating parameters that may affect the process performance have to be identified and accounted for. Performance of a complex process, such as struvite crystallization in a fluidized bed crystallizer, can effectively be evaluated by employing a mathematical model for the reactor. The currently available crystallization modeling tools are limited by their application to predict only the solubility and supersaturation of the reactive crystallization of struvite. A comprehensive modeling effort is, therefore, needed to facilitate an efficient design of the UBC MAP crystallizer.  182  Although a substantial amount of research has been documented in the literature on developing mathematical model for the industrial crystallizers (based on continuous stirred tank reactors, CSTR), very few researchers have attempted to develop models for a fluidized bed crystallizer. This may be due to the complex nature of a fluidized bed reactor and the limited scope of the latter type of reactor for crystallization processes. Frances et al. (1994) developed a model for a continuous fluidized bed crystallizer. In order to take into account segregation and mixing of particles within the bed, the model was developed based on the description of the fluidized bed as a multistage crystallizer. The model provided better prediction of mean size of the product crystals over the model, developed 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. Influences of various parameters on ammonium sulphate crystallization in a fluidized bed crystallizer were simulated by Belcu and Turtoi (1996). The model was developed based on a phenomenological approach and results demonstrated significant influence of equipment geometry on process performance. Shiau and Liu (1998) developed a theoretical model for a continuous fluidized bed crystallizer. It was assumed that the liquid phase moves 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 vertical position within the reactor, and allows one to study the effects of various operating parameters, such as feed rate of seed crystals and height/diameter ratio, on the performance of a continuous fluidized bed crystallizer. Later, Shiau and Lu (2001) performed a study on the interactive effects of particle mixing and segregation on the performance characteristics of a batch fluidized bed crystallizer. In this model, the liquid phase was assumed to flow in a  183  plug flow pattern and the solid phase was represented by a series of equal-sized, ideally mixed beds of crystals. However, the crystals in different beds are totally segregated. This single parameter model could be employed to investigate both the extreme conditions (completely mixed and segregated), as well as for the intermediate region of mixing. In most of the cases found in the literature, the fluidized bed crystallizer is modeled and designed based on perfect size classification of the particles in the crystal bed (Mullin and Nyvlt, 1970). Therefore, in this work, mathematical relationships are derived, based on complete segregation of the bed crystals, to model the UBC MAP fluidized bed reactor. A similar approach was also adopted by Shiau and Liu (1998) in modeling the fluidized bed reactor for potassium alum crystallization.  6.2  Process description The basic design of the UBC MAP crystallizer follows the concept of a fluidized bed  reactor. As depicted in Figure 6.1, the reactor has four distinct zones depending on the diameter of the column. The bottom part of the fluidized bed reactor is called the harvest zone (A; inner diameter, (ID) 26 mm); above that the active zone (B; ID 39 mm), while the top fluidized section is the ‘fine zone’ (C; ID 65 mm). There is a settling zone, also called ‘seed hopper’ (D; ID 206 mm) at the top. The heights of the bottom three sections (A, B and C) are the same, 410 mm, but the seed hopper (D) has a height of 305 mm. In the struvite crystallization process, synthetic 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 to avoid any encrustation problem in inlet pipes. Seed crystals are added into the crystallizer from the seed  184  hopper and are allowed to grow in the supersaturated solution. The superficial liquid velocity is maintained in such a way that all the 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 in the bottom and the smaller crystals rise to the top of the crystallizer. The larger crystals at the bottom, once they have achieved the desired size, are settled into the harvest zone and are withdrawn from the bottom of the reactor.  6.3  Mathematical model development In developing the model, it is assumed that the process is isothermal, the crystals in  the fluidized bed are perfectly classified, aqueous solutions moved upward through the bed in plug flow, seeds are of uniform size, no uncontrolled nucleation, crystals growth is size dependent and a constant number of seed crystal ‘N’ is added into the crystallizer from the seed hopper, and both agglomeration and breakage are negligible. To understand the behaviour of the UBC MAP continuous fluidized bed reactor, the species concentration of struvite, crystal sizes and bed voidage within the reactor, need to be derived. In order to derive those expressions, mass balances for both solute and the crystals are performed over an incremental height along the fluidized bed. A similar approach was adopted by Shiau and Liu (1998) for the case of potassium alum crystallization in a fluidized bed reactor. Other necessary correlations are documented in the literature to complete the model. The steady-state mass balance of the solute, struvite over an incremental height AH (as shown in Figure 6.1) can be described as,  185  —  (1 +‘C ) 0  (CH  (1  —  2 )(Gp:) =0 (flL  -(6.1)  Since the struvite crystals are composed of three constituent ions, 4 P0 Mg and NH , , here the 4 single-species solute concentration will be replaced by the independent dissolved concentration of the constituent species of struvite. Hence, the solute concentration ‘C’ in the above equation denotes the concentration of struvite in the liquid phase and it is the sum of all the constituent species (Mg, NH 4 and P0 ) dissolved in the solution, expressed as mass of 4 species per mass of water. In Equation 6.1, the first term represents the time rate of disappearance of the crystal’s constituent species in the liquid phase. Where,  Q: flow rate; Pt: density of water; Co: concentration of struvite in the liquid phase at  entry; CH: struvite concentration at bed height H; and CH+AH: struvite concentration at the height increment, AH, above H. The second term represents mass deposition of constituent species, Mg, NH 4 and P0 4 onto the suspended crystals in the horizontal slice, per unit time. Where, at: liquid volume fraction (bed voidage); A: cross-sectional area of the reaction zone; AH: height increment; a: volume factor; L: crystal (particle) radius; /3: surface factor; G (mIs): linear growth rate of struvite crystals; and Ps *: density of stuvite excluding the weight of the water of crystallization. By mathematical manipulation of Equation 6.1 and considering the limit as AH approaches zero, we get: )(1 + C 1 dC = A/3p:(1 a ) 0 G dH QL 1 ap —  (62)  186  where, C is the struvite concentration in liquid phase at the bed height of H. In Equation 6.2, all variables other than C, L and H must be eliminated from the expression. A close look at Equation 6.2 reveals that all the parameters, except G and a!, are constant. Therefore G and al are needed to be expressed in terms of known variables and parameters. Widely accepted and extensively used in fluidization study, the Richardson and Zaki correlation (1954) is used to describe the expansion characteristic (voidage) of the UBC MAP fluidized bed crystallizer.  1  1na  QIA /  ) g 1 4 ( P P L 225p p 1  l0(_LT)1  Where, D: bed (column) diameter; particle;  j.t:  ‘:  1I3  1  ,)  Ly  dimensionless diameter factor for a solid struvite  kinematic viscosity of water; and g: acceleration due to gravity.  For struvite growth, the rate expression, derived by Bowers and Westerman (2005), is adopted and expressed as, —  —  0 —C])x([A] 0 —7.331[C mk{([M] 0 —7.331[C 0 —7.331[C 0 —C])x([P] 0 _CJ)_P}(__L_)() 0 —C]) [3(7.331[C —2([M1 0 +[A] 0 )(7.331[C —C])+([M] +[P] 20 [A] +[A] 0 [P] 0 0 3 [ +[P] ) A] ]p  (6.4) where, [Mj 0 represents the molarity of magnesium, ammonium and phosphate , [A] 0 0 and [P] in the liquid phase at the entry of reaction zone, respectively. ‘m’ is the bed surface area per volume of reacting liquid and k’ is the surface area specific rate constant. Pe is the conditional solubility product at equilibrium. MW is the molecular weight of struvite. The second mass balance, with respect to struvite crystals, over the same horizontal slice can be illustrated as:  187  pNa(L  —  ) 1 3 L 14  =  (1(M  (flL ) 2 (Gp)  -(6.5)  where, the left hand side represents particle mass rate difference between exiting and entering particles (LH: radius of struvite crystals at bed height H; LH+: radius of struvite crystals at bed height H+rlH) and the right hand side represents time rate of mass increase of particles within the slice. By rearranging Equation 6.5 and taking the limit as AH approaches zero we get: dL dH  —  —  —  Afi(1 a ) 1 G 3 L 2 3Na —  (6 6)  The differential Equations 6.2 and 6.6, along with the Equations 6.3 and 6.4, can now be solved simultaneously to determine the variations of stnivite concentration and crystal size distribution within the UBC MAP fluidized bed crystallizer.  6.4  Experimental In order to validate the modeling approach and to compare the model predictions with  the experimental results, experimental runs were conducted in a lab-scale, fluidized bed reactor. The reactor configuration and the processes involved were the same as illustrated in the process description section. Struvite seed crystals, of 250 p.m size, were added from the seed hopper and the flow rates of synthetic supernatant, magnesium and caustic additions were such that the resulting upflow liquid velocity in the harvest zone was 0.0362 mIs. The upflow velocity was selected in such a way that crystals of all size range keep uniformly fluidized in the reaction zone. In order to maintain fluidization of the crystals, the upflow velocity is set to a value which is higher than the minimum fluidization velocity of the largest particle (product crystals) and lower than the terminal velocity of the smaller particles (seed 188  crystals). This velocity will ensure fluidization of all the particles involved in the whole process. Other operating conditions and the process parameters are listed in Table 6.1. The pH of the reaction solution was maintained constant (8.4) during the experiment by using a pH controller. Once the steady state was reached, both the liquid and solid sample were collected from different heights of the crystals bed (HIlt  =  0, 0.2, 0.4, 0.6 and 1.0; H 1 is the total  expanded bed height), using a long tube connected to a plastic syringe. The solid crystals were then separated and the size distribution was analyzed using a particle size analyzer, Malvem Mastersizer 2000. The liquid sample was filtered through a 0.45 m filter and the filtered samples were then analyzed for 4 -N and Mg. Analyses for P0 4 P0 P, NH -P and 4 NH 4 N were done using the flow injection method on a LaChat QuikChem 8000 analytical instrument.  Magnesium  analysis  was  performed  by  flame  atomic  absorption  spectrophotometry, using a Varian Inc. SpectrAA22O Fast Sequential Atomic Absorption Spectrophotometer. In order to estimate the overall bed voidage, pressure drop across the bed was measured by installing two L shaped water manometers; one is just right above the liquid distributor and another is connected above the bed of crystals.  6.5  Results and discussion The model described in the earlier section is applied for simulating the bench scale  UBC MAP fluidized bed crystallizer. In this simulation, seed struvite crystal was considered as 250 im in diameter and the product crystals were expected to be 750 urn in diameter. All of the operating conditions and necessary process parameters were kept the same as those for the experimental runs, and are provided in Table 6.1. Equations 6.2 and 6.6 along with the  189  boundary conditions, (H0; C=Co and H=H; L=L. ) were solved numerically in Matlab to 0 generate struvite concentration and crystal size (radius) as a function of bed height. The boundary condition for C was considered as the C , which is sum of the species concentration 0 of struvite in the inlet (H=0) and for L, the boundary condition was considered as the seed crystal size (L ) at the bed height 0 By solving Equation 6.2, one obtains the profile for mass concentration (C) of struvite in the liquid phase. Since, in dilute solutions, the molarity of struvite crystals is approximately equal to 7.331 times the mass concentration of struvite, the predicted C values are then converted to amount of struvite precipitated (x) by subtracting the C value from C 0 values and then multiplying by 7.33 1. These struvite values are then converted to predicted values of dissolved 4 P0 P and NFL-N by subtracting ‘x’ values from the respective initial values. Figure 6.2 depicts the variation of both 4 P0 P and 4 NH N concentrations along the height of the reactor. As shown in Figure 6.2, the simulated concentrations of both P0 -P and 4 NH 4 N decrease with increasing bed height. A similar trend was observed in the experimental results. Immediately after the injection of supersaturated solution into the reactor, the supersaturated solution comes in contact with the bed particle, and starts relieving the excess supersaturation onto the growing crystals. Since it is assumed that the bed is perfectly classified, the larger crystals are likely to be present at the lower part of the reactor. As such, the crystals at the bottom of the reactor provide less surface area than that of crystal bed in the upper section. However, the solid volume fraction is higher at the bottom of the reactor, which also affects the total amount of surface area available for crystal growth. More importantly, the supersaturation, which is the main driving force for crystal growth, is higher at the bottom of the reactor. However, as observed in Figure 6.2, the initial rate of  190  decrease in P0 -P is relatively slow at the bottom of the reactor. The rate (represented by the 4 slope in Figure 6.2) is reasonably higher in the middle part of the reactor and then it slowly decays near the top of the reactor. An almost identical trend is observed for the case of NH 4 N. The reason for a steeper slope in the middle zone may be due to the fact that the middle portion of the reactor possesses reasonably high surface area as well as comparable supersaturation, which results in higher growth rate of the crystals. Figure 6.3 compares the values of the predicted removal efficiencies for P0 -P and NH 4 -N, with the corresponding 4 values observed in the experimental runs. A reasonably good agreement is observed between the predicted values and the experimental results. Figure 6.4 displays modeled variation of particle size with respect to the bed height. A monotonic decrease in the crystal size is observed along the bed height. This phenomenon resembles the desirable size classification of the bed crystals. For Lmax/L> 2.2, Al-Dibouni and Garside (1979) found that classification dominates the behaviour of the fluidized bed, and hence, the perfect size classification assumption works reasonably well for this current study.  Experimental results, as shown in Figure 6.4, also support the perfect size  classification assumption. With the variation in crystal size in the struvite crystal bed, variation in bed voidage is also observed along the height of the reactor. As shown in Figure 6.5, the bed voidage increases with increasing the crystal bed height. The crystal beds are dense (mean less voidage) at the bottom of the reactor and the bed becomes progressively lean along the bed height. This is due to the fact that the lower part of the reactor contains particles of larger size than those sitting in the upper part of the reactor; according to Richardson and Zaki’ s (1954) observation, the bed voidage decreases with increasing particle size. In order to validate the model predictions, the overall bed voidage was calculated from  191  the bed pressure drop and found to be in close agreement with the predicted average bed voidage.  6.6  Conclusions The quasi-empirical analytical model, developed in this study predicts both the P0 -P 4  and 4 NH N concentrations to be decreased with increasing bed height; the prediction was consistent with the experimental results. The rate of disappearance is relatively slow at the bottom part of the reactor and the higher rate is observed in the middle section of the crystal bed. A reasonably good fit of the model predictions with the experimental data on removal of both 4 P0 P and 4 NH N is observed, for the case presented in this current study. Other predictions include: crystal size decreases along the bed height and, hence, the bed voidage increases with increasing the crystal bed height. The model predictions, with respect to crystal size and overall bed voidage, were also found to match reasonably well with the experimental data. Therefore, this model could be extended further to study the effect of different operating conditions, such as varying species concentrations, seeding rate, upflow velocity and aspect ratio on reactor performance, thus helping to optimize the crystallization process in the UBC MAP crystallizer.  192  Nomenclature  Symbols A 0 [A]  = =  C  =  CH  = = =  CH+H  Co D G g H 1 H L 0 L  k  = = = = = = = = = =  m  =  MW 0 [MI  = =  N 0 [P]  = =  Fe  =  Q  = =  LH LH+H  AH  Cross-sectional area of the reaction zone (m ) 2 Molarity of ammonium in the liquid phase at the entry of reaction zone (molfL) Represents the concentration of struvite in liquid phase and it is the sum of all the constituent species (Mg, NH 4 and P0 ) dissolved in the 4 solution, expressed as mass of species per mass of water (kg of struvitefkg of water) Struvite concentration at bed height H Struvite concentration at the height increment, AH, above H concentration of struvite in the liquid phase at entry (kg of struvite/kg of water) Column diameter (m) Linear growth rate of the struvite crystals (mIs) Acceleration due to gravity (9.81m1s ) 2 Bed height (m) Total bed height (m) Crystal size (radius) (m) Seed crystal size (radius) (m) Crystal size at bed height H (m) Crystal size at the height increment, AH, above H (m) Surface area specific rate constant (mlsec) )fiL 1 (1—a 2 Bed surface area per volume of reacting liquid ( —i-) aaL Molecular weight of struvite Molarity of magnesium in the liquid phase at the entry of reaction zone (moIJL) Number of seed particles added per unit time (/sec) Molarity of phosphate in the liquid phase at the entry of reaction zone (molIL) Conditional solubility product at the equilibrium condition 3 fL (mol ) (Fe varies with pH) Flow rate (m /s) 3 Height increment (m)  Greek letters p’ Ps ps*  = = =  a 1 a  = =  Density of water (kg/rn ) 3 Density of struvite crystals (kg/rn ) 3 Density of struvite excluding the weight of the water of crystallization ) 3 (kg/m Liquid volume fraction (bed voidage) Volume factor (for sphere, 4ir/3) 193  18  =  y  = =  surface factor (for sphere, 47t) Dimensionless diameter factor for a solid struvite particle Viscosity of water. (kg/mis)  Others A B C D  = = = =  Harvest zone Active zone Fine zone Seed hopper  Abbreviations BNR CSTR ID MAP UBC  = = = = =  Biological Nutrient Removal Continuous Stirred Tank Reactor Inner Diameter Magnesium Ammonium Phosphate University of British Columbia  194  Table 6.1  Operating conditions and basic physicochemical properties of struvite crystals and the reaction solution  Parameters  Values  Parameters  Upflow velocity in section A (mIs)  0.0362  Volume factor, cx  4t/3  Upflow velocity in reaction zone  0.02  Surface factor, f3  47t  Initial P0 -P Conc. (mgIL) 4  45  Diameter factor, ‘  Initial Mg Conc. (mgIL)  55  Density of struvite particle, Ps  Values  (mis) 2 1650  ) 3 (kglm Initial 4 NH N Conc. (mgIL)  490  Density of liquid phase,  Pt  998.2  ) 3 (kglm Total expanded bed height, H  250  9 Pe x10  2  Seed size, (radius) 0 L (urn)  125  k’ (dmlhr)  12  Seeding rate, N (s’)  20  (mm)  195  0 C  L, N  H  C-AC  L-AL  1•  4,  H C  L  H  Centrate  H=O  ‘1r  At. ,Q 0 C  Figure 6.1  L  Schematic of the fluidized bed UBC MAP crystallizer and the model development  196  — — —  45  o  P04-P_Predicted NN4-N_Predicted  P04-P_Experimental NH4-N_Experimental  490  40  485  35  480  30  475  25  470 465  420  C  z  -  15  460  10  455  5  450  0  445 0  0.2  0.4  0.6  0.8  Wilt  Figure 6.2  -P and NH 4 P0 -N concentrations along the bed height 4  197  100 90 80 D Model Predicted • Experimental  70  60 50 40 30  20 10  [  0  P04-P  Figure 6.3  NH4-N  Removal of P0 -P and NH 4 -N 4  198  3 Model predicted • Experimental  —  2.8 C  2.6  I  4 0  0.2  0.4  0.6  0.8  1  Dimensionless crystal bed height, HIHt  Figure 6.4  Variation of crystal sizes along the bed height  199  I  3  :ZZ —  0.55  — -  0.5 0  —  -  Voidage_Model predicted Overall bed voidage_Predicted Overall bed voidage_Experimental  I  I  I  0.2  0.4  0.6  0.8  1  Dimentionless crystal bed height, H/Ht Figure 6.5  Variation of bed voidage along the bed height  200  6.7  References  Adnan, A., Mavmic, D.S., and Koch, F.A. (2003) Pilot-scale study of phosphorus recovery through struvite crystallization examining the process feasibility. J. Environ. Eng. Sci. 2, 315-324. —  Al-Dibouni, M.R., and Garside, 3. (1979) Particle classification and mixing in liquid fluidized beds. Trans IChemE, 57, 94-103. Battistoni, P., De Angelis, A., Pavan, P., Prisciandaro, M., and Cecchi, F. (2001) Phosphorus removal from a real anaerobic supernatant by struvite crystallization. Water Res., 35 (9), 2167-2178. Belcu, M., and Turtoi, D. (1996) Simulation of the fluidized bed crystallizers (I) influences of parameters. Cryst. Res. Technol. 31, 10 15-1023. Booram, C. V., Smith, R.J., and Hazen, T.E., (1975) Crystalline phosphate precipitation from anaerobic animal waste treatment lagoon liquors. Trans. ASAE, 18, 340-343. Bowers, K.E., and Westerman, P.W. (2005) Design of cone-shaped fluidized bed struvite crystallizers for phosphorus removal from wastewater. Trans. ASAE, 48(3), 1217-1226. Frances, C., Biscans, B., and Laguerie, C. (1994) Modeling of a continuous fluidized-bed crystallizer. Chem. Eng. Sci. 49, 3269-3276. Mullin, J.W., and Nyvlt, 3. (1970) Design of classifying crystallizers. Trans. Instn. Chem. Engrs. 48, T7-T14. Parsons, S.A., Wall, F., Doyle, J., Oldring, K., and Churchley, J. (2001) Assessing the potential for struvite recovery at sewage treatment works. Environ. Technol. 22, 1279-1286. Richardson, J.F., and Zaki, W.N. (1954) Sedimentation and fluidization. Part I. Trans. lnstn Chem. Engrs. 32, 35-53. Shiau, L.D., and Liu, Y.C. (1998) Simulation of a continuous fluidized bed crystallizer Perfect classified crystallizer model. J. Chinese Institute of Chem. Eng. 29(6), 445-452.  —  Shiau, L.D., and Lu, T.S. (2001) Interactive effects of particle mixing and segregation on the performance characteristics of fluidized bed crystallizer. md. Eng. Chem. Res. 40, 707-7 13. Yoshino M., Tsuno H., and Somiya I. (2003) Removal and recovery of phosphate and ammonium as struvite from supematant in anaerobic digestion. Water Sci. Technol. 48, 171178.  201  Phosphorus recovery from anaerobic digester  Chapter 7  supernatant by struvite crystallization: Modeling of a fluidized bed reactor incorporating thermodynamics, kinetics and reactor hydrodynamics 6  7.1  Introduction Phosphorus  is  a  non-renewable,  non-interchangeable  finite  resource.  The  simultaneous reduction of natural phosphorus resources available for the phosphate industry, and the increasing awareness of pollution problems such as eutrophication due to phosphorus release in wastewater effluents, have led to the research into new processes to remove and recover phosphorus from sewage effluents. The conventional methods of phosphorus removal is by fixing it into the sludge, either chemically by precipitation of soluble phosphate with iron or aluminum salts of insoluble phosphate compounds, or biologically, as is the case in Biological Nutrient Removal (BNR) or Enhanced Biological Phosphorus Removal (EBPR) processes, using the ability of some micro-organism to store phosphate as polyphosphate for their own metabolism. Both approaches are effective in removing phosphorus from the process streams, but they lead to high volumes of sludge production, containing very high amounts of phosphate, which become an important issue in any further downstream processing. In particular, the sludge produced from the biological nutrient 6  A version of this chapter will be submitted for publication.  Rahaman, M.S., Mavinic, D.S. & Ellis, N. (2009). Phosphorus recovery from anaerobic digester supernatant though struvite crystallization: Modeling of a fluidized bed reactor incorporating thermodynamics, kinetics and reactor hydrodynamics. In preparation.  202  removal, while digested anaerobically, releases a significant level of phosphate into the supernatant. Occasionally, this high level of phosphate combines with magnesium and ammonium and precipitated out as struvite of [MAP (Mg.NH4.P04.6H2O)] from the digester supematant. The precipitation of struvite causes plugging and encrustation problem in the pumps and the process pipe lines, requiring regular maintenance. In order to avoid this unwanted deposition of struvite crystals in the process lines, measures can be introduced that will hinder struvite precipitation. One of the sustainable methods of solving this problem is to recover phosphorus as struvite, before it forms and accumulates. Recovery of phosphorus, as struvite, can offer several potential benefits, such as a significant decrease in sludge production and the associated cost of disposal and potential use of struvite as a slow release fertilizer. Different types of reactors have been developed and studied for recovering phosphate from waste streams. A fluidized bed type reactor is the one that has been employed for struvite crystallization from wastewaters. The Environmental Engineering Group at the University of British Columbia (UBC) has developed a fluidized bed reactor that can convert more than 80% of soluble phosphate into struvite crystals, from centrate/anaerobic digester supernatant (Adnan et al., 2003). Although, a lot of effort has been dedicated towards the study of the struvite crystallization process with reasonable success, a clear “methodology” to implement the laboratory results to the design and operations of the plant scale crystallization has not been reported until now. In the design of fluidized bed crystallizers, the kinetic data are obtained from the initial experiments performed in a laboratory. However, the design of a crystallizer depends on a variety of different complex processes such as nucleation, crystal growth, attrition and agglomeration of the crystals, and governed by fluid  203  dynamics and mass transfer in the crystallizers. Some of these mechanisms are not fully understood, although the design and operation of large scale crystallizers require a reliable knowledge of the most essential processes. An efficient design and scale-up method can be established through a mathematical modeling, which includes the kinetic processes, as well as the reactor hydrodynamics and mass transfer. Until now, much work has been performed on developing mechanistic models for the industrial crystallizers (stirred tank reactor). However, few articles can be traced to modeling of a fluidized bed crystallizer. A mathematical model was formulated for a continuous, fluidized bed crystallizer by Frances et al. (1994). In order to take into account the segregation and mixing of particles within the bed, the model was developed based on the description of the fluidized bed as a multistage crystallizer. The model predicted the mean size of the product crystals, matching quite well with the experimental results. Shiau and Liu (1998) developed a theoretical model for a continuous fluidized bed crystallizer assuming that the liquid phase moves 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 vertical position within the reactor, and also allows one to study the effects of various operating parameters, such as the feed rate and height/diameter ratio, on the performance of a continuous, fluidized bed crystallizer. 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, ideal-mixed beds of crystals. However, the crystals in different beds are totally segregated. This one parameter model can be employed  204  to investigate both the extreme conditions (completely mixed and segregated) and also for the intermediate region of mixing. Several attempts have been taken recently 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 the struvite formation potential (Lowenthal et al., 1994). This model can be used to estimate struvite formation potential from the ionic concentrations of the reactive species, using the Extended Debye-Huckel [EDH] method for activity coefficient correction. The influence of the partial pressure of C0 , and its influence on carbonate 2 equilibria, was also considered, to calculate 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 higher than 8.5 (Doyle and Parsons, 2002; Parsons et al., 2001). A number of chemical equilibrium models such as MINEQL÷, 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 (K and change in specific enthalpy, AH°) need to be user-defined as well. Several studies have used these programs to calculate the solubility curves of struvite (Ohlinger et al., 1998; Miles and Ellis, 2000). Modeling has 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  205  used for anaerobic digester liquors, where CO 2 stripping by aeration is being 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 (Yoshmo et al., 2003). More recently Forrest et al. (2007) used a chemical equilibura 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 performance of a fluidized bed crystallizer and claimed that the ANN based model better predicted the process performance than the equilibria based model, Crystallizer v.20. One large limitation of equilibrium models is that they are developed based on chemical equilibrium. 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.  Also, none of the  above mentioned models for the struvite crystallization process have taken reactor hydrodynamics into account and no information on product quality, in terms of particle size, has been conducted. Very recently, Rahaman et al. (2008) have incorporated both kinetics and reactor hydrodynamics in one single model, following the work done by Shiau and Liu (1998), and Bowers and Westerman (2005). The model uses the analytical concentration of struvite constituent species and the solution pH as the model inputs, and predicts the removal efficiencies of the species, as well as average product crystal size. In this model, the conditional solubility product of struvite was used to determine the crystal growth. The main problem of using the conditional solubility product is that it requires inputting the conditional  206  equilibrium solubility product, which heavily depends on the solution pH. The values of found in the literature are diverse and, therefore, a reliable value for a specific  conditional  system run at a specific pH is very hard to find. In order to overcome this problem, in this cunent method, the thermodynamic solubility product of stuvite is used to determine the growth rate; this requires the activity based solubility of struvite and, hence, ionic concentrations need to be determined from the total analytical concentration. Thus, a chemical speciation model, based on equilibrium is linked to the reactor model to make this model more generic and robust. A chemical equilibrium model is first developed, and using that model, the speciation based on the thermodynamic equilibriums is determined.  7.2  Model development In nutrient recovery through struvite crystallization process, solution chemistry plays  a vital role in struvite crystal formation, thus affecting the overall removal/recovery of the nutrients  from  wastewater.  Magnesium  ammonium  phosphate  hexahydrate  2 P (MgNH . 4 0 6H O ), more commonly known as struvite, is a white crystalline substance and is formed by chemical reaction of the free magnesium, ammonium and phosphate, along with six molecules of water. The simplified form of the reaction involving the struvite formation is as follows: 2 Mg  +  4 NH  +  4 PO  +  0 2 6H  —  2 P MgNH . 4 0 6H O  Like any other reactive crystallization processes, struvite precipitation also depends on solution supersaturation, while the generation of supersaturation depends on the constituent species concentration, as well as the solution pH. A reactive solution containing struvite species; Mg, NH 4 and P0 , once mixed, undergoes chemical transformation and, based on 4  207  _____________________ _______________________  species concentration and solution pH, those species can form different compound and  4 NH  complexes. In a synthetic solution, containing Mg,  P0 HP0 2 H , , P0 2 4 , 3 4 H3P 4 0 (aq)’ 4  be formed:  and P0 , the following species can 4  4 P 2 MgH , O 4 , Mg 4 , 2 MgHPO ( aq), MgPO  MgOH, NH , H, OH, NH3(aq). 4 The reactions of formation of the above mentioned species equilibrium constants  MgOH  (Michalowski  and Pietrzyk,  their associated  2006):  = 2 8 y f 0 +y ] [OHJ f[Mg 2  <  MgHPQ( q 0 )  are  and  2 +0H Mg  <  K 1 1  4 P 2 MgH O  (7.1)  [MgOH] MgOH  2 + HPQ >Mg  2—  ) Mg + 4 P0 2 H  Kjgjjp,  —  2 YMg  7HPO42  2 I [ HPQ [Mg 1 2  (7.2)  —  [MgHPQ(q)]  ; K4 PO 2 MgH  —  4 P 2 H 7 0  Mg T  2I4 [Mg P0 2 [H  I  4 P 2 [MgH OI MgH T P 2 4 O  —  (7.3) -  [g2+[pQ _ 3 4 ]  4 MgPO  0 K  <  2 ‘Mg  +  4 ; PO  4 KMgPo  =  TMg2+ TPO4  MgPO T 4  K 3 0  4 P 3 H ( aq) O  4 P 2 H 0  >H  +  0 K  >  H  +  4 P 2 H 0  2 4 HP0  3 ; K  =  HH2PO4I 0 p 2 7Ff+TH 4  K  2  HPO4  -  H  +  3 4 P0  = 7H,hffPO 2lhPO4j 4  ;  ; KHp 2 = 0  K÷  <  3 +H ; KNH÷ NH  4 P 2 [H 0  (7.6)  I  YH+7Po43[1[1041 7HPO42  4 NH  (75)  4 P 3 [H ( aq) 0I  H2PO4  4 HPO  (7.4)  I 4 [MgPO  ] 2 4 [HP0  (7.7) -  = TH*NH 1 3 NH 7 4  ] 4 [NH  208  KH2O  0< 2 H  7H  >H +0H  HH][0H1 0 TH*7  0 ; K 2  [H 0 2 ]  ]= 10”  [H  (7.10)  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, 2 K  =  can be expressed as  +}{Po 4 {Mg2+}{NH 3 _}, where,  { } represents species activity.  The struvite precipitation reaction can be expressed as, P MgNH . 4 0 2 ) 6H O (  <  2 Mg  +  4 + NH  +  6H 0 2 ; (7.11)  =  K SP where,  2 P [MgNH . 4 O 6H ]() O  [1 shows the molar concentration and yj represents activity coefficient of species i.  The equilibrium constants for the all the reaction mentioned here are reported in Table 7.1. The activity coefficient of a species depends on the solution ionic strength and the valance charge of that specific species. If the ionic strength (I) is less than 0.005, the Debye Huckel relationship can be used to determine the species activity coefficients (y) as, Log  =  1 2 —0.5Z,  (7.12)  where, Z 1 is the valence of ion i and I is the ionic strength The activity coefficients can also be estimated using Guntelberg approximation, for the solutions with ionic strength less than 0.1 as, Log  =  _ADHZI2[l  (1051  (7.13)  where, ADH is the Debye-Huckel constant that can be estimated as  209  ADH  =  5 ( 6 1.82x10 eT)’  -(7.14)  where, 6 =  dielectric constant and T= temperature in degree Kelvin.  The Davis equation is the most commonly used expression for determining species activity coefficients (for ionic strength less than 0.5). The equation is as follows: Log  =  1 5 _ADHZj2[l)o  —0.31  (7.15)  where, ADH =  0.486  —  6.07 x 10 T + 6.43 x 10 T 2  (7.16).  Now, the ionic strength of a solution can be estimated using two different approaches. Method 1: Ionic strength can be calculated from the species ionic concentrations as, I  =  2 Z 1 0.5C  (7.17)  Where, C 1 is the molar concentration (molIL) and Z 1 is the valence of species ion i. The ionic concentrations of different species can be determined from the equilibrium equations speciation chemistry described above. Method 2: Ionic strength can also be estimated from the correlations relating ionic strength and the solution electrical conductivity (EC). Several correlations have surfaced in the literature and they are presented below: A correlation between ionic strength and conductivity for 13 waters of varying composition was derived by Russell, (1976) as: 210  I(mol/L)  =  16X lff x EC 6 25 (Scm’)  -(7.18)  where, EC 25 is the electrical conductivity at 25 °C. Utilizing extracts of flooded soils and electrolyte solutions of ionic strength less than 0.06 molelL, a relationship between ionic strength (I) and specific conductance (EC) was developed by Ponnamperuma et al. (1966) as, I (mol/L)  =  16 X 1ff 6 x EC 25 (pScm’)  (7.19).  Griffm and Jurinak (1973) provided a relationship between ionic strength (I) and electric conductance of 27 arid-zone soil extracts and 124 river waters as: I (mol/L)  =  6 x EC 13 X 1ff 25 (pScm’)  (7.20).  Rahaman et al. (2006) proposed a correlation, based on analyzing different water and wastewaters for a range of temperature 10—20 °C, as follows: I (mol/L)  =  6 x EC (pScm 5 X1ff ) 1  (7.21)  Very recently, Bhuiyan (2007) proposed a correlation based on a variety of anaerobic digester supematants as, I  =  25 (pScm’) 7.22 x 10 EC  (7.22)  The equilibrium constants (K), mentioned with the corresponding reactions, are 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: )— 25 ln(K)=ln(K  ori  1  R  211  where, K 25 equilibrium constants at 25 °C, AH° is the enthalpy of reaction and R is the gas constant. The value of R is equal to 0.0083 l4kJmol’deg’ and AH° values for different equilibrium reactions are reported in Table 7.1. Now, the species mole balance, at equilibrium condition, can be written as: ) 4 CT(Po +  =  4 MgPO  CT(Mg)  4 P 3 H 0 +  +  4 P 2 H 0  +  2 4 HP0  +  3 4 P0  +  4 P 2 MgH O  +  4 MgHPO  (7.23)  2 P [MgNH . 4 O 6H O ]  2 +MgOH +MgH =Mg 4 +MgPO 4 P 2 O +MgHPO 2 P +[MgNH . 4 6H 4 O O ] (7.24)  ] 3 =[NH ] P . 4 O +[MgNH +[NH 6H ]() O CT(NH) 2  (7.25)  Thus, there are 14 unknowns and 14 equations. Solving all of the equations simultaneously using the optimization tools available in MatLab is difficult. Hence, the system of equations is manipulated to express the struvite species concentration in terms of the known values: [Mg2+]=  * 2 TM  (7.26)  31  4 j a+b[P0 [p0 3 4 _ _. —  CT P0 3 4 c+b[Mg2+]  [Mg2+] = —(ac+bCTP  (7.27)  + )±[(ac+bCp —bcMg 2 —bcMg * 2  2ab 4 [NH  I  )2  ÷ 2 4acCTMg  (7.28)  .29)  =  kNH. 4 NH T  (rH.’H1)  212  where,  (  1+  y 1 k 10 Mg 2* 2 kMgOH (7H*  I=a  (7.30)  [Hi))  =b kMgHpQkpQ2  (7.31)  YMgp kMgPQ  and  1’l+  3 -(rH+u’1) 43 rPO  110 kHpQ k  +  2 (7H*[H1) 43 YPO  +  YpQ43  (YH+  [1) = c  kHpQ2  H,P0 T 4  kHpokHpQz  (7.32)  HP0 kHpo2 7 2 4  By solving the equilibrium equations (7.26) through (7.32), the amount of struvite precipitated, as well as the concentrations of each individual are determined at equilibrium condition.  7.3  Reactor modeling Performing a complete process modeling for struvite crystallization, which is  dynamic in nature, requires thermodynamics, reaction kinetics and hydrodynamics to represent the reactor system completely. In doing so, the reactor model, which includes crystallization kinetics and the reactor hydrodynamics, is linked to the chemical speciation model for the reactions involved in creation of super-saturation, with respect to struvite. The equilibrium model takes care of the supersaturation generation, while the reactor model determines the mass deposition of constituent species onto the seed crystals and subsequently determines the process performance. 213  The thermodynamic equilibrium model, described in the earlier section, is used to determine the supersaturation within the reactor system. Furthermore, a recently developed kinetic expression (Bhuiyan, 2007), is used instead of the Westerman’s kinetic model, used earlier in Chapter 6. The new kinetic expression is used as this relationship was developed by using data generated from the UBC MAP fluidized bed crystallizer. In general, the type of reactor should not affect the intrinsic kinetic parameters. However, the kinetic prediction with the same type of reactor may be beneficial to use as the mass transfer effect is not explicitly dealt with, in this study. It is worth mentioning that the new version of kinetic expression is also more straightforward and easier to incorporate into the reactor model. The following assumptions were taken into consideration during model development. 1. In this process, the reactions are rapid and hence the dynamics of the reactions are ignored and equilibrium relationships are used to determine the species concentrations in the reaction. However, the crystallization process, involving crystal growth, is dynamic in nature, and therefore the crystal growth kinetics will be incorporated in order to determine the species mass deposition onto the crystals. 2. The system is run at isothermal conditions; 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. Moreover, the numerical investigation of the hydrodynamics of struvite crystals in a fluidized bed (Chapter 6) also supports this nearly perfect size classification. 4. The reactive solution is circulated as a plug flow pattern; the diffusionldispersion along the height of the reactor is negligible.  214  5. Nucleation, agglomeration and breakage are neglected. As such the in-reactor supersaturation is not very high, the generation of primary nuclei can be neglected. However, the secondary nucleation and agglomeration may still be present in the process. For simplicity, both the secondary nucleation and agglomeration are lumped into the crystal growth, to determine the overall growth and the resulting crystal size distribution in the reactor. The crystal growth is considered size independent. 6. The systems are considered as a seeded process. The seed could be added externally or the process could be itself a self-seeded one. The seed crystals are of uniform size and added to the crystallizer at a constant rate. The basic model development for the reactor is the same as described in Chapter 6. The only changes are as follows: The mole balance for each individual constituent species of struvite is formulated. Whereas, in the earlier version (Chapter 6) only the mass balance of the struvite was used, with the species concentration is lumped together into one single equation. In this model, a pilot-scale reactor is considered and the dimensions are reported in Table 7.2, with a schematic presented in Figure 7.1. 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 intended to be used only for seed crystals addition and any processes occurred in this section is neglected. As mentioned in Chapter 6, mass/mole balance over an infinitesimal height (AH) of the reactor, (as shown in Figure 7.2) is taken. At steady state conditions, the mole balance of  215  struvite constituent species i, (P0 , Mg, NH 4 ) on a differential segment, AH can be expressed 4 as: )AHA 1 (1 -a -  CIH+)  -  2 )(Gp (flL  MW  =  (7.33)  The first term, in Equation (7.33), represents the time rate of disappearance of struvite constituent species ‘i’ from the liquid phase. Where,  Q: flow rate;  ,C 1 H:  concentration of species ‘i (mole/L) at bed height H; and C,H+AH:  concentration at the height increment, AH (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: cross-sectional area of the reactor; AH: height increment; a: volume factor; L: crystal diameter; /J: surface factor; G (mis): linear growth rate of the struvite crystals; ps: density of stuvite 3 (kg/rn ) ; and MW: molecular weight of struvite. By rearranging Equation (7.33) and taking the limit as AH approaches zero, the gradient of species concentration ‘i’ can be defined as, dC, dH  =  Aflp(1 a ) 1 —  2aQLMW  G  (7.34)  where, the bed height, H is the only independent variable and C 1 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 concentration.  216  In Chapter 4, it is documented that the struvite bed expansion characteristics can be explained by Richardson-Zaki (R-Z) relation (1954) with a newly developed correlation for expansion index:  1 a  =  ILAUD)  (7.35)  where, U 1 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, Re  L 1 Up  where, p, for digester supernatant is not found in the literature and  ‘LII  thus it is taken to be the same as for water. For the range of Re used in this current study, the expansion index is expressed (Rahaman et al., 2009; Chapter 4) as: n  =  4.77 18 x Re[°° 89  for 26< Re <302  ( 7.36)  For spherical particles, the terminal settling velocity (Us) can be determined using the Newton’s equation as  =  I---  ‘j3C  —  L  Pi  (7.37)  Where Cd values can be determined using the modified version of Clift et al. (1979) correlation as Cd =__(1+0.563Re,083) Re  (7.38)  As can be found in Bhuiyan (2007), the growth rate can be expressed as G  =  kS’  (7.39)  217  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  —1  Where,  (7.40)  is the supersatuation ratio and can be expressed as  =  (7.41) where,  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: pNa(L  —  =  2  (fi[ )(Gp) 2  (7.42)  By rearranging Equation 7.42 and taking the limit as AH approaches zero we get: dL dH  =  —  413(1 G 3 L 2 6Na —  (7.43)  where, N is number of seed crystals added per unit time. Thus, after mass deposition of species on struvite crystals, the species equilibrium will be shifted. This will cause a change in ionic strength of the solution. Since the ionic strength has a profound effect on struvite solubility, hence the supersaturation, the equilibrium species activities is updated based on the existing ionic strength values.  7.4  Experimental In order to calibrate and validate the model, the experimental results acquired by a  former student, from the pilot scale struvite crystallizer (operated in Lulu Island Wastewater 218  Treatment plant), are used in this study. The struvite crystallization process is described as follows: The basic design of UBC MAP crystallizer follows the concept of a fluidized bed reactor. As depicted in Figure 7.1, the reactor has four distinct zones depending on the diameter of the column. The bottom part of the fluidized bed reactor is called the harvest zone; above that the active zone, while the top fluidized section is the ‘fine zones’. There is a settling zone, also called ‘seed hopper’ at the top. The dimensions of the different sections are reported in Table 7.2. In the struvite crystallization process, the anaerobic digester supematant 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. 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 the 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 in the bottom and the smaller crystals rise to the top of the crystallizer. The larger crystals at the bottom, once achieve the desired size are settled into the harvest zone and are withdrawn from the bottom of the crystallizer.  219  7.5  Results and discussion  7.5.1  Sensitivity analysis With increasing reactor height, the ionic species concentrations, and hence the  solution ionic strength change due to the struvite precipitation. Since ionic strength plays a significant role on struvite solubility, hence the generation of supersaturation, precise detennination of ionic strength is of importance. As already mentioned, ionic strength can either be calculated from the ionic concentrations of the species or estimated, using the correlations available in the literature. The commonly found correlations are described in the earlier section. In this study, the supersaturation ratio (SSR) for struvite is determined for the ionic strengths of that solution, estimated using different methods of ionic strength calculations. The results are reported in Figure 7.3. It is observed that the method of ionic strength calculation has a significant effect on SSR determination. The SSR calculated with all four correlations show peak values at pH value 10.2. However, the peak SSR values differ significantly from one correlation to the other. The correlation provided by Russel (1976) was found to generate the lowest SSR values; on the other hand, the correlation provided by Rahaman et al. (2006) was found to generate the highest values of SSR. The difference in SSR values may be due to fact that the individual correlation was developed for a specific aqueous solution, at a specific experimental condition. Hence, it is recommended that the ionic strength be calculated using the equilibrium chemistry model (method #1). Therefore, in this work, SSR values are calculated using the equilibrium speciation model.  220  7.5.2  Reactor performance evaluation Considering the crystallization kinetics expression presented by Equation (7.39), the  effluent concentrations of P0 , NH 4 4 and Mg are determined using the model developed in this study. The model parameters and setting are the same as the reactor operating conditions listed in Table 7.3. Using the influent and effluent concentrations of different species, the percent removal of each species are calculated and plotted in Figures 7.4, 7.5 and 7.6. It is observed that removal efficiencies of all three species are over-predicted by the chemical equilibrium model and under-estimated by the reactor model. These predictions are logical and since the chemical equilibrium model assumes that the thermodynamic equilibrium has been attained for struvite precipitation, and the maximum possible conversion has taken place. In other words, all of the supersaturated species concentrations have been used up by the crystal growth and the remaining SSR in the effluent is 1. This is the lowest level of SSR up to which the precipitation reaction can occur. On the other hand, the reactor model generates results which are significantly lower than the corresponding experimental values. The reason behind this is that the kinetics parameters, used in this model, were estimated by Bhuiyan (2007) 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, meaning there is no nucleation at all (either primary or secondary). Also, as the reactor hydrodynamics were different for those two reactor set-ups; the difference in agglomeration between the particles could be another possible explanation for this poorer model prediction. This fact is more evident by the difference found in average particle size determination between the  221  experimental and the model predictions (Figure 7.7). The predicted particle size is significantly lower than the experimental values. It implies that, in the pilot scale operation, the overall processes taking place is different from those occurring in the lab scale reactor. Thus, the size enlargement by the crystal growth mechanism alone is not sufficient to represent the actual growth of struvite crystals in the pilot-scale reactor. Since no studies have been performed to identify exactly what processes are taking place within the crystallizer, in this current study, everything has been included into the process of crystal growth. Hence, in order to improve the predictive capability of the model, it is necessary to calibrate it for the pilot-scale operation. The calibration was performed by using the experimental data gathered by running the reactor for a different time periods.  7.5.3  Model calibration Since the individual kinetic parameters for various probable processes taking place in  the crystallizer are not available in the literature, the current model is 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 P04 concentrations. The MSE values used for the model calibration is defined as, I  MSE  =  1Iir’tmocieIji Z  P  I  2 Xdataji  Xdataji  7.44  )  Where, x 3 are the values of model output and the measured data on Z species (Mg, NH 4 and ) and P is the number of data points for each j species used in the calibration process. 4 P0 The experimental conditions for the model calibration are presented in Table 7.4. The  222  estimated K and n values, along with the MSE values, are presented in Table 7.5. It is observed that, the values of 46 and 1.48 for K and n, respectively, result in the lowest MSE value. Hence, those values of K and n are taken as the estimated model parameters.  7.5.4  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 7.6. The model was run with the estimated kinetics parameters and the predicted results on process performance are then compared with those of the experimental results. Figures 7.8, 7.9 and 7.10 represent the model predicted removal efficiencies along with those predicted by the equilibrium model and the experimental results. By comparing the values on these figures with those found in the earlier ones, it is clear that the predictive capability of the model has been improved significantly (around 10%). The predicted values match fairly well with the experimental results, but as seen before, the equilibrium model still overestimates the removal efficiencies. The model-predicted mean crystal sizes also match quite well with the experimental observation (Fig. 7.11) and the predictive capability increased considerably (around 10%).  7.6  Conclusions The struvite crystallization process, in pilot scale operation, involves not only the  crystal growth, but also other processes such as nucleation (most possibly the secondary one), and agglomeration. Attrition/breakage can also be present in the reactor. Also, the crystal segment created by breakage may serve as the seed crystals. The model developed in this  223  work can be used for the reactor performance evaluation in terms of the removal efficiencies of struvite constituent species (Mg, NI-I 4 and P0 ) and the average product crystal sizes. 4 Although the product crystals are found to have some gradation in terms of its sizes, this mean size estimation provides some prior knowledge about the average product crystal size, for a specific operating condition, at any one treatment site.  224  Nomenclature Symbols A ADH Cd  = =  Molar concentration of the species (molIL) Concentration of species i (molfL) at bed height H Concentration of species i at the height increment, AH, above H Electrical conductivity (jiS cm’) Electrical conductivity at 25 °C Linear growth rate of the struvite crystals (mis) Ionic strength (molL’) 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  C Cj,H CI,H+AH  EC 25 EC G I K k L N  Expansion index Flow rate (LIs) Ideal gas constant (8.3 14 Jmol’K’) Reynolds number  n  Q R Re S U  =  y  =  =  =  T AH AR°  Cross-sectional area of the bed (column) [m ] 2 Debye-Huckel constant Drag coefficient  = = =  Relative supersaturation Terminal settling velocity of struvite crystals (mis) Order of struvite growth kinetics Valence of ion species i Temperature in degree Kelvin Infinitesimal height of the reactor (m) Enthalpy of the reaction (Jmor’)  Greek letters at a  = =  fi  =  p1 Ps  =  8  =  = = =  Liquid volume fraction (bed voidage) Volume factor (for sphere, 4ic13) Surface factor (for sphere, 4t) Density of water (kg/rn ) 3 Density of struvite crystals (kg/rn ) 3 Activity coefficient of ion i Dielectric constant Supersatuation ratio  225  Others A B C D  =  Harvest zone Active zone Fine zone Seed hopper Species activity Species molar concentration  =  Artificial Neural Network Biological Nutrient Removal Enhanced Biological Phosphorus Removal Extended Debye-Huckel Magnesium Ammonium Phosphate Mean Squared Error  { } [1 Abbreviations ANN BNR EBPR EDH MAP MSE  = = = = =  R-Z SSR  = =  Richardson-Zaki relation Supersaturation Ratio  UBC  =  University of British Columbia  226  Table 7.1  Equilibrium constants and the enthalpies of the reactions involved in struvite precipitation (Rahaman, et al., 2006; Bhuiyan, 2007)  Equilibrium constant  pK (25 °C)  Enthalpy (AHr°) (KJmoi ) 1  KH3po4  2.148  3.744  KH2p04  7.198  -4.205  KHpo4j  12.375  -14.769  KMgoH  2.56  66.743  KMgH2po4  1.207  14.225  KMgHpo4  2.428  13.807  KMgpo4  4.92  12.970  KNH4  9.24  -51.920  KH2O  13.997  -55.906  13.26  29.29  227  Table 7.2  Section A B C D  Dimension of the pilot scale fluidized bed UBC MAP crystallizer in relation to Figure 7.1 Diameter (mm) 76 102 152 381  Height (mm) 749 1549 1270 457  228  Table 7.3  Date  28-Mar 29-Mar 30-Mar 31-Mar 01-Apr 02-Apr  Reactor operating conditions at pilot scale for process evaluation phase (Source: Fattah, 2004) Flowrate (L/min)  Influent species conc. (mgIL) 4 NH 4 P0 Mg 11.4 60.74 716.45 75.16 14.3 66.60 742.40 71.89 15.3 61.18 761.89 68.81 13.95 70.25 762.58 85.18 13.65 67.43 801.26 123.45 13.35 79.03 858.25 86.90  pH  Temperature (°C)  Seed size (pm)  Seeding rate (#Is)  7.7 7.7 7.7 7.7 7.8 7.6  19.6 22.6 22.3 21.1 19.4 23.5  300 300 300 300 300 300  5 7 8 10 8 7  229  Table 7.4  Date  07-Jun 08-Jun 09-Jun 11-Jun 12-Jun 13-Jun 14-Jun 16-Jun 17-Jun 18-Jun  Reactor operating conditions (pilot-scale) for the reactor calibration phase (Source: Fattah, 2004) Flowrate (L/min) 21.3 14.4 21.9 22.2 22.8 17.1 18.15 17.7 18.9 15.6  Influent species conc. (mglL) 4 P0 4 NH Mg 60.25 742.66 86.25 36.18 678.50 180.32 61.11 676.01 179.55 65.54 693.81 75.73 56.77 663.87 73.96 57.10 697.70 83.85 51.00 664.38 58.08 61.46 693.25 63.94 59.01 633.07 58.71 46.52 672.97 59.80  pH  Temperature (°C)  Seed size (pm)  Seeding rate (#/s)  7.5 7.7 7.6 7.6 7.5 7.6 7.6 7.6 7.6 7.6  25.4 23.6 26 27.5 24.5 26.6 25.1 24.2 23.2 30.1  350 350 350 350 350 350 350 350 350 350  8 10 10 10 8 7 10 8 8 7  230  Table 7.5 Run# 1 2 3 4 5  Estimated parameters for struvite crystallization kinetics K 38 40 42 46 48  n 1.45 1.46 1.5 1.48 1.5  MSE 7.21 5.35 4.07 3.18 5.28  231  Table 7.6  Date  21-Jun 22-Jun 23-Jun 24-Jun 25-Jun 26-Jun 27-Jun 28-Jun 29-Jun 30-Jun  Reactor operating conditions (pilot-scale) for the reactor validation phase (Source: Fattah, 2004)  Flow rate (Llmin) 15 23.1 17.4 15.9 13.5 13.85 14.4 14.6 15.6 16.5  Influent species conc. (mglL) 4 NH 4 P0 Mg 41.19 742.45 62.27 42.46 709.84 67.83 42.91 718.17 69.32 47.59 745.18 72.92 61.38 756.82 67.18 62.27 737.78 70.74 63.95 725.75 93.10 65.11 734.28 83.26 65.48 508.71 76.35 66.30 795.17 54.99  pH  Temperature (°C)  7.6 7.7 7.7 7.6 7.6 7.6 7.6 7.6 7.7 7.7  27.3 26.2 26.8 26.3 30.5 30.2 31.3 28.1 27.5 30.5  Seed size (aim) 300 300 300 300 300 300 300 300 300 300  Seeding rate (#Is) 7 8 10 6 8 10 7 8 6 10  232  Centrate Flow  Figure 7.1  Recycle Flow  Schematic diagram of the fluidized bed UBC MAP crystallizer  233  ______  ,N 0 L lit  C-tIC  L-\L  H C  L  H=O  Figure 7.2  A schematic of the model development  234  -  -  — —  80  Russell (1976) Rahanian et al. (2006)  -  Griffin and Jurinak (1973) Bhuiyan et al. (2007)  70  /  /  60  / 50  /  40 30 20 10  6  7  8  9  10  12  13  pH  Figure 7.3  Variation of supersaturation ratio (SSR) with pH, estimated using different correlations. ([Mg]T =60 mgIL; [NH4]T=450 mgfL; [PO4]T=5O mglL; Conductivity =6.5mS)  235  100 D D  90  C C  80 C  70 6O  40 30 20 10  • Experimental  0  27-Mar  a EquilibriumModel  -  28-Mar  29-Mar  30-Mar  ReactorModel  -----a  31-Mar  1-Apr  -  2-Apr  3-Apr  Day Figure 7.4  Phosphate removal efficiency: comparison between model predictions and experimental results  236  • Experimental  9  I  EquilibriumModel  A  ReactorModel  8  C  7 C C  5,  C  C  2 A  1  0 27-Mar  -  28-Mar  29-Mar  30-Mar  31-Mar  1-Apr  2-Apr  3-Apr  Day Figure 7.5  Ammonium removal efficiency: comparison between model predictions and experimental results  237  • Experimental  0  EquilibriumModel  ReactorModel  90 80 70  0 0  0  60 50  0  40..  20 10 0” 27-Mar  28-Mar  29-Mar  30-Mar  31-Mar  1-Apr  2-Apr  3-Apr  Day Figure 7.6  Magnesium removal efficiency: comparison between model predictions and experimental results  238  Experimental  [I] ReactorModel  1.8 1.6  I  I  1.4 1.2 1 0.8 0.6 0.4  iIIII  0.2 0 31-Mar  1-Apr  2-Apr  3-Apr  4-Apr  5-Apr  6-Apr  7-Apr  8-Apr  Day Figure 7.7  Mean crystal size: comparison between model predictions and experimental results  239  • Experimental  120  lOOi  ci  ci  ci  ci  EquilibriumModel  ci 4 A  A  ReactorModel  ci A  ci  80 0  S  60  40  20  0 20-Jun 21-Jun 22-Jun 23-Jun 24-Jun 25-Jun 26-Jun 27-Jun 28-Jun 29-Jun 30-Jun  1-Jul  Day Figure 7.8  Phosphate removal efficiency: comparison between model predictions and experimental results for the validation phase  240  16  • Experimental  D  EquilibriumModel  t  ReactorModel  14 12  8  C  20-Jun 21-Jun 22-Jun 23-Jun 24-Jun 25-Jun 26-Jun 27-Jun 28-Jun 29-Jun 30-Jun  1-Jul  Day  Figure 7.9  Ammonium removal efficiency: comparison between model predictions and experimental results for the validation phase  241  120  • Experimental  100 0  D  EquilibriumModel  ReactorModel  0  0  0  80 C:  60  40  20  20-Jun 21-Jun 22-Jun 23-Jun 24-Jun 25-Jun 26-Jun 27-Jun 28-Jun 29-Jun 30-Jun  1-Jul  Day Figure 7.10  Magnesium removal efficiency: comparison between model predictions and experimental results for the validation phase  242  Experimental  ReactorModel  4  3.5  I  I  3  2.5 2 1.5 1  0.5  Or 21-Jun  22-Jun 23-Jun  24-Jun  25-Jun 26-Jun 27-Jun 28-Jun 29-Jun 30-Jun  Day Figure 7.11  Mean crystal size: comparison between model predictions and experimental results for the validation phase  243  7.7  References  Adnan, A., Mavinic, D.S., and Koch, F.A. (2003) Pilot-scale study of phosphorus recovery through struvite crystallization examining the process feasibility. J. Environ. Eng. Sci. 2 (5), 315-324. -  Bhuiyan, M.I.H. (2007) Investigation into struvite solubility, growth and dissolution kinetics in the context of phosphorus recovery from wastewater. Ph.D. Thesis, Department of Civil Engineering, University of British Columbia. Bhuiyan, M.I.H., Mavinic, D.S., and Beckie, R.D. (2007) A solubility and thermodynamic study of struvite. Environ. Technol. 28, 10 15-1026. Bowers, K.E., and Westerman, P.W. (2005) Design of cone-shaped fluidized bed struvite crystallizers for phosphorus removal from wastewater. Trans. ASAE, 48(3), 12 17-1226. Doyle, J.D., and Parsons, S.A. (2002) Struvite formation, control and recovery. Water Res. 36, 3925—3940. Fattah, K.P. (2004) Pilot scale struvite recovery potential from centrate at Lulu Island Wastewater Treatment Plant. M.A.Sc. Thesis, Department of Civil Engineering, University of British Columbia, Vancouver, BC, Canada. Forrest, A.L., Fattah, K.P., Mavinic, D.S., and Koch, F.A. (2007) Application of artificial neural networks to the recovery of phosphorus from wastewater. J. Environ. Eng. Sci. 6 (6), 713-725. Frances, C., Biscans, B., and Laguerie, C. (1994) Modeling of a continuous fluidized-bed crystallizer. Chem. Eng. Sci. 49, 3269-3276. Griffin, R.A., and Jurinak, 3.3. (1973) Estimation of activity coefficients from the electrical conductivity of natural aquatic systems and soil extracts. Soil Science, 115(1), 26-30. Lowenthal, R.E., Kornmuller, U.R.C., and van Heerden, E.P. (1994) Modelling struvite precipitation in anaerobic treatment systems. Water Sci. Technol. 30, 107—116. Michalowski, T., and Pietrzyk, A. (2006) A thermodynamic study of struvite+water system. Talanta, 68, 594-601. Miles, A., and Ellis, T.G. (2000) Struvite precipitation potential for nutrient recovery from an aerobically treated wastes. Water Sci. Technol. 43, 259—266. Musvoto, E.V., Wentzel, M.C., and Ekama, G.A. (2000) Integrated chemical-physical processes modelling I. Development of a kinetic based model for weak acid/base systems. Water Res. 34, 1857—1867.  244  Ohlinger, K.N., Young, T.M., and Schroeder, E.D. (1998) Predicting struvite formation in digestion. Water Res. 32, 3607—36 14. Parsons, S.A., Wall, F., Doyle, 3., Oldring, K., and Churchley, J. (2001) Assessing the potential for struvite recovery at sewage treatment works. Environ. Technol. 22, 1279—1286. Ponnamperuma, RN., Tianco, E.M., and Loy, T.A. (1966) Ionic strengths of the solutions of flooded soils and other natural aqueous solutions from specific conductance. Soil Science, 102, 408-413. Rahaman, M.S., Mavinic, D.S., and 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), 1321-1327. Rahaman, M.S., Mavinic, D.S, Bhuiyan, M.I.H., and Koch, F.A. (2006) Exploring the determination of struvite solubility product from analytical results, Environ. Technol. 27, 951-961. Richardson, J.F., and Zaki, W.N. (1954) Sedimentation and fluidization. Part I. Trans. lnstn Chem. Engrs. 32, 35-53. Russell, L.L. (1976) Chemical aspects of groundwater recharge with wastewaters, Ph.D. Thesis, University of California, Berkeley, USA. Shiau, L.D., and Liu, Y.C. (1998) Simulation of a continuous fluidized bed crystallizer Perfect classified crystallizer model. J. Chin. Inst. Chem. Eng. 29(6), 445-452.  —  Shiau, L.D., and Lu, T.S. (2001) Interactive effects of particle mixing and segregation on the performance characteristics of fluidized bed crystallizer. md. Eng. Chem. Res. 40, 707-713. Yoshino M., Tsuno H., and Somiya, I. (2003) Removal and recovery of phosphate and ammonium as struvite from supernatant in anaerobic digestion. Water Sci. Technol. 48, 171178.  245  Chapter 8  General conclusions and direction for future research  8.1  Introduction As global reserves of high-quality phosphate ore continue to be diminished,  alternative sources of phosphates are needed to be developed, in order to satisfy growing demand generated by the fertilizer market. In the wastewater industry, significant levels of phosphates are released in the secondary digestion phase of the biological nutrient removal (BNR) process. Therefore, the recovery of phosphates from wastewater is one such potential source that, not only has economic merit, but also makes the wastewater industry more sustainable. A secondary benefit of exploiting this resource is to remove phosphates from the actual treatment process. Often, if this is not done, these anions will precipitate as their relatively insoluble salt, commonly known as struvite 0 2 P (MgNH . 4 6H H ); this causes encrustation on the pipe walls and fittings in the plant and eventually leads to costly repairs of the plant and downtime for operations. Over the last few years, the Environmental Engineering Group at UBC has developed a novel fluidized bed reactor configuration that converts 80—90% of soluble phosphate from anaerobic digester supernatant into crystalline struvite, both in the lab and the pilot scale operations. In order to implement this green technology at the plant scale operations, an efficient design and scale up of the reactor is required, which mostly relies on the process kinetics, thermodynamics and hydrodynamics of the system. The fluidized bed struvite crystallization is a very complex process, with regards to both scientific and engineering aspects. Although the P-recovery group at UBC has 246  engineered the MAP fluidized bed crystallizer system to ensure 80—90% recovery of soluble phosphate from the waste streams (Adnan, et al., 2003), there is still a significant amount of “missing knowledge” deficiency in designing and optimizing the system. Therefore, this dissertation is aimed at exploring those challenging issues and filling the knowledge gap. The first and foremost point is the thermodynamics of the struvite crystallization process. In order to achieve better control of struvite recovery systems, a proper understanding of struvite chemistry is required, whereby an exact knowledge of the solubility of struvite becomes essential. Extensive studies, involving the calculation of the solubility product (K,) value for struvite, have been conducted by several researchers. The reported values of K ,, range from 4.37x10’ 3 4 to 3.89x10  °  ,[pK 3 ,from 9.41 to 13.36] and differ by as  much as four orders of magnitude. The struvite precipitation potential of any aqueous solution primarily depends on its supesaturation level and the use of an incorrect value of solubility will yield erroneous information about the level of saturation of an effluent sample, with respect to struvite. In this dissertation, the subject matter of struvite solubility has been dealt with and the findings are presented in Chapter 2. Once the struvite precipitation potential is known, the next step is to design a reactor system which will exploit that precipitation potential to recover phosphate from the waste stream. Since struvite crystallization is a dynamic process, an adequate knowledge of kinetics of the crystallization process is essential for designing an efficient reactor system. Unfortunately, usable information on struvite precipitation kinetics is lacking in the literature. Hence, the next logical step in this research program was to study the kinetics of struvite precipitation. It can be cited from the literature that various process parameters, such as supersaturation ratio, pH, Mg:P ratio, degree of mixing, temperature and seeding conditions,  247  are likely to affect the struvite precipitation process. In this dissertation, a sizable study on struvite precipitation kinetics was performed and the findings are presented in Chapter 3. The process kinetics is not the only factor affecting the crystallizer performance. Several other factors, such as reactor hydrodynamics flow pattern of the phases and mixing -  and segregation of struvite crystals can play a significant role in overall process performance. Therefore, the complex hydrodynamics of the liquid-solid fluidized bed crystallizer was studied using sophisticated instrumentation, such as optical probes, and advanced numerical techniques, such as computational fluid dynamics (CFD). This is one of the major components of this research and the findings should significantly impact on optimal design and operating conditions of commercial reactors. The findings on hydrodynamics are presented in Chapters 4 and 5. The UBC MAP crystallizer has been designed and scaled up by conducting studies on a multitude of reactor scales. This method is very expensive in terms of both money and time. The other way to scale up a reactor is to develop reactor models that elucidate the key features of the multiphase flow pattern, measure the relevant physical quantities, and model them with suitable accuracy. Since the information on both the process kinetics, thermodynamics and the hydrodynamics of liquid-solid fluidized bed of struvite crystals have been gained through the studies presented in the previous chapters, it is then very logical to develop a reactor model at this stage, based on the information gathered. In this research, a reactor model was developed by taking into account the facts of various equilibrium reactions, precipitation kinetics and the reactor hydrodynamics. This model possesses predictive capability of evaluating the reactor the process performance, as well as predicting  248  the product crystal size of the UBC MAP fluidized bed crystallizer. The fmdings are presented in Chapters 6 and 7.  8.2  Overall conclusions The solubility product of struvite, determined in different water and wastewater  samples, varies significantly with PH, as well amongst each other samples. The average pK values, thus determined, varied from 13.43—14.10, for different solutions, at a temperature of 20 °C. In the range of ionic strength tested in the current study, a linear relationship (with good correlation coefficients) was found between pK and ionic strength (i). A possible correlation between ionic strength and conductivity (,u  =  5E O6EC, with an R 2 —  0.8523)  was developed using different solution matrices; it was found to yield lower values of ionic strength than those predicted by the existing correlations for the same electrical conductivity. This information can be used for assessing the struvite precipitation potential for any waste stream (Chapter 2). The experimental results reveal that supersaturation plays an important role in struvite precipitation kinetics. Since the desired supersaturation ratio (SSR) of bulk solutions was achieved by adjusting the pH values, it can be inferred that pH is also an important factor influencing the precipitation reaction kinetics. The rate of disappearance of optho-P in bulk solution increases with increasing SSR values. The estimated rate constants are 2.034, 1.716 and 0.69 h’ for supersaturation ratios of 9.64, 4.83 and 2.44, respectively, with a constant Mg:P ratio of 1.3 at 20 °C. The results for struvite precipitation kinetics, with varying Mg:P ratio, reveal that the higher the ratio (in the range of 1.0—1.6), the better is the ortho-P removal efficiency. The rate constants were found to be 0.942, 2.034 and 2.7 12 h’ for Mg:P  249  ratios of 1.0, 1.3 and 1.6, respectively. The experimental observations for kinetics of struvite precipitation, with different stirrer speeds, clearly show that the mixing intensity used in this study had little effect on the intrinsic rate constants. K values were found to be 2.034 and 1.902 h 1 for 100 and 70 rpm, respectively. Seeding, with 250—500iim of seed crystals, during the struvite precipitation kinetics test, was found to have very little effect on ortho-P removal (Chapter 3). A comprehensive characterization of the struvite crystals, in terms of its intrinsic static parameters such as size, density, shape and morphology, as well as their dynamic behaviour in relation to liquid flow, such as terminal settling velocity, minimum fluidization velocity and the bed expansion characteristics for both mono-sized and the multi-particle systems, was performed. The volume equivalent diameter can be used as a characteristics dimension of the struvite crystal. The shape of the struvite crystals was found to be spheroidal and sphericity was found to be greater than 0.8 for the range of struvite particles studied in this research. None of the well-established correlations was found to be successful in predicting the precise terminal settling velocity of struvite particles. However, a very good correlation between average experimental terminal velocities and those predicted by Clift et al. (1978), was found. Although none of the correlations for determining the minimum fluidization velocities can predict the experimental minimum fluidization velocity (U), the relationship provided by Riba et al. (1978) was found to provide conservative values of U for the range of struvite particles used in this research. For mono-sized struvite crystals, the bed expansion behaviour can be represented reasonably well by the Richardson-Zaki (1954) relation, n  =  with  4.7718 x Re  —0.089  an  expansion  index  calculated  using  the  correlation:  for 26< Re <302. For poly-dispersed struvite crystals, the bed .  250  expansion behaviour was better predicted by the ‘serial model’, than the ‘average model’ (Chapter 4). The CFD simulated bed expansion behaviour of different sizes of struvite crystals was found to be consistent with the experimental results. A successful CFD simulation for struvite crystals was possible using volume equivalent diameter as the characteristic dimension of the crystals groups. The mixing and segregation characterizes of the liquidsolid fluidized bed of different sizes of struvite crystals were found to be captured adequately by the CFD simulations. The CFD predictions are also found to be consistent with the established hypothesis found in the literature (Chapter 5). A model was developed (based on perfect size classification of struvite crystals) that -P and 4 4 predicts both P0 NH N concentrations in a decreasing trend with increasing bed height; this trend was observed in actual fluidized bed experimental results. The rate of disappearance was somewhat slow at the bottom part of the reactor, with a higher rate observed in the middle section of the crystal bed. A reasonably good fit of the model prediction with the experimental data, on the removal of both 4 P0 P and 4 N11 N, was observed for the case presented in this current study. Other predictions include crystal size decreasing along the bed height and the bed voidage increasing with increasing crystal bed height. The model predictions, with respect to crystal size and overall bed voidage, were also found to match reasonably well with the experimental data. Therefore, this model could be extended further to study the effect of different operating conditions, such as varying species concentrations, seeding rate, upflow velocity and aspect ratio, on reactor performance; thus, optimizing the crystallization process in the UBC MAP crystallizer (Chapter 6) is now possible.  251  The struvite crystallization process, in a pilot scale operation, involves not only the crystal growth, but also the other phenomena such as nucleation (most possibly the secondary one), and agglomeration. Attrition andlor breakage can occur in the reactor, with the crystal segments created by the breakage serving as the seed crystals. A modified version of the model developed in Chapter 6, can be used for reactor performance evaluation, in terms of removal efficiencies of struvite constituent species (Mg, NH 4 and P0 ) and the mean sizes of 4 crystal products. Although the product crystals were found to have some gradation in terms of sizing, this ‘mean size estimation’ approach provides some prior knowledge about the average product crystal size, for specific operating conditions (Chapter 7).  8.3  Practical implications for wastewater industries Phosphorus recovery from wastewater is no longer a possibility, rather an obvious  reality. The wastewater industry has started adopting this new technology to remove and recover phosphorus from waste streams. As has already been discussed, effective design of a fluidized bed crystallizer seriously depends on the knowledge of process kinetics, thermodynamics and the system hydrodynamics. All these issues are directly related to the effective design and optimization of the crystallizer and have been dealt with in this research program. Therefore, the engineering significance of this research is substantial. Some of the key points for practical application of these research findings are summarized below: 1. In order to achieve better operational control of struvite recovery systems, an appropriate knowledge of the solubility of struvite is required. A widely varying value has been reported in the literature for struvite solubility product but the use of an incorrect value can yield erroneous information about the level of saturation of an effluent sample. In this  252  research, the struvite solubility products are determined from the analytical results of the solubility tests, performed for a wide variety of wastewaters. These findings (Chapter 2) will definitely help the wastewater industry in selecting an appropriate value of solubility product for designing and controlling phosphorus removal from wastewater, through a struvite crystallization process. 2. A proper estimation of the process kinetic parameters assists the design of a reactor and establishes optimum process conditions. However, adequate information in terms of struvite precipitation kinetics is lacking in the literature. Therefore, design engineers will find this kinetic study (Chapter 3) very useful for preliminary design purposes. 3. Hydrodynamics play a key role in the crystallization process, especially having a critical effect on mixing and mass transfer within the system; this affects the growth rate and quality of the crystals, in terms of size and shape. In this research work, both experimental and numerical investigations of hydrodynamics of liquid-solid fluidized bed of struvite crystals were performed. The findings of this study provide insight into the actual hydrodynamics of the reactor (Chapters 4 and 5), which eventually contribute to the development of an overall, improved reactor model. This study also opens up an avenue for further study on CFD analysis of a full scale crystallizer. 4. Based on the information obtained from the kinetics and hydrodynamics study, a mathematical model has been developed, by assuming complete segregation of the bed crystals and liquid movement as plug flow in the reactor. The model was tested for the reactor performance evaluation at different operating conditions and its predictions provide a reasonably good fit with experimental results. Therefore, the model can be used as a “tool” for performance evaluation of a fluidized bed crystallizer. This model can be  253  extended to optimize the struvite crystallization process in the UBC MAP Crystallizer, to ensure more efficient reactor design (Chapters 6 and 7).  8.4  Future work The current study opens up many exiting research questions that could not be  addressed during the tenure of a single Ph.D. student. The recommendations are summarized as action items for future research and include: 1. Process identification: In all previous studies performed by the UBC P-recovery group. including the current one, crystal growth is considered as the only process to be responsible for P-recovery and for the size enlargement of the struvite crystals. However, during the modeling effort of this current study, this assumption was proven to be erroneous, as the kinetic parameters estimated, based on crystal growth, failed to predict the process performance in terms of removal of species constituents and the mean size of the product crystals. The model consistently under-estimated the mean product crystal size; implying that processes (other than crystal growth) are also taking place in the pilotscale reactor. Therefore, in order to better predict the reactor performance with confidence, a better understanding of the fundamentals of the process is required. Hence, a comprehensive study including different processes such as nucleation, growth, agglomeration and breakage is recommended for future research. 2. Once the fundamental processes are identified, the kinetics parameters of those processes are required for a more successful model development, resulting in another avenue for future research.  254  3. CED simulation of the full scale UBC MAP fluidized bed crystallizer will provide insight into the hydrodynamics of the reactor. Hence, the CFD simulation of the actual full scale reactor is warranted and highly recommended for future research. 4. Since crystallization is a multi-particle system, the CFD analysis, incorporating a population balance model, will capture the actual size distribution of the crystals; hence, this area is also recommended for further study.  255  8.5  References  Adnan, A., Mavinic, D.S., and Koch, F.A. (2003) Pilot-scale study of phosphorus recovery through struvite crystallization examining the process feasibility. J. Environ. Eng. Sci. 2 (5), 315-324. -  Clift, R., Grace, J.R., and Weber, M.E. (1978) Bubbles, Drops, and Particles. Academic Press, New York, p. 114. Riba, J.P., Routie, R., and Couderc, J.P. (1978) Conditions minimales de mise en fluidisation par un liquide. Can. J. Chem. Eng. 56, 26-30. Richardson, J.F., and Zaki, W.N. (1954) Sedimentation and fluidization: Part I. Trans Instn Chem Engrs. 32, 35-53.  256  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0072391/manifest

Comment

Related Items