1. INTRODUCCIÓN
1.1 Antecedentes
The coliform die-off coefficient (Kb) has a great influence on the estimation of the effluent coliform concentration. The literature presents a great scatter of reported coefficients, together with the additional complication that the different values of Kbhave been obtained assuming different hydraulic regimes (not always reported). Besides that, there are other influencing factors, such as DO concentration, pH, solar radiation, BOD loads and the physical configuration of the pond.
The depth exerts a great influence in Kb: shallower ponds have higher Kbvalues because of the following points: (a) higher photosynthetic activity throughout the pond depth, leading to high pH and DO values; (b) higher penetration of the UV radiation throughout the pond depth (Catunda et al, 1994; van Haandel and Lettinga, 1994; von Sperling, 1999). However, the combined effect of the shallower ponds should be analysed: Kbis larger, but the detention time t is smaller (for a given surface area). The impact on the product Kb.t can be evaluated through the formulas presented for the different hydraulic regimes.
In ponds located in warm-climate regions and with a tendency to stratification, the anaerobic layer at the bottom plays a negative role. The bacterial die-off in anaerobic conditions is lower than in aerobic conditions. Therefore, in a facultative pond, the coliform removal efficiency in the summer may be lower than in a mild winter, in which there is a larger predominance of the aerobic conditions (Arceivala, 1981).
In a review of the international literature, von Sperling (1999) identified values of Kbfor facultative and maturation ponds varying from 0.2 to 43.6 d−1(20◦C). This is an extremely wide range, which gives little reliability for design purposes. The highest values were due to the fact that, in case the complete-mix regime had been assumed for a pond that did not behave in practice as an ideal complete mix, there was a tendency of obtaining overestimated values of Kb.
Von Sperling (1999) investigated data from 33 facultative and maturation ponds in Brazil. The ponds analysed were distributed from the Northeast (latitude 7◦S) to the South (latitude 23.5◦S) of the country, covering a tropical to subtropical range of climates. The ponds had different volumes and physical configurations, with 13 being pilot units and the other 20 in full scale. The ponds represented a wide spectrum of operational conditions, with the length / breadth ratio (L/B) varying from 1 to 142 and the detention times from 0.5 to 114 days. In most cases, the coliform removal efficiency was based on average or long-term geometric means. The total number of data used was 66.
Complete-mix and dispersed-flow regimes were analysed in the work. It was observed that the values of the coefficient Kb for dispersed flow were related to the depth of the pond and to the hydraulic detention time. The lower the depth and the detention time, the larger the value of the coefficient Kb. As mentioned, the influence of the smaller depths is a result of the larger penetration of sunlight in the whole water mass (larger photosynthesis, larger dissolved oxygen, and larger pH values), besides the greater penetration of the ultraviolet radiation, which is bactericide. No significant relationship was observed between Kband the depth or detention time for the complete-mix model.
An equation correlating Kb(dispersed flow) with the depth and the hydraulic detention time was determined through non-linear regression analysis with the available data (von Sperling, 1999):
Kb(dispersed)= 0.917.H−0.877.t−0.329 (33 ponds in Brazil) (6.4)
The Coefficient of Determination was very high (R2 = 0.847), indicating a
good fitting of the proposed model to the experimental data. Even though it was known, a priori, that a model with such a simple structure would have difficulty in reproducing the wide diversity of situations that occur in practice, there was the advantage of depending only on variables which, in a design application, are known beforehand (H and t). Some of the models available in the literature are
Table 6.3. Values of Kb(dispersed flow), obtained from Equation 6.5
(Kb= 0.542.H−1.259), for facultative and maturation ponds
H (m) 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Kb(d−1) 1.03 0.72 0.54 0.43 0.35 0.30 0.26 0.23 0.20 0.18
Kb AS A FUNCTION OF THE DEPTH H
Kb=0.542*H−1.259 82 ponds; n = 140; R2 = 0.500 H (m) Kb (20 °C) –0.5 0.5 1.5 2.5 3.5 4.5 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
Figure 6.5. Regression analysis between Kb(20◦C, dispersed flow) and the depth H of
the ponds. Dispersion number adopted as d= 1/(L/B). 140 results from 82 facultative and maturation ponds in the world.
less practical, because they depend on variables that are not known at the design stage. In spite of the limitations, the model lead to a very good prediction of the logarithm of the effluent coliform concentrations from the 33 ponds (R2= 0.959). Subsequently, the author enlarged the database to 82 ponds (140 mean data) in Brazil and in other countries (Argentina, Colombia, Chile, Venezuela, Mexico, Spain, Belgium, Morocco and Palestine). Equation 6.4 was still shown to be valid,
although the Coefficient of Determination was reduced to R2 = 0.505. In this
enlarged data set, it was observed that the hydraulic detention time exerted a smaller influence and that it could be removed from the equation, without significantly affecting the performance of the model. The new equation obtained is presented below (see also Figure 6.5 and Table 6.3, showing the values of Kband the best-fit curve). The prediction of the log of the effluent coliform concentration was still entirely satisfactory.
Kb(dispersed)= 0.542.H−1.259 (82 ponds in the world) (6.5)
To allow a better visualisation of the results from both equations (Equations 6.4 and 6.5), Figure 6.6 presents the resulting curves for detention times varying
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 H (m) 3 d 5 d 10 d 20 d 30 d 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Kb 20 °C (1/d)
Kb (dispersed flow), as a function of H and t
Kb = 0.542*H−1.259 (solid line)
Figure 6.6. Relation between Kb, H, and t, according to the models proposed for Kb
(20◦C, dispersed flow), for facultative and maturation ponds. Dashed curves: Equation 6.4 (33 ponds in Brazil); solid curve: Equation 6.5 (82 ponds in the world).
from 3 to 30 days, and depths varying from 0.5 to 2.5 m. It can be observed that the simpler model (Equation 6.5), based only on the depth H of the pond, is situated in an intermediate range between the curves of the model based on H and t (Equation 6.4), especially for depths greater than 1.0 m. For depths lower than 1.0 m, Equation 6.5 approaches Equation 6.4 only for low values of the hydraulic detention time. Low values of H and t occur simultaneously in maturation ponds in series, which also justifies that the simpler model keeps its practical applicability also for this range of values of H and t.
With the 140 data from the 82 facultative and maturation ponds in the world, it was tested whether the position of the pond in the series would have any influence on the coefficient Kb. The reason is due to the fact that primary and possibly secondary ponds tend to receive a higher BOD surface loading rate, not being, therefore, optimised for the production of high DO and pH values, as in tertiary and subsequent ponds. Even though an statistically significant difference has not been detected, if a refinement in the calculation is desired, the data suggest the following corrections in the values obtained from Equation 6.5 (Kb= 0.542.H−1.259):
• Primary and secondary ponds−Kb: 5 to 15% lower than the value from the general equation
• Tertiary and subsequent ponds−Kb: 5 to 15% higher than the value from the general equation
Although Equation 6.5 has been derived from a large number of ponds dis- tributed in several places of the world, specific local conditions can always prevail and lead to different values of Kb. For instance, places with very high solar radiation are prone to having high Kbvalues (higher UV radiation, higher photosynthesis, higher DO and higher pH). As mentioned, to incorporate this and other factors in the equation would lead to a very sophisticated model structure, requiring input data difficult to obtain in practice.