A method to determine reaction kinetic data for waste treatment

Water Research Pergamon Press 1973. Vol. 7, pp. 547-557. Printed in Great Britain

A METHOD TO DETERMINE REACTION KINETIC DATA FOR WASTE TREATMENT M. Bo~.s and L. H~TMANN Leiter des Lehrgebietes Ingenieurbiologie, Universit~it Karlsruhe, D-7500 Karlsruhe, I, Kaiserstrasse 12, Federal Republic of Germany (Received 11 May 1972)

BSB -- BOD ELIM FAB FASB 1/KKVS Km Lo So VBL Vm.,

NOTATION Biochemical oxygen demand Final value of activity Autoxidation factor, g bacteria-N mg-t 02 Growth factor, g bacteria-N rag-t Oz Inhibition factor of substrate 2 by substrate 1, I rag- t Oz Michaelis constant, mg Oa 1-t Total oxygen demand, mg O, 1-t Substrate concentration, (T = 0) ml 1- t Endogenous respiration, mg 02 g-t bacteria-N, min Maximal velocity, mg 02 g-t bacteria-N, min

1. INTRODUCTION FURTHER progress in biological sewage treatment as in all other industrial processes is, after a certain level has been reached mainly based on a thorough understanding o f the fundamentals and the ability to describe these fundamentals in a specific way, using mathematical expressions. This then makes it possible to transform the art of designing sewage treatment plants for special purposes into a science. The background of knowledge industrial fermentation processes can be used for this purpose. In this paper a method is outlined to study and describe oxidation processes. Emphasis is put on the possibilities and also on the limits of this method. The data gained by this method finally are shown on graphs, which allow the design of treatment plants. Basic information has been published already previously (Bog, 1970; BLr~U, 1971; HARTMANN, 1968; HARTMANN and WILDERER, 1969, 1971; HARTMANN et aL, 1971 ; WILDERER,1969). 2. MATHEMATICAL BACKGROUND The method is based on the fact that processes in bacteria-nutrition-broth systems are governed mainly by biochemical processes, if the physical processes are not limiting factors. This concept is outlined in several papers (Mo~roD, 1947; PgErOR~S, 1969). The process can be studied by observing the growth (using the M o n o d equation), the rate of substrate removal or the rate of oxygen requirements (BOD-curve). This paper is based on the evaluation of BOD-curves, though the mathematical model can also be applied for the reactions mentioned above. The approach is described graphically in FIG. 1. After the BOD-curves have been obtained (which can be of very different shape-line (a)) the most probable biochemical reactions responsible for the shape of the curves have to be outlined (Bogs, 1970). 547

548

M. Bogs and L. HARTMANN

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Fro. 1. Scheme o f operation.

(Example 1 is described as a normal enzyme reaction plus endogenous respiration plus increase of bacteria; example 2 is characterized by substrate inhibition, adaptation and increase of bacteria; example 3 is characterized by two normal reactions either following each other plus growth, respectively as the addition of two reactions with reaction 1 ending earlier than reaction 2.) The mechanisms of other well known biochemical reactions such as competitive inhibition, adaptations by allosteric enzymes etc. can also be included. After the most probable mechanisms have been selected, the number and the character of the parameters responsible have to be given (line d). In the next step (line e) rough data for the most probable numerical values for the parameters chosen have to be given, and depending on the system, certain limits for the parameters, which the computer is not allowed to exceed, can be set. The computer then checks the possibilities of the parameters within this range, by iteration (line f), and finally prints the theoretical curve which has the least "sum of the squares" compared to the experimental data and also gives the biochemical parameters that describe the reaction. The computer cannot yield better information than is supplied to it. Therefore the results depend upon the evaluation of the BOD-curves.

Example In a theoretical experiment two enzyme reactions with the characteristic parameters given in TABLE 1 were assumed to start at the same time and run independently of each other, the total reaction then being the sum of the two separate reactions.

Determination Of Reaction Kinetic Data

549

TABLE I

Reaction 1

Reaction 2

6

I0

mg Oz g- ~, N, min

30

20

mg O2 I- t

1000

500

mg O. 1- ~

Vnl=~

(maximal velocity) K. (Michaelis constant) BOD (total) Endogenous respiration

2"00

Autoxidation-factor Growth factor

0-0006 0-001

mg O=g-1 N, min g N mg- ' O2 g N mg-t O.

It was further assumed, that endogenous respiration is continued, and that there is an increase in the endogenous respiration according to the progress of the substrate oxidation. The experimental data are given in FIo. 2 (symbols). Altogether this problem contains nine parameters and the computer has the task by iteration to find that combination which yields the minimal mathematical error. Fiouem 3 shows the process of the iteraction and the results. (In FtGtatE 3a the relation between iterated parameters (Pa and input parameters P,== is given depending on the number of iterations.) FxotrR~ 3b contains the minimal error sum of squares depending on the number of iterations. T-kip -'0-0 S (L/GN) o---(>--c2 0000

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80 T,

240

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FIG. 2. Theoretical example for analytical data (symbols) and computer results for the input parameters (lines). System: two independent enzyme reactions plus endogenous respiration (see text and compare with F[o. 4).

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FIG. 3. (a) Change of parameter combination with the number of iteration. (b) Declining error sum of squares with the number of iteration.

After 25 iterations the difference between input and checkout values is less than 1 per cent. The method proved to be successful, as shown again in FIG. 4. It can be concluded, that also other problems can be solved, if the proper biochemical mechanisms can be selected for the input. 3. L I M I T S

OF THE

METHOD

(a) Limits of mathematical nature In the example given above up to nine parameters were handled by the computer. Theoretically a much higher number of parameters can be handled. But with increasing number of parameters the difficulties also increase. For example, a combination may result, which is at a certain level o f a mathematical error, being surrounded by combinations with a higher mathematical error. The computer is then unable to leave this valley and walk over a small hill to continue its way to the lowest valley. In FIG. 3 between the iteration steps 7 and 12 such a possibility is indicated by a plateau. Only the dight inclination allowed the computer to continue its work. The only way to overcome these difficulties is an improved and more exact input with increasing number of parameters. (b) Non-mathematical limits The greater difficulties lay in selecting the proper mechanisms. In many e,ases more than one combination leads to a result which can be mathematically correct. In this

Determination of Reaction Kinetic Data

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FIG. 4. Theoretical example for analytical data (symbols) and computer results after 25 iterations (lines). System; two independent enzyme reactions plus endogenous respiration (compare with Fm. 2).

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FIG, 5, Theoretical example for analytical data (symboLs)and computer result after 17 iterations (lines). Theoretical example. Two independent enzyme reactions plus endogenous respiration plus increase in activity for the second reaction during the degradation. But wmlyaed as the system: Two enzyme reactions, number two inhibitod by number one, plus endogenous respiration [compare with Fro. 6(a) and Co)]. w.g.

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FIe. 6(a). System of FIG. 4. tested by second substrate addition proves that the combination "two enzyme reactions, number two inhibited by number one, plus endogenous respiration" is not correct.

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FXO. (~qO). System of FIG.. 4 proves that the combination "two independent enzTm¢ reactions

plus endol~nous respiration plus incnm~ in activity for the second reaction during the degradation" is correct.

Determination of Reaction KineticData

553

case also more than one combination has to be proved. This can be done by mathematical approximation. The final step then is the comparison of the results, which yields the most probable of the selected combination of mechanisms. But ff all of them fail to be probable, new combinations have to be selected. If more than one show the same probability a further test with the computer allows further improvement. Example. Two additive enzyme reactions with an increase in activity and an increase in endogenous respiration can also be described by two consecutive enzyme reactions. The computer analysis resulted in the same probability (FIo. 5). In this case a mathematical check-up showed that a second addition of substrate allowed the two systems to be separated [FIG. 6(a) and 6(b)]. 4. APPLICATION OF THE METHOD FOR PRACTICAL PURPOSES Two practical examples analysing short term BOD-tests are given. The following has to be kept in mind (a) Each set of data may be connected with an arror. Therefore even if the exact combination of mechanisms is selected, errors will occur. (b) Activated sludge (which was used for the experiments) is a heterogenous system, which allows only a rough prediction and description of the endogenous repiration. For the description of endogenous respiration (the sum of many separate enzyme reactions) a first order reaction was selected. It proved to fit the data best. E:cample 1. Oxidation of a brewery waste by activated sludge. (FIO. 7). T - k i p -- 0"0 0"--"0'--~ ~--'-'~--"~

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50

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150

200

mill

FIG. 7. Practical example; degradationof brewerywaste by activated sludge. Experimental data = symbols.Computer data = lines.

554

M. Bof;s and L. HARTM,-~.';:';

The best fit between the analytical data (symbols) and the computer results (line) proved to be a combination of two additive enzyme reactions. This means, that two substances (or groups of substances) are oxidized independently. It is assumed, that the two substances are maltose and protein. The reaction parameters to be found were: for reaction No. I (Maltose): Maximal velocity: 5.44 mg oxygen g-1 bacteria-N leer m i n - t Michaelis constant: 15 mg oxygen equivalent lTotal BOD: 1200 mg oxygen 1- ~ ; for reaction No. 2 (Protein): Maximal velocity: 2.25 mg oxygen g - t bacteria-N rain - t Michaelis constant: approximating to zero order kinetics Total BOD: 165 mg oxygen 1-~ Protein oxidation therefore ends earlier than maltose oxidation. Example 2. Oxidation of cheese factory wastes. It proved to be more difficult to interpret the data than in example 1. Three combinations gave a good approach. Combination I: II:

Two additive enzyme reactions + endogenous respiration. (error: 1.03 %) Two additive enzyme reactions with an inhibition of reaction one by reaction two. (error: 0-83 %) T-kip u

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~_ : . : ~ 80

160 T,

: 240

320

rain

Fio. 8. Practical example: degradation of cheese factory waste by adapted activated sludge. Experimental data = symbols. Computer data = lines.

Determination of Reaction Kinetic Data

III:

555

Two additive enzyme reactions with increase in activity plus endogenous respiration. (error: 0.63 %)

According to the mathematical error, combination III may be the most probable one (FIG. 8).

A further observation with unadapted activated sludge also supports combination II[. In this case the initial velocity only amounted to one-third of the velocity of adapted sludge. But during the experiments an increase in activity occurred, which finally reached the values of the adapted sludge. Also in this case, two substances (or groups) are present and are degraded separately. Degrodotion 9 5 % o .....

1 0 0 0 mg B o c t e r i o

.....

250

500 mgBact"eria -' 0

mg 8 c c t e r i o

4000C

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F[o. 9. Oxygen demand and contact time depending on substrate concentration for the system "cheese factory waste--adapted activated sludge". Parameter: MLSS (expressed as bacterianitrogen).

5. A P P L I C A T I O N OF M E T H O D F O R D E S I G N I N G T R E A T M E N T PLANTS

The data and information gained by this method, allow a nearly exact mathematical description of the process, but they are still too theoretical to be directly applied for designing treatment plant. Further graphs are therefore given, in order to assist the practical engineer. Of course, certain parameters have to be fixed. In this case, this is the quality of the effect required. F I o u ~ 9 shows the results based on calculations with the purification effect set at 95 per cent. Depending on the aeration time and sewage strength a certain concentration of activated sludge is necessary to yield this purification effect.

556

M. Bo~:s and L. HARTMANN

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Oeg~ada~'~on 952/°

4 ~C~2

--

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IO00mg 8octeria -N -~ 500 mg Ba~eria-N 250 mq Bacteria-N-

r~

L~

. . . . Incregse in bacteria - nitrogen

FIG. 10. Oxygen demand and contact t i ~ defending on substmt¢ concentration for the system "brew¢~ w~t¢-activaled sludge", l ~ m ~ t e r : MLSS (exp~ssed as b~tcda-nitm~n).

Furthermore the oxygen demand (both for endogenous respiration and substrate oxidation) can be read in the upper part of the graph. FIGtrg~ 10 gives the same values for the brewery waste described in example 1. 6. A P P L I C A T I O N

TO

MORE

COMPLEX

SYSTEMS

The two examples given are rather simple compared to other systems which may occur in practice. In such cases no exact description may be obtainable. But in many cases a description which at least covers the analytically gained results though not describing the real nature of the reactions, may be claimed to be an improvement compared to the first order BODs-kinetics.

Additional information needed For a better understanding and a higher degree of accuracy in all the eases mentioned additional information is needed and can be gained by special chemical observations. A combined analysis which includes chemical observations of substrate removal and growth observation in conjunction with the BOD-curve will give such a better insight. Research that includes this is already in progress on simple and complex biosystems. SUMMARY

(I) A method, based on enzyme kinetics, has been described to study the true nature of BOD-curvcs.

Determination of Reaction Kinetic Data

557

(2) By mathematical iteration, using the computer, the most probable combination of enzyme reactions can be evaluated. (3) Using this method, the background of BOD-curves of a brewery waste and a cheese factory waste were tested. (4) It is assumed that a combination of BOD-curves plus chemical analysis of simple and complex systems will lead to a more thorough understanding of the degradation processes and will also give better data for plant design. (5) Improved data for plant design are given for two types of waste. REFERENCES Bogs M. (1970) Mathematische Analyse der Kinetik des biochemischen Sauerstoffbedarfs. Karlsruher Berichte zur lngenieurbiologie, Heft 4. BUgAU F. (1971) Stofftransport und Stoffabbau in einem Modelltropfk/Srper mit laminarem Fl~sigkeitsfilm. Karlsruher Berichte zur lngenieurbiologie, Heft 5. HAgTMAt,~ L. (1968) Biochemische Parameter beim BelebtschlammL, erfahren. GWF 109 942. HARTMAh~qL. and WU.D~REgP. (1969) Physical and biochemical aspects of BOD-kinetics. IV. Int. Conf. Water PoUut. Res., Prag I 14. HARTMAt,r~ L. and WILDEReR P. (1971) Reaktionskinetische Analyse mikrobiologischer Vorggnge. Zentralblatt f. Bakt. 1, 216, 225-267. HARTMA~ L., WILt)EgEgP. and JANECKOVAJ. (1971) Kartierung der biochemischen AktivatAt von Mikroorganismen. Zentralblatt f, Bakt. 1, 216, 339-344. MosoD J. (1947) The phenomon of enzymatic adaptation. Growth 11, 223. PRrrot~trsW. A. (1969) Anaerboic digestion--IIL Kinetics of anaerobic fermentation. Water Research 3, 545--558. WU.DEt~ER P. (1969) Die Enzymkinetik als Grundlage der BSB-Reaktion. Karlsruher Berichte zur Ingenieurbiologie, Heft 2.