This study proposes that calculating and interpreting removal coefficients (*K*_{20}) for bacteriophages in activated sludge (AS) and trickling filter (TF) systems using stochastic modelling may provide important information that may be used to estimate the removal of phages in such systems using simplified models. In order to achieve this, 14 samples of settled wastewater and post-secondary sedimentation wastewater were collected every 2 weeks, over a 6-month period (May to November), from two AS and two TF systems situated in southern England. Initial results have demonstrated that the removal of somatic coliphages in both AS and TF systems is considerably higher than that of F-RNA coliphages, and that AS more effectively removes both phage groups than TF. The results have also demonstrated that *K*_{20} values for phages in AS are higher than in TF, which could be justified by the higher removal rates observed in AS and the models assumed for both systems. The research provides a suggested framework for calculating and predicting removal rates of pathogens and indicator organisms in wastewater treatment systems using simplified models in order to support integrated water and sanitation safety planning approaches to human health risk management.

## INTRODUCTION

Human enteric viruses are commonly found in municipal wastewaters and many are capable of causing illnesses in humans (Bosch 1998; Metcalf & Eddy 2003). Viruses have been shown to be more resistant to wastewater treatment processes than other microorganisms. Furthermore, the limitations of traditional bacterial water quality indicators (e.g., faecal coliforms and *Escherichia coli*), such as differences in their occurrence and persistence compared with enteric pathogenic microorganisms (both in engineered and natural environments), have led to research into the use of numerous novel viral indicators (Jofre *et al.* 1995; Ebdon *et al.* 2007; Purnell *et al.* 2011).

Emerging potential indicators include bacteriophages (phages), which are a group of viruses capable of infecting prokaryotic organisms and which are (as are all viruses) obligate intracellular parasites (Metcalf & Eddy 2003; Withey *et al.* 2005). The phages commonly used in water and wastewater quality monitoring fall into three main groups: (i) somatic coliphages – phages that infect *E. coli* strains; (ii) phages infecting *Bacteroides* spp. – strict anaerobic bacteria comprising the major part of the human gastrointestinal microbiota; and (iii) male-specific F-RNA coliphages – phages commonly used as indicators of human enteric viruses (Grabow 2001).

To estimate the concentration of physico-chemical or microbiological parameters in treated effluents from wastewater treatment plants (WWTPs), different models are required, depending on the nature of the treatment hydraulics (e.g., plug-flow and mixed reactors) (Levenspiel 1999; Metcalf & Eddy 2003) and the kinetics of such reactions (e.g., first and second order) (Metcalf & Eddy 2003; von Sperling 2007a). In terms of their hydraulic flow characteristics, wastewater treatment reactors may be divided into two ideal models (Levenspiel 1999; Metcalf & Eddy 2003; von Sperling 2007a): plug-flow reactors, in which there is no mixing or dispersion; and complete-mix reactors, where fluid elements are instantaneously and totally dispersed after entering the reactor. In reality, reactors tend to be more complex, with flow characteristics corresponding to a position between the two idealised models, which is normally referred to as dispersed ‘non-ideal’ flow (Short *et al.* 2010). However, for many practical applications, the simplified ideal hydraulic models have commonly been used to describe the flow characteristics of wastewater treatment reactors (Gresch *et al.* 2011). Examples of the application of plug-flow and complete-mix reactors to a range of wastewater treatment systems, including activated sludge (AS) and trickling filters (TF), have been reported by Liotta *et al.* (2014).

Although traditional tracer studies can be used to provide valuable information about certain parameters (e.g., the hydrodynamics flow characteristics of reactors) of the hydraulic model assumed, the alternative approach of using stochastic modelling is a potentially more useful way of accounting for uncertainties around specific parameters, especially in studies involving more than one WWTP. In the stochastic modelling approach, value ranges are assigned to the input variables according to their specific frequency or probability distributions (Morgan & Herion 2007; Vose 2008).

This initial study (part of an ongoing investigation that also considers enteric viruses and faecal indicator bacteria) demonstrates the potential application of stochastic modelling to improve our understanding of the removal of phages in AS and TF treatment systems, using simple models and data collected from four WWTPs situated in southern England. As such, it potentially supports an effective multiple barrier approach to disease control, as part of a sanitation safety plan.

## MATERIAL AND METHODS

Samples of settled wastewater and post-secondary sedimentation wastewater were collected every 2 weeks, over a 6-month period (May to November 2013), from two AS and two TF systems situated in southern England. The WWTPs may be regarded as small to medium-scale, having population equivalents of 14,554 and 44,930 for the AS systems and 5,084 and 33,229 for the TF systems. For all samples, somatic coliphage (WG-5) and F-specific coliphages (WG-49) were enumerated using standardised double-layer techniques (BSI 2001, 2002) and expressed in terms of plaque-forming units (pfu) per 100 mL. The temperature (*T*) of the settled wastewater was also measured at all sites.

In order to calculate the removal coefficients (K_{T}), a complete-mix model based on hydraulic retention time (*t*) was selected for AS systems (Equation (1)), while for TF, a plug-flow model, based on hydraulic loading rate (*HLR*), was adopted (Equation (2)). However, in order to compare the removal coefficients obtained from both AS and TF systems, certain mathematical adjustments were made (Equations (3) to (5)) to obtain Equation (6). In this case, the unit for removal coefficient in TF systems is d^{−1}, as with AS. In order to standardise the removal coefficients according to an ambient temperature of 20 °C, the Arrhenius equation was also adopted (Equation (7)). The final models used to calculate removal coefficients at 20 °C (*K*_{20}) for AS (as d^{−1}) and TF (as d^{−1} and m^{3}.m^{−2}.d^{−1}) systems are presented in Equations 8, 9 and 10, respectively. All equations used are presented in Table 1.

Eq. (1) | Eq. (6) | ||

Eq. (2) | Eq. (7) | ||

Eq. (3) | Eq. (8) | ||

Eq. (4) | Eq. (9) | ||

Eq. (5) | Eq. (10) |

Eq. (1) | Eq. (6) | ||

Eq. (2) | Eq. (7) | ||

Eq. (3) | Eq. (8) | ||

Eq. (4) | Eq. (9) | ||

Eq. (5) | Eq. (10) |

*N*_{f} = final conc. (pfu.100 mL^{−1}); *N*_{0} = initial conc. (pfu.100 mL^{−1}); *t* = hydraulic retention time (d); *HLR* = hydraulic loading rate (m^{3}.m^{−2}.d^{−1}); *Q* = flow (m^{3}.d^{−1}); *Vol* = volume (m^{3}); *A* = surface area (m^{2}); *h* = height (m); *n* = porosity; *K*_{T} = removal coefficient at temperature *T* (d^{−1} or m^{3}.m^{−2}.d^{−1}); *K*_{20} = removal coefficient at 20 °C (d^{−1} for AS; d^{−1} and m^{3}.m^{−2}.d^{−1} for TF); *θ* = temperature coefficient; *T* = temperature (°C).

Probability density functions (PDF) were fitted to the concentrations of somatic and F-specific coliphages in the settled wastewater (*N*_{o}) and post-secondary sedimentation wastewater (*N*_{f}), and also to the temperature (*T*) of both AS and TF systems. For all PDF the lower bound limit was fixed as zero. For this, the chi-squared (Chi^{2}) goodness-of-fit statistic was performed using the statistical software @Risk, version 5.5.0 (Palisade Corporation, Ithaca, USA), which calculates the value of the Chi^{2} test for different theoretical distributions. Whether or not a particular PDF was chosen depended on the value of the Chi^{2} test and the probability–probability (P–P) goodness-of-fit plots generated. For the other parameters used in the proposed models, PDF were assumed in accordance with the literature, as follows: hydraulic retention time (t) (uniform PDF: min = 0.25; max = 0.33 d); *HLR* (uniform PDF: min = 1; max = 4 m^{3}.m^{−2}.d^{−1}); temperature coefficient (θ) (triangular PDF: min = 1.00; max = 1.19; most likely = 1.07); height (*h*) (uniform PDF: min = 1.8; max = 2.5 m); and porosity (*n*) (uniform PDF: min = 0.5; max = 0.6) (Marais 1974; Castagnino 1977; Thomann & Mueller 1997; Metcalf & Eddy 2003; von Sperling 2007b, c). The removal coefficients were then estimated by stochastic simulation (Equations 8, 9 and 10) with Latin Hypercube sampling and 100,000 iterations, again using the software @Risk, version 5.5.0 (Palisade Corporation, Ithaca, USA).

In order to verify the applicability of the proposed models, an exercise was undertaken to calculate the final concentrations (*N*_{f}) of somatic and F-specific coliphages in AS and TF effluents. For this, mean initial concentrations (*N*_{0}), obtained from the monitoring programme, and mean and median *K*_{20} values, obtained from the simulations, were used. The other parameters of the proposed models were assumed as follows: the AS sites studied demonstrated a mean hydraulic retention time (*t*) of 0.58 day, and the mean monitored temperature (*T*) of the settled wastewater was 17.53 °C; the TF plants comprised filter units with a mean height (h) of 2.10 m, a mean *HLR* of 1.52 m^{3}.m^{−2}.d^{−1}, and an average monitored temperature (*T*) of 16.54 °C. The porosity (*n*) of the packing medium in TF systems was considered to be 0.55.

## RESULTS AND DISCUSSION

Figure 1 presents the concentrations of somatic and F-specific coliphages in the settled wastewater (*N*_{o}) and post-secondary sedimentation wastewater (*N*_{f}) of both AS and TF systems. The initial and final concentrations of somatic coliphages were approximately 2 log_{10} higher than those of F-specific coliphages in the systems monitored. Furthermore, it is apparent that, in general, the concentrations of somatic coliphages varied more than those of F-specific coliphages. With regard to the geometric mean values of initial and final concentrations, the removal of somatic coliphages in the AS systems was of the order 1.86 log_{10}, while for F-specific coliphages it was 1.41 log_{10}. In the TF systems, the removal of somatic and F-specific coliphages was of the order 0.44 and 0.46 log_{10}, respectively. These results demonstrate that the removal rate of somatic coliphages was higher than that of F-specific coliphages in AS systems, while for TF, the removal rates of both phage groups were very similar. Furthermore, AS systems appear to remove both phage groups more effectively than TF systems. Similar removal rates of somatic and F-specific coliphages in AS systems and of somatic coliphages in TF systems have been reported by other investigators (Zhang & Farahbakhsh 2007; Ebdon *et al.* 2012; De Luca *et al.* 2013), but no study involving the removal of F-specific coliphages in TF systems has been identified in the scientific literature to date.

Probability distribution functions were fitted to the initial and final concentrations (*N*_{0} and *N*_{f}) and temperature (*T*) data collected using the chi-squared adherence tests, whereas for the other parameters (hydraulic retention time (*t*), *HLR*, temperature coefficient (θ), height (*h*), and porosity (*n*)) used in the proposed models, PDF were assumed in accordance with the literature, as previously described. Table 2 summarises the PDF of each input variable of the models. The removal coefficients were then estimated by stochastic simulation (Equations 8, 9 and 10) with Latin Hypercube sampling and 100,000 iterations using the software @Risk, version 5.5.0. Figure 2 presents the histograms, cumulative frequency curves and descriptive statistics for the removal coefficients at 20 °C for somatic and F-RNA coliphages in AS and TF systems.

Microorganisms | |||
---|---|---|---|

System | Input variable | Somatic coliphages | F-specific coliphages |

AS | N_{f} | LogN (1.29 × 10^{4}; 9.78 × 10^{3}) | Exp (1.74 × 10^{2}) |

N_{o} | Gamma (1.78; 5.75 × 10^{5}) | Gamma (0.35; 5.56 × 10^{4}) | |

θ | Triang (1.00; 1.07; 1.19) | Triang (1.00; 1.07; 1.19) | |

T | Weibull (6.86; 18.70) | Weibull (6.86; 18.70) | |

t | Uniform (0.25; 0.33) | Uniform (0.25; 0.33) | |

TF | N_{f} | Gamma (1.81; 3.31 × 10^{5}) | Weibull (0.77; 6.90 × 10^{3}) |

N_{o} | Exp (1.91 × 10^{6}) | LogN (2.52 × 10^{4}; 6.19 × 10^{4}) | |

θ | Triang (1.00; 1.07; 1.19) | Triang (1.00; 1.07; 1.19) | |

T | Weibull (6.88; 17.69) | Weibull (6.88; 17.69) | |

HLR | Uniform (1.0; 4.0) | Uniform (1.0; 4.0) | |

h | Uniform (1.8; 2.5) | Uniform (1.8; 2.5) | |

n | Uniform (0.5; 0.6) | Uniform (0.5; 0.6) |

Microorganisms | |||
---|---|---|---|

System | Input variable | Somatic coliphages | F-specific coliphages |

AS | N_{f} | LogN (1.29 × 10^{4}; 9.78 × 10^{3}) | Exp (1.74 × 10^{2}) |

N_{o} | Gamma (1.78; 5.75 × 10^{5}) | Gamma (0.35; 5.56 × 10^{4}) | |

θ | Triang (1.00; 1.07; 1.19) | Triang (1.00; 1.07; 1.19) | |

T | Weibull (6.86; 18.70) | Weibull (6.86; 18.70) | |

t | Uniform (0.25; 0.33) | Uniform (0.25; 0.33) | |

TF | N_{f} | Gamma (1.81; 3.31 × 10^{5}) | Weibull (0.77; 6.90 × 10^{3}) |

N_{o} | Exp (1.91 × 10^{6}) | LogN (2.52 × 10^{4}; 6.19 × 10^{4}) | |

θ | Triang (1.00; 1.07; 1.19) | Triang (1.00; 1.07; 1.19) | |

T | Weibull (6.88; 17.69) | Weibull (6.88; 17.69) | |

HLR | Uniform (1.0; 4.0) | Uniform (1.0; 4.0) | |

h | Uniform (1.8; 2.5) | Uniform (1.8; 2.5) | |

n | Uniform (0.5; 0.6) | Uniform (0.5; 0.6) |

^{a}Exp (λ) = exponential distribution with decay constant λ; Gamma (α; β) = gamma distribution with shape parameter α and scale parameter β; LogN (μ; σ) = lognormal distribution with specific mean μ and standard deviation σ; Triang (min; most likely; max) = triangular distribution with defined minimum, most likely and maximum values; Uniform (min; max) = uniform distribution between minimum and maximum; Weibull (α; β) = Weibull distribution with shape parameter α and scale parameter β.

Stochastic modelling revealed that the *K*_{20} values for the AS systems were an order of magnitude higher than those of the TF systems, possibly as a result of the different models used for each system. Median *K*_{20} values for AS were 324.4 d^{−1} for somatic coliphages and 215.3 d^{−1} for F-specific coliphages (Figure 2(a) and 2(b)), while median *K*_{20} values for TF were 2.33 and 2.18 d^{−1} for somatic and F-specific coliphages, respectively (Figure 2(c) and 2(d)). With regard to the mean values of *K*_{20}, the numbers were higher for both systems: 549.9 and 5822.1 d^{−1} for somatic and F-specific coliphages, respectively, in AS systems (Figure 2(a) and 2(b)); 2.65 and 3.18 d^{−1} for somatic and F-specific coliphages, respectively, in TF systems (Figure 2(c) and 2(d)).

The differences between *K*_{20} values obtained here for each system, and more specifically the considerably higher *K*_{20} values observed for TF systems compared with AS systems, could be explained by the inability of the idealised models to describe accurately the hydrodynamics of real reactors. As mentioned by von Sperling (2007a), even for the same conditions (initial and final concentrations, hydraulic retention time), the equations representing the ideal plug-flow and complete-mix reactors would result in different removal coefficient (*K*) values. This is because, in theory, the ideal complete-mix reactors are the least efficient reactors for first-order removal kinetics. In other words, the lower efficiency is compensated for by a higher *K* value (von Sperling 2007a). Conversely, ideal plug-flow reactors are the most efficient reactors, and the *K* value necessary to produce the same effluent quality is reduced (von Sperling 2007a). It is important to highlight that, in the study described here, simple ideal complete-mix and plug-flow reactor models were used to describe the hydraulics of AS and TF systems, respectively, which, again, could explain the discrepancy between the *K*_{20} values observed for both systems. However, in order to overcome the limitation outlined above, more complex dispersed flow models can be used.

The *K*_{20} values for TF systems previously discussed, given as d^{−1}, were obtained from Equation (9) for comparison with the *K*_{20} of AS systems (Equation (8)). However, the parameter that is normally used for the design of biofilters is the *HLR*. Thus, Equation (10) was also used to calculate *K*_{20} values for TF systems, given as m^{3}.m^{−2}.d^{−1}. Using both Equations (9) and (10), median *K*_{20} values were very similar for each microorganism: 2.33 and 2.18 d^{−1} for somatic and F-specific coliphages, respectively, from Equation (9); and 2.76 and 2.58 m^{3}.m^{−2}.d^{−1} for somatic and F-specific coliphages, respectively, from Equation (10) (Figure 2(c)–2(f)). Again, mean values of *K*_{20} were higher than median values, but were similar for each microorganism: 2.65 and 3.18 d^{−1} for somatic and F-specific coliphages, respectively, from Equation (9); and 3.10 and 3.71 m^{3}.m^{−2}.d^{−1} for somatic and F-specific coliphages, respectively, from Equation (10) (Figure 2(c)–2(f)). The similar values of *K*_{20} obtained from Equations (9) and (10) result from the PDF assumed for the input variables height (*h*) (uniform PDF: min = 1.8; max = 2.5 m) and porosity (*n*) (uniform PDF: min = 0.5; max = 0.6) in Equation (10).

Interestingly, the cumulative frequency curves for both AS and TF were markedly different in their appearance, as the output data are skewed towards the left side of the distribution for both phage groups in the AS systems (Figure 2(a) and 2(b)), while in the TF systems, the data appear to follow a normal distribution (Figure 2(c)–2(f)). With regard to the variation around the mean/median values, the standard deviation was higher for F-specific coliphages than for somatic coliphages, in both the AS and TF systems (Figure 2).

In order to verify the effectiveness of the proposed models (Equations (8), (9) and (10)), the final concentrations (*N*_{f}) of somatic and F-specific coliphages in AS and TF effluents were estimated using the mean and median values of *K*_{20} that were obtained from the simulations (Figure 2). A summary of the observed and estimated N_{f} values is presented in Table 3. In general, the proposed models appear to overestimate slightly the removal of the two studied microorganisms in both AS and TF systems, though monitored and estimated *N*_{f} values were very similar. All but one of the estimated final concentrations, calculated using either the mean or median value of *K*_{20}, were lower than the observed concentrations (Table 3). In only a single case (final concentration of F-specific coliphages in AS effluent estimated using the median value of *K*_{20}) was the estimated *N*_{f} higher than the observed *N*_{f} (Table 3). For TF systems, the plug-flow model based on the *HLR* was shown to describe better the removal of the two studied microorganisms compared with the same model based on the hydraulic retention time (*t*). Comparing the use of mean and median values of *K*_{20}, the first of these appears to estimate better the removal of somatic and F-specific coliphages in both AS and TF systems. Therefore, because the *N*_{f} estimated values were very close to the *N*_{f} observed values, the simplified models proposed here appear to be a useful tool to estimate the removal of the two studied microorganisms in AS and TF systems. A review of the available literature suggests that the approach taken here is innovative and the authors envisage that the value of applying simplified models to estimate the removal of microorganisms in conventional WWTPs, such as AS and TF systems, will be further supported by the application of the approach in future studies.

Somatic coliphages | F-specific coliphages | |||||
---|---|---|---|---|---|---|

Estimated using: | Estimated using: | |||||

System | Observed^{a} | Mean K_{20} | Median K_{20} | Observed^{a} | Mean K_{20} | Median K_{20} |

AS^{b} | 4.13 | 3.58 | 3.80 | 2.24 | 0.84 | 2.26 |

TF^{c} | 5.78 | 5.59 | 5.67 | 3.90 | 3.49 | 3.75 |

TF^{d} | 5.78 | 5.68 | 5.75 | 3.90 | 3.60 | 3.83 |

Somatic coliphages | F-specific coliphages | |||||
---|---|---|---|---|---|---|

Estimated using: | Estimated using: | |||||

System | Observed^{a} | Mean K_{20} | Median K_{20} | Observed^{a} | Mean K_{20} | Median K_{20} |

AS^{b} | 4.13 | 3.58 | 3.80 | 2.24 | 0.84 | 2.26 |

TF^{c} | 5.78 | 5.59 | 5.67 | 3.90 | 3.49 | 3.75 |

TF^{d} | 5.78 | 5.68 | 5.75 | 3.90 | 3.60 | 3.83 |

Concentrations given as pfu.100 mL^{-1}; ^{a}Mean of observed concentrations; ^{b}Complete-mix model based on the hydraulic retention time (t); ^{c}Plug-flow model based on the hydraulic retention time (t); ^{d}Plug-flow model based on the hydraulic loading rate (*HLR*).

## CONCLUSION

This study has demonstrated that the removal of somatic coliphages in both AS and TF systems is higher than that of F-RNA coliphages and that AS more effectively removes both phage groups than TF systems. If similar patterns are observed for human pathogenic viruses in similar treatment systems, the assumption that phages may be good indicators of viral pathogens is corroborated. Furthermore, this study has demonstrated that appropriate forms of stochastic modelling may elucidate the behaviour of enteric bacteriophages in traditional biological wastewater treatment processes. Moreover, using the approach outlined here it may be possible to export the results obtained from monitored treatment systems to other similar treatment systems in order to predict final concentrations of bacteriophages using simple models. However, the outcome of this approach should be interpreted with caution, as simplified models potentially inadequately represent the complex hydrodynamic characteristics of real reactors, which depend on flow turbulence, reactor dead volumes and hydraulic short circuits that may be present in such systems. Although system-specific information about these parameters could be obtained by performing non-reactive tracer studies, a key advantage of the stochastic modelling approach used here is that it can take into account variations observed around specific parameters.

Future work will compare the behaviour of these novel indicators with the behaviour of specific enteric viral pathogens of human health significance. It is envisaged that the research will contribute new knowledge to inform better design and more effective operation of wastewater treatment systems. At a time when greater emphasis is being placed on human health protection by minimising the transmission of pathogens at several points within the water cycle, this work will support more integrated water and sanitation safety planning approaches to human health risk management.

## ACKNOWLEDGEMENTS

The authors would like to thank the Brazilian programme Science without Borders for funding the PhD studies of Edgard Dias, and also Southern Water Services Ltd for its cooperation. This paper was presented at WWTmod2014 and the fruitful discussions that followed are also kindly acknowledged.