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The implementation of biokinetics and conservation principles in ASIM
eJ
Pergamon 0273-1223(95)00198-0
Will. ScL Tech. Vol. 31, No. 2,pp. 257-266,1995. Copyrigbt@ 1995IAWQ Printed iu Great Britain. All rigbts reserved. 0273-1223195 $9'50 + 0'00
THE IMPLEMENTATION OF BIOKINETICS AND CONSERVATION PRINCIPLES IN ASIM Willi Gujer and Tove A. Larsen Swiss Federallnstitute!or Aquatic Science and Technology (EA WAG) and Swiss Federal Institute o/Technology (ETH), 8600 Dubendorf, Switzerland
ABSlRACf The Activated Sludge SIMulation program ASIM is introduced as a didactic tool to be used in design courses for the simulation of the dynamic behaviour of modem nutrient removal activated sludge systems. It allows for free definition of the biokinetic model, the flow scheme, process control strategies and load variation. Its user interface is simple enough to be used in the classroom but powerful enough to support even professional work. The most difficult aspect of ASIM is the preparation of the biokinetic model (transformation processes) to be used. A systematic use of stoichiometric conservation principles simplifies this task and at the same time reduces the number of empirical parameters. The practical application of conservation principles for charge, elements and theoretical COD is presented in detail. Composition equations are introduced as a link to the wastewater treatment plant reality. KEYWORDS
ASIM, mathematical modelling, biokinetics, theoretical COD, stoichiometric conservation equation, composition matrix, Activated Sludge Model No.2. INTRODUCfION Dynamic simulation of the behaviour of toclay's nutrient removal activated sludge systems is an effon which is based on the simultaneous application of a variety of different entities; 1A Biokinetic Model. This model describes the compounds which are used to characterize the wastewater and the activated sludge. It includes a description of the rate (kinetics) and the extent (stoichiometry) of the interaction of the different microbial transformation processes with the model compounds. 2A Model of the Transport Processes. This model describes the tlow scheme, the distribution of the influent, the recirculation streams, the mixing conditions in the reactor compartments, the sedimentation processes, the gas exchange properties, the solids removal mechanisms, etc. of the activated sludge system to be simulated. 3A Set of Operating Strategies. For the successful operation of an activated sludge system a set of operating strategies is required. These strategies may be implemented in reality with the aid of on-line process control or in the form of operator decisions. Simulation of activated sludge systems requires that these strategies may be simulated as wen. 4Extemal Forcing Functions. Wastewater treatment is never a steady state process. Extemalload is subject to daily, weekly and seasonal as well as random (storm) variations which must be considered in simulation. SA Computer Program. The implementation (application) of a mathematical model as complex as today's activated sludge models typically requires numeric techniques for the forward integration of the mass balance equations. The computer program which provides the user interface and the numeric techniques should clearly be distinguished from the mathematical model. The program ASIM can implement a whole 257
W. \.JUJeK ana I. 1\. LI\K;)t:.I'I
array of different biokinetic models and many different programs can implement the Activated Sludge Model No.1. Whereas the consulting engineer concentrates on system operation, design and optimisation (transport processes and operating strategies), the prime task of research and education in environmental engineering is the development and understanding of biokinetic models. Both activities cannot be performed without computer programs. A program which supports these activities must allow for free definition of the biokinetic model, must include a generally accepted version of the models for the transport processes (flow schemes), should include a general set of operating strategies (process control) and must be able to consider variation of loading (forcing functions). If such a program is to be used in a teaching environment, it must be possible to master the application of its prime options after less than an hour of training. The program ASIM IS designed to fulfil these requirements. ASIM-,1CfIVATEDSLUDGESlMULATIONPROGRAM
ASIM has been developed as a didactic teaching tool. It is designed to support the student in the development of biokinetic models for constant volume batch and continuous flow biological growth systems under steady state and dynamic loading conditions. ASIM is large enough to fit the Activated Sludge Models No. I (Henze et al., 1987) and No.2 (Gujer et al., 1995) and may simulate most biological nutrient removal activated sludge system flow schemes which are used today. Many consulting companies use ASIM to deal with their specific problems. Major Options of ASIM
ASIM offers the following major options. I Free definition of the biokinetic model (Definition of soluble and particulate compounds, number of transformation processes, stoichiometry and kinetics of these processes). 2Free definition of the flow scheme: Constant volume batch reactors, continuous flow chemostats and series of chemostats, activated sludge systems with secondary clarifier. internal recirculation. two independent influents, etc. 3 Free definition of process control strategies (only proportional controllers are implemented). 4 Computational routines to find steady state solutions as well as free dynamic simulations (diurnal, seasonal variation, batch experiments, tracer curves, etc.). 5 Graphic support of the analysis of simulation results as well as experimental data. 6Communication with spreadsheet programs. ASIM Verso 3 is delivered in three versions: (i) A reduced version, which is typically sufficient for student work and which has reduced capacity for the size of models and flowschemes. (ll) The full version which may be useful for project, research and thesis work for more advanced students. (iii) A batch version of the full interactive version which is useful if time-consuming. repetitive simulation work must be performed. The full version is used by consulting companies as well
Applying ASIM to the Activated Sludge Model No.2 In order to demonstrate the potential of ASIM, the Activated Sludge Model No.2 (Gujer et all995) will be used. The kinetic and stoichiometric parameters as well as the influent composition are given by Gujer et at. (1995). A tlow-scheme as shown in Fig. 1 is defmed (BioI. P removal, ucr Process). The internal recirculation and excess sludge removal rate D are automatically controlled such that the nitrate concentration in the second reactoris maintained at around 0.75 g m-3 NO'f-N and the total activated sludge concentration in the influent to the secondary clarifier(reacoor 5) is maintained at around 3500 g m-3 TSS. y
Table I shows the results computed for the steady state for the flow-scheme in Fig. 1. The required SRT (Solids Retention Time) predicted to maintain the predefined activated sludge concentration is IS days. This steady state is predicted based on average stationary loading of the system and is chosen as the initial condition for the simulation of the dynamic behaviour of the system (Figures 2 and 3). Fig. 2 is a summary of the defmed variation of the influent flow rate and the predicted (controlled) required internal recirculation rate as well as the required (controlled) excess sludge removal rate DII• Fig. 3 demonstrates that the dominant storage of poly-hydroxy-alkanoates is shifted from the first to the second and
Biokinetics and conservation principles in ASIM
259
Flowscheme of the plant Contol loops aCllv.1 02 u'uration " 10.00 SludQ.aQ•• SQT • 15.00
"20000.00
Inllu.nt
;
I
!
I
i; !
3
2
I•
5
1
!
i Q.OIurnsludQa " 20000.00
AIi~c1or
Uolu...
I
2
3
2000.00
2000.00
2000.00
2.0
2.0
2.0
02 Conc. Kia Ualu.
5
1
3000.00
3000.00
2.00
2.00
Fig. 1. Flowscheme of the activated sludge system as drawn by ASIM. TABLE I PREDICTED STEADY STATE AT 20°CFOR TIIE FLOWSCHEME SHOWN IN FIG. 1. 1lIE UNITS ARE GRAMS, METERS, DAYS. OXYGEN CONSUMPTION IS IN 1m m-3 dol. (Table provided by ASIM)
02 S Oxygen S Substrate COD COD S Acetate S Ammonium N N S Nitrate P S Phosphate S Alkalinity Mol COD S Inert S N2-Nitrogen N COD X Inert X Substrate COD X BM HETerot COD COD X BM PAD P X FP in PAO X PHA in PAO COD X BM AUTotro COD X Susp.So1idsTSS Oxyqenconsumotion
Influent Reactor Nr. 1 2 0.00 0.01 0.00 5.21 1. 09 30.00 17.75 0.89 20.00 11. 93 6.92 16.00 0.00 0.73 0.00 21.45 14.31 3.60 3.96 4.12 5.00 28.91 29.79 30.00 6.51 0.00 11. 74 659.93 1240.26 25.00 57.61 125.00 41.05 398.40 30.00 754.42 199.90 0.00 388.31 42.54 0.00 104.25 43.53 0.00 29.98 0.00 20.19 39.10 180.00 1857.97 3493.68 20.04 50.44
3 0.00 1.18 1.42 7.70 0.08 18.20 4.01 29.98 12.40 1239.13 36.78 748.78 385.71 100.35 37.94 38.88 3472.41 20.22
4 2.00 0.42 0.05 2.30 4.85 2.86 4.03 30.24 12.63 1239.98 25.28 752.55 396.07 115.37 10.83 39.71 3509.22 760.12
5 2.00 0.33 0.01 0.44 6.87 0.30 3.87 30.47 12.79 1235.71 19.42 748.36 394.88 117.36 1.58 39.69 3492.08 371.17
third reactor during periods of high organic loading. This is possible because the deniIrifying reactors 2 and 3 are operated under continuous nittate limitation with the aid of process control. Graphic results such as shown in Figs. 2 and 3 are easily available in ASIM for all process rates, state variables (concentrations) and forcing functions. They suppon the student in analyzing the behaviour of a system.
The use of ASIM is simple enough, such that a student who is able to understand the Activated Sludge Model No.2 may perform the simulation which is shown here after about one hour of training with the program. This requires that the simulation is perfonned with a biokinetic model which is provided together with ASIM.
w. GUIER and T. A. LARSEN
260
_I"'l~
ASM No. 2 simplified
................ Aedrculetton
•••••••• Ox
D,u.. nal va.. ,at,on Pel' cent 100-----------~-~-""!"'"-""!"'"-~-~--,
90 80 70
50 40 30
:··•.·.·IT:l········r:.;J=::FT':;F:,l~:l;;.E .
o ot.:.:··;';;·';;··;";';;-;;';·;';;·':'~:.l·........;6---8;..&.;-1..0-....;,12-...14---1;.6--1~8--2:'"0-~22~~24
Hou.. s
Fig. 2. The variation of the influent Q;. as dermed by the user and the internal recirculation R together with the excess sludge removal Ox as predicted by ASIM. 100% is equal to 30000 m3 dol for Qm and R and 1.00 dol for Ox. Figure provided by ASIM.
ASM No.2 simplified PHA Sto.. aQe
PAD
_ A t o a c l o r ..... ................ hK1Of" .... 2
•••••••• -"ac1or
_.ac1or ................
~lCtor
3 1
Hr. I
700 630
560
420
350 280 210 140
70
o ~?:b=b:::b::::±::::::::=::±:~~~d o 2 4 6 8 10 12 14 16 18 20 22 24 Hou.. s
Fig. 3. The diurnal variation of the process rate p for storage of poly-hydroxy-alkanoates in g PHA m-3 dol.
PREPARING BIOKINETIC MODELS FOR ASIM The most difficult task when applying ASIM is the dermition of a new biokinetic model In this chapter principles will be introduced which allow to simplify this task. As it is easier to introduce these principles for a specific case, a bioldnetic model is introduced in Tables 2 and 3 with the following information.
Biokinetics and conservation principles in .4SIM
261
1Soluble compounds are defined as compounds which are transponed together with water (advection). These compounds cannot be concentrated by settling, their concentration is given by the symbol Sj. Particulate compounds in addition to being transponed with water may at the same time be separated bY sedimentation and removed via excess sludge lIlelI' concentration is given by lIle symbol ~. Compounds which include soluble as well as particulate fractions will be introduced below with the symbol G; it must be remembered however lIlat ASIM cannot deal with such compounds. 2The concentration array Ca defmes lIle concentrations of all compounds used in the model. The index i (here 1 .. 10) runs over all compounds: Soluble compounds Sj: CI • S02 • Dissolved oxygen (g m-' Oil C2 .. Ss • Readily biodegradable organic substrate [g m-l COD] C, .. SNH ... Ammonium concentration h~ m-' Nl4+.N] C. =SN03 • Nitrate concentration [g m:rNOi-N] y • Sm • Dissolved dinitrogen [g m-l Nil C6 .. SALX ... Alkalinity Imol m-3 HCOi) Particulate compounds X;: C, =Xu =Heterotrophic biomass [g m-l CODI CS .. XA .. Autotrophic, nitrifier biomass [g m- COD) C9 =Xs .. Slowly biodegradable substrate [g m-l COD] CIO .. XTSS .. Total suspended solids [g m-3 TSS] 3The stoichiometric matrix vJ)' where j stands for the number of the process (here 1 •• 6) and i for the compound (here 1 .. 10). For each process one stoichiometric coefficient is chosen as dimensionless wilh a value of +1 or -I indicated in bold. Some coefficients are given based on empirical stoichiometry (eg v'.2 = -IIYu) which must be obtained from experiments. For each process 3 stoichiometric coefficients are given with the variables xJ' YJ and zt. These coefficients may be obtained from stoichiometric conservation equations as introduced t5elow. The stoichiometric coefficients for TSS, vj.TSS - Vj lOt may be obtained from a stoichiometric composition equation, as introduced below. • 4The composition matrix \k,1 defmes the composition of the different compounds of the model Information is given in terms of the malerials defmed at Ihe left of each row (COD, nitrogen, electrical charge, TSS, total Kjeldahl nitrogen TKN), for which the index k (here 1 .. 5) is used. Eg oxygen is defined as negative COD which results in \11 • -I g COD I g 0lor in any 14 g of NIJ..+-N (l mol) 1 mol of positive charge is contained, this results in \3 ~ = 1/14 mol Charges g-1 N. The compositIon of the heterotrophic biomass (iNXH and iTSXH ) may be obuimed from chemical analysis of 'purified' biomass. 5 Table 3 contains the array PJ of the process rate equations, which are needed to predict the transformation rates for the different compounds in the mass balance equations. Details will be introduced below. Conceptional Model/Observables A conceptual model must fulfil the following criteria. 1In terms of the conservatives of the model (here COD, N, Charge), all imponant educts, products and transformation processes must be contained I 2A conceptual model cannot include overlapping compounds (eg TKN includes NH., these two compounds are therefore overlapping). Compounds which do not follow this criterion may be included in the model, they are termed 'observables' and are not part of the conceptual model. 3 All compounds which affect kinetics must be part of the conceptual model A few examples might help clarify this notion of a conceptual model.
If one has chosen carbon as a conservative element in a model, according to criterion number one, ~ must be included as a model compound. In the Activated Sludge Model No.1 (Henze et al., 1987), the theoretical COD was chosen as a conservative and not carbon. Since the theoretical COD of ~ is zero (for definition see below), lIle conceptual model could be written without including COJ. Criterion number two is nonnally applied intuitively. Problems arise when one wants to include 'observabtes' in the model in order to describe process control strategies. As an exanwle. it is often useful to include the observable TSS in the model in order to control the sludge concentration m the reactors. Since TSS overlaps wilh the particulate compounds XH, XI and Xs, TSS may not be considered part of the conceptual model.
....,...
W.
UUJt:.~
ana 1.
~ L.~t:.I'l
Of course, it is possible to cons~ct conceptual JOOdels which do not profit from any conservation princip!es. For such models at least critena number two and three must be fulfilled. As a consequence, any a pnori
information from conservation principles is 10SL
Conservation Principles I Conservation Equation
Olemical elements (here nitrogen), electrical charges and a theoretical COD, as introduced below, are conservative and may neither be produced nor consumed in a biological or chemical transformation process. This conservation principle is expressed in mathematical fonn in the stoichiometric conservation equation:
, LV i-I
(1)
IJ '\I
The index i runs over the compounds 1 .. 9, which are expressed in terms of conservatives. XTSS (i '" 10) is not subject to conservation since TSS overlaps with the particulate compounds Xu' X A and Xs . The index Ie runs over the conservatives 1 .. 3 and does not include the observables (k '" 4 .. 5). The stoichiometric conservation equation (1) is only valid for conservatives (elements, charges, COD) and cannot be applied to observables which are not subject to conservation such as TSS or Kjeldahl nitrogen. The conservation equation (1) may be applied to all biological transformation processes (j = 1 .. 6) and all conservatives (k = 1 .. 3). Here, this results in 3 x 6 = 18 conservation equations which provide a priori infonnation and result in a corresponding reduction of the degrees of freedom of the biolcinetic model Typically the system of conservation equations may easily be solved for the unknowns, here the three vectors xJ (COD conservation), YJ (N cons.) and ~ (charge cons.). Leaving out all products v ~ . \u which are equal to zero, an example of a conservation equanon is provided below: Yl
1 =VI,3 =-(Vu '\2,2 +V1,7 '\2,7)/\2,3 =-(--'\NSS + 1'\NXH)11 Y H
(2)
Since ASIM is applicable to a variety of biokinetic models. it is not possible to solve equation (2) within the program. Preparing a biokinetic model for ASIM must therefore include solving these equations by hand. Composition Equation H the production of an observable is fully described within the conceptual roodel and if the observable is
either entirely soluble or entirely particulate. a stoichiometric coefficient may be computed and the observable included in the stoichiometric matrix. From the stoichiometric composition equation (3), the stoichiometric coefficient is computed.
v·J,Il • ;'1 rv··J,I ·tt·.. 9
(3)
Here for a particulate compound, vj,i • 0 for i = 1 .. 6 and for a soluble compound, vj,i ... 0 for i ... 7 .. 9.
ASIM will only perform correct mass balances when an inlet concentration ofthe observable is also determined. The inlet concentration of an observable is computed from the composition eq'~ation (4).
(4)
c,: the concentration the observable compound in the inlet which is not accounted for by the compounds of the conceptual model In the case of TSS. it might be the particulate inorganic compounds in is
of
Ie
the inlet which are normally not included in the biolcinetic model Not including these compounds in the inlet concentration of TSS would however lead to an error in the mass balances performed by ASIM. Please note that an inlet concentration computed according to equation (4) might not be identical to the corresponding measured concentration. As an example. the enmeshment of colloidal material into the floes is normally not modelled. Instead, this colloidal material is described as particulate already in the inlet to the treannent plant although it would at this point not be measured as TSS. Such phenomena arise from model simplifications and emphasize the importance of a detailed mechanistic understanding of a given model
TABLE 2
ARRAY OF MODEL COMPOUNDS, STOICHIOMETRIC MATRlX AND COMPOSmON MATRIX
SOl No.j 1 2 3 4 5 6 No.k 1 2 3 4
5
No.i Processes
GrowthOfXH LysisofXH Hydrolysis Denitrification GrowthofXA LysisofXA Conservatives
roo
~
1
Ss COD 2
SNH N 3
XI
-IIYH
VI Y2 Yl Y. Ys Y,
Xl -IIYa Xs
-1
I
N Mole Otarl!e
Observables TSS TKN
b,••
1 1/14
SN01 N 4
X4
INA
Concentration Array C; SAlK SN2 XH Mole HCOJ - COD N 6 5 7 Stoichiometric Matrix v· j 1 ZI .1 Z2 Z3 +1 -x. Z4
Xs COD 9
XTSs TSS 10 v •• n
X2
-1 +1 ·1
X6
1
1
1
tNXH
tNXA
tNXS
Zs Z4
Com position Matrix tJc . -4.57 -1.71 1 I -1/14 -1
XA COD 8
V, In V1tn V4tn
Within the double frame, a conceptual model is presented. Outside the double frame, observables are given as a link: to the reality as observed at the wastewater treat· mentplant ttl
~ =>
Ve.n
g.
V~tn
'"
§
Q.
n
g
~.
g '0
::I.
I b,••
1
~
tTSXH
\TSXA
\TSXS
-[
\'IXH
\NJ(A
\!llXS
~
or
». Process 1 Growth ofXH 2 Lysis of Xu
. 3 HydrolysIs 4 Denitrification
5 Growth ofXA 6LysisofX&
Process rate equation S S S02 __S_s_. NIl • AL!C -X H PI = ~_.' K +S02 K +Ss K +SNII K +SALIt 02 s NH ALIt P2 bH • X H . Xs/X H ·X P, -K. K +X IX H X 5 H S S . K 02 ._8_s__ NIl _ NO' ,X P. = ~_ •. 1'11«)) -K + SOl K + Ss K + SNII K tIrn + Stirn H NH 01 s 802 SNIl. 8 AL1t .X Ps =~-a.A' K +S . K +SNH K ALIt +SALIt A 01 02 NH P, bA ,X A
TABLE 3 ARRAY OF PROCESS RATE EQUAnONS
~
~
~
w
264
W. GUIER and T. A. LARSEN
ASIM applies different transport processes for particulate and soluble compounds (sedimenta~on: exce~s sludge removal). For observables which are not entirely soluble or particulate, eg TKN, t!te stolchiometric composition equation (3) may therefore not be applied Consequently, ~t is n~t possl~le to use such observables for process control purposes within ASIM. However for companson Wlth ~xpenmental data, the composition equation (4) may be applied to all concentrations computed by ASIM (outside of the program). Oearly the use of observables in a biokinetic model requires a detailed undet:Standing ~f the method of analysis as well as the processes used in the model itselfl Since the conservanon equ~~on (1). cll;M0t ~ applied to observables, less a priori information is available and therefore more empmcal stolchlometric parameters will be necessary. Definition of the theoretical COD The theoretical (conceptual) COD is a property of a given compound. It is based on the principle of conservation of electrical charge and elements and is therefore conservative itself. The theoretical COD is derived very much the same way as the oxidation levels known from general chemistry. In chemistry, the oxidation levels are defined arbitrarily based on the definition of a few reference values (oxidation levels zero for free elements, etc.). In order to reduce unnecessary complications, we define the reference values for the theoretical COD such that we obtain the best compatibility with the analytical COD. Per definition, we assign a COD of zero to the following compounds: H~O, H+, COZ' N}4+, S042-, P043-, Fel+. According to the standard definition of COD, oxygen has a theoreucal COD of -32 &00 / mole of O2, Using the principles of conservation, the theoretical COD of the elements C, N, H, 0, S, P, Fe and of charge can be computed from these eight definitions (see Table 4). The theoretical (conceptual) COD differs from the analytically determined COD. For most organic compounds the analytical COD approximates the theoretical COD with sufficient accuracy. Care must be taken in the context of nitrogen: e.g. nitrite exerts a positive analytical COD whereas the theoretical COD of nitrite is negative. The analytical COD cannot determine any theoretical COD which is predicted to be negative. TABLE 4 THEORETICAL COD OF ELEcrRICAL CHARGE AND TIlE MAIN ELEMENTS RELEVANT FOR WASTE WATER TREATMENT Negative charge Positive charge
(-)
(+)
+S -8
~omol·l
Carbon Nitrogen
C N
+32 -24
~omol·l·
Example computations:
~omol·l
&Oomol-·
COD(C02) COD(H+) COD(NOf)
Hydrogen Oxygen Sulphur Phosphorus Iron
H 0 S P Fe
+S -16 +48 +40 +24
~omol') ~omol')' ~omol-)
koo mol-) gcoo mol -·
=COD(C) + 2 COD(O) =32 + 2·(-16) =0 &00 mol'· =COD (H) + COD(+) =S + (-S) =0 ~o mol'· H+
=COD(N) + 3·COD(O)+COD(-)
=-24 + 3·(-16)+8 =-64 ~o mol')
= - 64/14 = - 4.57 grnn /
CO2
NOf
gNm-.N
Kinetic Considerations The concentration of any compound in a biokinetic model may become negative in the course of forward integration of the mass balance equations if the processes which consume this compound (ea. where the stoichiometric coefflcient Vj,i is negative) are not stopped. ASIM therefore requires us to choose a kinetic expression which becomes zero if any educt concentration tends towards zero. Tne following expressions fulfil this requirement and are implemented in ASIM: first- and second-order kinetics, Monod kinetics Adsorption kinetics. '
ASIM provides the following general possibility to characterise the kinetics of the biological transformation processes: 10
Pi =k·rr f(CI,C.,C a )
where k stands for the process rate constant (eg !!max)' I-I The following functions f(CI,C.,C.)are available.
Biokinetics and conservation principles in ASIM
For soluble compounds: Zero-order: First-order: Second-order: Monod kinetics: Inhibition kinetics: Two-substrate kinetics: Three-substrate kinetics:
Gas-stripping:
265
·1 ,Si · Sr Si
Sil (K + ,Si)
· K/(K+Si) · Si/(K + Si)
· Si/(K+ Si) ·kLa· Si'
Sil (Si + Sm) Si I (Si + Sm + Sn)
For particulate compounds: Zero-order, first-order and second-order analogous to soluble compounds. Adsorption kinetics: . (Xi I Xm) I (K + ~ I Xm) Inhibition kinetics 1: . K I (K + Xi I Xm) Inhibition kinetics 2: . (K - Xi I Xm) I (l.05·K - Xi I Xm)· The transformation rate (reaction or production rate) of a specific compound r· as entered into the mass balance equations is computed from the process rate p and the stoichiometric coefficients v according to: 6
ri =
2.
VJ,i
'Pj
ri has the dimension of~ L-3 T-1
jool
Procedure Suggested for Model Preparation If a new biokinetic model is to be prepared for the application with the aid of ASIM, it is suggested to
proceed as follows.
1The list of compounds which are to be considered in the model must be defmed. Compounds which are defmed in tenns of conservatives are preferred. This leads to the concentration array. 2 The list of biological or chemical reaction processes to be considered must be defmed. 3For each process one stoichiometric coefficient v is chosen as +1 or -I (dimensionless). The process rate p will relate to the compound for which v has been chosen. 4For some processes an empirical stoichiometric coefficient must be defined. Typically this is a yield coefficient. 5For each conservative considered an array of unknown stoichiometric coefficients is introduced. Here ~' Yt and zt. With this all stoichiometric coefficients of the conceptual model, expected to be different from zero, should be defmed. 6The composition matrix \ must be evaluated for all conservatives and all observables. 7With the aid of stoichiometric conservation and composition equations the absolute values of all stoichiometric coefficients must now be established. 8Then the array of rate equations must be defmed, considering that for each negative stoichiometric coefficient the process rate must tend towards zero if the concentration of the relevant compound tends towards zero. Absolute values for all kinetic parameters must be available for one temperature. 9 Since kinetic parameters typically depend upon temperature, information on the dependence of all kinetic parameters on temperature must be available. 10 The characterisation of wastewater composition depends strongly upon the model compounds chosen. Rules to transform observables into conservatives must be established. Mter going through these 10 steps, the new biokinetic model may be entered into ASIM and stored in the model library.
CONCLUSIONS The Activated Sludge SIMulation Program ASIM is a didactic program which allows us to implement most of today's biokinetic models used for the simulation of activated sludge systems. The program has all the features
266
W. GUIER and T. A. LARSEN
necessary to train students in the field and at the same time it is powerful enough to suppon the professiOnal engineer in his or her design work. The most difficult aspect of using ASIM is the development of a new biokinetic model The matrix format for the presentation of such models was first introduced together with the Activated Sludge Model No. 1 This format is extended here with a composition matrix which is the basis for sys~tic use of th~ stoichiometric conservation equations. Conservation equations are used to reduce the degrees of freedom of the biokinetic models and therefore reduce the number of empirical stoichiometric coefficients which are necessary in model application. Composition equations are introduced as a link to wastewater treatment plant reality. Understanding the principles of model presentation and accepting the very rigid requirements for the definition of conservatives and observables will facilitate model developmenL AVAILABll.JTY OF ASIM
ASIM Version 3 may be copied freely. An original is available from W. Gujer. EAWAG, 8600 Duebendorf. • Switzerland. It runs under MS DOS. REFERENCES
W.Gujer, M.Hen~, T.~o, T.Matsuo, M.C.W~ntzel and G.v.R.Marais (1995) The Activated Sludge Model No.2: Blologtcal Phosphorus Removal, Wat. Sci. Tech., 31 (2) Henze, M., W.Oujer, T.Mino, T.Matsuo, M.e.Wentzel and G.v.R.Marais (1995) 'Activated Sludge Model No.2', fA WQ Scientificand TechnicalReports, No.3. IAWQ, London . Henze, M., C.P.LJr.Grady, W'Ouier, G.v.R.Marais and T.Matsuo (1987) 'Activated Sludge Model NO.I" fAWPRC Scientificand TechnicalReports. No. f. IAWQ, London. aSSN 1OIO-707X) • Gujer W. and M. Henze (1991) 'Activated Sludge Modelling and Simulation', 1011- 1023.
WaL
Sci. Tech., 23 (4-6),
Pergamon 0273-1223(95)00198-0
Will. ScL Tech. Vol. 31, No. 2,pp. 257-266,1995. Copyrigbt@ 1995IAWQ Printed iu Great Britain. All rigbts reserved. 0273-1223195 $9'50 + 0'00
THE IMPLEMENTATION OF BIOKINETICS AND CONSERVATION PRINCIPLES IN ASIM Willi Gujer and Tove A. Larsen Swiss Federallnstitute!or Aquatic Science and Technology (EA WAG) and Swiss Federal Institute o/Technology (ETH), 8600 Dubendorf, Switzerland
ABSlRACf The Activated Sludge SIMulation program ASIM is introduced as a didactic tool to be used in design courses for the simulation of the dynamic behaviour of modem nutrient removal activated sludge systems. It allows for free definition of the biokinetic model, the flow scheme, process control strategies and load variation. Its user interface is simple enough to be used in the classroom but powerful enough to support even professional work. The most difficult aspect of ASIM is the preparation of the biokinetic model (transformation processes) to be used. A systematic use of stoichiometric conservation principles simplifies this task and at the same time reduces the number of empirical parameters. The practical application of conservation principles for charge, elements and theoretical COD is presented in detail. Composition equations are introduced as a link to the wastewater treatment plant reality. KEYWORDS
ASIM, mathematical modelling, biokinetics, theoretical COD, stoichiometric conservation equation, composition matrix, Activated Sludge Model No.2. INTRODUCfION Dynamic simulation of the behaviour of toclay's nutrient removal activated sludge systems is an effon which is based on the simultaneous application of a variety of different entities; 1A Biokinetic Model. This model describes the compounds which are used to characterize the wastewater and the activated sludge. It includes a description of the rate (kinetics) and the extent (stoichiometry) of the interaction of the different microbial transformation processes with the model compounds. 2A Model of the Transport Processes. This model describes the tlow scheme, the distribution of the influent, the recirculation streams, the mixing conditions in the reactor compartments, the sedimentation processes, the gas exchange properties, the solids removal mechanisms, etc. of the activated sludge system to be simulated. 3A Set of Operating Strategies. For the successful operation of an activated sludge system a set of operating strategies is required. These strategies may be implemented in reality with the aid of on-line process control or in the form of operator decisions. Simulation of activated sludge systems requires that these strategies may be simulated as wen. 4Extemal Forcing Functions. Wastewater treatment is never a steady state process. Extemalload is subject to daily, weekly and seasonal as well as random (storm) variations which must be considered in simulation. SA Computer Program. The implementation (application) of a mathematical model as complex as today's activated sludge models typically requires numeric techniques for the forward integration of the mass balance equations. The computer program which provides the user interface and the numeric techniques should clearly be distinguished from the mathematical model. The program ASIM can implement a whole 257
W. \.JUJeK ana I. 1\. LI\K;)t:.I'I
array of different biokinetic models and many different programs can implement the Activated Sludge Model No.1. Whereas the consulting engineer concentrates on system operation, design and optimisation (transport processes and operating strategies), the prime task of research and education in environmental engineering is the development and understanding of biokinetic models. Both activities cannot be performed without computer programs. A program which supports these activities must allow for free definition of the biokinetic model, must include a generally accepted version of the models for the transport processes (flow schemes), should include a general set of operating strategies (process control) and must be able to consider variation of loading (forcing functions). If such a program is to be used in a teaching environment, it must be possible to master the application of its prime options after less than an hour of training. The program ASIM IS designed to fulfil these requirements. ASIM-,1CfIVATEDSLUDGESlMULATIONPROGRAM
ASIM has been developed as a didactic teaching tool. It is designed to support the student in the development of biokinetic models for constant volume batch and continuous flow biological growth systems under steady state and dynamic loading conditions. ASIM is large enough to fit the Activated Sludge Models No. I (Henze et al., 1987) and No.2 (Gujer et al., 1995) and may simulate most biological nutrient removal activated sludge system flow schemes which are used today. Many consulting companies use ASIM to deal with their specific problems. Major Options of ASIM
ASIM offers the following major options. I Free definition of the biokinetic model (Definition of soluble and particulate compounds, number of transformation processes, stoichiometry and kinetics of these processes). 2Free definition of the flow scheme: Constant volume batch reactors, continuous flow chemostats and series of chemostats, activated sludge systems with secondary clarifier. internal recirculation. two independent influents, etc. 3 Free definition of process control strategies (only proportional controllers are implemented). 4 Computational routines to find steady state solutions as well as free dynamic simulations (diurnal, seasonal variation, batch experiments, tracer curves, etc.). 5 Graphic support of the analysis of simulation results as well as experimental data. 6Communication with spreadsheet programs. ASIM Verso 3 is delivered in three versions: (i) A reduced version, which is typically sufficient for student work and which has reduced capacity for the size of models and flowschemes. (ll) The full version which may be useful for project, research and thesis work for more advanced students. (iii) A batch version of the full interactive version which is useful if time-consuming. repetitive simulation work must be performed. The full version is used by consulting companies as well
Applying ASIM to the Activated Sludge Model No.2 In order to demonstrate the potential of ASIM, the Activated Sludge Model No.2 (Gujer et all995) will be used. The kinetic and stoichiometric parameters as well as the influent composition are given by Gujer et at. (1995). A tlow-scheme as shown in Fig. 1 is defmed (BioI. P removal, ucr Process). The internal recirculation and excess sludge removal rate D are automatically controlled such that the nitrate concentration in the second reactoris maintained at around 0.75 g m-3 NO'f-N and the total activated sludge concentration in the influent to the secondary clarifier(reacoor 5) is maintained at around 3500 g m-3 TSS. y
Table I shows the results computed for the steady state for the flow-scheme in Fig. 1. The required SRT (Solids Retention Time) predicted to maintain the predefined activated sludge concentration is IS days. This steady state is predicted based on average stationary loading of the system and is chosen as the initial condition for the simulation of the dynamic behaviour of the system (Figures 2 and 3). Fig. 2 is a summary of the defmed variation of the influent flow rate and the predicted (controlled) required internal recirculation rate as well as the required (controlled) excess sludge removal rate DII• Fig. 3 demonstrates that the dominant storage of poly-hydroxy-alkanoates is shifted from the first to the second and
Biokinetics and conservation principles in ASIM
259
Flowscheme of the plant Contol loops aCllv.1 02 u'uration " 10.00 SludQ.aQ•• SQT • 15.00
"20000.00
Inllu.nt
;
I
!
I
i; !
3
2
I•
5
1
!
i Q.OIurnsludQa " 20000.00
AIi~c1or
Uolu...
I
2
3
2000.00
2000.00
2000.00
2.0
2.0
2.0
02 Conc. Kia Ualu.
5
1
3000.00
3000.00
2.00
2.00
Fig. 1. Flowscheme of the activated sludge system as drawn by ASIM. TABLE I PREDICTED STEADY STATE AT 20°CFOR TIIE FLOWSCHEME SHOWN IN FIG. 1. 1lIE UNITS ARE GRAMS, METERS, DAYS. OXYGEN CONSUMPTION IS IN 1m m-3 dol. (Table provided by ASIM)
02 S Oxygen S Substrate COD COD S Acetate S Ammonium N N S Nitrate P S Phosphate S Alkalinity Mol COD S Inert S N2-Nitrogen N COD X Inert X Substrate COD X BM HETerot COD COD X BM PAD P X FP in PAO X PHA in PAO COD X BM AUTotro COD X Susp.So1idsTSS Oxyqenconsumotion
Influent Reactor Nr. 1 2 0.00 0.01 0.00 5.21 1. 09 30.00 17.75 0.89 20.00 11. 93 6.92 16.00 0.00 0.73 0.00 21.45 14.31 3.60 3.96 4.12 5.00 28.91 29.79 30.00 6.51 0.00 11. 74 659.93 1240.26 25.00 57.61 125.00 41.05 398.40 30.00 754.42 199.90 0.00 388.31 42.54 0.00 104.25 43.53 0.00 29.98 0.00 20.19 39.10 180.00 1857.97 3493.68 20.04 50.44
3 0.00 1.18 1.42 7.70 0.08 18.20 4.01 29.98 12.40 1239.13 36.78 748.78 385.71 100.35 37.94 38.88 3472.41 20.22
4 2.00 0.42 0.05 2.30 4.85 2.86 4.03 30.24 12.63 1239.98 25.28 752.55 396.07 115.37 10.83 39.71 3509.22 760.12
5 2.00 0.33 0.01 0.44 6.87 0.30 3.87 30.47 12.79 1235.71 19.42 748.36 394.88 117.36 1.58 39.69 3492.08 371.17
third reactor during periods of high organic loading. This is possible because the deniIrifying reactors 2 and 3 are operated under continuous nittate limitation with the aid of process control. Graphic results such as shown in Figs. 2 and 3 are easily available in ASIM for all process rates, state variables (concentrations) and forcing functions. They suppon the student in analyzing the behaviour of a system.
The use of ASIM is simple enough, such that a student who is able to understand the Activated Sludge Model No.2 may perform the simulation which is shown here after about one hour of training with the program. This requires that the simulation is perfonned with a biokinetic model which is provided together with ASIM.
w. GUIER and T. A. LARSEN
260
_I"'l~
ASM No. 2 simplified
................ Aedrculetton
•••••••• Ox
D,u.. nal va.. ,at,on Pel' cent 100-----------~-~-""!"'"-""!"'"-~-~--,
90 80 70
50 40 30
:··•.·.·IT:l········r:.;J=::FT':;F:,l~:l;;.E .
o ot.:.:··;';;·';;··;";';;-;;';·;';;·':'~:.l·........;6---8;..&.;-1..0-....;,12-...14---1;.6--1~8--2:'"0-~22~~24
Hou.. s
Fig. 2. The variation of the influent Q;. as dermed by the user and the internal recirculation R together with the excess sludge removal Ox as predicted by ASIM. 100% is equal to 30000 m3 dol for Qm and R and 1.00 dol for Ox. Figure provided by ASIM.
ASM No.2 simplified PHA Sto.. aQe
PAD
_ A t o a c l o r ..... ................ hK1Of" .... 2
•••••••• -"ac1or
_.ac1or ................
~lCtor
3 1
Hr. I
700 630
560
420
350 280 210 140
70
o ~?:b=b:::b::::±::::::::=::±:~~~d o 2 4 6 8 10 12 14 16 18 20 22 24 Hou.. s
Fig. 3. The diurnal variation of the process rate p for storage of poly-hydroxy-alkanoates in g PHA m-3 dol.
PREPARING BIOKINETIC MODELS FOR ASIM The most difficult task when applying ASIM is the dermition of a new biokinetic model In this chapter principles will be introduced which allow to simplify this task. As it is easier to introduce these principles for a specific case, a bioldnetic model is introduced in Tables 2 and 3 with the following information.
Biokinetics and conservation principles in .4SIM
261
1Soluble compounds are defined as compounds which are transponed together with water (advection). These compounds cannot be concentrated by settling, their concentration is given by the symbol Sj. Particulate compounds in addition to being transponed with water may at the same time be separated bY sedimentation and removed via excess sludge lIlelI' concentration is given by lIle symbol ~. Compounds which include soluble as well as particulate fractions will be introduced below with the symbol G; it must be remembered however lIlat ASIM cannot deal with such compounds. 2The concentration array Ca defmes lIle concentrations of all compounds used in the model. The index i (here 1 .. 10) runs over all compounds: Soluble compounds Sj: CI • S02 • Dissolved oxygen (g m-' Oil C2 .. Ss • Readily biodegradable organic substrate [g m-l COD] C, .. SNH ... Ammonium concentration h~ m-' Nl4+.N] C. =SN03 • Nitrate concentration [g m:rNOi-N] y • Sm • Dissolved dinitrogen [g m-l Nil C6 .. SALX ... Alkalinity Imol m-3 HCOi) Particulate compounds X;: C, =Xu =Heterotrophic biomass [g m-l CODI CS .. XA .. Autotrophic, nitrifier biomass [g m- COD) C9 =Xs .. Slowly biodegradable substrate [g m-l COD] CIO .. XTSS .. Total suspended solids [g m-3 TSS] 3The stoichiometric matrix vJ)' where j stands for the number of the process (here 1 •• 6) and i for the compound (here 1 .. 10). For each process one stoichiometric coefficient is chosen as dimensionless wilh a value of +1 or -I indicated in bold. Some coefficients are given based on empirical stoichiometry (eg v'.2 = -IIYu) which must be obtained from experiments. For each process 3 stoichiometric coefficients are given with the variables xJ' YJ and zt. These coefficients may be obtained from stoichiometric conservation equations as introduced t5elow. The stoichiometric coefficients for TSS, vj.TSS - Vj lOt may be obtained from a stoichiometric composition equation, as introduced below. • 4The composition matrix \k,1 defmes the composition of the different compounds of the model Information is given in terms of the malerials defmed at Ihe left of each row (COD, nitrogen, electrical charge, TSS, total Kjeldahl nitrogen TKN), for which the index k (here 1 .. 5) is used. Eg oxygen is defined as negative COD which results in \11 • -I g COD I g 0lor in any 14 g of NIJ..+-N (l mol) 1 mol of positive charge is contained, this results in \3 ~ = 1/14 mol Charges g-1 N. The compositIon of the heterotrophic biomass (iNXH and iTSXH ) may be obuimed from chemical analysis of 'purified' biomass. 5 Table 3 contains the array PJ of the process rate equations, which are needed to predict the transformation rates for the different compounds in the mass balance equations. Details will be introduced below. Conceptional Model/Observables A conceptual model must fulfil the following criteria. 1In terms of the conservatives of the model (here COD, N, Charge), all imponant educts, products and transformation processes must be contained I 2A conceptual model cannot include overlapping compounds (eg TKN includes NH., these two compounds are therefore overlapping). Compounds which do not follow this criterion may be included in the model, they are termed 'observables' and are not part of the conceptual model. 3 All compounds which affect kinetics must be part of the conceptual model A few examples might help clarify this notion of a conceptual model.
If one has chosen carbon as a conservative element in a model, according to criterion number one, ~ must be included as a model compound. In the Activated Sludge Model No.1 (Henze et al., 1987), the theoretical COD was chosen as a conservative and not carbon. Since the theoretical COD of ~ is zero (for definition see below), lIle conceptual model could be written without including COJ. Criterion number two is nonnally applied intuitively. Problems arise when one wants to include 'observabtes' in the model in order to describe process control strategies. As an exanwle. it is often useful to include the observable TSS in the model in order to control the sludge concentration m the reactors. Since TSS overlaps wilh the particulate compounds XH, XI and Xs, TSS may not be considered part of the conceptual model.
....,...
W.
UUJt:.~
ana 1.
~ L.~t:.I'l
Of course, it is possible to cons~ct conceptual JOOdels which do not profit from any conservation princip!es. For such models at least critena number two and three must be fulfilled. As a consequence, any a pnori
information from conservation principles is 10SL
Conservation Principles I Conservation Equation
Olemical elements (here nitrogen), electrical charges and a theoretical COD, as introduced below, are conservative and may neither be produced nor consumed in a biological or chemical transformation process. This conservation principle is expressed in mathematical fonn in the stoichiometric conservation equation:
, LV i-I
(1)
IJ '\I
The index i runs over the compounds 1 .. 9, which are expressed in terms of conservatives. XTSS (i '" 10) is not subject to conservation since TSS overlaps with the particulate compounds Xu' X A and Xs . The index Ie runs over the conservatives 1 .. 3 and does not include the observables (k '" 4 .. 5). The stoichiometric conservation equation (1) is only valid for conservatives (elements, charges, COD) and cannot be applied to observables which are not subject to conservation such as TSS or Kjeldahl nitrogen. The conservation equation (1) may be applied to all biological transformation processes (j = 1 .. 6) and all conservatives (k = 1 .. 3). Here, this results in 3 x 6 = 18 conservation equations which provide a priori infonnation and result in a corresponding reduction of the degrees of freedom of the biolcinetic model Typically the system of conservation equations may easily be solved for the unknowns, here the three vectors xJ (COD conservation), YJ (N cons.) and ~ (charge cons.). Leaving out all products v ~ . \u which are equal to zero, an example of a conservation equanon is provided below: Yl
1 =VI,3 =-(Vu '\2,2 +V1,7 '\2,7)/\2,3 =-(--'\NSS + 1'\NXH)11 Y H
(2)
Since ASIM is applicable to a variety of biokinetic models. it is not possible to solve equation (2) within the program. Preparing a biokinetic model for ASIM must therefore include solving these equations by hand. Composition Equation H the production of an observable is fully described within the conceptual roodel and if the observable is
either entirely soluble or entirely particulate. a stoichiometric coefficient may be computed and the observable included in the stoichiometric matrix. From the stoichiometric composition equation (3), the stoichiometric coefficient is computed.
v·J,Il • ;'1 rv··J,I ·tt·.. 9
(3)
Here for a particulate compound, vj,i • 0 for i = 1 .. 6 and for a soluble compound, vj,i ... 0 for i ... 7 .. 9.
ASIM will only perform correct mass balances when an inlet concentration ofthe observable is also determined. The inlet concentration of an observable is computed from the composition eq'~ation (4).
(4)
c,: the concentration the observable compound in the inlet which is not accounted for by the compounds of the conceptual model In the case of TSS. it might be the particulate inorganic compounds in is
of
Ie
the inlet which are normally not included in the biolcinetic model Not including these compounds in the inlet concentration of TSS would however lead to an error in the mass balances performed by ASIM. Please note that an inlet concentration computed according to equation (4) might not be identical to the corresponding measured concentration. As an example. the enmeshment of colloidal material into the floes is normally not modelled. Instead, this colloidal material is described as particulate already in the inlet to the treannent plant although it would at this point not be measured as TSS. Such phenomena arise from model simplifications and emphasize the importance of a detailed mechanistic understanding of a given model
TABLE 2
ARRAY OF MODEL COMPOUNDS, STOICHIOMETRIC MATRlX AND COMPOSmON MATRIX
SOl No.j 1 2 3 4 5 6 No.k 1 2 3 4
5
No.i Processes
GrowthOfXH LysisofXH Hydrolysis Denitrification GrowthofXA LysisofXA Conservatives
roo
~
1
Ss COD 2
SNH N 3
XI
-IIYH
VI Y2 Yl Y. Ys Y,
Xl -IIYa Xs
-1
I
N Mole Otarl!e
Observables TSS TKN
b,••
1 1/14
SN01 N 4
X4
INA
Concentration Array C; SAlK SN2 XH Mole HCOJ - COD N 6 5 7 Stoichiometric Matrix v· j 1 ZI .1 Z2 Z3 +1 -x. Z4
Xs COD 9
XTSs TSS 10 v •• n
X2
-1 +1 ·1
X6
1
1
1
tNXH
tNXA
tNXS
Zs Z4
Com position Matrix tJc . -4.57 -1.71 1 I -1/14 -1
XA COD 8
V, In V1tn V4tn
Within the double frame, a conceptual model is presented. Outside the double frame, observables are given as a link: to the reality as observed at the wastewater treat· mentplant ttl
~ =>
Ve.n
g.
V~tn
'"
§
Q.
n
g
~.
g '0
::I.
I b,••
1
~
tTSXH
\TSXA
\TSXS
-[
\'IXH
\NJ(A
\!llXS
~
or
». Process 1 Growth ofXH 2 Lysis of Xu
. 3 HydrolysIs 4 Denitrification
5 Growth ofXA 6LysisofX&
Process rate equation S S S02 __S_s_. NIl • AL!C -X H PI = ~_.' K +S02 K +Ss K +SNII K +SALIt 02 s NH ALIt P2 bH • X H . Xs/X H ·X P, -K. K +X IX H X 5 H S S . K 02 ._8_s__ NIl _ NO' ,X P. = ~_ •. 1'11«)) -K + SOl K + Ss K + SNII K tIrn + Stirn H NH 01 s 802 SNIl. 8 AL1t .X Ps =~-a.A' K +S . K +SNH K ALIt +SALIt A 01 02 NH P, bA ,X A
TABLE 3 ARRAY OF PROCESS RATE EQUAnONS
~
~
~
w
264
W. GUIER and T. A. LARSEN
ASIM applies different transport processes for particulate and soluble compounds (sedimenta~on: exce~s sludge removal). For observables which are not entirely soluble or particulate, eg TKN, t!te stolchiometric composition equation (3) may therefore not be applied Consequently, ~t is n~t possl~le to use such observables for process control purposes within ASIM. However for companson Wlth ~xpenmental data, the composition equation (4) may be applied to all concentrations computed by ASIM (outside of the program). Oearly the use of observables in a biokinetic model requires a detailed undet:Standing ~f the method of analysis as well as the processes used in the model itselfl Since the conservanon equ~~on (1). cll;M0t ~ applied to observables, less a priori information is available and therefore more empmcal stolchlometric parameters will be necessary. Definition of the theoretical COD The theoretical (conceptual) COD is a property of a given compound. It is based on the principle of conservation of electrical charge and elements and is therefore conservative itself. The theoretical COD is derived very much the same way as the oxidation levels known from general chemistry. In chemistry, the oxidation levels are defined arbitrarily based on the definition of a few reference values (oxidation levels zero for free elements, etc.). In order to reduce unnecessary complications, we define the reference values for the theoretical COD such that we obtain the best compatibility with the analytical COD. Per definition, we assign a COD of zero to the following compounds: H~O, H+, COZ' N}4+, S042-, P043-, Fel+. According to the standard definition of COD, oxygen has a theoreucal COD of -32 &00 / mole of O2, Using the principles of conservation, the theoretical COD of the elements C, N, H, 0, S, P, Fe and of charge can be computed from these eight definitions (see Table 4). The theoretical (conceptual) COD differs from the analytically determined COD. For most organic compounds the analytical COD approximates the theoretical COD with sufficient accuracy. Care must be taken in the context of nitrogen: e.g. nitrite exerts a positive analytical COD whereas the theoretical COD of nitrite is negative. The analytical COD cannot determine any theoretical COD which is predicted to be negative. TABLE 4 THEORETICAL COD OF ELEcrRICAL CHARGE AND TIlE MAIN ELEMENTS RELEVANT FOR WASTE WATER TREATMENT Negative charge Positive charge
(-)
(+)
+S -8
~omol·l
Carbon Nitrogen
C N
+32 -24
~omol·l·
Example computations:
~omol·l
&Oomol-·
COD(C02) COD(H+) COD(NOf)
Hydrogen Oxygen Sulphur Phosphorus Iron
H 0 S P Fe
+S -16 +48 +40 +24
~omol') ~omol')' ~omol-)
koo mol-) gcoo mol -·
=COD(C) + 2 COD(O) =32 + 2·(-16) =0 &00 mol'· =COD (H) + COD(+) =S + (-S) =0 ~o mol'· H+
=COD(N) + 3·COD(O)+COD(-)
=-24 + 3·(-16)+8 =-64 ~o mol')
= - 64/14 = - 4.57 grnn /
CO2
NOf
gNm-.N
Kinetic Considerations The concentration of any compound in a biokinetic model may become negative in the course of forward integration of the mass balance equations if the processes which consume this compound (ea. where the stoichiometric coefflcient Vj,i is negative) are not stopped. ASIM therefore requires us to choose a kinetic expression which becomes zero if any educt concentration tends towards zero. Tne following expressions fulfil this requirement and are implemented in ASIM: first- and second-order kinetics, Monod kinetics Adsorption kinetics. '
ASIM provides the following general possibility to characterise the kinetics of the biological transformation processes: 10
Pi =k·rr f(CI,C.,C a )
where k stands for the process rate constant (eg !!max)' I-I The following functions f(CI,C.,C.)are available.
Biokinetics and conservation principles in ASIM
For soluble compounds: Zero-order: First-order: Second-order: Monod kinetics: Inhibition kinetics: Two-substrate kinetics: Three-substrate kinetics:
Gas-stripping:
265
·1 ,Si · Sr Si
Sil (K + ,Si)
· K/(K+Si) · Si/(K + Si)
· Si/(K+ Si) ·kLa· Si'
Sil (Si + Sm) Si I (Si + Sm + Sn)
For particulate compounds: Zero-order, first-order and second-order analogous to soluble compounds. Adsorption kinetics: . (Xi I Xm) I (K + ~ I Xm) Inhibition kinetics 1: . K I (K + Xi I Xm) Inhibition kinetics 2: . (K - Xi I Xm) I (l.05·K - Xi I Xm)· The transformation rate (reaction or production rate) of a specific compound r· as entered into the mass balance equations is computed from the process rate p and the stoichiometric coefficients v according to: 6
ri =
2.
VJ,i
'Pj
ri has the dimension of~ L-3 T-1
jool
Procedure Suggested for Model Preparation If a new biokinetic model is to be prepared for the application with the aid of ASIM, it is suggested to
proceed as follows.
1The list of compounds which are to be considered in the model must be defmed. Compounds which are defmed in tenns of conservatives are preferred. This leads to the concentration array. 2 The list of biological or chemical reaction processes to be considered must be defmed. 3For each process one stoichiometric coefficient v is chosen as +1 or -I (dimensionless). The process rate p will relate to the compound for which v has been chosen. 4For some processes an empirical stoichiometric coefficient must be defined. Typically this is a yield coefficient. 5For each conservative considered an array of unknown stoichiometric coefficients is introduced. Here ~' Yt and zt. With this all stoichiometric coefficients of the conceptual model, expected to be different from zero, should be defmed. 6The composition matrix \ must be evaluated for all conservatives and all observables. 7With the aid of stoichiometric conservation and composition equations the absolute values of all stoichiometric coefficients must now be established. 8Then the array of rate equations must be defmed, considering that for each negative stoichiometric coefficient the process rate must tend towards zero if the concentration of the relevant compound tends towards zero. Absolute values for all kinetic parameters must be available for one temperature. 9 Since kinetic parameters typically depend upon temperature, information on the dependence of all kinetic parameters on temperature must be available. 10 The characterisation of wastewater composition depends strongly upon the model compounds chosen. Rules to transform observables into conservatives must be established. Mter going through these 10 steps, the new biokinetic model may be entered into ASIM and stored in the model library.
CONCLUSIONS The Activated Sludge SIMulation Program ASIM is a didactic program which allows us to implement most of today's biokinetic models used for the simulation of activated sludge systems. The program has all the features
266
W. GUIER and T. A. LARSEN
necessary to train students in the field and at the same time it is powerful enough to suppon the professiOnal engineer in his or her design work. The most difficult aspect of using ASIM is the development of a new biokinetic model The matrix format for the presentation of such models was first introduced together with the Activated Sludge Model No. 1 This format is extended here with a composition matrix which is the basis for sys~tic use of th~ stoichiometric conservation equations. Conservation equations are used to reduce the degrees of freedom of the biokinetic models and therefore reduce the number of empirical stoichiometric coefficients which are necessary in model application. Composition equations are introduced as a link to wastewater treatment plant reality. Understanding the principles of model presentation and accepting the very rigid requirements for the definition of conservatives and observables will facilitate model developmenL AVAILABll.JTY OF ASIM
ASIM Version 3 may be copied freely. An original is available from W. Gujer. EAWAG, 8600 Duebendorf. • Switzerland. It runs under MS DOS. REFERENCES
W.Gujer, M.Hen~, T.~o, T.Matsuo, M.C.W~ntzel and G.v.R.Marais (1995) The Activated Sludge Model No.2: Blologtcal Phosphorus Removal, Wat. Sci. Tech., 31 (2) Henze, M., W.Oujer, T.Mino, T.Matsuo, M.e.Wentzel and G.v.R.Marais (1995) 'Activated Sludge Model No.2', fA WQ Scientificand TechnicalReports, No.3. IAWQ, London . Henze, M., C.P.LJr.Grady, W'Ouier, G.v.R.Marais and T.Matsuo (1987) 'Activated Sludge Model NO.I" fAWPRC Scientificand TechnicalReports. No. f. IAWQ, London. aSSN 1OIO-707X) • Gujer W. and M. Henze (1991) 'Activated Sludge Modelling and Simulation', 1011- 1023.
WaL
Sci. Tech., 23 (4-6),