TIME SERIES ANALYSIS OF THE HEAVY METALS LOADED WASTEWATERS RESULTED FROM CHROMIUM ELECTROPLATING...

Environmental Engineering and Management Journal March 2011, Vol.10, No.3, http://omicron.ch.tuiasi.ro/EEMJ/

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TIME SERIES ANALYSIS OF THE HEAVY METALS LOADED WASTEWATERS RESULTED FROM

CHROMIUM ELECTROPLATING PROCESS

Daniel Dunea, Ştefania Iordache

Valahia University of Târgovişte, Faculty of Environmental Engineering and Biotechnology, 18-24 Unirii Blvd., 130082 Târgovişte, Romania

Abstract This paper presents a time series analysis of the effluent pollution load resulted from the neutralization station of electroplating industry wastewaters originating from the chemical and electrochemical etching lines for the purpose of better understanding the appropriateness of selected linear modeling approaches. For this research were investigated pH, hexavalent chromium (Cr6+), total chromium, total iron (Fe2+; Fe3+), chemical oxygen demand (COD - potassium dichromate), nitrates (NO3-), and suspended solids (TSS), using time series recorded for one year. Multiple range tests were performed with Tukey HSD testing all pair wise comparisons among monthly means for each monitored parameter series. Time series analysis was applied to establish the general trend of concentration for each effluent parameter. The forecasting performance of the selected statistical models was evaluated and discussed. ARIMA models gave satisfactory results for hexavalent chromium, total iron, COD and TSS. As far as it concerns the pH, total chromium and nitrates, linear models including ARIMA did not perform well when using real data time series. Exploratory Factor Analysis has determined the main latent factor, which was related with suspended solids and nitrates, whose concentrations in the effluent often exceeded the standard limit value. Future work will consider the use of artificial neural networks, fuzzy logic and nonlinear models. Key words: ARIMA model, electroplating industry effluent, hexavalent chromium, multivariate methods, time series analysis Received: May, 2010; Revised final: January, 2011; Accepted: January, 2011

Author to whom all correspondence should be addressed: e-mail: [email protected]; Phone: +40(245)206108; Fax: +40(245)206108

1. Introduction

The interest for diminishing the negative effects of water pollution has been materialized in modern sewage systems of the human and industrial wastes discharged in rivers and streams. Originating from industrial by-products, runoff, and maltreated waste, poor water quality can lead to health problems for the public and stressful living conditions for aquatic life.

Potential human exposure to heavy metals occurs in a broad number of operations and processes such as chromium plating, metallurgy and metals processing, and decontamination activities at hazardous waste sites. Previous works have shown that the waters generated from the mining sediments and storage facilities, with high concentration of

heavy metals, affect the ecosystem on significant surfaces after the closure of the mining exploitations, if not subjected to an appropriate management and to the best available technologies (Ozunu et al., 2009).

Several case studies of industrial water polluted with hexavalent chromium and its impact to river receptors are discussed in literature (Christensen and Delwiche, 1982; Cvijovic et al., 2010; Mount and Hockett, 2000). In the case of chromium, a widely-used element in industry (Stoecker, 2004), specific attention has been devoted to establish the relative toxicity to aquatic organisms of trivalent and hexavalent redox forms; i.e., the predominant oxidation states in surface waters.

An overview of the environmental, health and safety regulations of the chromium utilization in the electroplating industry can be found in Regulatory

“Gheorghe Asachi” Technical University of Iasi, Romania

Dunea and Iordache/Environmental Engineering and Management Journal 10 (2011), 3,

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Analysis (1995). Metal surface treatment is one of the major metal working processes that generates a large amount of liquid and solid (sludge) wastes containing heavy metals.

The traditional techniques used for metal control are based on chemical precipitation coupled to pre- or post-oxidation/reduction followed by filtration in order to concentrate the species of interest (Cavaco et al., 2007). Effective control of these potential fugitive emissions in natural streams requires efficient monitoring plans.

Water quality standards provide the obligatory framework through physical, chemical, biochemical, radiological and microbiological methods, as well as sampling methods and terminology, to obtain standardized information with an important communication role in supplying answers concerning trends of the environmental conditions (Greenberg, 1985). Rules, regulations and administrative laws are put in force in many countries, adopting the requirements for industrial water discharging and for target values and minimal values for water quality (Oprea and Dunea, 2008).

In Romania, the industries prone to polluting waters are required to conduct analyses (auto-monitoring) in their own laboratories, and to send monthly reports to the Environmental Protection Agency. The traditional operation of monitoring natural waters and effluents is discrete sampling followed by chemical analysis in the laboratory. This action provides information on the constituents of the sample in a precise manner only for a subset of parameters specifically chosen for analysis, at a particular moment in time.

Examples of system categories for water monitoring include security water monitoring technologies, multi-parameter surface water probes, on-line turbidimeters, portable water analyzers for pollutants, nutrient monitors for wastewater and ambient waters, and waterborne pathogen detectors. A number of existing environmental, health, and safety regulations currently affect the chromium electroplating industry.

Many of these regulations have been increasing in scope of coverage and stringency over recent years and this trend is expected to continue in the future, particularly in the areas of wastewater discharges, air emissions, and worker exposure to hexavalent chromium (Regulatory Analysis, 1995).

An advanced monitoring system for controlling the treatment process of wastewater containing chromium (VI) was developed using a flow method as a chemical sensing probe. In this system, the acquisition of monitoring information and the control of the treatment process is computer-controllable (Zhou et al., 1993). The quick development of monitoring devices for water quality studies requires new approaches to data analysis. Vast quantities of collected data occur in the form of time series where observations are dependent.

Environmental problems are characterized by high degrees of complexity, mainly due to the use of

collected data that can have different data structures and data formats (e.g. time series, spatial data), uncertainty due to incomplete data (monitoring system failures), inaccurate data (random or systematic errors), approximate estimations (difficult-to-measure process), incomparability of data (resulting from varying conditions of the observations and measurements). The solution to some of these problems is to test and identify proper approaches: the appropriateness of statistical models is discussed in this work. Environmental components, especially water, are characterized by the high complexity of the involved processes, which are difficult to be translated into deterministic models (Oprea and Dunea, 2010).

One objective in time-series analysis is to develop models that can be used to obtain optimal forecasts of future values. Being able to forecast optimally is practical and important for environmental planning, where forecasting is based on fitting a model to past observations in a monitored time series.

Wastewater treatment is a complex multivariate process with highly variable inputs, nonlinear time varying dynamics, and a time series structure with autocorrelation that is subject to large disturbances (Lindberg, 1997). A number of studies on the use of linear ARIMA (Autoregressive Integrated Moving Average) models for process control applications exists in literature (Apley and Tsung, 2002; Ateinza et al., 2002; Mastrangelo and Forreset, 2002). More recent researches in environmental monitoring showed that ARIMA presents good forecasting capabilities for air pollutant time series (Dunea et al., 2008, Nicolescu et al., 2009), wastewater time series (Dellana and West, 2009), and water quality (Faruk, 2010), but less accurate than artificial neural networks.

The model appropriateness is judged based on how the forecast will be used, the degree of accuracy required from the forecast, the amount of time and resources available, the amount and type of available data, and how far ahead is required to forecast.

The fitted model also allows seeing how the forecasts use past data to determine the variation of the forecast errors and to calculate limits within which a future value of the series will stand with a given probability.

A wide range of data sets was investigated in this study, involving real effluent quality data, for the purpose of better understanding the appropriateness of selected linear modeling approaches.

Real data sets were employed to forecast a variety of wastewater variables from an industrial wastewater neutralization facility. pH, hexavalent chromium (Cr6+), total chromium, total iron (Fe2+, Fe3+), Chemical Oxygen Demand (COD - potassium dichromate), nitrates (NO3-), and suspended solids were investigated using one year recorded time series. Special attention was accorded to hexavalent chromium and total chromium variables since they present high risk due to toxicity.

https://www.researchgate.net/publication/234819217_Comparing_statistical_and_neural_network_approaches_for_urban_air_pollution_time_series_analysis?el=1_x_8&enrichId=rgreq-aa1c0c0b-064e-42b7-8a4a-c74e33be1ac7&enrichSource=Y292ZXJQYWdlOzI1NjQ1MzM5NDtBUzo5ODQ5MzIyMTgzNDc2NUAxNDAwNDk0MDIyODYz

https://www.researchgate.net/publication/220119263_A_hybrid_neural_network_and_ARIMA_model_for_water_quality_time_series_prediction?el=1_x_8&enrichId=rgreq-aa1c0c0b-064e-42b7-8a4a-c74e33be1ac7&enrichSource=Y292ZXJQYWdlOzI1NjQ1MzM5NDtBUzo5ODQ5MzIyMTgzNDc2NUAxNDAwNDk0MDIyODYz

Time series analysis of the heavy metals loaded wastewaters resulted from chromium electroplating process

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2. Experimental 2.1. Neutralization station

The experiments have been carried out with rinse wastewaters originating from electroplating plant: chemical etching-bath, molten-salt bath, electrochemical etching bath and degreasing-washing bath. Samplings were performed in the neutralization station, which discharges effluents through industrial sewerage in the city wastewater treatment plant before discharging into river.

The Cr6+ is first reduced to less toxic and less soluble Cr3+, the Cr3+ ions are then precipitated as Cr(OH)3 at high pH, and the insoluble metal hydroxides are settled afterwards. Finally the sludge has to be dewatered and disposed of properly (Kratochvil et al., 1998). Industrial chemical treatment follows the abovementioned process precipitating the trivalent chromium hydroxide along with other heavy metals present in wastewater.

Ferrous salt generally used to reduce hexavalent chromium in electroplating wastewater is

the ferrous sulfate, FeSO4•7H2O. The main drawback of using ferrous sulfate for precipitating chromium is that it results a much larger quantity of sludge than for the reduction with sulfite and subsequent neutralization. However, a technological advantage to be considered is the simultaneous precipitation of iron hydroxides and chromium resulting in a precipitate that settles and filters more easily. A filtration process is required after sedimentation because the particle size of resulted sludge is relatively small and difficult to settle completely.

Operating parameters and effluents level are surveyed based on specific procedures ensuring the optimal functioning of the environmental protection installations. Fig. 1 presents the neutralization process flux showing each step from A to I used in the treatment of the heavy metals loaded wastewater.

Consequently, the wastewater neutralization station treats the pickling wastewaters originating from the etching lines of a stainless steel factory that uses chromium electroplating process. The monitored effluents from this type of treatment station were statistically analyzed.

Fig. 1. The synoptic scheme of the wastewater neutralization station


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A - FeSO4 is added to the wastewater to reduce Cr6+

to Cr 3+ at a acid pH (2-3); B - in the first phase, Ca(OH)2 is added to increase

the pH value to 6-7 forming insoluble compounds (F- and Cr3+);

C - in the second phase, Ca(OH)2 is added to increase the pH value to 9-10 forming insoluble compounds (Ni2+ and Fe 2+); The reactions from 1st reduction and 2nd reduction basins are as follows: 2HF + Ca(OH)2 → CaF2 + 2H2O 2HNO3 + Ca(OH)2 → Ca(NO3)2 + 2H2O Ni(NO3)2 + Ca(OH)2 → Ni(OH)2 + Ca(NO3)2 Fe(NO3)2 + Ca(OH)2 → Fe(OH)2 + Ca(NO3)2 2Cr(NO3)3 + 3Ca(OH)2 → 2Cr(OH)3 + 3Ca(NO3)2

D - in the 1st and 2nd sedimentation basins, CaF2, Fe(OH)2, Ni(OH)2, Cr(OH)3 are separated as solid sludge being insoluble in water;

E - 1st and 2nd filters are used for removal of suspended solids and turbidity;

F - sulfuric acid is added to reduce the water pH from 10 to 6.5-8.5 in the neutralization basin;

G - back wash system is used to clean the 1st and 2nd filters;

H - solids (sludge) produced in the sedimentation stage are periodically removed in the thickener;

I - resulted sludge is sent to a dewatering stage removing excess water and leaving only solids. 2.2. Wastewater monitoring

The monitoring of the effluents was accomplished by discrete sampling followed by chemical analysis in the laboratory. Table 1 summarizes the monitored parameters, their methods of analysis and the corresponding standard, but most important the average and maximum values of the influent stream that enters into neutralization station. The same methods of analysis were applied to determine the effluent characteristics, effluent that is discharged in the industrial sewerage.

Influent wastewater resulted from the etching processes of stainless steel coils (production lines)

enters the neutralization station. The resulted effluent was monitored through specific analysis three times a day. Then, this data was subjected to statistical analysis, serving two related purposes: description and inference. As expected, the effluent samples were weakly concentrated in chromium, containing also other heavy metals in low quantities (Fe2+, rare traces of Ni2+). 2.3. Statistical and time series analysis

Statistical techniques for analyzing time-series data can range from simple to very complex. However, the first step in an analysis is always to identify the characteristics of the data. In the preliminary phase, multiple range tests were performed using Tukey HSD (Tukey, 1977), testing all pair wise comparisons among monthly series means for each monitored parameter. The most important statistical indicators (mean, variance, standard deviation, standard error, minimum, maximum, and coefficient of variation - C.V.%) were presented in the results section. Time series analysis (TSA) was applied to establish the general trend of each effluent parameter concentration. In time series analysis it is assumed that the data consist of a systematic pattern (identifiable component) and random noise (error), which makes the pattern difficult to assess. Most time series analysis techniques involve some form of filtering out noise in order to make the pattern more salient.

However, in this paper, the raw data sets obtained through programmed monitoring were used in statistical models without any preprocessing steps because of the interest in testing the model performances to forecast upper and lower limits of the wastewater parameters. The performance of the selected statistical models were evaluated and discussed according to the root mean square error (RMSE), the statistical significance of the terms in the forecasting model and the results of five tests run on the residuals to determine whether each model is adequate for the data. Models for time series data can have many forms and represent different stochastic processes. When modeling variations in the level of a process, three broad classes of practical importance are the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models.

Table 1. Wastewater influent characteristics and the corresponding method of analysis

No. Parameter Samples Average value (mg L-1)

Maximum value (mg L-1) Analysis type Measurement

Standard 1 pH 955 2.92 5.30 pH-meter SR ISO 10523-97 2 Cr6+ 955 8.94 10.25 Spectrophotometry STAS 11083-98 3 Cr3+ 955 20.72 32.25 Spectrophotometry STAS 11083-98 4 Ni2+ 955 17.21 23.84 Spectrophotometry STAS 7987-67 5 Total Iron 955 294.00 416.00 Spectrophotometry SR ISO 6332-96 6 NO3

- 955 723.00 860.00 Spectrophotometry STAS 8900/1-71 7 COD - K2Cr2O7 - - - Gravimetric STAS 6953-81 8 Suspended solids - - - Complexonometry SR ISO 6060-96


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These three classes depend linearly on

previous data points. Combinations of these ideas produce autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models. Special attention was accorded to ARIMA model, which estimates and forecasts using the methods prescribed by Box and Jenkins (1976) and Box et al. (1991).

A relevant description of the analyzed multivariate system required the use not only of TSA but also of multivariate methods. The classification structures of variables and latent factors controlling wastewater quality were retrieved using exploratory factor analysis (EFA) with principal components factoring, which is a successfully used analysis technique in environmental monitoring (Temme et al., 2007; Tsakovski et al., 2000). EFA reduces the number of measured variables identifying specific latent factors and the corresponding underlying factor structure. The input matrix is 912 objects (number of daily measurements) by 6 selected variables (water quality parameters). The Varimax rotated mode was applied. 3. Results and discussion

Sewage, treated to leave the industrial plant is monitored through several parameters according to the water management authorization, from which there have been selected for time series analysis the ones that were present in the effluent as follows: pH, hexavalent chromium (Cr6+), total chromium, total iron (Fe2+, Fe3+), Chemical Oxygen Demand (COD - potassium dichromate), nitrates (NO3

-), and total suspended solids. Descriptive statistics have summarized the population data by describing what was observed in the sample. Numerical descriptors included mean, variance, standard deviation, standard error, minimum, maximum, and C.V.% for continuous data types. The practical advantage of the C.V. is that it is without unit. This allows C.V.s to be compared to each other in ways that other indicators, like standard deviations or root mean squared

residuals, cannot be. Tukey HSD 99.9% (p<0.001) was used to test for significant differences amongst the monthly means. It is a single-step multiple comparison procedure and statistical test generally used in conjunction with ANOVA to find which means are significantly different from one another. The ANOVA decomposes the variance of the data into two components: a between-group component and a within-group component. The F-ratio is a ratio of the between-group estimate to the within-group estimate. Finally, the most appropriate statistical model for each parameter was identified and tested. Regressions were used to correlate observed data with predicted data and four steps ahead ARIMA predicted values were compared to the recorded values. 3.1. Monitoring of wastewater parameters 3.1.1. pH

As a qualitative parameter, pH has a significant influence on other water parameters. pH determination is a frequently used test in every phase of water supply and wastewater treatment that are pH-dependents (e.g. acid-base neutralization, water softening, precipitation, coagulation and corrosion control). The discharging limits with pollutants on the release in natural receivers, extracted from the current regulations (GD, 2002) for pH is between 6.5 and 8.5. Table 2 shows various statistics for each of the 12 months of data representing the pH series recorded during one year. In the analyzed samples (955 values), pH did not exceed the maximum allowed by the Romanian legislation, but in June was less than the lower limit (Table 2). The coefficient of variation was relatively constant. The monthly variable with the smaller C.V. (May) was less dispersed than the variable with the larger C.V. (August). Consequently, pH time series showed homogeneity: stability across time as opposed to a trend and stability of local fluctuations over time. Since the p-value of the F-test was less than 0.05, there was a statistically significant difference between the means of the 12 variables at the 95.0% confidence level.

Table 2. Descriptive statistics of pH time series

Month Samples Average Variance Standard Deviation

Standard Error Minimum. Maximum C.V.%

January 89 7.691 0.293 0.542 0.057 6.52 8.50 7.04 February 86 7.631 0.296 0.544 0.059 6.63 8.50 7.13

March 97 7.434 0.248 0.498 0.051 6.50 8.50 6.70 April 89 7.667 0.222 0.471 0.050 6.55 8.48 6.14 May 98 7.567 0.166 0.408 0.041 6.64 8.50 5.39 June 93 7.476 0.211 0.460 0.048 6.41 8.46 6.15 July 96 7.717 0.192 0.438 0.045 6.68 8.50 5.67

August 34 7.393 0.304 0.551 0.094 6.50 8.50 7.45 September 77 7.654 0.199 0.446 0.051 6.50 8.45 5.83 October 82 7.542 0.184 0.429 0.047 6.50 8.41 5.68

November 51 7.395 0.164 0.404 0.057 6.52 8.21 5.47 December 63 7.286 0.250 0.500 0.063 6.50 8.33 6.87

Total 955 7.557 0.238 0.488 0.016 6.41 8.50 6.46


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As far as it concerns the multiple comparison

test for significant differences amongst the pH monthly means, using Tukey HSD 99.9%, statistical highly significant differences (p<0.001) occurred between January and December (difference = 0.4043; DL = 0.3201), February and December (difference = 0.3449; DL = 0.3224), March and July (difference = -0.2835; DL = 0.2799), April and December (difference = 0.3805; DL = 0.3201), July and December (difference = 0.4311; DL = 0.3152), and September and December (difference = 0.3680; DL = 0.3303) – 6 pairs.

The most adequate configuration for predicting future values of pH was ARIMA (0,0,3) model. The p-value for the moving average – MA (3) term was less than 0.05 (0.0025), so it was significantly different from 0.0. The p-value for the constant term was less than 0.05, so it was significantly different from 0.0. Looking at the error statistics, this was the statistical model with the smallest root mean squared error (RMSE = 0.458) during the estimation period, with the smallest mean absolute error (MAE = 0.379) and with the smallest mean absolute percentage error (MAPE = 5.044) as compared to other ARIMA configurations and statistical models. The results of five tests run on the residuals to determine whether the model is adequate for the data, showed that ARIMA (0,0.3) applied to pH time series passed four tests excepting the test for excessive runs above and below median.

Evaluation of the statistical significance based on correlation coefficient and R-squared between the forecasted variables and observed raw data showed that the correlation coefficient equaled 0.314, indicating a relatively weak relationship between the variables. The R-Squared statistic indicated that the regression model as fitted explained only 9.86% of the variability in forecasted series. Fig. 2 presents the plots of pH observed data and ARIMA (0,0,3) modeled results of the effluent that left the neutralization station during one year of monitoring.

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Fig. 2. pH observed time series and ARIMA (0,0,3) modeled plot of the effluent that left the neutralization

station from chromium electroplating industry Modeled data were inconsistent with the

ARIMA model and gave a small observed/predicted correlation coefficient.

The model tended to underestimate upper and lower limits by applying excessive moving average smoothing.

Since the time series showed nonlinear characteristics, this suggests that other type of modeling approaches should be considered. 3.1.2. Hexavalent chromium

Chromium hexavalent (VI) compounds exist in several forms. Industrial uses of hexavalent chromium compounds include chromic acid electroplated onto metal parts to provide a protective coating, chromate pigments in dyes, paints, inks, and plastics, and chromates added as anticorrosive agents to paints, primers, and other surface coatings. It causes allergic and asthmatic reactions, is carcinogenic and is 1000 times as toxic as trivalent chromium. Chromium (VI) compounds are divided up in water hazard class 3 (Dunea and Oprea, 2010).

The discharging limits with pollutants on the release in natural receivers (GD, 2002) for hexavalent chromium is 0.1 mg l-1.

Table 3 shows the main statistical indicators for the hexavalent chromium time series. The limit value for hexavalent chromium allowed by the Romanian legislation in the industrial effluent was exceeded several times during the year of study. The most dispersed variable was recorded in April (C.V. = 538.45%), and the annual C.V. presented high values (143.67%), indicating that many values were much higher than the average. When performing ANOVA, there was a statistically significant difference between the means of the 12 months data at the 95.0% confidence level, because the F-ratio equaled 32.59 and the p-value of the F-test was less than 0.05. Table 4 indicates the results of the multiple comparison test for significant differences amongst the Cr6+ monthly means, using Tukey HSD 99.9%, showing only statistical highly significant differences (p<0.001) between corresponding months (35 pairs).

The appropriate statistical model for predicting future values of hexavalent chromium (Cr6+) was ARIMA (3,0,3); p-value for the moving average – MA (3) term was less than 0.05, being significantly different from 0.0. As compared to other ARIMA configurations and statistical models (exponential smoothing of moving average techniques), the selected ARIMA configuration had the smallest RMSE (0.0274) during the estimation period, with the smallest mean absolute error (MAE = 0.0174).

The MAPE and MPE were not calculated because the smallest data value was equal to 0.0. ARIMA (3,0,3) applied to Cr6+ time series passed two tests excepting the test for excessive runs above and below median, Box-Pierce test for excessive autocorrelation and the test for difference in variance 1st half to 2nd half (p0.001). The observed vs. predicted correlation coefficient was 0.678, indicating a moderately strong relationship between the variables.


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Table 3. Descriptive statistics of hexavalent chromium time series



January 89 0.0053 0.00026 0.016 0.0017 0 0.11 303.72 February 86 0.0074 0.00058 0.024 0.0026 0 0.10 325.38 March 97 0.0081 0.00056 0.023 0.0024 0 0.10 292.46 April 89 0.0013 0.00005 0.007 0.0007 0 0.04 538.45 May 98 0.0180 0.00083 0.028 0.0029 0 0.10 159.73 June 93 0.0334 0.00138 0.037 0.0038 0 0.10 111.32 July 96 0.0415 0.00157 0.039 0.0041 0 0.10 95.37

August 34 0.0567 0.00151 0.038 0.0066 0 0.12 68.53 September 77 0.0654 0.00147 0.038 0.0043 0 0.10 58.63

October 82 0.0369 0.00183 0.042 0.0047 0 0.10 116.05 November 51 0.0241 0.00109 0.033 0.0046 0 0.10 137.06 December 63 0.0395 0.00149 0.038 0.0048 0 0.10 97.83

Total 955 0.0257 0.00137 0.037 0.0012 0 0.12 143.67

Table 4. Multiple-Sample Comparison using Tukey HSD for the hexavalent chromium (Cr6+) time series with statistical highly significant differences (p<0.001) between months; shows the direction to compute the difference between months

Jan. Feb. March April May June July August Sept. October Nov. Dec.

January - -0.0280 -0.0361 -0.0513 -0.0601 -0.0315 -0.0341 February - -0.0259 -0.0341 -0.0493 -0.0580 -0.0295 -0.0320

March - -0.0252 -0.0334 -0.0486 -0.0573 -0.0288 -0.0313 April - -0.0320 -0.0402 -0.0554 -0.0641 -0.0356 -0.0381 May - -0.0235 -0.0387 -0.0473 -0.0214 June - -0.0320 July - -0.0238

August - 0.0326 September -0.0641 - 0.0285 0.0413 0.0259

October - November - December -

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Fig. 3. Hexavalent chromium observed time series and ARIMA (3,0,3) modeled plot of the effluent that left the

neutralization station from chromium electroplating industry

The R-Squared statistic showed that the

observed vs. predicted regression model as fitted explained 46.07% of the variability in forecasted series. Fig. 3 presents the plots of hexavalent chromium observed data and ARIMA (3,0,3) modeled results of the industrial effluent. ARIMA did

not meet the requirements for high concentration predictions. However, these plots offer support to the practical significance of the results, as well as allowing looking for possible assumptions underlying potential nonlinear model selection. 3.1.3. Total chromium

Majority of existing regulatory standards refers to total chromium levels, which is the combined concentrations of trivalent and hexavalent chromium compounds. The discharging limits with pollutants on the release in natural receivers (GD, 2002) for total chromium (Cr3+ and Cr6+) is 1.0 mg l-1. The amount of heavy metal ions concentration should not exceed 2 mg l-1.

The total chromium concentration in the effluent did not exceed the maximum admissible limit value. November showed the highest C.V. of 47.21% being the most dispersed variable. The annual C.V. presented intermediate values (33.07%), indicating that the series was relatively constant. ANOVA showed statistically significant difference between the means of the 12 months data at the 95.0% confidence level (F-ratio = 5.32; p < 0.05) – Table 5.

The multiple comparison test using Tukey HSD 99.9% for significant differences amongst the total chromium monthly means showed only few (4 pairs) statistical highly significant differences (p<0.001) as follows: January and October (difference


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= -0.0447; DL = 0.0413), April and October (difference = -0.0480; DL = 0.0413), September and October (difference = -0.0582; DL = 0.0428), October and November (difference = 0.0566; DL = 0.0481). Two homogenous groups of months were identified within total chromium time series. The suitable statistical model to total chromium data was ARIMA (1,0,1) with RMSE of 0.0629, and MAE of 0.0453. The MAPE and MPE were not calculated because the smallest data value was equal to 0.0. The model passed three tests and failed two: Box-Pierce test for excessive autocorrelation (0.01<p0.05) and the test for difference in variance 1st half to 2nd half (p0.01). R-squared statistic explained 13.49% of the variability in forecasted series.

The correlation coefficient was 0.367, indicating a relatively weak relationship between the observed and forecasted series. It may be observed that the model underestimated upper and lower limits of the monitored total chromium series (Fig. 4).

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Fig. 4. Total chromium observed time series and ARIMA (1,0,1) modeled plot of the effluent that left the


3.1.4. Total iron The chemical components of the waterway and

pollution sources determine the presence and concentration of iron compounds in water. The primary forms of concern in the aquatic environment are ferrous (II) and ferric (III) ions. However, it appears to have reduced potential health hazard. Other forms may be in either organic or inorganic wastewater streams.

The ferrous (II) form can persist in water void of dissolved oxygen. Some wastewaters may contain iron concentrations of several mg l-1 in the presence or absence of dissolved oxygen, but this iron form has little effect on aquatic life. The current effluent discharge maximum admissible limit value is 5.0 mg l-1 based on toxic effects (GD, 2002). Table 6 contains the main statistical indicators for the total iron (Fe2+, Fe3+) time series. The limit value for total iron in the industrial effluent was achieved often during the monitoring period. December was characterized as the most dispersed variable (C.V.=72.03%). In contrast, March had the lowest coefficient of variation. ANOVA provided statistically significant difference between the means of the 12 months data (95.0% confidence level). F-ratio was 36.2 and p < 0.05.

Table 7 indicates the results of the multiple range tests for significant differences amongst the total iron monthly means, based on Tukey's honestly significant difference (HSD) procedure.

The selection shows only statistical highly significant differences (p<0.001) between corresponding months. It can be observed that the number of differences is relatively significant (34 pairs). The ARIMA configuration closest to the collected data representing effluent total iron concentrations was (3,0,3), (Fig. 5) having the autoregressive term (3) and moving average term (3), which were significantly different (p<0.05). Selected model had the smallest RMSE (1.056), and MAE (0.8022).

Table 5. Descriptive statistics of total chromium time series



January 89 0.1908 0.0043 0.0658 0.0070 0.03 0.54 34.46 February 86 0.2034 0.0038 0.0618 0.0067 0.05 0.39 30.41

March 97 0.2141 0.0028 0.0527 0.0054 0.04 0.42 24.63 April 89 0.1874 0.0042 0.0650 0.0069 0.03 0.40 34.67 May 98 0.1997 0.0041 0.0643 0.0065 0.00 0.49 32.22 June 93 0.2154 0.0032 0.0562 0.0058 0.03 0.30 26.09 July 96 0.2084 0.0017 0.0410 0.0042 0.09 0.31 19.68

August 34 0.2121 0.0040 0.0636 0.0109 0.08 0.34 30.00 September 77 0.1773 0.0046 0.0677 0.0077 0.00 0.31 38.19

October 82 0.2355 0.0104 0.1021 0.0113 0.00 0.60 43.36 November 51 0.1788 0.0071 0.0844 0.0118 0.04 0.34 47.21 December 63 0.2203 0.0033 0.0573 0.0072 0.06 0.36 26.00

Total 955 0.2038 0.0045 0.0674 0.0021 0.00 0.60 33.07


477

Table 6. Descriptive statistics of total iron (Fe2+, Fe3+) time series



January 89 2.746 1.251 1.118 0.119 0.00 5.00 40.73 February 86 3.222 1.568 1.252 0.135 0.28 5.00 38.86 March 97 3.462 1.416 1.190 0.121 0.50 5.00 34.37 April 89 2.415 1.725 1.313 0.139 0.09 5.00 54.39 May 98 2.504 1.647 1.283 0.130 0.00 5.00 51.25 June 93 1.948 1.007 1.004 0.104 0.16 5.00 51.51 July 96 1.241 0.282 0.531 0.054 0.00 3.22 42.82



Total 955 2.218 1.721 1.312 0.042 0.00 5.00 59.15

Table 7. Multiple-Sample Comparison using Tukey HSD for total iron (Fe2+, Fe3+) time series with statistical highly significant differences (p<0.001) between monthly means; shows the direction to compute the difference between months

Jan. Feb. March April May June July August September October November December

January - -0.7163 0.7972 1.5045 1.0682 1.2405 0.9923 1.4132 0.9106 February - 0.8072 0.7176 1.2737 1.9810 1.5447 1.7170 1.4688 1.8897 1.3871

March - 1.0471 0.9574 1.5135 2.2209 1.7846 1.9568 1.7086 2.1296 1.6270 April - 1.1737 0.9097 1.0824 May - 1.2634 0.9994 0.7511 1.1721 June - 0.7073 July -

August - September -


It passed three tests, failing the test for excessive runs above and below median (p0.01) and the test for difference in variance 1st half to 2nd half (p0.001). The R-Squared indicated that the model as fitted explained 34.94% of the variability in forecasted time series and the correlation coefficient of 0.591 denoted a moderately strong relationship between observed and predicted variables.

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Fig. 5. Total iron (Fe2+, Fe3+) observed time series and ARIMA (3,0,3) modeled plot of the effluent that left the


3.1.5. Chemical Oxygen Demand Chemical Oxygen Demand (COD) is a key test

for assessing the effluents and wastewaters status prior to discharge in natural streams or sewerages. The effluent impact on the receiving water is predicted by its oxygen demand, because the removal of oxygen from the natural water reduces the capacity of sustaining the aquatic life.

The COD test estimates the oxygen requirement of the effluent and is used for monitoring and control of discharges, and for assessing treatment facility performance. The COD test is therefore performed in laboratories of water utilities and industrial companies determining the capacity of water to consume oxygen during the decomposition of organic matter and the oxidation of inorganic chemicals such as ammonia and nitrite. In this study, potassium dichromate (K2Cr2O7) was used, being a commonly used oxidant in COD assays. The effluent discharge maximum admissible limit value for COD is 70.0 mg O2 l-1 (GD, 2002). The main statistical indicators for the COD time series are presented in Table 8. The limit value for COD in the industrial effluent was not achieved during the monitoring period. September data showed the most dispersed variable (C.V.=20.26%). February had the lowest coefficient of variation (10.42%), indicating that many values were close to the average. ANOVA provided statistically significant difference (95.0% confidence level) between the means of the 12


478

months data. F-ratio was 15.79 and p < 0.05. Table 9 summarizes the results of the multiple-sample comparison for significant differences amongst the COD monthly means, based on Tukey's HSD procedure. Between the corresponding months, 21 pairs showed statistical highly significant differences (p<0.001). The most adequate ARIMA configuration to the effluent COD observed data was (3,0,3), having the autoregressive term (3) and moving average term (3), which were significantly different (p<0.05). This statistical model had the smallest RMSE (4.258), MAE (3.027) and MAPE (10.104) as compared to other ARIMA configurations or linear models. It passed only the test for excessive runs up and down. The correlation coefficient of 0.586 showed a moderately strong relationship between COD observed time series and forecasted series (Fig. 6).

The R-Squared statistic indicated that the identified model substantiated 34.38% of the variability in ARIMA time series.

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Fig. 6. Chemical Oxygen Demand - K2Cr2O7 observed time series and ARIMA (3,0,3) modeled plot of the effluent that left the neutralization station from chromium electroplating

industry

3.1.6. Nitrates (NO3-)

Nitrates enter water supplies from the decay of vegetation, the excessive use of chemical and organic fertilizers in agriculture and from the oxidation of nitrogen compounds in sewage effluents and industrial wastes.

The presence of both nitrate and bacteriological contamination may indicate possible contamination from surface drainage, feedlots, sewage systems, or other sources. The primary health hazard from drinking water with nitrates occurs when nitrate is transformed to nitrite in the digestive system. The effluent discharge maximum admissible limit value for nitrates is 25.0 mg l-1.

Table 10 depicts a relative constancy of the nitrates’ concentrations with similar monthly averages and small C.V.%. ANOVA test showed that since the p-value of the F-test (0.14) was greater than 0.05, there was not a statistically significant difference between the means of the 12 variables at the 95.0% confidence level.

Computed F-ratio was 1.46. Consequently, in the case of nitrates time series, it was considered a homogenous group. The only statistically significant differences were found with Fisher's least significant difference (LSD) procedure p<0.01 as follows: July - November (difference = 1.0369; DL = 1.0101) and November - December (difference = -1.1826; DL = 1.0980).

ARIMA (0,0,1) was the only possible configuration with significant terms (p<0.05). This model had the smallest RMSE (2.268), MAE (1.244) and MAPE (7.558) as compared to other linear models. It passed four tests, failing the test for difference in variance 1st half to 2nd half. Correlation coefficient (0.0519) indicated that there is not a statistically significant relationship between nitrates and ARIMA forecasts at the 90% or higher confidence level. The ARIMA model did not manage to forecast nitrates time series. Fig. 7 highlights many outliers in the nitrates time series making very difficult the use of linear models.

Table 8. Descriptive statistics of chemical oxygen demand time series



January 89 32.790 14.389 3.793 0.402 21.0 39.0 11.57 February 86 33.173 11.952 3.457 0.373 24.5 40.0 10.42 March 97 33.940 17.313 4.161 0.422 18.5 42.8 12.26 April 89 32.079 13.684 3.699 0.392 23.0 40.5 11.53 May 98 32.422 31.966 5.654 0.571 20.0 58.0 17.44 June 93 30.413 21.766 4.665 0.484 18.0 42.0 15.34 July 96 36.009 22.960 4.792 0.489 22.5 58.8 13.31



Total 906 32.351 27.562 5.250 0.174 9.0 58.8 16.23


479

Table 9. Multiple-Sample Comparison using Tukey HSD for total iron (Fe2+, Fe3+) time series with statistical highly significant differences (p<0.001) between monthly means; shows the direction to compute the difference between months

Jan. Feb. March April May June July August Sept. October November December

January - -3.2193 4.8424 February - 5.2250

March - 3.5269 3.3497 5.9925 5.5810 April - -3.9301 4.1317 May - -3.5874 4.4743 June - -5.5962 -5.4917 July - 4.9942 5.4190 8.0618 7.6503

August - 4.8896 5.3144 7.9572 7.5457 September -


Table 10. Descriptive statistics of nitrates time series



January 89 23.340 7.818 2.796 0.296 4.5 25 11.98 February 86 23.286 5.008 2.238 0.241 10.5 25 9.61 March 97 23.874 2.182 1.477 0.150 16.5 25 6.19 April 89 23.658 5.193 2.279 0.242 12.0 25 9.63 May 98 23.622 6.381 2.526 0.255 2.41 25 10.69 June 93 23.871 6.757 2.599 0.270 8.5 25 10.89 July 96 23.933 2.551 1.597 0.163 11.0 25 6.67

August 34 23.877 2.923 1.710 0.293 16.21 25 7.16 September 77 23.468 3.365 1.834 0.209 15.4 25 7.82

October 82 23.565 4.864 2.205 0.244 11.0 25 9.36 November 51 22.896 11.919 3.452 0.483 9.25 25 15.08 December 63 24.079 3.622 1.903 0.240 12.31 25 7.90

Total 955 23.633 5.149 2.269 0.073 2.41 25 9.60

Table 11. Descriptive statistics of suspended solids time series



January 89 48.040 38.687 6.220 0.659 30 59.6 12.95 February 86 49.785 27.203 5.216 0.562 28 60 10.48 March 97 48.918 25.842 5.084 0.516 25 58 10.39 April 89 44.138 29.286 5.412 0.574 30 56 12.26 May 98 45.945 28.766 5.363 0.542 28 59 11.67 June 93 45.557 34.387 5.864 0.608 24 60 12.87 July 96 44.066 21.181 4.602 0.470 32 58 10.44

August 34 43.977 12.528 3.539 0.607 35.2 54 8.05 September 77 40.074 57.432 7.578 0.864 24 54 18.91

October 82 41.549 38.003 6.165 0.681 22 56 14.84 November 51 40.204 28.873 5.373 0.752 27 57 13.37 December 19 42.453 26.493 5.147 1.181 29.6 49 12.12

Total 911 45.054 40.922 6.397 0.212 22 60 14.20 Table 12. Multiple-Sample Comparison using Tukey HSD for total suspended solids time series with statistical highly significant

differences (p<0.001) between monthly means; shows the direction to compute the difference between months

Jan. Feb. March April May June July August Sept. October November December January - 3.9028 3.9748 7.9669 6.4915 7.8365

February - 5.6472 3.8399 4.2284 5.7192 5.8084 9.7113 8.2359 9.5809 7.3322 March - 4.7798 3.3610 4.8519 4.9410 8.8440 7.3686 8.7136 6.4649 April - 4.0641 May - 5.8714 4.3960 5.7409 June - 5.4829 4.0075 5.3525 July - 3.9921

August - September -



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Fig. 7. Nitrates observed time series and ARIMA (0,0,1) modeled plot of the effluent that left the neutralization

station from chromium electroplating industry 3.1.7. Total Suspended solids (TSS)

TSS are solid materials, organic and inorganic, which are suspended in the water body including silt, drifting organisms (animals, plants or bacteria) and industrial wastes. High concentrations of suspended solids can lower water quality by absorbing light, lessening the ability of the water to hold oxygen required for aquatic life. TSS sources can result from erosion, urban runoff and agricultural land, industrial wastes, bank erosion, algal growth or wastewater discharges.

The main statistical indicators for the total suspended solids (TSS) time series are presented in Table 11. The maximum admissible limit value (GD, 2002) for TSS (35 mg l-1) in the industrial effluent was exceeded in each month during the monitoring period. September data showed the most dispersed variable (C.V.=18.91%). August had the lowest dispersion (10.42%). ANOVA provided statistically significant difference (95.0% confidence level) between the means of the 12 months data. F-ratio was 24.99 and p < 0.05.

Table 12 summarizes the results of the multiple-sample comparison for significant differences amongst the TSS monthly means, based on Tukey's HSD procedure. Between the corresponding means of months, 30 pairs showed statistical highly significant differences (p<0.001). ARIMA (1,0,1) configuration with significant terms (p<0.05) was selected for TSS time series (Fig. 8). This model had the smallest RMSE (4.793), MAE (3.433) and MAPE (8.16) as compared to other linear models.

It passed two tests, failing the test for excessive runs up and down (p<0.01), test for excessive runs above and below median (p<0.01) and the test for difference in mean 1st half to 2nd half (p<0.001). Correlation coefficient (0.662) indicated that there is a moderately strong statistically significant relationship between TSS and ARIMA forecasts at the 99% confidence level. R-squared was 43.95%.

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Fig. 8. Total suspended solids observed time series and ARIMA (1,0,1) modeled plot of the effluent that left the


3.2. General overview of the statistical model forecasting performances

Summarizing the results after performing a

wide range of statistical models using the effluent specific time series of most important parameters, has showed that ARIMA model with corresponding configuration was the most appropriate linear forecasting tool. Time series have been used without any preprocessing steps being obtained through effluent monitoring. The performance of the selected statistical models was evaluated and discussed according to the root mean square error (RMSE), the statistical significance of the terms in the forecasting model and the results of five tests run on the residuals to determine whether each model is adequate for the data. A comprehensive indicator was the correlation coefficient between observed and forecasted series. Table 13 presents the correlation coefficients for each of the seven analyzed parameters.

Adding the predicted concentrations (4 values ahead) and the corresponding real monitored data should provide a better image of the statistical model performances. ARIMA models gave satisfactory results for four effluent parameters (Hexavalent Chromium, Total Iron, Chemical Oxygen Demand and Total Suspended Solids) based on model performance parameters, predicted values and moderately strong correlations. As far as it concerns the other three parameters (pH, Total Chromium and Nitrates), linear models including ARIMA did not perform well when using the corresponding time series. Future work will consider the use of artificial neural networks, fuzzy logic and non linear models.

3.3. Exploratory factor analysis

The purpose of this multivariate analysis is to obtain a small number of factors, which account for most of the variability in the 6 selected variables (pH, Total Chromium, Total Iron, Chemical Oxygen Demand, Nitrates and Total Suspended Solids).


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Table 13. General overview of the ARIMA model forecasting performances for the treated effluent originating from the

chromium electroplating process

Parameter Statistical Model

Correlation coefficient

observed/predicted

4 values ahead predicted concentration

4 Recorded data (real concentration)

1 pH ARIMA (0,0,3) 0.314 7.39; 7.49; 7.54; 7.57 7.62; 7.09; 7.01; 7.12

2 Hexavalent Chromium ARIMA (3,0,3) 0.678 0.043; 0.039; 0.041; 0.038 0.07; 0.00; 0.06; 0.04

3 Total Chromium ARIMA (3,0,2) 0.367 0.233; 0.225; 0.219; 0.215 0.24; 0.24; 0.25; 0.28

4 Total Iron ARIMA (3,0,3) 0.591 2.179; 2.147; 2.042; 2.033 4.86; 3.90; 2.50; 2.51

5 COD - K2Cr2O7

ARIMA (3,0,3) 0.586 31.31; 31.14; 31.62; 31.68 31.00; 35.20; 33.80; 28.50

6 Nitrates ARIMA (0,0,1) 0.052 23.66; 23.62; 23.62; 23.62 24.68; 23.50; 25.00; 24.50

7 Suspended solids ARIMA (1,0,1) 0.662 44.64; 44.70; 44.74; 44.78 40.00; 45.00; 47.00; 44.00

Three factors have been extracted, since the

scree plot of the eigenvalues revealed three eigenvalues meeting the Kaiser criterion (>1). Together they account for 66.75% of the variability in the data. Rotation was performed in order to simplify the explanation of the factors. Varimax method was used to simplify the column of the factor matrix so that the extracted factors were clearly associated in order to allow some separation among the variables.

The latent factors content based on the respective values of the significant factor loadings estimated by EFA had the following structure: Factor 1 (COD, Nitrates, Total Suspended Solids), Factor 2 (Total Iron) and Factor 3 (pH, Total Chromium). The main variability in the original data (31.74%) was accounted in Factor 1 (COD, nitrates and suspended solids), which characterizes the resulted residues from the wastewater neutralization process. The second latent factor consists of total iron, which had time series with high coefficients of variation and explained 18.04% of the data set variability. Since the main objective of the neutralization station is to perform the industrial chemical treatment by precipitating the trivalent chromium hydroxide along with other heavy metals present in the influent and the pH correction, the effluent has presented constant time series for pH and Total Chromium characterized by small variance (16.83%). EFA modeling results indicated the most important latent factor that controls the structure of wastewater parameter data set, suggesting that further wastewater treatments should be considered to reduce the nitrates and suspended solids concentrations in the effluent. 4. Conclusions

The main contributions of this study are two-fold.

First, it provides a methodical and comprehensive statistical analysis of the time series for seven effluent parameters of wastewater treatment facility.

Second, it reveals information about the identification of the most appropriate statistical model

to a specific effluent variable time series and expected individual performance of identified linear ARIMA models based on the characteristics of the data used. Some of the statistical modeling techniques can provide approximations to supplement results from expensive analytic methods.

More complex models are required for wastewater time series analysis due to the domain complexity. Such models should assess auto-regressive tendencies, nonlinear relationships, interactions, and time varying dynamics.

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TIME SERIES ANALYSIS OF THE HEAVY METALS LOADED WASTEWATERS RESULTED FROM CHROMIUM ELECTROPLATING...

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