Problems of River Water Quality Modelling and Control: A Review

PROBLEMS OF RIVER WATER QUALITY MODELLING AND CONTROL: A REVIEW M. B. Beck Control and Management Systems Division, University Engineering Department, Mill Lane, Cambridge CB2 lRX, England

1.

INTRODUCTION

is the anaerobic digestion of waste sludges, the activated sludge method o f waste liquids treatment, and dissolved oxygen (DO) - biochemical oxygen demand (BOO) - algae interaction in a reach of river.

In many countries the future organisation and operation of water resources is likely to depend strongly upon the control of water quality in freshwater river systems . This is a consequence of a new "philosophy" of water resources management, see e.g . (1), and of current planning decisions being taken by government authorities. The major importance of the new philosophy is that it implies a change of emphasis from a reliance upon the catchment and exploitation of relatively clean water sources (aquifers and upland reservoirs) to a greater, intensive utilisation and reuse of flowing surface waters . The practice of river basin management is becoming ever more comp lex, and complicated resource management schemes require sophisticated operation. A sophisticated operating policy should likewise imply an appreciation of the dynamics of water resource systems and of the need to manage such time variations through the appli cation of techniques of automatic control.

2.

BIOLOGICAL PROCESSES IN WASTEWATER TREATMENT AND RIVER WATER QUALITY

2.1 Some Relevant Biochemical Aspects of Process Dynamics* There are distinct parallels between microbiological activity in a river (algal growth and the decomposition of oxygen-demanding material) and microbiological activi ty in the activated sludge and anaerobic digestion processes of wastewater treatment. The simi lariti es between these latter are more immediately evident; their differences are that the organisms of activated sludge are predominantly aerobic, whereas those of anaerobic digestion are, as the name suggests, anaerobic . In both processes complex organic waste materials act as substrates in the metabolism o f vario us micro-organism species. The wastes are thus "treated" partly through their assimilation into new bacterial cell material and partly by being broken down into simple end-products. Algae are rather different in that they utilise an inorganic substrate (nutrient), e.g. nitrate, phosphate, and require sunlight as an energy source for their metabolism, i.e. photosynthesis. Their importance to river water quality management stems both from the l ow DO conditions created by the respiration of a large algal population, and from the high BOO load that can be exerted by dead and decomposing algal matter.

The aims of this paper are: (i) to present a brief review of analytical and practical problems experienced in the identification of dynamic models from field data; and (ii) to point out some essential practical problems of wastewater treatment and river water quality control. A question of primary importance is that of how the management of water quality interacts and overlaps with the broader aspects of quantitative water resources management. A suitable study-reference framework, which should aid in visualising an answer to this question, is given by the definition in Fig. 1 of the water quality system associated with an urban community (2), (3). This reference diagram enab l es us to retain an image of the more macroscopic features of water resources management while pursuing a systematic analysis of the dynamic behaviour of each individual process unit (3). Although substantial progress has already been achieved in water quality modelling and control studies, e.g. (4), (5), (6), (7), (8), (9), (10), there is still a discernible gap in the literature between the broad appreciation of the dynamic, stochastic nature of hydrological problems, e.g. (11), (12), (13), and a similar awareness in water quality problems . In the following special attention is paid to the study of biological processes: more specifica lly, that

The distinctive feature of organism/substrate interaction is the wide application of a Monod-type function (16) as a representation of the underlying biochemical kinetics, i. e. R. (t) 1

~i (t)

P. 1[

x. SJ (t) xsj(t) + Kil

1

~. (t) 1

(1)

in which ~i is the concentration of microorganism species i, Ri(t) is the rate of * A more complete introduction to this subject is given in two papers by Andrews (14) and Olsson (15).

341

342

M.B. Beck

~02

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SUBSYSTEMS :POTABLE WATER ABSTRACTION, PURIFICATION, AND SUPPLY NETWORK

(2) URBAN LAND RUNOFF AND THE SEWER NETWORK (3) WASTEWATER TREATMENT PLANT (4) A STRETCH OF RIVER

Figure 1.

The water quality system.

QUALITY

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CONSUMERS

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River water quality modelling and control

growth of that species, x

. is the concen-

S]

tration of (growth-rate limiting) substrate j, and Pi and Kil are constants; the dot notation refers to differentiation with respect to time t. Eqn (1) is interesting in that i t also extends to the case of predator-prey interaction: for instance it is well known that protozoa prey upon sewage bacteria in the activated sludge process (17). To some extent, therefore, the biological processes of wastewater treatment can be viewed as (controlled) microscopic ecological systems. In section 3 we shall demonstrate an example of the characteristic oscillatory nature in the balance between food and organisms. 2.2 Dynamic Model Structure Identification Modelling process dynamic behaviour can proceed from two premises. Either one takes existing theory and develops this model so that it may be tested against experimental data - a deductive reasoning approach; or, assuming no a priori knowledge (theory) of process behaviour, one attempts to develop the Specific information acquired from the data into a more general model - an inductive reasoning approach. A fair reflection on the studies carried out so far with fullscale plant field data is that both approaches have yielded only limited success. It is important to analyse why this is so. Eqn (1) marks the starting point for the discussion of the first approach to modelling. Assuming that ~i and x would be components sj of the state vector in any state-space dynamic model representation, such a model is clearly non-linear. In theory, the Monod function refers to a pure, single species culture of organisms metabolising a single substrate. In practice, waste water is a very heterogeneous mixture of multiple groups of organisms and substrates, and each bacterial species ~i may metabolise a number of substrates x

..

S]

Current theoretical

models are not of an exceptionally high order, some five or six ordinary differential equations (18), (19), (20), but analytical and computational aspects require additional measured information on up to, say, ten input and flow variables, with a similar number of parameters to be evaluated in some manner. So the basic problems of this approach are complexity and the poor correspondence between practice and theory, see (21). A black box modelling approach, in contrast, has the immediate advantage of simplicity, and would appear to be extremely attractive in the context of establishing basic cause/effect mechanisms (what inputs affect what outputs, by how much and how quickly) within a biological process unit. This approach too, however, is fraught with problems because it relies strongly upon the ability to implement specialised experimentation, upon reliable, robust instrumentation,

343

and upon good signal/noise ratios - all of which factors do not obtain in the water and wastewater industries. Qualified successes of black box model identification under these constraints are reported in (22) and (23). A lack of instrumentation and experimentation is, then, an additional crucial difficulty of dynamic model identification. Experience shows that a thorough dynamic analysis of biological processes in wastewater treatment and river water quality is in its infancy (24). In terms of system identification and parameter estimation it can be said that all the current problems reside in the area of model structure identification. A useful interpretation of identification is one of a procedure of hypothesis testing/decision making (25). There are two pOints about this view which are of some considerable importance: firstly, it reinforces the notion that modelling is subjective - it depends on the analyst's decision to accept or reject a hypothesis (model); secondly, it emphasises the fact that the ultimate problem of modelling is the generation of a Subsequent hypothesis given that the current hypothesis is inadequate. In this particular subject area and for a black box approach where hypothesis generation can be formalised to a degree (i.e. by extending (26) or reducing the order of polynomials in the backward shift operator) it is believed that a fuzzy algorithmic (27) interpretation of decision making may yield useful results. 3.

MEASUREMENT AND STATE ESTIMATION IN BIOLOGICAL PROCESSES

Instrumentation is clearly the fundamental problem both for model identification and for biological process control. The situation at present is summarised by Fig. 2. Although this figure refers specifically to the process of anaerobic digestion, its featur"e s can be assumed to be generally applicable; notice that substrate/organism interaction is represented by a modificat~on of eqn (l) due to Andrews (28). The kernel, as i t were, of biological process dyna~mic behaviour, i.e. block 1 in Fig. 2, is net directly measurable and is perceived only in an oblique fashion. A large portion of the (ideal) process state vector is unmeasurable, that is !.u' and much of the observed process dynamics is a function of unmeasurable stochastic process disturbances, I, and of random measurement errors, ~. But the problem of instrumentation is not simply a problem of technological innovation; it is rather more subtle. Let us consider the case of predicting DO-BOD-algae interaction in a reach of river. Figure 3 shows a comparison of the deterministic downstream responses of two models with DO and BOD field data from a 4.7 km stretch of the River Cam in

M. B. Beck

344

(3)

PROCESS ENVIRONMENT AND INSTRUMENTATION

PROCESS STATE DYNAMICS VARIATIONS IN (e.g.) : pH, TOXIC CHEMICAL AGENT, NET CATION, DISSOLVED CARBON DIOXIDE CONCENTRATIONS, PARTIAL PRESSURE OF GASEOUS CARBON DIOXIDE

BIOCHEMICAL KINETICS MICRO-ORGANISM / SUBSTRATE INTERACTION

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Observations and deterministic model responses for DO-BOD interaction.

River water quality modelling and control

Eastern England (25). The dashed lines in Fig. 3 are the responses derived essentially from the classical Streeter-Phelps (29) model of Do-BOD interaction. The other model hypothesises the presence of a significant population of algae in the river, whose growth-rate is governed by a Monod function with sunlight as a rate-limiting "nutrient" (25). The nature of algal interaction with the DO and BOD is assumed to be as follows: (i) through the processes of photosynthesis and respiration a "live" population of algae respectively produces and consumes oxygen; (ii) a "dead" population of algae, as degradable organic matter, creates an additional load on the river's oxygen resources. This latter is a critical assumption. Since BOD measurement is carried out on a bottled sample of river water over a period of five days and in the absence of light, it can be argued that this measurement is itself a distorted, biased observation of the true in situ river BOD. The reason is that just as algae respire in the river, so they respire if present in the bottled BOD test (Fig. 4). In formal terms we require ideally a measurement equation which simulates the batch reactor dynamics of the BOD test, i.e.

~(~) +~:{X~(T) o

mediated by two species of aerobic bacteria, Nitrosomonas Nitrobacter ammonia

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ni trate

(4)

The same process may be observed within the river (31). In the activated sludge process, Fig. 5, it may be assumed that measurements of the influent ammonia concentration at A and the effluent ammonia, nitrite, nitrate concentrations at Bare available, together with measurements of the flow variables QI' Q~, Qw: The problems at hand are those of estimating bacterial population magnitudes and of investigating the stability of population dynamics as a prelude to the analysis of operating rules for activated sludge units (see also section 4). A relatively simple model for the balance between substrate ammonia concentration and the nitrosomonas population in the aerator basin is described by the following non-linear relationships (20) , X (t) = fl {x (t) '~l (t) ,u (t) sl Sl sl ~l (t) '/;1 (t)}

)

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+ nB (1c)

345

)

with a single noisy observation (6)

where

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(3)

where x and in

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zB is the measured value of

BOD, x

is the in situ river BOD concenB tration, and f is some function of x'D'

the bottled sample DO concentration, and of x'A' the concentration of live algae in the bottle.

x

is the concentration of live A algae in the river, tk is the kth sampling

instant, and T is a d~~y variable of time (in days). So our assumptions about algal death and decay, which are not directly verifiable against field data and which are primarily responsible for the better BOD predictions of the second model are certainly open to debate. There are, however, other studies which partially substantiate these assumptions (30). It seems natural, therefore, that the reconstruction of information about the state vector, i.e. state estimation, from more readily available measurements should be potentially a most fruitful area for control applications. For illustrative purposes let us consider a part of the treatment effected by the activated sludge process for the removal of ammonia, a substance toxic to the aquatic environment. This example will also serve to demonstrate some of the analytical difficulties of identification and estimation. Ammonia removal is a two-stage oxidation process

~l

is the concentration of ammonia, sl is the concentration of nitrosomonas

bacteria, u centration,

sl ~l

is the influent ammonia conand

~2

are vectors rep-

resenting the relevant parameters and flow variables, and /;l'/;2 are appropriate stochastic disturbance terms. The analytical difficulties in dealing with eqn (5) are underlined by eqn (5ii) which reduces to the general form, :idt)

=

a(t)x(t)

(7)

Hence, at least in theory, growth and decay of the bacterial population are a function of alternate periods of marginal instability and stability, respectively, in the system dynamics of eqn (7); a type of problem which seems to be of fairly broad relevance in the modelling of biological and ecological systems (32). Figure 6 shows the state estima~as derived from eqns (5) and (6) using an extended Kalman filter with historical data from Norwich sewage works in England. Note the oscillating balance between substrate and organisms and the tendency for ammonia removal to be lost immediately subsequent to highly efficient treatment, e.g. t50 - t , and t - t ' It is 60 loo l09 this kind of behaviour which should be

M. B. Beck

Oxygen remaining in bottled sample In situ river BOD

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Oxygen consumed through algal respiration - (days)

Oxygen uptake in the BOD bottle test.

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• OBSERVATIONS

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45

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TII1E (days)

Figure 6.

State estimates of nitrosomonas and ammonia concentrations in the activated sludge aerator basin.

River water quality modelling and control

347

examined in order to determine the effectiveness of process operating rules. A measure of the filter's performance is afforded by inspection of the estimates of ammonia concentration during intervals where no state observations are available, e.g. t69 - t 80 ,

Provided zone 1 of the aerator basin is virtually anaerobic it is feasible (vii) to reduce the nitrate products (recycled from the clarifier) through nitrite to free gaseous nitrogen, thus achieving yet another objective.

and t l05 - t l08 '

Now juxtapose these complex operational constraints and objectives with the imprecision of models available for control system design and with the lack of measured information on those variables which we would wish to control. Given further that certain vital operational measurements, such as a rising or a bulking sludge, are amenable only to human observation and detection (8), there is a strong argument in favour of some preliminary examination of fuzzy control applications (36) in wastewater treatment. Indeed, certain studies in this direction, although not recognised as such by their authors, have already been made in respect of anaerobic digester operation (37).

Other areas in which state estimation may be of considerable benefit are discussed in (8). Of particular relevance to the activated sludge process is the determination of organism activity from observations of dynamic variations in the spatial distribution of DO in the aerator channel, i.e. the dashed line in Fig. 5 (33). 4.

THE APPLICATION OF CONTROL

The crucial problems of instrumentation at the microscopic level of monitoring biological process behaviour should require no further emphasis. Within the macroscopic context of, say, a national water resources management programme instrumentation problems extend to the almost prohibitively large costs of telemetry schemes for data transmission. Nevertheless, in certain very sensitive stretches of river such schemes may well be justified (34); and where telemetry systems exist for flood control and reservoir regulation there are attractive possibilities of interlocking an accompanying quality monitoring network (35). Yet instrumentation is but one problem in applying control to the water quality system. The fact that methods of treatment should satisfy a set of multiple objectives is consistent with the broad spectrum of characteristics attaching to the definition of water quality. The problem is that not all of the objectives can be achieved simultaneously. It is with this in mind that the theme of activated sludge process control is resumed. An analysis of the activated sludge unit indicates that the primary activities of the aerator basin are: (i) to provide an aerobic and stable environment for the growth of organisms; (ii) to effect removal of BOD and suspended solids substrates; (iii) to maintain some appropriate balance between organisms and substrate; and (iv) to assist organism/substrate interaction by agitation and thus intimate contact between the biological floc (sludge) and the liquid sewage stream. The primary and opposite purpose of the clarifier is (v) to afford as much separation as possible between liquid and floc phases. A secondary, but incr~asingly important, objective of the activated sludge process is (vi) that of ammonia removal; this takes place in the aerobic portion of the aerator basin zone 2 in Fig. 5. From eqn (4) the end-p~oduct of ammonia oxidation is nitrate: a substance which poses health hazards in potable water supplies, an essential nutrient for algal growth in the river, and therefore an undesirable constituent of effluent discharges.

5.

CONCLUSIONS

This paper has presented a catalogue of current problems in water quality modelling and control. There are three accounts on which some concluding remarks may be offered. Modelling Emphasis has been placed on biological process modelling. In view of the poor correspondence between theory and practice and the immediate prospects for process control, it is highly pertinent to question why there should be a need for dynamic process models. Perhaps here the only relevant answer is the engineer's abiding motivation to understand how a system behaves and to find ways of making it perform better. A systematic approach A framework has been proposed for a thorough analysis of individual process units in a water quality system. The ultimate objective thereof would be to evolve a coherent view of the system, that is the capability of analysing, for instance, interplay between the operation of activated sludge and anaerobic digestion units, and the relevance of the nitrogen cycle to DO-BODalgae interaction in a river. Control The application of control has been discussed as a problem of analysis and technology. No mention has been made of equally important amenity-value problems (3). It may well be that the most immediately practicable form of water quality control will derive from the co-ordination of flow regulation activities widely dispersed throughout the water quality system (33), (38), (39), (40), (41). The control engineer possesses a box of most effective tools. What is really required of him at present is that he employs

M. B. Beck

348 the correct tool on the correct problem. ACKNOOLEDGEMENT

The author is grateful to the Royal Society for support under an Ernest Cook research fellowship in Environmental Sciences. REFERENCES (1) Water Resources Board, Water resources in England and Wales, W.R.B. Publication No. 22, HMSO, London (1973). (2) Beck M.B., Dynamic modelling and control applications in water quality maintenance, Water Res. 10, 575 (1976). (3) Beck M.B., Dynamic aspects of water quality modelling and control, in ref.(ll). (4) Andrews J.F., Dynamic models and control strategies for wastewater treatment processes, Water Res. 8, 261 (1974). (5) Buhr H.O., Andrews J. F., and Keinath T.M. (Eds.), Research needs for automation of wastewater treatment systems, Proc. U.S.E.P.A./Clemson University Workshop, Sept. (1974). (6) Olsson G., State of the art in sewage treatment plant control, in Proc. Asilomar Engineering Foundation Conference on Chemical Process Control, Pacific Grove, California, Jan. (1976). (7) Olsson G., and Hansson 0., Stochastic modelling and computer control of a full scale wastewater treatment plant, in Proc. Symp. Systems and Models in Air and Water Pollution, Institute of Measurement and Control, London, Sept. (1976). (8) Olsson G., Estimation and identification problems in wastewater treatment, in ref. (11) . (9) Powers W.F., and Canale R.P., Some applications of optimisation techniques to water quality modelling and control, IEEE Trans. SMC-5, 312 (1975). (10) Sawaragi Y., and Ikeda S., Identification methods in environmental pollution problems, in Proc. IVth IFAC Symp. Identification and System Parameter Estimation, 1, 169, Institute of Control Sciences, Moscow (1976). (11) Sz~ll~si-Nagy A., and Wood E.F., Recent developments in real-time forecasting/~l of water resource syste~s, Proc. IIASA Workshop, Laxenburg, Austria Oct. (1976). (12) Duong N., Winn C.B., and Johnson G.R., Modern control concepts in hydrology, IEEE Trans. SMC-5, 46 (1975). (13) Ikeda S., Fujishige S., and Sawaragi Y., Non-linear prediction model of river flow by self-organisation method, Int. J. Systems Sci. 7, 165 (1976).

(14) Andrews J.F., Kinetics of biological processes used for wastewater treatment, in Proc. Workshop on Research Problems in Air and Water Pollution, University of Colorado, Boulder, Colorado (1970). (15) Olsson G., Activated sludge dynamics I Biological models, Report 75ll(C) , Lund Institute of Technology, Dept. of Automatic Control, Lund, Sweden (1975). (16) Monod J., Recherches sur la croissance des cultures bacteriennes, Hermann, Paris (1942) . (17) Curds C.R., A theoretical study of factors influencing the microbial population dynamics of the activated sludge process - I, Water Res. 7,1269 (1973). (18) Graef S.P., and Andrews J.F., Stability and control of anaerobic digestion, J. Wat. Poll. Control Fed. 46, 666 (1974). (19) Busby J.B., and Andrews J.F., Dynamic modelling and control strategies for the activated sludge process, J. Wat. Poll. Control Fed. 47, lOSS, (1975). (20) Poduska R.A., and Andrews J.F., Dynamics of nitrification in the activated sludge process, J. Wat. Poll. Control Fed. 47, 2599 (1975) • (21) Beck M.B., and Young P.C., Systematic identification of DO-BOO model structure, Proc. A.S.C.E., J. Env. Eng. Div., 102, 909 (1976). (22) Berthouex P.M., Hunter W.G., Pallesen L., and Shih C.Y., Dynamic stability of activated sludge plants, Technical Report 431, Dept. of Statistics, University of Wisconsin, Madison (1975). (23) Beck M.B., An analysis of gas production dynamics in the anaerobic digestion process, Technical Report CUED/F - CAr-lS/TRl35, University Engineering Dept., Cambridge (1976) • (24) Beck M.B., Identification and parameter estimation of biological process models, in Systems simulation in Water Resources (Ed. G.C. Vansteenkiste), North-Holland, Amsterdam, 19 (1976). (25) Beck M.B., Random signal analysis in an environmental sciences problem, in Proc. lEE COlloquium on Random Signal Analysis; London Apr. (1977). (26) Chan C.W., Harris C.J., and Wellstead P.E., An order-testing criterion for mixed autoregressive moving average processes, Int. J. Control, 20, 817 (1974). (27) Zadeh L.A., Outline of a new approach to analysis of complex systems and decision processes, IEEE Trans. SMC-3, 28, (1973).

River water quality modelling and control (28) Andrews J.F., Dynamic model of the anaerobic digestion process, Proc. A.S.C.E., J. Sanit. Eng. Div. 95, 95 (1969). (29) Streeter H.W., and Phelps E. B., A study of the pollution and natural purification of the Ohio River, Bulletin No. 146, U.S Public Health Service (1925). (30) Whitehead P.G., and Young P.C., A dyn~ amic-stochastic model for water quality in part of the Bedford-Ouse river system, in Computer Simulation of Water Resources Systems (Ed. G.C. Vansteenkiste), NorthHolland, Amsterdam, 417 (1975). (31) Curtis E.J.C., and Garland J.H.N., Nitrification in rivers, in The use of mathematical models in water pollution control (Ed. A. James), Wiley, London (in press) • (32) Di Cola G., Guerri L., and Verheyden N., Parametric estimation in a compartmental aquatic ecosystem, in Proc. IVth IFAC Symp. Identification and System Parameter Estimation, Institute of Control Sciences, Moscow, 2, 157 (1976). (33) Andrews J.F., Buhr H.O., and Stenstrom M.K., Control systems for the reduction of effluent variability from the activated sludge process, in Proc. International Conf. on Effluent Variability from Wastewater Treatment Processes and its Control, IAWPR/Tulane, Vanderbilt Universities, New Orleans, Dec. (1974). (34) Wakeford A.C., and Knowles G., Enhance-

349

of water-quality monitoring systems by incorporating water-quality and quantity modelling and time-series analyses, in Proc. Symp. Systems and Models in Air and Water Pollution, Institute of Measurement and Control, London, Sept. (1976). m~nt

(35) Salamin A., and Beck M.B., Some control problems in the management of a Hungarian river basin, Technical note CAMS/76/6b, University Engineering Dept., Cambridge (1976) . (36) Mamdani E.H., Advances in the linguistic synthesis of fuzzy controllers, Int. J. Man-Machine Studies 8, 669 (1976). (37) Koch C.M., An experiment in computer assisted control of the anaerobic digestion process at Philadelphia's Northeast Pollution Control Plant, in Proc. 47th Annual Water Pollution Control Federation Conference, Oct. (1974). (38) Pew K.A., Callery R.L., Brandsetter A., and Anderson J.J., Data acquisition and combined sewer controls in Cleveland, J. Wat. Poll. Contr. Fed. 45, 2276 (1973). (39) Beck }l.B., The identification and adapti ve prediction ofJ urban sewer flows, Int. J. Control (in press). (40) LaGrega M.D., and Keenan J.D., Effects of equalising wastewater flows, J. Wat. Poll. Control Fed. 46, 123 (1974). (41) Young P.C., and Beck M.B., The Modelling and control of water quality in a river system, Automatica 10, 455 (1974).