Modeling of ultraviolet ( UV ) radiation under a large pilot-scale designed for wastewater disinfection and inactivation of selected bacteria of Pseudomonas aeruginosa in a laboratory UV device

The aim of this paper was to propose a modeling system of water ultraviolet (UV) disinfection. Results reveal that application of the model of Chick-Watson in its original form or modified are not representative of the kinetics of disinfection. For this reason, the application of a new kinetic model of Collins-Selleck in UV inactivation of Pseudomonas aeruginosa in secondary wastewater appeared to be the best applied model. The modeling of the reactivation process at range of 7.5-50°C temperature was shown. First-order saturation does not fit the obtained data in photoreactivation; a modification of the model is proposed coinciding with the classical logistic equation. To better explain the process of inactivation, we have assumed that the action of disinfectant on the survival of lonely microorganisms is faster than its action on suspended solids protected or agglomerated to each other. For this reason, the application of a new kinetic model by introducing a third factor reflecting the influence of suspended solids in water on disinfection kinetics appeared to be determinant for modeling UV inactivation of P. aeruginosa in secondary treated wastewater.


INTRODUCTION
Many pathogens are responsible for waterborne diseases.Currently, despite the development of mole-cular methods, most studies in this area were mainly focused on the concentration of fecal indicator bacteria to *Corresponding author.E-mail: brahmounaouer@yahoo.fr.Tel: +216 79412199.Fax: +216 79412802.
Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abbreviations: FLW, Fermented liquid whey; LAB, lactic acid bacteria; MDA, malondialdihyde, MUFA, monounsaturated fatty acid; PUFA, polyunsaturated fatty acid; SFA, saturated fatty acid; TBARS, thiobarbituric acid reactive substance.estimate the population of pathogens.Recent studies showed that the species of P. aeruginosa are valid indicator of the water sanitary quality (Xuexiang et al., 2012;Brahmi et al., 2010).This parameter is actually used as a criterion in the regulation of wading and swimming pools.Likewise, the absence of P. aeruginosa is important not only in terms of its role as an indicator, but also because it is an opportunistic pathogen whose transmission is often associated with water.Its use for evaluating the effectiveness of a treatment of UV disinfection seems therefore reliable.
Ultraviolet (UV)-C (short-wavelength ultraviolet) radiation has been suggested as one of the successful disinfection practices for water treatment.Therefore, UVdisinfection has become a practical solution for the safe disinfection of water.
Actually, UV-disinfection has gained widespread use for municipal wastewater and more recently, interest in using UV for water reuse applications has also increased (Kamani et al., 2006).It accepts the following inherent advantages over all other disinfection methods: no chemical consumption, thereby wiping out large scale storage; no transit, handling and potential safety risks; low contact time; no contact basin is necessary and space demands are thus brought down; no harmful byproducts are formed; a minimum of, or no, moving sections; and high reliability and low energy requirements (USEPA, 2003b).
UV 254 radiations interact with nucleic acids and other cellular compounds, such as proteins and lipids (USEPA, 2003b).The knowledge acquired in this study indicates the use of UVc for disinfection is a quick, effective, secure and cost-effective (Meiting et al., 2009).It has been practiced for many years in several countries to disinfect water (USEPA, 2003b).However, microorganisms have evolved repair and can reactivate, once their DNA is partially denatured.Visible light and time may have a positive influence on this process known as reactivation (Eccleston, 1998).UV-disinfection of water employs low-pressure mercury lamps.The lamps generate short-wave UV radiation at 253.7 nm, which is lethal to micro-organisms, including bacteria, protozoa, viruses, molds, yeasts, fungi, nematode eggs and algae.
The mechanism of micro-organisms destruction is currently believed to be that in which UV causes molecular rearrangements in DNA and RNA, which in turn blocks replication (Brahmi and Hassen, 2012).The adoption of UV-disinfection at wastewater plants treating in excess of one billion gallons daily is proof that UV is no longer an emerging technology, but quite an accepted technology to be applied routinely by engineers to safeguard human health and alleviate environmental pressures.Wastewater reuse has been drilled in several configurations for decades, with the United States leading the way in reuse research.It is nowadays a major topic in the U.S., where large areas of the Western and Southern states experience chronic water shortages (Min et al., 2006).
UV water purification lamps produce UV-C or germicidal UV, with radiation of much greater intensity than sunlight.Virtually, entirely a UV lamp's output is concentrated in a 254 nm region in order to get total advantage of the germicidal properties of this wavelength.Most UV purification systems are combined with various forms of filtration, as UV light is only capable of killing micro-organisms such as bacteria, viruses, molds, algae, yeast and oocysts such as Cryptosporidium and Giardia.UV light generally has no impact on chlorine, volatile organic compounds (VOCs), heavy metals and other chemical contaminants (Oparaku et al., 2011).
The models are based on a mathematical representation of the mechanisms that govern natural phenomena to explain a procedure by identifying some variables or the main factors prevailing to suggest a representation or a simulation that will be interpretable and reproducible (Sterman, 2002).For disinfection, modeling helps to accept a mathematical expression of the disinfection kinetics needed for predicting performance of a reactor operating under conditions similar to that experience.However, exposed micro-organisms may repair damage and can be reactivated.Storing of microbial irradiated cells under visible light condition may have a positive influence on the reactivation, and this is commonly known as photoreactivation.Only UV lamps with low or medium pressure are capable of destroying cellular components such as proteins and enzymes, by preventing cell reactivation.This is justified when the water to be treated must meet certain conditions to get the best effect of UV radiation.The different compounds of water may weaken the transmission rate and deposits can also smear the UV reactor and clog quartz tubes protecting the UV lamp (Oparaku et al., 2011;Sellami et al., 2003).The regular replacement of UV lamps and cleaning their ducts provide good permeability to UV and so increase the UV treatment effectiveness.
Several parameters can influence the rate of inactivetion of micro-organisms such as the physical-chemical parameters (pH, temperature, etc), the UV dose applied, the UV-water contact time, and the number and the type of microorganisms existing in the water.The relationship between these parameters can be evaluated using analytical measurements in the laboratory.
This research was aimed at first to understand and evaluate the germicidal UV water disinfection, secondly to establish the influence of UV doses on the kinetics of disinfection, to study UV-resistant strains of Pseudomonas aeruginosa, to study the phenomenon of photoreactivation and thirdly to establish and to diagnose a mathematical model for simulation and improvement of the UV C water disinfection.
Meanwhile, another important target of this work was to study the influence of suspended solids on the kinetics of disinfection and to exploit the results for proposing a formulation of the UV disinfection kinetic of secondary treated wastewater.

Main characteristics of treated wastewater
The wastewater sampled in this study was collected at the outflow of trickling filter of the pilot wastewater treatment plant (WWTP) belonging to the Water Research and Technology Center, Tunisia.The WWTP is connected to the sewage network of the city of Tunis and it has a processing capacity of 150 m 3 per day.The pilot plant is composed of four treatment lines running in parallel: trickling filter.It is composed of four treatment lines operating in parallel: trickling filter, rotating biological discs, soil and lagoon optional filter.The values fluctuated between 47 to 49% for UV transmission, 15 to 27 mg L -1 for total suspended solids (TSS), 20 to 29 mg L -1 for BOD 5 and 90 to 102 mg L -1 for COD.

UV processing
The laboratory UV device used in this study was previously described by Hassen et al. (2000).A collection of 22 strains of Pseudomonas aeruginosa was used in this work.This collection includes 20 strains of clinical origin (hospital of La Rabta, Service of Bacteriology, Dr C. Fendri, Tunis, Tunisia).Strains 21 and 22 were isolated from raw wastewater of the pilot plant.All these strains were grown in the laboratory for long periods on a nutrient broth (Institute Pasteur production).These 22 strains were referenced from S1 to S22, respectively.
All bacterial strains were cultivated to mid-log phase at 37°C in 20 mL of nutrient broth.Each culture was centrifuged at 5000 xg min -1 for 15 min and the pellet was washed twice with sterilized distilled water.The washed pellet was then suspended in 10 mL of sterilized distilled water.Test organisms were afterwards seeded separately into 20 mL of sterilized wastewater having a UV transmittance of 50%, to give a viable cell count of approximately 10 5 to 10 6 mL -1 , the same mean count as in the secondary-treated wastewater.
The suspension was exposed to UV light for periods varying from 2 to 90 s.All irradiation experiments were performed at laboratory temperature of 25 ± 5°C.Petri dishes of 90 mm diameter, containing 20 mL of seeded wastewater, were shaken carefully with a mechanical shaker (Edmond Bühler) for at least 15 min in order to remove all bacterial aggregates.Seeded wastewater served for counting bacteria, before (N 0 ) and after exposure (N) to a definite UV dose.For bacteria counting, a volume of 100 µL collected from decimal dilution of each sample was placed on the surface.Petri dishes contain nutrient agar (Pasteur Institute Production, Paris).After incubation at 37°C for 24 h, colonies were counted and the results were expressed by colony-forming units, CFU/mL.
The layer of water crossed with UV rays was 3-mm depth and each experiment was repeated at least four times.Measurements of incident intensity at the liquid surface, at 254 nm, were made with a Vilbert-Lourmat digital radiometer.
Irradiation dose (mW.s.cm -2 ) was determined as the average incident intensity over exposure time and regulated by controlling the exposure time.A low-pressure mercury vapor discharge lamp that emits short-wave ultraviolet radiation with a radiation peak at 253.7 nm (UV-C) for germicidal action UV-C was used.This lamp emitted an average intensity of about 7 mW.cm 2 .To avoid the phenomenon of photoreactivation, bacterial counting was performed immediately by standards decimal dilution method using the nutrient agar medium.

Mounaouer and Abdennaceur 1737
Photoreactivation study To confirm the DNA repair after a visible light exposure of bacteria previously irradiated by UV 254 , only 3 strains of P. aeruginosa S1, S2 and S5, respectively, were chosen arbitrary.Similarly, only one strain S5 was used arbitrarily to verify the possible application of Kashimada penny model on its original form and to show if this model is representative or not, mainly, when an induction period appeared.
All strains were cultivated to mid-log phase (at 37°C) in nutrient broth and cell suspensions were treated as previously described.Test organisms were then seeded separately into 20 mL of sterile distilled water on the basis of 10 5 -10 6 bacteria/ml and exposed to the UV light during 50 s with a relatively fixed UV intensity of 7 mW cm -2 which corresponds to approximately UV 254 dose of 80 mW.s.cm -2 .The UV dose supplied was calculated as a product of the average UV intensity rate into the reactor (mW.cm -2 ) and the irradiation time (s).Irradiation was performed at room temperature, between 25 and 30°C.
Each suspension of bacteria was collected and divided before and after exposure to the UV illumination in two sterile flasks for microbiological assays.Three of the six sterile flasks were exposed to laboratory light for 0, 4, 8 and 12 h, and the enumeration of cultivable bacteria was then carried out as previously summarized.The other three sterile flasks were covered immediately with aluminum foil and incubated at room temperature for 12 h (dark repair).
All reactivation experiments (photoreactivation and dark repair) were repeated at least five times and data were subjected to analysis of variance, and means were separated by the leastsignificant-difference, according to the Student Newman-Keuls test (SPSS for Windows, SPSS, 17 June, 1993).
To further confirm the process of photoreactivation according to the Student Newman-Keuls test (SPSS for Windows, SPSS, 17 June, 1993) and to better visualize the influence of temperature on the process, the same protocol of preparation of strains was suggested as previously described.After UV-C radiation, each suspension of bacteria was transferred into sterile flasks for microbiological assays (95% transparent for 360 nm light).The three sterile flasks were thermostated in a controlled-environment incubator (refrigerated incubator, model no.FOC 225E; VELP Scientifica), which was equipped with one fluorescent lamp (3.7 W; Philips TLD) at six different temperatures: 7.5; 12.5; 17.5; 22.5; 27.5; 37 and 50°C (photoreactivation).Irradiation periods were in the range of 60 to 480 min.
The count of bacteria was made every 60 min by standards decimal dilution method using the nutrient agar medium.This second data photoreactivation experiments were replicated at least five times.All data photoreactivation experiments were subjected, firstly for analysis of variance, and means were separated by the least significant difference, according to the Student Newman-Keuls test (SPSS for Windows, SPSS, 17 June, 1993); secondly, to adapt the kinetic model (Kashimada et al., 1996) as proposed.

Effects of bacterial density associated with particulate matter
Bacteria in wastewater are often bonded together as a floc, or associated with particulate matter (suspended solids).The bacterial density associated with particulate matter, Np, can be achieved by the UV process, and is determined as a function of suspended solid (SS) concentration (a regression analysis of the log of the effluent (after exposure) P. aeruginosa density as a function of the log of the effluent SS concentration showed the relationship to be linear).The linear regression analysis of the combined data yielded the expression: Np= a (Sheible, 1987).

The kinetic models used for UV-C inactivation
The design and the management of the disinfection systems require knowledge of the removal kinetics of pathogenic microorganisms to control the influence of UV dose on disinfection kinetics (Brahmi et al., 2010).To determine the best combination of contact time-UV dose and to predict the yield of UV disinfection, we used more or less empirical approaches.The simulation models, from the simplest, model of Chick-Watson (Chick, 1908;Watson, 1908) reduced to first-order kinetics, to complex model such as Collin Selleck (1972) model.The model of Chick-Watson is primarily used to express the kinetics of disinfection with chemical disinfectants (Hart and Votgiatzis, 1982;Roustan et al., 1991).The first-order kinetics is expressed as follows: The integration of this expression gives: C: Concentration of disinfectant in the environment; K: A coefficient reflecting the specific case of disinfecting lethality potential; n: Coefficient of dilution, which is a function of disinfectant and pH of the medium (the value of n is usually close to unit) and t: Exposure time to disinfect.
In the case of UV disinfection, an amendment to this model in replacing the concentration of chemical disinfectant (C) by the intensity of UV radiation is done as proposed by Haas (1990).The disinfection kinetics could be rewritten as follows: The integration of this expression gives: - The change in logarithmic form and using a linear regression, the kinetic parameters (K and n) of the latter expression could be determined as follows: When, n < 1, the disinfection process is more controlled by the contact time than the UV dose.When n > 1, the UV dose takes precedence over the contact time in the control of the process (Leahy et al., 1987).

Modeling of the kinetics of disinfection by UV irradiation
In this study, the determination of ε, a representative parameter of the difference between the experimental values (N/N 0 ) mes and values calculated by the model (N/N 0 ) cal , appears important for all strains (Tables 1 and  2).Therefore, the model of Chick-Watson, reduced to a first-order kinetic with n = 1, showing its limits, and that the inactivation process is most often non-uniform, and does not necessarily comply, as implies a first-order kinetics, with an exponential law (Shayeb et al., 1998;Nicholson and Galeano, 2003).In addition, the adopted experimental protocol showed a very noticeable reduction rate for low doses of irradiation.
The importance of UV radiation intensity of the lamp allows achieving a yield rate of 2 log-units after only 2 s of exposure.A reduction of additional log-units could not be reached, even after an exposure time of 90 s.To improve the representativeness of the model of Chick-Watson, taking into account the decrease in speed during the disinfection process, the existence of two stages, each with different kinetics is admitted (Figure 1).Fast inactivation kinetics with doses varying between 0 and 200 (mW.s. cm -2 ) and a coefficient of lethality ranging between -0.0259, -0.0689 and -0.056 for strains S3, S14 and S15, respectively, were taken as examples.Slow kinetics with doses ranging between 200 and 600 (mW.s. cm -2 ), and a coefficient of relative low lethality situated between -0.0012 and -0.0034 have been reported by several authors (Mamane-Gravetz and Linden, 2005; Manas and Pagan, 2005).It is therefore necessary to assume the existence of at least two stages during the inactivation process of which only the second was explored during the tests.
The application of a first order kinetic during the second stage needs to adjust the model by introducing a dimensionless coefficient A, to reflect the decline achieved during the first fast kinetics stage (Mamane- Gravetz and Linden, 2004).The expression of bacterial inactivation model becomes as follows: With A representing the initial decline or decrease in the number of bacteria.The parameters to identify in this case are, K and A.
In the same way, passing to the logarithm scale, the expression becomes: The kinetic equations and the coefficient of reliability of the model for each strain studied were seen utilizing a linear regression.The kinetic parameters of this modified model (A, K, R 2 and ε) are listed in Tables 1 and 2. Results showed a remarkable similarity between the values of the kinetic constant K for some strains, despite the divergence observed for the values of the initial abatement A. This result showed that these strains therefore follow the same kinetics of disinfection.
By calculating the difference these two models, the values obtained using the model of Chick-Watson in its modified form appeared smaller than those calculated using the same model in its initial form.
In the same way, the coefficients of determination, R 2 obtained using the amended model of Chick-Watson were generally higher than those obtained using the same model in its original form.Thus, the adjustment of the same model but considering an initial decline describes quite well the kinetics of disinfection for most of the studied strains.

 
A key feature of kinetic modelling is not only to simplify, but also to idealize a complex phenomenon of the disinfection systems.Observation and mathematical modelling of microbial inactivation provides indirect information on the physiological mechanism of inactivetion and, conversely, the mechanisms of resistance.Various models have been suggested to explain the kinetics of inactivation resulting in the existence of latency period following the contact of water and disinfectant (Fair et al., 1948;Shayeb et al., 1998).During this period, the decrease rate of number of bacteria is not measurable and quantifiable.This fact was observed for Escherichia coli in the presence of chlorine dioxide taken as disinfectant (Kerwick et al., 2005).The latency period may also be due to the probability of contact between the disinfectant molecules and microorganisms present in water as conglomerates of different sizes (Mounaouer and Hassen, 2011).The existence of many species of microorganisms and their varying sensitivities to the product used for disinfection may also explain the latency period, which is detected through a comprehensive measure giving an apparent rate of inactivation (Berney et al., 2006).
In UV disinfection, several models, for instance, the model of Collins-Selleck (1992), Series event model (Isaac et al., 2007) and the multi-shock model (Kowalski and Witham, 2001) have been built up to identify the initial plateau observed when microorganisms are exposed to a sublethal UV dose.In this case, bacterial inactivation is not significant and the decline is of low amplitude (Pruitt and Kamau, 1993;Kowalski et al., 2000).This latency phase of inactivation for certain strains of P. aeruginosa, using UV low doses, has been observed (Figure 1) (Brahmi et al., 2010) and put into evidence by the model proposed by Collins and Selleck (1972) cited by Li et al. (2002).
On the other hand, a stage of initial delay was sometimes found in the majority of bacterial strains used in this experiment (Brahmi et al., 2010).The use of the proposed model of Collins and Selleck (1972) was justified in this situation (Li et al., 2002).In fact, besides the slowdown in the inactivation rate for high doses of UV radiation (Shayeb et al., 1998), this model admits the existence of a period of initial latency.The two following relations expressed this model:  is the least dose of radiation to be reached to start the process of micro-organism inactivation, n: a constant, I: the radiation intensity and t is the exposure time.
Accordingly, the parameters  and n could be determined by the transition to the logarithmic form and using a linear fit showed, for instance, the position of experimental points as compared to the curve of adjustment for the studied strains.The obtained values seemed to be valid for all examined strains, below the UV dose of 5.5 (mW.s.cm -2 ).In the same way, the determination of ε, a parameter representing the difference between the measured values (N/N 0 ) mes and the calculated ones by the model (N/N 0 ) cal , appeared very low for all strains as compared to the values calculated using the model of Chick-Watson in its original or modified form (Tables 2  and 3).Consequently, the model of Collins and Selleck was likely to be the most efficient in terms of changing kinetics during the disinfection process.
For overall approach (Figure 2), and for all regression models, the correlation coefficient (R 2 ) varies from 0.17 for the original Chick-Watson, 0.33 for the amended Chick-Watson model and 0.69 for Collin-Selleck, respectively.Agreeing to this criterion, a sufficient part of the variability of response may be due the explanatory variables.Still, even an R 2 close to 1 is not always a sufficient criterion to validate the quality of a regression model (Thomas et al., 2010).Consequently, other criteria must be analyzed for a better description and better understanding of phenomena involved in the kinetics of inactivation.
In this regard, the determination of ε by the comprehensive approach seems to be important.This parameter is variable, 0.35, 0013 and 0.0071 for the original Chick-Watson, amended Chick-Watson and Collin-Selleck, respectively.As compared to all existing models and based on these two parameters (R 2 and ε), the model of Collin-Selleck gave the best results for describing the inactivation curves of P. aeruginosa.(Figure 2)

Impact of suspended solids content on UV disinfection
The turbidity of water makes the UV ray transmission difficult and therefore reduces their effectiveness.Scheible (1987) found that the number of fecal coliform associated with suspended particles was dependent on water solid content.He proposes to subdivide the whole micro-organism load in water into two categories: microorganisms isolated and so vulnerable, and microorganisms associated with suspended particles and so invulnerable.This subdivision of microorganisms in two groups led to the following expression of inactivation kinetics: Where, N 0 is the number of micro-organisms isolated per unit volume of water (N' 0 = N 0 -Np); Np is the number of micro-organisms per unit volume of water inaccessible to UV radiation; and N' is the number of micro-organisms remaining after water treatment with UV radiation D (N' = N -Np).Agreeing to this model, it was accepted that the ]; S m : the maximum limit of the survival ratio of the microorganisms by reactivation (S m = 100 x (N m /N o )); where, N m is the maximum concentration of microorganisms reached by reactivation and N o is the concentration of microorganisms before disinfection (% survival).isolated micro-organisms were inactivated according to first-order kinetics.It was also recognized that a residual number of micro-organisms (Np) persist in the water, whatever the radiation dose applied.Under these adopted operating conditions, it was not possible to fall below a level of microorganisms of 10 3 per 100 mL for most of the tested strains.During the experimental study, the physico-chemical characteristics of treated wastewater by trickling filter did not greatly change.
Values fluctuated between 47 and 49% for UV transmission and 15 and 27 mg/L for total suspended solids (TSS) on average.This concentration of suspended particles was unlikely to be the only reason for hindering the process of inactivation at this high level.
Other factors related to the operating conditions or to the type of micro-organisms could have been responsible for this observation.The research work of Scheible (1987) on the installation of Port Richmond in France has led to propose a power function expressed as follows: Where, Css is the concentration of suspended solids in water; a, b are two constants.For fecal coliform, a and b were 0.26 and 1.96, respectively (Scheible, 1987).In the case of treated wastewater by trickling filter and for all studied strains of P. aeruginosa, these constants were As mentioned above, we assumed that the microorganisms were inactivated according to first-order kinetics and that the experimental exploration only concerned with the second stage of inactivation process.The number of microorganisms that are still viable in water having received a D dose of UV radiation is thus given by: The product AN' 0 represents the number of microorganisms still viable at the end of the first and fastest stage of UV inactivation process.In the case of P. aeruginosa and the treated wastewater used, this relationship was: 4 .9 7 0 . 2 8 C s s + -0 .0 0 0 0 7 D e ' 0 0 .0 5 5 5 N = N ' (15) This equation could be written as the form below based on the experimental results illustrated in Figure 3.We have reported the first-order kinetics frequently observed during the inactivation of different types of abatement).Beyond this limit, a slowdown in inactivation microorganisms with a certain limit (nearly 2 U-log of rate was often noticed.This decrease in radiation efficiency, usually observed when increasing the radiation dose, was often attributed at first to the formation of microorganism aggregates, and secondly to the association of these microorganisms with suspended particles in water.Aggregate-borne microorganisms are protected against the action of UV rays.As previously underlined.Scheible, (1987) divided all microorganisms into two types: free or isolated microorganisms and those associated with suspended solid particles in water.It is assumed that only the first type was available to UV radiation, and therefore vulnerable.By slightly deviating from this hypothesis, we assume that two categories of microbiological population existed in water: 1. Microorganisms which, for one reason or another, were readily exposed to radiation.The rate of inactivation of these microorganisms is rapid.2. Microorganisms less accessible to radiation, therefore inactivated according to a slower kinetic.
By assuming that these two concomitant mechanisms of the first order were independent, we can express the rate of inactivation of the total number of microorganisms by applying the multi kinetics model of first order, expressed by the relationship as follows: Where, P is a fraction of microorganisms which is more susceptible to UV radiation; D is UV dose in (mW.s cm -2 ); K 1 and K 2 : Kinetic constants for each class of microorganisms.
In this study, the applicability of this model was tested to characterize the inactivation of P. aeruginosa in treated wastewater by determining the values of the constants p,  K 1 and K 2 (Figure 5).We were able to express the turnover rate by the following equation: 0 .0 0 6 D -0 .0 0 1 9 e + 0 .0 7 1 D -0 .9 9 8 1 e = 0 N N This model assumed that it was yet possible to reach the complete inactivation of all microorganis ms if we applied enough UV dose.We noted, however, that during UV disinfection experiments, it was practically not possible to lead down under a sure degree of abatement.Shawn et al. (2011) attributed this fact to the high concentration of suspended solids in water.To integrate this concept, we assumed that the fraction of the vulnerable microbiological population in water does not exhibit the same sensitivity to UV radiation.In the case of homogeneous populations, the non-uniformity of radiation throughout the reactor's area (irradiation room) or the heterogeneity of the environment might explain the non-uniformity of radiation efficacy.The status of an organism with regard to radiation source and the nature of the environment penetrated by rays have a substantial influence on the kinetics of inactivation.Taking into consideration the experimental results shown in Tables 1 and 2, three main stages could be identified as follows: 1.A first point during which the density of microorganisms is important, therefore, radiation efficiency is the superlative.During this stage, the most vulnerable microorganisms are inactivated.2. A second stage concerning lonely organisms, but less accessible to the radiation, hence showing a slower rate of inactivation.3. A third stage related to organisms which are inaccessible to radiation because they are associated with suspended solid particles.During this period, the number of viable microorganisms remain stable.This result corresponds to a null inactivation kinetic.Taking into consideration this approach, the number of microorganisms remaining viable in water and irradiated with a D dose was given by the following expression: The characteristic kinetic parameters of P. aeruginosa  inactivation in secondary treated wastewater used in this study were 0.9529 for p, 0.047 for K 1 and 0.00007 for K 2 , respectively; for this reason, the expression became: 4 .9 7 0 . 2 8 C s s + 0 .0 0 0 0 7 D -0 .0 4 7 1 e + 0 .0 4 7 D -0 .9 5 2 9 e 4 .9 7 0 . 2 8 C s s An illustration of this model is shown in Figure 4.

Impact of temperature on the photoreactivation repair
Reactivation is frequently expressed as a function of the survival ratio with respect to the initial microorganism concentration existing before the inactivation treatment.Therefore, survival values were calculated using the following equation: Where, S is the survival ratio at time t, N o is the concentration of microorganisms before disinfection (bacteria/100 ml), and N r is the concentration at time t after the beginning of the reactivation phase bacteria/100 ml).A typical inactivation-reactivation curve as a function of time is shown by Salcedo et al. (2007).In the figure, it is possible to separate the various phases of (the process: exponential UV inactivation and the reactivation process, which includes an induction period, the growth phase, the stabilization phase and the decay period.To study the photoreactivation kinetic, Kashimada et al. (2006) proposed an asymptotic model, simulating that the photoreactivation phenomenon follows a saturation-type first-order reaction, as expressed by the following equation: Where S m is the maximum survival ratio (N m /N o • 100 [N m is the maximum concentration of microorganisms {bacteria/100 ml}]) and k 1 is the first-order reactivation rate constant.As the survival ratio, S is achieving its upper limit value (Sm), the process decelerates, showing an asymptotic tendency (Figure 5).
After application of the model of Kashimada et al. (2006), results showed that the model did not fit the data correctly, mainly at the beginning of the curve, when an induction period is observed (Figure 5).Hence, by utilizing the new model represented by Equation 3, the relationship became a combination of the second-order equation and the driving force concept employed by Kashimada et al. (2006).
Where k 2 is the new growth, second-order reactivation rate constant.The equation is really not new because it coincides in its mathematical form with the logistic equation proposed by Verhulst (1883) to interpret the biological population growth.Nevertheless, the originality of our work acted in the innovative application of the equation to microorganism reactivation prediction.The model has the advantage that both kinetic parameters, S m and k 2 , have clear physical significance.On one hand, S m is the maximum limit of the survival of the microorganisms by reactivation and, on the other hand, k 2 represents the rate at which that value is reached.It can be visualized in Figure 5 that this proposed model fits correctly the experimental data.
By the integration of Equation 23, the following equation is obtained: Where S o is the survival immediately after UV disinfection (N d /N o • 100 [N d is the concentration of microorganisms after disinfection {before reactivation} {bacteria/100 ml}]).
From equation 24, it is possible to express the variable S as a function of the kinetic parameter k 2 , S m , S o and time (equation 24) and, as a result, both parameters S m and k 2 were related by nonlinear regression: Equation 13 allows the photoreactivation curve to be simulated over time (Figure 6).As stated, reference strains were exposed to an inactivating UV-C dose of 80 mW.s.cm -2 and then to six reactivation temperatures (7, 5; 12, 5; 17, 5; 22, 5; 27, 5; 37 and 50°C).Figure 6 represent the survival ratio (on a logarithmic scale) versus time for S1, S2, and S5, and the asymptotic shape of the curves can be seen, including an induction period, an exponential growth phase, and finally a stabilization phase.The model described in Equation 15was applied to experimental data using nonlinear regression.This study showed similar behavior with regard to the reactivation temperature for the three reference strains.However, if a number greater than or equal to 10 2 organisms/100 ml of P. aeruginosa in treated wastewater was considered, this will pose a potential risk to the environment (Kristina and Charles, 2009).In which case S1, S2, and S5 all showed an expected result: the higher the temperature, the greater the maximum reactivation in which case S1, S2, and S5 all showed an anticipated result: the higher the temperature, the larger the maximum reactivation observed.Inspite of this apparently low percentage, for a N o of 10 6 organisms/100 ml, a reactivation of 10 4 organisms/100 ml would be produced; this could cause serious health and environmental problems (Brahmi et al., 2010).
Contrary to the hypothesis advanced by Salcedo et al. (2007), that chemical and biochemical rates are supposed to increase by increasing temperature, according to the Arrhenius relationship; however, in the studied case the opposite was observed (Table 3).In fact, k 2 is not a pure reaction rate constant, but rather is a model parameter that is adjusted to predict the experimental data.Its physical meaning is related to the time required to reach the maximum survival ratio and then the stabilization phase: high k 2 values signify short induction and growth phases.The trend of k 2 versus temperature found in these experiments could be explained as follows: since an elevated temperature provides a higher maximum of reactivation (S m ), reaching the maximum, needs certainly more time to be realized.
At the same time, another quantification review of photoreactivation was applied to the same strains and data were subjected to analysis of variance, and means were separated by the least significant difference according to the Student Newman-Keuls test (SPSS for Windows, SPSS, 17 June, 1993).The examination of cell number obtained after different periods of exposure to visible light showed that only strain S5 had a major revival after UV irradiation exposition and an exposure of 0, 4, 8 and 12 h to visible light at room temperature (25± 5°C) and in a non-nutrient suspension.Concerning the results obtained for S1 and S2, the statistical analysis did not show significant difference in the results after 12 h of exposure to visible light exposure (Table 4).These results obtained are inconsistent with those mentioned by Logistic model, especially for strains S1 and S2.The results raise nevertheless questions about the effectiveness of UV to inactivate microorganisms.These irradiated or inactivated' microorganisms did not appear surely in the growth media (uncultivable) but they could be still metabolically active and virulent in the precise case of pathogenic.Conversely, higher photoreactivation rates and levels were observed with increasing fluorescent light intensities.When exposed to nearoptimum growth temperatures (23-37°C), photoreactivation levels were higher than those high (50°C) or low (7.5°C) temperatures.Since UV irradiation occurs at room temperature (20 to 25°C), the reactivation experiences at the most extreme temperatures (7.5 and 50°C) could cause a temperature shock to the bacteria and therefore alter the reactivation process.
Results shown in Table 5 indicate that in the case of P. aeruginosa S1, S2 and S5, statistical analysis did not show any significant differences in bacterial reduction in conditions of darkness after different periods of exposure to laboratory light, suggesting that reactivation was not perceptible.These results could be corroborated by the work advanced by Hassen et al. (2000).
In general, variation in the bacterial photoreactivation is seriously discussed in the literature; and it seems that certain micro-organisms are able to repair some of the damage caused by UV light when exposed to light in the near-UV or violet-blue spectral range (Hassen et al., 2000).Different mechanisms are proposed to explain the process of photoreactivation.Dimers of pyrimidine, resulting from the UV alteration, are reduced in situ to monomers by an active enzyme through the action of visible light in the near-UV or violet-blue spectral range (310 ± 480 nm).The second mechanism is the substitution of damaged nucleotides.The best known example is cutting-repairing: a sequence of low adjacent bases is excised from DNA submitted to the UV radiance, and then it is resynthesized correctly (Hassen et al., 2000;Kashimada et al., 2006).Nevertheless, the process of photoreactivation is not general in all bacteria.Different factors affecting photoreactivation are discussed, such as UV dose, wastewater quality, exposure time to photoreactivating light, and particularly the species of the micro-organism.

Conclusions
As compared to overall approach, for all the regression models and based on the two parameters (the correlation coefficient R 2 and ), the model of Collin-Selleck gave the best results for the description of UV inactivation.
The application of a first order law to the kinetic model of disinfection was therefore possible, if we assumed the existence of two successive steps of different kinetics.Only the second stage was explored during these experiments.The first stage of fast kinetics could only be studied when considering an initial abatement.In the case of the second stage of this model, the presence of suspended particles in water had an important effect on dissipating the radiation energy and therefore on protecting the microorganisms against UV rays.In conclusion, suspended particles affected directly the effectiveness of the UV disinfection.
The examination of cell number obtained after different periods of exposure to visible light showed that only strain S5 had a major revival after UV irradiation but results obtained for S1 and S2 did not show significant difference in the results after 24 h of exposure to visible light exposure.
Results also showed higher photoreactivation rates with increasing fluorescent light intensities.The survival bacteria after UV irradiation would be a consequence of the combined effect of reactivation and temperature shock.Nevertheless, S5, S2, and S1 are each heterogeneous group and the composition of these indicators may change; this new model has the capability of fitting to experiment data from different wastewaters, resulting in new parameters that will permit the prediction of the reactivation process.
In conclusion, the use of special germicidal UV lamps, during a relatively uniform short time release and high flux of energy (notion of flash lamps), and the optimization of UV emission in the irradiation chamber would be of major interest in order to guarantee a good disinfection.This would also present the major advantage of avoiding the phenomena of bacterial revitalization and the release of mutants in the environment.

Figure 1 .
Figure1.Determination of the variation in the kinetics of disinfection of P. aeruginosa as a function of contact time with the approach of Chick-Watson.y: Reduction = N/N 0 with N; number of micro-organisms at the instant T; N 0 ; Number of micro-organisms at the instant T= 0; R 2 : Coefficient of determination; dose (mW.s. cm -2 ) = X= IT= UV Intensity (mW.cm -2 ).Time of contact (seconds).

Figure 2 .:
Figure 2. Kinetics of bacterial inactivation according to the models of Chick-Watson (a), Amended chick-Watson (b) and Collin-Selleck (c), respectively.y: reduction = N/N 0 with N; Number of bacteria at the instant T; N 0 ; Number of bacteria at the instant T= 0; R 1 2 , R 2 2 and R 3 2 : Coefficients of determination; m: Kinetic characteristic of the model; Dose (mW.s.cm -2 )= I×T= UV Intensity (mW.cm -2 )×Time of contact (seconds).

Figure 3 .
Figure 3. Kinetics of UV inactivation of P. aeruginosa according to amended Chick Watson model and taking into consideration the impact of suspended solid content of water.a and b: characteristics of the model; Css: concentration of suspended solids.

Figure 4 .
Figure 4. Kinetics of UV inactivation of selected P. aeruginosa according to a multi-action of first order with (a) and without suspended solid content (b).Css: Concentration of suspended solids; a, b, P, K 1 and K 2 : kinetic characteristics of the model; R 1 2 and R 2 2 : coefficients of determination; with n=1, X (dose UV) = D = I×t = UV Intensity (mW/cm 2 ) × Time of contact (seconds).

Table 1 .
The kinetic characteristics of all the disinfection models studied during UV irradiation.
a A, K1, K2 and K3: Characteristics of the models; R 1 2 : Coefficients of determination; , m and n: Parameters of adjustment of the model;  : Difference between calculated and measured or experimental values

Table 2 .
The kinetic characteristics of all the disinfection models studied during UV irradiation a .Parameters of adjustment of the model;  : Difference between calculated and measured or experimental values 2 : Coefficients of determination; , m and n:

Table 3 .
Kinetic parameters of the logistic model applied to photoreactivation experiments.