Stoichiometric deduction of activated sludge process for organic carbon and nitrogen removal

J Shanghai Univ (Engl Ed), 2009, 13(1): 88-94Digital Object Identifier(DOI): 10. 1007/s 141-00-0117-1Stoichiometric deduction of activated sludge process for organic carbonand nitrogen removalLIU Jian-yong (刘建勇)，ZOU Lian-pei (邹联沛)School of Environmental and Chemical Engineering, Shanghai University, Shanghai 20444, P. R. ChinaAbstract The activated sludge proces (ASP) is the most generally applied biological wastewater treatment method. TheASP for the removal of organic carbon and nitrogen can be looked as the combination of eight processes. In order to setup an ASP model, the stoichiometric cofficients should be deduced so that the stoichiometric matrix can be presented.The important assumptions and simplfications behind the model for ASP are enumerated. Using the matrix, mass balanceequation and consistent units, the stoichiometric coeficients in the eight processes are exclusively deduced one by one.Keywords activated sludge process (ASP), stoichiometric cofficients, nitrogen removal, modelNomenclatureSo: axygen demand (gm^ 3)Ss: readily biodegradable substrate (gm^ -3)ASM activated sludge modelXB,A: active autotrophic biomass (gm -3)ASP activated sludge processXB,H: active heterotrophic biomass (gm~bA: decay coefficient for autotrophic biomass (d- ")X; particulate inert organic matter (gm-bx: decay cofficient for heterotrophic biomass (d-1)XND: particulate biodegradable organic nitrogen (gm- 3)COD: chemical oxygen demandfp: fraction of biomass yielding particulate products (dimen-Xp: particulate products arising from biomas8 decay (gm- )sionless)Xs: slowly biodegradable substrate (gm~ 3)ixB: massCOD in biomass (g~-)YA: autotrophic yield (gg~ 1)ixp: mass Masss COD in products from biomass (gg ")Y: heterotrophic yield (g8~ 1)ka: ammonifcation rate (m3 (gd)- 1)7ng: correction factor for A4H under anoxic conditions (dimen-th: maximum specific hydrolysis rate (gg 1)KNHammonia half-saturation cofficient for autotrophic加: correction factor for hydrolysis under anoxic conditionsbiomass (gm-3 )(dimensionless)KNo: nitrate half-saturation coefficient for denitrifying het-A: maximum specifc growth rate for autotrophic biomasserotrophic bioma8s (gm- 3)(d-)Ko,a: oxygen half- saturation cofficient for autotrophicPH: maximum specific growth rate for heterotrophic massbiomass (gm" 3)Ko,H: oxygen half- 8aturation coeficient for heterotrophicIntroductionbiomass (gm~ 3)Ks: half- saturation coeficient for heterotrophic biomassThe ASP is the most generally applied biologicalwastewater treatment technique. In the ASP, a bacterialKx: half-saturation coeficient for bhydrolysis of slowlybiomass suspension (the activated sludge) is responsiblebiodegradable substrate (g~)N: nitrogenfor the removal of pollutants. Depending on the designSALK: alkalinity (mol:L- 1)and the specifc application, an activated sludge waste-water treatment plant (WWTP) can achieve biologicalS: soluble inert organic matter (gm- 3SND: soluble organic nitrogen (gm~ )nitrogen removal and biological phosphorus (P) removal,SNH: ammonia, both the free compound and its saltsbesides removal of organic carbon substances. Ev(gm-3)dently, many different ASP configurations have evolvedSNo: nitrate and nitrite (gm~3)during中国煤化工nistorical evolutionReceived Sept.18, 200; Revised Dec.16, 2007MH. CNMH GA7052Project supported by the Special Foundation of Shanghai Municipal EducCorresponding author LIU Jian- yong, PhD, Assoc. Prof, E mail: hnmljy@163.comJ Shanghai Univ (Engl Ed), 2009, 13(1): 88 -9489of the activated sludge process can be found in [1].(i) The pH is constant and near neutral.Modeling of the activated sludge processes has be-(i) No consideration has been given to changes income a common part of the design and operationthe nature of the organic matter within any given frac-of WWTP2. In 1983 the International Associationtion (e.g. the readily biodegradable organic matter).on Water Pollution Research Control (IAWPRC, nowThat is, the cofficients in the rate expressions have beencalled International Water Association, IWA), as it wasassumed to have constant values.then called, establisbed a Task Group on Mathematical(iv) The efects of limitations of nitrogen, phospho-Modeling for Design and Operation of Activated Sludgerus, and other inorganic nutrients on the removal of or-Processes. Three years later, a model for nitrogen-ganic substrate and on cell growth have not been con-removal activated sludge processes called the Activatedsidered.Sludge Model No.1 (ASM1) was worked out3)] The(v) The correction factors for denitrification are fixedASM1 model can be considered as the reference model,and constant for a given wastewater. It is possible thatsince this model triggered the general acceptance oftheir values may be influenced by system configurationWWTP modeling, first in the research community andbut this is not considered.later on also in industry. Even today, the ASM1 model(vi) The cofficients for nitrification are assumed tois in many cases still the state of the art for modelingbe constant and incorporate any inhibitory efects thatactivated sludge systemsl4i.other waste constituents are likely to have on them.After that， the Activated Sludge Model No.2(vi) The heterotrophic biomass is homogeneous and(ASM2)问，the Activated Sludge Model No.2ddoes not undergo changes in species diversity with time.(ASM2d)6]，and the Activated Sludge Model No.3(vili) The entrapment of particulate organic matter(ASM3)门1 were published in the IAWPRC Scientfic andin the biomass is assumed to be instantaneous.Technical Report Series successively in 1995, 1999, and(ix) Hydrolysis of organic matter and organic nitro-2000. The series of Activated Sludge Models (ASMs)gen are coupled with equal rates and occur simultane-were studied and applied widely, especially in Europeously. .and Americal8-11]. Today models are being used in(x) The type of electron acceptor present does notdesigning, controling, teaching and researching.affect the loss of active biomass by decay.When an ASP model is to be set up, the stoichio-(xi) There are no heterotrophic biomass and au-metric cofficients in the model which set out the masstotrophic biomass in the influent.relationships among the components in the individual(xi) Only ammonia but other kinds of nitrogen areprocesses should be worked out. Once the stoichiomet-imposed in biomass synthesis.ric cofficients are deduced, the stoichiometric matrix(xi) Readily biodegradable organic matter is lookedcan be presented; and then the model can be set up[12].upon the only substrate of the heterotrophic biomasThe first part of this paper will focus on the assump-growth.tions or simplifcations behind the model for ASP. These(xiv) The inert soluble organic matter and the in-model assumptions are often not considered carefully byert suspended organic matter are not comprised in anythe model, although they provide an indication of sit-process. The inert suspended organic matter becomesuations where the models are not valid or provide onlyenmeshed in the activated sludge and removed from thea poor description of the process. The second part ofsystem through sludge wastage.this paper will focus on the stoichiometric deduction(xv) Positive sign represents generation, and nega-approaches of ASP, and the third part will exclusivelytive sign represents consumption.deduce the stoichiometric coefficients one by one.2 Approaches1 Simplifications and assumptions2.1 Setting up the matrixWhen an ASP system is to be modeled, a cer-The concentration of one component is probably af-tain number of simplifcations and assumptions must befected by diferent processes within the system. Themade in order to get the model tractable. Some of themtransformation prnces of Pach component can be un-are associated with the physical system itself, whereas中国煤化工ing a matrix.others concern the mathematical model. The simplif-MHCNMH(the top of the matrixcations and assumptions can be included as followg[13):and prucssses are lII8U 1 ue reftmost column of the(i) The system operates at a constant temperature.matrix. The 13 components are SI, Ss, XI, Xs, XBH,)0J Shanghai Univ (Engl Ed), 2009, 13(1): 88-94XBA, Xp, So, SNo, SNH, SND, XND and SALK, respec-is the utilization of oxygen. Since COD units are usedtively.The indexes i and j are assigned to each com-for both substrate and biomass, and oxygen may be con-ponent and each process respectively. In the ASM1, isidered to be negative COD, continuity requires thatranges from 1 to 13, and j ranges ftom 1 to 8. Thethe oxygen demand equals the net COD removal (sol-elements within the matrix comprise the stoichiometricuble substrate minus cells formed). Ammonia nitrogencoefficients Uij.will be removed from solution and incorporated into cell2.2 Consistent unitsmass.All organic constituents have been expressed as(i) Ssequivalent amounts of COD, likewise, oxygen is ex-From the definition of heterotrophic yield coefficientpressed as negative oxygen demand. The stoichiometric(Yx),cofficients are greatly simplified by working in consis-dSs1 dXB.Htent units.dt YH dtThe unit of alkalinity is mol/L. Incorporation of al-kalinity into the model is not essential, but its inclusionSo, U21= -前is desirable because it explains whereby undue changes(i) XB.HApparently,in pH can be predicted.2.3 Compute approachdX.,B_ dXB.HIn each system with given limits, the basic mass bal-ddtance equation isSo, 051= 1.(ii) Soaccumulation = mass in inflow - mass in outfowOxygen demand equals the net removal of CODB),+ mass formed by reacton3l.that is soluble substrate minus cells formed,dSs_ dSo dXB,HThe mass in inflow and mass in outfow is transporta-tion item and determined by the physics characteristicSo,of the system. The mass formed by reacton item is ex-pressed as the following equation:dSo_ dSs. dXB,Hdt dtrn= SvuP.dXB.HjYH dt1- YH dXp,Hwhere ri is mass formed by reacton, Uj is stoichiometric=-YHcofficients, Pj is process rate of component i.3 Deduction of the stoichiometric coeffi-1- YHcientsHThe ASP can be looked as the combination of eight(iv) SNHprocesses. They are aerobic growth of the heterotrophicFrom the defnition of ixB(3,biomass, anoxic growth of the heterotrophic biomass,dSNHaerobic growth of the autotrophic biomass,“decay” ofit= -ixBthe heterotrophic biomass,“decay" of the autotrophicSo, V101 = -ixB.biomass, ammonification of soluble organic nitrogen,(v) SALK“hydrolysis" of entrapped organics and“hydrolysis" ofThe utilization of 1 mol NHg-N (14 g) correspondsentrapped organic nitrogen. Hereinafter, stoichiometricto the expense of 1 mol SALK3.analysis of the eight processes is worked out, and the sto-ichiometric cofficients of each component are deducted.3.1 Aerobic growth of the heterotrophicdSALK = 1 dSNH__ ixB dXB,Hbiomass中国煤化工Aerobic growth of heterotrophic biomass occurs atMHCNMHGthe expense of soluble substrate and results in the production of heterotrophic biomass. Associated with this14”J Shanghai Univ (Engl Ed), 2009, 13(1): 88-94913.2 Anoxic growth of the heterotrophicSo，biomassdSALK1 dSNH1 dSNo .Such as aerobic growth, it occurs at the expenselt14 dtof readily biodegradable substrate and results in bet-_ixB1- YHdXB.H.erotrophic biomass. Nitrate nitrogen serves as the ter-14T 14- 2.86YH dminal electron acceptor and its removal is in propor-tion to the amount of readily biodegradable substrateixB1- Yremoved minus the quantity of cells formed. Ammo-U132=-t 14.2.86Yunia nitrogen is converted into organic nitrogen in thebiomass. The conversion of ammonia nitrogen to amino3.3 Aerobic growth of the autotrophicacid results in the expense of alkalinity, at the same timethe denitrifcation results in the increment of alkalinity.Soluble ammonia nitrogen serves as the energy(i) Ss .source for the growth of nitrifiers resulting in au-From the definition of Y;(3),totrophic cell mass and nitrate nitrogen as end products.In addition, a small amount of ammonia is incorporateddSs.1 dXB.Hinto the biomass. Oxygen is used in proportion to thedt=YH dtamount of ammonia nitrogen oxidized. The utilizationof ammonia results in the expense of alkalinity, at theSo,same time, the generation of nitrate also results in theexpense of alkalinity.02=看(i) XB,AApparently,(i) XB,HdXB.A_ dXB.AdtSo, 0U63= 1.dXB,H_ dXB,H(i) SodIn this process, the oxygen is used by oxidation ofSo, U52= 1.the ammonia and removal of the cells formed.(ili) SNo .From the definition of YA, the increment of SNo canTo obtain 1 mol electron needs 0.2 mol NOz orbe expressedas去1 dXB.s{3)0.25 mol O2同，that is, 1 g NO3-N corresponds toFrom the reaction, NH3+2O2=HNO3+H2O, we can0.2x2 =2.86 g O2.know that 14 g NH3-N is equivalent to 64 g O2. Thatis, 1 g NH3-N is equivalent to 4.57 g O2. The amountof oxygen used by oxidation of the ammonia isdSvo1 dSo__ 1- YH dXB.Hdt 2.86 dt 2.86YH dt4.57_ dXB,A不dtU92=-dSo __ 4.57dXB.A + dXB.A__ 4.57- YA dXB.A2.86YH .dt一-有dtYA(iv) SNH4.57- YAFrom the defnition of ixg3),dSNH __ ;r。 dXB.H(ii) SNoat=-ixB-From the deinition of YAB, .1 dXB.ASo, V102 = -ixB.(心) SALK中国煤化工The utilization of 1 mol NH3-N (14 g) corresponds toTMYHCNMHGthe expense of 1 mol SALK, the utilization of 1 mol NO3-N (14 g) corresponds to the increase of 1 mol SALK3.V93可92J Shanghai Univ (Engl Ed), 2009, 13(1): 88 94(iv) SNH(i) XB,HPart of it is used by the synthesis of autotrophicHeterotrophic biomass decreases in this process ap-mass, and the other is oxidized into nitrate.parently, so, U54 =-1.From the definition of ixB3, the part used by the(ii) Xs .synthesis can be expressed as -ixB DA . The part oxi-Part of it is converted into Xp, the other is converteddized into nitrate can be expressed as去dxg▲3). Thereinto Xs3). Therefore,fore,dXs_ dXB.H_ dXp=(1-. ,)Kx.B.dSNH__i. dXB,A_. 1 dXB.adt dt dtdtdt YA dtSo,=(-ixB-l )dXBA.v44=1-fp可厂dtSo，(iv) XNDFrom the definition of ixg(3), the organic nitrogen1V103= -ixB -YA 'in heterotrophic biomass can be expressed as ixBdIM.From the definition of ixp and fp3), particulate inert or-ganic nitrogen in products arising from biomass decay(") SALKThe utilization of 1 mol NH3-N (14 g) correspondscan be expressed as fpixp af . So,to the expense of 1 mol SALK, and the generation ofdXND= ixBdXB.H- fpixn1 mol NO3-N (14 g) corresponds to the expense of 1 molltItSAL.3]. So,)dXB.H= (ixB - fpixp)dSALK_ 1 dSNH_ 1 dSNo14 dtixB__ 1 \ dXB,A_ 1 dXB,A=14 14YA)it 14YA dtV124 = ixB- fpixp._ixB__1\dXB,A.3.5 "Decay” of the autotrophic biomass14-灭)The decay of the autotrophic biomass is handledin exactly the same manner as the decay of the het-erotrophic biomass.ixB_ 1(i) XpV133 = -14- YA'From the definition of fpB,3.4 "Decay” of the heterotrophic biomassdXp_ , dXB,AThe death-regeneration concept of Dold, et al. isdused as fundamental of the decay of heterotrophicbiomassl4l. Decay acts to convert biomass to a com-bination of particulate products and slowly biodegrad-075= fp.able substrate. No loss of COD is involved in this split(i) XB,Aand no electron acceptor is utilized. Decay continues atAutotrophic biomass decreases in this process appar-a constant rate regardless of the environmental condi-ently. So, U6s=-1.tions (i.e. bH is not a function of the type of electron(ii) Xsacceptor or its concentration).(i) Xinto Xs[3]. Therefore,From the definition of f@,dXs = dXB.A _ dxp =(1- j,)dXB.A.dXp =。dXB.H_dt中国煤化工:CH.CNMHGFrom tne aennition oI axB", tne organic nitrogen in074= fp.heterotrophic biomas can be expressed a8 ixB.dI^.J Shanghai Univ (Engl Ed), 2009, 13(1): 88 -9493From the definition of ixp and fp3), particulate inert or~3.8 "Hydrolysis” of entrapped organic ni-ganic nitrogen in products arising from biomass decaytrogencan be expressed as fpixpXa-A . So(i) SNDIt increases in this process apparently. So,dXNDdXB,AdXB,A，dt= ixB一fpixpV118= 1.= (ixB- fix)HXBA.(i) XND .It decreases in this process apparently. AndSo，dXND__ dSNDU125 =ixB - Jpixp.3.6 Ammonification of soluble organic ni-So, V128 = -1. Thus, all vij have been deduced.4 ConclusionsBiodegradable organic nitrogen is converted into am-The ASP for the organic carbon and nitrogen remonia nitrogen. The increase of ammonia nitrogen removal can be looked as the synthesis of eight processes.sults in the increase of alkalinity.The stoichiometric cofficients set out the mass relation-(i) SNHIt increases in this process apparently. So, 0V106 = 1.ships among the components in the individual processesof ASP. The concentration of one component is probablyaffected by different processes within the system. TheIt decreases in this process apparently, and,transformation process of each component can be un-dSNp__ dSNHderstood easily and directly by using a matrix. Whendan ASP model is to be set up, the stoichiometric co-efficients should be deduced so that the stoichiometricSo,matrix can be presented.All organic constituents have been expressed as016=-1.equivalent amounts of COD. Likewise, oxygen is ex-pressed as negative oxygen demand. The stoichiometric(ii) SALKcofficients are greatly simplfied by working in consis-The generation of 1 mol NH3-N (14 g) correspondstent units.to the increase of 1 mol SALK3). So,The main principal of the stoichiometric deduction ineach system with given limits is the basic mass balancedSALK__ 1 dSNHequation.14 dtWhen an ASP system is to be modeled, a cer-So, .tain number of simplifications and assumptions mustbe made in order to make the model tractable. Some1V136 =14of them are associated with the physical system itself,whereas others concern the mathematical model.3.7“Hydrolysis” of entrapped organicsReferences(i) SsIt increases in this process apparently. So, 027= 1.[1] JEPPSSON U. Modelling aspects of wastewater treat-(i)Xsment processes [D]. Doctoral Dissertation, Sweden:Lund Institute of Technology, 1999.[2] GERNAEY K V, VAN LOOSDRECHT M C M, HENZEdXs_dSsM, et al. Activated sludge wastewater treatment plante of the art [J]. 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Water Sci Technol, 2002, 45(6):127-136.(Editor CHEN Hai-qing)中国煤化工MYHCNMHG