energy efficiency in waste water treatments plants: optimization of activated sludge process coupled...

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Energy 41 (2012) 153e164

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Energy

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Energy efficiency in waste water treatments plants: Optimization of activatedsludge process coupled with anaerobic digestion

N. Descoins a,*, S. Deleris b, R. Lestienne b, E. Trouvé b, F. Maréchal a

a Industrial Energy Systems Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 9, CH1015 Lausanne, SwitzerlandbAnjou Recherche, Veolia Environnement, Chemin de la Digue, BP 76, F-78603 Maisons Laffite, France

a r t i c l e i n f o

Article history:Received 30 September 2010Received in revised form28 March 2011Accepted 31 March 2011Available online 4 May 2011

Keywords:WWTPPlant-wideSteady-stateOptimizationModelingEnergy efficiency

* Corresponding author. Tel.: þ41 21 693 3521; faxE-mail address: [email protected] (N. Desco

0360-5442/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.energy.2011.03.078

a b s t r a c t

This paper presents a study concerning the optimization of a Waste Water Treatment process. Theprocess deals with carbon and nitrogen removal and includes activated sludge reactors coupled with ananaerobic digestion reactor. Nitrification and de-nitrification biochemical reactions are due to the bio-logical activity of heterotrophic and autotrophic micro-organisms occurring inside the reactors. RigorousPlant-Wide models that represent the main biochemical transformations have been constructed as perthe CEIT approach [1]. The energy consumption for each Physical Unit Operation (P.U.O.) involved in theflow-sheet is evaluated and a full link is made between the biological activity and the electrical demandor production. Steady-state mathematical optimizations are then computed and the influence of primarysettling efficiency on electrical autonomy is quantified and demonstrated. The ammonium recycling fromdigestion to activated sludge reactors is also demonstrated to be a limiting factor for the overall energyefficiency, as well as the C-substrate availability for denitrifying. Some conclusions are then drawn toimprove the global electrical efficiency of the system.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction and general context

Wastewater treatment consists mainly of threemajor processes:biochemical treatments, liquid/solid separations operation andthermal processes for sludge treatment and valorization. The Fig. 1is an overview of a classical WasteWater Treatment Plant (WWTP),each unit representing a Physical Unit Operation (PUO). Thewastewater is first treated by mean of biochemical and settlingprocesses in the water stream.

This water stream finally results in two new streams: the “puri-fied” water and a “sludge” stream concentrated in biomass. Thesludge streamprocesses consist then in stabilizing andvalorizing thesludge before the remaining matter is released to the environment.

The most used technology for liquid/solids separation is thesettling process. Due to the phenomena of gravity, the particlessettle down and finally two streams are produced: a particle clar-ified stream and a particle concentrated stream. The settlers aregenerally classified into primary and secondary settlers. Theprimary settling is applied directly to the raw wastewater andproduces a carbon-rich primary sludge, while the secondary

: þ41 21 693 3502.ins).

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settling process is applied to separate the biomass produced in theActivated Sludge reactors from the water (see Fig. 1).

Aerobic biological treatment consists of supplying oxygen insidethe Activated Sludge reactors in order to maintain and growmicro-organisms. Both the carbon-based pollutants and the nitrogen-based pollutants are then degraded inside the reactors by thecombined biological activities of heterotrophic and autotrophicbacteria [2]. Anaerobic digestion is a biological phenomenon thatappears when oxygen and nitrate concentrations are very low inthe sludge. Under specific temperature and for sufficient residencetimes, specialized micro-organisms become active. The organicnutrients present in the sludge are then used by these micro-organisms which partially convert it into a mix of methane andcarbon dioxide [3]. This anaerobic biological treatment is thereforecombined with dewatering and drying processes and a stabilizedsludge is finally obtained. The biogas produced by the digester canbe burned inside a cogeneration engine. Heat and electricity cantherefore be produced locally and contribute to reduce the energycosts.

Up to now the scientific community involved in the field ofwaste water treatment has focusedmainly on the water quality andassociated modelling issues. In our opinion, efforts must be done tolink water quality and WWTP pollutants removal efficiency withenergy aspects, because future industrial practice in the context of

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Nomenclature

AbbreviationsASM Activated Sludge ModelADM Anaerobic Digestion ModelCOD Chemical Oxygen DemandPUO Physical Unit OperationPW-AD Plant-Wide Anaerobic DigestionPW-AS Plant-Wide Activated SludgeThOD Theoretical Oxygen DemandTSS Total Suspended Solids (gm�3)WWTP Waste Water Treatment Plant

SymbolsCi Compound concentration in liquid phase (g m�3)Ci

sat Saturation concentration in liquid phase (g m�3)Dpipe Pipe diameter (m)_E Electrical power (kWh day�1)

g Gravitational constant (9.81 m s�2)Lpipe Pipe length (m)Haer Height of liquid above air diffusers (m)Hp Polytropic head (J mol�1)KL

ia Mass transfer coefficient for compound i (day�1)Mi,k Molar equivalent (gm�3)_mliq Liquid mass flow rate (kg day�1)nk Compound concentration in gas phase (mol liter�1)P,DP Pressure (Pa)_ri Source term for compound i (gm�3 day�1)T Temperature (K)Vliq,gas Liquid or gas volume (m�3)_Vliq;gas Liquid or gas volume flow rate (m�3 day�1)DZ Altitude difference (m)np Polytropic efficiency (e)rj Kinetic rate of process j (gm�3 day�1)rliq Density of liquid (kgm�3)h Efficiency (e)

N. Descoins et al. / Energy 41 (2012) 153e164154

global warming and fossil resource rarefaction will be greatlyimpacted by the energy costs. On another side, environmentalpressure on aquatic resources become more and more severe andthe energy consumption to purify wastewater and keep rivers andlakes in an ecologically acceptable state will probably increase.

Mathematical models and rigorous optimization algorithms arereally helpful in this context, as they capture the main features ofeach PUO. Furthermore models bring a deep understanding of thephysical and biological mechanisms and their interactions. Themathematical models used in this study were developed based onthe scientific literature and are implemented on the gPROMS�

platform [4]. Efforts have been done to systematically link thebiological activity and the corresponding energy consumption orproduction, providing by this way a link between water qualityand energy efficiency. The objective of the study presented in thispaper was in fact to determine how the global energy efficiency ofWWTP could be improved, by acting on process design. In thiscontext, the key factors are the trends given by the models, ratherthan a very accurate prediction of the pollutants concentration atthe exit of the plant. All the computations presented in this paperhave been done using the numerical solvers provided by ProcessSystem Enterprise.

Fig. 1. Studied Waste Water Treatment Plant (WWTP) flow-she

2. Modeling methodology

The first section introduces the main equations used to runsteady-state optimizations. Some equations are not introduced asthey are classical models available in the extensive literature con-cerning WWTP modeling. This is the case for the settling processes,including one-dimensionalmodels and pointmodels. Actually, thesemodels are the basis for all the liquid/solid separation processesincluded on the flow-sheet studied in this paper (see Fig. 1).

The biochemical reactions modeling have been the subject ofspecial attention. The models developed are fully conservative interms of mass, by opposition to the original ASM1 model thatconserve only the Theoretical OxygenDemand (ThOD), nitrogen andionic charge [2]. The mass transfer between the liquid and gaseousphases is also included in the reactor’s model. Each chemicalcompound is described by a stoichiometric formula and quantifiedby a concentration expressed asmole, grams of nitrogen or grams ofThOD. The ThoD is assumed tobe equivalent to the Chemical OxygenDemand (COD). The COD is a specific chemical measurement thatcharacterizes the Carbon content of the wastewater and it is widelyused in thefieldofWWTPengineering. Theplant-widemethodusedto quantify the biochemical reactions implies a homogeneous

et. Water Quality constraints and recycles lines are located.

N. Descoins et al. / Energy 41 (2012) 153e164 155

matter composition in all the different PUO.No special interfaces arethen needed to connect the Activated Sludge process with theAnaerobic Digestion reactor. These models are based on the CEITmethodology [1]. The reactors models as well as the compressorsand pumps models are also introduced in this section.

2.1. Plant-wide biochemical modeling

The plant-wide models included in the reactors models arepresented under the form of a Petersen matrix and a kinetic vector,similarly to the ASM [2] and ADM [3] models. They are called PW-AS (Plant-wide Activated Sludge) and PW-AD (Plant-Wide Anaer-obic Digestion) models and are able to reproduce all the features ofASM and ADM models. The full details and the methodology usedto develop these models will be given in a dedicated paper. Themodels have been compared successfully with literature bench-marks. The Fig. 2 presents for example a comparison of the PW-ASmodel with the classical ASM1 model in the context of theBenchmark Simulator n�1 (BSM1) [5]. The quantity plotted on Fig. 2is the rejected concentration of ammonium.

2.1.1. Common set of speciesThefirst step tobuild thebiochemicalmodels consists of defining

the set of species that is included in the plant-wide models. This setmustbe able to reproduce all the featuresofASMandADMmodels. Aparticular effort has been made to avoid the use of lumped compo-nents and all the chemical species needed to fully describe thedifferent biological activities are included.Minerals compounds andcorresponding acids/bases equilibriums are also taken into account.The plant-wide models include 39 species (except water) dividedinto 25 soluble species and 14 particulate species. Each componentincluded in themodel is characterized in term of C, H, O, N, P, chargeand equivalent ThOD. The elemental compositions for eachcompound are the same as those reported in [1].

Some species are considered to be aqueous and are included inthe liquid/gas mass transfer. Biological inerts are represented bothin soluble and particulate forms. These fractions are assumed to becommon to the different biological models. Some particulatescomponents are considered as substrates and others as groups of

Fig. 2. Comparison of PW-AS model with the ASM1 model in the context of the Bench

micro-organisms which degrade and transform the organic matter,producing in the same time minerals and gaseous species. Onecomposite compound is also included in the models and representsthe biggest organic particles and macromolecules.

2.1.2. Petersen matrix and kinetics vector for PW-AS and PW-ADmodels

The mathematical equations and formulas employed to buildthe Activated Sludge and Anaerobic Digestion plant-wide modelsconsists of writing stoichiometry matrices and kinetics vectors(Petersen formalism). The behavior of the different kinds of micro-organisms considered in the aerobic/anoxic and anaerobic reactorsis described by assuming that the different groups are fully differ-entiated. The matrixes are then balanced for each element: C, H, O,N, P and ThOD. This is done for each process j by computing correctvalues for the sink or sources coefficients in the matrices (noted qj

k,with k e {C, N, P, H, O, ThoD}, see appendix A). The species chosen tofulfill the elemental balances are mineral ones: dissolved oxygen,ammonium, protons, phosphates, water and dissolved carbondioxide or bicarbonate (HCO3

�).Each biochemical process introduced in the PW matrices are

linked to kinetics expressions that follow general rules concerningthe modeling of micro-organisms growth (Monod kinetics formu-lation). Generally-speaking and for a biological process corre-sponding to a growth referred by index j, the general kineticmathematical form is:

rj ¼ kmSsub

Hsub þ Ssub

SsubStot

ANHþ4AHPO�

4/I1IpH/Xbio (1)

The terms noted ANHþ4AHPO�

4/ are called activation terms and are

related to the sink/source terms used to balance the stoichiometrymatrix. The terms I1IpH.are inhibition terms related to somespecific chemicals compounds or pH. Each process correspondingto a growth includes a rate kinetic parameter named km which iscorresponding to a substrate uptake.

Themacro substrates (particles) are first hydrolyzed by enzymesto become available to the micro-organisms. Corresponding disin-tegration and hydrolysis rates expressions are expressed as func-tions of the ratio between the hydrolyzed substrate concentration

mark Simulator n�1. The simulation is corresponding to the dry weather setting.


and the total micro-organisms concentration [2]. The full expres-sions for the PW-AS and PW-AD kinetics vector are writtenfollowing these rules. The source term involved in mass balanceequations for each specie i is then computed by the followingrelationship:

_ri ¼XNpro

j¼1

�nijrj

�(2)

nij are the stoichiometry matrices coefficients, rj the kinetics ratesand Npro the number of chemical processes included in the bio-logical model. As an example, the complete stoichiometry matrixfor the PW-AS model is given in Appendix: Table A-1eTable A-3.The kinetics expressions are reported in Table A-4.

Fig. 3. Mass balances during initialization.

2.2. Completely stirred tank reactors (CSTR) models

Activated Sludge processes are usually operated in aeratedtank reactors and channels. Part of the mixing is ensured bymechanical work (impellers) and the other part by aerators.Concerning Anaerobic Digestion, more sophisticated reactorsexist and particles could be separated from water usingmembranes and/or settling effects. The reactors involved in thiswork are modeled using the CSTR hypothesis. Each reactor modelincludes two phases: a liquid and a gaseous phase. This is donemainly because all the energy aspects involved in Waste WaterTreatment are strongly associated to gaseous mass transfer(oxygen transfer to activated sludge and methane production bydigestion).

2.2.1. Liquid phase mass balancesThe mass conservation equations for the liquid phase are

written under the following form for each compound i, where Ci isa concentration referring to one of the soluble or particulatecomponents included in the plant-wide models.

dCidt

¼_V liq

Vliq

�Cini � Cout

i

�þ _ri þ kiLai

�Csati � Cout

i

�(3)

Some compounds are then subjected to mass transfer with the gasphase (but not all the compounds). The Henry’s law coupled withan experimental law for computing the liquid gas exchange coef-ficient quantifies the mass transfer phenomenon for the activatedsludge reactors. The exchange coefficient kLia is then a function ofgas flow rate, gas composition and diffusers characteristics. For thedigester, the exchange coefficient is set to the constant value indi-cated in [3]. Combined with plant-wide models, 40 OrdinaryDifferential Equations (ODE) must be solved for each reactor if thewater compound is included.

2.2.2. Gas phase mass balancesThe use of mole per liter (noted n) as the unit for gases is

convenient and mass balances equations for gaseous componentscould be deduced from general mass balance equation:

dnoutidt

¼_Vingasn

ini � _V

out

gasnouti

Vgas� kiLai

Vliq

Vgas

CsatiMi

� CiMi

!(4)

Chemical interactions are not considered to occur in the gas phaseand consequently no source terms appear in the Eq. (4). The masstransfer between liquid and gas is still taken into account bymeans of the kL

iai coefficient and the associated term involvingsaturation constants for aqueous compound. The total gas flow

rate is then deduced from the ideal gas law by including the masstransfer from the liquid phase to the gaseous phase:

_Voutgas ¼ Pingas

Poutgas

Toutgas

T ingas_Vingas � R

Toutgas

PoutgasVliq

XNgas

k¼1

klak

CsatkMk

� CoutkMk

!(5)

The gas pressure at the entry (the bottom of the reactor) is corre-sponding to the pressure required to compensate the pressuresurrounding the bubbles which is mainly caused by the diffuserssubmergence (water column above the diffusers). The inlet pres-sure Pgas

inis then deduced from Eq. (6) where Haer is the height ofthe water column above the diffuser:

Pingas ¼ Patm þ rliqgHaer (6)

It means that the aeration system (usually compressors) mustpressurize the gas to the required pressure Pgas

in to form bubblesinside the reactor, but it also need to compensate the head lossesdue to the network distribution pipes and diffusers.

2.3. Pumps and compressor modeling

WWTPs involve the flow of many different liquids and gasesthrough pipes monitored by pumps and compressors. Even if themain water stream is powered by gravity only (caused by heightdifferences), the electric consumption caused by pumping andpressurizing is the main plant energy consumer. In practice, pumpsaccount for 25 percent of the total electrical consumption whilecompressors used for aeration accounts for almost 70 percent. Thehead losses insides the pipes are quantified by mathematicalexpressions. The following well-known semi-empirical relation-ship (Lechapt-Calmon formulae) is employed for the head lossescomputations:

DP ¼ rliqg�0:0011� _m1:89

liq D�5:01pipe Lpipe þ DZ

�(7)

The pipe dimensions are taken into account, as well as the altitudedifferences between the start and the end of the flow (DZ). Theexponents upon the liquid mass flow rate and the pipe diametercould be identified from experiments. The energy requirement forpumping the liquid through the pipe considered is then deducedfrom the following law (assuming incompressible flow):

_Epumps ¼ 100h

_V liqDP (8)

Fig. 4. Layout of the computation algorithm for parametric optimization.

Table 2Main constraints imposed to the system.

RejectedCOD

RejectedNH4

þRejectedNO3

-Sludgeage

ResidenceTime indigester

TSS in ASreactorn�5

TSS in sludgeto digester

gCOD/m3 gN/m3 gN/m3 Days Days g/l g/l

Min 0 0 0 5 10 1 50Max 60 Vary 8,12,20 35 50 9 50


_Epumps is expressed in kWhday�1, and h is the pump efficiency,usually ranges within 60 and 85 percent.

Oxygen is supplied to the micro-organisms growing in thereactors bymean of a pressurized gas stream (usually air). This air isdistributed by a network of pipes and diffusers placed on thebottom of the tanks. Only subsurface aeration is considered in thiswork as it is the most efficient way from an energy point of view toblow air into the reactors [6]. The gas must be pressurized to therequired pressure (deduced from Eq. (6)) in order to produce a gasflow through the reactor and to transfer the oxygen needed by themicro-organisms to grow.

A simple compressor model is used to estimate the energyconsumption. Themodel is based on the assumption of a polytropicflow, the corresponding law is given by Eq. (9):

PVnp ¼ cst (9)

The polytropic head Hp (in J mol�1) is deduced from Eq. (9) andrepresent the energy required to pressurize one mole of gas:

Hp ¼ npnp � 1

RT in

264 Pout þ DP

Pin

! npnp�1

�1

375 (10)

The term DP represents the uniform losses inside the pipe networklinked to the diffusers and used to distribute the gas to the aeratedreactor surface. It is calculated using the singular head lossesrelationship given by Eq. (7). The power _Ecomp consumed to pres-surize the gas from Pin to Pout is then given by Eq. (11):

_Ecomp ¼ 100h

Hp_VinPin

RT in(11)

3. Steady-state optimizations

The PUO models are linked on a flow-sheet to reproduce theActivated Sludge process combined with the Anaerobic Digestionprocess. The resulting model is a set of equations that could besolved both for dynamic or steady-state cases. The WWTP config-uration studied is reproduced on Fig. 1.

Table 1Main decision variables and units.

_V1gas

_V2gas

_V3gas

_V4gas

_V5gas

Air flow rate inAS reactor n�1



Air flow rate in ASreactor n�4

Air flow rAS reacto

M3/day m3/day M3/day m3/day m3/day

3.1. Initialization and steady-state

In order to compute a steady-state solution, an influent streamto the process is first specified by defining the inlet temperature,the volumetric flow rate of water and the concentration of thedifferent species considered in the PW models. A complete set ofparameters is also provided and the ASM1 benchmark (BSM1) [5]with the ADM1 [3] report has been used as references for thebiochemical, aeration and settlers models. The influent stream tothe WWTP was also specified similarly to the BSM1 dry weatherconfiguration. The characteristics of each pumps and compressorsare deduced from the energetic data consumption available in theBSM1 [5] or in the Swiss Federal Office for Energy report [6].

The models are solved for steady-state, by an initializationprocedure that consists in applying a step at initial time to thewastewater influent to the plant. The system is then relaxed and thedynamic equations converge to the final steady-state, accordinglyto the step and the parameters settings chosen for the differentmodels. The mass balances are systematically checked to ensurethat a steady-state is effectively reached (see Fig. 3).

3.2. Optimal point and parametric procedure

In order to optimize the WWTP some variables are set as deci-sion variables. The optimization algorithm next computes this set(within a predefined range) to minimize or maximize a predefinedobjective function. Some constraints are also imposed on thesystem andmust be satisfied during this procedure. The optimal setof variables obtained is then corresponding to a minimum ora maximum of the objective function that satisfies the constraintsimposed. The methodology used to solve the optimization problemis a gradient-based method (Sequential Quadratic Programmingalgorithm) included in the gPROMS� software.

If one (or more) constraint(s) is(are) modified, a new set ofdecision variables and a new value for the objective function areobtained. This procedure is called parametric optimization anda special algorithm has been developed in order to obtaina complete range of optimal points that corresponds to differentconstraints on water quality.

The procedure is resumed on Fig. 4. For each optimal set ofdecision variables (corresponding to each constraint value)a steady-state optimal point is recomputed and saved as a text file(including all the models variables). The final result could be, forexample, the optimal value of the objective function as a function ofthe varying constraint, but any model variable (decision variablesor not) could be represented as a function of the varying constraint.This method provides a valuable tool for analysing the optimal

Rdig _Vwasliq

_Vnoliq

_Vrecyliq hpri

ate inr n�5

Digesterradius

Secondary settlerwastage

Nitraterecycle

Secondarysettler recycle

Primary settlerefficiency

m m3/day m3/day m3/day e

Fig. 5. Optimal electrical autonomy for different values of primary settler efficiencyand as a function of rejected ammonium concentration. The nitrate rejected concen-tration is equal to 8 gN/m3.


results and understanding what the limiting factors are, as shownin the last section of this paper. The variables selected as decisionvariables are reported in the Table 1.

These constraints define the water quality by specifying indexeson COD and nitrogen concentration at the exit of the WWTP (in theclarified and treated water), as indicated on Fig. 1. Ammonium andnitrate are differentiated and the values are expressed by cubicmeter of water.

A constraint is also specified for the sludge age, ensuring a tech-nical acceptable range. The sludge age is a quantity representing theresidence time of particles in the Activated Sludge process and it isan important design variable for the Activated Sludge process.Constraints are also imposed for the residence time in digester, forTotal Solids Suspended (TSS) in Activated Sludge reactors and in theincoming sludge to the digester reactor. For all computations the pHin the digestion reactor ismaintained above 7. This is done byaddingbicarbonate to the reactor (buffer effect). The Table 2 summarizesthe constraints and the associated units and range.

The constraint on rejected NH4þ is varying and it is the object of

the parametric optimization procedure, because the removal ofammonium is known to be a strong limiting factor to the overallenergy efficiency of WWTP. The constraint on rejected NO3

� is alsovaried and set to predefined values (8, 12 and 20 gN/m3).

Fig. 6. Optimal electrical autonomy for different values of primary settler efficiencyand as a function of rejected ammonium concentration. The nitrate rejected concen-tration is equal to 20 gN/m3.

4. Results

The parametric optimization procedure has been applied to theflow-sheet reported on Fig. 1. The objective function to maximizewas defined as the electrical autonomy of the WWTP, described bythe following equation:

Eauto ¼_EcogenPNcomp

k¼1_Ekcomp þPNpump

n¼1_Enpump þPNpuo

m¼1_Emmix

(12)

Where _Emmix is the electrical consumption for mixing and operate

the PUO indexed by m. Ncomp, Npump and Npuo are respectively thenumbers of compressors, pumps and PUO involved in the process.Consequently, the optimizer algorithm will compute optimalconfiguration corresponding to a minimal operating electricalconsumption and maximal biogas production (or maximal elec-tricity production by the cogeneration engine, which is equivalent).The cogeneration engine is assumed to be efficient to 30 percentconcerning the electricity production [6]. The thermal autonomywas not directly investigated during the computations. If necessaryit could be included in the objective function or as a new constraint.The electrical autonomy and the electrical consumption are knownto be critical issues of WWTP and the results presented in thispaper focus on electrical aspects. Anyway, most of the conclusionsdeduced from the computations presented in this paper are stillvalid if considering the thermal autonomy.

4.1. Primary settling efficiency as a parameter

The first computations presented have been done by setting theprimary settler efficiency as a parameter varying between 0% and100%. 0% efficiencymeans that the particles incoming to theWWTPare not segregated by the primary settler. The particles concen-trations in the main water flux and in the primary sludge flux arethen equal. 100% efficiency means that all the particles incoming tothe WWTP are sent to the primary sludge and consequently in thedigester. The thickener before the digester reactor ensures that themix of secondary and primary sludge is sufficiently concentrated inall the cases (the particles concentration in the sludge to digest isconstrained to 50 g/l). The results corresponding to the rejectedNO3

� concentration equal to 8 gN/m3 are presented on Fig. 5.As reported, the optimal electrical autonomy is strongly sensi-

tive to the nitrogen concentration at the exit of the WWTP (in theclarified water stream). The plant is non electrical autonomous forhigh N-removal (corresponding to values for rejected NH4

þ inferiorto 10 gN/m3). For low-N removal (corresponding to values forrejected NH4

þ superior to 40 gN/m3) it can be noticed that the planthas a big potential as an energy producer. The computations showsthat the electricity produced could be almost four times the elec-tricity required to aerate the reactors and drive the pumps in theplant. The active constraint in this case is only the constraint onCOD and the objective function become independent of thenitrogen removal (the curves become flat).

Some comments could also be made on the influence of theprimary settling efficiency: The more efficient the primary settler isand the more particulate organic substrates are sent to the digester.In this case, the primary sludge is richer in C-substrate available tothe micro-organisms and consequently the potential of biogasproduction is increased. The electrical autonomy is effectivelyincreased when the primary settler efficiency is increased, but thistrend reverses for efficiencies superior to 50% and for high NH4

þ

removal (see Fig. 5). This characteristic could be linked with the de-nitrification process, as explained in the Section 4.2.

To further investigate this point the same calculations have beendone, except, here the rejected nitrate concentration constraint has

Fig. 7. Optimal nitrogen rates by biochemistry as a function of rejected ammonium concentration in the different reactors (Activated Sludge and digester). The primary settlerefficiency is equal to 100 % and the rejected nitrate concentration is equal to 8 gN/m3.


been increased to 20 gN/m3. The corresponding results are reportedon Fig. 6.

In this case, the primary settler efficiency still exhibits a stronginfluence on the electrical autonomy. But compared to the previouscase an increase of the objective function is noticed for primarysettler efficiency values superior to 25%. For 75% and 100% primaryefficiency the electrical autonomy is more than 100 %.

These results demonstrate that both the nitrification and de-nitrification process by autotrophic and heterotrophic micro-organisms are limiting the overall energy efficiency of the system.The nitrification biological process results in the transformation ofthe NH4

þ ions into nitrate NO3- by consuming some dissolved

oxygen and someelectricity. So themoreNH4þ removal is requested,

the higher the electrical consumption is. To visualise the intensity ofnitrification/de-nitrification in theActivated Sludge reactors and theammonium production in the digester for optimal points, the cor-responding optimal production or consumption by biochemicalreactions of NH4

þ and NO3� species are plotted on Fig. 7.

Fig. 8. Optimal contributions to total ammonium load as a function of rejectedammonium concentration. The primary settler efficiency is equal to 100 % and therejected nitrate concentration is equal to 8 gN/m3.

More biogas is effectively produced by the digester when theprimary sludge is richer in available C-substrate (the primarysettler efficiency is then equal to 100%). But in the same time extraammonium is also produced. This ammonium production is causedby the hydrolysis of the proteins present in the primary sludge sentto the digester, which contains both C and N elements. Theammonium produced is then returned at the entry of the ActivatedSludge process when the sludge outgoing from the digester isdewatered, as shown on Fig. 1.

As the liquid recycling fromdewatering is highly concentrated inammonium ions, the contribution to the total load is quite impor-tant. It can be noticed that the optimal solutions consists of limitingthe size of the digestion reactor in order tomaintain the productionof NH4

þ to reasonable levels (accounting for no more than 25%percent of the total load, see Fig. 8). This is easily checked by plottingthe optimal residence time in the digestion reactor, see Fig. 9.

Another point is that by limiting the size of the digestion reactor,the degradation of carbon substrates is not complete. Consequently,

Fig. 9. Optimal residence time in digester for different values of primary settler effi-ciency and as a function of rejected ammonium concentration. The rejected nitrateconcentration is equal to 8 gN/m3.

Fig. 10. Optimal sludge age for different values of primary settler efficiency and asa function of rejected ammonium concentration. The rejected nitrate concentration isequal to 8 gN/m3.

Fig. 12. Optimal electrical autonomy as a function of rejected ammonium concentra-tion. The primary settler efficiency is a decision variable for the two cases (with andwithout carbon addition).


some organic carbon is sent back to the Activated Sludge process tofulfil the requirements on carbon for denitrifying.

The lack of Carbon in the anoxic reactors for denitrifying is alsocompensated by increasing the sludge age in the Activated Sludgeprocess, as reported on Fig. 10. The optimizer increases the sludgeage when the primary settler efficiency increases. More particulatesubstrate and biomass is then maintained in the Activated Sludgereactors and the consequence is a production of some availableCarbon substrates in the first reactor (the source term is positive),as indicated on Fig. 11. This sludge age increase also has a negativeimpact on the oxygen requirements. As a result, to maintain thepopulation of active micro-organisms, more air must be blowninside the reactors and consequently the electrical energyconsumption for aeration is increased.

4.2. Primary settling efficiency as a decision variable

The results presented in the previous section demonstrate boththe importance of primary settling and the availability of organic

Fig. 11. Optimal C-substrates rates by biochemistry as a function of rejected ammonium coequal to 100% and the rejected nitrate concentration is equal to 8 gN/m3.

carbon in the different reactors: carbon is required for de-nitrification in the AS process but it is also required for biogasproduction in the digestion reactor. It means that the optimal elec-trical autonomyof thewholeprocess is strongly related to the carbonand nitrogen splitting between the aerobic and anaerobic treatment.

In the next computations, the primary settling efficiency was setas a decision variable. The optimizer can now estimate optimumvalues for this efficiency. The others decision variables andconstraints are identical. The optimal electrical autonomy iscomputed for two values of NO3

� concentrations at the exit of theWWTP and the results are reported on Fig. 12.

Compared to the case where the efficiency of the primary settleris fixed a priori, the electrical autonomy is increased (superior forall cases to 50%). The corresponding optimal values for the primarysettler efficiency are reported on the Fig. 13.

As shown, optimal values for the primary settling efficiencyexists and the more ammonium and nitrate removal is required,lesser particulate substrates are sent to the digester. Indeed, boththe ammonium production by the digester and the carbon

ncentration in the different Activated Sludge reactors. The primary settler efficiency is

Fig. 13. Optimal primary settler efficiency as a function of rejected ammoniumconcentration for the cases with carbon addition and without.

Fig. 15. Optimal added carbon flow rate as a function of rejected ammoniumconcentration. The primary settler efficiency is a decision variable.


requirement for denitrifying are limiting the overall energy effi-ciency of the system.

This result appears to be an interesting feature that can beevaluated by model-based and system analysis. As is known, theprimary settling process is not sized by considering the overallenergy efficiency but only by considering the load to treat and thewater quality requested.

In order to further increase the electrical autonomy, the effect ofcarbon addition to the Activated Sludge process has been investi-gated. A source unit has been added to the Activated Sludge process(see Fig. 1) and represent the addition of methanol for enhancingde-nitrification. The added carbon flow rate to the Activated Sludgeprocess is then set as a decision variable. The primary settlingefficiency is still a decision variable. The decision variables and theconstraints introduced in Table 1 and Table 2 are also still valid.

For high N-removal (corresponding to low values for rejectedNH4

þ) the optimal electrical autonomy is greatly increased byadding available carbon for micro-organisms, as reported on Fig. 12.The addition of external carbon to the activated sludge process forde-nitrification allows the optimizer to maximize the primarysettler efficiency (see Fig. 13). In other words, all the particulatesubstrate contained in the influent stream is now sent to thedigester and the biogas production is increased, as reported onFig. 14. The production of ammonium ions by the digestion is still

Fig. 14. Optimal biogas production as a function of rejected ammonium concentrationfor the cases with carbon addition and without. The primary settler efficiency isa decision variable.

a limiting factor for the overall efficiency in this case, as shown onthe Fig. 8. The optimum contribution of digestion to the totalammonium load counts for almost 25 % in the case of carbonaddition. This is greater than the results obtained for the casewithout the carbon addition and this is especially true for high N-removal where the production of ammonium by digestion stronglylimit the overall energy efficiency.

Another interesting feature achieved by running optimizationsis that the exact quantity of carbon needed for satisfying theconstraint on rejected nitrate is quantified, as reported on Fig.15. Asexpected, additional carbon is required for the highest nitrogenremoval. The quantities are quite important (a few tons per day)and some economic costs could be included in the objective func-tion. The optimizer should then be able to determine the optimalquantity of carbon to add to the process, depending on the relativeeconomic costs of electricity and carbon.

5. Conclusions and perspectives

Mathematical models for most of the PUO involved in WWTPhave been developed and implemented on the gPROMS� platform.The resulting sets of equations are solved to compute optimal steady-state configurations. The results presented in this paper focus onelectrical efficiency but others studies are possible. For exampleeconomic costs and/or thermal criterion could be easily included intheobjective functions. Twomechanismshavebeendemonstrated tobe limiting factors to the overall energy efficiency: the production ofammonium by the digestion process and the lack of available C-substrate for denitrifying in the Activated Sludge reactors.

The interest of specialized treatment for ammonium highlyconcentrated streams is highlighted, as well as the interest toprovide carbon substrates form external sources. Wastes fromothers industries could be, for example, very attractive dependingon their bio-degradability. Future work will focus on includingSharon-Annamox [7] process to the models library. A rigorousmethodology to identify models parameters from a real pilot plantis also planned by using the identification parameters and experi-ments design methodology available on gPROMS� software.Model-based analysis seems to be a promising method forimproving energy efficiency in the field of wastewater treatment.Process variables can be optimized and tuned and technologies canbe compared in a rigorous way, especially by including energyaspects in the computations. Investigations concerning the PUOinteractions at system level are also possible and could reveal someunintuitive issues.


Appendix. Tables for plant-wide activated sludge model(parameters settings not included)

Table A-1Plant-Wide Activated Sludge Model stochiometry matrix: soluble components (part 1).

Process jY i/ Component 1 2 3 4 5 6 7 8 9 10 11 12 13

So Ssu Saa Sfa Shva Sva� Shbu Sbu� Shpro Shpro� Shac Sac� Sno�3

1 Dis q1ThOD

2 Hy_Ch q2ThOD 1

3 Hy_Pr q3ThOD 1

4 Hy_Li q4ThOD 1� fsli;fa 1� fsli;fa

5 Ae_Up_Su q5ThOD �1

6 Ae_Up_Aa q6ThOD �1

7 Ae_Up_Fa q7ThOD �1

8 Ae_Up_hVa q8ThOD �1

9 Ae_Up_Va q9ThOD �1

10 Ae_Up_hBu q10ThOD �1

11 Ae_Up_Bu q11ThOD �1

12 Ae_Up_hPro q12ThOD �1

13 Ae_Up_Pro q13ThOD �1

14 Ae_Up_hAc q14ThOD �1

15 Ae_Up_Ac q15ThOD �1

16 An_Up_Su �1 q16ThOD

17 An_Up_Aa �1 q17ThOD

18 An_Up_Fa �1 q18ThOD

19 An_Up_hVa �1 q19ThOD

20 An_Up_Va �1 q20ThOD

21 An_Up_hBu �1 q21ThOD

22 An_Up_Bu �1 q22ThOD

23 An_Up_hPro �1 q23ThOD

24 An_Up_Pro �1 q24ThOD

25 An_Up_hAc �1 q25ThOD

26 An_Up_Ac �1 q26ThOD

27 Up_nh4 q27ThOD 1

28 Dec_Xh q28ThOD

29 Dec_Xa q29ThOD

30 Dec_Xsu q30ThOD

31 Dec_Xaa q31ThOD

32 Dec_Xfa q32ThOD

33 Dec_Xc4 q33ThOD

34 Dec_Xpro q34ThOD

35 Dec_Xac q35ThOD

36 Dec_Xh2 q36ThOD

Table A-2Plant-Wide Activated Sludge Model stochiometry matrix: soluble components (part 2).

Process jY i/ Component 14 15 16 17 18 19 20 21 22 23 24 25

Sh2po�4

Shpo2�4

Snh4þ Snh3Sn2 Sh2

Sch4Sco2 Shco�

3Shþ Soh� Si

1 Dis q1P q1

N q1C q1

H fXc ;Si2 Hy_Ch q2

P q2N q2

C q2H

3 Hy_Pr q3P q3

N q3C q3

H

4 Hy_Li q4P q4

N q4C q4

H

5 Ae_Up_Su q5P q5

N q5C q5

H

6 Ae_Up_Aa q6P q6

N q6C q6

H

7 Ae_Up_Fa q7P q7

N q7C q7

H

8 Ae_Up_hVa q8P q8

N q8C q8

H

9 Ae_Up_Va q9P q9

N q9C q9

H

10 Ae_Up_hBu q10P q10

N q10C q10

H

11 Ae_Up_Bu q11P q11

N q11C q11

H

12 Ae_Up_hPro q12P q12

N q12C q12

H

13 Ae_Up_Pro q13P q13

N q13C q13

H

14 Ae_Up_hAc q14P q14

N q14C q14

H

15 Ae_Up_Ac q15P q15

N q15C q15

H

16 An_Up_Su q16P q16

N �q16ThOD q16

C q16H

17 An_Up_Aa q17P q17

N �q17ThOD q17

C q17H

18 An_Up_Fa q18P q18

N �q18ThOD q18

C q18H

19 An_Up_hVa q19P q19

N �q19ThOD q19

C q19H

20 An_Up_Va q20P q20

N �q20ThOD q20

C q20H

21 An_Up_hBu q21P q21

N �q21ThOD q21

C q21H

22 An_Up_Bu q22P q22

N �q22ThOD q22

C q22H

23 An_Up_hPro q23P q23

N �q23ThOD q23

C q23H

24 An_Up_Pro q24P q24

N �q24ThOD q24

C q24H

Table A-2 (continued )

Process jY i/ Component 14 15 16 17 18 19 20 21 22 23 24 25

Sh2po�4

Shpo2�4

Snh4þ Snh3Sn2 Sh2

Sch4Sco2 Shco�

3Shþ Soh� Si

25 An_Up_hAc q25P q25

N �q25ThOD q25

C q25H

26 An_Up_Ac q26P q26

N �q26ThOD q26

C q26H

27 Up_nh4 q27P q27

N q27C q27

H

28 Dec_Xh q28p

q28N q28

C q28H fbio;Si

29 Dec_Xa q29p

q29N q29

C q29H fbio;Si

30 Dec_Xsu q30p

q30N q30

C q30H fbio;Si

31 Dec_Xaa q31p

q31N q31

C q31H fbio;Si

32 Dec_Xfa q32p

q32N q32

C q32H fbio;Si

33 Dec_Xc4 q33p

q33N q33

C q33H fbio;Si

34 Dec_Xpro q34p

q34N q34

C q34H fbio;Si

35 Dec_Xac q35p

q35N q35

C q35H fbio;Si

36 Dec_Xh2 q36p

q36N q36

C q36H fbio;Si

Table A-3Plant-Wide Activated Sludge Model stochiometry matrix: particulate components.

Process jY i/ Component 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Xc Xch Xpr Xli Xh Xa Xsu Xaa Xfa Xc4 Xpro Xac Xh2Xi Sh2o

1 Dis �1 fXc ;XchfXc ;Xpr

fXc ;Xliq1O

2 Hy_Ch �1 q2O

3 Hy_Pr �1 q3O

4 Hy_Li �1 q4O

5 Ae_Up_Su Yh,ae q5O

6 Ae_Up_Aa Yh,ae q6O

7 Ae_Up_Fa Yh,ae q7O

8 Ae_Up_hVa Yh,ae q8O

9 Ae_Up_Va Yh,ae q9O

10 Ae_Up_hBu Yh,ae q10O

11 Ae_Up_Bu Yh,ae q11O

12 Ae_Up_hPro Yh,ae q12O

13 Ae_Up_Pro Yh,ae q13O

14 Ae_Up_hAc Yh,ae q14O

15 Ae_Up_Ac Yh,ae q15O

16 An_Up_Su Yh,an q16O

17 An_Up_Aa Yh,an q17O

18 An_Up_Fa Yh,an q18O

19 An_Up_hVa Yh,an q19O

20 An_Up_Va Yh,an q20O

21 An_Up_hBu Yh,an q21O

22 An_Up_Bu Yh,an q22O

23 An_Up_hPro Yh,an q23O

24 An_Up_Pro Yh,an q24O

25 An_Up_hAc Yh,an q25O

26 An_Up_Ac Yh,an q26O

27 Up_nh4 Ya q27O

28 Dec_Xh fbio;Xchfbio;Xpr

fbio;Xli�1 fbio;Xi

q28O

29 Dec_Xa fbio;Xchfbio;Xpr


q29O

30 Dec_Xsu fbio;Xchfbio;Xpr


q30O

31 Dec_Xaa fbio;Xchfbio;Xpr


q31O

32 Dec_Xfa fbio;Xchfbio;Xpr


q32O

33 Dec_Xc4 fbio;Xchfbio;Xpr


q33O

34 Dec_Xpro fbio;Xchfbio;Xpr


q34O

35 Dec_Xac fbio;Xchfbio;Xpr


q35O

36 Dec_Xh2 fbio;Xchfbio;Xpr


q36O

Table A-4Kinetics expressions for plant-wide activated sludge model.

N � Process description Reference Process rate rj

1 Disintegration Dis kasdisððXc=XhÞ=ðXc=XhÞÞ þ HasdisXh

2 Hydrolysis Carbohydrates Hy_Ch kashyd;chððXch=XhÞ=ðXch=Xh þ Hashyd;chÞÞXh

3 Hydrolysis Proteins Hy_Pr kashyd;prððXpr=XhÞ=ðXpr=Xh þ Hashyd;prÞÞXh

4 Hydrolysis Lipids Hy_Li kashyd;liððXli=XhÞ=ðXli=Xh þ Hashyd;liÞÞXh

5 Aerobie uptake of sugars Ae_Up_Su km;XhðSsu=ðHae

su þ SsuÞÞðSsu=SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

6 Aerobie uptakes of amino acids Ae_Up_Aa km;XhðSaa=ðHae

aa þ SaaÞÞðSaa=SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

7 Aerobie uptake of LCFA Ae_Up_Fa km;XhðSfa=ðHae

fa þ SfaÞÞðSfa=SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

(continued on next page)


Table A-4 (continued )

N � Process description Reference Process rate rj

8 Aerobie uptake of h-Valerate Ae_Up_hVa km;XhðShva=ðHae

hva þ ShvaÞÞðShva=SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

9 Aerobie uptake of Valerate Ae_Up_Va km;XhðSva�=ðHae

va þ Sva� ÞÞðSva� =SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

10 Aerobie uptake of h-Butyrate Ae_Up_hBu km;XhðShbu=ðHae

hbu þ ShbuÞÞðShbu=SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

11 Aerobie uptake of Butyrate Ae_Up_Bu km;XhðSbu�=ðHae

bu þ Sbu� ÞÞðSbu�=SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

12 Aerobie uptake of h-Propionate Ae_Up_hPro km;XhðShpro=ðHae

hpro þ ShproÞÞðShpro=SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

13 Aerobie uptake of Propionate Ae_Up_Pro km;XhðSpro� =ðHae

pro þ Spro� ÞÞð Spro�

SsÞXhAhco�

3Ao2Anhþ

4Ahpo�

4Iulph

14 Aerobie uptake of h-Acetate Ae_Up_hAc km;XhðShac=ðHae

hac þ ShacÞÞðShac=SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

15 Aerobie uptake of Acetate Ae_Up_Ac km;XhðSac� =ðHae

ac þ Sac� ÞÞðSac� =SsÞXhAhco�3Ao2Anhþ

4Ahpo�

4Iulph

16 Anoxic uptake of sugars An_Up_Su hkm;XhðSsu=ðHan

su þ SsuÞÞðSsu=SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

17 Anoxic uptake of amino acids An_Up_Aa hkm;XhðSaa=ðHan

aa þ SaaÞÞðSaa=SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

18 Anoxic uptake of LCFA An_Up_Fa hkm;XhðSfa=ðHan

fa þ SfaÞÞðSfa=SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

19 Anoxic uptake of h-Valerate An_Up_hVa hkm;XhðShva=ðHan

hva þ ShvaÞÞðShva=SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

20 Anoxic uptake of Valerate An_Up_Va hkm;XhðSva� =ðHan

va þ Sva� ÞÞðSva� =SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

21 Anoxic uptake of h-Butyrate An_Up_hBu hkm;XhðShbu=ðHan

hbu þ ShbuÞÞðShbu=SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

22 Anoxic uptake of Butyrate An_Up_Bu hkm;XhðSbu� =ðHan

bu þ Sbu� ÞÞðSbu�=SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

23 Anoxic uptake of h-Propionate An_Up_hPro hkm;XhðShpro=ðHan

hpro þ ShproÞÞðShpro=SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

24 Anoxic uptake of Propionate An_Up_Pro hkm;XhðSpro� =ðHan

pro þ Spro� ÞÞðSpro� =SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

25 Anoxic uptake of h-Acetate An_Up_hAc hkm;XhðShac=ðHan

hac þ ShacÞÞðShac=SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

26 Anoxic uptake of Acetate An_Up_Ac hkm;XhðSac� =ðHan

ac þ Sac� ÞÞðSac�=SsÞXhAhco�3Ano�

3Anhþ

4Ahpo�

4IulphIo2

27 Uptake of Ammonium Up_nh4 km;XaðSnhþ

4=ðHnh4

þ Snhþ4ÞÞXaAco2Ao2Ahpo�

4Iulph

28 Decay of Xh Dec_Xh kdec;XhXh

29 Decay of Xa Dec_Xa kdec;XaXa

30 Decay of Xsu Dec_Xsu kdec;XsuXsu

31 Decay of Xaa Dec_Xaa kdec;XaaXaa

32 Decay of Xfa Dec_Xfa kdec;XfaXfa

33 Decay of Xc4 Dec_Xc4 kdec;Xc4Xc4

34 Decay of Xpro Dec_Xpro kdec;XproXpro

35 Decay of Xac Dec_Xac kdec;XacXac

36 Decay of Xh2 Dec_Xh2 kdec;Xh2Xh2


References

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[7] van Dongen U, Jetten MSM, and van Loosdrecht MCM, The SHARON�-Anammox� process for treatment of ammonium rich wastewater. WaterScience and Technology, 44 (No. 1) pp 153e160.

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