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On the modelling and simulation of a BNR activated sludge process based on distributed parameter approach
e>
Pergamon
War. Sci Tech Vol. 39, No.6, pp. 79-88, 19991999IAWQ
Published by ElsevIer Science lid Pnntcd ,n Greal 8nlaon All nghts teSefVed
pn: S0273-1223(99)OOI25-0
0273-1223199 520.00 + 0.00
ON THE MODELLING AND SIMULATION OF A BNR ACTIVATED SLUDGE PROCESS BASED ON DISTRIBUTED PARAMETER APPROACH T. T. Lee*. F. Y. Wang* and R. B. Newell*'·· • Computer-Aided Process Engineering Centre, Department o/Chemical Engineering. St. Lucia 4072. Brisbane. Australia .. Advanced Wastewater Management Centre, The University o/Queensland, St. Lucia 4072, Brisbane, Australia
ABSTRACT A computational algontlun, based on an orthogonal collocation approach is developed to simulate a BNR achvated sludge process consisting of anaerobic, anoxIc and aerobic zones in a back-to-back scheme. The hydrauhc model employed in this study considers backmixmg or intermixing, which can represent the actual process more accurately than the ideahsed flow schemes commonly employed for modelling and/or deSIgn of the activated sludge bioreactor. The kinetic model of the International Association on Water Quality (IAWQ) - Activated Sludge Model No.2 (ASM No.2) was reduced to submodels representtng the anaerobiC, anoxIC and aerobIC zones. Validation of simulated results agamst pilot-scale expenmental data suggested that the new computanonal algorithm is able to predict the behaViour of components of mterest reasonably well despite uncertainties With processes and parameters related to phosphorus accumulating orgamsms. Predicted transient properties may be gainfully employed for IJ11provement to the operation and control of the process. to 1999 IAWQ Published by Elsevier Science Ltd All rights reserved
KEYWORDS BNR activated sludge process; distributed parameter; orthogonal collocation; axial dispersion; ASM No.2. INTRODUCTION The activated sludge process traditionally developed for the oxidation of carbonaceous materials to carbon dioxide, biomass and water has during the recent decades been extended to allow nitrogen and phosphorus removal. Under mounting pressure of problems caused by eutrophication, design and construction of fullscale biological nutrients removal (BNR) activated sludge processes have moved ahead, despite of the lack of mechanistic understanding of the process, in particular biological phosphorus removal and the related scientific research. Evidently, mathematical models in conjunction with prototype models such as pilot plants are important not only for optimising design but also for improving operation and control of the BNR processes. Much of the work done on BNR activated sludge modelling in recent years has been largely concentrated on improving the kinetics of the process. Process hydraulics on the other hand receives less attention and its importance has often been overlooked. The continuously stirred tanks in series (CSTR-in-series) technique (see eg. Lee et ai" 1997a) is frequently employed to model the hydraulics of continuous channelled-bioreactors due to its simplicity. Nevertheless, 79
80
T. T. LEE et al.
employment of the CSTR-in-series model to predict the transient properties of bioreactors is thought to be rather crude and could be misleading in some cases. For less than 2 tanks, the CSTR-in-series model predicts an immediate rapid rise in the exit concentration, which is incorrect. In such a case, the axial dispersion theory originated from Chemical Engineering (Levenspiel, 1972) may be applied to the BNR system. A pioneering tracer study on the activated sludge process by Murphy and Timpany (1967) showed that their dispersion model appear to fit the experimental data significantly better than either equi-size CSTR-in-series or unequal sized CSTR-in-series models. In this study, we shall formulate distributed parameter models for the BNR activated sludge process based on the axial dispersion theory and reduced-order kinetic models of the Activated Sludge Model No.2 (ASM No.2), recently developed by Henze et ai. (1995). Using the global orthogonal collocation (GOC) technique and based on our previous study on a distributed parameter model for carbon-only removal activated sludge process (Lee et al., 1997b), we shall introduce a new numerical algorithm for the BNR activated sludge process in this study. Steady-state and dynamic simulation results are compared with experimental data of an existing BNR acttvated sludge pilot plant. The results of this study should provide a very important contribution to the hydraulics ofBNR activated sludge processes. MATHEMATICAL MODEL OF BNR ACTIYATED SLUDGE PROCESS HydrauUc and kinetic model The practical continuous channelled-reactor such as the activated sludge bioreactor has demonstrated some degree of backmixing or intermixing, stagnant regions and shortcircuiting or channelling. Failure to consider this nonideality may lead to gross error in design (Levenspiel, 1972). According to the classical axial dispersion theory, nonideality within a flowing reactor may be largely accounted for by considering only backmixing or intermixing. Some recent industrial appUcations of the axial dispersion theory are modelling of bubble and packed columns (Degaleesan et ai., 1996; Romanainen, 1997). The original kinetic model of the ASM No. 2 is reduced such that 3 separate matrices representing the anaerobic, anoxic and aerobic processes are obtained. Chemicals for precipitation of phosphorus are not used in this study and hence not considered. Soluble and particulate inerts, which do not take part in the bioreaction, are removed from the models. Total suspended solid is essentially a summation of all particulate components and is therefore removed. The final reduced order models of the ASM No. 2 consists of 8 processes and II components for the anaerobic reactor; 11 and 12 processes and 13 components each for the anoxic and aerobic reactors respectively. While there exists conflicting evidence in the literature concerning the fate of nitrate in biological phosphorus removal, our pilot plant experience indicates that there has been a consistent net reduction of nitrate and phosphorus in the anoxic zone. This finding which is in good agreement with a number of workers, recently reviewed by Baker and Dold (1996) suggested that some PAOs can use nitrate as an electron acceptor in the absence of oxygen for oxidation of stored poiy-fJ hydroxy aikanoates (PHA). The stoichiometry and process rates for denitrifying PAOs are incorporated into the reduced-order ASM No.2 for the anoxic reactor, thus the original ASM No.2 is slightly modified. Mass balance Based on the axial dispersion theory, a general mass balance equation for a component, Cj within a plug flow reactors with dispersion model is given by:
ac, = iii
I (I-;;;ij'iT'""a' c, -ac) a:-
HRT
+ reae/Ion + external mass transfer
(1)
where Pe is the Peclet number of the system; z is the dimensionless length of bioreactor and HRT, the hydraulic retention time of fluid in a bioreactor is defined as volume ofbioreactor to total inlet flow. Equation (1) is used in conjunction with the reduced-order reaction kinetics of the ASM No.2 to model the behaviour of components within the compartmentalised anaerobic, anoxic and aerobic zones. Example of mass balance for nitrate at the anoxic zone is formulated as follows:
BNR achvated sludge process as HO , dt
= _1_
(....!.- a'SH", _ aSHf),) _ (I -
HRT' Pe
az'
dZ
YH) (
2.86YH ,., •.,
+
/lH.'
)+
81
(2)
/l,."
where:
Mass balance equations for the remaining components may similarly be written, based on equation (I) and the reduced-order kinetic models. An identical Peclet number has been assumed for all the components investigated. Justifications for this assumption are detailed in Lee et al. (1997b). Additional equations, describing the inlet and outlet flow conditions are required in order to solve equation (2). In this study, the following Danckwert's boundary conditions are employed:
..!-.
dC = C _ C
Pe' dz
, UPP'
z = 0 "if t
z = I "if t
(3)
(4)
where C"ppr is the approach concentration to bioreactor in mg/!. Equations (3) and (4) are applicable to all the components under investigation. Models ofauxilia[y equipment The returned activated sludge (RAS) tank and the non-aerated compartment of the aerobic zone are assumed to be well-mixed, i.e. modelled as simple lumped-parameter schemes. The RAS tank and the unaerated compartment models used the kinetics of the anoxic and the aerobic zone. Dynamics of sludge thickening have been ignored in this study. The sludge concentration at bottom outlet of settler is assumed to be directly proportional to its concentration at the inlet (Olsson and Andrews, 1978). A NEW NUMERICAL ALGORITHM FOR DISTRIBUTED PARAMETER BNR ACTIVATED SLUDGE PROCESS The Monod-type kinetics appearing in most of the rate equations in the ASM No.2 makes it impossible to derive analytical solutions. Employment of numerical technique is therefore inevitable. In this work, we employed the global orthogonal collocation (GOe) technique to reduce the partial differential equations (PDEs) to a coupled system of ordinary differential equations (ODEs). This technique was shown to give relatively better numerical accuracy than the commonly-employed finite-difference techniques (Villadsen, 1978). On the basis of a computational algorithm developed earlier (Lee et al., 1997b), we now extended the technique to model the BNR activated sludge process. Applying orthogonal collocation to equation (2) we have: dS •.j
1 (1-IBj"SHO,.,-IA""SHO", H+' H+' ) Y.) ) --286Y (/l.,I.I+"'H.,., +JJ,.o,j
HO --=--. dt HRT
(1-
Pe '.1
'.1
.
H
(5)
The Monod terms for f.lH.lj , f.lll.lj and f.lPAOJ in equation (5) are essentially the same as in equation (2) with addition ofa subscript) in all state variables.}=1 to N; N is the number of internal collocation points. A and B are the orthogonal collocation matrices for the first and second order PDEs. Similar equations can be developed for other components in the BNR model of anaerobic, anoxic and aerobic zones. Collocation on the generalised Danckwerts boundary conditions for the inlet and exit ofbioreactor results in Equations (6) and (7) are applicable to all the components under investigation. N.I
N+I
AN+,.•o,cI A'.rC, + Pe.C.",)- A,.Nolk ANo1J 'C,) c, = ,., '.l A"N+2AN+ll - A N + 1.N + 1 ·(A'.1 -
P~)
(6)
I. T. I.U:
,'(III.
('OMI'IIIA IlONA!. STRATEeiY SIL';ldv-,Llle Slnlldalioll or Ihe di'lrihuled paramclcr IlNR activated sludgc modd was carried oul hy simult;1l1v\Hlsly L'\'aluatin),: rvsldues or Ihv discrCliscd m;JSS h;d;JIlCV vLJlwlions (such as cLJuation (5»); eqllatlons lle'cnhing pl'lleess houndary vonditions (vqllations (11) amI (7)) amI eqlIalions flJr calculating sludge Ihiekemng. slrvam mixing and splitling, This means that Ihe time derivativv terms in the mass h;danev vqllatiolls arv svl 10 Ino, i,e, rvducctl to algchraie vquations, Altcrnatil'Clv. a di ITerenlial-algehraic eqllatlon IJ)."d') sohn can hv used to simlllaiv the elltirc procvss IIntil dynamics or eomponvn{ dies Ollt. i,e, sleady-sl;tlv s"llllion has reached, Sol III ions li'om the stcady-statc simulation hecomc Ihc Initial conditions Illl' dynamic simllialions, .II. ()AI' solvcr is thcn IIsed 10 integralc the ODb and simulwneollsly soh'ing other algvhLlie vqllaliolls, All L:\lmputational work were accomplished IIsing IM13US ( t:well and Camcron. I')') I), an v'lllation-hascd dynamic sinwlatitln package, MODI:!. V AI.1DATION Thc' l'olliIHllatlon;d algorithm t1vleloped in Ihis slUdy \\ ill ntlw he applivd 10 mod<:l an cxisting Llllltinllous pilot-s,'ale IlNI< ;Iclivaled silldgc plant at the Liverpotl' Scwage Treatmcnt plant in Sydncy, Australia, The pilol-planl IHocl'sses a L'onstanl flo\\' or ahollt 70 Iitrcs pcr hour or scrcened. lkgriltcd scwage with ahoul 1(1(10 Iilrl's l'apacity in thl' ma\ll hior<:actors. The plant sci-Up is <:sscnlially simil;tr 10 Figur<:, I. Sewage used In thiS stlltl\ "as nllllliCipal wastewater, sOllrced rrom a Itdl scale wast<:water treatmcnl plant located at the ~;lIlll'
SI!1..:.
Validalion or the distrihulctl param<:lcr BNR activated sludge nwdd procccded in 4 stages: (I) I-I'aslcwatcr ehar:leterlsatlt>n ttl lktermine al'crage influent conccntration or components of intt:resl, (2) r<:t<:ntion tillle dlSlrihlltltHI (I< Ill) stndies 10 characlcrise tank hydraulics. (3) application of the nUlllcrical algorithm to pl'l'I"1'I1I ,'lL'adl'-slatc simulation to match slnlulated rcsults at various collocation points with a sct or steadyslalL' npl'l'lllIl'nlal t1;lta at cOlTespundtng spatial positions along thc hinreac\llrs, This is aecllmplished hy cdihrating paramclers or high uncertainty such as thosc related to PAOs, i.e, maximum rale of lermcnlation ('flo'!; ralL' L'onstalll I,'r storage or I'IIA ('1"h,,); rate constant IiII' storage Clr poly-phosphate (PI') (lj",,) and ratc l'onslanl 1(,1' Ivsis of I'A() (h",,), Ikn/.e ,'I III, (I')l))) suggcsted that ehanges to the n:duction factor for ,knllrilieallon (Ih".) may hc ncccssary I(,r moddling of Ihe anoxic I.onc, (4) applic:J1ion or the nllmerical ;t1gorililin ;1I1d thL' rL's"lts or ( I), (~) and (~) to simulate dynamics or components in one of the lones, under dlll,:reni l'olHlltit>ns and lL'st their I'alicilty againsl dynamic experimental I'(;sults,
__"ri,
I
-t
NOvo'....
HO P
RTI l l'.\pl'l'lllIenh wnL' l'onduclL'd to naluatc Ihc Pcckt numhcrs which arc singk-paramctcrs that "har,,,'ll'l'lSl' Ihc' hl'tlr;utllcs t>I' hioreactors al thcir rL'sp''l'li\,; 1'"1l'S, (llll'-shot Rhodamine tracn was Intlcpcndl'llllv Inlroduced to 'hl' inlet or the ;lnaerohiL'. ;lIltl.\ie and acrohie loncs, Samples werc' collectcd at IhL' tlullel tll eal'll Itlt1e IInder IIlvesti"ation and an;t1l'svd I"l' traccr concentration, I'xpL'rimcnts Illr stl'adysl:,tl' valHbt'tlll tlf the nlo,lel arc as lililows: When til~' planl is in stcady-stalc condition, i.c, all flOll's with;n
BNR activated sludge process
83
the plant are kept constant and routine monitoring of the influent wastewater fed to the plant showed consistently stable influent qualities, samples are collected at various spatial positions within each bioreactor zone for routine analysis of the components of interest. Experiments for dynamic validation of the model were conducted under three different conditions at the anaerobic zone of the pilot-plant, i.e.: • • •
Experiment A: Step changes to influent flowrate from 70 IIhr to 140 IIhr for 90 minutes, before returning the influent to its original flow. Experiment B: Step changes to the return activated sludge (RAS) flowrate from 44 IIhr to 98 IIhr for 90 minutes, before returning the RAS to its original flow. Experiment C: Step changes to the influent acetate from 100 mg CODII to 300 mg COD/I by introducing external acid dosages for 90 minutes.
For all dynamic validation experiments, samples were collected at every 10 minutes at the outlet of the second compartment, within the anaerobic zone. RESULTS AND DISCUSSION Waslewater characterisation COD fractionation for components of interest has been done as follows: • • •
fennentation products, considered to be acetate (SA), were estimated from measurement of individual acids ie : acetic, propionic, butyric and valerie acids. fennentable, readily biodegradable organic substrates (SF) were calculated from estimated biodegradable soluble COD (SCOD) and SA. The estimated biodegradable SCOD is assumed to be the measured SCOD less the estimated inerts, taken to be effluent SCOD measurement. Slowly biodegradable substrate (Xs) was evaluted from OUR test results.
Biomass in the influent was not characterised but the fractions are needed in order to explain the bloom and the wash-out of certain groups ofmicro-organisms (Henze et al., 1995). Heterotrophic organisms (XH) are assumed to be 15 percent of the measured total COD, which is within the range recommended by Henze (1992), Henze et al. (1995) and which is also used by other workers (e.g. Johansson, (994). Characterisation of nutrients unlike COD or biomass is rather straightforward since the components of interest, that is ammonia-nitrogen (SNH4) and soluble phosphate (SPQ4) assumed to be orthophosphate, are measurable. Nitrate and nitrite nitrogen (SN03) in the influent is usually negligible and assumed 10 be 0.1 mg Nil in the simulation. Bjoreactor hydraulic characterisation The dimensionless tracer's concentration (Cal at the outlet of each zones expressed in tenns of the Peclet number and dimensionless time (()) can be approximated by the following expression: C
1
• '" 2'J1C8(1 / Pel
( -(1- 8)' ) exp 48(1/ Pe)
(8)
Derivation and shapes of curves described by equation (8) are detailed in Levenspiel and Smith (1957). The results of RTD studies in this work are shown in Figure 2. The aerobic zone is considered to be well fitted for an axial dispersion model with a Peclet number of 2.5. On the other hand. dispersion models for the anoxic and the anaerobic zones are rather poorly fitted at the 'second half of the experimental data. This is attributable to the fact that recycled tracer was not accounted for in equation (8) and furthermore. some difficulties were encountered in collecling samples al the outlet of the anaerobic zone, which is in fact the first compartment of the anoxic zone. On the other hand, fitting of the models with a Peclet number of I and 3.5 to the 'first half of the experimental data are considered to be fair. This is largely because the tracer had not yet recycled during this period. Since the evaluated Peclet numbers of the bioreactors are not considered
84
T. T. LEE el al.
to be too large for this process (Arceivala, 1981),5 collocation points should be sufficiently accurate for simulation with the GOC algorithm . •7
.0 os
I·· t.. .
is
II
"
"
"A
" os
.. -2
U
07
...
...
l~·
.
10.1 II
OJ
1.1
-2
U
3
U
.
Figure 2. Evaluatlo nofPeciet number ofbioreact ors using correlation of Levensple
l and Smith (1957).
Steady-state simulation Parameters related to PAOs ie qr., qpha, qpp and b pp considered to be highly uncertain (Henze et al., 1995) are 'optimised' such that simulated steady-state results and experimental data are fairly-well matched. The value of parameters used in this work compared to Henze et al. (1995) is given in Table I. In order to obtain a reasonably good fit to the nitrate profile in the anoxic zone, our simulatio n experience suggested that 'llN03 should be reduced, contrary to the suggestion by Henze et al. (1995). Other parameters are kept identical to the values suggested by Henze et al. (1995) since it is expected that they are reasonably stable. The fate of 5N03 at various zones are shown in Figure 3. Evidently, there is a net reduction of this component throughout the anoxic zone as predicted since the modified kinetic model of the ASM No. 2 allows for denitrification by PAOs, at the expense ofPHA. Since the concentration of predicted SNOJ is slightly higher than the experimental data close to the outlet of the anoxic zone, consequently the predicted 8N03 concentration along the aerobic zone is correspondingly higher. Difficult y arises in improving profiles of SN03 further due to the high coupling of the processes within the different zones. Our simulation experience indicated that small changes to the value of parameters such as qpp and qph affects the simulated results considerably.
BNR activated sludge process
85
ano)Cjc
anaerobic
••roble
t2
'2
12
'0
'0
'0
8
8
6
6
4
4
4
2
2
2
o o~-O....-Oo!'.';-5-"0--....,
°0
dImensionless length
0.5
0
0
0
0
°0
,
0
0.5
1
dirnenalonlo•• length
dimenaionht•• length
Figure 3. Steady-slale profile OfS'Ol at the anaerobic. anoxic and aerobic zones.
Table I. Optimisation of fA WQ parameters PARAMETER qpha qpp bpp
T)"".'
Henze et al. (1994) 0.125 0.0625 0.0417 0.8
This work 0.14 0.031 0.001 0.2
Unit g COD/g COD/hr g COD/g COD/hr hr- I g PP/g PAO
Dynamic simulation Location of the sampling point within the anaerobic zone of the pilot-plant corresponds to collocation point no. 3 of the numerical algorithm. Simulations were performed on the entire plant, allhough only the anaerohic zOlle was investigated. Simulation results compared with data from experiment A for a step change of influent flowrate are shown ill Figures 4 and 5. Evidently, the model predicts dynamics of acetate and soluble phosphate remarkably well. The components dynamic behaviour are as expected since increased influent flowrate means that the HRT within the system drops. Consequently, the rates of acetate uptake and soluhle phosphate released by PAOs arc reduced. It is also expected that concentration of all other particulates will also be reduced due to the decreased residence time.
1·-·
00
00 70
~
r
!
J
00
40
20
to 0
Fig'lfe
-+.
0
20
00
eo
tOO
TIme.
"*'
uo
tOO
Effect of mfluent flow step to the dynamics of SA at the outlet nf 2nd compartment in anaerobic zone.
I T. LEE ('/ nl. Soluble phoaphl!l11l1 concentration V. time
30
.lll'"
1:llt.TI 01" influl'tlt
~tl'P
n(H\!
to the dyn:lITIICS ofSI'()4 at the outlet of 2nd compartmellt In ..t nat'robic zon Acel"te conc9nlratlon Vs limo
- ----r
-------,--------, - - -
[-'-~---J -- p'."".O o>
><
°o::-----;!:;;---:;:;---,;;;---.;;;--~w;;;o;--;-;;;----;-::;;-~~~-~:;;_-~ Time min
I,PUll' (I.
I·j kct
01 IllllUl'1Jt
S\ sll'p
10
the dynamics of \\ at the outlet of 2nd compartment
III ;:mJc'whK :lone.
Soluble phosphat. concanlrallon Vs time
70
-- -- .
I-~'----T'--~---- r"
---,-----------,--.-
-=_=...==='=P='=.d="='.'=d==;-l
r-==.-'
~_ __
experiment
65
40
1!'lIll'
I
I, ni.'ll
_-"-
o
.
:20
(It 11l11Ul'lIt
S\
.l..
...L
40
60
',{l'p 10
~J
80
_....L.~_~_.L.
100 Time, min
Ihe d~!nJIllI(~ III Sj', i~ Jt
1.20
till'
1. _ _
140
'"0
200
outiL'! of 2nd UlIl11xlrtment
In JnJLTOhlL: /Ullt
T. T. LEE et al.
J-.
-
..-
Figure 5. Effect of influent flow step to the dynamics of SPO
'00
f
I
eo
00
aD
'0
00
MJ
100 'Tlnw. min
120
140
100
,eo
Figure 6. Effect of influent SA step to the dynamics of SA at the outlet of 2nd compartment in anaerobic zone.
_ , ._ _nv._ 7or-..,.---.---;":=:":";~:::""'--r--;:I::==:::c==::r::::::;;l
1·-·
.
eo
50
•• "O~--:..; ---:.. f=---;;IO~--OO;;;-----;';OO;--~''':O-',;"O--;:,,,:o-,,,,,:,,O-~_ - . - . mln
Figure 7. Effect of influent SA step to the dynamics of Spo< at the outlet of 2nd compartment in anaerobic zone.
88
T. T. LEE et al.
To reflect the reality of full-scale plants, verification of the model, following diurnal variation of influent flows and concentration of components of interest should be conducted, before using it for design of new plants or improving operation and control of full-scale plants.
REFERENCES Arceivala, S. J. (1981). Wastewater Treatment and Disposal. Marcel Dekker, New York. Baker, P. S. and 001<1, P. L. (1996). COD and mtrogen mass balances m activated sludge systems. Wat. Res., 19(2), 633-643. Danckwert, P. V. (1953). Contmuous flow systems, dIStributions of residence times. Chem Engng. SCI., 1, I-B. Degaleesan, S., Roy. S., Kumar, S. B. and Dudukovic, M. P. (1996). Application of the plug flow WIth axial dispersIOn model for continuous polymenzation In a pulse packed column. Chern. Engng SCI., St( I0), 1967-1976. Henze, M. (1992). Charactenzatlon of wastewater for modelling of activated sludge processes. Wat. Sci. Tech., 15(6), 1-15. Henze, M., Gujer, W., Mmo, T., Matsuo, T., Wentzel, M. C. and Marais, G. v. R. (1995). Activated Sludge Model No.2. IAWQ Scientific and Technical Report No.2, IAWQ, London. Lee, T. T., Wang, F. Y. and Newell, R. B. (1997a). A generalised procedure for modelling and snnulation of activated sludge process based on lumped-parameter approach. J. Env. Sci Health, PART A - Env Sci. Engng, 32(1), 83-104. Lee, T. T., Newell, R. B. and Wang, F. Y. (1997b). Dynarmc modelling and simulation of activated sludge process using global orthogonal collocation approach (submitted to Wat. Res.). Levensplel, O. and Smith, W. K. (1957). Notes on the diffusion-type model for the logintudinal mixmg of fluids in flow. Chem. Engng. SCI., 6, 227-233. Levenspiel, O. (1972). Chemical ReactIOn Engineering. John WIley & Sons Inc., New York. Murphy, K. L. and Timpany, P. L. (1967). Design and analySIS of mixing for an aeration tank. J. Santt. Engng Div., Am. Soc. Ov. Engrs. 93(SA5), 1-15. Newell, R. B. and Cameron, I. T. (1991). NIMBUS Users' gUIde, Dept. ofChem. Engng. The University of Queensland. Olsson, G. and Andrews, J. F. (1978). The dIssolved oxygen profile - A valuable tool for control oflbe activated sludge process. Wat Res., 11,986-1004. Romanamen, 1. J. (1997). Numericalapproach to modeling of dynamic bubble columns. Chern. Engng. Proc., 36(1), 1-15. V.lladsen, J. and Michelsen, M. L. (1978). Solution ofDifferential Equation Models by Polynomial Approximation. Prentice Hall, N.J.
Pergamon
War. Sci Tech Vol. 39, No.6, pp. 79-88, 1999
Published by ElsevIer Science lid Pnntcd ,n Greal 8nlaon All nghts teSefVed
pn: S0273-1223(99)OOI25-0
0273-1223199 520.00 + 0.00
ON THE MODELLING AND SIMULATION OF A BNR ACTIVATED SLUDGE PROCESS BASED ON DISTRIBUTED PARAMETER APPROACH T. T. Lee*. F. Y. Wang* and R. B. Newell*'·· • Computer-Aided Process Engineering Centre, Department o/Chemical Engineering. St. Lucia 4072. Brisbane. Australia .. Advanced Wastewater Management Centre, The University o/Queensland, St. Lucia 4072, Brisbane, Australia
ABSTRACT A computational algontlun, based on an orthogonal collocation approach is developed to simulate a BNR achvated sludge process consisting of anaerobic, anoxIc and aerobic zones in a back-to-back scheme. The hydrauhc model employed in this study considers backmixmg or intermixing, which can represent the actual process more accurately than the ideahsed flow schemes commonly employed for modelling and/or deSIgn of the activated sludge bioreactor. The kinetic model of the International Association on Water Quality (IAWQ) - Activated Sludge Model No.2 (ASM No.2) was reduced to submodels representtng the anaerobiC, anoxIC and aerobIC zones. Validation of simulated results agamst pilot-scale expenmental data suggested that the new computanonal algorithm is able to predict the behaViour of components of mterest reasonably well despite uncertainties With processes and parameters related to phosphorus accumulating orgamsms. Predicted transient properties may be gainfully employed for IJ11provement to the operation and control of the process. to 1999 IAWQ Published by Elsevier Science Ltd All rights reserved
KEYWORDS BNR activated sludge process; distributed parameter; orthogonal collocation; axial dispersion; ASM No.2. INTRODUCTION The activated sludge process traditionally developed for the oxidation of carbonaceous materials to carbon dioxide, biomass and water has during the recent decades been extended to allow nitrogen and phosphorus removal. Under mounting pressure of problems caused by eutrophication, design and construction of fullscale biological nutrients removal (BNR) activated sludge processes have moved ahead, despite of the lack of mechanistic understanding of the process, in particular biological phosphorus removal and the related scientific research. Evidently, mathematical models in conjunction with prototype models such as pilot plants are important not only for optimising design but also for improving operation and control of the BNR processes. Much of the work done on BNR activated sludge modelling in recent years has been largely concentrated on improving the kinetics of the process. Process hydraulics on the other hand receives less attention and its importance has often been overlooked. The continuously stirred tanks in series (CSTR-in-series) technique (see eg. Lee et ai" 1997a) is frequently employed to model the hydraulics of continuous channelled-bioreactors due to its simplicity. Nevertheless, 79
80
T. T. LEE et al.
employment of the CSTR-in-series model to predict the transient properties of bioreactors is thought to be rather crude and could be misleading in some cases. For less than 2 tanks, the CSTR-in-series model predicts an immediate rapid rise in the exit concentration, which is incorrect. In such a case, the axial dispersion theory originated from Chemical Engineering (Levenspiel, 1972) may be applied to the BNR system. A pioneering tracer study on the activated sludge process by Murphy and Timpany (1967) showed that their dispersion model appear to fit the experimental data significantly better than either equi-size CSTR-in-series or unequal sized CSTR-in-series models. In this study, we shall formulate distributed parameter models for the BNR activated sludge process based on the axial dispersion theory and reduced-order kinetic models of the Activated Sludge Model No.2 (ASM No.2), recently developed by Henze et ai. (1995). Using the global orthogonal collocation (GOC) technique and based on our previous study on a distributed parameter model for carbon-only removal activated sludge process (Lee et al., 1997b), we shall introduce a new numerical algorithm for the BNR activated sludge process in this study. Steady-state and dynamic simulation results are compared with experimental data of an existing BNR acttvated sludge pilot plant. The results of this study should provide a very important contribution to the hydraulics ofBNR activated sludge processes. MATHEMATICAL MODEL OF BNR ACTIYATED SLUDGE PROCESS HydrauUc and kinetic model The practical continuous channelled-reactor such as the activated sludge bioreactor has demonstrated some degree of backmixing or intermixing, stagnant regions and shortcircuiting or channelling. Failure to consider this nonideality may lead to gross error in design (Levenspiel, 1972). According to the classical axial dispersion theory, nonideality within a flowing reactor may be largely accounted for by considering only backmixing or intermixing. Some recent industrial appUcations of the axial dispersion theory are modelling of bubble and packed columns (Degaleesan et ai., 1996; Romanainen, 1997). The original kinetic model of the ASM No. 2 is reduced such that 3 separate matrices representing the anaerobic, anoxic and aerobic processes are obtained. Chemicals for precipitation of phosphorus are not used in this study and hence not considered. Soluble and particulate inerts, which do not take part in the bioreaction, are removed from the models. Total suspended solid is essentially a summation of all particulate components and is therefore removed. The final reduced order models of the ASM No. 2 consists of 8 processes and II components for the anaerobic reactor; 11 and 12 processes and 13 components each for the anoxic and aerobic reactors respectively. While there exists conflicting evidence in the literature concerning the fate of nitrate in biological phosphorus removal, our pilot plant experience indicates that there has been a consistent net reduction of nitrate and phosphorus in the anoxic zone. This finding which is in good agreement with a number of workers, recently reviewed by Baker and Dold (1996) suggested that some PAOs can use nitrate as an electron acceptor in the absence of oxygen for oxidation of stored poiy-fJ hydroxy aikanoates (PHA). The stoichiometry and process rates for denitrifying PAOs are incorporated into the reduced-order ASM No.2 for the anoxic reactor, thus the original ASM No.2 is slightly modified. Mass balance Based on the axial dispersion theory, a general mass balance equation for a component, Cj within a plug flow reactors with dispersion model is given by:
ac, = iii
I (I-;;;ij'iT'""a' c, -ac) a:-
HRT
+ reae/Ion + external mass transfer
(1)
where Pe is the Peclet number of the system; z is the dimensionless length of bioreactor and HRT, the hydraulic retention time of fluid in a bioreactor is defined as volume ofbioreactor to total inlet flow. Equation (1) is used in conjunction with the reduced-order reaction kinetics of the ASM No.2 to model the behaviour of components within the compartmentalised anaerobic, anoxic and aerobic zones. Example of mass balance for nitrate at the anoxic zone is formulated as follows:
BNR achvated sludge process as HO , dt
= _1_
(....!.- a'SH", _ aSHf),) _ (I -
HRT' Pe
az'
dZ
YH) (
2.86YH ,., •.,
+
/lH.'
)+
81
(2)
/l,."
where:
Mass balance equations for the remaining components may similarly be written, based on equation (I) and the reduced-order kinetic models. An identical Peclet number has been assumed for all the components investigated. Justifications for this assumption are detailed in Lee et al. (1997b). Additional equations, describing the inlet and outlet flow conditions are required in order to solve equation (2). In this study, the following Danckwert's boundary conditions are employed:
..!-.
dC = C _ C
Pe' dz
, UPP'
z = 0 "if t
z = I "if t
(3)
(4)
where C"ppr is the approach concentration to bioreactor in mg/!. Equations (3) and (4) are applicable to all the components under investigation. Models ofauxilia[y equipment The returned activated sludge (RAS) tank and the non-aerated compartment of the aerobic zone are assumed to be well-mixed, i.e. modelled as simple lumped-parameter schemes. The RAS tank and the unaerated compartment models used the kinetics of the anoxic and the aerobic zone. Dynamics of sludge thickening have been ignored in this study. The sludge concentration at bottom outlet of settler is assumed to be directly proportional to its concentration at the inlet (Olsson and Andrews, 1978). A NEW NUMERICAL ALGORITHM FOR DISTRIBUTED PARAMETER BNR ACTIVATED SLUDGE PROCESS The Monod-type kinetics appearing in most of the rate equations in the ASM No.2 makes it impossible to derive analytical solutions. Employment of numerical technique is therefore inevitable. In this work, we employed the global orthogonal collocation (GOe) technique to reduce the partial differential equations (PDEs) to a coupled system of ordinary differential equations (ODEs). This technique was shown to give relatively better numerical accuracy than the commonly-employed finite-difference techniques (Villadsen, 1978). On the basis of a computational algorithm developed earlier (Lee et al., 1997b), we now extended the technique to model the BNR activated sludge process. Applying orthogonal collocation to equation (2) we have: dS •.j
1 (1-IBj"SHO,.,-IA""SHO", H+' H+' ) Y.) ) --286Y (/l.,I.I+"'H.,., +JJ,.o,j
HO --=--. dt HRT
(1-
Pe '.1
'.1
.
H
(5)
The Monod terms for f.lH.lj , f.lll.lj and f.lPAOJ in equation (5) are essentially the same as in equation (2) with addition ofa subscript) in all state variables.}=1 to N; N is the number of internal collocation points. A and B are the orthogonal collocation matrices for the first and second order PDEs. Similar equations can be developed for other components in the BNR model of anaerobic, anoxic and aerobic zones. Collocation on the generalised Danckwerts boundary conditions for the inlet and exit ofbioreactor results in Equations (6) and (7) are applicable to all the components under investigation. N.I
N+I
AN+,.•o,cI A'.rC, + Pe.C.",)- A,.Nolk ANo1J 'C,) c, = ,., '.l A"N+2AN+ll - A N + 1.N + 1 ·(A'.1 -
P~)
(6)
I. T. I.U:
,'(III.
('OMI'IIIA IlONA!. STRATEeiY SIL';ldv-,Llle Slnlldalioll or Ihe di'lrihuled paramclcr IlNR activated sludgc modd was carried oul hy simult;1l1v\Hlsly L'\'aluatin),: rvsldues or Ihv discrCliscd m;JSS h;d;JIlCV vLJlwlions (such as cLJuation (5»); eqllatlons lle'cnhing pl'lleess houndary vonditions (vqllations (11) amI (7)) amI eqlIalions flJr calculating sludge Ihiekemng. slrvam mixing and splitling, This means that Ihe time derivativv terms in the mass h;danev vqllatiolls arv svl 10 Ino, i,e, rvducctl to algchraie vquations, Altcrnatil'Clv. a di ITerenlial-algehraic eqllatlon IJ)."d') sohn can hv used to simlllaiv the elltirc procvss IIntil dynamics or eomponvn{ dies Ollt. i,e, sleady-sl;tlv s"llllion has reached, Sol III ions li'om the stcady-statc simulation hecomc Ihc Initial conditions Illl' dynamic simllialions, .II. ()AI' solvcr is thcn IIsed 10 integralc the ODb and simulwneollsly soh'ing other algvhLlie vqllaliolls, All L:\lmputational work were accomplished IIsing IM13US ( t:well and Camcron. I')') I), an v'lllation-hascd dynamic sinwlatitln package, MODI:!. V AI.1DATION Thc' l'olliIHllatlon;d algorithm t1vleloped in Ihis slUdy \\ ill ntlw he applivd 10 mod<:l an cxisting Llllltinllous pilot-s,'ale IlNI< ;Iclivaled silldgc plant at the Liverpotl' Scwage Treatmcnt plant in Sydncy, Australia, The pilol-planl IHocl'sses a L'onstanl flo\\' or ahollt 70 Iitrcs pcr hour or scrcened. lkgriltcd scwage with ahoul 1(1(10 Iilrl's l'apacity in thl' ma\ll hior<:actors. The plant sci-Up is <:sscnlially simil;tr 10 Figur<:, I. Sewage used In thiS stlltl\ "as nllllliCipal wastewater, sOllrced rrom a Itdl scale wast<:water treatmcnl plant located at the ~;lIlll'
SI!1..:.
Validalion or the distrihulctl param<:lcr BNR activated sludge nwdd procccded in 4 stages: (I) I-I'aslcwatcr ehar:leterlsatlt>n ttl lktermine al'crage influent conccntration or components of intt:resl, (2) r<:t<:ntion tillle dlSlrihlltltHI (I< Ill) stndies 10 characlcrise tank hydraulics. (3) application of the nUlllcrical algorithm to pl'l'I"1'I1I ,'lL'adl'-slatc simulation to match slnlulated rcsults at various collocation points with a sct or steadyslalL' npl'l'lllIl'nlal t1;lta at cOlTespundtng spatial positions along thc hinreac\llrs, This is aecllmplished hy cdihrating paramclers or high uncertainty such as thosc related to PAOs, i.e, maximum rale of lermcnlation ('flo'!; ralL' L'onstalll I,'r storage or I'IIA ('1"h,,); rate constant IiII' storage Clr poly-phosphate (PI') (lj",,) and ratc l'onslanl 1(,1' Ivsis of I'A() (h",,), Ikn/.e ,'I III, (I')l))) suggcsted that ehanges to the n:duction factor for ,knllrilieallon (Ih".) may hc ncccssary I(,r moddling of Ihe anoxic I.onc, (4) applic:J1ion or the nllmerical ;t1gorililin ;1I1d thL' rL's"lts or ( I), (~) and (~) to simulate dynamics or components in one of the lones, under dlll,:reni l'olHlltit>ns and lL'st their I'alicilty againsl dynamic experimental I'(;sults,
__"ri,
I
-t
NOvo'....
HO P
RTI l l'.\pl'l'lllIenh wnL' l'onduclL'd to naluatc Ihc Pcckt numhcrs which arc singk-paramctcrs that "har,,,'ll'l'lSl' Ihc' hl'tlr;utllcs t>I' hioreactors al thcir rL'sp''l'li\,; 1'"1l'S, (llll'-shot Rhodamine tracn was Intlcpcndl'llllv Inlroduced to 'hl' inlet or the ;lnaerohiL'. ;lIltl.\ie and acrohie loncs, Samples werc' collectcd at IhL' tlullel tll eal'll Itlt1e IInder IIlvesti"ation and an;t1l'svd I"l' traccr concentration, I'xpL'rimcnts Illr stl'adysl:,tl' valHbt'tlll tlf the nlo,lel arc as lililows: When til~' planl is in stcady-stalc condition, i.c, all flOll's with;n
BNR activated sludge process
83
the plant are kept constant and routine monitoring of the influent wastewater fed to the plant showed consistently stable influent qualities, samples are collected at various spatial positions within each bioreactor zone for routine analysis of the components of interest. Experiments for dynamic validation of the model were conducted under three different conditions at the anaerobic zone of the pilot-plant, i.e.: • • •
Experiment A: Step changes to influent flowrate from 70 IIhr to 140 IIhr for 90 minutes, before returning the influent to its original flow. Experiment B: Step changes to the return activated sludge (RAS) flowrate from 44 IIhr to 98 IIhr for 90 minutes, before returning the RAS to its original flow. Experiment C: Step changes to the influent acetate from 100 mg CODII to 300 mg COD/I by introducing external acid dosages for 90 minutes.
For all dynamic validation experiments, samples were collected at every 10 minutes at the outlet of the second compartment, within the anaerobic zone. RESULTS AND DISCUSSION Waslewater characterisation COD fractionation for components of interest has been done as follows: • • •
fennentation products, considered to be acetate (SA), were estimated from measurement of individual acids ie : acetic, propionic, butyric and valerie acids. fennentable, readily biodegradable organic substrates (SF) were calculated from estimated biodegradable soluble COD (SCOD) and SA. The estimated biodegradable SCOD is assumed to be the measured SCOD less the estimated inerts, taken to be effluent SCOD measurement. Slowly biodegradable substrate (Xs) was evaluted from OUR test results.
Biomass in the influent was not characterised but the fractions are needed in order to explain the bloom and the wash-out of certain groups ofmicro-organisms (Henze et al., 1995). Heterotrophic organisms (XH) are assumed to be 15 percent of the measured total COD, which is within the range recommended by Henze (1992), Henze et al. (1995) and which is also used by other workers (e.g. Johansson, (994). Characterisation of nutrients unlike COD or biomass is rather straightforward since the components of interest, that is ammonia-nitrogen (SNH4) and soluble phosphate (SPQ4) assumed to be orthophosphate, are measurable. Nitrate and nitrite nitrogen (SN03) in the influent is usually negligible and assumed 10 be 0.1 mg Nil in the simulation. Bjoreactor hydraulic characterisation The dimensionless tracer's concentration (Cal at the outlet of each zones expressed in tenns of the Peclet number and dimensionless time (()) can be approximated by the following expression: C
1
• '" 2'J1C8(1 / Pel
( -(1- 8)' ) exp 48(1/ Pe)
(8)
Derivation and shapes of curves described by equation (8) are detailed in Levenspiel and Smith (1957). The results of RTD studies in this work are shown in Figure 2. The aerobic zone is considered to be well fitted for an axial dispersion model with a Peclet number of 2.5. On the other hand. dispersion models for the anoxic and the anaerobic zones are rather poorly fitted at the 'second half of the experimental data. This is attributable to the fact that recycled tracer was not accounted for in equation (8) and furthermore. some difficulties were encountered in collecling samples al the outlet of the anaerobic zone, which is in fact the first compartment of the anoxic zone. On the other hand, fitting of the models with a Peclet number of I and 3.5 to the 'first half of the experimental data are considered to be fair. This is largely because the tracer had not yet recycled during this period. Since the evaluated Peclet numbers of the bioreactors are not considered
84
T. T. LEE el al.
to be too large for this process (Arceivala, 1981),5 collocation points should be sufficiently accurate for simulation with the GOC algorithm . •7
.0 os
I·· t.. .
is
II
"
"
"A
" os
.. -2
U
07
...
...
l~·
.
10.1 II
OJ
1.1
-2
U
3
U
.
Figure 2. Evaluatlo nofPeciet number ofbioreact ors using correlation of Levensple
l and Smith (1957).
Steady-state simulation Parameters related to PAOs ie qr., qpha, qpp and b pp considered to be highly uncertain (Henze et al., 1995) are 'optimised' such that simulated steady-state results and experimental data are fairly-well matched. The value of parameters used in this work compared to Henze et al. (1995) is given in Table I. In order to obtain a reasonably good fit to the nitrate profile in the anoxic zone, our simulatio n experience suggested that 'llN03 should be reduced, contrary to the suggestion by Henze et al. (1995). Other parameters are kept identical to the values suggested by Henze et al. (1995) since it is expected that they are reasonably stable. The fate of 5N03 at various zones are shown in Figure 3. Evidently, there is a net reduction of this component throughout the anoxic zone as predicted since the modified kinetic model of the ASM No. 2 allows for denitrification by PAOs, at the expense ofPHA. Since the concentration of predicted SNOJ is slightly higher than the experimental data close to the outlet of the anoxic zone, consequently the predicted 8N03 concentration along the aerobic zone is correspondingly higher. Difficult y arises in improving profiles of SN03 further due to the high coupling of the processes within the different zones. Our simulation experience indicated that small changes to the value of parameters such as qpp and qph affects the simulated results considerably.
BNR activated sludge process
85
ano)Cjc
anaerobic
••roble
t2
'2
12
'0
'0
'0
8
8
6
6
4
4
4
2
2
2
o o~-O....-Oo!'.';-5-"0--....,
°0
dImensionless length
0.5
0
0
0
0
°0
,
0
0.5
1
dirnenalonlo•• length
dimenaionht•• length
Figure 3. Steady-slale profile OfS'Ol at the anaerobic. anoxic and aerobic zones.
Table I. Optimisation of fA WQ parameters PARAMETER qpha qpp bpp
T)"".'
Henze et al. (1994) 0.125 0.0625 0.0417 0.8
This work 0.14 0.031 0.001 0.2
Unit g COD/g COD/hr g COD/g COD/hr hr- I g PP/g PAO
Dynamic simulation Location of the sampling point within the anaerobic zone of the pilot-plant corresponds to collocation point no. 3 of the numerical algorithm. Simulations were performed on the entire plant, allhough only the anaerohic zOlle was investigated. Simulation results compared with data from experiment A for a step change of influent flowrate are shown ill Figures 4 and 5. Evidently, the model predicts dynamics of acetate and soluble phosphate remarkably well. The components dynamic behaviour are as expected since increased influent flowrate means that the HRT within the system drops. Consequently, the rates of acetate uptake and soluhle phosphate released by PAOs arc reduced. It is also expected that concentration of all other particulates will also be reduced due to the decreased residence time.
1·-·
00
00 70
~
r
!
J
00
40
20
to 0
Fig'lfe
-+.
0
20
00
eo
tOO
TIme.
"*'
uo
tOO
Effect of mfluent flow step to the dynamics of SA at the outlet nf 2nd compartment in anaerobic zone.
I T. LEE ('/ nl. Soluble phoaphl!l11l1 concentration V. time
30
.lll'"
1:llt.TI 01" influl'tlt
~tl'P
n(H\!
to the dyn:lITIICS ofSI'()4 at the outlet of 2nd compartmellt In ..t nat'robic zon Acel"te conc9nlratlon Vs limo
- ----r
-------,--------, - - -
[-'-~---J -- p'."".O o>
><
°o::-----;!:;;---:;:;---,;;;---.;;;--~w;;;o;--;-;;;----;-::;;-~~~-~:;;_-~ Time min
I,PUll' (I.
I·j kct
01 IllllUl'1Jt
S\ sll'p
10
the dynamics of \\ at the outlet of 2nd compartment
III ;:mJc'whK :lone.
Soluble phosphat. concanlrallon Vs time
70
-- -- .
I-~'----T'--~---- r"
---,-----------,--.-
-=_=...==='=P='=.d="='.'=d==;-l
r-==.-'
~_ __
experiment
65
40
1!'lIll'
I
I, ni.'ll
_-"-
o
.
:20
(It 11l11Ul'lIt
S\
.l..
...L
40
60
',{l'p 10
~J
80
_....L.~_~_.L.
100 Time, min
Ihe d~!nJIllI(~ III Sj', i~ Jt
1.20
till'
1. _ _
140
'"0
200
outiL'! of 2nd UlIl11xlrtment
In JnJLTOhlL: /Ullt
T. T. LEE et al.
J-.
-
..-
Figure 5. Effect of influent flow step to the dynamics of SPO
'00
f
I
eo
00
aD
'0
00
MJ
100 'Tlnw. min
120
140
100
,eo
Figure 6. Effect of influent SA step to the dynamics of SA at the outlet of 2nd compartment in anaerobic zone.
_ , ._ _nv._ 7or-..,.---.---;":=:":";~:::""'--r--;:I::==:::c==::r::::::;;l
1·-·
.
eo
50
•• "O~--:..; ---:.. f=---;;IO~--OO;;;-----;';OO;--~''':O-',;"O--;:,,,:o-,,,,,:,,O-~_ - . - . mln
Figure 7. Effect of influent SA step to the dynamics of Spo< at the outlet of 2nd compartment in anaerobic zone.
88
T. T. LEE et al.
To reflect the reality of full-scale plants, verification of the model, following diurnal variation of influent flows and concentration of components of interest should be conducted, before using it for design of new plants or improving operation and control of full-scale plants.
REFERENCES Arceivala, S. J. (1981). Wastewater Treatment and Disposal. Marcel Dekker, New York. Baker, P. S. and 001<1, P. L. (1996). COD and mtrogen mass balances m activated sludge systems. Wat. Res., 19(2), 633-643. Danckwert, P. V. (1953). Contmuous flow systems, dIStributions of residence times. Chem Engng. SCI., 1, I-B. Degaleesan, S., Roy. S., Kumar, S. B. and Dudukovic, M. P. (1996). Application of the plug flow WIth axial dispersIOn model for continuous polymenzation In a pulse packed column. Chern. Engng SCI., St( I0), 1967-1976. Henze, M. (1992). Charactenzatlon of wastewater for modelling of activated sludge processes. Wat. Sci. Tech., 15(6), 1-15. Henze, M., Gujer, W., Mmo, T., Matsuo, T., Wentzel, M. C. and Marais, G. v. R. (1995). Activated Sludge Model No.2. IAWQ Scientific and Technical Report No.2, IAWQ, London. Lee, T. T., Wang, F. Y. and Newell, R. B. (1997a). A generalised procedure for modelling and snnulation of activated sludge process based on lumped-parameter approach. J. Env. Sci Health, PART A - Env Sci. Engng, 32(1), 83-104. Lee, T. T., Newell, R. B. and Wang, F. Y. (1997b). Dynarmc modelling and simulation of activated sludge process using global orthogonal collocation approach (submitted to Wat. Res.). Levensplel, O. and Smith, W. K. (1957). Notes on the diffusion-type model for the logintudinal mixmg of fluids in flow. Chem. Engng. SCI., 6, 227-233. Levenspiel, O. (1972). Chemical ReactIOn Engineering. John WIley & Sons Inc., New York. Murphy, K. L. and Timpany, P. L. (1967). Design and analySIS of mixing for an aeration tank. J. Santt. Engng Div., Am. Soc. Ov. Engrs. 93(SA5), 1-15. Newell, R. B. and Cameron, I. T. (1991). NIMBUS Users' gUIde, Dept. ofChem. Engng. The University of Queensland. Olsson, G. and Andrews, J. F. (1978). The dIssolved oxygen profile - A valuable tool for control oflbe activated sludge process. Wat Res., 11,986-1004. Romanamen, 1. J. (1997). Numericalapproach to modeling of dynamic bubble columns. Chern. Engng. Proc., 36(1), 1-15. V.lladsen, J. and Michelsen, M. L. (1978). Solution ofDifferential Equation Models by Polynomial Approximation. Prentice Hall, N.J.