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Performance evaluation and mathematical modelling of coliform die-off in tropical and subtropical waste stabilization ponds
PII: S0043-1354(98)00331-5
Wat. Res. Vol. 33, No. 6, pp. 1435±1448, 1999 # 1999 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0043-1354/99/$ - see front matter
PERFORMANCE EVALUATION AND MATHEMATICAL MODELLING OF COLIFORM DIE-OFF IN TROPICAL AND SUBTROPICAL WASTE STABILIZATION PONDS M MARCOS VON SPERLING**
Department of Sanitary and Environmental Engineering, Federal University of Minas Gerais, Av. Contorno 842, 7o andar, 30110-060 Belo Horizonte, Brazil (First received November 1997; accepted in revised form July 1998) AbstractÐThe paper investigates the coliform removal in 33 facultative and maturation ponds in Brazil. The ponds were located in dierent parts of the country, with climates ranging from tropical to subtropical and latitude from 7 to 248S. The ponds had dierent physical con®gurations, temperature and detention times. The total number of data used in the study, mostly comprising long-term averages, was 66. Two ¯ow regimes were investigated: CSTR and dispersed ¯ow. In the dispersed-¯ow model, the dispersion number was estimated using the formulae by Agunwamba et al. and Yanez, and both were found to give similar results. The coliform die-o coecient Kb was correlated with the pond depth and hydraulic detention time in the dispersed-¯ow model (R2=0.847). A regression equation, using theoretically generated data, was proposed, correlating Kb for the CSTR model with Kb for dispersed-¯ow model, using the length-to-breadth ratio and detention time of the pond (R2=0.997). Use of this equation yields virtually the same removal eciency values as those obtained directly by the dispersed-¯ow model. Utilisation of the Kb values calculated by the proposed regression models gave a very good prediction of the log euent coliform concentration of the 33 ponds (R2=0.951 for the CSTR model and R2=0.959 for the dispersed-¯ow model). Applying the proposed model for dispersed ¯ow, it was concluded that, for a given removal eciency, a shallow pond, due to its larger Kb, requires less surface area, compared to a deep pond, even though the latter has a higher detention time. # 1999 Elsevier Science Ltd. All rights reserved Key wordsÐfacultative ponds, maturation ponds, completely-mixed reactor, dispersed ¯ow, faecal coliforms, coliform die-o coecient
NOMENCLATURE
n y
B pond breadth (m) BOD biochemical oxygen demand COD chemical oxygen demand CSTR completely stirred tank reactor d dispersion number D coecient of longitudinal dispersion (m2/d) DO dissolved oxygen (mg/l) FC faecal coliform H pond height (m) Kb coliform die-o coecient (dÿ1) L pond length (m) n number of ponds in series N euent coliform concentration (org/100 ml) No in¯uent coliform concentration (org/100 ml) Q ¯ow (m3/d) R2 coecient of determination t hydraulic detention time (d) T liquid temperature (8C) U average ¯ow velocity in the reactor (m/d)
kinematic viscosity of the water (m2/d) temperature coecient
INTRODUCTION
*Author to whom all correspondence should be addressed. Tel.: +55-31-238-1882; Fax: +55-31-238-1879; E-mail: [email protected].
One of the main objectives of the use of waste stabilization ponds, especially in tropical countries, is pathogen removal. The mathematical modelling of the bacterial die-o rate in the pond is important, in order to allow the estimation of the euent coliform concentration. This, in turn, determines compliance with the pertinent legislation and establishes the allowable uses of the euent and receiving water body, such as irrigation, bathing, aquaculture, water supply and others. Coliform decay is usually modelled through ®rstorder kinetics. The euent coliform concentration is a function of the pond con®guration, represented by one of the following hydraulic models: plug¯ow, ponds-in-series, dispersed ¯ow and completely mixed (CSTR). Depending on the hydraulic regime assumed for the pond, dierent formulae are available for the estimation of the euent coliform con-
1435
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Marcos von Sperling
Table 1. Formulae for the estimation of the euent coliform concentration of a facultative or maturation pond. For symbols see the nomenclature. d = D/UL = Dt/L2 (dimensionless). L is the length of the longitudinal distance in the reactor (m).
centration of a facultative or maturation pond. These are summarized in Table 1. The CSTR model has been more frequently used to represent the hydraulic regime of facultative and maturation ponds. However, the assumption of an ideal CSTR pattern can be only ful®lled in reactors in which the length-to-breadth (L/B) ratio is not signi®cantly greater than one. In facultative ponds, this ratio is usually within 2 to 4 (EPA, 1983). In maturation ponds, due to the need for extremely high coliform removal eciencies, the designer normally has two choices: to either adopt a series of ponds or only one pond with a large L/B ratio, obtained through the introduction of baes. Under these conditions, the assumption of an ideal CSTR misrepresents reality, and the dispersed-¯ow model should be used to model coliform decay in the pond. The objective of this paper is to investigate and propose models for CSTR and dispersed-¯ow
regimes for the representation of the coliform dieo rate in facultative and maturation ponds. Data from 33 stabilization ponds located in dierent parts of Brazil are used, allowing the determination of the coecient of coliform die-o (Kb). The paper presents two equations for the estimation of Kb, one to be used in the dispersed-¯ow model and the other to be used in the CSTR model. REPORTED VALUES OF THE COLIFORM DIE-OFF COEFFICIENT Kb
In the modelling of the coliform decay, the use of an adequate value of the Kb coecient assumes a major importance. Even though, as previously mentioned, the dispersed-¯ow model is a closer representation of reality, researchers have frequently estimated the Kb coecient using the CSTR model, independent of the geometrical con®guration of the pond. Similarly, designers have resorted to the CSTR model, due to its greater conceptual simpli-
Table 2. Some Kb (208C) values available in the literature ÿ1
Kb values (d ) 2.6 0.8 0.2±10 0.71 0.62 0.84 0.33±0.90 1.3±12.0 1.2±4.82 0.4±12.2 0.45±5.89 0.5±1.5 0.39±43.6 2.0 0.73 1.1 1.2 0.74±0.84 0.26±2.42
Flow regime considered
Country/region
Reference
CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR plug ¯ow plug ¯ow dispersed ¯ow dispersed ¯ow dispersed ¯ow
Central and South Africa
Marais (1974) Mancini (1978) Sherry and Parker (1979) Mills et al. (1992) SaÂenz (1992) IMTA (1992) Saqqar and Pescod (1992) Van Haandel and Lettinga (1994) Dixo et al. (1995) Pearson et al. (1995) Mayo (1995) DELM/DPIF (1996) Pearson et al. (1996) Johansson et al. (1996) Auer and Niehaus (1993) Yanez (1993) Arceivala (1981) Yanez (1993) Von Sperling (1996b)
Australia Kenya Mexico Jordan Brazil Brazil Brazil Tanzania Tasmania Brazil Cape Verde Turkey Peru Brazil
Coliform die-o in waste stabilization ponds
1437
Table 3. Main data from the 33 ponds investigated Pond
Position in series
L (m)
B (m)
H (m)
Q (m3/d)
t (d)
L/B
Latitude (8S)
Temperature (8C)
Eciency
Kb CSTR
d-Yanez
d-Agun
Pilot scale (13 ponds in series and F21 2 12.9 F22 2 12.9 F23 2 12.9 F24 2 12.9 F25 2 4.9 M16 4 10.4 M17 4 10.4 M18 4 10.4 M19 4 10.4 M20 4 10.4 M21 5 8.5 M22 5 8.5 M24 5 66.8
parallel; 1st experiment) Pearson et al. (1995) 2.0 1.00 8.0 3.2 6.5 7.1 2.0 1.33 8.0 4.3 6.5 7.1 2.0 1.67 8.0 5.4 6.5 7.1 2.0 2.00 8.0 6.5 6.5 7.1 4.9 2.00 8.0 6.0 1.0 7.1 3.8 0.90 5.0 7.0 2.8 7.1 3.8 0.64 5.0 5.0 2.8 7.1 3.8 0.39 5.0 3.0 2.8 7.1 3.8 0.39 5.0 3.0 2.8 7.1 1.3 0.39 5.0 1.1 8.0 7.1 3.7 0.60 3.8 5.0 2.3 7.1 3.7 0.60 3.8 5.0 2.3 7.1 0.5 0.60 3.8 5.0 142.0 7.1
25 25 25 25 25 25 25 25 25 25 25 25 25
0.8571 0.8781 0.8791 0.8977 0.8744 0.9770 0.9711 0.9683 0.9737 0.9327 0.9473 0.9369 0.9756
1.33 1.20 0.96 0.97 0.83 4.31 4.80 7.16 8.66 9.38 2.56 2.12 5.68
0.52 0.43 0.34 0.33 0.50 0.76 0.96 1.52 1.64 2.35 0.78 0.71 0.54
0.51 0.41 0.32 0.29 0.41 0.61 0.77 1.20 1.28 2.25 0.61 0.57 0.53
Pilot scale (13 ponds in series and F21 2 12.9 F22 2 12.9 F23 2 12.9 F24 2 12.9 F25 2 4.9 M16 4 10.4 M17 4 10.4 M18 4 10.4 M19 4 10.4 M20 4 10.4 M21 5 8.5 M22 5 8.5 M24 5 66.8
parallel; 2nd experiment) Oragui et al. (1995) 2.0 1.00 16.0 1.6 6.5 7.1 2.0 1.33 16.0 2.1 6.5 7.1 2.0 1.67 16.0 2.7 6.5 7.1 2.0 2.00 16.0 3.2 6.5 7.1 4.9 2.00 16.0 3.0 1.0 7.1 3.8 0.90 10.0 3.5 2.8 7.1 3.8 0.64 10.0 2.5 2.8 7.1 3.8 0.39 10.0 1.5 2.8 7.1 3.8 0.39 10.0 1.5 2.8 7.1 1.3 0.39 10.0 0.5 8.0 7.1 3.7 0.60 7.5 2.5 2.3 7.1 3.7 0.60 7.5 2.5 2.3 7.1 0.5 0.60 7.5 2.5 142.0 7.1
25 25 25 25 25 25 25 25 25 25 25 25 25
0.5338 0.5785 0.6628 0.6436 0.6541 0.9182 0.9434 0.8889 0.8426 0.7878 0.9243 0.9669 0.9909
0.51 0.46 0.52 0.40 0.45 2.28 4.76 3.75 2.51 5.02 3.48 8.33 31.09
0.36 0.32 0.33 0.26 0.36 0.83 1.43 1.58 1.25 2.42 1.28 1.95 1.38
0.36 0.32 0.31 0.24 0.36 0.75 1.27 1.43 1.14 2.44 1.11 1.64 1.35
26
0.9962
2.88
0.19
0.17
22 22 28.6 28.6 28.6 28.6 28.6 19.8
0.7921 0.9589 0.9853 0.9705 0.9955 0.9000 0.9972 0.9709
0.04 1.42 0.67 1.83 1.81 0.41 17.33 2.75
0.03 0.36 0.13 0.37 0.16 0.17 0.74 0.57
0.02 0.32 0.09 0.35 0.11 0.16 0.66 0.51
24.4 24.5 25.0 25.3 23.9 24.9 24.4 25.5
0.9985 0.9581 0.9954 0.9807 0.9988 0.9392 0.9976 0.9839
5.53 2.40 1.55 4.50 5.57 1.21 2.95 4.98
0.20 0.56 0.12 0.65 0.17 0.35 0.15 0.64
0.15 0.57 0.09 0.65 0.12 0.34 0.11 0.63
Ceballos et al. (1995) F1 1
118.0
2.20
950
60.1
1.9
7.1
2 ponds; 5 experiments Vidal (1983) F 1 84.0 68.0 M 2 64.0 24.0 F 1 84.0 68.0 M 2 64.0 24.0 F 1 84.0 68.0 M 2 64.0 24.0 M 2 64.0 24.0 M 2 64.0 24.0
1.50 1.00 1.50 1.00 1.50 1.00 1.00 1.00
107 107 153 153 124 124 133 125
80.1 14.4 56.0 10.0 69.1 12.4 11.5 12.3
1.2 2.7 1.2 2.7 1.2 2.7 2.7 2.7
20.5 20.5 20.5 20.5 20.5 20.5 20.5 20.5
Years 1992, 1993, 1994, Con®ns-F 1 Con®ns-M 2 Con®ns-F 1 Con®ns-M 2 Con®ns-F 1 Con®ns-M 2 Con®ns-F 1 Con®ns-M 2
220.0
1995, respectively (average, 2 ponds) COPASA-MG (1995) 190.0 115.0 1.90 475 87.5 1.7 20.0 119.0 35.0 0.80 475 7.0 3.4 20.0 190.0 115.0 1.90 422 98.4 1.7 20.0 119.0 35.0 0.80 422 7.9 3.4 20.0 190.0 115.0 1.90 363 114.4 1.7 20.0 119.0 35.0 0.80 363 9.2 3.4 20.0 190.0 115.0 1.90 394 105.3 1.7 20.0 119.0 35.0 0.80 394 8.5 3.4 20.0
Years 1992 and 1993, respectively (average) COPASA-MG (1995) Cid. Verde 1 190.0 86.0 2.30 363 103.6 2.2 Cid. Verde 1 190.0 86.0 2.30 371 101.4 2.2
20.0 20.0
25.0 26.0
0.9923 0.9948
0.89 1.25
0.08 0.09
0.07 0.08
Years 1996/1997 CEMIG (1997) Miranda 1 86.0 44.5
1.20
256
17.9
1.9
19.0
25.0
0.9395
0.62
0.21
0.20
Ref. Aguiar and Mendonc° a (1996) M. Serra 1 122.0 47.0 Eldorado 2 200.0 95.0 Maringa 2 96.0 41.0
1.10 1.25 1.70
233 544 130
27.1 43.7 51.5
2.6 2.1 2.3
20.5 20.5 20.5
26.9 29.4 25.6
0.9940 0.9976 0.9957
3.81 4.98 3.07
0.29 0.22 0.19
0.24 0.19 0.15
Years: 1986/1987 (average) Andrade Neto (1997) 1 135.0 52.0 1.84 473 27.3 2.6 2 105.0 39.0 1.89 473 16.4 2.7 3 105.0 39.0 1.78 473 15.4 2.7
15.0 15.0 15.0
25.7 25.7 25.7
0.9965 0.9411 0.9019
7.09 0.66 0.41
0.36 0.20 0.16
0.35 0.21 0.17
21.2 21.2 20.3
25.0 19.3 23.3
0.5625 0.8000 0.9091
0.07 0.29 0.97
Ponds in series. CuiabaÂ-F CuiabaÂ-M CuiabaÂ-M
CETESB (1981) PradoÂpolis 2 PradoÂpolis 2 Itapira 2
157.0 157.0 238.0
70.0 70.0 210.0
1.00 1.00 1.00
795 760 6048
13.8 14.5 8.3
2.2 2.2 1.1
0.05 0.05 0.17 0.17 0.49 0.53 Ðcontinued overleaf
1438
Marcos von Sperling Table 3 (continued )
Pond
Position in series
Itapira Pindamon. Guararapes Guararapes Nhandeara ValparaõÂ so MairiporaÄ
2 2 1 1 1 1 2
Years 1993, 1994, 1995, IbiporaÄ 2 IbiporaÄ 2 IbiporaÄ 2 IbiporaÄ 2
L (m)
238.0 240.0 162.0 162.0 144.0 116.0 124.0
B (m)
210.0 180.0 80.0 80.0 50.0 74.0 94.0
H (m)
1.00 0.90 1.60 1.60 0.90 0.90 1.00
Q (m3/d)
5210 8623 994 1097 648 302 743
t (d)
9.6 4.5 20.9 18.9 10.0 25.6 15.7
1996, respectively (averages) FNS (1996) 213.0 74.0 1.00 1216 22.3 213.0 74.0 1.00 2090 20.7 213.0 74.0 1.00 2539 23.0 213.0 74.0 1.00 2363 21.5
L/B
Latitude (8S)
Temperature (8C)
Eciency
Kb CSTR
d-Yanez
d-Agun
1.1 1.3 2.0 2.0 2.9 1.6 1.3
20.3 22.6 21.5 21.5 20.4 21.1 23.2
18.0 24.2 26.9 22.4 26.9 22.4 16.8
0.8500 0.9259 0.9400 0.7941 0.9000 0.9818 0.8250
0.68 2.09 0.47 0.17 0.56 1.79 0.37
0.42 0.90 0.16 0.11 0.22 0.35 0.24
0.44 1.05 0.16 0.11 0.23 0.28 0.22
2.9 2.9 2.9 2.9
23.5 23.5 23.5 23.5
22.3 20.7 23.0 21.5
0.8868 0.9401 0.7761 0.6259
0.30 0.73 0.12 0.07
0.13 0.22 0.07 0.05
0.12 0.21 0.07 0.05
L = length (m); B = breadth (m); H = height (m); Q = ¯ow (m3/d); t = detention time (d); Eciency = faecal coliform removal eciency. CSTR = Kb (208C) for CSTR reactor (dÿ1). d-Yanez = Kb (208C) for dispersed ¯ow, with d according to Yanez, 1993 (dÿ1). d-Agun = Kb (208C) for dispersed ¯ow, with d according to Agunwamba et al., 1992 (dÿ1).
city. For a given removal eciency, the estimation of Kb based on the hydraulic detention time and on the in¯uent and euent coliform concentrations, using the CSTR model leads to an overestimation of the Kb value, compared to that obtained if the dispersed-¯ow model had been used. This is due to the fact that the CSTR model is implicitly associated with lower removal eciencies (a CSTR reactor is the least ecient for the removal of ®rstorder decay constituents), which forces the increase of Kb in order to compensate for the underestimation of its removal eciency. Table 2 lists some Kb values available in the literature. No further information about the ponds is included in the tables, since they have not been presented by many of the publications. The wide scattering of the Kb values re¯ects the speci®c in¯uencing factors in each case, such as DO, pH, solar radiation, BOD loading, besides the physical con®guration. Additionally, it re¯ects the inadequacy of the idealised hydraulic models (CSTR or plug-¯ow) for the prediction of the behaviour of nonideal reactors. This scattering was one of the main motivations for the present study. POND SYSTEMS INVESTIGATED IN THE STUDY
The study investigated 33 facultative and maturation ponds in Brazil. The ponds analysed were distributed from the northeast (latitude 78S) to the south (latitude 23.58S) of Brazil, encompassing a climate range from tropical to subtropical. The ponds had dierent volumes and physical con®gurations, with 13 being pilot-scale units and the other 20 being full-scale ponds. In this study, no distinction was made between facultative and maturation ponds, apart from their position in the series of ponds (e.g. primary, secondary, tertiary, etc.) and their depth. The ponds represented a wide spectrum of operating conditions, with the length-to-breadth ratio (L/B) varying from 1 to 142, while the deten-
tion time varied from 0.5 to 114 days. In most cases, the removal eciency of faecal coliforms was based on medium or long-term geometric means of the coliform concentrations. In many systems, more than one set of data was available, representing either dierent experiments which have been undertaken or yearly averages from a series of years. The total number of data analysed in this study is 66. The results were obtained from operating records and published papers and not collected directly by the author. It was not easy to gather representative results, since most of the papers available in the literature had no information on the L/B ratio of the pond. Also many papers presented the values of ¯owrates based on the design ®gures, and not the actually measured ones. Table 3 presents the relevant data from the ponds investigated, while Fig. 1 presents the frequency distribution histograms of the main descriptive parameters, showing the wide range of operating conditions covered by the study. DETERMINATION OF THE COLIFORM DIE-OFF COEFFICIENT Kb
Two ¯ow regimes were considered in the study: CSTR and dispersed ¯ow. For the CSTR model, the Kb values were calculated through a simple rearrangement of Eq. (2), leading to: Kb
No =N ÿ 1 t
6
For the dispersed ¯ow model, the dispersion number d was calculated using two empirical formulae available in the literature, the former with a more complex structure (Agunwamba et al., 1992) and the latter with a simple structure (Yanez, 1993), in which d depends only on the L/B ratio: . Agunwamba et al. (1992), original formulae simpli®ed by Von Sperling (1996a)
Coliform die-o in waste stabilization ponds
1439
Fig. 1. Frequency distribution histograms of the main descriptive parameters of the ponds investigated.
3 B 2H tu ÿ0:410 H d 0:102 4LBH L ÿ 0:9811:385H=B H B
7
. Yanez (1993) d
L=B ÿ0:261 0:254 L=B 1:014 L=B 2
8
where L is the pond length (m); B the pond breadth (m); H the pond depth (m); t the hydraulic detention time (d); n the kinematic viscosity of the water (m2/d) (regression analysis done in the paper: n = 0.325Tÿ0.450, for T = 10 to 308C, with n = 6, R2=0.986). Although in the present study the author preserved the original formulation of Yanez (equation 8) for the dispersion number d, it is interesting to note that a formula as simple as d = 1/(L/B) gives very similar results to those obtained through the utilisation of Yanez's equation. Given the diculty in making Kb explicit in Eqs. (4) and (5) for dispersed ¯ow, Kb was calculated by trial-and-error iterations, using both equations, based on the previously calculated t and d values (the latter estimated by equations 7 and 8). The iteration stopped when the Kb value gave an estimated removal eciency equal to the observed one.
For both the CSTR and dispersed ¯ow models, the Kb values were converted to the standard temperature of 208C using equation 9 and the temperature coecient y = 1.07. Although Marais (1974) proposed the value of 1.19, other more recent texts (Mancini, 1978; Thomann and Mueller, 1987; WHO, 1987; Yanez, 1993; Johansson et al., 1996) use the value of 1.07. In this study, no elements were available in order to allow the speci®c determination of y. Kb 208C Kb T y 20ÿT
9
where Kb(208C)=Kb coecient at the temperature of 208C (1/d); Kb(T)=Kb coecient at a temperature T (1/d). The resulting Kb (208C) values for the two ¯ow regimes and for the two formulae for the dispersion number d are presented in Table 2. Figure 2 shows the frequency distribution histograms of the three versions of the Kb coecient. The Kb coecient for the CSTR regime has a wide distribution (minimum = 0.04 dÿ1 and maximum = 31.09 dÿ1) due to the inability of the CSTR model to represent well ponds with an L/B ratio substantially greater than 1. Under these conditions, the Kb value is overestimated, in order to accommodate the lower eciency inherent to the CSTR. The distribution of the Kb coecients for the dispersed-¯ow regime are much narrower (minimum = 0.02 dÿ1 and maximum = 2.44 dÿ1), indicating the better adequacy of the dispersed-¯ow model.
1440
Marcos von Sperling
Fig. 2. Frequency distribution histograms of the coecients Kb (208C) for the two ¯ow regimes (CSTR and dispersed ¯ow) and the two formulae for calculating the dispersion number d (equations 7 and 8). RELATIONSHIP BETWEEN THE COEFFICIENT Kb, THE POND DEPTH AND THE DETENTION TIME
It is well known that some of the main mechanisms of pathogen removal are associated with the pond depth (penetration of the solar radiation, photosynthesis/pH/DO). Catunda et al. (1994) and Von Sperling (1996b), studying the series of ponds in the Northeast of Brazil (pilot-scale ponds in Table 2), observed a relationship between Kb and the pond depth H: the lower the pond depth, the greater the coecient Kb. Other authors (Sarikaya et al., 1987; Mayo, 1989, 1995), in other countries, also observed an in¯uence of the pond depth on Kb. Some studies (Gamini, 1981; Sarikaya et al., 1987; Mayo, 1989, 1995; Qin et al., 1991; Saqqar and Pescod, 1992; Silva et al., 1996) have presented models for the prediction of Kb as a function of
variables such as pH, algal concentration, soluble BOD, applied COD load, solar radiation, light extinction coecient and also depth. In the present case, it was observed that the coef®cient Kb for dispersed ¯ow was related to the pond depth, as expected, and also with the hydraulic detention time. The lower the depth and the detention time, the greater the coecient Kb. Figure 3 exempli®es these relationships for the Kb coecient determined with d according to Yanez. For the CSTR model, no signi®cant relationship was observed between Kb and the variables H and t, as can also be seen on Fig. 3. The advantage, for design purposes, of expressing Kb as a function of the depth and the hydraulic detention time is that those are design variables, whereas most of the other variables suggested in the literature need to be assumed, and will depend on a number of factors, not easily predictable.
Fig. 3. Relationship between the coecient Kb (CSTR and dispersed-¯ow, with d according to Yanez) and (left) the pond depth and (right) the hydraulic detention time.
Coliform die-o in waste stabilization ponds
1441
Table 4. Regression equations for estimating Kb as a function of the pond depth H and the hydraulic detention time t, for the dierent hydraulic regimes Hydraulic regime CSTR Dispersed ¯ow (d according to Yanez, 1993) Dispersed ¯ow (d according to Agunwamba et al., 1992)
In the present study, a regression analysis was made between the 66 values of Kb calculated and presented in Table 3 with the corresponding pond depth H and hydraulic detention time t, for the CSTR and dispersed-¯ow patterns, the latter with the two formulae for the estimation of the dispersion number d. The best ®tting was obtained with the multiplicative function Kb=aHbtc. Table 4 presents the resulting equations. It can be observed that the CSTR model leads to a very poor ®tting (low value of the R2 coecient), and that the dispersed-¯ow model with d according to Yanez (1993) (R2=0.847) and Agunwamba et al. (1992) (R2=0.858) leads to the best estimation. A value of R2=0.847 means that 84.7% of the variance of Kb can be explained by the model. The results for the dispersed ¯ow model are considered very satisfactory, given the diculty in modelling Kb and the simplicity of the proposed models. Regression models with Kb as a function of the depth only were also tried and, for the dispersed¯ow model, gave R2 values of 0.757 ÿ1.532 (Kb=0.437H for d according to Yanez). Figure 4 plots together the best-®t lines for the dispersed-¯ow model, for d according to Yanez (1993) and Agunwamba et al. (1992), for hydraulic detention times of 5 and 30 days. It can be seen that the results obtained by the two models are not substantially dierent, especially for the more frequently used pond depths. As a result, due to its
Equation
R2
Equation number
Kb=2.928Hÿ0.987tÿ0.011 Kb=0.917Hÿ0.877tÿ0.329 Kb=0.958Hÿ0.752tÿ0.401
0.142 0.847 0.858
(10) (11) (12)
greater structural simplicity and ease of data input, the equation with d based on Yanez is adopted in the remainder of the paper. For the dispersed-¯ow model, with d according to Yanez, Fig. 5 shows the values of Kb according to Eq. (11), for dierent values of the hydraulic detention time. DETERMINATION OF THE Kb COEFFICIENT FOR CSTR BASED ON THE Kb FOR DISPERSED FLOW
It is recognised that the CSTR model is much more widely employed by designers than the dispersed-¯ow model. However, the previous sections showed the inadequacy of the CSTR model, which led to a very wide range of possible Kb values, making it dicult to select the one to be used in the pond design. Additionally, no signi®cant relationship seemed to exist between Kb and the variables H and t. The present section derives an equation for the estimation of Kb for the CSTR model, based on H, t and L/B. The derivation of the Kb values for CSTR was based on theoretical considerations. It was initially calculated, for dierent values of the dimensionless product Kbt (Kb for dispersed ¯ow) and dispersion number d, the corresponding Kb for CSTR, which yields the same eciency of coliform removal (®rst-order kinetics). Table 5 presents the results from a practical viewpoint. In the table, the
Fig. 4. Comparison between the estimated values of Kb as a function of H for the dispersed-¯ow model, with d according to Yanez and Agunwamba, and for hydraulic detention times of 5 d and 30 d (Eqs. (11) and (12)).
1442
Marcos von Sperling
Fig. 5. Estimated values of Kb, for dierent values of H and t, according to Eq. (11) (d from Yanez)
dispersion numbers d have been substituted by L/B, using Yanez equation (equation 8 rearranged). The values presented in the table are the ratio between the Kb for CSTR and Kb for dispersed ¯ow (Kb CSTR/Kb dispersed ¯ow). The interpretation of the table is as follows. A pond with L/B = 2, detention time t = 10 days and Kb (dispersed) = 0.5 dÿ1 has the dimensionless product Kbt = 10 0.5 = 5.0. For L/B = 2 and Kbt = 5, the table shows that the Kb for CSTR is equal to 2.65 times the Kb for dispersed ¯ow. In other words, the Kb for CSTR is 2.65 0.5 = 1.33 dÿ1. The estimation of the coliform removal eciency using the dispersed-¯ow model (Eqs. 4 and 5, with Kb for dispersed ¯ow) and the CSTR model (Eq. (2) with Kb for CSTR) leads to the same results. In order to extend the applicability of Table 5, a regression analysis was done, having as dependent variable the ratio Kb (CSTR)/Kb (dispersed) and as independent variables the Kbt product (dispersed ¯ow) and the L/B ratio. Using the 44 values presented in Table 5, the equation of best ®t obtained was:
Kb CSTR Kb dispersed 1:753 0:0011 Kb dispersed t3:189 1:509
L=B
13
n 44; R2 0:997 The ®t was excellent, as indicated by the high R2 value obtained. Equation 13 can be further developed, passing the denominator of the left-hand side to the right-hand side: Kb CSTR 1:753 Kb dispersed 0:0011 3:189 K 4:189 L=B 1:509 b dispersed t
14
Equation 14 allows the direct estimation of the Kb for CSTR based on the previous determination of the Kb for dispersed ¯ow and the previous knowledge of t and L/B. If Kb for dispersed ¯ow is estimated based on the regression equation with H and t (Kb=0.917Hÿ0.877tÿ0.329, Eq. (11) for d
Table 5. Ratio between the Kb coecients obtained for the CSTR model and the dispersed-¯ow model, for dierent values of the dispersion number d and of the product Kbt (dispersed ¯ow) Kbt (dispersed ¯ow)
0 1 2 3 4 5 6 7 8 9 10
Ratio Kb (CSTR)/Kb (dispersed ¯ow) d = 1.0, L/B 11
d = 0.5, L/B 12
d = 0.2, L/B1 5
d = 0.1, L/B1 10
1.00 1.14 1.29 1.46 1.64 1.83 2.04 2.27 2.53 2.79 3.08
1.00 1.23 1.52 1.83 2.21 2.65 3.15 3.73 4.39 5.14 6.01
1.00 1.40 1.95 2.68 3.66 4.95 6.62 8.81 11.60 15.16 19.66
1.00 1.52 2.32 3.55 5.39 8.18 12.28 18.21 26.81 39.11 56.50
Coliform die-o in waste stabilization ponds
according to Yanez), then equation 14 can be further developed into the following one: Kb CSTR 1:608 H ÿ0:877 tÿ0:329 7:656 10ÿ4 H ÿ3:674 t1:811 L=B 1:509 15 Equation 15 is then the ®nal expression, which can be used to estimate the coecient Kb for use with the CSTR model. Although the equation has been derived for L/B = 1 to 10 and Kbt = 1 to 10, its utilisation for values slightly outside these boundaries was shown to be satisfactory, as demonstrated in the next section. Other regression equations with greater limits for Kbt were tried but, although the overall ®tting was good, the accuracy for the smaller values of Kbt, which are very frequent for maturation ponds, was decreased. Table 6 presents the values of Kb (CSTR, 208C) obtained through equation 15, for some typical values of H, L/B and t.
VERIFICATION OF THE PROPOSED MODELS WITH THE OBSERVED DATA
In order to assess the performance of the two proposed models for Kb, the euent coliform concentration from each pond was estimated and compared with the observed one. The following equations were used:
Table 6. Values of Kb (CSTR, 208C) (dÿ1) for dierent values of H, L/B and t (according to equation 15) H (m)
L/B 1
2
3
4
6
8
10
t = 5 days 1.0 0.96 1.5 0.67 2.0 0.52 2.5 0.42
0.99 0.67 0.52 0.43
1.02 0.68 0.52 0.43
1.06 0.69 0.52 0.43
1.16 0.71 0.53 0.43
1.27 0.74 0.54 0.44
1.40 0.77 0.55 0.44
t = 10 days 1.0 0.80 1.5 0.54 2.0 0.41 2.5 0.34
0.89 0.56 0.42 0.34
1.01 0.59 0.43 0.35
1.16 0.62 0.44 0.35
1.49 0.70 0.47 0.36
1.90 0.79 0.50 0.38
2.35 0.89 0.54 0.39
t = 20 days 1.0 0.77 1.5 0.46 2.0 0.34 2.5 0.27
1.09 0.53 0.37 0.29
1.51 0.63 0.40 0.30
2.01 0.74 0.44 0.32
3.20 1.01 0.53 0.36
4.61 1.32 0.64 0.41
6.21 1.69 0.77 0.46
t = 30 days 1.0 0.89 1.5 0.45 2.0 0.31 2.5 0.25
1.56 0.60 0.37 0.27
2.43 0.80 0.43 0.30
3.46 1.03 0.52 0.34
5.94 1.59 0.71 0.42
8.88 2.25 0.94 0.52
12.22 3.01 1.20 0.64
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CSTR model: . Estimation of Kb (208C): equation 15 (even though some ponds were outside the applicability limits of L/BR 10 and KbdispersedtR 10). . Correction of Kb for the actual temperature: equation 9. . Estimation of the euent coliform concentration: equation 2. Dispersed ¯ow model: . Estimation of Kb (208C): equation 11. . Estimation of the dispersion number d: equation 8. . Correction of Kb for the actual temperature: equation 9. . Estimation of the euent coliform concentration: equations (4) and (5). Figure 6 presents the 66 values of the estimated observed coliform concentrations, for both the CSTR and the dispersed ¯ow models. Visually, it can be seen that both models were able to satisfactorily predict the order of magnitude of the euent coliform concentration from each pond. The Coecients of Determination (R2) for the estimation of the log of the concentrations were excellent and very similar (R2=0.951 for the CSTR model and R2=0.959 for the dispersed-¯ow model). Figure 7 compares the estimated values of the euent concentrations from both models, and it can be seen that the results are in most cases very similar, lying very close to the 458 line of perfect ®t.
POND VOLUME AND SURFACE AREA REQUIREMENTS FOR COLIFORM REMOVAL
Table 7 presents the pond requirements in terms of volume (m3 of pond volume per m3/d of wastewater) and surface area (m2 of pond surface area per m3/d of wastewater) for dierent pond depths and L/B ratios, using the proposed approach for the dispersed-¯ow model, in order to achieve 90% (1 log), 99% (2 log) and 99.9% (3 log) coliform removal in a single pond, at a liquid temperature of 208C. Figure 8 illustrates the corresponding volume and surface area requirements. In the table and ®gure, the unit volume requirements (m3 per m3/d) are equivalent to the detention time (d). The values in Table 7 and Fig. 8 emphasise the in¯uence of H and L/B in the eciency of coliform removal: the lower the pond depth H and/or the greater the L/B ratio, the lower the pond volume and surface area required. The pond depth has an important and somewhat unexpected in¯uence on the surface area requirements: according to the results obtained, even though a shallower pond has a lower volume, and consequently a lower detention time, the coliform die-o coecient is larger, leading to an overall better eciency compared to a pond of equal area and greater depth, volume and
1444
Marcos von Sperling
Fig. 6. Comparison between the observed and estimated euent coliform concentrations using the proposed approaches for the CSTR and dispersed ¯ow models.
detention time. In other words, for a given eciency of coliform removal, according to the present data, the best land-saving alternative is associated with shallow ponds. These results contrast with those found by Van Haandel and Lettinga (1994) and Silva et al. (1996), both based on the pilot-scale ponds in the Northeast of Brazil, described in Table 3. The former study concluded that the pond depth had a negligible in¯uence on the required area (m2/inhab), while the latter one reported that land savings of 30% could be obtained by using ponds of 2.2 m depth, as compared with ponds with 1.0 m (series of ponds, each with 5.0 to 5.8 days of detention time).
CONCLUSIONS
The paper emphasises the importance of the adoption of the correct hydraulic model and the associated die-o coecient (Kb) for the estimation of the coliform removal eciency of facultative and maturation ponds. Based on the analysis of data from 33 ponds located in dierent parts of Brazil (tropical to subtropical regions), covering a wide range of physical con®gurations, temperature and detention times, the coliform die-o coecient was calculated for the CSTR and the dispersed-¯ow models. For the utilisation of the dispersed-¯ow model, the dis-
Coliform die-o in waste stabilization ponds
1445
Fig. 7. Comparison between the estimated euent coliform concentrations from the two proposed approaches for the CSTR and dispersed ¯ow models
Table 7. Volume and surface area requirements for a single pond in order to achieve 1, 2 and 3 log removals, using the proposed approach for dispersed ¯ow (208C) Volume requirements (m3 per m3/d) L/B ratio
H (m) 1
2
4
Surface area requirements (m2 per m3/d) L/B ratio
8
16
32
1
2
4
8
16
32
Removal eciency: 90% (1 log removal) 0.4 3.7 3.0 2.5 0.6 6.3 5.1 4.2 0.8 9.2 7.4 6.2 1.0 12.4 9.9 8.3 1.2 15.7 12.6 10.5 1.4 19.2 15.4 12.8 1.6 22.9 18.3 15.3 1.8 26.7 21.4 17.8 2.0 30.6 24.5 20.4 2.2 34.7 27.8 23.2
2.2 3.7 5.4 7.2 9.1 11.1 13.3 15.5 17.8 20.1
2.0 3.3 4.9 6.5 8.3 10.1 12.0 14.1 16.1 18.3
1.9 3.2 4.6 6.2 7.8 9.6 11.4 13.3 15.2 17.3
9.3 10.6 11.5 12.4 13.1 13.7 14.3 14.8 15.3 15.8
7.5 8.5 9.2 9.9 10.5 11.0 11.4 11.9 12.3 12.6
6.2 7.1 7.7 8.3 8.7 9.2 9.5 9.9 10.2 10.5
5.4 6.1 6.7 7.2 7.6 8.0 8.3 8.6 8.9 9.1
4.9 5.6 6.1 6.5 6.9 7.2 7.5 7.8 8.1 8.3
4.6 5.3 5.7 6.2 6.5 6.8 7.1 7.4 7.6 7.8
Removal eciency: 99% (2 log removal) 0.4 23.4 16.2 12.0 0.6 39.6 27.3 20.4 0.8 58.0 40.0 29.8 1.0 77.5 53.5 39.8 1.2 98.0 67.6 50.4 1.4 120.0 82.8 61.7 1.6 143.0 98.7 73.5 1.8 167.0 115.3 85.9 2.0 192.0 132.5 98.7 2.2 217.0 149.8 111.6
9.5 16.1 23.5 31.5 39.8 48.7 58.1 67.8 77.9 88.1
8.1 13.6 20.0 26.7 33.7 41.3 49.2 57.5 66.1 74.7
7.2 12.2 17.9 23.9 30.3 37.1 44.2 51.6 59.3 67.0
58.5 66.0 72.5 77.5 81.7 85.7 89.4 92.8 96.0 98.6
40.4 45.6 50.0 53.5 56.4 59.2 61.7 64.0 66.3 68.1
30.1 33.9 37.3 39.8 42.0 44.1 45.9 47.7 49.4 50.7
23.8 26.8 29.4 31.5 33.2 34.8 36.3 37.7 39.0 40.0
20.1 22.7 24.9 26.7 28.1 29.5 30.7 31.9 33.0 33.9
18.1 20.4 22.4 23.9 25.2 26.5 27.6 28.7 29.7 30.5
Removal eciency: 99.9% (3 log removal) 0.4 75.9 47.9 33.2 0.6 128.5 81.1 56.2 0.8 187.5 118.3 82.0 1.0 251.0 158.4 109.8 1.2 318.0 200.7 139.1 1.4 390.0 246.1 170.6 1.6 463.0 292.2 202.5 1.8 540.0 340.8 236.2 2.0 620.0 391.3 271.2 2.2 703.0 443.7 307.5
24.6 41.6 60.6 81.2 102.9 126.1 149.8 174.7 200.5 227.4
19.7 33.3 48.5 65.0 82.3 101.0 119.9 139.8 160.5 182.0
17.0 28.7 41.9 56.1 71.0 87.1 103.4 120.6 138.5 157.0
189.8 214.2 234.4 251.0 265.0 278.6 289.4 300.0 310.0 319.5
119.8 135.2 147.9 158.4 167.2 175.8 182.6 189.3 195.6 201.7
83.0 93.7 102.5 109.8 115.9 121.9 126.6 131.2 135.6 139.8
61.4 69.3 75.8 81.2 85.7 90.1 93.6 97.0 100.3 103.4
49.1 55.4 60.7 65.0 68.6 72.1 74.9 77.7 80.3 82.7
42.4 47.8 52.3 56.1 59.2 62.2 64.6 67.0 69.2 71.4
1446
Marcos von Sperling
Fig. 8. Pond volume and surface area required for achieving 1 log and 2 log coliform removal, as a function of the depth H and the L/B ratio (dispersed ¯ow) (208C).
persion number was estimated using Agunwamba et al. (1992) and Yanez (1993) formulae. Both were found to give similar results, and the Yanez formulae was used in other parts of the paper, due to its greater simplicity. The Kb values found with the CSTR model varied over a very wide range (0.04 to 31.09 dÿ1), illustrating the inadequacy of the CSTR model, especially for ponds with length-to-breadth (L/B) ratios signi®cantly greater than one. The Kb coecients obtained with the dispersed-¯ow models had a much narrower distribution (0.02 to 2.44 dÿ1), suggesting the better adequacy of this model in the representation of the coliform decay. In the dispersed-¯ow model, the pond depth (H) and the hydraulic detention time (t) were found to have a major in¯uence on the value of the coecient Kb. A regression analysis was undertaken, leading to the following relationship: Kb 0:917H ÿ0:877 tÿ0:329
n 66; R2 0:847
Recognising that the CSTR model is more widely applied than the dispersed-¯ow model by designers, an equation was developed for the conversion of the Kb for dispersed ¯ow into the Kb for the CSTR model, based on the L/B ratio and the detention time. The equation was derived via regression
analysis of theoretical data concerning the relationship between the coecients under both hydraulic models: Kb CSTR 1:753 Kb dispersed 0:0011 3:189 K 4:189 L=B 1:509 b dispersed t
n 44; R2 0:997 The utilisation of both Kb models for the estimation of the 66 values of the log euent concentration of faecal coliforms in the 33 ponds led to: (a) very similar results and (b) very good prediction capability (R2=0.951 for the CSTR model and R2=0.959 for the dispersed-¯ow model). Based on the proposed model for dispersed ¯ow, the required pond volumes and surface areas for dierent depths and L/B ratios were calculated. The results show that a shallow pond, due to its greater Kb coecient, requires less surface area, for a given eciency of coliform removal, compared to a deep pond. Although the results are based only on ponds situated in Brazil, the large number of units included in the study encompass a wide range of climatic, physical and operating conditions, thereby
Coliform die-o in waste stabilization ponds
supporting the conclusion that the models presented in the study are based on a larger and more representative data set than most other studies available in the literature world-wide. Naturally further studies are always required in order to con®rm or adjust the derived models. It is important to point out that any modelling study of coliform decay should explicitly present basic information, which are not always included in most of the papers. The minimum information required are: ¯ow regime adopted, physical data of the pond (length, width, depth), liquid temperature and ¯owrate. AcknowledgementsÐThe author wishes to thank CEMIG (Energy Company of Minas Gerais), COPASA-MG (Water and Sanitation Company of Minas Gerais) and FNS (National Health Foundation, ParanaÂ) for the kind permission to use their data on this research, and Mr. Eduardo Cohim for his useful suggestion. REFERENCES
Aguiar M. M., Mendonc° a A. S. F. (1996) Wastewater stabilization ponds fecal coliform removal eciencies. In 3rd Italo-Brazilian Symposium on Sanitary and Environmental Engineering (Proceedings), Italy, June 1996. Agunwamba J. C., Egbuniwe N. and Ademiluyi J. O. (1992) Prediction of the dispersion number in waste stabilization ponds. Water Research 21(1), 85±89. Andrade Neto, C. O. (1997) Sistemas simples para tratamento de esgotos sanitaÂrios. ExperieÃncia brasileira. ABES, Brazilian Association on Sanitary and Environmental Engineering, 300 pp. (in Portuguese). Auer M. T. and Niehaus S. L. (1993) Modeling fecal coliform bacteria. I. Field and laboratoty determination of loss kinetics. Water Res. 27(4), 693±701. Catunda P. F. C., Van Haandel A. C, Lettinga G. (1994) Post treatment of anaerobically treated sewage in waste stabilization ponds. In Anaerobic digestion, 7th Symposium, Capetown, pp. 405±415. Ceballos B. S. O., Konig A., Lomans B., Athayde A. B. and Pearson H. W. (1995) Evaluation of a tropical single-cell waste stabilization pond system for irrigation. Water Sci. Technol. 31(12), 267±273. CEMIG (1997) Dados operacionais da lagoa de estabilizac° aÄo de Miranda, Minas Gerais (planilhas de dados). Companhia EnergeÂtica de Minas Gerais (in Portuguese). CETESB (1981) Condic° oÄes de funcionamento de sete lagoas de estabilizac° aÄo no Estado de SaÄo Paulo. Revista DAE, XLI (124), pp. 55±74 (in Portuguese). COPASA-MG (1995) Dados operacionais das lagoas de estabilizac° aÄo de Con®ns e da Cidade Verde Ð Minas Gerais (planilhas de dados). Companhia de Saneamento de Minas Gerais (in Portuguese). DELM (Tasmanian Department of Environment and Land Management)/DPIF (Department of Primary Industries and Fisheries) (1996) Design and management of Tasmanian sewage lagoon systems, 146 pp. Dixo N. G. H., Gambrill M. P., Catunda P. F. C. and Van Haandel A. C. (1995) Removal of pathogenic organisms from the euent of an up¯ow anaerobic digester using waste stabilization ponds. Water Sci. Technol. 31(12), 275±284. EPA, (1983) Design manual. Municipal wastewater stabilization ponds. United States Environmental Protection Agency. 327 pp.
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FNS (1996) Dados operacionais da lagoa de estabilizac° aÄo de IbiporaÄ, Parana (planilhas de dados). National Health Foundation (in Portuguese). Gamini M. (1981) Kinetics of bacterial die-o in waste stabilization ponds. Ph.D. thesis, Asian Institute of Technology. IMTA (Instituto Mexicano de Tecnologia del Agua) (1992) Manual de agua potable y saneamiento (lagunas de estabilizacioÂn). CoordinacioÂn de tecnologia urbano industrial, Mexico (in Spanish). Johansson P., Pernrup M. and Rangeby M. (1996) Lowcost upgrading of an oversized waste water stabilisation pond system in Mindelo, Cape Verde. Water Sci. Technol. 33(7), 99±106. Mancini J. L. (1978) Numerical estimates of coliform mortality rates under various conditions. J. Water Pollut. Contr. Fed. 50(11), 2477±2484. Marais, G.v.R. (1974) Faecal bacteria kinetics in stabilisation ponds. J. Env. Eng. Div., ASCE, 100(EE1), 119±139. Mayo A. W. (1989) Eect of pond depth on bacterial mortality rate. J. Environ. Eng. ASCE 115(5), 964±977. Mayo A. W. (1995) Modelling coliform mortality in waste stabilization ponds. J. Environ. Eng. ASCE 121(2), 140± 152. Mills S. W., Alabaster G. P., Mara D. D., Pearson H. W. and Thitai W. N. (1992) Eciency of faecal bacterial removal in waste stabilisation ponds in Kenya. Water Sci. Technol. 26(7-8), 1739±1748. Oragui J. I., Cawley L., Arridge H. M., Mara D. D., Pearson, H. W., Silva, S. A. (1995) Pathogen removal kinetics in a tropical experimental waste stabilisation pond in relation to organic loading, retention time and pond geometry. In 3rd IAWQ International Specialist Conference. Waste stabilization ponds: technology and applications. JoaÄo Pessoa, PA, 27±31 March 1995. Pearson H. W., Mara D. D. and Arridge H. M. (1995) The in¯uence of pond geometry and con®guration on facultative and maturation waste stabilisation pond performance and eciency. Water Sci. Technol. 31(12), 129±139. Pearson H. W., Mara D. D., Cawley L. R., Arridge H. M. and Silva S. A. (1996) The performance of an innovative tropical experimental waste stabilisation pond system operating at high organic loadings. Water Sci. Technol. 33(7), 63±73. Qin D., Bliss P. J., Barnes D. and Fitzgerald P. A. (1991) Bacterial (total coliform) die-o in maturation ponds. Water Sci. Technol. 23(7-9), 1525±1534. SaÂenz, F. C. (1992) PrediccioÂn de la calidad del e¯uente en lagunas de estabilizacioÂn. POS/OMS, Programa HPE, Washington, DC (in Spanish). Saqqar M. M. and Pescod M. B. (1992) Modelling coliform reduction in wastewater stabilization ponds. Water Sci. Technol. 26(7-8), 1667±1677. Sarikaya H. Z., Saatci A. M. and Abdulfattah A. F. (1987) Eect of pond depth on bacterial die-o. J. Environ. Eng. ASCE 113(6), 1350±1362. Sherry G. P. and Parker C. D. (1979) Development of an improved quantitative relationship between bacterial die-o, design and operational factors for anaerobicaerobic and maturation type lagoon systems. Progr. Water Technol. 11(4/5), 427. Silva S. A., Oliveira R., Mara D. D. (1996) Performance of waste stabilization ponds in Northeast Brazil. Research Monographs in Tropical Public Health Engineering. Research Monograph No. 9, University of Leeds, 139 pp. Thomann R. V., Mueller J. A. (1987) Principles of surface water quality modeling and control. Harper International Edition, 644 pp.
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Van Haandel A. C., Lettinga G. (1994) Tratamento anaeroÂbio de esgotos. Um manual para paõÂses de clima quente p. VII-4-17 (in Portuguese). Vidal W. L. (1983) Aperfeic° oamentos hidraÂulicos no projeto de lagoas de estabilizac° aÄo, visando reduc° aÄo da aÂrea de tratamento: uma aplicac° aÄo praÂtica. In Congresso Brasileiro de Engenharia SanitaÂria e Ambiental, 12, CamboriuÂ, 20±25 novembro 1983. ABES (in Portuguese). Von Sperling M. (1996a) PrincõÂpios do tratamento bioloÂgico de aÂguas residuaÂrias. Vol. 3, Lagoas de estabilizac° aÄo. Departamento de Engenharia SanitaÂria e Ambiental Ð UFMG, 134 pp. (in Portuguese).
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Wat. Res. Vol. 33, No. 6, pp. 1435±1448, 1999 # 1999 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0043-1354/99/$ - see front matter
PERFORMANCE EVALUATION AND MATHEMATICAL MODELLING OF COLIFORM DIE-OFF IN TROPICAL AND SUBTROPICAL WASTE STABILIZATION PONDS M MARCOS VON SPERLING**
Department of Sanitary and Environmental Engineering, Federal University of Minas Gerais, Av. Contorno 842, 7o andar, 30110-060 Belo Horizonte, Brazil (First received November 1997; accepted in revised form July 1998) AbstractÐThe paper investigates the coliform removal in 33 facultative and maturation ponds in Brazil. The ponds were located in dierent parts of the country, with climates ranging from tropical to subtropical and latitude from 7 to 248S. The ponds had dierent physical con®gurations, temperature and detention times. The total number of data used in the study, mostly comprising long-term averages, was 66. Two ¯ow regimes were investigated: CSTR and dispersed ¯ow. In the dispersed-¯ow model, the dispersion number was estimated using the formulae by Agunwamba et al. and Yanez, and both were found to give similar results. The coliform die-o coecient Kb was correlated with the pond depth and hydraulic detention time in the dispersed-¯ow model (R2=0.847). A regression equation, using theoretically generated data, was proposed, correlating Kb for the CSTR model with Kb for dispersed-¯ow model, using the length-to-breadth ratio and detention time of the pond (R2=0.997). Use of this equation yields virtually the same removal eciency values as those obtained directly by the dispersed-¯ow model. Utilisation of the Kb values calculated by the proposed regression models gave a very good prediction of the log euent coliform concentration of the 33 ponds (R2=0.951 for the CSTR model and R2=0.959 for the dispersed-¯ow model). Applying the proposed model for dispersed ¯ow, it was concluded that, for a given removal eciency, a shallow pond, due to its larger Kb, requires less surface area, compared to a deep pond, even though the latter has a higher detention time. # 1999 Elsevier Science Ltd. All rights reserved Key wordsÐfacultative ponds, maturation ponds, completely-mixed reactor, dispersed ¯ow, faecal coliforms, coliform die-o coecient
NOMENCLATURE
n y
B pond breadth (m) BOD biochemical oxygen demand COD chemical oxygen demand CSTR completely stirred tank reactor d dispersion number D coecient of longitudinal dispersion (m2/d) DO dissolved oxygen (mg/l) FC faecal coliform H pond height (m) Kb coliform die-o coecient (dÿ1) L pond length (m) n number of ponds in series N euent coliform concentration (org/100 ml) No in¯uent coliform concentration (org/100 ml) Q ¯ow (m3/d) R2 coecient of determination t hydraulic detention time (d) T liquid temperature (8C) U average ¯ow velocity in the reactor (m/d)
kinematic viscosity of the water (m2/d) temperature coecient
INTRODUCTION
*Author to whom all correspondence should be addressed. Tel.: +55-31-238-1882; Fax: +55-31-238-1879; E-mail: [email protected].
One of the main objectives of the use of waste stabilization ponds, especially in tropical countries, is pathogen removal. The mathematical modelling of the bacterial die-o rate in the pond is important, in order to allow the estimation of the euent coliform concentration. This, in turn, determines compliance with the pertinent legislation and establishes the allowable uses of the euent and receiving water body, such as irrigation, bathing, aquaculture, water supply and others. Coliform decay is usually modelled through ®rstorder kinetics. The euent coliform concentration is a function of the pond con®guration, represented by one of the following hydraulic models: plug¯ow, ponds-in-series, dispersed ¯ow and completely mixed (CSTR). Depending on the hydraulic regime assumed for the pond, dierent formulae are available for the estimation of the euent coliform con-
1435
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Marcos von Sperling
Table 1. Formulae for the estimation of the euent coliform concentration of a facultative or maturation pond. For symbols see the nomenclature. d = D/UL = Dt/L2 (dimensionless). L is the length of the longitudinal distance in the reactor (m).
centration of a facultative or maturation pond. These are summarized in Table 1. The CSTR model has been more frequently used to represent the hydraulic regime of facultative and maturation ponds. However, the assumption of an ideal CSTR pattern can be only ful®lled in reactors in which the length-to-breadth (L/B) ratio is not signi®cantly greater than one. In facultative ponds, this ratio is usually within 2 to 4 (EPA, 1983). In maturation ponds, due to the need for extremely high coliform removal eciencies, the designer normally has two choices: to either adopt a series of ponds or only one pond with a large L/B ratio, obtained through the introduction of baes. Under these conditions, the assumption of an ideal CSTR misrepresents reality, and the dispersed-¯ow model should be used to model coliform decay in the pond. The objective of this paper is to investigate and propose models for CSTR and dispersed-¯ow
regimes for the representation of the coliform dieo rate in facultative and maturation ponds. Data from 33 stabilization ponds located in dierent parts of Brazil are used, allowing the determination of the coecient of coliform die-o (Kb). The paper presents two equations for the estimation of Kb, one to be used in the dispersed-¯ow model and the other to be used in the CSTR model. REPORTED VALUES OF THE COLIFORM DIE-OFF COEFFICIENT Kb
In the modelling of the coliform decay, the use of an adequate value of the Kb coecient assumes a major importance. Even though, as previously mentioned, the dispersed-¯ow model is a closer representation of reality, researchers have frequently estimated the Kb coecient using the CSTR model, independent of the geometrical con®guration of the pond. Similarly, designers have resorted to the CSTR model, due to its greater conceptual simpli-
Table 2. Some Kb (208C) values available in the literature ÿ1
Kb values (d ) 2.6 0.8 0.2±10 0.71 0.62 0.84 0.33±0.90 1.3±12.0 1.2±4.82 0.4±12.2 0.45±5.89 0.5±1.5 0.39±43.6 2.0 0.73 1.1 1.2 0.74±0.84 0.26±2.42
Flow regime considered
Country/region
Reference
CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR CSTR plug ¯ow plug ¯ow dispersed ¯ow dispersed ¯ow dispersed ¯ow
Central and South Africa
Marais (1974) Mancini (1978) Sherry and Parker (1979) Mills et al. (1992) SaÂenz (1992) IMTA (1992) Saqqar and Pescod (1992) Van Haandel and Lettinga (1994) Dixo et al. (1995) Pearson et al. (1995) Mayo (1995) DELM/DPIF (1996) Pearson et al. (1996) Johansson et al. (1996) Auer and Niehaus (1993) Yanez (1993) Arceivala (1981) Yanez (1993) Von Sperling (1996b)
Australia Kenya Mexico Jordan Brazil Brazil Brazil Tanzania Tasmania Brazil Cape Verde Turkey Peru Brazil
Coliform die-o in waste stabilization ponds
1437
Table 3. Main data from the 33 ponds investigated Pond
Position in series
L (m)
B (m)
H (m)
Q (m3/d)
t (d)
L/B
Latitude (8S)
Temperature (8C)
Eciency
Kb CSTR
d-Yanez
d-Agun
Pilot scale (13 ponds in series and F21 2 12.9 F22 2 12.9 F23 2 12.9 F24 2 12.9 F25 2 4.9 M16 4 10.4 M17 4 10.4 M18 4 10.4 M19 4 10.4 M20 4 10.4 M21 5 8.5 M22 5 8.5 M24 5 66.8
parallel; 1st experiment) Pearson et al. (1995) 2.0 1.00 8.0 3.2 6.5 7.1 2.0 1.33 8.0 4.3 6.5 7.1 2.0 1.67 8.0 5.4 6.5 7.1 2.0 2.00 8.0 6.5 6.5 7.1 4.9 2.00 8.0 6.0 1.0 7.1 3.8 0.90 5.0 7.0 2.8 7.1 3.8 0.64 5.0 5.0 2.8 7.1 3.8 0.39 5.0 3.0 2.8 7.1 3.8 0.39 5.0 3.0 2.8 7.1 1.3 0.39 5.0 1.1 8.0 7.1 3.7 0.60 3.8 5.0 2.3 7.1 3.7 0.60 3.8 5.0 2.3 7.1 0.5 0.60 3.8 5.0 142.0 7.1
25 25 25 25 25 25 25 25 25 25 25 25 25
0.8571 0.8781 0.8791 0.8977 0.8744 0.9770 0.9711 0.9683 0.9737 0.9327 0.9473 0.9369 0.9756
1.33 1.20 0.96 0.97 0.83 4.31 4.80 7.16 8.66 9.38 2.56 2.12 5.68
0.52 0.43 0.34 0.33 0.50 0.76 0.96 1.52 1.64 2.35 0.78 0.71 0.54
0.51 0.41 0.32 0.29 0.41 0.61 0.77 1.20 1.28 2.25 0.61 0.57 0.53
Pilot scale (13 ponds in series and F21 2 12.9 F22 2 12.9 F23 2 12.9 F24 2 12.9 F25 2 4.9 M16 4 10.4 M17 4 10.4 M18 4 10.4 M19 4 10.4 M20 4 10.4 M21 5 8.5 M22 5 8.5 M24 5 66.8
parallel; 2nd experiment) Oragui et al. (1995) 2.0 1.00 16.0 1.6 6.5 7.1 2.0 1.33 16.0 2.1 6.5 7.1 2.0 1.67 16.0 2.7 6.5 7.1 2.0 2.00 16.0 3.2 6.5 7.1 4.9 2.00 16.0 3.0 1.0 7.1 3.8 0.90 10.0 3.5 2.8 7.1 3.8 0.64 10.0 2.5 2.8 7.1 3.8 0.39 10.0 1.5 2.8 7.1 3.8 0.39 10.0 1.5 2.8 7.1 1.3 0.39 10.0 0.5 8.0 7.1 3.7 0.60 7.5 2.5 2.3 7.1 3.7 0.60 7.5 2.5 2.3 7.1 0.5 0.60 7.5 2.5 142.0 7.1
25 25 25 25 25 25 25 25 25 25 25 25 25
0.5338 0.5785 0.6628 0.6436 0.6541 0.9182 0.9434 0.8889 0.8426 0.7878 0.9243 0.9669 0.9909
0.51 0.46 0.52 0.40 0.45 2.28 4.76 3.75 2.51 5.02 3.48 8.33 31.09
0.36 0.32 0.33 0.26 0.36 0.83 1.43 1.58 1.25 2.42 1.28 1.95 1.38
0.36 0.32 0.31 0.24 0.36 0.75 1.27 1.43 1.14 2.44 1.11 1.64 1.35
26
0.9962
2.88
0.19
0.17
22 22 28.6 28.6 28.6 28.6 28.6 19.8
0.7921 0.9589 0.9853 0.9705 0.9955 0.9000 0.9972 0.9709
0.04 1.42 0.67 1.83 1.81 0.41 17.33 2.75
0.03 0.36 0.13 0.37 0.16 0.17 0.74 0.57
0.02 0.32 0.09 0.35 0.11 0.16 0.66 0.51
24.4 24.5 25.0 25.3 23.9 24.9 24.4 25.5
0.9985 0.9581 0.9954 0.9807 0.9988 0.9392 0.9976 0.9839
5.53 2.40 1.55 4.50 5.57 1.21 2.95 4.98
0.20 0.56 0.12 0.65 0.17 0.35 0.15 0.64
0.15 0.57 0.09 0.65 0.12 0.34 0.11 0.63
Ceballos et al. (1995) F1 1
118.0
2.20
950
60.1
1.9
7.1
2 ponds; 5 experiments Vidal (1983) F 1 84.0 68.0 M 2 64.0 24.0 F 1 84.0 68.0 M 2 64.0 24.0 F 1 84.0 68.0 M 2 64.0 24.0 M 2 64.0 24.0 M 2 64.0 24.0
1.50 1.00 1.50 1.00 1.50 1.00 1.00 1.00
107 107 153 153 124 124 133 125
80.1 14.4 56.0 10.0 69.1 12.4 11.5 12.3
1.2 2.7 1.2 2.7 1.2 2.7 2.7 2.7
20.5 20.5 20.5 20.5 20.5 20.5 20.5 20.5
Years 1992, 1993, 1994, Con®ns-F 1 Con®ns-M 2 Con®ns-F 1 Con®ns-M 2 Con®ns-F 1 Con®ns-M 2 Con®ns-F 1 Con®ns-M 2
220.0
1995, respectively (average, 2 ponds) COPASA-MG (1995) 190.0 115.0 1.90 475 87.5 1.7 20.0 119.0 35.0 0.80 475 7.0 3.4 20.0 190.0 115.0 1.90 422 98.4 1.7 20.0 119.0 35.0 0.80 422 7.9 3.4 20.0 190.0 115.0 1.90 363 114.4 1.7 20.0 119.0 35.0 0.80 363 9.2 3.4 20.0 190.0 115.0 1.90 394 105.3 1.7 20.0 119.0 35.0 0.80 394 8.5 3.4 20.0
Years 1992 and 1993, respectively (average) COPASA-MG (1995) Cid. Verde 1 190.0 86.0 2.30 363 103.6 2.2 Cid. Verde 1 190.0 86.0 2.30 371 101.4 2.2
20.0 20.0
25.0 26.0
0.9923 0.9948
0.89 1.25
0.08 0.09
0.07 0.08
Years 1996/1997 CEMIG (1997) Miranda 1 86.0 44.5
1.20
256
17.9
1.9
19.0
25.0
0.9395
0.62
0.21
0.20
Ref. Aguiar and Mendonc° a (1996) M. Serra 1 122.0 47.0 Eldorado 2 200.0 95.0 Maringa 2 96.0 41.0
1.10 1.25 1.70
233 544 130
27.1 43.7 51.5
2.6 2.1 2.3
20.5 20.5 20.5
26.9 29.4 25.6
0.9940 0.9976 0.9957
3.81 4.98 3.07
0.29 0.22 0.19
0.24 0.19 0.15
Years: 1986/1987 (average) Andrade Neto (1997) 1 135.0 52.0 1.84 473 27.3 2.6 2 105.0 39.0 1.89 473 16.4 2.7 3 105.0 39.0 1.78 473 15.4 2.7
15.0 15.0 15.0
25.7 25.7 25.7
0.9965 0.9411 0.9019
7.09 0.66 0.41
0.36 0.20 0.16
0.35 0.21 0.17
21.2 21.2 20.3
25.0 19.3 23.3
0.5625 0.8000 0.9091
0.07 0.29 0.97
Ponds in series. CuiabaÂ-F CuiabaÂ-M CuiabaÂ-M
CETESB (1981) PradoÂpolis 2 PradoÂpolis 2 Itapira 2
157.0 157.0 238.0
70.0 70.0 210.0
1.00 1.00 1.00
795 760 6048
13.8 14.5 8.3
2.2 2.2 1.1
0.05 0.05 0.17 0.17 0.49 0.53 Ðcontinued overleaf
1438
Marcos von Sperling Table 3 (continued )
Pond
Position in series
Itapira Pindamon. Guararapes Guararapes Nhandeara ValparaõÂ so MairiporaÄ
2 2 1 1 1 1 2
Years 1993, 1994, 1995, IbiporaÄ 2 IbiporaÄ 2 IbiporaÄ 2 IbiporaÄ 2
L (m)
238.0 240.0 162.0 162.0 144.0 116.0 124.0
B (m)
210.0 180.0 80.0 80.0 50.0 74.0 94.0
H (m)
1.00 0.90 1.60 1.60 0.90 0.90 1.00
Q (m3/d)
5210 8623 994 1097 648 302 743
t (d)
9.6 4.5 20.9 18.9 10.0 25.6 15.7
1996, respectively (averages) FNS (1996) 213.0 74.0 1.00 1216 22.3 213.0 74.0 1.00 2090 20.7 213.0 74.0 1.00 2539 23.0 213.0 74.0 1.00 2363 21.5
L/B
Latitude (8S)
Temperature (8C)
Eciency
Kb CSTR
d-Yanez
d-Agun
1.1 1.3 2.0 2.0 2.9 1.6 1.3
20.3 22.6 21.5 21.5 20.4 21.1 23.2
18.0 24.2 26.9 22.4 26.9 22.4 16.8
0.8500 0.9259 0.9400 0.7941 0.9000 0.9818 0.8250
0.68 2.09 0.47 0.17 0.56 1.79 0.37
0.42 0.90 0.16 0.11 0.22 0.35 0.24
0.44 1.05 0.16 0.11 0.23 0.28 0.22
2.9 2.9 2.9 2.9
23.5 23.5 23.5 23.5
22.3 20.7 23.0 21.5
0.8868 0.9401 0.7761 0.6259
0.30 0.73 0.12 0.07
0.13 0.22 0.07 0.05
0.12 0.21 0.07 0.05
L = length (m); B = breadth (m); H = height (m); Q = ¯ow (m3/d); t = detention time (d); Eciency = faecal coliform removal eciency. CSTR = Kb (208C) for CSTR reactor (dÿ1). d-Yanez = Kb (208C) for dispersed ¯ow, with d according to Yanez, 1993 (dÿ1). d-Agun = Kb (208C) for dispersed ¯ow, with d according to Agunwamba et al., 1992 (dÿ1).
city. For a given removal eciency, the estimation of Kb based on the hydraulic detention time and on the in¯uent and euent coliform concentrations, using the CSTR model leads to an overestimation of the Kb value, compared to that obtained if the dispersed-¯ow model had been used. This is due to the fact that the CSTR model is implicitly associated with lower removal eciencies (a CSTR reactor is the least ecient for the removal of ®rstorder decay constituents), which forces the increase of Kb in order to compensate for the underestimation of its removal eciency. Table 2 lists some Kb values available in the literature. No further information about the ponds is included in the tables, since they have not been presented by many of the publications. The wide scattering of the Kb values re¯ects the speci®c in¯uencing factors in each case, such as DO, pH, solar radiation, BOD loading, besides the physical con®guration. Additionally, it re¯ects the inadequacy of the idealised hydraulic models (CSTR or plug-¯ow) for the prediction of the behaviour of nonideal reactors. This scattering was one of the main motivations for the present study. POND SYSTEMS INVESTIGATED IN THE STUDY
The study investigated 33 facultative and maturation ponds in Brazil. The ponds analysed were distributed from the northeast (latitude 78S) to the south (latitude 23.58S) of Brazil, encompassing a climate range from tropical to subtropical. The ponds had dierent volumes and physical con®gurations, with 13 being pilot-scale units and the other 20 being full-scale ponds. In this study, no distinction was made between facultative and maturation ponds, apart from their position in the series of ponds (e.g. primary, secondary, tertiary, etc.) and their depth. The ponds represented a wide spectrum of operating conditions, with the length-to-breadth ratio (L/B) varying from 1 to 142, while the deten-
tion time varied from 0.5 to 114 days. In most cases, the removal eciency of faecal coliforms was based on medium or long-term geometric means of the coliform concentrations. In many systems, more than one set of data was available, representing either dierent experiments which have been undertaken or yearly averages from a series of years. The total number of data analysed in this study is 66. The results were obtained from operating records and published papers and not collected directly by the author. It was not easy to gather representative results, since most of the papers available in the literature had no information on the L/B ratio of the pond. Also many papers presented the values of ¯owrates based on the design ®gures, and not the actually measured ones. Table 3 presents the relevant data from the ponds investigated, while Fig. 1 presents the frequency distribution histograms of the main descriptive parameters, showing the wide range of operating conditions covered by the study. DETERMINATION OF THE COLIFORM DIE-OFF COEFFICIENT Kb
Two ¯ow regimes were considered in the study: CSTR and dispersed ¯ow. For the CSTR model, the Kb values were calculated through a simple rearrangement of Eq. (2), leading to: Kb
No =N ÿ 1 t
6
For the dispersed ¯ow model, the dispersion number d was calculated using two empirical formulae available in the literature, the former with a more complex structure (Agunwamba et al., 1992) and the latter with a simple structure (Yanez, 1993), in which d depends only on the L/B ratio: . Agunwamba et al. (1992), original formulae simpli®ed by Von Sperling (1996a)
Coliform die-o in waste stabilization ponds
1439
Fig. 1. Frequency distribution histograms of the main descriptive parameters of the ponds investigated.
3 B 2H tu ÿ0:410 H d 0:102 4LBH L ÿ 0:9811:385H=B H B
7
. Yanez (1993) d
L=B ÿ0:261 0:254 L=B 1:014 L=B 2
8
where L is the pond length (m); B the pond breadth (m); H the pond depth (m); t the hydraulic detention time (d); n the kinematic viscosity of the water (m2/d) (regression analysis done in the paper: n = 0.325Tÿ0.450, for T = 10 to 308C, with n = 6, R2=0.986). Although in the present study the author preserved the original formulation of Yanez (equation 8) for the dispersion number d, it is interesting to note that a formula as simple as d = 1/(L/B) gives very similar results to those obtained through the utilisation of Yanez's equation. Given the diculty in making Kb explicit in Eqs. (4) and (5) for dispersed ¯ow, Kb was calculated by trial-and-error iterations, using both equations, based on the previously calculated t and d values (the latter estimated by equations 7 and 8). The iteration stopped when the Kb value gave an estimated removal eciency equal to the observed one.
For both the CSTR and dispersed ¯ow models, the Kb values were converted to the standard temperature of 208C using equation 9 and the temperature coecient y = 1.07. Although Marais (1974) proposed the value of 1.19, other more recent texts (Mancini, 1978; Thomann and Mueller, 1987; WHO, 1987; Yanez, 1993; Johansson et al., 1996) use the value of 1.07. In this study, no elements were available in order to allow the speci®c determination of y. Kb 208C Kb T y 20ÿT
9
where Kb(208C)=Kb coecient at the temperature of 208C (1/d); Kb(T)=Kb coecient at a temperature T (1/d). The resulting Kb (208C) values for the two ¯ow regimes and for the two formulae for the dispersion number d are presented in Table 2. Figure 2 shows the frequency distribution histograms of the three versions of the Kb coecient. The Kb coecient for the CSTR regime has a wide distribution (minimum = 0.04 dÿ1 and maximum = 31.09 dÿ1) due to the inability of the CSTR model to represent well ponds with an L/B ratio substantially greater than 1. Under these conditions, the Kb value is overestimated, in order to accommodate the lower eciency inherent to the CSTR. The distribution of the Kb coecients for the dispersed-¯ow regime are much narrower (minimum = 0.02 dÿ1 and maximum = 2.44 dÿ1), indicating the better adequacy of the dispersed-¯ow model.
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Marcos von Sperling
Fig. 2. Frequency distribution histograms of the coecients Kb (208C) for the two ¯ow regimes (CSTR and dispersed ¯ow) and the two formulae for calculating the dispersion number d (equations 7 and 8). RELATIONSHIP BETWEEN THE COEFFICIENT Kb, THE POND DEPTH AND THE DETENTION TIME
It is well known that some of the main mechanisms of pathogen removal are associated with the pond depth (penetration of the solar radiation, photosynthesis/pH/DO). Catunda et al. (1994) and Von Sperling (1996b), studying the series of ponds in the Northeast of Brazil (pilot-scale ponds in Table 2), observed a relationship between Kb and the pond depth H: the lower the pond depth, the greater the coecient Kb. Other authors (Sarikaya et al., 1987; Mayo, 1989, 1995), in other countries, also observed an in¯uence of the pond depth on Kb. Some studies (Gamini, 1981; Sarikaya et al., 1987; Mayo, 1989, 1995; Qin et al., 1991; Saqqar and Pescod, 1992; Silva et al., 1996) have presented models for the prediction of Kb as a function of
variables such as pH, algal concentration, soluble BOD, applied COD load, solar radiation, light extinction coecient and also depth. In the present case, it was observed that the coef®cient Kb for dispersed ¯ow was related to the pond depth, as expected, and also with the hydraulic detention time. The lower the depth and the detention time, the greater the coecient Kb. Figure 3 exempli®es these relationships for the Kb coecient determined with d according to Yanez. For the CSTR model, no signi®cant relationship was observed between Kb and the variables H and t, as can also be seen on Fig. 3. The advantage, for design purposes, of expressing Kb as a function of the depth and the hydraulic detention time is that those are design variables, whereas most of the other variables suggested in the literature need to be assumed, and will depend on a number of factors, not easily predictable.
Fig. 3. Relationship between the coecient Kb (CSTR and dispersed-¯ow, with d according to Yanez) and (left) the pond depth and (right) the hydraulic detention time.
Coliform die-o in waste stabilization ponds
1441
Table 4. Regression equations for estimating Kb as a function of the pond depth H and the hydraulic detention time t, for the dierent hydraulic regimes Hydraulic regime CSTR Dispersed ¯ow (d according to Yanez, 1993) Dispersed ¯ow (d according to Agunwamba et al., 1992)
In the present study, a regression analysis was made between the 66 values of Kb calculated and presented in Table 3 with the corresponding pond depth H and hydraulic detention time t, for the CSTR and dispersed-¯ow patterns, the latter with the two formulae for the estimation of the dispersion number d. The best ®tting was obtained with the multiplicative function Kb=aHbtc. Table 4 presents the resulting equations. It can be observed that the CSTR model leads to a very poor ®tting (low value of the R2 coecient), and that the dispersed-¯ow model with d according to Yanez (1993) (R2=0.847) and Agunwamba et al. (1992) (R2=0.858) leads to the best estimation. A value of R2=0.847 means that 84.7% of the variance of Kb can be explained by the model. The results for the dispersed ¯ow model are considered very satisfactory, given the diculty in modelling Kb and the simplicity of the proposed models. Regression models with Kb as a function of the depth only were also tried and, for the dispersed¯ow model, gave R2 values of 0.757 ÿ1.532 (Kb=0.437H for d according to Yanez). Figure 4 plots together the best-®t lines for the dispersed-¯ow model, for d according to Yanez (1993) and Agunwamba et al. (1992), for hydraulic detention times of 5 and 30 days. It can be seen that the results obtained by the two models are not substantially dierent, especially for the more frequently used pond depths. As a result, due to its
Equation
R2
Equation number
Kb=2.928Hÿ0.987tÿ0.011 Kb=0.917Hÿ0.877tÿ0.329 Kb=0.958Hÿ0.752tÿ0.401
0.142 0.847 0.858
(10) (11) (12)
greater structural simplicity and ease of data input, the equation with d based on Yanez is adopted in the remainder of the paper. For the dispersed-¯ow model, with d according to Yanez, Fig. 5 shows the values of Kb according to Eq. (11), for dierent values of the hydraulic detention time. DETERMINATION OF THE Kb COEFFICIENT FOR CSTR BASED ON THE Kb FOR DISPERSED FLOW
It is recognised that the CSTR model is much more widely employed by designers than the dispersed-¯ow model. However, the previous sections showed the inadequacy of the CSTR model, which led to a very wide range of possible Kb values, making it dicult to select the one to be used in the pond design. Additionally, no signi®cant relationship seemed to exist between Kb and the variables H and t. The present section derives an equation for the estimation of Kb for the CSTR model, based on H, t and L/B. The derivation of the Kb values for CSTR was based on theoretical considerations. It was initially calculated, for dierent values of the dimensionless product Kbt (Kb for dispersed ¯ow) and dispersion number d, the corresponding Kb for CSTR, which yields the same eciency of coliform removal (®rst-order kinetics). Table 5 presents the results from a practical viewpoint. In the table, the
Fig. 4. Comparison between the estimated values of Kb as a function of H for the dispersed-¯ow model, with d according to Yanez and Agunwamba, and for hydraulic detention times of 5 d and 30 d (Eqs. (11) and (12)).
1442
Marcos von Sperling
Fig. 5. Estimated values of Kb, for dierent values of H and t, according to Eq. (11) (d from Yanez)
dispersion numbers d have been substituted by L/B, using Yanez equation (equation 8 rearranged). The values presented in the table are the ratio between the Kb for CSTR and Kb for dispersed ¯ow (Kb CSTR/Kb dispersed ¯ow). The interpretation of the table is as follows. A pond with L/B = 2, detention time t = 10 days and Kb (dispersed) = 0.5 dÿ1 has the dimensionless product Kbt = 10 0.5 = 5.0. For L/B = 2 and Kbt = 5, the table shows that the Kb for CSTR is equal to 2.65 times the Kb for dispersed ¯ow. In other words, the Kb for CSTR is 2.65 0.5 = 1.33 dÿ1. The estimation of the coliform removal eciency using the dispersed-¯ow model (Eqs. 4 and 5, with Kb for dispersed ¯ow) and the CSTR model (Eq. (2) with Kb for CSTR) leads to the same results. In order to extend the applicability of Table 5, a regression analysis was done, having as dependent variable the ratio Kb (CSTR)/Kb (dispersed) and as independent variables the Kbt product (dispersed ¯ow) and the L/B ratio. Using the 44 values presented in Table 5, the equation of best ®t obtained was:
Kb CSTR Kb dispersed 1:753 0:0011 Kb dispersed t3:189 1:509
L=B
13
n 44; R2 0:997 The ®t was excellent, as indicated by the high R2 value obtained. Equation 13 can be further developed, passing the denominator of the left-hand side to the right-hand side: Kb CSTR 1:753 Kb dispersed 0:0011 3:189 K 4:189 L=B 1:509 b dispersed t
14
Equation 14 allows the direct estimation of the Kb for CSTR based on the previous determination of the Kb for dispersed ¯ow and the previous knowledge of t and L/B. If Kb for dispersed ¯ow is estimated based on the regression equation with H and t (Kb=0.917Hÿ0.877tÿ0.329, Eq. (11) for d
Table 5. Ratio between the Kb coecients obtained for the CSTR model and the dispersed-¯ow model, for dierent values of the dispersion number d and of the product Kbt (dispersed ¯ow) Kbt (dispersed ¯ow)
0 1 2 3 4 5 6 7 8 9 10
Ratio Kb (CSTR)/Kb (dispersed ¯ow) d = 1.0, L/B 11
d = 0.5, L/B 12
d = 0.2, L/B1 5
d = 0.1, L/B1 10
1.00 1.14 1.29 1.46 1.64 1.83 2.04 2.27 2.53 2.79 3.08
1.00 1.23 1.52 1.83 2.21 2.65 3.15 3.73 4.39 5.14 6.01
1.00 1.40 1.95 2.68 3.66 4.95 6.62 8.81 11.60 15.16 19.66
1.00 1.52 2.32 3.55 5.39 8.18 12.28 18.21 26.81 39.11 56.50
Coliform die-o in waste stabilization ponds
according to Yanez), then equation 14 can be further developed into the following one: Kb CSTR 1:608 H ÿ0:877 tÿ0:329 7:656 10ÿ4 H ÿ3:674 t1:811 L=B 1:509 15 Equation 15 is then the ®nal expression, which can be used to estimate the coecient Kb for use with the CSTR model. Although the equation has been derived for L/B = 1 to 10 and Kbt = 1 to 10, its utilisation for values slightly outside these boundaries was shown to be satisfactory, as demonstrated in the next section. Other regression equations with greater limits for Kbt were tried but, although the overall ®tting was good, the accuracy for the smaller values of Kbt, which are very frequent for maturation ponds, was decreased. Table 6 presents the values of Kb (CSTR, 208C) obtained through equation 15, for some typical values of H, L/B and t.
VERIFICATION OF THE PROPOSED MODELS WITH THE OBSERVED DATA
In order to assess the performance of the two proposed models for Kb, the euent coliform concentration from each pond was estimated and compared with the observed one. The following equations were used:
Table 6. Values of Kb (CSTR, 208C) (dÿ1) for dierent values of H, L/B and t (according to equation 15) H (m)
L/B 1
2
3
4
6
8
10
t = 5 days 1.0 0.96 1.5 0.67 2.0 0.52 2.5 0.42
0.99 0.67 0.52 0.43
1.02 0.68 0.52 0.43
1.06 0.69 0.52 0.43
1.16 0.71 0.53 0.43
1.27 0.74 0.54 0.44
1.40 0.77 0.55 0.44
t = 10 days 1.0 0.80 1.5 0.54 2.0 0.41 2.5 0.34
0.89 0.56 0.42 0.34
1.01 0.59 0.43 0.35
1.16 0.62 0.44 0.35
1.49 0.70 0.47 0.36
1.90 0.79 0.50 0.38
2.35 0.89 0.54 0.39
t = 20 days 1.0 0.77 1.5 0.46 2.0 0.34 2.5 0.27
1.09 0.53 0.37 0.29
1.51 0.63 0.40 0.30
2.01 0.74 0.44 0.32
3.20 1.01 0.53 0.36
4.61 1.32 0.64 0.41
6.21 1.69 0.77 0.46
t = 30 days 1.0 0.89 1.5 0.45 2.0 0.31 2.5 0.25
1.56 0.60 0.37 0.27
2.43 0.80 0.43 0.30
3.46 1.03 0.52 0.34
5.94 1.59 0.71 0.42
8.88 2.25 0.94 0.52
12.22 3.01 1.20 0.64
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CSTR model: . Estimation of Kb (208C): equation 15 (even though some ponds were outside the applicability limits of L/BR 10 and KbdispersedtR 10). . Correction of Kb for the actual temperature: equation 9. . Estimation of the euent coliform concentration: equation 2. Dispersed ¯ow model: . Estimation of Kb (208C): equation 11. . Estimation of the dispersion number d: equation 8. . Correction of Kb for the actual temperature: equation 9. . Estimation of the euent coliform concentration: equations (4) and (5). Figure 6 presents the 66 values of the estimated observed coliform concentrations, for both the CSTR and the dispersed ¯ow models. Visually, it can be seen that both models were able to satisfactorily predict the order of magnitude of the euent coliform concentration from each pond. The Coecients of Determination (R2) for the estimation of the log of the concentrations were excellent and very similar (R2=0.951 for the CSTR model and R2=0.959 for the dispersed-¯ow model). Figure 7 compares the estimated values of the euent concentrations from both models, and it can be seen that the results are in most cases very similar, lying very close to the 458 line of perfect ®t.
POND VOLUME AND SURFACE AREA REQUIREMENTS FOR COLIFORM REMOVAL
Table 7 presents the pond requirements in terms of volume (m3 of pond volume per m3/d of wastewater) and surface area (m2 of pond surface area per m3/d of wastewater) for dierent pond depths and L/B ratios, using the proposed approach for the dispersed-¯ow model, in order to achieve 90% (1 log), 99% (2 log) and 99.9% (3 log) coliform removal in a single pond, at a liquid temperature of 208C. Figure 8 illustrates the corresponding volume and surface area requirements. In the table and ®gure, the unit volume requirements (m3 per m3/d) are equivalent to the detention time (d). The values in Table 7 and Fig. 8 emphasise the in¯uence of H and L/B in the eciency of coliform removal: the lower the pond depth H and/or the greater the L/B ratio, the lower the pond volume and surface area required. The pond depth has an important and somewhat unexpected in¯uence on the surface area requirements: according to the results obtained, even though a shallower pond has a lower volume, and consequently a lower detention time, the coliform die-o coecient is larger, leading to an overall better eciency compared to a pond of equal area and greater depth, volume and
1444
Marcos von Sperling
Fig. 6. Comparison between the observed and estimated euent coliform concentrations using the proposed approaches for the CSTR and dispersed ¯ow models.
detention time. In other words, for a given eciency of coliform removal, according to the present data, the best land-saving alternative is associated with shallow ponds. These results contrast with those found by Van Haandel and Lettinga (1994) and Silva et al. (1996), both based on the pilot-scale ponds in the Northeast of Brazil, described in Table 3. The former study concluded that the pond depth had a negligible in¯uence on the required area (m2/inhab), while the latter one reported that land savings of 30% could be obtained by using ponds of 2.2 m depth, as compared with ponds with 1.0 m (series of ponds, each with 5.0 to 5.8 days of detention time).
CONCLUSIONS
The paper emphasises the importance of the adoption of the correct hydraulic model and the associated die-o coecient (Kb) for the estimation of the coliform removal eciency of facultative and maturation ponds. Based on the analysis of data from 33 ponds located in dierent parts of Brazil (tropical to subtropical regions), covering a wide range of physical con®gurations, temperature and detention times, the coliform die-o coecient was calculated for the CSTR and the dispersed-¯ow models. For the utilisation of the dispersed-¯ow model, the dis-
Coliform die-o in waste stabilization ponds
1445
Fig. 7. Comparison between the estimated euent coliform concentrations from the two proposed approaches for the CSTR and dispersed ¯ow models
Table 7. Volume and surface area requirements for a single pond in order to achieve 1, 2 and 3 log removals, using the proposed approach for dispersed ¯ow (208C) Volume requirements (m3 per m3/d) L/B ratio
H (m) 1
2
4
Surface area requirements (m2 per m3/d) L/B ratio
8
16
32
1
2
4
8
16
32
Removal eciency: 90% (1 log removal) 0.4 3.7 3.0 2.5 0.6 6.3 5.1 4.2 0.8 9.2 7.4 6.2 1.0 12.4 9.9 8.3 1.2 15.7 12.6 10.5 1.4 19.2 15.4 12.8 1.6 22.9 18.3 15.3 1.8 26.7 21.4 17.8 2.0 30.6 24.5 20.4 2.2 34.7 27.8 23.2
2.2 3.7 5.4 7.2 9.1 11.1 13.3 15.5 17.8 20.1
2.0 3.3 4.9 6.5 8.3 10.1 12.0 14.1 16.1 18.3
1.9 3.2 4.6 6.2 7.8 9.6 11.4 13.3 15.2 17.3
9.3 10.6 11.5 12.4 13.1 13.7 14.3 14.8 15.3 15.8
7.5 8.5 9.2 9.9 10.5 11.0 11.4 11.9 12.3 12.6
6.2 7.1 7.7 8.3 8.7 9.2 9.5 9.9 10.2 10.5
5.4 6.1 6.7 7.2 7.6 8.0 8.3 8.6 8.9 9.1
4.9 5.6 6.1 6.5 6.9 7.2 7.5 7.8 8.1 8.3
4.6 5.3 5.7 6.2 6.5 6.8 7.1 7.4 7.6 7.8
Removal eciency: 99% (2 log removal) 0.4 23.4 16.2 12.0 0.6 39.6 27.3 20.4 0.8 58.0 40.0 29.8 1.0 77.5 53.5 39.8 1.2 98.0 67.6 50.4 1.4 120.0 82.8 61.7 1.6 143.0 98.7 73.5 1.8 167.0 115.3 85.9 2.0 192.0 132.5 98.7 2.2 217.0 149.8 111.6
9.5 16.1 23.5 31.5 39.8 48.7 58.1 67.8 77.9 88.1
8.1 13.6 20.0 26.7 33.7 41.3 49.2 57.5 66.1 74.7
7.2 12.2 17.9 23.9 30.3 37.1 44.2 51.6 59.3 67.0
58.5 66.0 72.5 77.5 81.7 85.7 89.4 92.8 96.0 98.6
40.4 45.6 50.0 53.5 56.4 59.2 61.7 64.0 66.3 68.1
30.1 33.9 37.3 39.8 42.0 44.1 45.9 47.7 49.4 50.7
23.8 26.8 29.4 31.5 33.2 34.8 36.3 37.7 39.0 40.0
20.1 22.7 24.9 26.7 28.1 29.5 30.7 31.9 33.0 33.9
18.1 20.4 22.4 23.9 25.2 26.5 27.6 28.7 29.7 30.5
Removal eciency: 99.9% (3 log removal) 0.4 75.9 47.9 33.2 0.6 128.5 81.1 56.2 0.8 187.5 118.3 82.0 1.0 251.0 158.4 109.8 1.2 318.0 200.7 139.1 1.4 390.0 246.1 170.6 1.6 463.0 292.2 202.5 1.8 540.0 340.8 236.2 2.0 620.0 391.3 271.2 2.2 703.0 443.7 307.5
24.6 41.6 60.6 81.2 102.9 126.1 149.8 174.7 200.5 227.4
19.7 33.3 48.5 65.0 82.3 101.0 119.9 139.8 160.5 182.0
17.0 28.7 41.9 56.1 71.0 87.1 103.4 120.6 138.5 157.0
189.8 214.2 234.4 251.0 265.0 278.6 289.4 300.0 310.0 319.5
119.8 135.2 147.9 158.4 167.2 175.8 182.6 189.3 195.6 201.7
83.0 93.7 102.5 109.8 115.9 121.9 126.6 131.2 135.6 139.8
61.4 69.3 75.8 81.2 85.7 90.1 93.6 97.0 100.3 103.4
49.1 55.4 60.7 65.0 68.6 72.1 74.9 77.7 80.3 82.7
42.4 47.8 52.3 56.1 59.2 62.2 64.6 67.0 69.2 71.4
1446
Marcos von Sperling
Fig. 8. Pond volume and surface area required for achieving 1 log and 2 log coliform removal, as a function of the depth H and the L/B ratio (dispersed ¯ow) (208C).
persion number was estimated using Agunwamba et al. (1992) and Yanez (1993) formulae. Both were found to give similar results, and the Yanez formulae was used in other parts of the paper, due to its greater simplicity. The Kb values found with the CSTR model varied over a very wide range (0.04 to 31.09 dÿ1), illustrating the inadequacy of the CSTR model, especially for ponds with length-to-breadth (L/B) ratios signi®cantly greater than one. The Kb coecients obtained with the dispersed-¯ow models had a much narrower distribution (0.02 to 2.44 dÿ1), suggesting the better adequacy of this model in the representation of the coliform decay. In the dispersed-¯ow model, the pond depth (H) and the hydraulic detention time (t) were found to have a major in¯uence on the value of the coecient Kb. A regression analysis was undertaken, leading to the following relationship: Kb 0:917H ÿ0:877 tÿ0:329
n 66; R2 0:847
Recognising that the CSTR model is more widely applied than the dispersed-¯ow model by designers, an equation was developed for the conversion of the Kb for dispersed ¯ow into the Kb for the CSTR model, based on the L/B ratio and the detention time. The equation was derived via regression
analysis of theoretical data concerning the relationship between the coecients under both hydraulic models: Kb CSTR 1:753 Kb dispersed 0:0011 3:189 K 4:189 L=B 1:509 b dispersed t
n 44; R2 0:997 The utilisation of both Kb models for the estimation of the 66 values of the log euent concentration of faecal coliforms in the 33 ponds led to: (a) very similar results and (b) very good prediction capability (R2=0.951 for the CSTR model and R2=0.959 for the dispersed-¯ow model). Based on the proposed model for dispersed ¯ow, the required pond volumes and surface areas for dierent depths and L/B ratios were calculated. The results show that a shallow pond, due to its greater Kb coecient, requires less surface area, for a given eciency of coliform removal, compared to a deep pond. Although the results are based only on ponds situated in Brazil, the large number of units included in the study encompass a wide range of climatic, physical and operating conditions, thereby
Coliform die-o in waste stabilization ponds
supporting the conclusion that the models presented in the study are based on a larger and more representative data set than most other studies available in the literature world-wide. Naturally further studies are always required in order to con®rm or adjust the derived models. It is important to point out that any modelling study of coliform decay should explicitly present basic information, which are not always included in most of the papers. The minimum information required are: ¯ow regime adopted, physical data of the pond (length, width, depth), liquid temperature and ¯owrate. AcknowledgementsÐThe author wishes to thank CEMIG (Energy Company of Minas Gerais), COPASA-MG (Water and Sanitation Company of Minas Gerais) and FNS (National Health Foundation, ParanaÂ) for the kind permission to use their data on this research, and Mr. Eduardo Cohim for his useful suggestion. REFERENCES
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