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Symbols used

cO [mg/L] concentration of distributed compoundin the octanol phase

cW [mg/L] concentration of distributed compoundin the water phase

f S [Pa] solid-phase fugacity of distributedcompound

fL [Pa] liquid-phase fugacity of distributedcompound

KOW [-] octanol/water partition coefficientcalculated from concentrations

Kx

OW[-] octanol/water partition coefficient

calculated from mole fractionsxO [-] mole fraction of distributed compound

in the octanol phasexW [-] mole fraction of distributed compound

in the water phase

Greek symbols

aO [±] interaction parameter of distributedcompound in the octanol phase

aW [±] interaction parameter of distributedcompound in the water phase

gO [±] activity coefficient of distributedcompound in the octanol phase

gW [±] activity coefficient of distributedcompound in the water phase

References

[1] Schüürmann, G.; Markert, B. (Eds.), Ecotoxicology, J. Wiley & SpektrumAkadem. Verlag, New York 1998, 900 pp.

[2] Rippen, G. (Ed.), Handbuch Umweltchemikalien ± Stoffdaten, Prüfver-fahren, Vorschriften, 3. Aufl. (Losblatt-Ausgabe), Ecomed, Landsberg/Lech, ab 1990.

[3] Mackay, D.; Shiu, W. Y.; Ma, K. C., Illustrated Handbook of Physical-Chemical Properties and Environmental Fate for Organic Chemicals, Vol.V ± Pesticide Chemicals, CRC Press LLC, Boca Raton (FL, USA) 1997.

[4] Partition Coefficient (n-octanol/water) ± Shake Flask Method. OECDGuideline for the Testing of Chemicals No. 107, OECD, Paris 1995.

[5] De Bruijn, J.; Busser, F.; Seinen, W.; Hermens, J., Determination ofoctanol/water partition coefficients for hydrophobic organic chemicalswith the ªslow-stirringº method, Environ. Toxicol. Chem. 8 (1989) pp.499±512.

[6] Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E., MolecularThermodynamics of Fluid-Phase Equilibria, 2nd Ed., PTR Prentice Hall,Englewood Cliffs (New Jersey, USA) 1986.

[7] Paschke, A.; Popp, P.; Schüürmann G., Water solubility and octanol/water-partitioning of hydrophobic chlorinated organic substances determinedby using SPME/GC, Fresenius J. Anal. Chem. 360 (1998) pp. 52±57.

[8] Kurihara, N.; Uchida, M.; Fujita, T.; Nakajima, M., Studies on BHCisomers and related compounds ± V. Some physicochemical properties ofBHC isomers (1), Pesticide Biochem. Physiology 2 (1973) pp. 383±390.

[9] Sangster, J., Octanol-water partition coefficients of simple organiccompounds, J. Phys. Chem. Ref. Data 18 (1989) pp. 1111±1229.

[10] Paschke, A.; Schüürmann, G., Octanol/water partitioning of four HCHIsomers at 5, 25, and 45 �C. Fresenius' Environ. Bull. 7 (1998) pp. 258±263.

[11] Klamt, A.; Jonas, V.; Bürger, T.; Lohrenz, J. C. W., Refinement andParametrizationofCOSMO-RS,J.Phys.Chem.A102(1998)pp.5074±5085.

This paper was also published in German in Chem. Ing. Tech. 72 (2000) No. 1+2,pp. 84±88.

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Kinetic Modeling of SimultaneousPhosphate Precipitation in MunicipalSewage Treatment Plants

By Dieter Bothe, Thorsten Waatsack,and Hans-Joachim Warnecke*

A kinetic model is developed which describes the decom-position of phosphate in sewage treatment plants withsimultaneous precipitation. In a precipitation process bymeans of metal salts, the formation of hydroxide always takesplace simultaneously. Determination of the correspondingkinetic parameters is not possible at the same time. As theionic reactions take place much faster than the biologicalincorporation of phosphate, this problem is solved by realisticassumption of instantaneous reactions. The chemical param-eter in the resulting model can be determined by separateprecipitation tests based on an overall reaction law forhydroxide formation. Adjustment to sewage plant data showsthat this model yields satisfactory results.

1 Introduction and Problem Approach

Over the last few years, requirements on sewage treatmentplants have been increased on the one hand by stricter legallimits (1st Administrative Regulation on Wastewater) and onthe other hand by an increased demand for lower costs. Thesebasic conditions have made it necessary to use the existingplants to an optimum extent while incorporating latestresearch results when erecting new sewage treatment plants.It is the task of the municipal sewage treatment plants to cleanthe wastewater from households and industry to an extent thatit can be discharged into a drainage, e.g. a river. In order toachieve this, the wastewater passes through three stages in asewage plant. In this case, great importance is attached to theprecipitation of phosphate in compliance with the legalregulations for wastewater.

1. mechanical stage: raking! sand trap!preliminary settling!

2. biological stage: aeration tank!secondary settling tank!

3. subsequent purification: filter! drainage

During the simultaneous precipitation process in theaeration tank, the phosphorus compounds are decomposed

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[*] Dr. rer. rat. D. Bothe, Universität-CH Paderborn, Fachbereich 17,Mathematik und Informatik, Warburger Str. 100, 33098 Paderborn;Dipl.-Chem. T. Waatsack, COLLTEC Farbaufbereitungsges. mbH & Co.KG, Wörheider Weg 1±5, 33739 Bielefeld; Prof. Dr.-Ing. H.-J. Warnecke,Universität-GH Paderborn, Fachbereich 13, Chemie und Chemietechnik,Warburger Str. 100, 33098 Paderborn, Germany.

as far as possible by physical recycling by means of trivalentmetal salts. The precipitation process of phosphate/trivalentmetal salt in practice never takes place at a mole ratio of 1 : 1because a part of the precipitant gives hydroxides and istherefore no longer available for the precipitation process.Although a part of the phosphate can additionally beeliminated by biological decomposition, the precipitantalways has to be proportioned over-stoichiometrically. Inorder to guarantee sufficient phosphate precipitation, there ispractically always additional overdosage. This paper presentsa dynamic model for a description of phosphate decomposi-tion in sewage treatment plants with simultaneous precipita-tion verified by measurement. The model developed tries todescribe the complexity of simultaneous precipitation in orderto further optimize the process and to finally reduce theoperating costs of sewage treatment plants.

2 Chemistry of Phosphate Precipitation andHydroxide Formation

The chemical process of phosphate precipitation by meansof trivalent metal salts according to Eq. (1) seems to be quitesimple at first glance:

Me3+ + PO43±!MePO4 # Me3+ = Al3+ and Fe3+ resp. (1)

According to the chemical equation above, the mole ratioshould be Me3+/PO4

3± = 1. This mole ratio is represented by the� factor (2):

� � �Me3���PO3ÿ

4 �(2)

In practice, the values for the� factor are always higher than1, this means that more precipitant has to be used thanexpected by the chemical reaction shown in (1). This effect isalso found if the reaction takes place in a biological system, e.g.an aeration tank, with biology playing an active part inphosphate reduction. It can therefore be concluded thatcompeting reactions take place which do not all participate inphosphate reduction. This is why the chemistry of phosphateprecipitation and of precipitation metal ions with chemicalequilibrium, acid-base reactions and solubility product isdiscussed first.

Orthophosphoric acid is a medium strong tribasic acid. Itdissociates into phosphate [1] in three stages:

H3PO4 + H2O� H3O+ + H2PO4± pK1 = 2.161 [25 �C]*

H2PO4± + H2O� H3O+ + HPO4

2± pK2 = 7.207 [25 �C]*

HPO42± + H2O� H3O+ + PO4

3± pK3 = 12.325 [25 �C]*

This shows that the equilibria always shift to the right whenthe pH value is increased and that phosphates correspondinglyresult in primary, secondary and tertiary phosphates. Inwastewater, the pH values often amount to approx. 6.5±8.5,thus practically resulting in dihydrogen and hydrogen

phosphates only. In aqueous systems, the precipitant cationsAl3+ and Fe3+ behave chemically similarly.

Al3+: If the aluminium salt of a strong acid (e.g. aluminiumhalogenide, sulfate) is dissolved in water, a hexaaquaaluminium ion is formed:

Al3+ + 6 H2O� [Al(H2O)6]3+

The hexaaqua aluminium ion is a weak cation acid:(pKS = 4.97):

[Al(H2O)6]3+� [Al(OH)(H2O)5]2+ + H+

In low Al3+ concentrations, approx. 10±5 mole, the cationacid [Al(H2O)6]3+ deprotonizes at different pH values asfollows:

[Al(H2O)6]3+� [Al(OH)(H2O)5]2+ + H+ pH = 3±7[Al(OH)(H2O)5]2+� [Al(OH)2 (H2O)4]+ + H+ pH = 4±8[Al(OH)2 (H2O)4]+� Al(OH)3(H2O)3 + H+ # pH = 5±9[Al(OH)3(H2O)3]� [Al(OH)4(H2O)2]± + H+ pH = > 6

Fe3+: The almost colorless hexaaqua(III) ion [Fe(H2O)6]3+

(pKS = 2.83) is only stable for negative pH values. It reactsinto:

[Fe(H2O)6]3+� [Fe(OH)(H2O)5]2+ + H+ pH = 0±22 [Fe(OH)(H2O)5]2+� [Fe2(OH)2(H2O)8]4+

+ 2 H2O pH = 2±3

At pH values of 3±5, complex [Fe2(OH)2(H2O)8]4+ formsisopolyoxo cations which precipitate as amorphous ªiron(III)-hydroxideº Fe2O3 � H2O when the pH value is furtherincreased.

In sewage treatment plants, the PO4±P concentrationsamount to approx. 5 mg/l (1.6 ´ 10±4 mol/l), such that very dilutesolutions can be assumed. If a PO4±P concentration is given,the calculation refers to the phosphorus (30.97 g/mol) of thephosphate (94.97 g/mol).

Since the precipitant cations Al3+ and Fe3+ in aqueoussystems behave chemically very similarly, they are jointlydiscussed as Me3+. Although a stoichiometric hydroxidecannot be formed from Fe3+ solutions, both precipitants indilute solutions are described for reasons of simplicity by thefollowing equilibria:

[Me(H2O)6]3+ ( [Me(OH)(H2O)5]2+ + H+

[Me(OH)(H2O)5]2+ ( [Me(OH)2 (H2O)4]+ + H+

[Me(OH)2 (H2O)4]+ ( Me(OH)3(H2O)3 + H+

[Me(OH)3(H2O)3] ( [Me(OH)4(H2O)2]± + H+ (only Al3+)

Because of these hydrolysis processes, Al3+ and Fe3+ exist ashydroxides in an extremely wide pH range. Depending on theprecipitant used (e.g. Fe(H2O)6

3+ or Al(OH)4±), a different

influence on the pH value of the wastewater which has to becleaned can be expected. At the same time, the precipitation

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result depends on the pH value and the respective solubilityproducts which are influenced by the pH value. In order toachieve good precipitation results, it is essential that theprecipitation products have a low solubility product. This islower for the precipitated hydroxides than for the respectivemetal phosphates [2].

In short, the following statements can be made: phosphateprecipitation by means of aluminium and iron precipitationsalts is always accompanied by the formation of hydroxides.This necessitates an over-stoichiometric dosage of theprecipitant. Because of the chemical complexity shown hereand because of the fact that the formation of phosphate andhydroxide takes place simultaneously and very fast, it is notpossible to experimentally determine the kinetic parametersnecessary for a dynamic modeling, which is why simplifiedformal kinetic approaches are used.

3 Mathematical Modeling

3.1 Balance Equations

In order to dynamically describe phosphate decompositionin sewage treatment plants with simultaneous precipitation,the following system of nonlinear differential equations hasbeen formulated1):

dcp

dt� V�F

VL

� �cfpÿ cp� ÿ k1 � cp � cMe ÿ k2 � cB �

cp

K1�cP

(3)

dcMedt� V�Me

VL

� cfMeÿ V�F

VL

� cMe ÿ k1 � cp � cMeÿ

k0 � cMe � f �cOH � (4)

dcC

dt� V�F

VL

� �cfCÿ cC � ÿ k3 � cB �

cC

K2�cC

(5)

dcBdt� ÿ � V

�F

VL

� cB ÿ �tot � cB � k4 � cB �cP

K1�cP

� cC

K2�cC

(6)

dcOH

dt� V�F

VL

� �cfOHÿ cOH � ÿ k0 � cMe � f �cOH �

+ further reaction terms (7)

The terms in Eq. (3) describe the change rates of thephosphate concentration caused by inflow and discharge,phosphate precipitation and the biological decomposition ofphosphate. The rate law for chemical phosphate precipitationcannot be determined because parallel reactions withhydroxide ions occur that falsify precipitation results. A ratelaw of first order for cP and cMe can be assumed. The biologicalprecipitation part is modeled by a simple Monod approach [3].

The terms in Eq. (4) describe the change rates of theprecipitant concentration at inflow and discharge, phosphateprecipitation and the competing formation of hydroxide. Therate law for chemical phosphate precipitation cannot bedetermined by precipitation tests.

Hydroxide formation takes place in several side reactionswhich are too complex to be considered individually. There-fore, hydroxide formation is modeled by means of k0 ´ cMe ´f(cOH) with an unknown function f, the determination ofwhich is discusses below.

The terms in Eq. (5) describe the change rates of the carbonconcentration by inflow and discharge, and the decompositionof carbon by biology. Here again, a simple Monod approach isused.

The terms in Eq. (6) describe the change rates of thebiomass concentration by discharge from the aeration tank, bybiomass decay, and by growth. A mixed Monod approach isused for growth.

The terms in Eq. (7) describe the change rates of thehydroxide concentration by inflow and discharge, as well ashydroxide precipitation. The hydroxide balance was notanalyzed further as this can be determined directly on-lineby pH measurement in the inflow of the aeration tank.

3.2 Discussion of the Model

The constants K1, K2, , �tot, the unknown constants for thereaction rate k0, k1, k2, k3, k4 and the unknown function f(cOH)are present in the model equations (3±7). The Monodconstants K1 and K2, can be estimated by approximationfrom bibliographical references. The proportionate biomassdischarge is a quantity which is adjusted by the respectivesewage treatment plant, the biomass decay �tot also is a knownconstant specific for the respective sewage treatment plant. Itis not possible to determine k0 and k1 by means of simpleprecipitation tests using real-time measurements of the pHvalue, because the precipitation of both phosphate andhydroxide are very fast, parallel ion reactions which bothinfluence the pH value. The determination of approximatevalues for k3 and k4 can be carried out under the assumptionthat the system is in a quasi-stationary state. It is possible toapproximately estimate the unknown constant k2 with (8) asthe maximum growth rate �max is approximately known.

k2 ��max

cBÿaverage

(8)

The function f(cOH) is unknown and determined approxi-mately by means of precipitation tests. To achieve this, theapproach is to use a law for a reaction of fractional order.

3.3 Model with Instantaneous Chemical Reactions

The ionic reactions of precipitation and hydroxide forma-tion take place much faster than biological phosphate

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1) List of symbols at the end of the paper.

incorporation. Therefore, this reaction can be assumed as agood approximation to be infinitely fast. To achieve this, limittransition k0, k1 !1 is carried out, where the proportion ofreaction rate constants

� � k0k1

(9)

must be kept constant, as l depicts the essential parameterfor precipitant splitting of the competing reactions forphosphate precipitation and formation of hydroxide, respec-tively. Considering the limiting case of instantaneous reactionshas an important advantage as the quotient l can bedetermined from simple precipitation tests, although k0 andk1 themselves are unknown.

Furthermore, the following applies in the case of infinitelyfast reactions:

cMe � cP � 0 and cMe � cOH � 0 (10)

i.e., a coexistence Me and P and of Me and OH is not possible.Because of a surplus of cOH and H2O respectively, it follows:

cMe � 0 and therefore c�Me � 0 (11)

which simplifies the model equations (3±7) substantially.This assumption corresponds extremely well with measure-ments from the sewage treatment plants, because practi-cally no remaining precipitant concentration could bedetected in the aeration tank processes. In the day-to-dayoperation of sewage treatment plants one tries to keepbiology in a stationary state, i.e., the concentration ofbiomass in the aeration tank is almost constant. In effect,the simulation data show that cB practically has nodynamics and can therefore be replaced in the modelequations by a slow-variable function cB(t). After appro-priate mathematical treatment, the equation system (3±7)can be simplified to:

dcp

dt� V�F

VL

� �cfpÿ cp� ÿ cP

cP��pH

� V�Me

VL

� cfMeÿ k2 �

cB�t� �cp

K1�cP

(12)

Here, the abbreviation apH for l ´ f(cOH) is used, since thispH-dependant relation represents the only chemical param-eter which remains. The function f(cOH) as well as l aredetermined to be

l � f �cOH � � 45:28 � c1:13OH

(13)

by means of adaptive calculations based on precipitation testsand a fractional order reaction approach.

4 Adaptation and Simulation

4.1 Measurements from the Sewage Treatment Plant BielefeldSennestadt

The data taken during the measurement period 19 Feb.±2 Mar. 1996 from the sewage treatment plant BielefeldSennestadt were used for the adaptation and simulation ofthe model (12). The sewage treatment plant Sennestadt has atank capacity of VL = 4704 m3. The precipitant is proportionedat constant volume flow.

V́F m3/dpHinflow 7.72cB 6700 mg/kgmmax 0.2 h±1

k2 2.98E-05�pH 2.18E-01K1 20

Fig. 1 shows the phosphate load into and out from theaeration tank. The values were measured every hour.

Figure 1. Inflow and discharge of phosphate load/aeration tank.

4.2 Adaptation and Simulation in the Sewage Treatment PlantBielefeld Sennestadt

Model (12) contains the chemical parameter apH as well asthe biological parameters k2 and K1, where apH can becalculated by means of (13). It is shown below that anacceptable simulation of the concentration processes ispossible when the model parameters k2 and K1 are adaptedat a given apH. As k2 can be estimated at least roughly from (8),the Monod constant K1 is used first for adaptation. This yieldsthe parameter values:

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apH = 2.18E-01 (fixed)k2 = 2.98E-05 (fixed)K1 = 20.00 (start value) ! K1 = 1120.72

The simulation result thus obtained is shown in Fig. 2.

Figure 2. Simulation process after adaptation with a free parameter.

The adaptation with K1 as a free parameter gives a verygood result, the value of the Monod constant, however,changes by two decimal powers.

When k2 and K1 are released, they result in:

apH = 2.1823E-01 (fixed)k2 = 2.9851E-05 (start value) ! k2 = 1.2744E-06K1 = 20.00 (start value) ! K1 = 31.83

when adapted.Here, the free parameters change in the range of one

magnitude. The result of the simulation is almost identical tothe result shown in Fig. 2.

5 Conclusion

During recent years, measurement and control technologyin sewage treatment plants has been continuously upgradedand changed over. The amount and accuracy of data willcontinue to increase. This is the necessary precondition for theoptimum use of simulation results based on kinetic models.

In this paper it is shown that an adequate understanding ofsimultaneous precipitation in sewage treatment plants can beachieved by means of dynamic model approaches. Thisresearch is a first important step towards a decrease and anoptimization of precipitant requirements.

Received: February 4, 2000 [K 2585]

Symbols used

cB [mg/l] biomass concentrationcfOH [mg/l] hydroxide inflow concentration

cfC [mg/l] carbon inflow concentration

cfMe [mg/l] precipitant inflow concentration

cfP [mg/l] phosphate inflow concentration

cOH [mg/l] hydroxide discharge concentrationcC [mg/l] carbon discharge concentrationcME [mg/l] precipitant discharge concentrationcP [mg/l] phosphate discharge concentrationk0, k1, k2,k3, k4 [s±1] reaction rate constantsK1, K2 [±] Monod constantV́F [m3/h] wastewater inflow volume flowV́Me [m3/h] precipitant inflow volume flowVL [m3] tank capacity

Greek symbols

[±] biomass discharge� [d-1] biomass growth rate�tot [d-1] biomass decay rate

References

[1] Hollemann; Wiberg, Lehrbuch der anorganischen Chemie, Walter deGruyter, Berlin, New York 1985.

[2] Stumm, W.; Sigg, L., Kolloidchemische Grundlagen der Phosphor-Elimination in Fällung, Flockung und Filtration, Z. Wasser- u. Abwasser-forschung 12 (1979) 2.

[3] Schügerl, K., Bioreaktionstechnik, Vol. 1, Otto Salle Verlag, VerlagSauerländer, 1985.

[4] Atkinson, B.; Mavituna, F., Biochemical Engineering and BiotechnologyHandbook, The Nature Press, 1983.

This paper was also published in German in Chem. Ing. Tech. 71 (1999) No. 12,pp. 1421±1425.

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Bubble-free Ozone Contacting withCeramic Membranes for Wet OxidativeTreatment

By Peter Janknecht, Peter A. Wilderer, CØline Picard,AndrØ Larbot, and Jean Sarrazin

A bubble-free ozone contacting process by means of porousceramic membranes was investigated and found to be anauspicious approach for the ozonation of highly pollutedorganic waste water displaying excessive foam formation with

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[*] Dipl-Ing. P. Janknecht and Prof. Dr.-Ing. Dr. h.c. P. A. Wilderer, Institutefor Water Quality Control and Waste Management, Technical UniversityMunich, Am Coulombwall, 85748 Garching, Germany; Dipl.-Ing. C.Picard, Prof. Dr. A. Larbot und Prof. Dr. J. Sarrazin, Laboratoire desMatØriaux et ProcØdØs Membranaires UMR 5635-CNRS, ENSCM,UMII, 8, rue de l'Ecole Normale, 34296 Montpellier cedex 5, France.