A mathematical model for waste water stabilization ponds with macrophytes and microphytes

|tlBIIIgtllt ELSEVIER

Ecological Modelling 91 (1996) 77-103

A mathematical model for waste water stabilization ponds with macrophytes and microphytes S. M o r e n o - G r a u a.*, A. Garcla-Sfinchez b j. M o r e n o - C l a v e l M.D. Moreno-Grau c

a

j. Serrano-Aniorte

a

Department of Chemical Engineering of Cartagena, Murcia University, Paseo de Alfonso XIII, 40, 30203 Cartagena, Spain b Department of Applied Mathematics and Statistics, Murcia University, Paseo de Alfonso Xlll, 40, 30203 Cartagena, Spain c Dames and Moore International, Caracas 16, 28010 Madrid, Spain Received 14 November 1994; accepted 14 September 1995

Abstract This paper presents a model for natural systems used in urban waste water treatment. The model includes thermal and biochemical submodels, derived from the physical and biochemical phenomena involved in the treatment process. The thermal submodel is based on a heat balance for the system and the numerical solution of the resulting differential equation. The biochemical submodel is based on the mass balances for the different variables, considering a one-dimensional flow within the ponds, which give rise to a system of linear equations subsequently solved by numerical methods. The model has been calibrated using experimental data from existing waste water treatment systems using both microphytes and macrophytes. The model may be applied to the design of new facilities and to improve operating conditions of existing facilities. Keywords." Biochemistry; Sewage treatment; Submodelling; Temperature; Wetland ecosystems

1. Introduction Stabilization ponds are considered among the easiest, most economical, and efficient methods for biodegradable waste water treatment (Abeliovich, 1982, 1984; Bryant, 1987). In the Murcia region in southeastern Spain, treated waste water is commonly used for irrigation, particularly during the summer months. Our laboratory became involved in researching the possible use of waste stabilization ponds in the region, combining their use as waste water treatment with that of irrigation storage facilities in dry areas (Moreno-Grau et al., 1988). Different authors have reported on the use of macrophytes systems to improve the effluent water quality of stabilization ponds, and have also assessed the potential profitability of these systems as sources of biomass (Reddy and De Busk, 1987; Wrigley et al., 1988). The use of aquatic macrophytes for treating waste water is gaining attention as a promising method to reduce

* Corresponding author. Fax: (34) (68) 505310. 0304-3800/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. SSDI 0304-3800(95)001 68 -9

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S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

pollutant levels in water bodies (Seidel, 1976; Splanger et al., 1976; Reddy and De Busk, 1985, 1987; Hammer, 1989), municipal sewage (Gearheart, 1992; Lienard et al., 1993; Chambers and McComb, 1994), industrial effluents (Noller et al., 1994; Saltabas and Akcin, 1994) and agricultural waste water (Hammer, 1989; Yeoh, 1993). In a wetland, plants utilize the nutrients and other soluble compounds present in the water, supporting a habitat for numerous organisms (Fetter et al., 1978; O'Brien, 1981; Bouitin, 1987). Constructed wetlands offer an attractive alternative to conventional systems for waste water treatment due to the following reasons: they are relatively inexpensive, have a high productivity, effectiveness, reliability, are relatively tolerant about fluctuating flow and contaminant loading rates, and also present indirect ecological benefits (Hammer, 1989; Moreno-Clavel et al., 1994). The relative efficiency of microphyte and macrophyte waste water ponds was studied in our laboratories using constructed wetlands operating in parallel, which received untreated urban sewage. The results of this study have been reported elsewhere (Moreno-Clavel et al., 1990; Moreno-Grau, 1990). Different authors have reported on the use of eutrophication models for lagoons and reservoirs, as well as ecological models for waste water treatment (Ostojski, 1987; Moreno-Grau et al., 1988; JCrgensen and Nielsen, 1994). Different types of ecological models have been developed for aquatic ecosystems (JCrgensen, 1995), including wetlands with the associated mathematical description of the behaviour of macrophytes (Costanza and SEar, 1985; Voinov and Tonkikh, 1987; Mitsch et al., 1988; Lauenroth et al., 1993; Aoki, 1994; Roig and Evans, 1994). Different authors have modelled constructed wetlands. Kadlec and Hammer (1988) developed a simple mathematical model which permits dynamic simulations of wetland hydrology and of nutrient-driven interactions between waste water and the wetland ecosystem. Computer simulations are compared with operating data from the Porter Ranch waste water treatment facility. Brown et al. (1994) developed a model to simulate the daily fate and transport of water influent pollutants in an effort to predict the effluent concentration, removal efficiency, and long-term bioaccumulation. Gale et al. (1994) reported the phosphorus retention by wetlands soils, and Tarutis and Unz (1994) described a steady-state model based on decomposition kinetics and reaction stoichiometry which simulates the removal of ferrous iron entering the wetlands constructed for mine drainage treatment. JCrgensen (1994) described models as a management tool, as well as an instrument in science. This paper presents a mathematical model developed in our laboratory to describe the behaviour of an experimental system for waste water treatment using microphytes and macrophytes. This model allows us to perform the following tasks: (1) evaluate the relative significance of the different variables involved in our process; (2) explore hypothetical working conditions; (3) use it as an engineering design tool for new facilities or improvement of existing ones.

2. Experimental setting The experimental facility layout was designed to compare the waste water treatment efficiencies achieved in ponds using microphytes versus those using macrophytes (Moreno-Clavel et al., 1990). To meet this objective, artificial wetlands were constructed and monitored under different working conditions (Moreno-Grau, 1990). The experimental facility, located in 'El Campo de Cartagena', Spain, 37°37'20"N latitude, 0°56'11"W longitude, and 35 m altitude, was supplied with untreated urban sewage from Cartagena, a city situated by the Mediterranean Sea on the southeast of the Iberian Peninsula, with a population of approximately 170000 inhabitants. The facility consisted of three 100-m channels, with a trapezoidal cross section of 1 m width at its bottom and a maximum width of 2 m at the surface. The channels were lined with a plastic membrane covered with a layer of washed sand to facilitate rooting of the aquatic macrophyte used in the study, Phragmites communis Tin. Two channels were planted with Phragmites communis Tin., while the third one was left unplanted to be used as a microphyte pond. The prevalent geni identified in the microphyte pond were; Chlorella, Scenedesmus,

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103 Table 1 Characteristics of the experimental facilities Channel length Lowerbase Upper base Pond depth Water depth

Average speed Water volume Residence time

100 m 1m 2m 0.90 m 0.43 m Treatment with microphytes

Treatment with macrophytes

3.2 m/day 75.0 m3 31.3 days

3.5 m/day 69.0 m3 28.8 days

79

Chlamydomonas, Euglena, Phacus and different diatoms. The design parameters of the experimental facilities are listed in Table 1. The following parameters were measured in samples taken weekly from the influent and final effluent of the ponds: chlorophyll a, raw and filtered chemical oxygen demand (COD), raw and filtered biochemical oxygen demand (BOD), dissolved oxygen, pH, alkalinity, total and faecal coliforms, water temperature, and suspended solids. The data used to calibrate the model were obtained during the year 1990.

3. Methods 3.1. Thermal submodel An accurate description of the thermal behaviour of the system is essential for the subsequent prediction of its biochemical performance, as most of the processes involved in waste water treatment in natural systems are deeply influenced by the temperature. Therefore, the characterization of the thermal cycle of the ponds is a necessary first stage for modelling the concentration of biomass, organic matter and nutrients (Mauersberger, 1979; Azov and Shelef, 1982; MorenoGrau, 1983; Aoki, 1987; Moreno-Grau et al., 1988). In different studies aimed at developing models for impoundments, simplified techniques have been used which provide only an approximate estimation of the temperature of the reservoirs. The most frequently used method was introduced by Eckenfelder in 1966 (Eckenfelder, 1989), and consists of an evaluation of the average temperature, based on the geometry of the system, residence time in the pond, temperature of the influent water and air temperature. Any calculation method capable of reproducing the seasonal and daily oscillations in temperature in the ponds must be based on the heat balance of the system (Moreno-Grau, 1983), a methodology which we have followed in order to prepare our thermal submodel. The most important component of the heat balance of the system is the heat exchange with the atmosphere. The flow of heat exchanged through the air-water interface for the mass of water in the pond is described as the algebraic sum of the different flows of energy, (Baca and Arnett, 1976; Fritz et al., 1980). The resulting equation is as follows: Hnet=l~+Ha-(!,~+Har+Hbr+He+H,)

(1)

where: Hnet = net heat flow through the surface (kJ m -2 day-1); I~ = short wave solar radiation (kJ m -2 day-l); H a = atmospheric infrared radiation (kJ m -2 day-l); i~r = reflected solar radiation from surface (kJ m -2 d a y - ' ) ; Ha~ = reflected atmospheric radiation from surface (kJ m 2 d a y - ' ) ; Hbr = infrared radiation

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s. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

emitted from the surface of the water (kJ m -2 day-1); H e = loss of heat caused by evaporation (kJ m -2 day-l); and H~ = sensible loss or gain of heat (kJ m -2 day-l). A positive value for the net flow of heat on the surface indicates that the pond is heating up, while a negative value indicates a net flow of heat from the surface toward the atmosphere, and thus cooling of the pond. Given that the pond and the adjoining land are in thermal equilibrium, a reasonable simplification is to assume that the exchange of heat through the bottom is zero. The terms of the heat balance may be estimated in different ways, from direct experimental measurement to different empirical or theoretical relations. The calculation procedure followed for every one of the components of Eq. (1) may be found in Moreno-Grau (1990), and is based on the use of equations which link these parameters with known meteorological values, provided by the meteorological observatory in Guadalupe (Murcia), located at 38°N latitude, I°10'W longitude, 69 m altitude, the only observatory in the province of Murcia which measures short wave solar radiation; and the San Javier observatory, located at 37°47'12"N latitude, 0048' 07"W longitude, 3 m altitude, 15 km away from the facilities. Since the experimental results showed that no horizontal or vertical temperature differences exist in the ponds, a zero-dimensional thermal submodel was used. The heat balance for the ponds contains terms for the inflow, outflow and interfacial transfer of heat. On the other hand, taking into account that the system is in thermal equilibrium, the water inflow temperature is equal to the water pond temperature and also equal to the water outflow temperature. Therefore, the temperature variation with time is determined by the equation (Moreno-Grau et al., 1991): dT

nne t

d-7 = pcpd

(2)

where: T = temperature of the water (°C); t = time (day); p = density of the water (kg m-3); Cp = specific heat of the water (kJ kg- ~ °C- 1); d = depth (m). This equation is solved numerically, using a finite difference scheme, to obtain the evolution with time of the temperature of the ponds. 3.2. Biochemical submodel

The quantitative description of the inflow, outflow and the internal cycles of materials in an ecosystem is based on the mass balance of the system (Whigham and Bayley, 1979). Several studies have conducted mass balances to describe the behaviour of wetlands and to determine the relative quantitative importance of sources, sinks and chemical transformations, (Mitsch and Gosselink, 1986). In order to prepare our biochemical submodel, we have carried out a detailed study of the physical and biochemical processes involved in the treatment process. The biochemical submodel considers the most important variables influencing pond behaviour (Bowie et al., 1985; Wlosinski and Desormeau, 1985), that is: bacterial biomass, divided into two groups: suspended and supported by macrophytes; organic matter, represented by chemical oxygen demand (COD); phytoplankton, zooplankton and macrophytes; detrital mass; nutrients, including nitrogen (ammonia and organic) and phosphorus (soluble and total); dissolved oxygen; total and f a e c a l coliforms. Chemical oxygen demand was chosen as a variable instead of biochemical oxygen demand (BOD) due to the greater reliability and reproducibility of the assay. A balance for nitrates and nitrites has not been prepared, as experimentally we have found that nitrification processes in our facilities are negligible. The model defines net growth rate of every one of the species as the algebraic sum of the individual rates of the processes involved: growth rate, respiration rate, mortality rate and sedimentation rate. r n x = r x + rr + rd + r ~

(3)

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

81

where: rnx = net growth rate (mg 1-l day-l); rx = cell growth rate (mg 1-1 day-1); r r = respiration rate (mg 1-1 day-l); rd = mortality rate (mg 1-l day-l); r~ = sedimentation rate (mg 1-1 day-1). The equations used to calculate the growth rate of suspended and supported bacteria, phytoplankton, zooplankton and macrophytes follow the general formula: r, = t . l . m a x f ( T ) f ( L ) K s +--"~S K s, + S' '~-------S Ks,, + S " "" X 1 -

(4)

where: ~max = maximum growth rate of cell type x (day- 1); f ( T ) = correction function of the growth rate by temperature of cell type x (non-dimensional); f ( L ) = correction function of the growth rate by light intensity of cell type x (non-dimensional); S, S', S", ... are the concentration of substrate 1, 2, 3, etc. (mg l - l ) ; K s, Ks,, Ks,,, . . . are the Michaelis-Menten constant for substrate 1, 2, 3, etc. (mg 1- l); X = concentration of cell type x (mg l - l ) ; and "qx = population maximal of cell type x (mg 1-1). Thus, a Monod type of kinetics was applied, corrected by a term which represents the maximum growth possible, (Hirsch and Smale, 1983; Jacobsen, 1983). The growth rate of suspended and supported bacteria was calculated according to the rate of assimilation of organic matter, correcting this term through the organic matter protoplasm yield. rB. ~ = YBxrMOBx

(5)

where: rBx = growth rate of suspended and supported bacteria (mg 1-I day-1); YBx = organic matter/protoplasm conversion yield (non-dimensional); and rMOBx -----rate of assimilation of organic matter by suspended and supported bacteria (mg l- 1 day- i). The equations representing the respiration and mortality processes were described using first-order kinetics, as follows: rr = --Krx X

(6)

rd = - K a x X

(7)

where: K r x = kinetic constant for respiration of cell type x (day l ); and Kax = kinetic constant for mortality of cell type x (day- t ). The sedimentation, which was applied to mass balances of suspended bacteria and phytoplankton, was represented by first-order kinetics with respect to the concentration of the cell type involved, and the specific rate of sedimentation of cell type x was calculated as the relation between the rate of sedimentation (m day- 1 ) and the pond depth (m) (Bowie et al., 1985; Jcrgensen, 1994). r~ = - - s x X

(8)

where: s x = specific rate of sedimentation of cell type x (day- ~). The same general equation was followed to represent the mass contribution to sediment by macrophytes. All kinetic parameters have an Arrhenius type temperature dependency, as well as the temperature correction functions for growth, which were calculated using the equation: K = K2o 0 (r- 20)

(9)

where: K = kinetic constant at temperature T (day- 1); K2° = kinetic constant at 20°C (day- l ). Dissolved and suspended organic matter concentrations in water depend on the input and output of organic matter with the influent and effluent water, and are affected by the death of bacteria, phytoplankton, zooplankton and macrophytes within the ponds, sedimentation and re-suspension of sediments, and mineralization of organic matter in the metabolism of heterotrophic species present in the ponds. The organic matter entering the pond with the influent must be evaluated experimentally through the chemical oxygen demand. The experimental values were corrected following the indications of Fritz et al. (1979). These corrections consider the refractory COD, that is, the fraction of influent total COD that goes into

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

82

temporary storage by sedimentation plus that which flows through the pond without being oxidized, as well as the COD that is released from temporary storage as a function of temperature, since the solubility of COD is temperature-dependent. The balance of organic matter contains both growth of suspended bacteria and bacteria attached to the macrophytes. Growth of phytoplankton, zooplankton and macrophytes is one of the most relevant components of the biochemical submodel. The evolution of these living organisms is intimately related to the availability of nutrients in the ponds. The photosynthetic activity of phytoplankton is the most important source of dissolved oxygen in ponds, which is necessary for aerobic decay of organic matter. This photosynthetic activity causes cyclical variations in the dissolved oxygen content both during the day and the year. Photosynthesis is also largely responsible for the pH changes within the ponds, which affect speciation of solved chemicals, and thus their toxicity. The presence of phytoplankton will influence the content of suspended solids in the final effluent and the eventual risk of eutrophication of the natural water courses where the effluent is finally discharged. The light intensity correction function for the growth rate of phytoplankton was represented as:

where

I=Iz(1.0-0.65C 2)

(ll)

where: C L = light intensity correction factor, which depending on the thickness of the plants takes values 0 ~ C L _~ l; I = light intensity at the pond surface (kJ m -2 day- 1); is = saturation intensity of solar radiation

(k3 m -2 day-1); and I z = sunlight intensity (kJ m -2 day-1). Zooplankton is included in the water quality models due to its effect on algae and nutrients. The dynamics of algae and zooplankton have a close predator-prey relationship. The most important difference with respect to phytoplankton is that zooplankton is mobile and migrates freely through the water column, so it is not affected by a sedimentation factor in the model. Fixed aquatic macrophytes have the same requirements as phytoplankton and are subject to similar processes (Bowie et al., 1985; Moreno-Grau, 1990). The main differences are as follows: • They are associated to the substrate on the bottom and thus are not subjected to hydrodynamic transport. • They do not settle out: however, one must consider their contribution to the detrital mass on the bottom due to the plant remains fallen or dragged by the water. The light intensity correction function for growth rate due of macrophytes was represented in a similar way as that for phytoplankton (Eqs. l0 and I l) where I = I Z. Suspended bacteria, algae, organic matter and plant detritus settle toward the bottom of the ponds, where nutrients are recycled by benthic processes. The mass balance for detrital mass can be expressed (Fritz et al., 1979) as the algebraic sum of terms representing settling of suspended bacteria, phytoplankton and macrophytes, and regeneration, this one expressed as follows: Reg =

- 10 - 3 f r O m

d

(12)

where: Reg = benthic regeneration (mg 1- J day- i ); Ur = benthic regeneration coefficient (day- 1); Dm = detrital mass (mg m-2); and d = depth (m). Mass balances for nutrients were prepared considering the following processes: mineralization, consumption during growth, settling and regeneration from the sediment. For inorganic phosphorus, an additional term representing precipitation as insoluble salts was included. Dissolved oxygen plays a fundamental role in natural waste water treatment methods. When situations of

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 7 7 - 1 0 3

83

anoxia appear, the processes responsible for organic matter decay proceed at a lower rate, thus leading to increased concentration of pollutants in the effluent water. The concentration of dissolved oxygen in the ponds is determined by the joint action of the following four mechanisms (Snodgrass, 1983; Nishimura et al., 1984; Summers, 1985; Guterman and Ben-Yaakov, 1987; Chen and Papadopoulos, 1988): • consumption of oxygen by the aerobic metabolism of suspended and attached bacteria; • generation and consumption of oxygen by phytoplankton photosynthesis and respiration processes; • consumption of oxygen by zooplankton metabolism; • re-aeration through the air-water interface: Rea =

K d C~ - C) d

(13)

where: Rea = re-aeration through the air-water surface (mg 1 ~ day- ~); K L = interfacial transfer coefficient (m day- 1) (Banks and Herrera, 1977); C s = dissolved oxygen saturation concentration (mg 1-1 ); C = concentration of dissolved oxygen (rag -l 1 1); and d = depth (m). K L = (0.384W °'5 - 0.088W + 0.029W2) O (r-2°)KL

(14)

where W = wind speed at 10 m over the surface (km h - I ). The dissolved oxygen saturation concentration depends on the temperature. The following equation to calculate dissolved oxygen saturation concentration was used according to Duke and Masch (1973) and Baca and Arnett (1976): C~ = 14.652 - 0.41022T+ 0.007991T 2 - 7.7774* 10 5T3

(15)

Total and faecal coliforms are indicators of the presence of pathogens in the water. The model predicts coliform persistence in the pond as a function of their concentration in the influent water and the retention time before exiting the system (Sarikaya and Saatci, 1988), using a first-order kinetics to represent the disappearance of coliforms as follows: rcw

(16)

= - KcTdCT

rcF d = --

KcFdCF

(17)

where: KCTd = specific rate of disappearance of total coliforms (day- 1); K C F O _ specific rate of disappearance of faecal coliforms (day-l); CT = concentration of total coliforms (mg l - l ) ; CF = concentration of faecal coliforms (mg l - 1 ). Fig. 1 shows a simplified schematic flow chart of the processes involved in the biochemical submodel described above. Due to the presence of a horizontal concentration gradient in our facilities, we chose a one-dimensional model to represent their behaviour. One-dimensional models have been used to represent rivers and deep lakes (Odob, 1981, 1982). The fundamental equation describing the temporal and spatial variations in one-dimensional models is as follows: cgt

D~

-fi--

cgx

+ Ox

Z=I

r. '

(18)

where: C = pollutant concentration (mg 1 ~); t = time (day); x = length (m); r z = rate of each one of the physical-chemical or biochemical processes responsible for modification of the concentration of the pollutant concerned (mg 1-1 day- ~); n = total number of processes in which the pollutant is involved; D x = longitudinal dispersion coefficient (m e day- 1) (Fischer et al., 1979). Dx = 3.134.

K*n*fi*d

5/6

(19)

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

84

at~e

Fig. 1. Simplified flow chart of the processes involved in the biochemical submodel. 02 = dissolved oxygen, O.N. = organic nitrogen, NH 3 = ammonia nitrogen, O.P. = organic phosphorus, S.P. = soluble phosphorus, O.M. = organic matter, D.M. = detrital mass, P = precipitated phosphate, Bj = suspended bacteria, B2 = attached bacteria, F = phytoplankton, M = macrophytes, Z = zooplankton, F.C. = faecal coliform micro-organisms,T.C. = total coliform micro-organisms.

where: K = dispersion constant (non-dimensional); n = Manning roughness coefficient (non-dimensional); fi = mean velocity of water (m d a y - ~); d = depth (m). Eq. (18) is applied to each one of the parameters which comprise the chemical submodel. At each time step and for each constituent it can be written I times, once for each of the I computational elements in the network. Thus, we obtain a system of partial differential equations. Since it is not possible to obtain analytical solutions to these equations under our situation, a finite difference method was used. The general basis of a finite difference scheme is to find the value of a variable as a function of space at the time step n + 1 when the spatial distribution at the nth time step is known. Time step zero corresponds to the initial conditions (Brown and Barnwell, 1985). To numerically solve this system of equations, the finite differences method was applied in two steps, with the following results:

cn+l-cn At

Dx(Cn+l l - C n + l = Ax ~x"

c n + l - c n + i-I l)i -~x"

cn+li -- c n + l ~ i - I -- "fi £x +

z=l

rz

(20)

where the sub-indexes for the concentration C (i + 1, i, i - 1) show the concentration of the simulated variables at the spatial node i and the time step n. The right-hand side of this equation is multiplied by A A x / A V , where A is the cross section of the ponds, A x is the length increase and AV is the incremental volume (Brown and Barnwell, 1985). Operating, reorganizing the terms and isolating, results in:

(DxAAt

c7=

fiAAt ] t..,+l

(

2DxAAt

,ava-------~+ a v 1.~i_1 + l + -Agz~x -

"fiAAt) ,+ " ~ ' - ~ - Ci l

DxAAt AVAx

cn++l1 -

n ~ rzAt z~l

(21)

This equation can be rewritten as:

C ~+ l + ciC~++ll Zi = a i C i-"+Il -~- b i--i

(22)

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

85

where

( DxAAt

fiAAt ]

ai= -

AVA----~+

(

2D~AAt

hi=l+

(23)

AV ] fiAAt )

(24)

D x A At ci =

(25)

AVAx

zi = C~' + ~ r~ At

(26)

Z=I

The values of a i, b~, c i and zi are all known at time n, while the C~ + 1 terms are the unknown ones at time step n+l. Eq. (22) represents a set of simultaneous linear equations, the solution of which gives the concentration of each parameter throughout the pond at a specific time. Expressed in matrix form, the result of this set of equations is: b I

cI

a2

b2

0

a3

0

0

0 0

0 0

0

0

0

0

c2

0

0

0

0

b3

c3

0

0

0

ai

bi

ci

0

0

0 0

0 0

al-1 0

bl-l at

cl-t bI

'C~+ l' C~+ l

0

¢

Zl Z2

C;+ l

Z3

*

(27)

c

[ C,+ 1 I+1 C7+ l

I =

Zi

z 1-

Zl

The biochemical submodel consists of a set of equauons, each one of them representing one of the parameters described above• This set of equations is solved numerically using the necessary initial and boundary conditions• The values of zi in our model for each parameter of the biochemical submodel are listed in Appendix A. The numerical solution of the system was conducted using the scientific utilities included in the HP-BASIC 4.0. The initial conditions required for the numerical operation were obtained by interpolating the input and output experimental data corresponding to the beginning of 1990 (2 January). Influent characteristics were measured weekly at the experimental facilities during 1990. Water temperature was obtained from the thermal submodel described above. Appendix B shows the values of the constants used in solving the model, and the literature source from which they were obtained• Abbreviations used are defined in Appendix C• The computational program was run for different time and space increments, within the stability margins of the system, until an optimal value for results usefulness and computational time was found• Finally, the used increments were A x = 2 m, and A t = 0.1 day. The programs used for thermal and biochemical submodels were developed by the authors, programmed in BASIC 4.0 and executed on an HP-9000, series 300, computer. The graphics were plotted using the PV-WAVE software•

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

86

4. Results

Fig. 2 presents a schematic representation of the three-dimensional diagram used for the simulation results. Figs. 3-8 show the simulation results for the most representative variables of the macrophytes pond: suspended bacteria (Fig. 3), phytoplankton (Fig. 4), macrophyte (Fig. 5), soluble phosphorus (Fig. 6), ammonia nitrogen (Fig. 7) and organic matter (Fig. 8). Figs. 9-14 show the simulation results for the representative variables of the microphytes pond: suspended bacteria (Fig. 9), phytoplankton (Fig. 10), zooplankton (Fig. 11), soluble phosphorus (Fig. 12), ammonia nitrogen (Fig. 13) and organic matter (Fig. 14). These plots allow us to analyze the behaviour of the system. Figs. 15-21 show the evolution over time of computed and measured values for the effluent of ponds. The agreement between predicted and measured data is very good. Water temperature is shown in Fig. 15, modelled and experimental results are the same for macrophyte and microphyte ponds. Figs. 16 and 19 show modelled and experimental values for chlorophyll a for both macrophyte and microphyte ponds. The predicted values for

c°ncentrsti°nAmg l't l///11i

~n i

time,weeks

d length, m o

Fig. 2. Coordinates used in Figs. 3-14. i = inflow; o = outflow.

400

E .~ a

S U S P E N D E D

__

BACTERIA

200

8

1

o

,

vo

~o

tl~e.-~o ~ka

.I

4o

~o

Fig. 3. Simulation results for suspended bacteria in macrophyte pond.

elo

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103 600

FZ~H Y T Q~ P L A N K T O

[_

N

I

4CO L

I 0

20

mo

.4o

mo

Fig. 4. Simulation results for phytoplankton in macrophyte pond.

50C~0 ~_

MAC~OP~YT~

%

0

10

20

,50 ti~,

"40

weeka

Fig. 5. Simulation results for macrophyte in macrophyte pond.

87

88

S. Moreno-Grau et al. // Ecological Modelling 91 (1996) 77-103 30

SOLUBLE

PHOSPHOF;~US

20

g-

.

o

~0

20

,.~0

40

.

.

.

I

.

.

50

.

.

.

.

.

.

.

60

Fig. 6. Simulation results for soluble phosphorus in macrophyte pond.

~O

AMMONIA

ri

NITROGEN

!

o

~ 0

20

.~o

~o

~o

Fig. 7. Simulation results for ammonia nitrogen in macrophyte pond.

~o

89

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103 ORGANIC

0

20

MATTER

.30 ~e~

40

~0

t

Fig. 8. Simulation results for organic matter in macrophyte pond.

~°o~

S ~ J S m E N D E D

B A C T E R I A

rg

im _

4"QO

~-

g g

o

I o

20

3O

,4o

~o

Fig, 9. Simulation results for suspended bacteria in microphyte pond.

~o

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

90

P ~"IYTO P L A N K T O N

4OO

E

u

200

1o

20

30

40

~0

Fig. 10. Simulation results for phytoplankton in microphyte pond.

OO T

ZOOPLANKTON

7 E

6o ~ t-

A

1o

20

30

~o

50

Fig. 11. Simulation results for zooplankton in microphyte pond.

S. Moreno-Grau et al. ~Ecological Modelling 91 (I996) 77-103 SOLUBLE

t o

2o

~HOSPHORUS

30

40

~o

Fig. 12. Simulation results for soluble phosphorus in microphyte pond.

,Lo r -

AM

t'~ 0 I",, I A

NLT~Q~GEN

Fig. 13. Simulation results for ammonia nitrogen in microphyte pond.

91

92

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103 500

ORGANIC

_

MATTER

000

.~o

g 501

0

i

J

.

j

.

.

i

m

.

.

20 t

e

~

.

.

.

.

.

Jo w~w

.

.

.

.

4o

.

.

.

.

.

.

J

~0

.

.

.

.

.

.

.

.

J

~o

Fig. 14. Simulationresults for organicmatterin microphytepond. phytoplankton were transformed into chlorophyll a by using the conversion factor recommended by JCrgensen (1982) in order to establish a comparison with the measured values. Figs. 17 and 20 show the modelled and experimental values for dissolved oxygen evolution through the year in the macrophyte and microphyte ponds, respectively. Predicted and experimental values for chemical oxygen demand (COD) are shown in Figs. 18 and 21, corresponding to the macrophyte and microphyte ponds. In order to assess the validity of the model in its simulation of the performance of the ponds, the test for differences between variances and between means were calculated and contrasted with the corresponding critical values, and the correlation coefficient between computed and experimental data. For dissolved oxygen the WATER TEMPERA-URE 40F

~2o

o! 0

L 200 Time, dcys

400

Fig. 15. Plot of temperatureversus time, modelled(--) and experimental(*) results in macrophyteand microphyteponds.

S. Moreno-Grau et a l . / Ecological Modelling 91 (1996) 77-103

200

CHLOROPHYLL o

F

~t

F

~

"5o-

}

L

,,"/V

~ooc

"

/

S

~ I 5O

v""L~, "

oL.......................... .yJ• 0

l

200

400

T;me, days

Fig. 16. Plot of chlorophyll a versus time, modelled ( - - ) and experimental (*) results in macrophyte pond.

D~SSOLVED OXYGEN

0

200 Time, days

400

Fig. 17. Plot of dissolved oxygen versus time, modelled ( - - ) and experimental ( * ) results in macrophyte pond.

CHEMkCAL OXYGEN D E M A N D i

4ooi

i

!

,

F

o

73

"

~

,

200 Tree, days

,

,

400

Fig. 18. Plot of chemical oxygen demand versus time, modelled ( - - ) a n d experimental ( * ) results in macrophyte pond.

93

94

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103 CHLOROPHYLL

a

2~ot

,5o~ i 100

0

200 T;me, doyS

400

Fig. 19. Plot of chlorophyll a versus time, modelled ( - - ) and experimental ( * ) results in microphyte pond.

,o[--

DFSSOLMED O X Y G E N

% E

i 20c

0 0

200 Time, deys

Fig. 20. Plot of dissolved oxygen versus time, modelled ( - - ) and experimental ( * ) results in microphyte pond.

CHEM CAL C×YGEN DEMAND

t 200

~5

-/

0

200

T~me,doys

40O

Fig. 21. Plot of chemical oxygen demand versus time, modelled ( - - ) and experimental ( * ) results in microphyte pond.

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

95

Table 2 Calculated (com) and critical (cr) values of the test of differences between variances ( F ) and between means (t), and correlation coefficient

Water temperature COD M.P. Chlorophyll a M.P. Dissolved oxygen M.P. COD SM.P. Chlorophyll a SM.P. Dissolved oxygen SM.P.

F(com)

F(cr)

t(com)

t(cr)

r2

1.317 1.013 0.949 1.109 0.956 0.899 1.282

1.592 1.592 1.592 1.592 1.592 1.592 1.592

0.039 0.820 0.373 1.126 0.428 0.709 2.140

1.660 1.660 1.660 1.660 1.660 1.660 1.660

0.893 0.984 0.975 0.836 0.987 0.961 0.367

M.P. macrophyte pond; SM.P. microphyte pond.

correlation coefficients were calculated using the simple moving average of experimental and computed data, due to the great variability shown by this parameter both hourly and daily. Table 2 presents the results for temperature and biochemical variables.

5. Discussion and conclusions

A simulation model is presented to predict the performance of waste water treatment ponds using either microphytes or macrophytes. The model simulates temperature, suspended and attached bacterial mass, phytoplankton, zooplankton, dissolved oxygen, COD and nutrients. The model is one-dimensional in order to accurately represent the behaviour of the ponds from which the experimental data used in the modelling effort were obtained. The main difference encountered in the performance of ponds using microphytes or macrophytes is the higher dependency of the microphyte ponds on temperature. This experimental finding was also reproduced by the model. As Figs. 9-11 indicate, all three micro-organisms responsible for waste water treatment in microphyte ponds, i.e. suspended bacteria, phytoplankton and zooplankton, maintain very low or zero concentrations during the cold season of the year, followed by rapid growth in late spring and summer. The rapid growth results in sharp decreases in nutrients. On the other hand, macrophyte growth is less dependent on temperature, showing an earlier development of the rooted plants in the year (Fig. 5), which in turn results in decreases of the concentration of nutrients. The use of macrophytes, therefore, aids in smoothing out the efficiency peaks shown by waste water treatment ponds. Suitable waste water treatment systems could be designed by combining microphytes and macrophyte ponds, thus extending over the year the usefulness of natural systems. These differences in behaviour between the two types of ponds were accurately reproduced with the model presented in this paper. Significant amounts of biomass accompany the effluent and cause the levels of raw COD to be high, especially in the summer. The average concentration of filtered COD in the experimental facilities is low, 55 mg O2/1 in summer, which indicates that the organic load in the influent has been degraded by bacteria. The rapid growth phase, accurately predicted by the model, results in an ensuing decrease of COD and nutrients which are incorporated into biomass. Removal of the biomass is therefore an efficient method to significantly improve the quality of the effluent. F statistics, for all analyzed variables, were lower than the critical value (e~ = 0.05). For all variables, except dissolved oxygen in the microphyte pond, t statistics were lower than the critical value ( a = 0.05). For dissolved oxygen in the microphyte pond, the t statistic was lower than the critical value with a significance level of 0.01. Correlation coefficients between modelled and experimental data, excluding dissolved oxygen in the microphyte pond, were larger than 0.8, showing an excellent accuracy.

96

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

The model may be used to devise hypothetical experiences, which should be experimentally tested. In view of our results, two tests could be developed: (1) to prune the aquatic macrophytes when the maximum growth has been reached, in order to promote a new growth phase while simultaneously removing organic matter and nutrients; (2) to design a system in series, with the influent to the macrophyte pond coming from a first step treatment in a microphyte stabilization pond. In conclusion, this model can be used to represent the behaviour of systems whose hydraulic regimes approach plug-flow conditions, including waste water treatment ponds, rivers, or channels where rooted vegetation is present. As a design tool, it can be used to upgrade the performance of existing facilities, or be applied to new facilities.

Acknowledgements

The authors wish to express their acknowledgment to Lorenzo Vergara-Pagfin and Lorenzo Vergara-Jufirez for their collaboration on the analytical control of the experimental facilities.

Appendix A. Values of z~ in the biochemical model

Bacterial biomass in suspension: Bl~," + Ys, tzB,

MO/' 0~, NH~, PS 7 ( B['.~s,] n 1B~iAt KMO~+ MO/~ KB, O: + O2i KB, N + NH~i KBI v + PSi' ] (28)

- ( K . , R + K., d + s . ) B ~ i A t

Fixed bacterial biomass MO~ O~i NH~i PS~[B~i B~i + YB2 tI'Bz KMO2 q- MOf KB:O2+ O2i n KB2N + NH3i n KB:p -I- PSi' 1

t

1 -

'

r/Bz ]

(29)

X B~iAt -- (K~2 R + Ks~ d) B~i At

Phytoplankton Fin + I ~ F f ( T ) f ( L ) KFN + NH~i KFp + PSi' 1 -

FinAt -- ( KFR + KFd + SF)FinAt

(30)

Zooplankton Z~ + I ~ z f ( T )

NH~i PS7 O~i (I_Z~Iz?At_(KzR+Kzd)Z.~At_KzN + NH~i Kzp + PS7 Kzo + O~i ~

(31)

Macrophytes M i.+ l Z u. f ( T ).f ( L ) .

NH~,

PSi'

KMN q- NH~i K g p q- PS 7

(M 1 -/ "~)

TIM

M•At - ( KMR + KMa + SM)M?At

(32)

97

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

Organic matter MO~ 0~, NH~, PSi' MO?(1 - Fr + Fn) -/%, KMO, + MO/" K~,o2 + O~i KB,N + NH~i KB,P + PS 7 1 - "OB2] B~iAt MO,

O~i

-- /£B2 KMO2 + MO n KB2O2 +

NH~i PS'/[B~i, O2in KB2N+ NH3in KB2p + PS7 1 ) --| --'OB2 B2i~t

(33)

Detrital mass: (34)

1 - --ff Dmi + SBB~i + SFFin + SMMin

Organic nitrogen: NO/" - aNNO/"At- T~ B~iAt(s B -KB~O) +

TB~B~,atKB~d-

TFFinZSt(S F - KFd ) + TzZ/"atKzd

- r m M y t t ( s M - KMd )

(35)

Ammonia nitrogen: MO/" 0~'i NH~ PSi' NA"~- T,n, at rs, t~, KMo, + MOT KB,o: + O~, K~,~ + NH~, K~,~ + PS7

× 1 - "OB, ] - KS~R - KB~a - TB2B~At YA2 1~82 KMO~+ MO/" K8202 + O~i

× KB2N + NH~i KB2 P + PS~ 1 - 'oa: ] - KB2R- K82d - r~t

-

.~I(r)I(L)K,~N+NH~ n~

TzZTAt ~zf(T)

KzN + NH~ Kzp + PS~ Kzo +~ 0 ~

. TMM . . A t ( .I x M f ( .T ) f ( L . )

+

-

. NH~i

At

d

sBB[' i + SFFi + SMM •

1

--

-K~-K~a

-

"oz -

PS 7 ( 1 - -Mi" ) PS7 "OM

tl

n

'OF]

n

(T"'s"BI' + TFSFFi

n

+ TMSMM'

--

K Z R

-- KMR--

KMN + NH~i KMp +

Ur Dm -

l-

--

Kzd

KMa

} +aNNO/"At

)

(36)

Organic phosphorus: PO/"- c%PO/"At-- rtts, B~iAt( s B --KRLd)+ ~B2B~iAtKB2d - ~FFi~At( S F - KFa ) + qtzZ'i'ZltKzd- ~MM~'At(SM- Kgd )

(37)

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

98

Soluble phosphorus:

(

MO7

O~

NH~i

PS7 (B~/)

PSi' - aItB,BiAt YB, tXB, KMOt ...}_MOT KB,02 q- O2in KB, N q- NH3in KB, P -k- PSi" 1 - -T~BI {

NH~ KB: N q-

MOT

O~i

-- ~8:B~ At Ys: tZz: KMO: + MO/~ KB~O:+ O~ i

--KB,R -- KBId

PSi'

NH~i KB2 P q- PSi'

~Tz: }

-- rttFFi~At IzFf(T)f( L) KFN + NH3i KFp + PS~ 1 - - -

~Tr

( (

- ~zZ'~At tZzf(T) KZN + NH~i Kzp + PS n Kzo + O~i

- KFR -- FFd

rlz }

NH, PS:(

t

-- ~FMM~At # M f ( T ) f ( L) KMN + NH3i KMp + PS7 1 "

rim ]

)

-- KMR -- KMd + apPO~At

UrDm At + m d snB~i + SFFi" + SMM; (~B'SBB~i + ~FSFFi" + ~MSMM?) -- Kp[PO43-]

(38)

Dissolved oxygen: OD 7 +

X

KL( C~ - C)

A t - aB Bi at YB, Izn,

Ko, N + NH~i KB, o + PS7

-- °tBzB~iAt

Ys~

I --

'r/B' ]

MOT KMO'

q-

O~i

MO:' KB,o2 + Ozi

-- KB, R

/~B~KMOMO~' 0~, NH~, PS7 + MO/~ Ks2o~ + O~i KB2 N + NH~i KB2 P + PS 7 NH~i KFN q-

PSi'

NH~i KFp

--°~zZ~At I~zf(T)f(L) KzN+NH~, Kzp+PS7 Kzo+O~i

+ PS n

~z]

(39)

Total coliforms: CTin - KCTCTinAt

(40)

Faecal coliforms: CFi" - KcFCFi"At

(41)

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

Appendix B. Values of the model constants

Constant

Value

Dimensions

Reference

Ctedisp, K Coefmanr, n Rtomob 1, Y~, Vspcrcbl20, /zB1 O vspcrcb 1 Kmmmobl, KMo' Kmmo2bl, KMo2 Kmmnh3bl, KB,N Kmmpsbl, Ks, P Kcinrbl20, KB,R O Kcinrb 1 Kcinmbl20, Kn~d O Kcinmb 1 Vspsedb 120, sB OVspsedb 1 Rtomob2, Ys_~ Vspcrcb220, t'%2 19vspcrcb2 Kmmmob2, KMo2 Kmmo2b2, KB:o' Kmmnh3b2, KB2N Kmmpsb2, KB2P Kcinrbl20, K~2R 19Kcinrb2 Kcinmb220, K82d O Kcinmb2 Vspcrcf20, IXF 19vspcrcf 19f(T)F Kmmnh3f, KFN Kmmpsf, KFp Kcinrf20, KFR OKcinrf Kcinmf20, KFO 19Kcinmf Vspsedf20, s r 19Vspsedf Vspcrcz20, i~z 19vspcrcz O f(T)Z Kmmnh3z, KzN Kmmpsz, Kzp Kmmo2z, Kzo ~

500 0.025 0.5 5.0 1.07 50.0 1.0 0.01 0.01 0.035 1.07 0.035 1.07 0.05 1.07 0.5 5.0 1.07 50.0 1.0 0.01 0.01 0.035 1.07 0.035 1.07 0.5 1.07 1.066 0.1 0.1 0.003 1.07 0.001 1.07 0.05 1.07 0.1 1.07 1.066 0.01 0.01 0.01

non-dimensional non-dimensional non-dimensional day- 1 non-dimensional mg/l mg/1 mg/l mg/l daynon-dimensional day- 1 non-dimensional daynon-dimensional non-dimensional day- t non-dimensional mg/l mg/1 mg/l mg/1 day- 1 non-dimensional day- 1 non-dimensional daynon-dimensional non-dimensional mg/1 mg/1 daynon-dimensional day- l non-dimensional day- I non-dimensional day- l non-dimensional non-dimensional mg/1 mg/1 mg/1

Fischer et al. (1979) Brown and Bamwell (1985) Metcalf and Eddy (1979) Metcalf and Eddy (1979) Bowie et al. (1985) Metcalf and Eddy (1979) Fritz et al. (1979) Fritz et al. (1979) Fritz et al. (1979) Metcalf and Eddy (1979) Bowie et al. (1985) Fritz et al. (1979) Bowie et al. (1985) Fritz et al. (1979) Bowie et al. (1985) Metcalf and Eddy (1979) Metcalf and Eddy (1979) Bowie et al. (1985) Metcalf and Eddy (1979) Fritz et al. (1979) Fritz et al. (1979) Fritz et al. (1979) Metcalf and Eddy (1979) Bowie et al. (1985) Fritz et al. (1979) Bowie et al. (1985) Bowie et al. (1985) Bowie et al. (1985) Moreno-Grau (1983) Chen (1970) Chen (1970) Baca and Amett (1976) Bowie et al. (1985) Baca and Amett (1976) Bowie et al. (1985) Bowie et al. (1985) Bowie et al. (1985) J0rgensen (1976) Bowie et al. (1985) Bowie et al. (1985) Baca and Arnett (1976) Baca and Amett (1976) Baca and Arnett (1976)

99

100

Kcinrz20, KZR OKcinrz Kcinmz20, Kzd ®Kcinmz Vspcrcm20, ixM O vspcrcm Of(T)M Kmmnh3m, KMN Kmmpsm, KMp

Kcinrm20, K MR OKcinrm Kcinmm20, KMd ®Kcinmm Vspsedm20, s M OVspsedm Vspminn20, otN OVspminn Vspminp20, et p OVspminp Vspprepp20, Kp OVspprepp Cregben20, Up OCregben Cestqnbl, TB~ Cestqnb2, T& Cestqnf, TF Cestqnz, Tz Cestqnm, TM Cestqpbl, ~B, Cestqpb2, qts2 Cestqpf, ~ Cestqpz, ~z Cestqpm, ~M Cono2mbl, as, Cono2mb2, as~ Cono2mz, az Prodo2ff, a r Vspmct20, Kcr OVspmct Vspmcf20, KcF OVspmcf Ilumsat, I~

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

0.003 1.07

0.0001 1.07

0.5 1.07 1.07

0.02 0.02 0.001 1.07

0.011 1.07

0.001 1.07

0.1 1.02

0.12 1.07

0.1 1.08

0.09 0.99 0.124 0.124 0.063 0.14 0.02 0.024 0.024 0.009 0.02 0.002 2.0 2.0 1.0 1.244 4.0 1.0893 4.0 1.0893 350

daynon-dimensional day non-dimensional day- 1 non-dimensional non-dimensional mg/1 rag/1 day- 1 non-dimensional day non-dimensional day- l non-dimensional daynon-dimensional day- 1 non-dimensional day- 1 non-dimensional day- 1 non-dimensional mg/mg mg/mg mg/mg mg/mg mg/mg mg/mg mg/mg mg/mg mg/mg mg/mg mg/mg mg/mg mg/mg mg/mg day- 1 non-dimensional day- 1 non-dimensional kcal m-2 day- l

Bowie et al. (1985) Bowie et al. (1985) Bowie et al. (1985) Bowie et al. (1985) Voinov and Tonkikh (1987) Bowie et al. (1985) Bowie et al. (1985) Oliver and Legovic (1988) Oliver and Legovic (1988) Voinov and Tonkikh (1987) Bowie et al. (1985) Oliver and Legovic (1988) Bowie et al. (1985) calibrated Bowie et al. (1985) Moreno-Grau (1983) Bowie et al. (1985) Moreno-Grau (1983) Bowie et al. (1985) Moreno-Grau (1983) Bowie et al. (1985) Fritz et al. (1979) Bowie et al. (1985) Bowie et al. (1985) Bowie et al. (1985) Moreno-Grau (1983) calibrated Reddy and De Busk (1987) Moreno-Grau (1983) Moreno-Grau (1983) Moreno-Grau (1983) Orlob (1982) Reddy and De Busk (1987) Orlob (1982) Orlob (1982) Orlob (1982) Moreno-Grau (1983) Baca and Arnett (1976) Moreno-Grau (1983) Baca and Amett (1976) Moreno-Grau (1983) Moreno-Grau (1983)

S. Moreno-Grau et al. / Ecological Modelling 91 (1996) 77-103

101

Appendix C. Notation

Symbol Cte Coef Vsp Rto crc Kmm Kcin 19 ..... m ..... r . . . . . sed ..... mo . . . . . 02 . . . . . nh3 . . . . . no

constant coefficient specific rate yield growth semi-saturation constant kinetic constant temperature d e p e n d e n c e factor mortality respiration sedimentation organic matter dissolved o x y g e n a m m o n i a nitrogen organic nitrogen

Symbol

Meaning

. . . . . ps . . . . . po ..... md ..... bl . . . . . b2 ..... f ..... z ..... m . . . . . cf . . . . . ct Cregben . . . . . 20 Cestq Cono2m Prodo2f

soluble phosphorus organic phosphorus detrital mass suspended bacteria supported bacteria phytoplankton zooplankton macrophytes faecal coliform m i c r o - o r g a n i s m s total coliform m i c r o - o r g a n i s m s benthic regeneration coefficient reference temperature 20 -~C stoichiometric coefficient o x y g e n c o n s u m p t i o n in m e t a b o l i s m o x y g e n production in photosynthesis

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