Scholarly article on topic 'Effect of Sulphate(VI) Ions on CSD of Struvite–Neural Network Model of Continuous Reaction Crystallization Process in a DT MSMPR Crystallizer'

Effect of Sulphate(VI) Ions on CSD of Struvite–Neural Network Model of Continuous Reaction Crystallization Process in a DT MSMPR Crystallizer Academic research paper on "Chemical sciences"

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{Struvite / "phosphprus recycling" / "sulphate(VI) ions" / "reaction crystallization" / "continuous DT MSMPR crystallizer" / "crystal size distribution" / "neural network model"}

Abstract of research paper on Chemical sciences, author of scientific article — K. Piotrowski, N. Hutnik, A. Matynia

Abstract Complex effect of sulphate(VI) ions on the continuous struvite (MgNH4PO4 6H2O, MAP) reaction crystallization process kinetics in DT MSMPR crystallizer and its final results was modeled numerically using artificial neural networks. Network was used as a multidimensional correlation between selected technological control process parameters (three inputs representing [SO42–]RM: 0.05 – 1.0 mass %, pH: 9–11 and mean residence time: 900 – 3600 s) and 43 size–channels of struvite product CSD (43 outputs corresponding to L within the 5.0 10–7–1.8 10–4 m range). Network model reproduces experimental, nonlinear lnn(L) data correctly and accurately. Presenting CSD in a form of population density distribution lnn(L) made direct theoretical insight and identification of potential various kinetic mechanisms dominating for required <[SO42–]RM, pH, > vectors in various L ranges possible.

Academic research paper on topic "Effect of Sulphate(VI) Ions on CSD of Struvite–Neural Network Model of Continuous Reaction Crystallization Process in a DT MSMPR Crystallizer"

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Engineering

Procedía

ELSEVIER

Procedía Engineering 42 (2012) 573 - 584

www.elsevier.com/locate/procedia

20th International Congress of Chemical and Process Engineering CHISA 2012 25 - 29 August 2012, Prague, Czech Republic

Effect of sulphate(VI) ions on CSD of struvite - neural network model of continuous reaction crystallization process

in a DT MSMPR crystallizer

"DepartmentofChemical & ProcessEngineering, Silesian University ofTechnology, ks. M. Strzody 7, 44-101 Gliwice, POLAND bWroclaw University ofTechnology, Faculty ofChemistry, Wybrzeze Wyspianskiego27, 50-370 Wroclaw, POLAND

Complex effect of sulphate(VI) ions on the continuous struvite (MgNH4P04 6H20, MAP) reaction crystallization process kinetics in DT MSMPR crystallizer and its final results was modeled numerically using artificial neural networks. Network was used as a multidimensional correlation between selected technological control process parameters (three inputs representing [S042~]RM: 0.05 -1.0 mass %, pH: 9-11 and mean residence time: 900 - 3600 s) and 43 size-channels of struvite product CSD (43 outputs corresponding to L within the 5.0 10"7-1.8 10"4 m range). Network model reproduces experimental, nonlinear ln^(Z) data correctly and accurately. Presenting CSD ina form of population density distribution ln^(Z) made direct theoretical insight and identification of potential various kinetic mechanisms dominating for required <[S042~]RM, pH, > vectors in various L ranges possible.

© 2012 Published by Elsevier Ltd. Selection under responsibility of the Congress Scientific Committee (Petr Kluson)

Keywords: Struvite; phosphprus recycling; sulphate(VI) ions; reaction crystallization; continuous DT MSMPR crystallizer; crystal size distribution; neural network model

a* Corresponding author. Tel/fax:+48-32-237-14-61. E-mail address', krzysztof.piotrowski@polsl.pl.

K. Piotrowskiaa*9 N. Hutnikb, A. Matynia1

Abstract

1877-7058 © 2012 Published by Elsevier Ltd. doi : 10. 1016/j .proeng.2012.07.444

1. Introduction

Cleaning technology of industrial, municipal and agricultural wastewater streams containing phosphate(V) ions integrated with effective phosphorus recovery is a subject of intensive research worldwide. One of promising technical variant to solve this problem is continuous reaction crystallization process in especially designed crystallizer construction. Controlled reaction between phosphate(V), magnesium and ammonium ions provides sparingly soluble product - struvite (MgNH4P04 6H20, MAP), which can be utilized directly in agriculture as a valuable mineral fertilizer [1-5]. Correct coupling, integration and control (within a possible range) of all process stages, including: supersaturation generation, its space distribution by multi-scale mixing effects and discharging through nucleation and crystals growth, accompanied by eventual aggregation/agglomeration or attrition/breakage creates attractive technological possibility of indirect affecting crystal size distribution (CSD) of crystalline struvite, thus product properties adjustment to meet the current market standards.

Wastewater, however, are the most often complex mixtures of various ingredients, regarded as impurities in respect to recyclable phosphate(V) ions. Since eventual large scale purification of wastewater from impurities is economically ineffective (frequent composition oscillations), research attention should be focused on reliable prediction of impurities co-presence effects, mainly resulting from their individual concentrations and proportions, on struvite continuous reaction crystallization process course and final results (mainly CSD).

One of inorganic impurities frequently present in industrial and municipal wastewater are sulphate(Vf) ions (usually from SOITEX (silk and textile industry) wastewater, where chloride, sulphate(Vf) and phosphate(V) ions are released from the postprocessed dyes decomposition [6]). Based on systematic measurements it was estimated, that in typical wastewater their average concentration is ca. 0.07 mass % [7]. Their presence in cleaned wastewater can potentially modify - in a complex and unpredictable manner - the struvite continuous reaction crystallization process course, resulting product CSD, struvite crystals shape, purity, characteristic sizes and other statistical parameters of CSD (Zm, L50, CV), as well as even partly control the aggregation/agglomeration phenomena [8]. Because potential deviations from the results attributed to pure NH4+ - Mg2+ - P043" model systems are essential for possibly precise estimation of struvite CSD, some efficient predictive tools are strongly required in design practice. Considering complexity of continuous struvite reaction crystallization process and not totally identified partial interrelations between all sub-processes in various scales, artificial neural network (ANN) technique was used for its numerical model elaboration [9-11].

2. Experimental

Laboratory experiments covering continuous phosphate(V) ions removal from its water solutions (1.0 mass % of P043 ) in co-presence of sulphate(Vf) ions (from 0.05 to 1.0 mass % of S042") by struvite reaction crystallization process with the use of magnesium and ammonium ions in stoichiometric proportions, were carried out in DT MSMPR (Draft Tube, Mixed Suspension Mixed Product Removal) crystallizer unit with internal circulation of suspension resulting from propeller stirrer. Reaction crystallization of struvite ran in isothermal conditions 298 K, at pH 9 arranging mean residence time of suspension in a crystallizer working volume 900 s. For two selected concentrations of sulphate(Vf) ions in a feed solution (0.1 and 0.5 mass % of S042") complementary tests at pH 10 and 11 ( 900 s), as well as for 1800 and 3600 s (pH 9) were also done [12, 13].

Crystallizer was continuously provided with a feed stream preprocessed in external mixer-reservoir using analytical grade components (magnesium chloride MgCl2-6H20, ammonium dihydrogenphosphate(V) NH4H2P04 and sodium sulphate(VI) Na2S04 - POCh Gliwice, Poland) and deionized water (Barnstead - NANOpure Diamond). Such defined mixture was continuously dosed by pump into circulation profile - DT section (mixing rate: 6.6 ±0.1 s"1; descending flow of circulated suspension). Between the crystallizer body and DT element (ascending suspension flow) water solution of sodium hydroxide (20 mass % of NaOH) was dosed adjusting the assumed, strictly controlled pH of continuous struvite reaction crystallization process environment.

Inlet reagent concentrations at a feed point were: [P043 ]RM =1.0 mass %, [Mg2+]RM = 0.256 mass % and [NH4+]rm = 0.190 mass % (stoichiometric molar ratio 1:1:1). Inlet concentration of sulphate(VI) ions was subject of controlled change within the 0.05 - 1.0 mass % range. After stabilization of the assumed process parameter values in a crystallizer the continuous struvite reaction crystallization process ran through the next 5 ina steady-state mode.

Product was analyzed using adequate laboratory procedures including: laser analyzer of solid particles COULTER LS-230, scanning electron microscope JEOL JSM 5800LV, plasma emission spectrometer ICP-AES CPU 7000 PHILIPS, spectrometer IR PU 9712 PHILIPS and spectrophotometer UV-VIS Evolution 300.

Constructional characteristic of the laboratory crystallizer used, its working parameters, experimental plant flowsheet, as well as test procedure details are presented elsewhere [12].

It should be noted, that measurement data precision corresponded to the discussed reaction crystallization process tested in a complex continuous laboratory plant was estimated to be ca. 10%.

3. Calculations

Authors own experimental data covering struvite continuous reaction crystallization process performance in diverse process conditions (regarded in this modeling approach as classical "black-box" object identification procedure by its sampling in a form of: multidimensional input signal object's multidimensional response) created dataset for ANN model preparation, including: training, testing and verifying procedures. It should be strongly emphasized, that this way any eventual troublesome assumptions and simplifications, commonly in use for classical models with all consequences, can be bypassed. The ANN numerical model created multidimensional correlation between process design parameters (pH: 9-11, mean residence time of crystal suspension : 900-3600 s, S042" ions concentration in a feed solution: 0.05-1.0 mass %) and resulting CSD of struvite in a form of population density distribution (PDD) Inn(L) (43 Inm points corresponding to selected 43 U values - original size channels of Coulter counter). Original experimental dataset was divided randomly into training, validating and testing subsets in proportion of 50% : 25% : 25%. Besides recalculation of original CSD data (mass/volumetric crystal size distribution) n1(L1) Inn1(L1), no additional preprocessing was necessary to start the ANN training/validating/testing algorithms carried out using STATISTICA Neural Network software. Various ANN types were systematically created, tested and compared each other including: multilayer perceptrons (MLP), general regression neural networks (GRNN), radial basis function (RBF) networks and linear networks, of different spatial combinations of hidden neurons in various ANN topologies (one or two hidden neuron layers). During the neural nets preparation some smaller "working data subsets" were also created for testing purposes, with reduced net inputs - thus with potentially lower number of design parameters accessible. However, such constructed neural networks provided higher prediction errors compared to a complete "standard 3-input" net error. It may be thus interpreted that all three design parameters: [S042"]rm, pH and contribute final CSD/PDD of crystalline struvite. Detailed sensitivity analysis based on error increment criterion proved, that the largest influence on PDD course exerts [S042"]rm parameter (9,5360), then mean residence time (8,9680) and finally pH (8,3191). It should be, however, noticed that there is not large scattering between the individual error increment criteria in respect to [S042"]rm, and pH, thus all three parameters are of nearly equivalent importance for the process results. Exemplary selected, representative neural network configurations created and tested, with adequate transfer functions, statistical quality of the net topology in respect to training, validating and testing subsets, as well as corresponding learning algorithms, procedures and iteration numbers are presented in Table 1. Considering the assumed statistical selection criteria (minimal value of validating dataset quality) a multilayer perceptron type network (MLP) with 3 inputs, one hidden layer with 21 neurons and 43 output neurons was selected. This configuration was trained initially with backpropagation error algorithm (BP) during 100 iterations, which were complemented by the next 187 iterations with conjugated gradient algorithm (CG). Its quality was independently verified using other statistical indicators:

- mean deviation (MD), Eq. (1):

in nfc' in «;ip

- and root-mean square deviation (RMSD), Eq. (2):

resulting in MD = 0.000738 and RMSD = 0.06682 (in respect to Inn values).

Table 1. Comparison of selected artificial neural networktypes and configurations tested.

Quality of neural network in respect to:

Neural network Neural network Training Validating Testing Training algorithms,

type configuration data set data set data set number of training

iterations

Radial Basis 1-9-43 0.9166 0.9384 0.9914 KM, KN, PI

Function (RBF) 2-9-43 4.1200 3.7425 4.1490 KM, KN, PI

network 3-9-43 0.1517 0.1036 0.1834 KM, KN, PI

General 1-66-44-43 0.9014 0.9093 0.9127 SS

Regression 2-66-44-43 0.5066 0.4545 0.5226 SS

Neural Network 3-66-44-43 0.0759 0.0625 0.0963 SS

(GRNN)

1-43 0.5215 0.4051 0.6147 PI

Linear network 2-43 0.4167 0.3697 0.4709 PI

3-43 0.4159 0.3665 0.4589 PI

3-8-43 0.1866 0.1612 0.1994 BP100, CG268

Multilayer 3-12-43 0.0824 0.0728 0.1017 BP100, CG257

Perceptron 3-21-43 0.0637 0.0533 0.0843 BP100, CG187

(MLP) 1-21-14-43 0.9927 0.9944 1.0020 BP100, CG103

2-21-21-43 0.3369 0.2123 0.4300 BP100, CG188

3-21-21-43 0.0790 0.0853 0.0707 BP100, CG209

Neural network configuration's notation: number of net inputs - number of hidden neurons (distributed within one or two hidden layers) - number of output neurons (artificial neural network configuration selected as a numerical model of the process indicated in bold). Neural network quality defined by quotient of standard deviations.

Training algorithm abbreviations: KM - ^-means; KN - ^-nearest neighbors; PI - pseudoinversion; SS - subsample; BP -backpropagation; CG - conjugated gradient.

It should be also noted, that more complex neural network structures (especially MLP, GRNN, RBF ones), with exceeded number of hidden neurons, provided practically similar quality what proved the existence of easily accessible error function minimum. However, relatively simple net structure of comparable quality was chosen as the numerical model of the process to prevent against eventual disadvantageous consequences of overtraining effect. Numerical ANN model regarded as optimal one (Table 1 - indicated in bold) was used as a tool for simulation of object (here: continuous MAP reaction crystallization process) response for different (pH, , [S042"]rm) combinations, especially for product crystal size distributions prediction. Converting original CSD in a more informative form of population density distribution (PDD) ln«1(Z1) made direct theoretical insight into various kinetic mechanisms (net effect) dominating for selected (pH, , [S042"]rm) combinations and affecting various crystal size fractions (for example size-dependent growth, growth rate dispersion) possible.

4. Simulations

Graphical presentation of neural network simulation results - object response planes - are presented in Fig. 1-3. Net simulations demonstrated behavior of struvite continuous reaction crystallization system under assumed, diverse technological conditions in respect to pH, , and [S042"]rm combinations. Special attention was paid on prediction of main process effect - full potential crystal size distribution (CSD) of product, in a PDD form. Fig. la-d demonstrates influence of gradually increasing concentration of S042" ions in a feed solution (within experimentally tested range 0.05 -1.0 mass %) in extreme process conditions: pH(9 orll) and mean residence time of crystal suspension in a crystallizer (900 or 3600 s).

Fig. 1. Neural network model simulations of continuous reaction crystallization process of struvite in presence of sulphate(VI) ions - prediction of product population density distributions for various process conditions. Influence of sulphate(VI) ions in a feed ([S042 ]EM = 0.05-1.0mass%)onPDDfor:a)pH9, 900s,b)pH9, 3600s,c)pH 11, 900s,d)pHll, 3600 s.

Influence of process environment pH on product PDDs for 900 s and two different inlet concentrations of sulphate(VI) ions (0.1 and 0.5 mass %) was shown in Fig. 2, while in Fig. 3 effect of systematic elongation of mean residence time of crystal suspension in a crystallizer working volume on its size-characteristic (in a PDD form) for pH 9 and assumed two inlet concentrations of S042" ions (identical with the ones used in Fig. 2) was shown.

Fig. 2. Neural network model simulations of continuous reaction crystallization process of struvite in presence of sulphate(VI) ions - prediction of product population density distributions for various pH ( 900 s): a) [S042"]rm 0.1 mass %, b) [S042"]rm 0.5 mass %.

Fig. 3. Neural network model simulations of continuous reaction crystallization process of struvite in presence of sulphate(VI) ions - prediction of product population density distributions for various mean residence time (pH 9): a) [S042"]rm 0.1 mass %, b) [S042-]em 0.5 mass %.

5. Discussion

Fig. 1 presents neural network model simulation results concerning influence of systematically increased inlet concentration of S042" ions on struvite continuous reaction crystallization process results assuming various (pH, ) combinations regarded as constant process parameters and representing extreme experimental conditions. Analyzing simulated PDD courses presented in Fig. la (pH 9, 900 s) one can initially observe practically insignificant decrease of Inn(L) values corresponding to the largest particles (for [S042 ]rM 0.05-0.3 mass %), followed by significant, local fall of Inn(L) within [S042]RM 0.3-0.7 mass % range and its final increase for [S042"]RM 0.7-1.0 mass % scope. It can be expected, that this experimentally identified local extreme in ln«([S042"]RM)i=const. may result from some effects, interactions and feedbacks within the complex P043", NH4+, Mg2+, CI", Na+, H+ and S042" ions system, demonstrating significant external effects within selected ion concentrations range only (here for [S042"]RM 0.3-1.0 mass %). However, some experimental error in CSD analysis cannot be also excluded. This characteristic behaviour is reproduced as a "gutter shape" in a Inn(L, [S042"]RM) simulated plane. Attention should be also paid on the fact, that this phenomenon is observed for crystal size fraction L > 8 10"5 m within [S042"]rm 0.3-1.0 mass % range only.

Comparing Fig la and lb, demonstrating simulated effect of mean residence time elongation 900 3600 s at constant pH 9, one can conclude that "gutter effect" is effectively dumped, probably by internal process feedbacks, more efficient during slower process run, thus practically no significant influence of sulphate(VI) ions co-presence within 0.05-1.0 mass % range on product PDD is observed. Moreover, significantly higher In« values for larger Z are visible. Such advantageous effect of mean residence time elongation is commonly observed for many continuous mass crystallization processes, including more complex continuous reaction crystallization ones. Longer contact of crystal phase with supersaturated mother solution, despite lower supersaturation level inducing lower growth rate - causes production of larger particles.

Increase in pH from 9 toll ( 900 s, Fig. lc) produces "gutter effect" similar to one observed for pH 9 (Fig. la), however less distinct and more diffused. Moreover, the Inn values corresponding to larger Z are significantly lower compared to crystal product manufactured at pH 9 (Fig. la). It speaks about disadvantageous effect of increased pH level on nucleation/growth relations in continuous struvite reaction crystallization process.

For pH 11 and 3600 s, Fig. Id, neural network simulations indicate some small-scale oscillations in Inn values corresponding to larger crystal sizes, not significant in respect to crystal product quality (which can be roughly assumed constant - unaffected by eventual sulphate(VI) ions co-presence.

Comparing the variants (a) - (d) in Fig. 1 it is possible to notice, that the largest struvite product crystals are manufactured under process conditions providing lower pH 9 and longer mean residence time

3600 s. This qualitative observation based on numerical neural network model predictions is in consistency with analytical data characterizing statistically the original experimental CSDs ( PDDs) [12, 13]. For example, for pH 9 and 900 s (Fig. la) change in [S042 ]RM 0.05 1.0 mass % produces corresponding changes in: Lm 32.6 30.4 m, Z5o 23,5 18,2 m and U 28,9 23,6 m (CV 91,5 96) [12, 13]. Small variation in Inn courses is reflected by small difference in CV.

Influence of process environment pH on PDDs of struvite product crystals is presented in Fig. 2a-b. Neural network simulations were carried out for two selected inlet concentrations of sulphate(VI) ions: [S042"]rm 0.1 and 0.5 mass %, assuming in both cases mean residence time of product crystal suspension 900 s. From physicochemical properties of NH4+/Mg2+/P043" systems it can be expected, that increase in pH results in higher struvite nucleation rate compared to growth rate of crystal phase. In result under such defined process conditions smaller crystals are produced. At higher pH population density values corresponding to larger crystals are significantly lower, what is reproduced clearly in Fig. 2a ([S042"]rm 0.1 mass %). It should be, however, noticed that two distinct pH-effect regions can be identified, namely for pH 9-10, where pH influence on the process results (PDD) is rather moderate, as well as for pH 1011 region, where its action is stronger. Thus ln«=/(pH)I=const dependency consists of two linear segments. However, for crystal fractions Z < 3 10"5 m influence of pH is insignificant, what can be valuable information in case of technology focused on the production of small-size crystals.

Higher feed concentration of sulphate(VI) ions ([S042"]rm 0.5 mass %, Fig. 2b) produces similar shape, however two linear segments are less recognizable while all In« values for larger crystal fractions are lower (compare withFig. la-c).

Also in this case neural network model simulation results are in consistency with statistical interpretation of original CSD data (Coulter counter). For [S042"]RM 0.1 mass % and 900 s change in pH 9 llproduces correspondingchanges in: Lm 27.9 18.3 m, Z50 20.5 13.2 m and Ld 24,1 15,7 m (CV 86.6 95.0), whereas for [S042"]RM 0.5 mass % and 900 s these sizes modify as follows: Lm 24.4 16.3 m,Z5018.3 11.2 mandZd21.4 14.6 m(CV87.6 98.3) [13].

Influence of mean residence time of crystals in apparatus on continuous struvite reaction crystallization process results is presented in Fig. 3a-b. Similarly to classical continuous mass crystallization processes (isohydrical, adiabatic, evaporative) elongation in produces advantageous effect of coarser crystals production under more stable growth conditions, in spite of generally lower average supersaturation level (this effect was also discussed above analyzing differences in Fig. la-b and Fig. lc-d, respectively). Neural network model, rendering the nonlinear trends identified within the raw experimental CSD( PDD) data, is able to identify and correctly model some other, local tendencies. Slight decreasing trend in Inn{ )i=const dependency is observed, suggesting insignificant - however experimentally recorded and correctly modeled by neural network - net influence of moderate attrition resulting from prolonged residence time of suspension, surpassing thus potentially advantageous effect of stable growth for longer . However, for > 2500 s advantageous effect of longer contact of growing crystal phase with supersaturated mother solution predominates and increase in ln«( )i=conit. relation followed by Inn stabilization is observed. For higher impurity concentration in a struvite reaction crystallization system ([S042"]RM 0.5 mass %) similar behaviour is observed, however decreasing trend's region in Inn{ )i=const is considerably smaller ( < 1500 s) thus convenient net effect of longer and more stable crystal growth predominates earlier.

Neural network model predictions are compatible with statistical data attributed to experimental CSD (Coulter counter reports). For [S042"]RM 0.1 mass % and pH 9 elongation of 900 3600 s produces corresponding changes in: Lm 27.9 44.2 m, Z5o 20.5 35.1 m and U 24.1 37.2 m(CV86.6 80.0) [13], while for [SO*,2"]™ 0.5 mass % (pH 9) these are as follows: Lm 24.4 44.2 m, L50 18.3 34.7 mandZd21.4 36.0 m(CV87.6 77.5) [13].

Another, important from kinetic viewpoint, aspect of struvite continuous reaction crystallization process, correctly modeled by neural network, is highly nonlinear PDD course in In« - L coordinate system. Such strongly nonlinear run of PDD indicates some more complex kinetic effects in the system under study. It should be noticed, that such characteristic PDD shape corresponds to all tested cases, regardless the [S042"]RM, pH and combinations. It can demonstrate the effect of size dependent growth (SDG) kinetics - net effect of complex phenomena depending on crystals size range. These include mainly hydrodynamic interactions between crystal phase and supersaturated mother liquor, defining convective mass transfer conditions and responsible for reduction of diffusional mass transfer resistances in a film layer (larger crystals), or - especially for smaller crystal fractions - strong physicochemical effect of size-dependent individual particle solubility. Other phenomenon responsible for the observed Inn(L) nonlinearity may be constant growth rate dispersion (GRD), considering individual surface morphology on specific crystal growth behaviour. Since both SDG and GRD can co-exist and both contribute complex reaction crystallization system covering, among others, P043", NH4+, Mg2+, CI", Na+, H+ and S042" ions producing in \an-L coordinate system identical effect - strongly nonlinear PDD run -separation of their individual contributions based only on PDD data is practically impossible. Thus their total net effect can be mathematically described using any SDG or GRD model. Artificial neural network, however, makes detailed enough reproduction and modeling of real PDD courses covering in its internal computational structure all nonlinear effects, complex - even unidentified and separated analytically -interrelations and feedbacks without any initial assumptions concerning individual kinetic mechanisms or models.

6. Conclusions

Numerical neural network model was applied for modeling of continuous struvite reaction crystallization process in the complex P043", NH4+, Mg2+, CI", Na+, H+ and S042" ions system. This approach is free from any simplifying assumptions and correctly identifies and reproduces all hidden relationships within the available data structure. Neural network topology trained, validated and tested with the use of representative raw experimental data only is an useful predictive tool for precise enough modeling of dispersed phase properties, representing the net effect of assumed technological constraints in a complex physicochemical system like struvite continuous reaction crystallization process. Analyzing the simulation results one is able to rationally select/adjust appropriate process conditions to obtain required CSD of struvite product crystals - considering also complex influence of S042" ions on the product properties. Neural network model predictions of population density distributions (PDDs) are coherent with the trends in characteristic sizes (Zm, L50, Ld) and CV parameters determined by independent analytical methods [12, 13]. The PDDs, however, provide one with broader information concerning, among others, kinetic effects and relations within the investigated system depending on process parameter values ([S042"]rM, pH, ). Based on neural network simulation results it can be concluded, that to produce the possibly largest struvite crystals it is recommended to run the continuous reaction crystallization process at pH 9 and assuming possibly long mean residence time 3600 s. High S042" ions content can be, to some extent, compensated with appropriate corrections of pH (lowering) and mean residence time (enlarging) according to neural network model predictions.

Acknowledgement

This work was supported by the Ministry of Science and Higher Education of Poland under grant No. NN209 4504 39 (2010-2013) andNo. NN209 0108 34 (2008-2011).

Nomenclature

cv - coefficient of (crystal size) variation, defined as 100(ZS4 - L16)/(2L50), %;

L - characteristic linear size of crystal, m;

L50 - median crystal size for 50 mass % undersize fraction, m;

Id - dominant crystal size, m;

Li - mean size of i-th crystal fraction, m;

- mean size of crystal population, defined as Ex^, m;

[Mg2+]RM - concentration of magnesium ions in a feed, mass %;

n(L) - population density (number of crystals within the specified size range in unit volume of the suspension per this size range width), l/(m m3);

[NH4+]rm - concentration of ammonium ions in a feed, mass %;

[P043 ]rm - concentration of phosphate(V) ions in a feed, mass %;

qv - volumetric (out)flow rate of crystal suspension from the crystallizer, m3/s;

[SO42 ]rm - concentration of sulphate(VI) ions in a feed, mass %;

vw - crystallizer working volume, m3;

Xi - mass fraction of the crystals of mean fraction size Li.

Greek letters

- mean residence time of suspension in a crystallizer working volume, defined as VJqv, s;

Abbreviations

ANN - Artificial Neural Network

BP - Backpropagation error training algorithm

CG - Conjugated Gradient training algorithm

CSD - Crystal Size Distribution

DT - Draft Tube (crystallizer type)

GRD - Growth Rate Dispersion (kinetic growth model)

GRNN - General Regression Neural Network

KM - ^-means training algorithm

KN - ^-nearest neighbours training algorithm

MAP - struvite, Magnesium Ammonium Phosphate(V) hexahydrate, MgNH4P04 6H20

MD - Mean Deviation

MLP - Multilayer Perceptron

MSMPR - Mixed Suspension Mixed Product Removal (crystallizer type)

- Population Density Distribution

- Pseudoinversion training algorithm

- Radial Basis Function network

- Root-Mean Square Deviation

- Size-Dependent Growth (kinetic growth model)

- Subsample training algorithm

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