Full Text CEPIS/OPS/OMS

Bacterial die-off kinetics in waste stabilization ponds

By: Polprasert, M.G.Dissanayake, N.C.Thanh


Waste stabilization ponds (WSP) are becoming popular for treating wastewater, particularly in tropical and subtropical regions where there is an abundance of sunlight, and the ambient temperature is normally high.
The ability of WSP systems to reduce the biochemical oxigen demand (BOD) of wastewater is well established.
Mathematical models have been developed to describe the kinetics of organic degradation in these ponds. However, equally important is the effectiveness of WSP systems in reducing pathogenic microorganisms. Because of a lack of sound design criteria, there are still some doubts as to whether WSP can meet presente effluent standards set by many authorities without disinfection.

Kinetic models of bacteria die-off can be expanded to include the effects of algae concentration and organic loading

The literature1-7 has revealed that die-off bacteria in WSP depends on environmental and climatological parameters. Several hypotheses have tried to explain the causes of bacterial reduction, including the presence of antibacterial substances produced by algae. the high pH levels common in the ponds, the production of toxic extracellular compounds by algae, the depletion of nutrients, the microbial antagonism, and the high oxidation reduction potencial in algal-bacteria cultures. Although no evidence was found buy Parker8 to support the view that the release of bactericidal substances from algal material was responsible for the reduction in coliform count, he reported that the complex pond environment, along with the involvement of a greater variety of algal species, resulted in increased die-off rates of the enteric bacteria. Parhad and Rao4 experimentally found that the growth of different algae in sterilized wastewater resulted in an increase of pH from 7.5 to more than 10.
This increased pH caused reduction of E. coli when grown in association with algae.
Based on first orden kinetics and assuming completely mixed conditions, Marais and Shaw9 proposed a model for the die-off of indicator bacteria in WSP. Because temperature was found to affect the bacterial removal efficiecy substantially, Marais6 altered the model and derived a first-order equation in which the first-order rate constant was assumed to be temperatue dependent. Other coliform decay models in WSP, developed by Klock,10 Bowles et al.,11  and Ferrara and Harleman,12 were of the first-order reactions in which the decay rate is temperature dependent.

In fact, the WSP should be considered as a complex system encompassing the existence of several living species, especially the interrelationship of algae and bacteria, which bring about an ecological patter different from pure culture behaviour. Numerous authors 11,13 have pointed to a need to improve existing models of coliform decay. The comprehensive model should include the relationship of coliform die-off to other major parameters: algal biomass concentration (Cs), temperature (T), organic loading (OL), sunlight intensity (l), sunlight duration (L), hydraulic detention time (0), substrate degradation rate (Ks), and pond dispersion number (d). A research program was undertaken to develop mathematical relationships of the bacterial die-off in WSP14 incorporating two proposed models, one for the algal concentration, Cs. Verification of the results obtained was made with experimental data from the fullscale WSP and some published data for existing ponds in northeast Brazil. 15.16  The portion of the work pertaining to mathematical relationships of bacterial die off (the k model) and data verifications is reported herein.

Development of mathematical model for bacterial die-off in WSP

Marais6 has proposed this first-order equation for the reduction of fecal bacteria in a series of n identical, completely mixed ponds:

                       Ne =           No                                                  (1)
                                   (1 + kT0)n

where Ne and No are effluent and influent fecal coliform numbers per 100 ml of wastewater, respectively; 0 is in days;

gra1.gif (9427 bytes)

Figure 1 - Mass balance of bacteria in axially mixed WSP.

and kt, the first-order rate constant for fecal coliform removal at TC, in days-1, has an approximate value in the temperature range 2 to 21C, or:

                                kt   = 2.6(1.19)T-20                                                                        (2)

A later study by Mara et al.16 found the above equations valid for termperatures up to 30C. Although 0 might appear to affect the bacterial die-off directly, it actually induces changes in the pond environment, such as the variation of d, Cs, pH, and nutrients that consequently influence the bacterial die-off process. To improve existing models, Thirumurthi17 considered the non-ideal flow in WSP for the model developed for BOD reduction, which included the dispersion number (d) to evaluate the liquid flow and mixing characteristics. The value of d incorporates physical flow characteristics, such as the pond shape, presence of inert zones, flow velocity, and mixing conditions such as wind currents, thermal stratification, and turbulence.

For ideal plug flow conditions, d is zero, whereas for ideal completely mixed conditions, d reaches infinity.
As the value of d becomes greater, the flow deviates from the plug flow towards the completely mixed conditions.
In view of the above mentioned factors, the bacterial die-off in WSP could be related as follows:

                                Die-off = f(k, d, 0)                                                     (3)

where

k = bacterial die-off rate coefficient, day -1

Since the movement of bacteria with seepage water to the outside pond environment could be regarded as minimal when compared to the amount present in the pond,18 the downward diffusion of coliform bacteria was disregarded in the model development. Under steady state conditions, Levenspiel's19 flow model for chemical reaction and dispersion was modified in this study to account for the bacterial die-off and dispersion. A steady flow WSP of length Lo through which fluid is flowing with a constant velocity, and in which bacteria is mixed axially with a dispersion coefficient, d was considered as shown in Figure 1. By referring to the elementary section of the pond, the bacterial density mass balance was written as:

input = output + disappearance by pond action + accumulation                 (4)

Equation 4 was modified as in Equation 5:

(output - input)bulk flow + (output - input)axial dispersion + disappearance by pond action + accumulation = 0  (5)

in which the final elementary equation is shown in Equation 6.

gra2.gif (409 bytes)                                                                (6)

Wehner and Wilhelm20 solved this type of equation for any kind of entrance and exit conditions. The solution of Equation 6 is given below:

gra3.gif (577 bytes)                                          (7)

where

a = gra4.gif (186 bytes);

and Ne, No, k, and d are as defined previously.
Equation 7 can be valid for WSP in which reactions are ocurring uniformly throughout the pond depth at a rate coefficent k. However, in field conditions, owing to uneven light penetration and possible stratification, the k value can be slightly different at various depths.
In this study the evaluation of the k value was made for the overall pond depth to compensate for uneven bacterial die-off rates.
The proposed k model. Although k is dependent on temperature (Equation 2), other investigators observed k to vary with pH, dissolved oxygen (DO), and nutrient content in the pond. 2,4,8 Because pH and DO vary as the algal concentration changes2 and mixed algal species enhance greater bacterial die-off rates,5 the dependence of k on the external factors can be related as:

k = f(T, Cs, OL)                                                                         (8)

Because the influence of T, OL, and Cs on k are complex, the k model was postulated to be non-linear as follows:

ek = R1w1Tw2Csw3OL                                                                   (9)

in which R1, w1, w2 and w3, are constans. In order to test the potential lethal effect of sunlight on bacterial die-off in WSP, as reported by Moeller and Calkins,21 the k model could be presented in an alternative form as in Equations 10 and 11.

k = f(T, Cs, OL, UVI)                                                                (10)

gra5.gif (3014 bytes)

ek = Ra1Wa1TWa2CsWa3OLWa4UVI                                     (11)

where UVI = ultraviolet rays index, dimensionless, and Ra1, Wa1, Wa2, Wa3, and Wa4 are constants. The UVI index was weighed in accordance with the sunlight intensity (I,cal/day/cm2).

UVI = 1 +    I                                                                         (12)
                  100

In the absence of sunlight, UVI was considered to be unity. The constants in Equations 9 and 11 were determined by entering a series of experimental values obtained from laboratory and pilot scale WSP for different combinations of T, OL, Cs   and UVI into the multiple regression equations. The accuracy of these parameters depends upon arriving at a low standard error, a high multiple correlation, and a high F-value. The total coliform species was chosen in the experiments as the indicator bacteria for the k-model, but it can be extended to predict the k-values of other enteric bacterial, a species constant, gra6.gif (84 bytes)was included in the model (Equation 9).

gra7.gif (291 bytes)                                                          (13)

Because total coliforms were chosen as the indicator bacteria in this model, the species constant, gra6.gif (84 bytes), is unity.
A series of kF values for fecal coliforms were obtained experimentally for a combination of T, OL, and Cs values.                                        gra8.gif (10448 bytes)

Figure 3 - Vertical profile of pilot-scale WSP (PWSP). Scale 1:100

Table 1 - Ranges of operating conditions for laboratory scale WSP.a

Parameter

Range

Temperature, C

20.0 - 33.0

Light intensity, cal/cm2.d

80.0 - 330.0

Light duration, h/d

8.0 - 14.0

Influent COD, mg/l

150.0 - 170.0

Dispersion number (d)

0.100 - 0.200

Detention time, days

3.0 - 10.0

a Each pond had the same width (w) and depth (d) of 0.40 m and 0.18 m, respectively, but length (l) was varied at 0.4, 0.6, 0.8, 1.0 and 1.5 m.

By entering these values into Equation 13, the average R1 value for fecal coliforms (RF) could be determined, in which:

RF = gra6.gif (84 bytes)1 R1                                                                                       (14)

where

RF   = R value for fecal coliforms,
R1   = R value for total coliforms, and
gra6.gif (84 bytes)1 = Species constant for fecal coliforms

Experimental investigation

Three experimental phases were undertaken that included studies of a laboratory-scale WSP operated under controlled conditions, a pilot-scale WSP operated under ambient conditions, and a full-scale WSP at the Asian Institute of Technology (AIT). The campus wastewater in the full-scale plant was used as the raw wastewater for the laboratory and pilot experiment as well.

Laboratory-scale WSP (LWSP). Five rectangular LWSP units, made of 6-mm thick PVC sheet, each with different dimensions, were used in the experiments (Figure 2). The LWSP inlet was connected to a flow inducer to obtain a constant influent flow, and two baffles were fixed near the pond inlet and outlet to minimize short-circuiting and free-flow conditions. A 500-1 polyethylene vessel with a stirrer was used as the feed tank to which feedlines and pumps were connected to facilitate continuous operation of the system. The experiment were conducted in a controlled temperature room and pond illumination was accomplished by providing a set of fluorescent bulbs fitted to a wooden stand.

Table 2 - Ranges of operating conditions for pilot-scale WSP.

                                                                                   Range                                                     

Parameter

PWSP 1

PWSP 2 & PWSP 3

Temperature, C 28.6-32.6

28.6-32.6

Light intensity, cal/cm2.d 321.6-643.5

321.6-643.5

Light duration, h/d 11.5-12.5

11.5-12.5

influent COD, mg/l 160.0-180.0

40.0-95.0

Dispersion number (d) 0.115-0.195

0.125-0.215

Detention time, days 5.8-17.9

3.6-11.1

Dimension time, days 4.5 x 2.0 x 0.86

4.0 x 2.0 x 0.6

To overcome the red and orange wavelength deficiency in fluorecent bulbs, a number of incandescent bulbs were added to the system. By varying the distance between the pond surface and the light plate or by independently switching off any number of bulbs, the light intensity at the pond surface could be chaged. A timer switch was attached to this device to automatically adjust the illumination period. The ranges of operating conditions of the LWSP experiments are given in Table 1. For each test, a few weeks was allowed for the system to attain steady-state conditions based on the effluent COD data, and the following measurements of the pond water were taken: influent and effluent total and fecal coliforms and algal concentrations.

Pilot-scale WSP (PWSP). The PWSP experiments were carried out under ambient conditions, with three ponds connected in series (Figure 3). A constant head tank was used to feed wastewater to PWSP 1 at a constant rate, but a pump with a timer was used for sewage feeding periodically to avoid pipe blockage. The ranges of operating conditions of the PWSP experiments are shown in Table 2. The same measurements taken for the LWSP, plus the diurnal variation of pH and DO, were taken for each PWSP.

Full-scale WSP (FWSP). The wastewater treatment facility (Figure 4) at AIT comprises two parallel sets of ponds in series (FWSP). The FWSP1 serves a facultative function, while the FWSP2 is a maturation pond. The final effluent is discharged into a nearby canal. The FWSP operation is under the control of the AIT physical plant, but cooperation was provided in the measurements of flows and other important parameters similar to the LWSP and PWSP.

Tracer study. To determine the dispersion characteristics of the LWSP, PWSP, and FWSP, tracer studies were carried out for different B of each pond. Sodium chloride (NaCI) was the impulse tracer matetrial for all the experiments, as in the experiments of Thirumurthi" According to Levenspiel,19 the response tracer concentration should be monitored at the exit stream at fixed time intervals. The amount of input impulse tracer concentration varied from 30 g in the LWSP to about 700 kg in the FWSP. The base amount of NaCI present in the wastewater was taken into consideration when the exit responses

gra9.gif (19018 bytes)

Figure 4 - Layout of AIT waste stabilization ponds (FWSP).

were monitored. The calculation of the d values was made with the method proposed by Levenspiel and Smith,22 which is described below:

gra10.gif (631 bytes)                                      (15)

gra11.gif (787 bytes)                                         (16)

gra12.gif (346 bytes)                                                       (17)

The term, d, can be calculated by trial and error from Equation 17 in which

i = time after impulse injection, days; and

Ci = tracer response concentration at the exit stream, mg/1.

Though tracer studies require careful attention and much time, th are one of the most reliable techniques for evaluati the actual flow pattern in a WSP. Previous investigat , such as Thirumurthi,17 Bowles et al.11 and Uhlmann,23 based their mathematical formulations of WSP performance on partial mixing conditions and flow pattern.

Analytical methods. All analyses were undertaken according to the methods described in "Standard Methods"24 DO measurements were conducted with a DO meter. pH of the water samples was measured with a pH meter. Five flow inducers were used to monitor influent flows of the LWSP. Intensity of artificial light and sunlight was measured with a bimetallic actinograph instrument. The samples for algal analysis were initially filtered through a 150-Am mesh to separate out zooplanktons, measured for the percent absorbance with a spectrophotometer at a wavelength of 650 mm, and weighed for dry algal concentration with the specimen curve prepared in advance.

Table 3 - AIT campus wastewater characteristics and performance of the FWSP

                                                         Raw wastewater                

Parameter

Range Mean Effluent of
FWSP 1
Effluent of
FWSP 2
COD, mg/l (filtered) 100-440 180 50 30
BOD5, mg/l (filtered) 60-150 120 35 15
SS, mg/l 20-120 110 80 115
VSS, mg/l 10-9- 45 - -
Org-N, mg/l 2-5 - - -
NH3-N, mg/l 4-10 5.5 3.0 Trace
PO4-3, mg/l 0.5-1.5 - 0.4 0.3
pH 6.2-7.5 7.3 7.5 8.0
Temperature, C 28-33 - 28-33 28.33
Total coliforms, MPN/100 ml 22 X 105-16 X 106 11 X 106 15 X 105 24 X 103
Fecal coliforms, MPN/100 ml 16 X 103-92 X 104 46 X 103 93 X 102 11 X 102
Detention time (), days     8 20
Dimension, l X w X d, m3     50 X 23 X 2.4 120 X 43 X 1.3

The total coliform counts were enumerated by the standard MPN method using the five-tube dilution technique. Appropriate dilutions, prepared in buffered dilution water, were inoculated into lactose broth, presumptively tested by incubation at 35C for 24 hours. All the positive tubes were then confirmatively tested by subculturing into brilliant green lactose bile broth at 35C for 48 hours. The fecal coliform MPN counts were determined by subculturing all the positive presumptive tubes into an EC medium at 44.5C for 24 hours.

Results and discussion

The characteristics of the campus wastewater used as the raw wastewater in the experiments are shown in Table 3. According to Metcalf and Eddy25 this is considered a weak concentration waste. But it contained sufficient nutrients, based on the BODS:N:P ratio, for biological stabilization. The levels of total and fecal coliforms present were normal for domestic wastewater. However, these coliform concentrations need to be greatly reduced if the bacteriological standard of less than 100 fecal coliforms/ 100 ml is to be achieved so that the effluent can be discharged or used for unrestricted irrigation and is suitable for many industrial and municipal purposes.26

Performance of LWSP. The data of LWSP performance, presented in Table 4, show the variation in percent reduction of total coliforms (PAT) and fecal coliforms (PAF) ranging from 73 to 96 and 78 to 97, respectively, with changes in the magnitude of other environmental factors. The COD removal as reported by Dissanayake" was found to range between 40 and 80%. Because the LWSP were operated as single-cell ponds, it is unlikely they could achieve better results than those

Table 4 - Results obtained from laboratory-scale WSP (Sept.1978-July 1979; average of three replications).

gra13.gif (38956 bytes)

reported above. Both Marais6 and Parke8 noted the superior performance of a series of ponds as compared with a single cell pond. The concentrations of CS in the ponds varied from 28 to 260 mg/1, depending on the values of d, B, OL, T, L, and I. No attempt was made to investigate the diurnal variation of pH, DO, and CS because I was made constant throughout the illumination period. It was observed that the minimum CS value corresponded with the highest d of 0.200, while the highest T, L, and I of 33C, 16 h/d, and 372 cal/ cm' • d, respectively, resulted in the highest PAT and PAF, 96.16 and 97.39, respectively. However, the different percentages of bacteria) die-off were observed for each of these parameters whose concentrations maintained at the same or similar ranges, indicating that there were various interactions taking place simultaneously in the WSP. The above information suggested that bacterial die-off is a complex phenomenon involving many factors that influence the physical and biochemical reactions of the pond itself.

Performance of PWSP. Similar to the LWSP, a high variation of PAT and PAF was observed for the PWSP when subjected to changes in the magnitude of the environmental factors (Table 5). The PAT and PAF values of the PWSP ranged from 77 to 99 and 80 to 99, respectively, which were mostly higher than those of LWSP (Table 4). Although the reasons for the increase in bacterial reduction were not determined, the values of B, T, and I for the PWSP operation were relatively higher than those of the LWSP, and previous literature2,4,6,21,27,28 have reported the direct effects of these parameters upon bacterial die-off. The PAT and PAF were calculated based on the influent and effluent coliform densities in each PWSP. Thus, in some cases, the PAF could be equal to or less than the PAT for the same pond, depending on the influent coliform densities and, probably, other environmental factors that had influence upon the pond behaviours. However, the PAF values for the whole series of ponds (PWSP1 to PWSP3) were mostly higher than the PAT values, indicating a more rapid die-off of fecal coliforms than total coliforms, similar to the LWSP experiments. The series of PWSP proved to be very effective in waste stabilization, as there were about 80 to 99% and 50 to 70% reductions of coliforms and COD," respectively, in each successive pond. The OL of PWSP1 were highest among the three ponds in series because it was the first to receive the raw wastewater, but the OL of PWSP2 were most of the time about equal to or less than that of PWSP3. Because PWSP2 always had high CS concentrations, it was possible that the algal by-products in the PWSP2 effluent contributed to the OL of the PWSP3. From Table 5, the lowest PAT and PAF of 77.14 and 80.00, respectively, occurred in the same PWSP3 (third data line from top) which had the largest d of 0.215, and smallest B of 3.58 days. The highest PAT and PAF of 99.86 and 99.85, respectively, occurred in the same PWSP1 (twenty-first data line from bottom), which had the smallest d of 0.125 and largest L and I of 12.5 h/d and 643.5 cal/cm2. d, respectively, when compared with the rest of the data. The pond that had the lowest bacterial reduction was also found to have higher d, and lower B, CS, OL, T, L, and I than the pond with the highest bacterial reduction (0.215:0.125, 3.6:12.8 days, 113.0:270.0 mg/1, 70.6:121.6 kg COD/ha-d, 29.2:32.2C, 11.5:12.5 h/d, and 459.7:543.5 cal/day/cm2, respectively). Similar to the LWSP, the different PAT and PAF could be observed for each of these environmental parameters whose concentrations maintained at the same or similar ranges, indicating the simultaneous occurrence of complex interactions in the WSP.

gra14.gif (65399 bytes)

Figures 5,6 and 7, respectively, show typical diurnal variation of pH, DO, and Cs in the PWSP3. Because the data shown in these figures were not from analyses of the same samples taken on the same day, they did not necessarily show correlation among each other. Only the same trend was observed. The basis phenomenon involved is that during dark periods, the algal cells do not consume the CO2 released by bacterial stabilization of organic matter, resulting in the formation of carbonic

gra15.gif (2071 bytes)

Figure 5 - Typical diurnal pH variation in pilot-scale WSP at mid cross-section

acid, causing a decrease in the pH. With the onset of the light period, the algae naturally start to rise to the water surface and consume CO2 for photosynthesis with the production of oxygen and more algal cells. This results in a gradual increase in pH, DO (up to supersaturation level), and CS in the pond water. In this study, the DO at dawn did not reach zero because the applied loadings of the PWSP were less than 280 kg COD/ha. d, the level considered as facultative.3,29 The decrease of CS in the later period of a day could be caused by light and nutrient limitations, competition for food, algal cell sedimentation, and unfavourable conditions existing at high pH conditions.

Performance of FWSP. The data in Table 3 indicated a considerable reduction of COD and BOD5 in the FWSP operated in series as their concentrations in the FWSP2 effluent were only about 30 and 15 mg/1, respectively. However, the SS concentration of 115 rng/1 was considered high, which was caused by algal cell suspension in the effluent. There were decreases in the total and fecal coliform densities of about 80% in the FWSP1 ( = 8 days); and about 90 to 98% in the FWSP2 ( = 20 days). The removal of organics and bacteria in the FWSP are comparable with other ponds reported in the

gra16.gif (2506 bytes)

Figure 6 - Typical diurnal dissolved oxygen (DO)
concentration in pilot-scale WSP at mid cross-section

gra17.gif (2375 bytes)

Figure 7 - Typical diurnal algal concentration in
pilot-scale WSP at mid cross-section

literature.29 It seems that another polishing pond, connected in series to the FWSP2, should be provided to achieve the stringent standards of SS and bacteria required by some regulatory agencies .26

It can be seen from the results of the LWSP, PWSP, and FWSP that bacterial die-off is a complex phenomenon involving various factors and interactions in the WSP. Because in actuality, the WSP are not in either completely mixed or plug-flow conditions, and not just a single parameter, such as T, controls the bacterial dieoff rate, the proposed Equations 7 and 9 or 11, as models for bacterial die-off, would better represent the pond performance.

The k model. The experimental k values were determined by entering each data set of PAT, d, and B in Tables 4 and 5 as input variables into Equation 7. Then, together with the respective values of T, OL, CS, and UVI, the experimental k values as determined were entered into the multiple regression equations (Equations 9 and 11) to evaluate the regression coefficients (or constants) using a computer program from a scientific subroutine package. The multiple regression results including the multiple correlation coefficients, standard errors of estimate, and F-statistic values obtained for Equations 9 and 11 were, respectively, 0.695 and 0.719, 0.152 and 0.294, and 19.039 and 16.109. Although Equation 9 had a slightly lower multiple correlation coefficient, its standard error of estimate and F-statistic value were lower and higher, respectively, than Equation 11, indicating that both equations represented a certain degree of correlation within the same range btween k and the parameters T, CS, OL, and I. In a WSP, k would depend on factors other than just those above mentioned parameters. But for practical reasons, Equation 9 was chosen to represent the k model, which can be written as in Equation 18:

ek = 0.6351(1.0281)T(1.0016)Cs(0.9994)OL                                                  (18)

The empirical relationship obtained for k in Equation 18 is essentially an extension of Equation 2, which quantifies the dependence of k on temperature only, and it eliminates the necessity for a temperature correction. However, a comparison of the k values based on Equations 18 and 2 is not relevant because the equations governing bacterial die-off (Equations 7 and 1, respectively) are of different order. Although Equation 18 does not include the parameter I or UVI, the direct relationship between I and CS has been substantially reported, 2 thus the term CS indirectly represents the influence of l on k.

The regression coefficients represent the factor by which each parameter (T, CS, and OL) contributes to the independent parameter (k); the sign of the regression coefficient of each parameter determining whether the contribution is negative or positive. For Equation 18, an increment in either T or CS results in an increase in the k value while the opposite is true for OL; these phenomena could be explained as follows. Although Marais6 observed that beyond a temperature of 21 C, k decreased as temperature increased, a later study by Mara and Silva16 showed that k increased with temperature up to at least   30C. At a temperature range of 21 to 30C, bacterial activity is stimulated and results in a higher obability of bacterial survival, but other factors, such increased algal activity and pH, cause higher die off dates by offsetting the stimulated bacterial activity. TX~e algal concentration in the pond was found to increase with the onset of the light period. With the consequent increase in pH (Oswald and Gotaas30 and Figures 5 and 7), the pH variation from about 8 to 10 can yield a hostile environment for bacterial survival.4 The regression coefficient for OL indicates that an increase in organic loading causes a slight decrease in k because of more nutrient availability for the bacterial activity." Therefore, the regression coefficients and their signs, as shown in Equation 18, are considered to be in accordance with actual pond performance and the literature, when operated within the ranges employed for the LWSP and PWSP in this study.

Species coefficient for fecal coliforms (gra6.gif (84 bytes)1). The fecal coliform die-off coefficients (kf ) were calculated by entering the respective values of PAF, d, and in Tables 4 and 5 into Equation 7. The values of R, a, or RF could be determined by entering the values of the calculated kF, T, CS, and OL into Equation 13, in which the values of w1, w2, and w3 were the same as in Equations 9 or 18. By entering the mean RF value into Equation 14, the species constant, X, was found to be 1.1274, and the kF is given as follows:

ekF = 1.1274(0.6351)(1.0281)T(1.0016)Cs(0.9994)OL

Though the k to kF ratio is constant, the resulting PAT to PAF ratio is variable because Equations 18 and 19 have to be used with Equation 7, which has a higher order to predict the bacterial survival ratio in WSP. From Equations 18 and 19, the value of kF is marginally higher than k, which is in accordance with the results of Fransmathes,31 who reported better survival of the total coliforms than the fecal coliforms in WSP.

Verification of model responses and application

The data of FWSP, Mara et a1.15 and Mara and Silva16 were used to evaluate responses of the models (Equations 7, 18, and 19) developed in this study.. Comparisons of the observed coliform reduction data and those predicted from Equations 1 and 7 were made to show the response accuracy and sensitivity. The results are summarized in Table 6.

Table 6 - Comparisons between observed and predicted coliform percentage reduction

  Comparison with predicted results                        Comparison with predicted result
            based on Equation 7                                      based on Equations 1 & 2
CC MPR SDPR MPR SDPR
Total coliform percentage reduction (PAT) based on 22 FWSP experimental dataa 0.986b 0.302 1.090 -2.730 3.934
Fecal coliform percentage reduction (PAF), based on 22 FWSP experimental dataa 0.988c 0.198 0.675 -2.451 3.302
Fecal coliform percentage reduction (PAF), based on 14 experimental data on ponds in NE Brazil 15-16 0.994c 0.352 1.061 -2.705 2.961

Note-CC  =  correction coefficient.
MPR       =  mean of percentage errors
SDPR     = standard deviation of percentage errors (excluding errors over 10%)
           a = the ranges of l, L and d were similar to those reported in Table 2.
           b = the values of k were determined from Equation 18.
           c = the values of kF were determined from Equation 19

Comparing the 22 experimental data of observed PAT in the FWSP with those predicted by Equations 7 and 18 gave the correlation coefficient of 0.986, indicating that the models developed in this study performed with a high degree of accuracy in the prediction of the total coliform die-off. The mean and standard deviation of percentage errors (MPR and SDPR, respectively) as resulted from the PAT prediction by Equation 7, were lower than that of Equation 1. Similar results were obtained for the fecal coliform reduction in FWSP, in which the comparison between the observed PAF and those predicted by Equation 7 yielded a correlation coefficient of 0.988, and there were lower mean and standard deviation of percentage errors in Equation 7 than that of Equation 1. By assuming the values of 1, L, and d to be 390 cal/cm2 • d, 11.5 h/d, and 0.150, respectively, for the pond data in northeast Brazil, the comparison between the fecal coliform percentage reduction and those predicted by Equations 7 and 1 could be made. The observed PAF and those predicted by Equation 7 had a correlation coefficient of 0.994, further asserting the accuracy of the proposed models. There were lower mean and standard deviation of percentage errors of the predicted PAF by Equation 7 than those by Equation 1. The main reasons for this difference are probably because Equation 1 assumes complete-mixing conditions in the pond and it includes only T and B, whereas the proposed models cater for actual dispersion characteristics of the pond and encompass other important parameters, such as CS and OL.
Because the values of the multiple regression coefficients in Equation 18 appear to be close to unity, it could be interpreted that the model was not sensitive. An attempt was made to observe the effects that variation of the T, Cs, and OL have upon the value of k. It was found that as T increases from 10 to 30C, k changes by as much as 0.55; as Cs increases from 25 to 300 mg/1, k changes by as much as 0.44; and when OL increases from 50 to 300 kg COD/ha. d, k decreases by as much as 0.15. For the parameter ranges mentioned above, k changes from a minimum value of -0.17 to a maximum of 0.68. Equation 7 was tested to observe the effects that variation in k and d have on the coliform survival ratio. By assuming the following: T = 25C, OL = 100 kg COD/ha- d, CS = 250 mg/1, B = 10 days, and d = 0.4; it was found that if k changes from 0.5 to 1.0, the Ne/Na ratio decreases from 0.061 to 0.012, a decrease in coliform density of about 80%. However, with the same values of T, OL, Cs, 0, and the k value of 0.5, it was observed that as d changes from 0.4 to 0.8, the Ne/No ratio increases from 0.061 to 0.089, an increase in coliform density of about 46%. Hence it is apparent that the changes in the values of T, Cs, and OL can cause significant changes in the k value, which in turn, together with the d value, can cause significant variations in effluent coliform quality.

The Wehner and Wilhelm equation (Equation 8) may seem complicated, but charts may be prepared similar to that of Thirumurth17 (for BOD reduction) to read off directly the coliform survival ratio as a function of the pond mixing pattern (d) and the value of kB. Because the second term in the denominator in Equation 7 is small, it may be neglected, in which case the equation can be simplified as:

Ne   = 4ae(1-a/2d)
No         (1 + a)2                                                                                  

The error of Equation 20 may be significant when the value of d exceeds 2.0. However, based on the data in Tables 4 and 5 of this study and of Nashashibi,32 d seldom exceeds 1.0 because of low hydraulic loads. In practice, the values of T, OL, CS, and d need to be known if the coliform survival ratio in WSP is to be predicted from Equations 7 and 18 or 19. T can be measured onsite directly and OL can be calculated or taken from the literature,25,29 thus only CS and d need to be determined. Oswald and Gotaas30 reported the rate of algal yield to vary from 2.5 tons/ha. month in the winter to 12.5 tons/ha. month in the summer. From continuous cultures, they found the dry weight algal cell material to be a logarithmic function of the substrate (BOD5), up to approximately 400 mg/1 (for the wastewater BOD5 ranging from 75 to 375 mg/1). The corresponding algal cell concentrations were from 125 to 325 mg/1, respectively. A model was recently developed 14 that relates the CS in WSP to the substrate degradation rate, hydraulic detention time, and other factors, such as T, L, arid 1. It was found to be satisfactory in predicting the algal concentration. The value of d can be obtained by conducting tracer studies in existing, similarly shaped ponds. It should be noted that the proposed equations (Equations 7, 18, and 19) are applicable to the types of single-cell ponds experimented with (facultative and maturation), and the ranges of operating conditions conducted in this study. Additional research is required to modify these equations so that they can be used to predict bacterial die-off in a series of WSP.

Design example. Determine the hydraulic detention time, B, of WSP treating domestic wastewater so that the final effluent will contain less than 100 fecal coliforms/ 100 ml, which is the standard for reuse in restricted irrigation. The initial COD and fecal coliform concentrations are 300 mg/1 and 105/100 ml, respectively. The expected monthly temperature in the pond in tropical areas is about 20C in winter. Tracer studies and water analyses in the existing, similarly shaped pond indicate that the values of d and CS are approximately 0.200 and 200 mg/l, respectively.

Solution 1. Select the OL value to be 200 kg COD/ ha. d. The value of kF can be determined according to Equation 19:

ekF = 1.1274(0.6435)(1.028)20(1.0016)200(0.9994)200

in which kF was found to be equal to 0.433 day-1 Take a = gra18.gif (189 bytes) and put it into Equation 20. By trial and error, the WSP hydraulic detention time () is found to be 34 days to produce effluent with fecal coliform concentration less than 100/ 100 ml.
Solution 2. If Equations 1 and 2 are to be used in the design, take from Equation 2, kT = 2.6(1.19)20-20=2.6 day-1
From Equation 1, the hydraulic detention time, , can be determined as follows:

if n =  1, = 384 days,
  n =  2,   = 12 days, and
  n =  3,   = 3.5 days.

It is difficult to say, based on the above results, which method is superior in terms of WSP design for bacterial reduction. Although Solution 2 gave the anomalous value of 0 for the case n = 1, for the case n = 2, the total is 12 X 2 = 24 days, which is less than the Solution 1 result. At.this stage, it could be generally stated that the proposed equations (Equations 7, 18, and 19) should be used in the design of single-cell facultative or maturation ponds, and that bacterial die-off in the ponds can-be predicted by these equations with high accuracy. Eruations 1 and 2 should be used in the design of WSP in series; as they gave more choices in selecting the nseries of ponds.

Summary and conclusions

Bacterial die-off in WSP is a complex phenomenon involving various physical-biochemical reactions and other environmental factors. Previous models describing the kinetics of bacterial die-off included only temperature and detention time as the major influential parameters, and pond contents were assumed to be completelymixed, which is far from realistic. This study attempted to investigate` further the kinetics of bacterial die-off in WSP through laboratory, pilot-scale, and full-scale experiments, in which the effects of other parameters, such as algal concentration and organic loading, on the dieoff rate coefficient were included. The diffusivity and mixing patterns in WSP were incorporated into the nonideal flow equation to predict the bacterial survival ratio. The outcomes of this study are as follows:

(1) A multiple linear regression equation was developed to relate the bacterial die-off rate coefficient (k) to other parameters, such as T, Cs, and OL. This equation can be extended to predict the k values of other bacterial species by the introduction of the species coefficients into the regression coefficient.

(2) The non-ideal flow equation of Wehner and Wilhelm was proposed for the prediction of the bacterial survival ratio in WSP. Besides the k value, this equation accounts for the pond dispersion factor, d, and the actual hydraulic detention time, .

3) The Wehner and Wilhelm equation was found to yield better results in predicting bacterial die-off in WSP than the first-order rate equation. This is probably because the former includes other important parameters influencing pond performance and bacterial die-off.
Verification of the model responses was made with data of the full scale WSP and some ponds in northeast Brazil.

4) Sensitivity analyses were carried out to show the effects that changes in magnitude of these influential parameters had upon the k value and the bacterial survival ratio.

Appendix

Abbreviations

Cs        =  algal concentration, mg/l
d          =  dispersion number, dimensionless
I           =  light intensity, calories/cm2, d
k          =  bacterial die-off rate coefficient, day-1
kF        =  fecal coliform die-off rate coefficient, day -1
kT        =  first-order rate constant for bacterial die-off, day-1
L          =   light duration, h/d
n          =   number of waste stabilization ponds in series
Ne, No  = effluent and influent bacterial densities, respectively, MPN/100 ml
OL       =   influent COD loading rate, kg COD/hA.D
PAF     = percentage fecal coliform reduction
PAT     = percentage total coliform reduction

gra19.gif (1694 bytes)

RF      =  a multiple regression coefficient for the k-model of fecal coliforms
  T      =  pond water temperature, C
UVI     =  ultra-violet ray index, dimensionless
        =  pond hydraulic detention time, days
gra6.gif (84 bytes)      =  bacterial species constant, dimensionless
gra6.gif (84 bytes)1   =   species constant for fecal coliforms, dimensionless

Acknowledgments

Credits. The authors wish to thank D.D Mara of Leeds University, U.K., for his critical review and comments of this research work. This paper was presented at the 54th Annual Conference of the Water Pollution Control Federation, Detroit, Mich., October 8, 1981.

Authors. Chongrak Polprasert, M. G. Dissanayake, and N.C. Thanh, are respectively, associate professor, senior research associate, and professor, Division of Environmental Engineering, Asian Institute of Technology, Bangkok, Thailand. Correspondence should be addressed to C. Polprasert, Environmental Engineering Division, Asian Institute of Technology, Box 2754, Bangkok, Thailand 10501.

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