analysis of the mechanism and mathematical modeling of diethylhexylphthalate degradation in aquatic...

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ISSN 00978078, Water Resources, 2010, Vol. 37, No. 3, pp. 399–410. © Pleiades Publishing, Ltd., 2010. Original Russian Text © V.A. Vavilin, 2010, published in Vodnye Resursy, 2010, Vol. 37, No. 3, pp. 356–367. 399 INTRODUCTION The intense use of phthalates (phthalic esters with different alcohols) originating from various diffuse and point sources makes them ubiquitous environmental pollutants [8]. More than 8 million t of phthalates was produced in the world in 2000 [3]. The best known among them is diethylhexylphthalate DEHP, which has long been in use as a plastifier. Phthalates enter the air and water as early as during their production, and overall, up to 15% of the total volume of produced phthalates reaches the environment in one way or another. The major accumulation sites are municipal landfills, where plastics and other phthalatecontaining wastes are only stored without any degradation. Phtha late wastes are ubiquitous in developing countries with poor waste collection infrastructure. Burning of wastes merely facilitates the discharge of phthalates into the atmosphere. Contained in human urine and faeces, phthalates reach treatment facilities, whence they are discharged into the soil or water bodies with the biologi cal solids. Water of the Volga, the major Russian river, was found to be heavily polluted by phthalates far from large industrial centers [1]. Stable substances, phthalates enter plants from the soil, and reach human and animal organ isms via food chains. When in higher concentration in the organism, phthalates increase the risk of vascular and cancerous diseases [7, 24]. Over several decades, phthalates have been studied by researchers in medicine, chemistry, and technology [22]. The degradation of phthalates in the aquatic environment is known to be strongly dependent on their solubility. For example, DEHP is almost insolu ble in water; hence its degradation is very slow [22]. However, DEHP is actively absorbed by various solid particles, resulting in that its concentration in waste water can exceed 100 μg/l [16]. Many researchers considered DEHP to be biologically nondegradable [17], and in the overwhelming majority of studies, DEHP degradation was regarded as a simple first order chemical reaction [10, 15]. Below, we analyze the degradation mechanism of DEHP and other phthalates. We show the modified firstorder kinetics to be but a formal description of a complex process involving biochemical reactions and physicochemical processes of sorption/desorption taking place in liquid and solid phases. The firstorder kinetics is not univer sally valid since biochemical reactions can be inhibited by high concentrations of intermediate products. Mathematical models in the form of a system of ordi nary differential equations and a system of partial dif ferential equations were used to describe laboratory experiments with different reactor volumes. WATER QUALITY AND PROTECTION: ENVIRONMENTAL ASPECTS Analysis of the Mechanism and Mathematical Modeling of Diethylhexylphthalate Degradation in Aquatic Environment V. A. Vavilin Water Problems Institute, Russian Academy of Sciences, ul. Gubkina 3, Moscow, 119333 Russia Received August 5, 2008 Abstract—Degradation mechanism of diethylhexylphthalate, a pollutant of water bodies, is analyzed. A modified firstorder equation with a correction for a nondegradable fraction is suggested. The succession of biochemical reactions in the process of anaerobic degradation of monoethylhexylphthalate is considered, and two stages—ester hydrolysis and phthalic acid transformation into methane and carbon dioxide—are identified as limiting the overall rate. A onedimensional distributed model is used to describe the degradation of three phthalates with different water solubility: diethylphthalate DEP, which has a relatively high solubility; dibutyl phthalate DBP, poorly soluble; and diethylhexylphthalate DEHP, almost insoluble. The physico chemical processes of sorption/desorption play an important role in the process of their degradation. The enzymatic splitting, carried out by microorganisms, reduces the concentration of dissolved diethylhexy lphthalate and can facilitate desorption processes. Keywords: anaerobic degradation, phthalate esters, reaction mechanism, kinetic coefficients, mathematical model. DOI: 10.1134/S0097807810030140

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ISSN 0097�8078, Water Resources, 2010, Vol. 37, No. 3, pp. 399–410. © Pleiades Publishing, Ltd., 2010.Original Russian Text © V.A. Vavilin, 2010, published in Vodnye Resursy, 2010, Vol. 37, No. 3, pp. 356–367.

399

INTRODUCTION

The intense use of phthalates (phthalic esters withdifferent alcohols) originating from various diffuse andpoint sources makes them ubiquitous environmentalpollutants [8]. More than 8 million t of phthalates wasproduced in the world in 2000 [3]. The best knownamong them is diethylhexylphthalate DEHP, whichhas long been in use as a plastifier. Phthalates enter theair and water as early as during their production, andoverall, up to 15% of the total volume of producedphthalates reaches the environment in one way oranother. The major accumulation sites are municipallandfills, where plastics and other phthalate�containingwastes are only stored without any degradation. Phtha�late wastes are ubiquitous in developing countries withpoor waste collection infrastructure. Burning of wastesmerely facilitates the discharge of phthalates into theatmosphere. Contained in human urine and faeces,phthalates reach treatment facilities, whence they aredischarged into the soil or water bodies with the biologi�cal solids. Water of the Volga, the major Russian river, wasfound to be heavily polluted by phthalates far from largeindustrial centers [1]. Stable substances, phthalates enterplants from the soil, and reach human and animal organ�isms via food chains. When in higher concentration in

the organism, phthalates increase the risk of vascular andcancerous diseases [7, 24].

Over several decades, phthalates have been studiedby researchers in medicine, chemistry, and technology[22]. The degradation of phthalates in the aquaticenvironment is known to be strongly dependent ontheir solubility. For example, DEHP is almost insolu�ble in water; hence its degradation is very slow [22].However, DEHP is actively absorbed by various solidparticles, resulting in that its concentration in waste�water can exceed 100 μg/l [16]. Many researchersconsidered DEHP to be biologically nondegradable[17], and in the overwhelming majority of studies,DEHP degradation was regarded as a simple first�order chemical reaction [10, 15]. Below, we analyzethe degradation mechanism of DEHP and otherphthalates. We show the modified first�order kineticsto be but a formal description of a complex processinvolving biochemical reactions and physicochemicalprocesses of sorption/desorption taking place in liquidand solid phases. The first�order kinetics is not univer�sally valid since biochemical reactions can be inhibitedby high concentrations of intermediate products.Mathematical models in the form of a system of ordi�nary differential equations and a system of partial dif�ferential equations were used to describe laboratoryexperiments with different reactor volumes.

WATER QUALITY AND PROTECTION: ENVIRONMENTAL ASPECTS

Analysis of the Mechanism and Mathematical Modeling of Diethylhexylphthalate Degradation

in Aquatic EnvironmentV. A. Vavilin

Water Problems Institute, Russian Academy of Sciences, ul. Gubkina 3, Moscow, 119333 RussiaReceived August 5, 2008

Abstract—Degradation mechanism of diethylhexylphthalate, a pollutant of water bodies, is analyzed. Amodified first�order equation with a correction for a nondegradable fraction is suggested. The succession ofbiochemical reactions in the process of anaerobic degradation of monoethylhexylphthalate is considered,and two stages—ester hydrolysis and phthalic acid transformation into methane and carbon dioxide—areidentified as limiting the overall rate. A one�dimensional distributed model is used to describe the degradationof three phthalates with different water solubility: diethylphthalate DEP, which has a relatively high solubility;dibutyl phthalate DBP, poorly soluble; and diethylhexylphthalate DEHP, almost insoluble. The physico�chemical processes of sorption/desorption play an important role in the process of their degradation. Theenzymatic splitting, carried out by microorganisms, reduces the concentration of dissolved diethylhexy�lphthalate and can facilitate desorption processes.

Keywords: anaerobic degradation, phthalate esters, reaction mechanism, kinetic coefficients, mathematicalmodel.

DOI: 10.1134/S0097807810030140

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VAVILIN

MODIFIED FIRST�ORDER CHEMICAL REACTION

In accordance with [29], let us consider a first�order reaction in the form

(1)

where S, S0 are the current and initial DEHP concen�trations, k is first�order reaction rate constant; α is acorrection for the nondegradable part of DEHP. Afterintegrating, DEHP concentration can be written as

(2)

Figure 1 gives degradation kinetics of DEHP inbiological solids of a treatment facility. Equation (2)can be seen to adequately describe experimental data.

Clearly, the first�order model (1) yields but a for�mal description of DEHP degradation process. DEHPaccumulates within biological solids as a result of sorp�tion or molecular diffusion [18]. Biodegradation cantake place both within silt and on its surface, or in theaquatic environment after desorption. In the lattercase, rate constant k in first�order models correspondsto desorption rate, and coefficient α accounts for thatpart of DEHP which cannot pass into water to experi�ence further biological degradation.

ENZYMATIC SPLITTING OF DEHP

The purely chemical hydrolysis of phthalates ismuch slower that their enzymatic splitting imple�mented by appropriate microorganisms [11]. Themicrobial degradation of phthalates has been knownover more than half century [21]. As shown in some

dSdt����� k S αS0–( ),–=

S S0 1 α–( )e kt– αS0.+=

studies, phthalates in soils are primarily degraded byfungi, while bacteria can only utilize their degradationproducts [2]. Microbial degradation of phthalatesunder anaerobic conditions was also recorded [19]. Inthe course of both aerobic and anaerobic degradation,phthalic esters, including DEHP, are hydrolyzed tophthalic acid and appropriate alcohols before bacteriamanage to utilize carbon for their growth. The reac�tion can either go directly via monoester formation, orbypass this stage [4, 11].

Under anaerobic conditions, alcohols furthertransform into methane and carbon dioxide. The sameend products can be obtained during anaerobic degra�dation of phthalic acid with benzoate forming as anintermediate product [14]. The main stoichiometricequations are as follows [5, 27]

(3)

(4)

(5)

(6)

CH3COOH CH4 + CO2 (acetate), (7)

(8)

Acetate and hydrogen further turn into methane(Fig. 2). Enzyme E, discharged by microorganisms, isresponsible for the hydrolysis stage.

MEHP is well soluble in water, facilitating theexamination of its biochemical degradation paths. Thescheme given in Fig. 2 can be described by the follow�ing system of equations:

DEHP H2O+MEHP + EH (diethylhexylphthalate),

MEHP H2O+PA + EH (monoethylhexylphthalate),

EH H2O+

4CH3COOH + 8H2 (diethylhexanol),

PA 6H2O 3CH3COOH+

+ 3H2 2CO2 phthalic acid( ) ,+

H2 0.25CO2 0.25CH4+

+ 0.5H2O hydrogen and carbon dioxide( ).

dDPdt

��������� vm1– E DPKDP DP+�������������������,=

dEdt����� k1B1 k2E,–=

dMPdt

���������� vm1E DPKDP DP+������������������� vm2E MP

KMP MP+��������������������,–=

dROHdt

������������� vm1E DPKDP DP+������������������� vm2E MP

KMP MP+��������������������+=

– ρm1B1ROH

KP ROH+���������������������,

dB1

dt������� Y1ρm1B1

ROHKMP MP+�������������������� kd1B1,–=

DE

HP

, m

g/l

40

35

30

25

20

15

10

5

0 10 20 30 40 50 60

So = 36 mg/l

So = 17 mg/l

So = 5.2 mg/l

Time, day

Fig. 1. Kinetics of DEHP withdrawal from activatedsludge in the batch experiment at different initial DEHPconcentrations and temperature of 35°C. Symbols areexperimental data [9], curves are solutions of model (1).k = 0.045 day–1, α = 0.5.

WATER RESOURCES Vol. 37 No. 3 2010

ANALYSIS OF THE MECHANISM AND MATHEMATICAL MODELING 401

(9)

dPAdt

�������� vm2E MPKMP MP+�������������������� ρm2B2

PAKPA PA+������������������,–=

dB2

dt������� Y2ρm2B2

PAKPA PA+������������������ kd2B2,–=

dAcdt

������� a* 1 Y1–( )ρm1B1ROH

KP ROH+���������������������=

+ 3 1 Y2–( )ρm2B2PA

KPA PA+������������������ c*kW ρm3B3

AcKAc Ac+�����������������,–+

dB3

dt������� Y3ρm3B3

AcKAc Ac+����������������� kd3B3,–=

dH2

dt�������� b* 1 Y1–( )ρm1B1

ROHKP ROH+���������������������=

+ 3 1 Y2–( )ρm2B2PA

KPA PA+������������������ d*kW ρm4B4

H2

KH2H2+

�����������������,–+

dB4

dt������� Y4ρm4B4

H2

KH2H2+

����������������� kd4B4,–=

dCH4

dt����������� V* 1 Y3–( )ρm3B3

AcKAc Ac+�����������������

⎩⎨⎧

=

+ 1 Y4–( )ρm4B4H2

KH2H2+

�����������������⎭⎬⎫

,

dWdt

������� kW.–=

where DP, MP, E, ROH, PA, Ac, H2, W are the concen�trations of dissolved phthalate, enzyme, and alcoholesters; phthalic acid; acetate; hydrogen; and residualorganic matter (OM) in the microorganism inoculum,respectively; B1, B2, B3, B4 are the concentrations ofrespective microorganisms; CH4 is the volume ofmethane produced in the system; KDP, KMP, KPA, KP,KAc, KH2 are half�saturation constants for appropriatesubstrates; ρm1 , ρm2 ,ρm3 , ρm4 are the maximal specificconsumption rates of appropriate substrates; Y1, Y2, Y3,Y4 are yield coefficients of bacteria; kd1 , kd2 , kd3 , kd4 arebiomass degradation rate constants of appropriatemicroorganisms; vm1 , vm2 are maximal specific rates ofenzymatic splitting of DP and MP, respectively; k1 andk2 are production and degradation rate coefficients ofhydrolytic enzymes, respectively; k is OM degradationrate constant in the microorganism inoculum; a and bare stoichiometric coefficients of acetate and hydro�gen production from alcohols; c and d are stoichio�metric coefficients of acetate and hydrogen produc�tion from W; V is reactor volume.

The concentrations of E and ROH can be regardedas fast variables, which is equivalent to the applicationof the well�known Bodenstein principle for quasista�tionary concentrations

(10)dEdt����� 0, dROH

dt������������� 0.= =

Hydrolysis Methanogenesis

Sorption/desorption

DPDPSE

MP R–OH

PA

aAc + bH2 +cCO2

3Ac + 3H2 + 0.5 CO2

E

B1

B2

B3 B4

CH3COOH CH4 + CO2

H2 + 0.25 CO2 0.25CH4 + 0.5H2O

Fig. 2. Scheme of anaerobic transformation of DP and MP into CH4 via Ac, H2, and CO2. Four types of microbes (B1–B4) takepart in the reaction.

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WATER RESOURCES Vol. 37 No. 3 2010

VAVILIN

Now the description of enzymatic reactions for DPand MP can be replaced by conventional Monod func�tions with microorganism biomasses growing on ROH

(11)

where ρ* = vm1k1/k2, ρ** = vm2k1/k2. Monod functionsgiven in (11) were used for the creation of the distrib�uted model (12) described below.

dPDdt

��������� vm1–k1B1

k2

��������� PDkPD PD+������������������ ρ*B1

PDkPD PD+������������������,–= =

dPMdt

����������k1B1

k2

��������� vm1PD

kPD PD+������������������ vm2

PMkPM PM+��������������������–

⎩ ⎭⎨ ⎬⎧ ⎫

=

= B1 ρ* PDkPD PD+������������������ ρ** PM

kPM PM+��������������������–

⎩ ⎭⎨ ⎬⎧ ⎫

,

dB1

dt������� Y1B1 ρ* PD

kPD PD+������������������ ρ** PM

kPM PM+��������������������+

⎩ ⎭⎨ ⎬⎧ ⎫

kd1B1,–=

Figure 3 gives the kinetics of MEHP degradationprocess at 35°С. Two reactions, which limit the generalrate, can be identifued in the degradation process:ester hydrolysis and the transformation of phthalicacid into methane and carbon dioxide. Visual calibra�tion of the model was carried out by successive exam�ination of parameter values within intervals knownfrom the literature and comparison of solutions on thecomputer display. Since the number of independentparameters was rather large, such method requiresmuch less time and the sum of deviations of measuredand calculated model variable can be made close tominimum. Finally, the values of maximal specific ratesof biomass growth for various microorganisms μmi =Yiρmi were found as follows:

μm1 = 0.258 day–1, μm2 = 0.085 day–1, μm3 = 0.5 day–1, μm4 = 2.0 day–1.

The microorganisms responsible for phthalic acidhydrolysis grow much slower (μm = 0.085 day–1) thanother bacterial groups. The maximal specific rate of

1000

800

600

400

200

100806040200

5

4

3

2

1

100806040200

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200

100806040200

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100806040200

МЕ

НР

, µ

M

Р�Н

2, b

ar

× 10–3

РА

, µ

M

СН

4, µ

M

Time, day Time, day

Fig. 3. Kinetics of MEHP degradation via the formation of phthalic acid PA as an intermediate product. Circles are experimentaldata [5], curves are solutions of mathematical model (9). Reactor volume is 50 ml.

WATER RESOURCES Vol. 37 No. 3 2010

ANALYSIS OF THE MECHANISM AND MATHEMATICAL MODELING 403

MEHP hydrolysis vm1 was 258 day–1, and the maximalconsumption rate of phthalic acid monoester ρ** was2.58 day–1.

ANAEROBIC PHTHALATE DEGRADATION IN LABORATORY LYSIMETERS

A typical cylindrical reactor—lysimeter, simulat�ing a municipal solid waste landfill—is ~100 l in vol�ume and can contain up to 40 kg of wastes. The mois�ture and temperature within the reactor can be regu�lated, resulting in that the processes that last fordecades in real landfills can be completed within sev�eral months in a reactor.

The focus of the study was the degradation kineticsof phthalates, including DEHP, in such reactors [13,28]. The initial moisture of domestic wastes was 65%.The wastes were pre�disintegrated to a maximal size ofa few centimeters. Experimental data from one of thefour reactors (R3) were used to calibrate the model.The rapid digestion caused acidification within severaldays (pH 5.5). Between the 18th and the 52nd week,water was added into the reactor from the top in orderto dilute the leachate. Next, after the dilution wasceased, the reactor featured acidogenic conditionswithin 3 years (53rd–143rd week) without significantchanges of pH and volatile fatty acids (VFAs).Between the 144th and 169th week, leachate from

methanogenic reactor R1 was added into R3. Thisstimulated methanogenesis in acidogenic reactor R3.The experimental data from reactors R2 and R4,where wastes had been pre�aerated, were used to vali�date the model. The experimental conditions, includ�ing a description of the phthalate measurement proce�dures, are described in detail in [6, 12].

Distributed Mathematical Model

A simplified kinetic scheme, which, in addition tomicrobiological processes, involves physicochemicalprocesses of phthalate sorption/desorption, is given inFig. 4. Various phthalates with different water solubil�ity were used, including diethylphthalate (DEP, with arelatively high solubility), dibutylphthalate (DBP,poorly soluble), and diethylhexylphthalate (DEHP,almost insoluble), each being represented in munici�pal wastes. The hydrolysis/acidogenesis and methano�genesis processes were represented as two rate�limitingstages of an anaerobic process (acidogenic and meth�anogenic) with a single intermediate product (VFA), aprecursor of the final product, methane. The organicwastes were divided into two fractions: readily andpoorly degradable. Two microorganism groups wereincluded in the model: phthalate�decomposing bacte�ria and methanogenic bacteria. Monoesters wereassumed to be completely soluble. The diffusion and

Readily degradable MSWAeration

Productinhibition (acid pH)

Hardly degradable

SMW

Desorption

Sorption

Hydrolysis

VFA

Methanogenesis

Substrate inhibition(acid pH)

DPS DP MP PA

CH4

Fig. 4. Scheme of parallel degradation of readily and hardly degradable wastes, including phthalic acid diesters DP. MP is phthalicacid monoester; PA is phthalic acid; DP, MP are dissolved phthalates; DPS is sorbed phthalate diester; MSW are municipal solidwastes.

404

WATER RESOURCES Vol. 37 No. 3 2010

VAVILIN

advection of dissolved substrates were taken intoaccount. The system of partial differential equationshas the form

(12)

where W1, W2, S, H are the concentrations of readilyand hardly soluble wastes, total VFAs, and protons,respectively; ∂P/∂t ≡ ∂P/∂t(Z, t) ≥ 0 is methane pro�duction rate; DP, MP are concentrations of phthalatediesters and monoesters (DP and MP); DPS isadsorbed DP; BM, BPAE are concentrations of phtha�

∂W1

∂t�������� kh1W1,–=

∂W2

∂t�������� kh2W2f1 I( ),–=

∂S∂t����� DS

∂2S

∂Z2������� q∂S

∂Z�����– χ1kh1W1+=

+ kh2W2f1 S( ) ρm1f2 I( )BMS

KS S+�������������,–

∂BM

∂t�������� DBM

∂2BM

∂Z2���������� Y1ρm1f2 I( )

BMS

KS S+������������� kd1BM,–+=

∂P∂t����� 1 Y1–( )ρm1f2 I( )

SBM

KS S+�������������,=

∂H∂t

������ DH∂2H

∂Z2�������� q∂H

∂Z������ bf2 I( )

SBM

KS S+�������������H,––=

∂DPS

∂t����������� k1DPS– k2DP,+=

∂DP∂t

��������� DDP∂2DP

∂Z2����������� q∂DP

∂Z���������– k2DP–=

+ k1DPS ρm2f3 I( )BPAEDP

KDP DP+�������������������,–

∂MP∂t

���������� DMP∂2MP

∂Z2����������� q∂MP

∂Z����������–=

+ 1 Y2–( )ρm2f3 I( )BPAEDP

KDP DP+������������������� ρm3f3 I( )

BPAEMP

KMP MP+��������������������,–

∂BPAE

∂t������������ DBPAE

∂2BPAE

∂Z2������������� BPAEY2f3 I( )+=

× ρm2DP

KDP DP+������������������� ρm3

MPKMP MP+��������������������+

⎩ ⎭⎨ ⎬⎧ ⎫

kd2BPAE,–

late�decomposing methanogenic microorganisms andbacteria; 0 ≤ t ≤ +∞ is time; kh1 and kh2 are rate con�stants of first�order hydrolysis; ρm1, ρm2, ρm3 are maxi�mal specific utilization rates of VFA, DP, and MP; kd1,kd2 are biomass degradation constants of appropriatemicroorganisms; k1 and k2 are desorption and sorptionconstants for DP; χ1, χ2 are stoichiometric coeffi�cients; KS, KDP, KMP are half�saturation constants forutilization rates of VFA, DP, and MP; Y1, Y2 are yieldcoefficients for biomasses; DS, DH, DDP, and DMP arediffusion coefficients of VFA, protons, DP, and MP,respectively; DBM, DBPAE are diffusion coefficients ofmethanogens and bacteria, decomposing phthalates; bis the rate constant of drop in proton concentrationsduring methanogenesis [28]; q is the specific rate ofliquid flow; fi(I) is pH inhibition function, which wastaken in the form

(13)

where Sn is the concentration of non�ionized VFAs;Ka = 2 × 10–5 –5 is dissociation constant for VFA; Ki isinhibition constant (i = 1, 2, 3). In formula (13), theconcentration of nonionized VFAs (Sn) is associatedwith the concentration of protons, introduced into themodel with the aim to account for the effect of pH [25,26]. The moisture content was not considered as anindependent variable, since it was assumed that themedium is saturated with water and hence the rate ofthe process does not depend on moisture content. Thedependence of the degradation process on moisturecontent was considered, for example, in [19, 25].

Boundary Conditions

Since cylindrical reactors were operated under var�ious regimes, appropriate boundary conditions werechosen: under normal conditions (equation 14), clear�water seepage through the upper bed of reactor (equa�tion 15), and leachate exchange between the aci�dogenic and methanogenic reactors (equation 16)

(14)

(15)

(16)

fi Sn( ) 1

1 SKi 1 Ka/H+( )���������������������������

2

+�����������������������������������������,=

∂c∂Z����� 0 Z = 0( ); ∂c

∂Z����� 0 Z = L( ),= =

weeks 1–17, 53–143, 170–250;

∂c∂Z�����

q1

D��� 0 c–( ) Z = 0( ); ∂c

∂Z����� 0 Z = L( ),= =

weeks 18–52;

∂c∂Z�����

q2

D��� c* c–( ) Z = 0( ); ∂c

∂Z����� 0 Z = L( ),= =

weeks 144–169,

WATER RESOURCES Vol. 37 No. 3 2010

ANALYSIS OF THE MECHANISM AND MATHEMATICAL MODELING 405

where q1 and q2 are the specific rates of liquid flowthrough the unit area during the dilution and exchangeof leachate, respectively. In equation (14), c implies allmodel variables; in equation (15), c implies VFA, DP,MP, BM, and BPAE concentrations; in equation (16),c and c* are concentrations of VFA, H, DP, MP, BM,and BPAE in the reactor and the incoming leachate,respectively; conditions (14) are applied to othervariables.

The initial conditions assume all model variables tobe uniformly distributed over the spatial coordinate Z.The final values of all variables in a stage of the process(boundary conditions) were taken as the initial condi�tions for the subsequent stage. The calculations werecarried out by using MATLAB package. The mainmodel parameters are as follows:

kh1 = 1.16 week–1, kh2 = 0.049 week–1,

ρm1 = 15.4 week–1 mg mg–1,

ρm2DEP = 6.3 week–1 mg mg–1,

ρm3MEP = 0.31 week–1 mg mg–1, ρm2DBP = 7.0 week–1 mg mg–1,

ρm3MBP = 0.28 week–1 mg mg–1, ρm2DEHP = 49 week–1 mg mg–1,

ρm3MEHP = 0.31 week–1 mg mg–1, kd1 = kd2 = 0.005 week–1,

k1DEP = 0.13 week–1, k2DEP = 0.5 week–1, k1DBP = 0.035 week–1,

k2DBP = 12 week–1, k1DEPH = 0.0055 week–1,

k2DEPH = 60 week–1,χ1 = 0.42, χ2 = 0.6, KS = 3.5 g l–1,

KDEP = 0.2 mg l–1, KMEP = 0.15 mg l–1,

KDBP = 0.005 mg l–1, KMBP = 0.005 mg l–1,

KDEHP = 0.001 mg l–1, KMEHP = 0.001 mg l–1,

Y1 = 0.1 g g–1, Y2 = 0.1 mg mg–1, K1 = 0.04 g l–1,

K2 = K3 = 0.065 g l–1, b = 0.23 week–1 l g–1,

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A,

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oge

nes

, g/

l

pH

Bio

gas,

l

(a)

Fig. 5. Dynamics of an anaerobic system in a cylindrical reactor. Symbols are experimental data [6], curves are solutions of dis�tributed model (12). Reactor volume is 100 l. (a) Concentrations of VFA, cations, and methanogenic microorganism biomassesin leachate, averaged over reactor volume, and the total biogas volume; (b–d) DEP, MEP, DBP, MBP, DEHP, MEHP concen�trations and the biomasses B of phthalate�decomposing microorganisms.

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q1 = 0.09L week–1, q2 = 0.03L week–1, H* = 10–7 g l–1,

= 0.5 g l–1, DVFA = DH = DDEP = DMEP = DBM

DBPAE = 0.001L2 week–1, L = 80 cm, S* = 0.001 g l–1,

= 0.0001 mg l–1, DP* = 0.001 mg l–1,

MP* = 0.001 mg l–1, where * are the values of concentrations in the incom�ing flow as the result of recirculation.

Degradation Kinetics of Municipal Solid Wastesin Acidogenic Reactor R3

VFA concentration kinetics and the dynamics ofmethanogenic microorganisms, biogas volume, andpH are given in Fig. 5a. Before dilution (weeks 1–17),accumulation of VFAs and a considerable drop in pHtakes place because of hydrolysis/acidogenesis. VFAconcentration decreases during dilution (weeks 18–52).Next (weeks 53–143) it varies slightly. Upon the intro�duction of methanogenic organisms (weeks 144–169),

BM*

=

BPAE*

methanogenic conditions gradually form in aci�dogenic reactor R3.

Phthalate Degradation Kinetics

The degradation kinetics of different phthalates isgiven in Figs. 5b–5d. The physicochemical processesof sorption/desorption are most significant in the ini�tial period, when the current concentration of phtha�late diesters in leachate is determined by sorbtion anddesorption constants, as well as the concentration ofphthalates DPS sorbed by solid wastes. DEP con�centration in leachate reaches 1500 μg l–1 since thedesorption/sorption rate ratio is relatively largek1/k2 = 0.13/0.5 = 0.26. With dilution, DEP andDEPS concentrations drop since the 18th week. Afterthe dilution is ceased (52nd week), DEP concentra�tion in leachate reaches a new equilibrium level of500 μg l–1. According to the model, the concentrationof dissolved DEP is governed only by physicochemical

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ht,

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Р, µ

g/l

(b)

Fig. 5. Contd.

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ANALYSIS OF THE MECHANISM AND MATHEMATICAL MODELING 407

processes (sorption, desorption, and dilution) over along time. About half DEPS (3.5 mg l–1) is washed awaybecause of dilution. Upon the introduction of methano�genic organisms into reactor R3 (144th week), methano�genesis develops in the acidogenic reactor as well. Thisfacilitates the hydrolytic degradation of hardly degrad�able wastes, including phthalates. According to themodel, the considerable decrease in nonionized VFAconcentrations stops the inhibition of DEP and MEPhydrolysis. The resulting decrease in dissolved DEPconcentration accelerates the desorption process,which proceeds until the disappearance of DEPS.

The equilibrium concentration of DBP is as low as40 μg l–1, which can be attributed to the low sorp�tion/desorption constant ratio k1/k2 = 0.035/12 ≈0.003. Unlike DEP, the concentration of dissolvedDBP remains constant during dilution (18th–52ndweek), since the dilution is compensated for by de�sorption. According to the model, the effect of dilu�

tion on DBPS is not significant. DBPS concentrationintensely drops parallel to the degradation of hardlydegradable wastes. The biodegradation, which reducesdissolved DBP concentration, facilitates desorption pro�cesses, resulting in a drop in DBPS concentration. Themodel yields a high concentration of monoester MBP(>2000 μg l–1), which is much larger than that of diesterDBP, since it was assumed that the initial DBPS con�centration was relatively high, and biodegradationgoes at ρm2 � ρm3 (see system of equations 12).

The very low DEHP concentration (less than 1 μg l–1)was obtained because of the very low ratio of desorp�tion/sorption rate constants, equal to k1/k2 =0.0055/60 ≈ 9 × 10–5. According to the model, dilutionhas no effect on DEHP concentration. The drop inDEHPS concentration coincides with a drop in theconcentration of difficultly degradable wastes. Unlikethe very low concentration of dissolved DEHP, theprocess of its hydrolysis is accompanied by the appear�

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PS,

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P, µ

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(c)

Fig. 5. Contd.

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ance of a relatively high concentration of MEHP(~200 μg l–1). The high DEHP concentration inleachate, measured in the end of the experiment,appears to account for broken away colloidal particles.The model predicts the propagation of DEHP con�centration front in the vertical direction during phtha�late transformation (149th–164th weeks).

Limiting ourselves by a description of degradationof sorbed phthalates DEHPS instead of the structuralmodel (12), we can apply the simple first�order model(1). Desorption process is a rate�limiting stage ofDEHP degradation. DEHPS degradation constant(Fig. 6), equal to 0.0055 week–1 for solid municipalwastes is much less than the corresponding value foractivated sludge (Fig. 1). The latter features a loosestructure and much greater specific surface area thanplastic pieces contained in solid municipal wastes.

Pre�aeration facilitates the onset of anaerobic deg�radation of hardly degradable pollutions, including

phthalates (reactors R2 and R4). According to themodel, aeration causes the oxidation of readilydegradable matter and upon the cessation of aeration,the rates of hydrolysis/acidogenesis and methanogen�esis become balanced. The result is that the systemavoids excessive acidification and inhibition of bio�degradation process.

CONCLUSIONS

Simple modified first�order kinetics with a correc�tion for nondegradable fraction adequately describesthe drop in DEHP concentration during activatedsludge degradation in treatment facilities. Physico�chemical sorption/desorption plays a key role in thisprocess. Phthalate biodegradation under anaerobicconditions starts simultaneously with the degradationof hardly degradable wastes. Hydrolysis, which

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(d)

Fig. 5. Contd.

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ANALYSIS OF THE MECHANISM AND MATHEMATICAL MODELING 409

reduces DEHP concentration in solution, can facili�tate desorption processes.

REFERENCES

1. Moiseenko, T.I., Gashkina, N.A., Sharova, Yu.N., andPokoeva, A.G., Ecotoxicological Assessment of After�Effects of the Volga River Water Contamination, Vodn.Resur., 2005, vol. 32, no. 4, pp. 410–424 [Water Resour.(Engl. Transl.), vol. 32, no. 4, pp. 369–383].

2. Bessems, E., The Biodegradation of Plasticized PVCand Its Prevention, J. Vinyl Tech, 1988, vol. 10, no. 1,pp. 3–6.

3. Blount, B.C., Milgram, K.E., Silva, M.J., et al., Quan�tative Detection of Eight Phthalate Metabolites inHuman Urine Using HPLC�APCI�MS/MS, Anal.Chem., 2000, vol. 72, no. 17, pp. 4127–4134.

4. Ejlertsson, J., Fate of phthalic acid esters during digestionof municipal solid waste under landfill conditions. PhDDissertation. Linkopping: Linkopping Univer., 1997.

5. Ejlertsson, J. and Svensson, B.H., Degradation ofBis(2�Ethylhexyl) Phthalate Constituents under Meth�anogenic Conditions, Biodegradation, 1997, vol. 7,no. 1, pp. 1–6.

6. Ejlertsson, J., Karlsson, A., Lagerkvist, A., et al., Effectof Co�Disposal of Wastes Containing Organic Pollut�ants with Municipal Solid Waste–A Landfill Simula�tion Reactor Study, Adv. Environ. Res, 2003, vol. 7,no. 4, pp. 949–960.

7. EU (2000). Directive (2000/60/EC) in the Field of WaterPolicy [Official Journal, London: 327 of 22.12, 2001.

8. Furtmann, K., Phthalates in the Aquatic Environment.European Council for Plasticisers & Intermediates, Brus�sels: ECPI, 1996.

9. Fountoulakis, M.S., Stamatelatou, K., and Lyberatos, G.,Simulation of DEHP Biodegradation and Sorptionduring the Anaerobic Digestion of Secondary Sludge,Proc. First Intern. Workshop on the IWA AnaerobicDigestion Model, no. 1.

10. Gavala, H.N., Alatriste�Monragon, F., Iranpour, R.,and Ahring, B.K., Biodegradation of Phthalate EstersDuring the Mesophylic Anaerobic Digestion of Sludge,Chemosphere, 2003, vol. 52, no. 4, pp. 673–682.

11. Jonsson, S., Phthalates in landfill leachates � a signatureof their degradation, analytical methods and toxicologicalconsiderations. PhD Dissertation. Linkopping: Linkop�ping Univer., 2003.

12. Jonsson, S., Ejlertsson, J., and Svensson, B.H., Behav�ior of Mono� and Diesters of O�Phthalic Acid inLeachates Released during Digestion of MunicipalSolid Waste Under Landfill Conditions, Adv. Environ.Res., 2003, vol. 7, no. 2, pp. 429–440.

13. Jonsson, S., Vavilin, V.A., and Svensson, B.H., Phtha�late Hydrolysis under Landfill Conditions, Water Sci.Technol., 2006, vol. 53, no. 8, pp. 119–127.

14. Kurane, R., Microbial Degradation of PhthalateEsters, Microbiol. Sci., 1986, vol. 3, no. 1, pp. 92–95.

6000

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0 700600500400300200100

100

DE

HP

S, µ

g/l

ME

HP

, µ

g/l

1 2

2

Time, week

Fig. 6. Kinetics of sorbed DEHPS and dissolved MEHP. (1) Model (12) with desorption rate coefficient k1 = 0.005 week–1;(2) approximation of solution of structural model (12) by simple first�order chemical kinetics (k = 0.0055 week–1, α = 0.04). Thearrow shows the moment when methanogenic microorganisms were introduced into the acidogenic reactor.

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VAVILIN

15. Madsen, P.L., Thyme, J.B., Henriksen, K., et al.,Kinetics of Dis�(2�Ethylhaxyl) Phthalate Mineraliza�tion in Sludge�Amended Soil, Environ. Sci. Technol.,1999, vol. 33, no. 15, pp. 2601–2606.

16. Marttinen, S., Potential of Municipal Sewage TreatmentPlants to Remove Bis(2�ethylhexyl) Phthalate. Doc. Dis�sertation. Jyvaskyala: University of Jyvaskyala, 2004.

17. Painter, S.E. and Jones, W.J., Anaerobic Bioconversionof Phthalic Acid Esters by Natural Inocula, Environ.Tech, 1990, vol. 11, no. 8, pp. 1015–1026.

18. Pignatello, J.J. and Xing, B., Mechanisms of SlowSorption of Organic Chemicals to Natural Particles,Environ. Sci. Technol., 1996, vol. 30, no. 1, pp. 1–11.

19. Pommier, S., Chenu, D., Quintard, M., and Lefebre, X.,A Logistic Model for the Prediction of the Influence ofWater on Solid Waste Methanization in Landfills, Bio�technol. Bioengn., 2007, vol. 97, no. 3, pp. 473–482.

20. Shelton, D.R., Boyd, S.A., and Tiedje, J.M., AnaerobicBiodegradation of Phthalic Acid Esters in Sludge,Environ. Sci. Technol., 1984, vol. 18, no. 2, pp. 93–97.

21. Stahl, W. and Pessen, H., The Microbial Degradationof Plastisizers I. Growth on Esters and Alcohols, Appl.Environ. Microbiology, 1953, vol. 1, no. 1, pp. 30–35.

22. Staples, C.H., Peterson, D.R., Parkerton, T.F., andAdams, W.J., The Environmental Fate of PhthalateEsters: Literature Review, Chemosphere, 1997, vol. 35,no. 4, pp. 667–749.

23. Qu, X., Vavilin, V.A., Mazeas, L., et al., Anaerobic Bio�degradation of Cellulosic Material: Batch Experimentsand Modelling Based on Isotopic Data and Focusingon Aceticlastic and Non�Aceticlasctic Methanogene�sis, Waste Manag., 2009, vol. 29, no. 6, pp. 1827–1837.

24. US EPA. List of substances on IRIS. Integrated RiskSystem Information. Washington: United States Envi�ronmental Protection Agency. 2006, http://www.epa.gov/iris

25. Vavilin, V.A., Rytov, S.V., Lokshina, L.Y., et al., A Dis�tributed Model of Solid Waste Anaerobic Digestion:Effect of Leachate Recirculation and pH Adjustment,Biotech. Bioeng., 2003, vol. 81, no. 1, pp. 66–73.

26. Vavilin, V.A., Rytov, S.V., Pavlostathis, S.G., et al.,A Distributed Model of Solid Waste Anaerobic Diges�tion: Sensitivity Analysis, Water Sci. Technol., 2003,vol. 48, no. 4, pp. 147–154.

27. Vavilin, V.A., Jonsson, S., and Svensson, B., KineticAnalysis of Phthalate Esters Transformation Consider�ing a Series of Stoichiometric Reactions, Appl. Microb.Biotech., 2005, vol. 69, no. 4, pp. 474–484.

28. Vavilin, V.A., Jonsson, S., and Svensson, B., Modellingof Municipal Solid Waste Decomposition under Land�fill Conditions Considering Hydrolytic and Methano�genic Inhibition, Biodegradation, 2006, vol. 17, no. 5,pp. 389–402.

29. Vavilin, V.A., Corrected First�Order Model of DEHPDegradation, Chemosphere, 2007, vol. 68, no. 10,pp. 1992–1995.