Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters

Waste Management xxx (2016) xxx–xxx

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Waste Management journal homepage: www.elsevier.com/locate/wasman

Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters Anjali G. Lothe, Alok Sinha ⇑ Department of Environmental Science and Engineering, Indian School of Mines, Dhanbad 826004, India

a r t i c l e

i n f o

Article history: Received 5 April 2016 Revised 15 July 2016 Accepted 18 July 2016 Available online xxxx Keywords: Landfill Leachate Leachate pollution index (LPI) Sub-index values Pollutant weight Error analysis Modelling

a b s t r a c t Leachate pollution index (LPI) is an environmental index which quantifies the pollution potential of leachate generated in landfill site. Calculation of Leachate pollution index (LPI) is based on concentration of 18 parameters present in leachate. However, in case of non-availability of all 18 parameters evaluation of actual values of LPI becomes difficult. In this study, a model has been developed to predict the actual values of LPI in case of partial availability of parameters. This model generates eleven equations that helps in determination of upper and lower limit of LPI. The geometric mean of these two values results in LPI value. Application of this model to three landfill site results in LPI value with an error of ±20% for Pn i wi P 0:6. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Leachate is the liquid generated during acid phase of landfill stabilization. During this phase pH of leachate generated decreases hence mobilises many heavy metals. Composition of leachate depends on many factors like characteristic of waste, landfill design and operation, other site specific characteristics and composition of waste (Rafizul et al., 2012). Poor management of the landfill sites is major concern for underground as well as surface water pollution in many underdeveloped and developing nations (Kumar et al., 2002; Pande et al., 2015). Due to improper installation of liners and leachate collection systems, leachate percolates into the ground water or nearby surface water bodies, degrading the water quality (Kumar and Alappat, 2003a, 2004). To regulate the pollution potential of leachate almost all countries have developed set of rules, but remedial measures are to be installed in phases which is a difficult process and are cost inefficient (Sharma et al., 2008; Kumar and Alappat, 2005a). Hence, to prevent unnecessary wastage of power and money, identification of vulnerable sites which would require immediate attention has become essential (Kumar and Alappat, 2005a). Development of Leachate Pollution Index (LPI) by Kumar and Alappat (2003b) made quantification of

⇑ Corresponding author. E-mail address: [email protected] (A. Sinha).

landfill pollution potential possible. It can be used as a comparative scale to measure which landfill is more hazardous and requires immediate remedial action. The Leachate Potential Index (LPI) is a mathematical method of calculating a single value from various physic-chemical and biological parameters of landfill leachate (Kumar and Alappat, 2004). LPI is an increasing scale index i.e. higher LPI value signifies that the landfill site has high pollution causing potential. It was developed using DELPHI technique, detailed procedures of which been discussed in Kumar and Alappat (2003a, 2005a). Total number of eighteen parameters is required for LPI calculation. The 18 leachate pollution parameters considered for calculating LPI are chromium, lead, chemical oxygen demand (COD), mercury, biochemical oxygen demand (BOD5), arsenic, cyanide, phenolic compounds, zinc, pH, Total Kjeldahl Nitrogen (TKN), nickel, total Coliform bacteria, ammonical nitrogen, total dissolved solids (TDS), copper, chlorides, and total iron (Kumar and Alappat, 2003a, 2003b). Each of these parameters has weights (wi) determined on the basis of significance value assigned to each variable through Delphi technique (Kumar and Alappat, 2005a). The weights assigned to different parameters are shown in Table 1. For each parameters average ‘‘sub-index curves” were drawn by the experts where the concentration of each parameters were plotted against the levels of leachate pollution (0–100). Hence for a given concentration the sub-index scores (pi) can be obtained from these curves. Value of pi varied from 0 to 100 and concentration of

http://dx.doi.org/10.1016/j.wasman.2016.07.026 0956-053X/Ó 2016 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026

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A.G. Lothe, A. Sinha / Waste Management xxx (2016) xxx–xxx

Table 1 Weights of the pollutant parameters included in leachate pollution index (LPI) (Kumar and Alappat, 2003a, 2003b; Kumar and Alappat, 2005a, 2005b; Sharma et al., 2008). Sr. No.

Pollutant

Significance

Pollutant weight

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

pH Total dissolved solids BOD5 COD TKN Ammonia nitrogen Total iron Copper Nickel Zinc Lead Total chromium Mercury Arsenic Phenolic compounds Chlorides Cyanide Total coliform bacteria Total

3.509 3.196 3.902 3.963 3.367 3.250 2.830 3.170 3.321 3.585 4.019 4.057 3.923 3.885 3.627 3.078 3.694 3.289 63.165

0.055 0.050 0.061 0.062 0.053 0.051 0.045 0.050 0.052 0.056 0.063 0.064 0.062 0.061 0.057 0.048 0.058 0.052 0.999

the pollutants varied up to the maximum concentration reported in the literatures. Determination of LPI includes analysis of concentration of pollutants to determine pi using the rating curves. Values of pi and wi are put in the following formula (Kumar and Alappat, 2005a): n X LPI ¼ pi wi i¼1

, n X wi

ð1Þ

i

where LPI = the weighted additive leachate pollution index, wi = the weight for the ith pollutant variable, pi = the sub index score of the ith leachate pollutant variable, n = number of leachate pollutant variables used in calculating LPI, P If, n = 18, ni wi ¼ 1, P and if n < 18, ni wi < 1. For estimation of correct value of LPI it is required to analyse concentration of all eighteen parameters. Analysis of some of these parameters can be difficult and time consuming process, which leads to unavailability of parameters, hence error in LPI value. In few cases where error is negative, value of LPI is exaggerated and when error comes out to be positive, the LPI value is understated. Kumar and Alappat (2005b) calculated the errors involved in LPI calculations in absence of 18 parameters. They calculated the errors involved in absence of data having low weights, high weights, low sub-index and high sub-index values. They concluded that the errors may be high if the data for the parameters having significantly high or low concentration are not taken into account. Use of randomized data in calculation of risk assessment has been used widely for providing authentic values of risk (Chen and Liao, 2006; Chen et al., 2012; Yang et al., 2014; Gungormus et al., 2014). However, use of randomized data for evaluation of LPI in absence of desired parameters has not been addressed. This paper aims at estimating the LPI values in absence of parameters through development of general equations by generating random data. These equations would facilitate calculation of the actual values of LPI even in the absence of some parameters. Validation of these equations is also demonstrated by presenting case studies for three landfill sites in India namely Okhla landfill site, Dhapa landfill site and Chittagong landfill site.

2. Methodology adopted 2.1. Data set generation Two types of data sets were generated. Both of these data sets included assignment of random values to sub-index score of each variable. Data set type 1: Objective of this data set was to determine relaPn  tion between i¼1 pi wi =LPI normalized value (ni) and % error. To create this data set random sub-index values were selected for all 18 variables. Randbetween() function present in Microsoft Excel was used to define these data sets. Sub-index values vary from 5 to 100, minimum sub-index value of 5 is assigned to each variable in order to obtain non-zero value of LPI (Kumar and Alappat, 2005a). Approximately more than 500 data sets were generated. Data set type 2: Objective of this data set was to plot boundary P P values of ni¼1 pi wi against corresponding % error for different ni wi values. To define these datasets groups of the parameters were formed such that each group had different number of parameters in the group. For instance, if group of parameters was determined to have 17 parameters, according to permutation and combination theory there were 18C17 i.e. 18 combinations possible. Groups were formed such that it had 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, or minimum 6 numbers of parameters. So, the total 226 combinations P were possible hence 226 values for ni wi were obtained. Random sub-index values were generated using same function as described above, for the group of parameters considered, while rest of the parameters were assigned 5 and 100 as sub-index in order to Pn obtain minimum and maximum i¼1 pi wi values, respectively. Pn For each i wi value, 24 sets of data were generated. Table 2 exemP plifies the data sets for ni wi ¼ 0:33 when only 6 parameters were considered. Pn As can be seen from the Table 2 for i wi ¼ 0:33 only six parameters including Cr, phenolic compounds, Zn, pH, TKN and Fe are assigned random values and rest of the parameters are assigned with 5 and 100. 2.2. Error analysis study Imitating the approach of Kumar and Alappat (2005b) and Rafizul et al. (2012) for estimating errors involved in calculation of LPI, in case of non-availability of concentration of pollutants, four cases were considered and pollutants were ignored on the basis of their weights. All these four cases were applied on both P type of data sets and calculated values of ni¼1 pi wi , % error and ni were collected for further estimation. To produce different cases, all the parameters were sorted according to decreasing weights and four cases were created. 2.2.1. CASE 1: Removing pollutants with higher weights (1) Table 3 exemplifies the first iteration of case 1 where number of parameters considered for LPI calculation is 6. It was assumed that concentration of chromium is not available and was ignored in first step of calculation of case 1, as reported in column 7 of Table 3. (2) In the next step parameter with second highest weight was ignored. Similar pattern was followed until minimum 6 parameters were left. (3) Calculation of LPI was done using Eq. (1). For each case the P values of LPI, ni¼1 pi wi , % error and ni are calculated. (4) Percentages error was calculated with respect to actual LPI P (based on 18 parameters) values and ni¼1 pi wi was normalized by corresponding LPI for that data set, for calculation of normalized values (ni).

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026

Pollutant

Wi

Sub- index values

Cr Pb COD Hg BOD5 As CN

0.064

5 5 5 5 5 5 5

5 5 5 5 5 5 5

14 5 5 5 5 5 5

25 5 5 5 5 5 5

39 5 5 5 5 5 5

43 5 5 5 5 5 5

51 5 5 5 5 5 5

70 5 5 5 5 5 5

76 5 5 5 5 5 5

81 5 5 5 5 5 5

99 5 5 5 5 5 5

100 5 5 5 5 5 5

5 100 100 100 100 100 100

5 100 100 100 100 100 100

14 100 100 100 100 100 100

25 100 100 100 100 100 100

39 100 100 100 100 100 100

43 100 100 100 100 100 100

51 100 100 100 100 100 100

70 100 100 100 100 100 100

76 100 100 100 100 100 100

81 100 100 100 100 100 100

99 100 100 100 100 100 100

100 100 100 100 100 100 100

Phenolic compounds Zn pH TKN Ni TCB NH3-N TDS Cu Cl Fe P wi

0.057 0.056 0.055 0.053

5 5 5 5 5 5 5 5 5 5 5

5 9 6 10 5 5 5 5 5 5 10

18 13 15 17 5 5 5 5 5 5 14

27 21 23 26 5 5 5 5 5 5 21

36 36 33 38 5 5 5 5 5 5 33

50 46 43 47 5 5 5 5 5 5 45

54 55 55 56 5 5 5 5 5 5 55

62 69 64 66 5 5 5 5 5 5 66

71 74 73 76 5 5 5 5 5 5 73

81 86 88 88 5 5 5 5 5 5 86

96 95 94 94 5 5 5 5 5 5 100

100 100 100 100 5 5 5 5 5 5 100

5 5 5 5 100 100 100 100 100 100 5

5 9 6 10 100 100 100 100 100 100 10

18 13 15 17 100 100 100 100 100 100 14

27 21 23 26 100 100 100 100 100 100 21

36 36 33 38 100 100 100 100 100 100 33

50 46 43 47 100 100 100 100 100 100 45

54 55 55 56 100 100 100 100 100 100 55

62 69 64 66 100 100 100 100 100 100 66

71 74 73 76 100 100 100 100 100 100 73

81 86 88 88 100 100 100 100 100 100 86

96 95 94 94 100 100 100 100 100 100 100

100 100 100 100 100 100 100 100 100 100 100

0.044 0.33

Table 3 Error estimation on removing parameters with higher weights. Sr. No.

Leachate variables

Weightage (wi)

Pollutant subindex (pi)

No. of parameters P

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Cr Pb COD Hg BOD5 As CN Phenolic compounds Zn pH TKN Ni TCB NH3-N TDS Cu Cl Fe

0.064 0.063 0.062 0.062 0.061 0.061 0.058 0.057 0.056 0.055 0.053 0.052 0.052 0.051 0.05 0.05 0.048 0.044

59 56 5 5 5 5 5 5 58 57 5 5 5 5 5 5 57 52

wi

piwi

P

piwi LPI %e ni

18 1

17 0.936

16 0.873

15 0.811

14 0.749

13 0.688

12 0.627

11 0.569

10 0.512

9 0.456

8 0.401

7 0.348

6 0.296

3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.26 0.255 0.25 0.25 2.736 2.288

22.06 22.056 0 1

18.28 19.530 11.453 0.829

14.75 16.898 23.386 0.669

14.44 17.808 19.262 0.655

14.13 18.868 14.455 0.641

13.83 20.097 8.880 0.627

13.52 21.566 2.221 0.613

13.23 23.255 -5.435 0.599

12.95 25.287 -14.65 0.587

9.699 21.270 3.565 0.440

6.564 16.369 25.784 0.298

6.299 18.101 17.934 0.286

6.039 20.402 7.499 0.274

A.G. Lothe, A. Sinha / Waste Management xxx (2016) xxx–xxx 3

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026

Table 2 Pn Data set for i wi ¼ 0:33.

8.534 22.818 3.456 0.387 8.824 20.426 7.391 0.400 9.109 18.628 15.543 0.413 12.357 22.673 2.799 0.560 15.492 25.82 17.07 0.702 15.757 24.130 9.404 0.714 16.017 22.719 3.007 0.726 16.277 21.502 2.512 0.738 16.532 20.460 7.234 0.750 16.782 19.559 11.319 0.761 17.032 18.758 14.954 0.772

3.776 3.528 0.31 0.31 0.305 0.305 0.29 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736

19.768 20.678 6.248 0.896 22.056 22.056 0 1 piwi LPI %e ni

P

18 1 wi

Cr Pb COD Hg BOD5 As CN Phenolic compounds Zn pH TKN Ni TCB NH3-N TDS Cu Cl Fe 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Weightage (wi)

(1) After performing calculations, as per case 1, 2, 3 and 4 mentioned in error analysis section, for both types of Pn datasets, values of % error and ni were i¼1 pi wi , collected. Pn (2) Corresponding to one value of i wi different values of Pn p w , % error and n were generated and were sorted i i¼1 i i Pn w values. Different values of according to ascending i i Pn p w , % error and n were obtained because of different i i i¼1 i sub-index values assigned to each parameter while forming data sets. P (3) Curves were plotted between ni¼1 pi wi and % error and also between % error and ni. Plotting of the data was done using curve fitting function i.e. cftool in MATLAB 7.10.0499 (R2010a) software.

Leachate variables

3. Data accumulation and plotting

Sr. No.

(1) In case 4 variables with highest weight and least weight i.e. Cr and Fe respectively, were eliminated simultaneously in the first iteration. (2) Next iteration eliminated second highest and second lowest weighed variable i.e. Pb and Cl respectively. Iterations repeated till first iteration was repeated. (3) Example of first iteration of this case is mentioned in Table 6 below.

Table 4 Error estimation on removing parameters with lower weights.

2.2.4. CASE 4: Removing pollutants with both highest and lowest weights simultaneously

Pollutant subindex (pi)

No. of parameters

17 0.956

16 0.908

15 0.858

14 0.808

13 0.757

(1) As total number of parameters being even in number, two variables whose weights stand in the middle of series, when arranged in descending order, i.e. Zn and pH, were eliminated first. (2) In next iteration variable having higher significance than Zn i.e. phenolic compounds and variable with lower weight than pH i.e. TKN were eliminated simultaneously; third iteration elimination started from variable with higher weight than phenolic compound i.e. CN and lower weight than TKN i.e. Ni, and so on the next iterations continued until first case was repeated. In each iteration minimum number of parameters left were 6. (3) Table 5 exemplifies case 3 and has same notifications as mentioned earlier.

3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

2.2.3. CASE 3: Removing two pollutants having moderate weights

piwi

12 0.705

11 0.653

10 0.6

9 0.545

(1) Similar to case 1 elimination of the parameters, in this case, started from lowest weighted parameter that is Fe in first iteration and in next iteration elimination started from next least weighted parameter that is Cl such that minimum 6 parameters are left. (2) Hence, the iterations continued till the first iteration was repeated i.e. lowest weighted parameter Fe was removed. Table 4 shows the first iteration of case 2. P (3) Similar to case 1, the values of LPI, ni¼1 pi wi , % error and ni were calculated for each iteration.

59 56 5 5 5 5 5 5 58 57 5 5 5 5 5 5 57 52

8 0.489

2.2.2. CASE 2: Removing pollutants with lower weights

0.064 0.063 0.062 0.062 0.061 0.061 0.058 0.057 0.056 0.055 0.053 0.052 0.052 0.051 0.05 0.05 0.048 0.044

7 0.432

6 0.374

(5) First iteration started with elimination of highest weighted parameter chromium. Next iteration followed same steps but elimination started from next highest weight parameter i.e. Pb and so on the pattern continued until iteration repeated and started elimination of chromium again. In each iteration minimum 6 parameters were left.

3.776 3.528 0.31 0.31 0.305 0.305

A.G. Lothe, A. Sinha / Waste Management xxx (2016) xxx–xxx

P

4

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026

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A.G. Lothe, A. Sinha / Waste Management xxx (2016) xxx–xxx

(4) Curves of % error vs ni was plotted using dataset type 1 for all P the ni wi values and total 226 curves were obtained. P P (5) Data for ni¼1 pi wi and % error obtained for each ni wi value, P after performing calculations on dataset type 2, ni¼1 pi wi vs Pn % error curves were plotted for each i wi value. As miniP mum and maximum values of ni¼1 pi wi were plotted against corresponding % error, two boundary curves were obtained. (6) After curve plotting curve fitting operation was carried out. In order to fit curves EXCLUDE tool and FITTING tool present in MATLAB 7.10.0499 (R2010a) software were used. Exclude P tool was used because ni¼1 pi wi vs % error plots contained

    P P both max ni¼1 pi wi vs % error and min ni¼1 pi wi vs % error curves, hence exclude tool helped in elimination of one of the curve when fitting for other was done. 4. Results and discussion 4.1. Plot of % error (ei) vs normalized

Pn

i¼1 pi wi

(ni)

 Plotting % error vs ni (Fig. 1a) resulted in family of lines. For all Pn 226 values of i wi , % error vs ni graphs were plotted sepaP rately. A typical case for ni wi ¼ 0:588 is shown in Fig. 1b.

Table 5 Error estimation on removing parameters with moderate weights. Sr. No.

Leachate Pollution variables

Weightage (wi)

Pollutant subindex (pi)

No. of parameters P

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Cr Pb COD Hg BOD5 As CN Phenolic compounds Zn pH TKN Ni TCB NH3-N TDS Cu Cl Fe

0.064 0.063 0.062 0.062 0.061 0.061 0.058 0.057 0.056 0.055 0.053 0.052 0.052 0.051 0.05 0.05 0.048 0.044

59 56 5 5 5 5 5 5 58 57 5 5 5 5 5 5 57 52

wi

piwi

P

piwi

LPI %e ni

18 1

16 0.889

14 0.779

12 0.669

10 0.556

8 0.444

6 0.332

3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285

3.776 3.528 0.31 0.31 0.305 0.305 0.29

3.776 3.528 0.31 0.31 0.305 0.305

3.776 3.528 0.31 0.31 0.305

3.776 3.528 0.31 0.31

3.776 3.528 0.31

0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.26 0.26 0.255 0.25 0.25 2.736 2.288

0.26 0.255 0.25 0.25 2.736 2.288

0.255 0.25 0.25 2.736 2.288

0.25 0.25 2.736 2.288

0.25 2.736 2.288

22.056 22.056 0 1

15.673 17.630 20.067 0.711

15.123 19.413 11.981 0.686

14.573 21.783 1.237 0.661

14.008 25.194 14.228 0.635

13.448 30.288 37.324 0.610

12.888 38.819 76.003 0.584

Table 6 Error estimation on removing parameters with both highest and lowest weights simultaneously. Sr. No.

Leachate pollution variables

Weightage (wi)

Pollutant subindex (pi)

No. of parameters P

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Cr Pb COD Hg BOD5 As CN Phenolic compounds Zn pH TKN Ni TCB NH3-N TDS Cu Cl Fe

0.064 0.063 0.062 0.062 0.061 0.061 0.058 0.057 0.056 0.055 0.053 0.052 0.052 0.051 0.05 0.05 0.048 0.044

59 56 5 5 5 5 5 5 58 57 5 5 5 5 5 5 57 52

wi

piwi

P LPI %e ni

piwi

18 1

16 0.892

14 0.781

12 0.669

10 0.557

8 0.445

6 0.332

3.776 3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736 2.288

3.528 0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25 2.736

0.31 0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25 0.25

0.31 0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255 0.25

0.305 0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26 0.255

0.305 0.29 0.285 3.248 3.135 0.265 0.26 0.26

0.29 0.285 3.248 3.135 0.265 0.26

22.056 22.056 0 1

15.992 17.928 18.715 0.725

9.728 12.456 43.526 0.441

9.168 13.704 37.867 0.416

8.608 15.454 29.932 0.390

8.048 18.085 18.002 0.365

7.483 22.539 2.191 0.339

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026

6

A.G. Lothe, A. Sinha / Waste Management xxx (2016) xxx–xxx

Fig. 2. Plot for slope (m) against corresponding cumulative weights

Pn i

 wi .

P  Curve of m vs ni wi was plotted using cftool. The same is represented in Fig. 2. General equation for the curve above is 3

f ðxÞ ¼ ax4 þ bx þ cx2 þ dx þ e

ð3Þ

P where f(x) represent ‘m’ and x represent ‘ ni wi ’. The values for the coefficients have been mentioned in Table 7. 4.2. Plot for % errors (ei) vs

P Fig. 1. (a) % Error (ei) vs normalized ni¼1 pi wi (ni) for cumulative data. (b) % Error vs P P normalized ni¼1 pi wi (ni) for ni wi ¼ 0:588.

 For this case the equation for the straight line obtained is y ¼ 169:78x þ 100, so generalised equation for family of straight line is

y ¼ mx þ 100

ð2Þ

where y represents % error corresponding to x which represents P normalized ni¼1 pi wi values i.e. ni. P  Similar equations were obtained for all ni wi values. As these curves represented family of lines, slope (m) of each straight P line was noted against ni wi value in a tabular form.

Pn

i¼1 pi wi

each

Pn i

wi value

P Pn  For all 226 values of ni wi , % errors vs i¼1 pi wi graphs were P n plotted. Fig. 3 depicts a specific plot for i wi ¼ 0:588 which shows the upper and lower limits of the plotted data. P  The general equation for upper limit of ni¼1 pi wi was fitted with Eq. (4) as follows:

f ðxÞ ¼ P1 x3 þ P2 x2 þ P3 x þ P4 for

ð4Þ

The coefficients of this equation (with 95% confidence bounds) Pn i wi ¼ 0:588 obtained are as follows:

P1 ¼ 0:0003128; P2 ¼ 0:05326; P3 ¼ 3:597; P4 ¼ 96:59 ðR-square : 0:9997Þ  Similarly the general equation for lower limits of % errors vs Pn i¼1 pi wi was fitted with Eq. (5) as follows:

f ðxÞ ¼ Q 1 x3 þ Q 2 x2 þ Q 3 x þ Q 4

ð5Þ

Table 7 Coefficients for Eqs. (3) and (6)–(13). Sr. No. 1. 2.

3.

a

b

c

d

e

f

R-square

5756

3331

928.9

–

0.9999

0.00503 13.3 861.1 1.344e+004

0.0005321 7.572 501.5 7196

0.0005375 2.166 149.7 1874

– 0.3026 22.34 289.7

0.9818 0.965 0.9959 0.9989

P1 P2 P3 P4

P vs w P i vs w P i vs w P i vs wi

Eq. Eq. Eq. Eq.

(6) (7) (8) (9)

1.833 82 1052 1271

0.8859 41.91 587.6 664.1

0.1617 8.266 131.9 147.2

– – – –

0.9939 0.9956 0.9971 0.9711

Q1 Q2 Q3 Q4

P vs w P i vs w P i vs w P i vs wi

Eq. Eq. Eq. Eq.

(10) (11) (12) (13)

P

m vs wi 1550

4801 P Upper limit of % error vs piwi 0.00442 0.008537 4.017 11.63 255.3 743.8 4403 1.226e+004 P Lower limit of % error vs piwi 0.5748 1.6282 23.95 72.27 276.5 872 401.3 1154

Eq. (3)

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026

7

A.G. Lothe, A. Sinha / Waste Management xxx (2016) xxx–xxx

The coefficients (with 95% confidence bounds) of equation 4 P obtained after curve fitting (R2 = 0.9613) for ni wi ¼ 0:588 are as follows:

Q 1 ¼ 0:0005815; Q 2 ¼ 0:07881; Q 3 ¼ 3:397; Q 4 ¼ 5:742

P  Similar types of curves were obtained for all 226 values of ni wi . Further, generalization of these curves was done by plotting P coefficients of upper and lower limit curves against ni wi . P 4.2.1. Plots for upper limit coefficients vs ni wi All the 226 values of coefficients of upper limit plots (P1, P2, Pn P3 and P4) were plotted against corresponding i wi values. Pn Fig. 4a shows the plot of P1 vs i wi . For generalising the values P of P1 for a given ni wi value, a curve was fitted to these values. The equation generated from the fitted data is represented as follows: 3

P1 ¼ aw4i þ bwi þ cw2i þ dwi þ e

ð6Þ

The values of coefficients of curve fitted to find P1 values for difP ferent ni wi are mentioned in Table 7. The goodness of fit for the fitted data is also mentioned in Table 7. Similarly, the values of Pn P2, P3, & P4 were plotted against corresponding i wi values (Fig. 4b–d). The equations generated by fitting the data thus obtained are as follows: 4

2

P2 ¼ aw5i þ bwi þ cw3i þ dwi þ ewi þ f

Fig. 3. Variation of % errors vs

Fig. 4. (a) P1 vs equation.

Pn i

Pn

i¼1 pi wi

for

Pn i

wi plot for upper limit equation, (b) P2 vs

wi ¼ 0:588.

Pn i

P3 ¼

aw5i

þ

P4 ¼

aw5i

þ

4 bwi 4 bwi

þ

cw3i

þ

þ

cw3i

þ

2 dwi 2 dwi

ð7Þ

þ ewi þ f

ð8Þ

þ ewi þ f

ð9Þ

Values of coefficients for all the above equations are reported in Table 7.

wi plot for upper limit equation, (c) P3 vs

Pn i

wi plot for upper limit equation, (d) P4 vs

Pn i

wi plot for upper limit

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026

8

A.G. Lothe, A. Sinha / Waste Management xxx (2016) xxx–xxx

Fig. 5. (a) Q1 vs limit equation.

Pn i

wi plot for lower limit equation, (b) Q2 vs

Pn i

wi plot for lower limit equation, (c) Q3 vs

Pn i

wi plot for lower limit equation, (d) Q4 vs

Pn i

wi plot for lower

P 4.2.2. Plots for lower limit coefficients vs ni wi In similar manner as upper limit plots, all the 226 values of coefficients of lower limit plots (Q1, Q2, Q3 and Q4) were plotted P against corresponding ni wi values. Fig. 5a, b, c, d shows the plot Pn of Q1, Q2, Q3 & Q4 vs i wi ; respectively. For generalising the values P of Q1, Q2, Q3 and Q4 for a given ni wi value, a curve was fitted. The equations obtained after fitting curves are represented as follows: 3

ð10Þ

3

ð11Þ

Q 1 ¼ aw4i þ bwi þ cw2i þ dwi þ e Q 2 ¼ aw4i þ bwi þ cw2i þ dwi þ e 3

Q 3 ¼ aw4i þ bwi þ cw2i þ dwi þ e Q4 ¼

aw4i

þ

3 bwi

þ

cw2i

þ dwi þ e

ð12Þ ð13Þ

The coefficients for the equations describing the values of upper limit of error i.e. P1, P2, P3, & P4 and lower limits of error i.e. Q1, Q2, P Q3 & Q4 for various values of ni wi are mentioned in Table 7. The flow chart for calculation of LPI values by the above developed model is shown in Fig. 6. 5. Case study To prove authenticity of the model, LPI was calculated for three landfill sites whose actual LPI values were known. Three landfill sites were considered viz., Okhla Landfill Site (Sharma et al., 2008), Dhapa Landfill Site (Polley, 2012) and Chittagong Landfill Site (Rafizul et al., 2012).

Fig. 6. Flow chart depicting calculation of LPI by developed model.

For all the landfill sites, availability of parameters was varied as P per the cases described above and ni¼1 pi wi values were generated. Two values required for calculation of LPI using this model are Pn Pn i¼1 pi wi and i¼1 wi . Steps for calculating LPI using this model are described below: P P P (1) Find the values for ni¼1 pi wi and ni¼1 wi . To find ni¼1 pi wi , determine the sub-index scores for each parameters using the sub-index vs concentration curves (Kumar and Alappat, 2004, 2003a, 2005a). In this case concentration of

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026

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A.G. Lothe, A. Sinha / Waste Management xxx (2016) xxx–xxx

parameters were known but in other cases there is a possibility that concentration for all parameters are not P P known, so find value of ni¼1 pi wi and ni¼1 wi for all available parameters. Pn (2) Determine value of slope (m) using i¼1 wi values, Eq. (3) and Table 7. (3) Use Eqs. (6)–(9) and coefficients in Table 7 to find P1, P2, P3 and P4 respectively. After finding these values, put these valPn ues and i¼1 pi wi in Eq. (4) to determine upper limit of % error.

(4) Use Eqs. (10)–(13) and coefficients in Table 7 to find Q1, Q2, Q3 and Q4 respectively. After finding these values, put these P values and ni¼1 pi wi in Eq. (5) to determine lower limit of % error. (5) Now using Eq. (2) and value of m determined in step 2, find Pn   upper and lower values of ni i¼1 pi wi LPI . As value of Pn i¼1 pi wi is known upper and lower limits of LPI are found. The calculated range of LPI values for all three landfill sites are mentioned in Table 8

Table 8 Comparison of range of LPI found through the model and actual LPI. Sr. No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Pn i

wi

0.295 0.308 0.33 0.359 0.401 0.456 0.495 0.52 0.555 0.599 0.627 0.663 0.707 0.745 0.777 0.829 0.852 0.894 0.902 0.938 0.947 0.952

Okhla landfill sites actual LPI (24.318) Pn Upper limit of Lower limit of i¼1 pi wi LPI LPI

Dhapa landfill site actual LPI (37.901) Pn Upper limit of Lower limit of i¼1 pi wi LPI LPI

Chittagong landfill site actual LPI (38.151) Pn Upper limit of Lower limit of i¼1 pi wi LPI LPI

11.016 7.16 3.26 11.528 12.466 12.796 13.093 13.308 11.265 17.851 14.396 12.432 19.241 14.46 16.174 22.654 20.616 22.868 21.766 23.977 23.258 23.166

17.073 20.017 8.229 23.345 18.074 18.349 29.082 24.346 25.381 32.722 19.636 21.86 33.686 25.602 25.162 30.524 28.726 36.9 31.251 34.925 37.212 33.101

11.507 12.579 9.187 17.779 13.674 13.949 25.326 20.221 21.954 30.838 14.928 23.544 32.968 27.512 31.986 23.934 35.991 35.984 36.891 37.841 36.296 37.191

82.4717 77.68813 71.6498 76.24568 73.23223 68.36715 64.85674 62.59416 57.48242 58.77836 53.17123 48.16442 49.63528 42.16342 40.43004 40.29221 36.36324 33.90017 32.22608 30.54013 29.12083 28.58804

14.24517 10.90773 6.966238 14.56001 15.26934 15.40527 15.54658 15.65274 13.74428 19.21728 16.17059 14.24193 19.77664 15.48404 16.69299 21.29068 19.51566 20.69221 19.82163 20.94024 20.38037 20.27228

87.98255 89.56681 75.974 87.93637 78.56535 73.38301 79.75238 72.55265 69.9669 72.49851 57.62166 56.06 62.04298 51.12195 47.53476 46.53198 42.7302 45.12036 39.75243 39.29268 40.30624 36.58136

14.68318 15.62236 12.60241 20.3285 16.31849 16.39202 26.42516 21.56971 22.87924 30.02583 16.62866 23.49386 29.78632 25.67984 28.23251 22.22015 29.51487 28.56978 28.76854 27.62428 26.67733 26.66934

20

0

0.2

0.4

0.6

0.8

-40

AM

-60

10

1

GM

Error (%)

Error (%)

-20

82.88948 82.38108 76.86403 82.36955 74.3606 69.37787 76.06381 68.6867 66.76617 70.67427 53.61712 57.51517 61.39412 52.71058 53.16655 41.29165 48.65716 44.36594 44.31791 41.63748 39.57308 39.83963

30

20 0

20.1357 23.20157 11.78307 26.11562 20.31241 20.2412 30.11471 25.25678 25.86702 31.6005 20.56967 22.16487 30.24143 24.32988 23.68371 26.65074 25.18377 29.02446 25.86368 26.59635 26.95124 25.3718

-80

0 -10

0

0.2

0.4

0.6

0.8

1

-20 -30 -40

-100

-50

-120

-60

AM GM

ΣWi

ΣWi

(b)

(a) 30

Error (%)

20 10 0 -10

0

0.2

0.4

0.6

0.8

1

-20

AM

-30 -40

GM

ΣWi

(c) Fig. 7. Graph of % error vs summation of weights for (a) Dhapa Landfill site, (b) Okhla Landfill site, (c) Chittagong Landfill site.

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026

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A.G. Lothe, A. Sinha / Waste Management xxx (2016) xxx–xxx

The arithmetic mean and geometric mean of the upper limit and lower limit of LPI thus obtained were calculated and it was found that the geometric mean of the values better predicted the LPI values for different weights of parameters. Fig. 7 shows the comparison of geometric mean values and arithmetic mean values of the LPI obtained from upper limit and lower limits plots for Okhla landfill site. The error in estimation of LPI values by model developed in this study varies from 40% to +8% for geometric mean values whereas up to 98% using arithmetic mean values. As the weightage of the parameters increases the % error in prediction of actual LPI values decreases (Fig. 7a). Similarly, for Dhapa landfill site the % error using geometric mean varied from 26% to +21% and 51% to +18% for arithmetic mean values (Fig. 7b). For Chittagong Landfill Site the prediction gave an error of 21% to +21% using geometric mean values whereas 34% to +13% using arithmetic mean values (Fig. 7c). Hence the prediction of actual LPI values in absence of all the parameters can be done by using developed model using geometric mean values of LPI which may result in an error of ±20% when Rwi exceeds 0.6. 6. Conclusions A model was developed for estimation of Leachate Potential Index (LPI) values in absence of few parameters. The model was Pn  nordeveloped by establishing relation between i¼1 pi wi =LPI malized value (ni) and % error and by plotting boundary values of Pn Pn i¼1 pi wi against corresponding % error for different i wi values, by generating random dataset. All the equations for % error vs ni P plots were family of straight lines and that of ni¼1 pi wi vs % error were cubic in nature. Values of slopes of straight line (m) plots P for % error vs ni were plotted against corresponding ni wi , similarly coefficients of cubic equations (P1, P2, P3, P4, Q1, Q2, Q3 P and Q4) were separately plotted against corresponding ni wi values. Ultimately, eleven major equations were developed. To authenticate the use of these equations, calculations were performed for three landfill sites whose actual LPI values were already known, then the geometric and arithmetic mean of the upper and lower LPI values obtained were found. Geometric mean was P observed to give % error of ±20% for ni wi ¼ 0:6 for all the landfill

sites. Hence, in absence of complete data for estimation of Leachate Potential Index (LPI) this method may provide an estimation of reliable values of LPI. References Chen, J.W., Wang, S.L., Hsieh, D.P.H., Yang, H.H., Lee, H.L., 2012. Carcinogenic potencies of polycyclic aromatic hydrocarbons for back-door neighbors of restaurants with cooking emissions. Sci. Total Environ. 417–418, 68–75. http:// dx.doi.org/10.1016/j.scitotenv.2011.12.012. Chen, S.-C., Liao, C.-M., 2006. Health risk assessment on human exposed to environmental polycyclic aromatic hydrocarbons pollution sources. Sci. Total Environ. 366, 112–123. http://dx.doi.org/10.1016/j.scitotenv.2005.08.047. Gungormus, E., Tuncel, S., Hakan Tecer, L., Sofuoglu, S.C., 2014. Inhalation and dermal exposure to atmospheric polycyclic aromatic hydrocarbons and associated carcinogenic risks in a relatively small city. Ecotoxicol. Environ. Saf. 108, 106–113. http://dx.doi.org/10.1016/j.ecoenv.2014.06.015. Kumar, D., Alappat, B.J., 2003a. A technique to quantify landfill leachate pollution. In: Proceedings Sardinia 2003, Ninth International Waste Management and Landfill Symposium S. Margherita di Pula, Cagliari, Italy; 6–10 October 2003. Kumar, D., Alappat, B.J., 2003b. Analysis of leachate contamination potential of a municipal landfill using leachate pollution index. In: Proceedings of the Workshop on Sustainable Landfill Management, 3–5 December, 2003, pp. 147–153. Kumar, D., Alappat, B.J., 2004. Selection of the Appropriate Aggregation Function for Calculating Leachate Pollution Index. Pract. Period. Hazard. Toxic Radioact. Waste Manage. 8 (4). Kumar, D., Alappat, B.J., 2005a. Evaluating leachate contamination potential of landfill sites using leachate pollution index. Clean Technol. Environ. Policy 7, 190–197. Kumar, D., Alappat, B.J., 2005b. Errors involved in the estimation of leachate pollution index. Pract. Period. Hazard. Toxic Radioact. Waste Manage. 9 (2), 103–111. Kumar, D., Khare, M., Alappat, B.J., 2002. Threat to groundwater from the municipal landfills in Delhi, India. In: Proc., 28th WEDC Conf. on Sustainable Environmental Sanitation and Water Services, Calcutta, India, pp. 377–380. Pande, G., Sinha, A., Agrawal, S., 2015. Impacts of leachate percolation on ground water quality: a case study of Dhanbad. Glob. Nest J. 17 (1), 162–174. Polley, D., 2012. Characterization of MSW Landfill Leachate and Evaluation of LPI for Dhapa, Kolkata Landfill Site PhD Thesis. Jadavpur University, Faculty of Engineering & Technology. Rafizul, I.M., Minhaz, M.M., Alamgir, M., 2012. Analysis of errors involved in the estimation of leachate pollution index due to nonavailability of leachate parameter. Iran. J. Energy Environ. 3 (3), 270–279. Sharma, A., Meesa, S., Pant, S., Alappat, B.J., Kumar, D., 2008. Formulation of a landfill pollution potential index to compare pollution potential of uncontrolled landfills. Waste Manage. Res. 26, 474. Yang, W., Lang, Y., Li, G., 2014. Cancer risk of polycyclic aromatic hydrocarbons (PAHs) in the soils from Jiaozhou Bay wetland. Chemosphere 112, 289–295. http://dx.doi.org/10.1016/j.chemosphere.2014.04.074.

Please cite this article in press as: Lothe, A.G., Sinha, A. Development of model for prediction of Leachate Pollution Index (LPI) in absence of leachate parameters. Waste Management (2016), http://dx.doi.org/10.1016/j.wasman.2016.07.026