Reliability assessment of pollution removal of wastewater treatment plant using the method of Weibull

. The aim of study was the analyze of the reliability pollution removal in wastewater treatment plant in Mińsk Mazowiecki. T he article presents the results of the reliability of BOD, COD and total suspended solids removal of wastewater treatment plant with actived sludge. Physical and chemical analyses of raw wastewater and treated effluent were carried out in the years 2016 – 2017 (2 years). The designed size of the treatment plant with actived sludge, expressed in PE is 82 200 residents. During this study period, 50 wastewater samples were collected and analyses. For each of pollution indicators descriptive statistic, percentage reduction and and treatment plant reliability factors (WN) were calculated. The average effectiveness of BOD 5 (Biochemical Oxygen Demand), COD Cr (Chemical Oxygen Demand) and TSS (Total Suspended Solid) removal in this period of study were respectively: 99.1%, 96.3% and 98.9%. A reliability analysis was performed using the Weibull probability model.


1.Introduction
Poland is one of the most populous and the biggest countries of the Baltic Sea region. According to the newest information from Central Statistical Office in the years from 2000-2016 the numbers of city which was served by the treatment plant increased by 116 cities (from 801 cities in 2000 to 917 in 2016, what is around 14%) [1]. The wastewater composition it is the one of the criterion in the choice of treated technology. The concentration and type of pollution in urban sewage is varied and changeable over time but also depends on many factors like -size of agglomeration and the participation of industrial wastewater [2]. Wastewater is a multiphase but also multicomponent system of dissolved gases, liquids and solids. The organic and inorganic compounds exist in sewage may be in the form of solutions, colloids or dispersed phases [3]. To choosing the technology of treated wastewater is necessary to consider economic technical and ecological aspects [4]. Improper way of sewage treated can be very danger for environmental safety, also for the groundwater's physicschemical and bacteriological properties [5,6].
Poland is obligated to implement and comply with the regulations of the Water Framework Directive (WFD 2000), for all European Union members. According to the WFD provision that all agglomerations with more than 2000 equivalent inhabitants should be equipped with a collective sewage system, completed with sewage treatment plant [7, 8,]. The wastewater treatment plants with actived sludge is one of the most commonly used solution for the treated sewage in for community (cities) but for household wastewater treatment plants also, because of the high effectiveness of reduction the pollutions in purification process [9,10].
Reliability is an important aspect in the evaluation of wastewater treatment plant work [11][12][13][14]. One of the primary method uses to properly evaluate the reliability of a wastewater treatment plant is Reliability Coefficient (RC). This coefficient is useful to specifying the technical reliability of the object. Moreover, in evaluating the reliability of a wastewater treatment plant work, statistical probability distributions are used to establish the probability of occurrence of selected values and concentration of pollutions indicators. Nowadays, the Weibull distribution is an accurate method for the evaluation of reliability of small and collective wastewater treatment plants [15,16]. The reliability of wastewater treatment plant working with actived sludge, has been widely presented by Eisenberg et al. [17], Oliveira and Von Sperling [18] and Bugajski et al. [19].

Location of the object
The wastewater treatment plant is located in the Mazowieckie voivodeship in Mińsk Mazowiecki city (Fig. 1). The object is working with the actived sludge technology, which is one of the most popular and effective methods recommended to treated domestic wastes. Wastewater from the city in flow to the sewage treatment plant by the two kind of sewage system: rain water sewer system and sanitary system. The sewage from both kind of system are and treated together. Effluent from the wastewater treatment plant is diverted to Srebrna River. Mean designed daily sewage supply for this object is Q ms = 11 500 m 3 ·d -1 . According to the population equivalent (PE) range is equal 82 200. As per the water permit issued in 2015, acceptable concentrations of the analysed parameters in the sewage discharged into a receiver should not exceed 15 mgO 2 ·dm -3 for BOD 5 , 125 mgO 2 ·dm -3 for COD Cr , 35 mg·dm -3 for TSS.

Materials and Methods
Additionally, during the two-years study period, 50 samples of raw and treated where: xvariable defining the concentration of given contamination indicator in treated sewage, bscale parameter, cshape parameter, θlocation parameter.
Weibull distribution parameters were estimated by means of maximum likelihood method. The applicability of Weibull distribution to the empirical data was assessed using Hollander Proschan test. The results were analyzed with STATISTICA 13 software.

Study results and discussion
The determined values of individual statistical parameters for the based pollution indicators in the raw and treated wastewater, were to characterized the dynamics changes of their compositions.
Results of the analysis of raw and treated effluent are shown in Table 1. According to the result of the composition of raw sewage, it was found that the concentration of BOD 5 was determined they varied from 250 to 990 mgO 2 •dm -3 , and average value was 485.5 mgO 2 •dm -3 .  -3 . Interval between minimum and maximum value of COD was 43.9 mgO 2 •dm -3 , and average value equal 33.8mgO 2 •dm -3 . The average concentration of TSS in effluent of wastewater treatment plant was 4.3 mg•dm -3 , the range between minimum and maximum value was equal 23 mg•dm -3 . The value of coefficient of variation for BOD 5 and COD in outflow, was on the average variability level. For TSS the coefficient of variation shaped on the high variability level for this pollution indicator in outflow [20]. The average pollution removal efficiency was high at 99.1%, 96.3% and 98.9% for BOD 5 , COD Cr and TSS respectively. Additionally, to analyze wastewater susceptibility to biological degradation, the COD Cr /BOD 5 ratio was calculated for both influent and effluent. In figure 2 was presented the results of analyze. According to the assessment presented by Miksch and Sikora [20], it can be observed, that for raw sewage biodegradability was on average level in research period. After the biological treated, was observed the increase of COD Cr /BOD 5 ratio in outflow.
Increase of COD Cr /BOD 5 ratio after biological treated process, indicates a high degree of reduction of organic compounds and the residue of hard-biodegradable compounds in outflow. This results indicate, the wastewater treatment plant in Mińsk Mazowieski worked properly in research period. Similar results was presented by Młyńska et al. [2017] [21]. In the paper authors observed the increase of COD Cr /BOD 5 ratio in wastewater after mechanical and biological treatment. Also results presented by Myszograj i in.
[2017] [22], for five wastewater treatments plants with mechanical and biological treatment, confirm that, observed increase of relation between COD Cr and BOD 5 indicate the high efficiency of organic compounds decomposition in bioreactor. Determine the COD Cr /BOD 5 ratio in particular stage of treated process can be simple way to definite the working quality in wastewater treatment plant. Analyzing the results of the estimation of the Weibull distribution parameters along to the measures of goodness matching the empirical data, it founded that the Weibull distribution describes empirical data at the significance level α = 0.05 in the case of: BOD 5 , COD and TSS, respectively with the probability of 69%, 62% and 94%.
Based on the BOD 5 distribution Table 2 . 3a) in treated wastewater, it was found that the reliability of the wastewater treatment plant according to the BOD 5 median was 69%. This mean that in an annual period, for approximately 245 days, the BOD 5 value in outflow will be ≤4 mgO 2 ·dm -3 . For the second of organic pollutant indicator -COD Cr ( fig. 3b) reliability effectiveness relative to the median in the outflow, was 62%. That is mean, that the value equal or less than 32.9 mgO 2 ·dm -3 appear in outflow around 226 days in one year period. Result of Weibull distribution for the total suspended solid, indicates the 94% work reliability, relative to median. Therefore, in the treated wastewater the median value of TSS (3.7 mg·dm -3 ) appear in almost 342 days per year. According to the recommendations presented in Andraka and Dzienis [2010] work, the wastewater treatment plant under 50 000 PE, should work at the reliability of at least 93.7% with operator risk equal α=0.05. Therefore, as per this recommendations, the acceptable failure rate for such object is only 22 days per year. It is mean, that during the two years of operation limit for BOD 5 , COD Cr and TSS had never been exceeded. It is worth noting that the analysed object achieved in the research period high effectiveness of removing contaminants. For all the indicators the average of effects were around 95% (table 1).