Kinetics of Reaction-Crystallization of Struvite in the Continuous Draft Tube Magma Type Crystallizers—Influence of Different Internal Hydrodynamics

PRODUCT ENGINEERING AND CHEMICAL TECHNOLOGY Chinese Journal of Chemical Engineering, 17(2) 330ü339 (2009)

Kinetics of Reaction-Crystallization of Struvite in the Continuous Draft Tube Magma Type CrystallizersüInfluence of Different Internal Hydrodynamics Joanna Koralewska1, Krzysztof Piotrowski2,*, Boguslawa Wierzbowska1 and Andrzej Matynia1 1 2

Department of Chemistry, Wroclaw University of Technology, 50-370 Wroclaw, Poland Department of Chemical and Process Engineering, Silesian University of Technology, 44-101 Gliwice, Poland

Abstract A laboratory-scale reaction-crystallization process of struvite synthesis from diluted water solution of Mg2+, NH 4 and PO34 ions was studied. The research covered the tests of two original constructions of continuous jet-pump Draft Tube Magma (DTM)-type crystallizers with internal circulation of suspension (upward/downward). Interactions between constructional, hydrodynamic and kinetic factors were established and discussed. Nucleation and linear growth rates of struvite crystals were calculated on the basis of population density distribution. Kinetic model of idealized Mixed Suspension Mixed Product Removal (MSMPR) crystallizer considering the size-dependent growth mechanism was applied (Rojkowski hyperbolic equation). For comparison purposes the kinetic data corresponded to a simpler, continuous draft tube-type crystallizer equipped with propeller agitator were analyzed. It was concluded that crystal product of larger size was withdrawn from the jet-pump DTM crystallizer of the descending flow of suspension in a mixing chamber. Keywords reaction-crystallization, struvite, phosphorus recycling, nucleation, crystals growth, DTM MSMPR crystallizers, size-dependent growth kinetics, liquid jet pump, propeller agitator

1 INTRODUCTION The new, original constructions of jet-pump crystallizers can be generally classified as DTM (draft tube magma) type units [1]. A jet-pump situated inside the crystallizer provides good mixing of the circulated suspension, thus enables one to receive a non-classified product of representative crystal size distribution (CSD). It may be approximately assumed that such apparatus fulfills the requirements of MSMPR (mixed suspension mixed product removal) crystallizer [2]. Essential advantages of a jet-pump crystallizer include

(a) DTMĹ crystallizer

absence of troublesome moving (especially rotating) elements and practical utilization of simple hydrodynamic phenomena. This results in lower probability of failure and relative simplicity in use [3]. Internal circulation of suspension generated by liquid jet-pump device is based on advantageous hydrodynamic effects connected with the merge of two circulated streams (see Fig. 1). It causes relatively fast and effective blending of the reagents, resulting in homogenization of concentration and temperature in the process environment, as well as prevention of excessive agglomeration of crystals. Incrustation inside the apparatus body is also strongly inhibited to

(b) DTMĻ crystallizer

Figure 1 A general scheme of the three crystallizer constructions under study 1üfeeding inlet; 2üpH-correction agent inlet; 3üoutlet of crystal suspension

Received 2008-01-07, accepted 2008-12-15. * To whom correspondence should be addressed. E-mail: [email protected]

(c) DT crystallizer

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achieve longer failure-free exploitation time possible. Jet-pump crystallizers have been designed and adopted for various mass crystallization processes [3], including the most complex reaction-crystallization ones (barium sulphate [4, 5], hydroxyapatite [6, 7] and struvite [6, 8, 9]). Synthesis of struvite crystals from diluted water solutions of Mg2+, NH 4 and PO34 ions can be included into modern processes of phosphorus recycling üan important technology currently developed worldwide. The general idea of the technology depends on selective removal of phosphate ions from the complex postindustrial liquid wastes, municipal sewage or manure solution by their precipitation in a chemical form of sparingly soluble complex inorganic salt MgNH4PO4˜6H2O ü magnesium ammonium phosphate (MAP), struvite (pKsp 9.4  13.26 ) [1012]. Precipitation of struvite (chemical synthesis of the product) followed by closely integrated mass crystallization process (forming of product particles) is carried out in alkaline environment (7˘pH˘11), mostly in room temperature (T 298 K), by contacting in appropriate proportions the initially purified liquid wastes rich in PO34 ions with water solution of Mg2+/ NH 4 ions (e.g. easily dissociable magnesium chloride and some ammonium salt). Rational construction of a crystallizer (e.g. with original application of a jet-pump device) is of essential importance, as well. Struvite crystals can be used as an important secondary source of phosphorus, in a physical form convenient for its further processing or utilization, e.g. as a valuable mineral fertilizer [1315]. The experimental data concerning reactioncrystallization of struvite in two continuous laboratory liquid jet-pump crystallizers of various internal hydrodynamic regimes [denoted as DTMĹ and DTMĻ, see Figs. 1 (a) and 1 (b)] andüfor comparison purposesüin a crystallizer equipped with a propeller agitator [1] [denoted later as DTüsee Fig. 1 (c)] are presented in this study. Laboratory test stand was precisely controlled by automatic control system driven by PC computer. Nucleation and growth rates of struvite crystals were estimated from the population density distributions of crystal product taking into account size-dependent growth (SDG) kinetic mechanism. 2 EXPERIMENTAL 2.1 Setup and procedure The simplified schemes of laboratory crystallizers used in the present research are shown in Fig. 1: Figure 1 (a)üDTMĹ type crystallizer with liquid jet-pump. Feeding nozzle of a jet-pump device was placed in the bottom of apparatus resulting in ascending flow of suspension in a mixing chamber ( VW 1.2 L ). Figure 1 (b)üDTMĻ type crystallizer with liquid jet-pump. Feeding nozzle of a jet-pump device was placed under free suspension level in a working vol-

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ume resulting in descending flow of suspension in a mixing chamber ( VW 1.2 L ). Figure 1 (c) ü DT type crystallizer with a three-paddle propeller agitator resulting in descending/ascending (current rotation direction) flow of suspension in a draft tube element ( VW 0.6 L ). A liquid jet-pump device [Figs. 2 (a), 2 (b)] installed in the laboratory crystallizers is characterized by the following dimensions: mixing chamber diameter, d k 15 mm; mixing chamber length, lk 125 mm; confusor diameter (inlet), do 30 mm; confusor length, lo 12 mm; feeding nozzle diameter (outlet), de 2.0 mm; distance between feeding nozzle outlet and free suspension level [Fig. 2 (a)], ho 65 mm or between feeding nozzle outlet and crystallizer bottom [see Fig. 2 (b)], ho 25 mm; distance between feeding nozzle outlet and mixing chamber inlet, b 0 mm.

(a) DTMĻ crystallizer

(b) DTMĹ crystallizer

Figure 2 Liquid jet-pump device applied in a laboratory DTMĻ and DTMĹ crystallizers under study 1üfeeding nozzle; 2üconfusor; 3ümixing chamber

Experimental test stand with the exemplary DTMĻ type crystallizer is presented in Fig. 3. It was a cylindrical tank of 90 mm diameter and 200 mm height, made of transparent Plexiglas. The diameter of a cylindrical part of the tank overflow was 120 mm, its height was 150 mm. Total height of the whole crystallizer construction was 330 mm while the height of its working part was 220 mm. A DTMĹ construction has the same external dimensions, however the jet-pump device arrangement is different. DT crystallizer construction was a tank of 120 mm diameter and 123 mm height with central tube (d 57 mm, h 53 mm) inside which a three-paddle propeller mixer ˉ [d 55 mm, N (6.6r0.15) s 1] was installed. Operation, control and online recording of the measurement data were controlled by a PC computer. Detailed characteristics of hydrodynamic regimes established

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Figure 3 Connection scheme of a test stand for reaction-crystallization of struvite 1üDTMĻ crystallizer with internal circulation of suspension; 2ücirculating pump; 3ürotameters; 4üheat exchanger; 5üPC computer; 6üfeeding tank (MgCl2 solution blended with NH4H2PO4 solution); 7üperistaltic pump; 8üalkaline agent’s tank (NaOH solution); 9üNaOH dosing pump; 10üpump for removal of crystal suspension from the crystallizer; 11üstorage tank for crystal product suspension; 12,13,14üelectronic balances; pHücontrol of the reaction environment’s pH; Tütemperature control

in all three constructions used were presented elsewhere [6, 8, 9, 1618]. All crystallizers in Fig. 1 were provided with water solutions of magnesium chloride MgCl2 (of adjustable concentration according to the controlled stoichiometric proportions) and with water solution of ammonium dihydrogen phosphate NH4H2PO4 (of constant mass concentration 25%). Both solutions were initially thoroughly premixed and blended in external vessel before introduction into the region between crystallizer wall and generator of circulation [jet-pump device in Figs. 1 (a), (b) or draft tube in Fig. 1 (c)] conventionally called crystal growth zone (injection point at h 100 mm from the bottom). The zone was also provided with 20% water solution (by mass) of NaOH to keep the adequate pH of reaction environment. Crystal product suspension (unclassified) was continuously and isokinetically removed from the bottom of the crystallizer. The experiments were carried out under the predetermined, constant conditions: T 298 K (thermostat LT5 control, temperature meter IKATRON DTM 11 with temperature sensor PT100.4/5, IKA Labortechnik, Germany);

pH 9 (pH-electrode EPP-3 integrated with universal measuring instrument ELMETRON CX-741, Elmetron, Poland); IJ 900 s (peristaltic pump PA-MI digital, IKA Labortechnik, Germany, driven by IKA Labworldsoft software); Mg2+/ PO34 / NH 4 ions composition in the feeding stream: [Mg2+]RM 0.25% (by mass) and 2.0% (by mass) and stoichiometrically [ PO34 ]RM 0.98% (by mass) and 7.81% (by mass), [ NH 4 ]RM 0.18% (by mass) and 1.48% (by mass), respectively. Minimal unit power of a jet-pump feeding stream (however sufficient enough for stable circulation of suspension) was used [19, 20]. Its value can be calculated using the following equation: Peu

pde qve

Usol ve2 qve 2 UsusVw

3 8Usol qve

S2 de4 UsusVw

(1)

In case of DTMĹ crystallizer this value was ˉ Peu 0.25 and 1.64 W·kg 1, while for DTMĻ crystalˉ lizer Peu 0.20 and 1.45 W·kg 1 [for [Mg2+]RM 0.25% (by mass) and 2.0% (by mass), respectively]. In a DT-type crystallizer minimal value of agitator’s revo-

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lution number was 7 s 1. Feeding nozzle of a jet-pump was powered with a stream of externally circulated solution (theoretically solid-free). Its minimal value, sufficient to keep all solid particles in a permanent movement, was assumed purposefully taking into consideration two important issues. First of all, the experimental results enable one to determine the possibly pure intrinsic kinetics of the process (not diminished by accompanying hydrodynamic/mechanical phenomena like attrition, breakage, etc.). The second reason was that in these mild conditions the number (mass) of the smallest particles detected in a sedimentation (clarifying) zone of the DTM-type crystallizers is reduced to minimum. These particles can unintentionally exit ü through the crystallizer’s overflowü into the external circulation loop where they reach circulation pump. Inside the pump they are potentially subjected to intensive attrition action of the pump rotor. Flowing through the feeding nozzle back into the crystallizer, they act as the primary source of secondary nucleation precursors. Moreover, since minimal unit power Peu is a function of physical (Usol, Usus), constructional (de, Vw) and hydraulic (qve) properties of the system [see Eq. (1)], it may be directly used as a convenient similarity index for scale-up from laboratory to industrial process conditions. Continuous reaction-crystallization process of struvite was run through the time of 5W starting from the moment as the assumed parameter values stabilized. After this period the solid phase concentration in the product suspension (MT) and its crystal size distribution (CSD) (laser particle size analyzer COULTER LS-230) were determined. Chemical analysis of mother liquor (plasma emission spectrometer ICP-AES Philips PU 7000) and solid phase (spectrometer IR Philips PU 9712) were done as well. ˉ

2.2 Reaction-crystallization kinetics

In mass crystallization processes the population balance equation enables one to evaluate the dependence between number of crystals and their size [CSD üespecially in a form of population density distribution (PDD)] [2]. CSD (or PDD) presents the resulting net effect of the complex, frequently opposite interrelations and feedbacks between the intrinsic process kinetics, suspension hydrodynamics, crystallizer structure, arrangement of the apparatus interior, decisive technological parameter values and actions of other accompanying processes. These distributions can be also interpreted as essential indicators of the crystal product applicability. It can be assumed, that regarding practically instant ionic reaction between Mg2+, NH 4 and PO34 species during struvite synthesis (in a liquid form), main mass transfer resistances of the overall reaction-crystallization process are essentially related to creation (nucleation) and size-increment (growth) of solid phase. Thus, mass crystallization kinetics itself practically corresponds to the kinetics of struvite synthesis process.

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For the basic, simplified approach to the mass crystallization process kinetics, assuming steady state in a continuous crystallizer with ideally mixed content and withdrawal of a non-classified, representative product (MSMPR type crystallizer), the population balance equation can be formulated in a general form of simple differential equation [21]: dn( L) dL dG ( L)   (2) n( L) G ( L)W G ( L) However, from the experimentally obtained population density distributions lnn(L) of struvite crystals [presented in Fig. 4 for [Mg2+]RM 2.0% (by mass)] it results that for the smallest-size crystals (L˘10 Pm) their courses are clearly concave to top.

Figure 4 Comparison between population density distributions (PDDs) of struvite [T 298 K, [Mg2+]RM 2.0% (by mass), W 900 s, k v 1] pointsüexperimental data; solid linesüvalues calculated using Eq. (10) and the data from Table 3 for Rojkowski hyperbolic SDG model (RH) (pH 9)

This characteristic behavior can be theoretically interpreted as the symptom of a complex kinetic mechanism ü Size-Dependent Growth (SDG). Its consequenceüa nonlinear increase in the number of finesü is very essential from the practical point of view since within this size range the largest fraction of the overall crystals number is located. Considering fine-grained morphology, this crystal fraction characterizes itself by the largest specific surface area in respect to the whole population. A more detailed description of the process kinetics, considering the SDG mechanism, thus rendering the experimentally observed strong nonlinearity of lnn(L) function course for struvite crystals of L˘10 Pm requires assuming some form of G(L) dependency before solving the general population balance equation of MSMPR crystallizer, Eq. (2). Empirical or semiempirical G(L) equations [2229] were analyzed in detail [30]. Theoretical analysis regarding mathematical construction of these functions proved that equations proposed in Refs. [22, 28, 29] are valid only for the crystals of finite size. Assumption of zero-size nucleus makes its further growth impossible from mathematical point of view. Thus, for practical application of these formulas it becomes necessary to assume arbitrarily starting size for nucleus Lz, which value can introduce some unpredictable calculation error.

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Selected analytical solutions of Eq. (2), derived as n(L) expressions comply with the assumed G(L) forms, are presented below [30]: Abegg, Stevens and Larson (ASL) model [24], Eqs. (3), (4) and (6): G

G0 1  aL

b

(3)

§ 1 · 1  aL ¨© G0 aW ¸¹

for b 1, n n0 1  [see Eq. (6) also] for 0˘b˘1, ª § 1 1b n n0 exp «  ¨ ¬ª1  aL  1¼º  G a W  1  b 0 © ¬ ·º b ln 1  aL ¸ » (4) ¹¼ Canning-Randolph (CR) model [23], Eqs. (5) and (6): G n

G0 1  aL § 1

n0 1  aL ¨© G0 aW

(5) · 1¸ ¹

(6)

Rojkowski exponential (RE) model [25], Eqs. (7) and (8): G

Gf   Gf  G0 exp  aL

L º °½ § 1 · »¾ ¨ G aW  1¸  © f ¹ GfW ¼ ¿°

n

§ G  G0 · Gf  ¨ f ¸ © 1  aL ¹

(8)

G0  aGf L 1  aL

(9)

­° ª 1 Gf  G0 § aGf L  G0 · ln ¨ n0 exp ® « ¸ 2 G0 © ¹ ¯° ¬W aGf § G  aGf L · º ½° 1 L  ln ¨ 0 ¸» ¾ W Gf © 1  aL G0 ¹ ¼ ¿°

n

G0Gf2W  Gf  Gf  G0 L Gf2W   Gf  G0 L

­° ª § G  G  G L  G G 2W · 0 0 f n0 exp ® «ln ¨ f f ¸¸  2 ¨ G G W °¯ ¬« © 0 f ¹ § G G 2W  Gf  Gf  G0 L · º ½° L  ln ¨ 02 f ¸» ¾ ¨ ¸ W Gf © GfW G0   Gf  G0 LG0 ¹ »¼ °¿

(13)

3 RESULTS AND DISCUSSION 3.1 Estimation of kinetic parameters of the model

On the basis of own experimental data the following parameters: n0, G0, Gf, a, b values in n(L) functions corresponded to the selected G(L) equations were determined. For each n(L) function (thus SDG model) and each experimental data set a mean square deviation (variance) was calculated by: 2 RMSD

¦ ª¬ln ncalc ( L)  ln nexp ( L) º¼

2

(14)

p 1

2 for Comparison in the sums of variance ¦ RMSD all measurement series (see Table 1) enabled one to select an n(L) model which is the best for the own experimental data description (based on the criterion 2 of minimized ¦ RMSD ), thus the corresponding G(L) equation.

Crystallizer type

[Mg2+]RM/ % (by mass)

DTMĹ

0.25

17 0.2717 0.5967 0.0732 0.1022 0.6127

2.0

19 0.4766 0.5548 0.3215 0.3444 1.8233

DTMĻ DT 2 6RMSD

(10)

Rojkowski hyperbolic II (RH II) model [27], Eqs. (11) and (12): G

n0 G0

Table 1 Kinetic models of struvite crystallization in DTMĹ, 2 2 and ¦ RMSD values for DTMĻ and DT crystallizers: RMSD the selected SDG equations

Rojkowski hyperbolic (RH) model [26], Eqs. (9) and (10): G

B

(7)

°­ ª G   Gf  G0 exp  aL ˜ n0 exp ® «ln f G0 ¯° ¬

n

can be calculated from the following relation:

(11)

2 RMSD for SDG models

p ASL

CR

RE

RH

RH II

0.25

17 0.0683 0.2188 0.0766 0.0719 0.5839

2.0

19 0.4026 0.5493 0.3399 0.3411 1.0738

0.25

14 0.2682 0.2464 0.4908 0.0660 0.0673

2.0

16 0.1823 0.2789 0.3494 0.0658 0.0920 1.6697 2.4449 1.6514 0.9914 4.2530

After analysis of the data in Table 1 it can be concluded that the Rojkowski hyperbolic model 2 ( ¦ RMSD 0.9914) suits fine to the own experimental data. This SDG model renders both steep curvature within the initial L range as well as an apparent linearity within the remaining L range very well. Kinetic parameters of the process corresponding to DTMĹ, DTMĻ and DT constructions calculated with the selected five SDG models are presented in Table 2 [for [Mg2+]RM 0.25% (by mass)] and Table 3 [for [Mg2+]RM 2.0% (by mass)] and discussed below. 3.2 DTMĹ crystallizer performance

(12)

Knowing nuclei population density, n0, and their linear growth rate, G0, the (overall) nucleation rate B

Kinetic parameter values of reaction-crystallization process of struvite in a jet-pump DTMĹ crystallizer, calculated with the RH SDG model, can be summarized as follows. Increase in Mg2+ ions mass concentration in

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Chin. J. Chem. Eng., Vol. 17, No. 2, April 2009 Table 2 The values of nucleation and crystal growth rate for the selected SDG models acquired in DTMĹ, DTMĻ and DT crystallizers (Struvite crystals obtained for Mg2+ ions mass concentration in a feeding solution equals to 0.25% at pH 9, W 900 s and kv 1) Crystallizer type

SDG model

DTMĹ

ASL

ˉ3

5.26×1022

G0/m·s

ˉ1

Gf/m·s

ˉ1

1.23×10

ˉ10

CR

5.65×10

6.35×10

ˉ10

RE

5.29×1022

1.83×10

ˉ10

6.38×10

ˉ9

RH

22

1.78×10

ˉ10

9.03×10

ˉ9

5.31×1022

6.91×10

ˉ11

5.91×10

ˉ9

5.29×10

b

2.108×107



ˉ

ˉ1

0.6023

6.47×1012



3.59×1012

76952



9.67×1012

57454



9.40×1012





3.67×1012

3.38×10



B/m 3·s

5

3.02×10

CR

5.77×10

21

5.29×10

ˉ10

RE

1.31×1022

3.36×10

ˉ10

5.62×10

ˉ8

6245



4.38×1012

RH

22

3.33×10

ˉ10

6.82×10

ˉ8

5244



4.27×1012

1.32×1022

6.13×10

ˉ9





1.73×1012

1231610

0.7323

6.14×1011

ASL

1.32×1022

ˉ1

a/m

ˉ10

1.28×10



1743840

0.8549

3.98×1012



503945



3.06×1012

1.31×10

ˉ10

ASL

1.05×10

21

5.85×10

ˉ10



CR

7.46×1019

1.97×10

ˉ9



RE

2.94×10

21

RH

2.73×1021

RH II DT

ˉ

21

RH II DTMĻ

n0/m 1·m

RH II

3.50×10

21

4.65×10

ˉ10

2.60×10

ˉ10

2.08×10

ˉ10

89242



1.47×1011

6.27×10

ˉ8

5752



1.37×1012

7.74×10

ˉ9

124798



7.09×1011

7.36×10

ˉ9





7.28×1011

Table 3 The values of nucleation and crystal growth rate for the selected SDG models acquired in DTMĹ, DTMĻ and DT crystallizers (Struvite crystals obtained for Mg2+ ions mass concentration in a feeding solution equals to 2.0% at pH 9, W 900 s and kv 1) Crystallizer type DTMĹ

SDG model

ˉ3

1.08×1024

G0/m·s

ˉ1

Gf/m·s

ˉ1

1.57×10

CR

2.47×10

24

1.65×10

ˉ10

RE

1.06×1024

1.52×10

ˉ10

RH

24

1.54×10

ˉ10

2.11×10

1.11×1024

3.01×10

ˉ11

8.16×10

ASL

1.06×10

ASL

9.09×10

22

CR

5.79×1023

RE

9.45×10

22

RH

9.48×1022

RH II DT

ˉ

ˉ10

RH II DTMĻ

n0/m 1·m

9.11×1022

4.08×1014

1.79×10

ˉ10

1.74×10

RE

2.03×10

22

RH

2.09×1022

2.25×10

ˉ10

a feeding solution from 0.25% to 2.0% results in: Increase in maximal linear growth rate, Gf, from ˉ ˉ ˉ 9.03×10 9 to 2.11×10 8 m·s 1; Increase in nuclei population density, n0, from ˉ ˉ 5.29×1022 to 1.06×1024 m 1·m 3, while a practically constant value of their linear growth rate (a minimal ˉ ˉ one) is observed, G0 ( 1.54  1.78 )×10 10 m·s 1; Increase in nucleation rate, B, from 9.40×1012 to ˉ ˉ 1.63×1014 m 3·s 1. From these data it results that the supersaturation

18976



1.63×1014

ˉ9





3.33×1013

3937247

0.9214

1.51×1013 7.52×1013

4.88×10

1027



1.70×1013

5.02×10

ˉ7

1003



1.69×1013

1.18×10

ˉ8





6.36×1012

6835098

0.5327

6.47×1012



ˉ10

1.61×1014



ˉ9

3.44×10



3209429



5.34×10

32739

ˉ7

ˉ10

ˉ10

ˉ8

ˉ8

1.23×10

1.79×10

9.94×1020

2.90×10





CR

RH II

1833088

ˉ10

3.52×10

22



ˉ10

1.84×10

ˉ1

1.70×1014

1.30×10

ASL

ˉ

0.8502



6.98×10

B/m 3·s

3412371

1.66×10

22

b



ˉ10

ˉ11

ˉ1

a/m

83120



1.73×1012

1.22×10

ˉ8

27965



1.08×1013

6.72×10

ˉ9

114691



7.20×1012

5.89×10

ˉ9





6.51×1012

level is a dominant technological parameter in the process under study. However, because of different kinetic sensitivity of nucleation and growth processes in respect to supersaturation, only ca. 2.3 times increase in Gf while ca. 17 times increase in nucleation rate, B, is observed. Nuclei population density, n0, increases ca. 20 times. It results from the increase in supersaturation as an effect of application of a more concentrated feeding solution and intrinsic non-homogeneity of mother liquor connected with relatively ineffective

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mixing (compared to DTMĻ and DT designs), thus possibility of primary nucleation. Evident contribution of attrition is also observed: the effect of increase in solid phase concentration enlarging frequency of mechanical interactions as well as destructive action of circulating pump unintentionally milling the smallest crystals. Disadvantageous consequences of external loop variant (especially presence of turbine-driven pump) as far as concerned the strategy of fines reduction is also clearly confirmed matching the corresponding values of nuclei population density (n0) and nucleation rate (B) for DTMĹ and DT (absence of external circulation) constructions: n0 DTMĹ 5.29×1022 ˉ ˉ ˉ ˉ m 1·m 3˚n0 DT 2.73×1021 m 1·m 3 for [Mg2+]RM 24 ˉ1 ˉ3 0.25% (by mass), n0 DTMĹ 1.06×10 m ·m ˚n0 DT ˉ ˉ 2.09×1022 m 1·m 3 for [Mg2+]RM 2.0% (by mass) ˉ ˉ and, by analogy, BDTMĹ 9.40×1012 m 3·s 1˚BDT ˉ3 ˉ1 ˉ3 ˉ1 11 14 7.09×10 m ·s , BDTMĹ 1.63×10 m ·s ˚BDT ˉ ˉ 7.20×1012 m 3·s 1. However, higher values of linear growth rate of larger crystals, Gf, in a DTMĹ construction compared to a DT one are responsible for the fact that the resulting mean sizes of product crystals are similar, ca. 14 Pm [6, 16]. Linear growth rate of struvite crystals increases with their size increase in a whole L range tested (see Figs. 47). Nevertheless, its increase is nonlinear-the most distinct increment corresponds to the smallest sizes (up to ca. L 20 Pm, see Figs. 57), what is also visible as a distinct curvature in a lnn(L) plot-see Fig. 4. 3.3 DTMĻ crystallizer performance

Reaction-crystallization of struvite in a DTMĻ crystallizer meets a little different hydrodynamic regime compared to both DTMĹ and DT constructions. Increase in Mg2+ ions concentration in a feeding solution results in a production of larger crystal sizes: from Lm 15.5 Pm ([Mg2+]RM 0.25%, by mass) to Lm 31.0 Pm ([Mg2+]RM 2.0%, by mass). It should be emphasized, that mean sizes of crystals were considerably larger than the corresponded ones produced both in DT [6] and DTMĹ [16] crystallizers [for [Mg2+]RM 2.0% (by mass) a 2-times increment was observed]. It can be supposed, that the main reason responsible for such behavior is the advantageously modified hydraulic regime of internal circulation. It influences the distribution of supersaturation within the process environment and suspension hydrodynamics. It should be noted, that in a DTMĻ type crystallizer (similarly to a DTMĹ construction) the smallest-size crystal mass fraction (3%5%) reached the pump in external circulation loop. However, it did not visibly influence mean crystal size since in this configuration other kinetic effects predominated. Theoretical confirmation of these observations is provided in the form of kinetic parameter values corresponding to a DTMĻ apparatus type, as well as their interrelations. Increase in Mg2+ ions mass concentration in a feeding solution

(0.25%ĺ2.0%) resultsüin this operation regimeüin: Significant increase in mean level of maximal ˉ ˉ linear growth rate, Gf, [( 6.82  50.2 )×10 8 m·s 1] ˉ8 ˉ1 compared to both DTMĹ [( 0.9  2.1 )×10 m·s ] and ˉ ˉ DT [( 0.77  0.67 )×10 8 m·s 1] constructions; Increase in nuclei population density, n0, from ˉ ˉ 1.28×1022 to 9.48×1022 m 1·m 3; these values are ca. one order of magnitude lower than mean level of n0 observed in DTMĹ crystallizer (5.29×1022  1.06×1024 ˉ ˉ m 1·m 3), however higher than mean level of n0 in a ˉ ˉ DT apparatus (2.73×1021  2.09×1022 m 1·m 3); Slight decrease in a linear growth rate of nuclei, G0 ˉ ˉ ˉ (a minimal one), from 3.33×10 10 to 1.79×10 10 m·s 1; however, these values are closely similar to the ones ˉ ˉ observed in a DTMĹ[(1.54  1.78)×10 10 m·s 1] and ˉ10 ˉ1 DT [(2.60  3.44)×10 m·s ] constructions; Increase in nucleation rate, B; however, the values of this parameter are clearly lower (B 4.27×1012  ˉ ˉ 1.69×1013 m 3·s 1) compared to the data from DTMĹ ˉ ˉ crystallizer (9.40×1012  1.63×1014 m 3·s 1) and higher compared to the data from DT (7.09×1011  7.20×1012 ˉ ˉ m 3·s 1) construction. From this analysis it results that in a DTMĻ crystallizer the considerably higher values of maximal linear growth rate are attainable. In consequence the product crystals of nearly 2-times larger mean sizes (compared to DTMĹ and DT constructions) are obtained. Nuclei population density, n0, as well as nucleation rate, B, are clearly lower in a DTMĻ crystallizer compared to a DTMĹ one. Lower mixing intensity, thus not effective enough blending of reagents with mother solution, leads to the occurrence of temporary, local supersaturation peaks responsible for higher nucleation rate in a DTMĻ crystallizer compared to a DT one (being free of these drawbacks). Attrition effects in external circulation pump contribute to this effect, as well. Elimination or at least significant reduction in these negative tendencies should be employed. Rational modification of DTMĻ construction can provide crystal product of higher quality. 3.4 Size-dependent growth phenomena in DTM crystallizers

Character of G(L) courses is qualitatively similar in DT and DTMĹ crystallizer types, where some rapid approach to an asymptotical, limiting Gf value is observed. In case of DTMĻ construction G increases practically linearly with crystal size within a 0˘L˘ 80 Pm range, what corresponds to the larger mean sizes in a crystal product population (Fig. 5). The G(L) dependences for DTMĹ and DTMĻ constructions are presented in Figs. 6 and 7 for all five SDG models used [ASL, CR, RE, RH and RH II, Eqs. (3)(12)]. Generally, from Fig. 6 it can be concluded that all five kinetic SDG models provide higher G values for higher [Mg2+]RM value within the whole size range tested (080 Pm). Relatively large initial increase in growth rate is observed (especially visible

Chin. J. Chem. Eng., Vol. 17, No. 2, April 2009

Figure 5 Dependence of linear growth rate of struvite crystals on their sizes, G(L), for all three crystallizer constructions under study (influence of circulation hydrodynamics)üEq. (9) and data from Table 3 [Rojkowski hyperbolic model (RH) applied] [ T 298 K, [Mg2+]RM 2.0% (by mass), W 900 s, k v 1]

Figure 6 Dependence of linear growth rate of struvite crystals on their sizes in a DTMĹ crystallizerüGeneral comparison of predictions using Eqs. (3), (5), (7), (9) and (11) and kinetic data from Tables 2 and 3 ( T 298 K, W 900 s, k v 1) 2+ 2+ [Mg ]RM 0.25% (by mass); üü [Mg ]RM 2.0% (by mass)

in RE, RH and RH II model courses where the maximal possible G is theoretically upper-limited by some asymptotical Gf value; in case of CR and ASL models the theoretically unlimited G(L) increase is observed). Contrary, different hydrodynamic regime in a DTMĻ construction is clearly demonstrated by modified arrangement of the G(L) curves family in Fig. 7. Both

Figure 7 Dependence of linear growth rate of struvite crystals on their sizes in a DTMĻ crystallizerüGeneral comparison of predictions using Eqs. (3), (5), (7), (9) and (11) and kinetic data from Tables 2 and 3 ( T 298 K, W 900 s, k v 1) 2+ 2+ [Mg ]RM 0.25% (by mass);üü [Mg ]RM 2.0% (by mass)

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RE and RH models present apparent linear courses, suggesting location of asymptotical Gf value in a considerably higher level compared to a DTMĹ variant (see also different G scale in both figures). Generally, all SDG kinetic models from Fig. 7, except RH II model, provide higher G(L) values in comparison with the data in Fig. 6. This confirms previous conclusions concerning a more convenient process environment for the crystal phase growth provided by a DTMĻ construction. The discrepancies between all five SDG model predictions for the analyzed systems are also visible in Table 1 (statistical analysis of variance). Comparison between experimental and simulated PDDs proves, that the suggested SDG equation provides adequate description of lnn(L) courses, both in characteristic, highly nonlinear segment corresponding to the smallest sizes and in apparently linear fragment for the larger ones. This flexibility enables one to apply a recommended SDG model in the calculationdesign works, covering a more detailed estimation of cumulative distribution of specific surface area F(L) or cumulative crystal mass distribution m(L) ü the “derivative relationships” based on the fundamental n(L) course. Contrary, frequent application of oversimplified SIG (size-independent growth) kinetic model, based on the assumption of lnn(L) function’s linearity in the whole crystal size range, thus excluding clear, nonlinear increment (even by several orders of magnitude) in n values within the smallest sizes, results in a significant accumulation of error thus incorrect prediction of m f(n(L)) or F f(n(L)) distributions within this the most interesting size range. 3.5 Hydrodynamic problems-overcoming suggestions

Among two jet-pump DTM crystallizer constructions tested: DTMĹ with a feeding nozzle situated in the apparatus bottom (upward circulation of suspension in a mixing chamber) and DTMĻ with a feeding nozzle located under free level of medium (downward circulation) a more convenient design proved to be a DTMĻ one. It was technically possible by appropriate arrangement of a DTMĻ crystallizer interior (e.g. appearance of the stable pseudo-fluidal layer in a “crystal growth zone”). Higher concentration of solid phase in a working volume acted here advantageously by creating local whirls, making better distribution of MAP supersaturation within the reaction environment possible. Relatively large specific surface area of crystal phase (positive influence of attritionühowever considerably restricted) reduces the mass transfer resistances. It protects also against appearance of the excessive supersaturation peaks, thus improves the process stability. As a result, larger crystals were withdrawn from a DTMĻ construction, of the size increasing with the increase in Mg2+ ions concentration in a feeding solution. Other considered criteria were: location and mode of introduction of a feeding solution, stability of operation and the final results (CSD of

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product). It should be emphasized, that both DTM crystallizers produce crystal populations of comparable or larger mean sizes than a DT crystallizer does. The only disadvantage observed during laboratoryscale tests of jet-pump DTM crystallizers was undesirable presence of crystal fines in the external circulation loop (however of small mass fraction in relation to the whole suspension). It resulted in their appearance in a circulation pump (intensive attrition and breakage of crystals). Constructional corrections in a classical design, e.g. increase in a cross-section area of overflow part, can only slightly improve the separation effectiveness in a sedimentation zone. However, decrease in a removable size is not sufficient enough for the total elimination of this unintentional behavior for the sake of extreme small size range (even below 1 Pm) of particles created in reaction-crystallization processes. It seems that the only rational engineering strategy to provide larger product-crystals is to eliminate the external loop totally, providing jet-pump with compressed gas stream (e.g. air). In reactioncrystallization processes of struvite and hydroxyapatite application of air (aeration) is also well-grounded by technological requirements [1012]. Application of compressed gas stream provides stable internal circulation coupled with efficient micro-and macromixing within the complex three-phase dispersed systems [31]. It should be noted, however, that in industrial-scale mass crystallization processes, where mean crystal sizes are several hundred times larger compared to the specific reaction-crystallization products, introduction of external circulation loop in a jet-pump DTM apparatus system does not affect the process run and its results substantially while other advantages predominate. 4 CONCLUSIONS

Based on the test results concerning reactioncrystallization process of struvite in two original constructions of a jet-pump crystallizer (DTMĹ and DTMĻ) it can be concluded that in both units this complex process operated without any disturbances. In a DTMĹ configuration, crystal product of mean size comparable to the value from a DT one was obtained. It results from the opposite tendencies, facilitating primary nucleation and external attrition in exchange for the limitation of internal attrition and increase in growth rate (a maximal one). On the contrary, mean size of crystal product from a DTMĻ apparatus was considerably larger, even 2-times (Lm 31 Pm) in case of [Mg2+]RM 2.0% (by mass). It can be concluded that the most convenient conditions for reactioncrystallization of struvite were provided in a DTMĻ crystallizer: stable and effective discharge of supersaturation coupled with the reduction of concentration gradients by intensive turbulent flow (however preventing excessive attrition effects). Moreover, circulating pump in the external loop was provided with lower mass of crystal fines. Experimentally verified RH SDG kinetic equa-

tion can be recommended for modeling of the struvite reaction-crystallization process in the presented conditions. It represents in practice the overall kinetics of closely integrated system: fast ionic reaction-struvite precipitation-MAP crystals growth, giving consideration to the essential dependency of growth kinetics on the crystal size, as well as incorporating the net effect of all, frequently opposite hydrodynamic and partial processes. Thus, adjusting the nucleation and growth kinetics by advisable modification of technological parameters vector it becomes possible to produce the crystal population of required CSD and quality, thus synthesize preliminary designed product demanding no further mechanical operations (e.g. milling, sieving, etc.). Summarizing, the DTMĻ crystallizer can be recommended as the most appropriate crystallizer construction for the continuous processes of reactioncrystallization of struvite from diluted water solutions of Mg2+, NH 4 and PO34 ions. NOMENCLATURE a B b de F(L) G Gf G0 Ksp kv L Lm Lz MT [Mg2+]RM m(L)

[NH 4 ]RM n(L)

ncalc nexp n0 Peu

[PO34 ]RM p pde qve qvs RMSD T Vw ve

Usol Usus W

parameter in ASL, CR, RE and RH SDG kinetic models, m 1 ˉ ˉ nucleation rate, m 3·s 1 exponent in ASL SDG kinetic model feeding nozzle diameter, m cumulative size-distribution of specific surface area of crysˉ tals, m2·m 3 ˉ linear growth rate of crystals, m·s 1 ˉ maximal linear growth rate of crystals, m·s 1 ˉ minimal linear growth rate of crystals (growth rate of nuclei), m·s 1 ˉ solubility product of struvite, mol3·dm 9 volumetric shape factor of crystal characteristic linear size of crystal, m mean size of crystal population, m linear size of nucleus, m ˉ concentration of crystal phase in suspension, kgcryst·m 3 mass concentration of magnesium ions in a feeding solution, % ˉ cumulative size distribution of crystals mass (undersize), kg·m 3 mass concentration of ammonium ions in a feeding solution, % population density (number of crystals within the specified size range in a unit volume of suspension per this size range ˉ ˉ width), m 1·m 3 ˉ ˉ population density calculated, m 1·m 3 ˉ1 ˉ experimental population density, m ·m 3 ˉ ˉ population density of nuclei (zero-size crystals), m 1·m 3 ˉ1 unit power of feeding stream, W·kg mass concentration of phosphate ions in a feeding solution, % number of experimental points dynamic pressure of feeding stream, Pa ˉ volumetric flow rate of feeding stream, m3·s 1 ˉ volumetric flow rate of crystal suspension, m3·s 1 root mean square deviation process temperature, K crystallizer working volume, m3 ˉ linear velocity of feeding stream, m·s 1 ˉ3 solution density, kg·m ˉ suspension density, kg·m 3 mean residence time of suspension in a crystallizer working volume (Vw/qvs), s ˉ

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