### Date: June 1, 2015 Memo 6

- 9.3

To: Ronald Jordan, USEPA

From: Luke Smith, John Rogers

Subject: Average Percent Removals of Selenium Species for Chemical Precipitation followed by Biological Treatment at Allen and Belews Creek

This memorandum presents the results of the average percent removal calculations for various

forms of selenium for the flue gas desulfurization (FGD) wastewater treatment system at Duke Energy’s Allen Station and Belews Creek Station

. The average percent removals for each selenium species are calculated for each plant for the following treatment stages: (i) chemical precipitation treatment (the percent removal calculated based on the chemical pre cipitation effluent and the FGD purge); (ii) biological treatment (the percent removal calculated based on the bioreactor effluent and the chemical precipitation effluent (or bioreactor influent) ) ; and (iii) the combination

of chemical precipitation follow ed by the biological treatment (the overall percent removal calculated based on the bioreactor effluent and the FGD purge). The selenium species are selenate, selenite, methylseleninic acid ( MeSe(IV) ), selenocyanate (SeCN)

, and selenomethionine ( SeMe )

.

T he percent removals presented in this memorandum are based on the self

- monitoring data from Allen and Belews Creek, which were provided to the EPA by Duke Energy.

The sections below provide a brief description of the treatment system at Allen and Belews Creek, summary statistics of the data at each plant, description of the percent removal calculations , and

the percent removal results for each of the plants together with the overall removals across both plants.

1. Description of the treatment system at Allen and Data at Allen and Belews Creek

Allen and Belews Creek power plants use chemical precipitation followed by anoxic/anaerobic biological treatment to treat FGD wastewater. In the chemical precipitation stage of the treatment system, chemicals a re added to the wastewater in a series of reaction tanks to convert soluble metals to insoluble metal hydroxide compounds, which precipitate from solution and are removed along with other suspended solids in a clarifier. Ferric chloride (or ferrous chlorid e) is also added to increase the removal of certain metals through iron coprecipitation, and to act as a coagulant to enhance solids removal in the clarifier.

### - 2

-

The biological stage of the treatment system is a fixed

- film bioreactor that consists of an activated carbon bed that is inoculated with microorganisms that reduce selenium and other metals, as well

as the nitrate

- nitrite form of nitrogen. The top part of the bioreactor, where the plant introduces the wastewater exiting the chemical precipitation stage, is aerobic with a positive oxidation

reduction potential ( ORP ) which allows nitrification to occur. As the wastewater moves down through the bioreactor, i t enters an anoxic zone (negative ORP) where denitrification and chemical reduction of selenium occurs. The microorganisms reduce the selenium species to elemental selenium, which adheres to the cell walls of the microorganisms. Because the activated

car bon substrate retains the microorganisms in the bioreactor, the selenium is essentially fixed to the activated carbon bed until it is removed from the system. For more details about the treatment system at these two plants, see the Technical Development D ocument for the steam electric effluent guidelines and standards (ELGs).

2 . Summary Statistics for the Self

- Monitoring Data at Allen and Belews Creek

The summary statistics, percent removal estimates, and plots presented in this memorandum are

based on data submitted by Allen and Belews Creek 1 

### . The Allen data spans dates from September 9, 2009 to October 22, 2013. The Belews Creek data spans dates from August 4, 2008 to November 28, 2013. These timespans do not include the initial commissioning period s for FGD wastewater treatment systems at Allen and Belews Creek.

Table s 1 and 2 below summarize the available selenium species data at Allen and Belews Creek

. For example, there were a total of 168 sampling dates for one or more selenium species at Al len

. Of the 168 sampling dates, there were 159 observations that were detected for the FGD Purge

and 0 non

- detected observations. For 9 of the 168 sampling dates, there were no samples collected at the FGD Purge for selenate

.

1 Data were received from the plants in the following Excel spreadsheets: “Allen Biochem and PhyChem monitoring since inception .xls”, “BC WWTS Analytical Data since inception.xls”, and “Allen_3_28_14.xlsx, Belews_3_28_14.xlsx.” The database for this evalua tion excludes analytical anomalies, samples collected during the initial commissioning period for the treatment system, and samples collected during t he period when the Allen Station treatment system was in an upset condition due to a broken pipe. This is consistent with the approach and data exclusions used to develop the numeric effluent limitations for the ELGs. See “Effluent Limitations for FGD Wastewater, Gasification Wastewater, and Combustion

Residual Leachate for the Final Effluent Limitations Guide lines and Standards for the Steam Electric Rulemaking.”

### - 3

-

Table 1

. Summary of sele n ium species data at Allen plant

Plant Species Summary Sampling Location

FGD Purge Chemical Precipitation

Effluent Bio reactor

Effluent

Allen Selenate Total Sampling Dates 168 168 168

N. Obs Detected 159 159 14

N. Obs Non

- detected 0 1 144

N. Not Sampled 9 8 10

Selenite Total Sampling Dates 168 168 168

N. Obs Detected 119 151 100

N. Obs Non

- detected 40 9 58
N. Not Sampled 9 8 10

MeSe(IV) Total Sampling Dates 168 168 168

N. Obs Detected 54 100 4

N. Obs Non

- detected 105 60 154
N. Not Sampled 9 8 10

SeCN Total Sampling Dates 168 168 168

N. Obs Detected 34 8 2

N. Obs Non

- detected 125 152 156
N. Not Sampled 9 8 10

SeMe Total Sampling Dates 168 168 168

N. Obs Detected 13 24 4

N. Obs Non

- detected 146 136 154
N. Not Sampled 9 8 10



### Table 2

. Summary of selenium species data at Belews Creek plant

Plant Species Summary Sampling Location

FGD Purge Chemical Precipitation Effluent Bio reactor

Effluent

Belews

Creek Selenate Total Sampling Dates 203 203 203

N. Obs Detected 196 194 65

N. Obs Non

- detected 0 1 118
N. Not Sampled 7 8 20

Selenite Total Sampling Dates 203 203 203

N. Obs Detected 196 194 70

N. Obs Non

- detected 0 1 113
N. Not Sampled 7 8 20

MeSe (IV) Total Sampling Dates 203 203 203

N. Obs Detected 58 123 36

N. Obs Non

- detected 87 21 96
N. Not Sampled 58 59 71

SeCN Total Sampling Dates 203 203 203

N. Obs Detected 24 8 38

N. Obs Non

- detected 121 136 94
N. Not Sampled 58 59 71

SeMe Total Sampling Dates 203 203 203

N. Obs Detected 2 3 37

N. Obs Non

- detected 143 141 95
N. Not Sampled 58 59 71

### - 4

-

Tables 3 and 4 below provide summary statistics for concentrations for each selenium species at Allen and Belews Creek, respectively. The summary statistics were based on the detected and

non

- detected observations combined. Note that for non

- detected observations, the concentration is set at the reporting limit.

Table 3. Summary statistics for selenium concentration (ug/L) for Allen

Plant Species Sampling Location N 1 Summary Statistics (μg/L)

Min Median Mean Max Std

Allen Selenate FGD Purge 159 5.9 181 572.3 4800 807.5
Chemical Precipitation Effluent 160 0.5 197.7 458.7 3200 591.8

Bioreactor Effluent 158 0.1 0.5 4.2 530.9 42.2

Selenite FGD Purge 159 0.4 33.1 202.4 4170 513.7
Chemical Precipitation Effluent 160 0.3 8.6 36.8 1440 140.4

Bioreactor Effluent 158 0.2 1 1.7 19.2 2.2

MeSe (IV) FGD Purge 159 0.6 3 5.4 74.4 8.9
Chemical Precipitation Effluent 160 0.3 1 3.8 57.7 7.4

Bioreactor Effluent 158 0.2 0.6 0.6 2.3 0.3

SeCN FGD Purge 159 0.3 2.5 11.1 217.5 31.3
Chemical Precipitation Effluent 160 0.1 0.5 1.4 119.6 9.4

Bioreactor Effluent 158 0.1 0.4 0.6 1.8 0.4

SeMe FGD Purge 159 0.6 2.3 2.5 9.2 1.3

Chemical Precipitation Effluent 160 0.2 0.6 0.7 3.4 0.5

Bioreactor Effluent 158 0.2 0.5 0.6 2.3 0.3

N 1 : includes detected and non

- detected observations. For the non

- detected observations, the concentration is set at the reporting limits.



### Table 4. Summary statistics for selenium concen tration (ug/L) for Belews Creek

Plant Species Sampling Location N 1 Summary Statistics (μg/L)

Min Median Mean Max Std

Belews

Creek Selenate FGD Purge 196 23.3 71.2 215 2470 431.5
Chemical Precipitation Effluent 195 1.5 62.8 181.5 2060 323.4

Bioreactor Effluent 183 0.1 0.6 1.5 31.1 3.2

Selenite FGD Purge 196 9.2 88 141.5 1450 185.5
Chemical Precipitation Effluent 195 0.4 22.7 38.8 538.2 61.5

Bioreactor Effluent 183 0.2 0.8 1.2 13.5 1.5

MeSe (IV) FGD Purge 145 0.6 3.3 3.7 13.8 2.1
Chemical Precipitation Effluent 144 0.2 2 2.5 9.3 1.7

Bioreactor Effluent 132 0.1 0.6 1 5.4 1.1

SeCN FGD Purge 145 0.3 2.4 3.8 41.6 5.2
Chemical Precipitation Effluent 144 0.1 0.5 0.8 13.5 1.3

Bioreactor Effluent 132 0.1 0.6 1.1 6 1

SeMe FGD Purge 145 0.5 2.4 2.9 16.8 2.2
Chemical Precipitation Effluent 144 0.1 0.6 0.7 2.4 0.5

Bioreactor Effluent 132 0.1 0.6 1 5.4 1.2

N 1 : includes detected and non

- detected observations. For the non

- detected observations, the concentration is set at the reporting limits.

### - 5

-

3 . Description of the Average Percent Removals Calculations

T he average percent removal is calculated for the following treatment stages :

i. Chemical precipitation treatment (the percent removal calculated based on the chemical precipitation effluent and the FGD purge);

ii. Biological treatment (the percent removal calculated based on the bioreactor effluent and the chemical precipitation effluent (bioreactor influent));

iii. The combination of chemical precipitation followed by the biological treatment (the overall percent removal for the treatment system calculated based on the bioreactor effluent and the FGD purge).

For a given treatment stage, th e percent removal is calculated by dividing the average of the effluent measurements by the average of the influent measurements. This method was selected because the calculation is transparent and facilitates interpretation, and because of its strong

per formance in simulations when compared to other possible approaches. In the Appendix we compare the selected method for calculating percent removal to two other methods that were

considered.

For those sampling dates where either the influent or the efflu ent was not sampled, both the influent and effluent measurements for that day were not included in the calculation. If the influent was not detected, then both measurements were removed. If the effluent was non

- detect, the effluent result (i.e., value eq ual to the detection limit) was replaced by the detection limit divided by 2. This is consistent with the approach EPA used to estimate pollutant removals for the ELGs. This approach recognizes that pollutants present in the wastewater, but at a

concentr ation below the level of detection/quantitation, are likely distributed below the detection/quantitation limit. For purposes of estimating pollutant removals, including percent removals, using “detection limit divided by 2” better reflects this distributi on than simply using

the detection limit itself for all non

- detected observations.

After the average percent removal was obtained at each plant, the overall average percent removal across both plants was calculated by averaging the removals for both plant s.

4 . Summary of the Average Percent Removals for Allen and Belews Creek

Table 5 below provides the average percent removal for each treatment stage at each plant by selenium species. F or selenate at Allen

, the average percent removal for the chemical

p recipitation stage of the treatment system is 19.4%, based on a total of 159 observations that

were available at both the FGD purge and chemical precipitation effluent sampling location s . The average percent removal for the biological treatment stage is 9 9.9 %, based on a total of 157

observations that were available at both the chemical precipitation effluent (bioreactor influent)

and bioreactor effluent sampling locations. The average percent removal of selenate for the entire

treatment system at Allen (i .e., chemical precipitation followed by the biological treatment ) is

99.3 %. Further results for other selenium species and Belews Creek are in Table 5.

### - 6

-

Table 5

. P ercent removal by plant and sampling location

Plant Species Percent Removal (N 1 )
Chemical Precipitation

Treatment 2 Biological Treatment 3 Overall Removal 4

Allen Selenate 19.4% (N = 159) 99.9% (N = 157) 99.3% (N = 157)

Selenite 82.9% (N = 119) 96.4% (N = 149) 99.5% (N = 119)
MeSe(IV) 18.7% (N = 54) 94.9% (N = 99) 97.4% (N = 54)

SeCN 90.8% (N = 34) 97.7% (N = 8) 99.4% (N = 34)

SeMe 74.7% (N = 13) 74.4% (N = 23) 93.1% (N = 13)

Belews

Creek Selenate 16.7% (N = 192) 99.4% (N = 180) 99.5% (N = 180)

Selenite 72.8% (N = 192) 97.6% (N = 180) 99.4% (N = 180)
MeSe(IV) 32.5% (N = 57) 78.5% (N = 109) 92.1% (N = 55)

SeCN 88.5% (N = 22) 71.9% (N = 7) 95.1% (N = 22)

SeMe 87.9% (N = 2) 80.7% (N = 3) 95.5% (N = 2)

1 : Number of observations available to calculate percent removal based on the criteria specified in Section 3.

2 : The percent removal calculated based on the chemical precipitation effluent and the FGD purge

3 : The percent removal calculated based on the bioreactor effluent and the chemical precipitation effluent

4 : The percent removal calculated based on the bioreactor effluent and the FGD purge.



### Table 6 below provides the average percent removal across both Allen and Belews Creek by treatment stage and selenium species. For example, the chemical precipitation treatment stage

removed 18.0% of selenate , which is based o n averaging the percent removals of 19.4% at Allen

and 16.7% at Belews Creek

.

Ta ble 6

. Average percent removal by selenium species and treatment stag e across Allen and

Belews Creek

Selenium Species Average Percent Removal for Allen and Belews Creek

C hemical Precipitation Effluent Biological Treatment Overall Removal

Selenate 18.0 % 99.7 % 99.4 %

Selenite 77.8 % 97.0 % 99.5 %

MeSe (IV) 25.6 % 86.7 % 94.8 %

SeCN 89.7 % 84.8 % 97.2 %

SeMe 81.3 % 77.6 % 94.3 %



### Tables 5 and 6 demonstrate that all forms of selenium were effectively removed across the treatment systems at Allen and Belews Creek , as measured by comparing data for the FGD Purge

and bioreactor effluent . Percent removals for the five species of selenium ranged from 9 3

. 1 % to

99. 5 % at All en, and from 92.1% to 99. 5 % at Belews Creek (see Table 5) . When averaging the removals for the two plants, the percent removals for the five species of selenium ranged from

9 4

. 3 % to 99.5% (see Table 6)

.

The Allen and Belews Creek treatment systems demons trated similar efficacy, both in term s of overall treatment system performance and in regards to the performance of the chemical precipitation and biological treatment stages. Table 5 shows that, for both plants, selenite , SeCN,

and SeMe were all removed more effectively by chemical precipitation than was the case for selenate and MeSe(IV). Table 5 also shows that the percent removals were lower in the biological treatment stage for SeMe at Allen, and for MeSe(IV), SeCN and SeMe at Belews Creek ; however, these species were all still substantially removed by the biological treatment stage

. Table 5 shows that the combination of chemical precipitation and biological treatment is highly effective at removing each of the selenium species. That finding is furt her illustrated by Table 6, where

### - 7

-

averaging the percent removals observed for Allen and Belews Creek shows that the combination of chemical precipitation and biological treatment results in every species of selenium being removed by more than 9 4 %.

As men tioned above, the A ppendix presents two other approaches for calculating percent removal. In addition, the A ppendix presents results of simulations to evaluate how the various approaches may be affected by the non

- detected observations. The information in the A ppendix shows that the approach used to calculate percent removal (as described above) is the better

a pproach because the calculation is transparent and facilitates interpretation, and because of its strong performance in simulations when compared to other possible approaches. Furthermore, the information in the Appendix shows that, regardless of the appr oach used to calculate percent removals, the percent removals calculated by the three approaches evaluated are generally consistent. The results presented in this memorandum show that the combination of chemical precipitation and biological treatment effec tively removes all five species of selenium.

### - 8

-

Appendix

This Appendix discusses three methods for calculating percent removal, discusses the handling of

non

- detects, and compares results using the three different methods for calculating mean percent

remov al for selenium species, with a focus on selenate and selenite. Based on this evaluation, Method 2 (described below) was selected as the preferred approach because it demonstrates relatively small bias across a range of conditions. Additionally, the calcul ation using this method is transparent and facilitates interpretation. Using this approach, the average influent concentration and the average effluent concentration are calculated, and then these values are used to calculate the overall percent removal.

“ Percent removal” refers to the fraction of the analyte in the influent that is removed by the processing system, generally between 0 and 1, which may be presented as a percentage by multiplying by 100. 2 

### Percent removal is the fraction of the influent conce ntration that is removed by the treatment system based on comparing the long

- term arithmetic average influent concentration to the long

- term arithmetic average effluent concentration. The data used for the analysis are influent and effluent measurements from two facilities (Allen and Belews Creek). Percent removal is calculated for 1) chemical precipitation; 2) biological treatment; and 3) the combination of chemical precipitation and biological treatment. This analysis excludes sample days for which the influent measurement was below the detection limit and days for which either the influent or effluent measurement was missing.

The three approaches for calculating the percent removal are:

 

### Method 1 : Calculating the percent removal for each sampling day , and then averaging the daily percent removal across sampling days to estimate the overall percent

removal.

 

### Method 2 : Calculating the average influent concentration and the average effluent concentration, and then using these values to calculate the overa ll percent removal.

 

### Method 3: Calculating the mean and standard deviation of the log

- transformed influent and effluent concentrations, from which the overall percent removal is

estimated.

Although Method 1 appears to be a reasonable approach, its estimate s of percent removal are biased and tend to be lower than the true percent removal. This bias persists even as the sample size increases. In contrast, in the absence of non

- detects, the bias of Method 2 goes to zero as the sample size increases. Method 2 does not make assumptions about the distribution of the data; however, the method relies on large sample approximations and may be slightly biased with small samples and highly skewed data. Method 3 assumes that influent and effluent concentrations are

lo g normally distributed, i.e., on the log scale are normally distributed. The distributions of influent and effluent of the selenium species often have characteristics of a lognormal distribution. However, Method 3 may perform poorly if the data do not be have like a lognormal distribution.

2 In this Appendix, with the exception of Tables A.1 through A.4, the percent removal is presented as a fraction between 0 and 1. For Appendix

Tables A.1 through A.4 and the main body of this memo, p ercent removal is presented as a percentage.

### - 9

-

In our simulation study where the data are log normally distributed, the point estimates for

Methods 2 and 3 are similar.

The handling of the non

- detects affects the estimates of percent removal, regardless of which method is used. This Appendix evaluates replacing the non

- detects by the detection limit and half the detection limit. In the equations below I i 

### stands for the influent concentration on day i and E i 

### stands for the effluent concentration on day i

. E i 

### is equal to the detection limit or the detection limit divided by 2 (depending on the assumptions). Pairs of influent and effluent concentrations from the same day are excluded from the calculations if the influent concentration is missing or

not detecte d and if the effluent concentration is missing. Table A1 summarizes the data used to

calculate the removal ratios.

Table A1. Summary of how the percent removal calculations are performed for each date the sample was taken at each plant

Influent Concentration Effluent Concentration Percent Removal Uses

Detected Detected Reported influent and

effluent concentrations

Detected Non

- detected Reported influent

concentration and the

effluent detection limit
divided by 2

Non

- detected Detected Data from these days are

excluded from the

calculations Non

- detected Non

- detected

Detected, Non

- detected, not sampled Not sampled
Not sampled Detected, Non

- detected



### Methods 2 and 3 give similar results and have less bias than Method 1. Due to the ease of calculation and relatively small bias across a range of conditions, Method 2 was selected as the preferred approach for calculating percent removal.

The rest of this Appendix provides additional detail on the different methods, simulation results comparing the methods, and estimates of selenite and selenite percent removal using the three

methods.

Methods for calculating percent removal

The analysis can estimate the ratio of the effluent to influent concentrations (call this the removal ratio):

R = E

I ,

from which the percent removal can be estimated:

P = 1

− R = I

− E

I .

The removal ratio can be calculated in different ways.

### - 10

-

Method 1

Using i to indicate different sampling days, calculating the arithmetic mean of the daily estimates of percent removal corresponds to:

R 1 

### = ∑ R i N i = 1



### N ; w h eee R i 

### = E i



### I i 

### .

The percent removal is P 1 

### = 1

− R 1


### . P 1 

### is the estimate previously calculated by EPA.

This calculation weights each sampling day equally when averaging the daily removal ratios. Using

W

i 

### to indicate the weight, the equation above is equivalent to:

R 1 

### = ∑ E i 

### I i 

### W i N i = 1


### ∑ W i N i = 1 

### ; W i 

### = 1

.

Thus days with small amounts of waste to process have the same weight (or influence on the calculated removal ratio) as days with large amounts of was te to process. Further, R 1 

### converges to the mean of daily effluent divided by daily influent, which is not necessarily the same as R.

Method 2 (the selected approach )

An alternative approach might weight days with higher influent concentration more than days with lower influent concentration. If the weight is proportional to the influent concentration ( I i 

### ),

the calculations become:

R 2 

### = ∑ E i 

### I i 

### I i N i = 1


### ∑ I i

N i = 1 

### = ∑ E i N i = 1 

### ∑ I i

N i = 1 

### = ∑ E i N i = 1



### N ∑ I i

N i = 1 

### N = E

I ,

where E is the sample mean of the effluent and I is the sample mean of the influent.

Using this method, the percent removal is P 2 

### = 1

− R 2 

### . This is a simple method of moments estimator that is commonly used for estimating ratios of means. This value does converge to the

true remov al ratio as the sample size increases. The variance of R 2 

### is approximately:

VV ( R 2 

### ) = � E

I � 2 

### � VV ( E )

E 2 

### + VV ( I )

I 2 

### − 2 CCC ( E

, I )

E ∗ I �

N .

### - 11

-

Method 3

The influent and effluent concentrations can often be reasonably described as having a lognormal distribution. The mean of a lognormal distribution can be calculated from the mean and standard deviation of the log

- transformed concentrations. As a result, the ratio of the mean of the effluent

concentrations to the mean of the influent conce ntrations can be calculated using the following

formula:

R 3 

### = eee � M M � l ( E i 

### ) � + VV � l ( E i 

### ) �

2 �

eee � M M � l ( I i 

### ) � + VV � l ( I i 

### ) �

2 �

R 3 

### is the ratio of the arithmetic mean of the effluent concentration to the arithmetic mean of the

influent concent ration where each mean is calculated from the mean and standard deviation of the log

- transformed influent or effluent concentrations. The percent removal is P 3 

### = 1

− R 3 

### . There is not a simple form for the standard error associated with R 3 

### . Bootstrap conf idence intervals

were calculated for the tables below.

Simulations comparing the various estimates

We performed simulations to evaluate the three approaches above for estimating percent removal. Separate simulations were run for combinations of settings for the true percent removal, the

fraction of effluent measurements that were non

- detects, and the substitute value used for the

non

- detects. The arithmetic mean influent concentration was either 2, 10, or 100 times the

arithmetic mean concentration in the effluent (which was set to equal 1.0). These values correspond to removal percentages of 50%, 90%, and 99%. The fraction of effluent non

- detects

was set to either 0% or 50%. Non

- detects were replaced by the detection limit divided by a scaling factor, eit her 1 or 2. For each set of simulation parameters we generated data for N = 100 days that was normally distributed (representing log transformed concentrations) with standard

deviations σ
I 

### = 0.5, 1, 2 and σ
E 

### = 0.5, 1, 2 for influent and effluent respectively. Standard deviations of 0.5, 1, and 2 correspond to coefficients of variation (CVs) of the simulated concentrations of 0.53 (a slightly skewed distribution), 1.31 (clearly skewed), and 7.32 (highly

skewed ). The mean of influent and effluent concentrations was used to calculate the mean of the simulated normally distributed log

- transformed concentrations. The detection limit was set to obtain the specified probability of effluent non

- detects. That detectio n limit was used to

determine if the simulated influent and effluent concentrations were non

- detects. We also added a daily random effect to both log distributions that was normally distributed with mean 0 and

standard deviation 0.3. For each combination o f settings we performed 1000 replications. The different simulation settings are listed in Table A2. We compare the three estimators using mean absolute deviation (MAD), 95% confidence interval coverage probability, and bias.

### - 12

-

Table A2. Different si mulation settings

Simulation setting ND % Scaling Factor Influent to effluent

concentration ratio

1 0% 2 100

2 50% 2 100

3 50% 1 100

4 0% 2 10

5 50% 2 10

6 50% 1 10

7 0% 2 2

8 50% 2 2

9 50% 1 2



### Simulation results

Figure A1 shows the mean absolute deviation (MAD) of the different estimators under different simulation settings. Small values of MAD indicate that the estimated percent removal values are close to the true value. MAD may be high because the estimates are biased (higher or lower than the true percent removal on average) or because the estimates have more variability. MAD is highest for Method 1 in all except simulation settings 8 and 9. Method 3 usually outperforms method 2. Note that each panel in the figures below uses a diffe rent scale on the vertical axis. When the coefficient of variation of the effluent concentrations is relatively low (lower row of the plot), the MAD is much smaller than when the coefficient of variation is much larger. The MAD using F=1 is similar to or s lightly higher than when using F=2, suggesting a preference for using

the detection limit over 2 as the substitute value for non

- detects as opposed to using the detection

limit.

In general, the estimates of percent removal using Method 1 are below those f or Method 2 and 3. In the simulation setting with 50% removal and 50% non

- detects (simulation settings 8 and 9), a significant fraction of the influent concentrations may be non

- detects. Influent

- effluent pairs from the same day are excluded from the calcu lations if the influent measurement is not detected. The remaining observations used to calculate percent removal have higher average influent concentrations and thus appear to have high percent removals. As a result, for low percent removal and a high pro portion of non

- detects, estimates using Method2 and 3 tend to overestimate the percent removal. Estimates using Method 1 are also higher than otherwise, but are still lower than those using Method 2 and 3 and generally lower than the true percent removal. Thus, for simulation settings 8 and 9, Methods 2 and 3 tend to over

- estimate the percent removal

and Method 1 tends to under

- estimate the percent removal, resulting in similar MAD for some

combinations of influent and effluent CVs.

As the simulation set ting number increases the true percent removal decreases which is often associated with a corresponding increase in the MAD (i.e., percent removal estimates are more variable when the true percent removal is near 50% than when it is near 100%). In addition , the percent removal estimates for Method 1 are particularly sensitive to the fraction of non

- detects, resulting in the “jagged” patterns for Method 1. As the simulation setting number increases, the drop in the MAD for Method 1 corresponds to a change fr om 0% to 50% non

- detects in the

effluent data.

### - 13

-

Figure A1. Summary of mean absolute deviation (MAD). Simulation setting is on the x axis, and MAD is on the y axis. The simulation settings are described in Table A2 

# Mean Absolute Deviation0.0050.0200.100E=20.0050.0200.1000.5005e-035e-025e-015e+000.0010.0050.0200.100E=10.0020.0100.0500.5005e-035e-025e-015e+005e-042e-031e-025e-02



###  I 

### = 0.5E=0.5

1 2 3 4 5 6 7 8 9

Method 1

Method 2
Method 30.0010.0050.0500.500



###  I 

### = 1 1 2 3 4 5 6 7 8 95e-035e-025e-015e+00



###  I 

### = 2 1 2 3 4 5 6 7 8 9

### - 14

-

Figure A2 shows the bias of the different estimators under different simulation settings. The bias is the average difference between the estimated and true percent removal. Across all simulation settings Method 1 is biased low, giving estimates of percent removal that are, on average less or much less than the true percent removal. In contrast, Method 2 and 3 are relatively unbiased (have bias close to zero on the vertical axis). However, as noted in the discussion above, for simulation settings 8 and 9, M ethod 2 and 3 can be biased high, sometimes by a similar amount that Method 1 is biased low. Note that each panel in Figure A2 uses a different scale on the vertical axis. When the effluent has a high coefficient of variation (top row) the Method 1 estimat es of percent removal can be negative and quite variable.

### - 15

-

Figure A2. Summary of bias. Simulation setting is on the x axis, and bias is on the y axis. The simulation settings are described in Table A2



# Bias-0.10.00.10.2E=2-0.8-0.6-0.4-0.20.00.2-25-20-15-10-50-0.20-0.100.000.05E=1-0.8-0.6-0.4-0.20.0-25-20-15-10-50-0.15-0.10-0.050.000.05



###  I 

### = 0.5E=0.5

1 2 3 4 5 6 7 8 9

Method 1
Method 2

Method 3-0.8-0.6-0.4-0.20.00.2



###  I 

### = 1 1 2 3 4 5 6 7 8 9-25-20-15-10-50



###  I 

### = 2 1 2 3 4 5 6 7 8 9

### - 16

-

Figure A3. Summary of coverage probabilities of the estimators. Simulation setting is on the x axis, and 95% coverage probabilities are on the y axis. The simulation setti ngs are
described in Table A2



# 95% Coverage Probability

Figure A4 shows boxplots for transformed estimated remo val ratios from the simulations where the true percent removal is 0.90, and 50% of the effluent observations are non

- detects replaced by the detection limit over two (simulation setting 5). The boxplots are provided to illustrate the typical distribution o f the percent removal estimates. The transformation was chosen to make the distributions roughly symmetric. The dashed black line shows the true percent removal in the transformed scale and the red dashed line shows a percent removal of zero. The inner axi s label (closest to the plot) shows the scale for the transformed percent removals. The outer axis label shows the corresponding values of percent removal. Note that, particularly for measurements withE=2

0 0.25 0.5 0.75 1E=1

0 0.25 0.5 0.75 1



###  I 

### = 0.5E=0.5

1 2 3 4 5 6 7 8 9 0 0.25 0.5 0.75 1

Method 1

Method 2

Method 3 

###  I 

### = 1 1 2 3 4 5 6 7 8 9 

###  I 

### = 2 1 2 3 4 5 6 7 8 9

### - 17

-

a high coefficient of variation, the estimated percent removal can be negative (below the red dashed line) and occasionally highly negative.

Using the transformed scale for this simulation setting, the percent removal estimated using Method 1 is less or much less than using Method 2 or 3. Estimates from Met hod 2 are generally similar to or closer to the true percent removal than using Method 3.

Figure A4. Distribution of simulated percent removal (P) estimates using the three calculation methods (true percent removal = 0.90, 50% non

- detects replaced by DL/ 2)



### In Tables A3 to A6 below we have calculated confidence intervals for the estimated percent removal using data from the Allen and Belews Creek plants. Figure A3 provides additional information on the performance of those confidence intervals. For stro ng estimators, we expect the confidence interval to cover the true percent removal 95% of the time (see the horizontal line-2024

-30 -9 -3 0 0.7 0.9 0.97 0.99P (Transformed scTransformed P = -lnE=2-2024

-30 -9 -3 0 0.7 0.9 0.97 0.99P (Transformed scale)Transformed P = -ln(1-P)E=1

Method1 Method2 Method3-2024

-30 -9 -3 0 0.7 0.9 0.97 0.99P (Transformed scale)Transformed P = -ln(1-P)E=0.5



###  E 

### = 0.5 Method1 Method2 Method3



###  E



### = 1 Method1 Method2 Method3



###  E



### = 2

### - 18

-

at 0.95). While Method 3 performs well across the board with respect to MAD, the coverage probabilities of Method 3 are uneven parti cularly when the coefficient of variation of the influent measurements is high (last column), as shown in Figure A3. The coverage probabilities are particularly sensitive to the fraction of non

- detects and the substitute value used for the non

detects (i. e., F = 1 or 2), resulting in the “jagged” patterns in some panels of the plot. Simulation setting numbers 1, 4, and 7 have no non

- detects, simulation setting numbers 2, 5, and 8 have 50%

non

- detects replaced by the detection limit over two, and simulation setting numbers 3, 6, and 9

have 50% non

- detects replaced by the detection limit.

Method 2 and 3 have similar coverage probabilities with Method 2 better than Method 3 for some panels in the plot and the reverse in other panels. Excluding simulation set tings 8 and 9, the minimum coverage for the Method 2 confidence intervals is higher than the minimum for Method 3. Excluding simulation settings 8 and 9, the coverage for Method 1 is consistently less than for

the other methods and Method 1 has instances w here the coverage is essentially zero.

The simulations were constructed to compare three relatively easy methods for calculating percent removal. Of these, we recommend Method 2. Method 2 is simple to calculate, and is competitive

with or better than Method 1 and 3 with respect to MAD, bias, and coverage probability across simulation settings. We believe the different patterns associated with a combination of low percent removal and a high proportion of non

- detects and the sensitivity of some estimate s to the presence and handling of non

- detects might be addressed using a model based approach; however, the calculations would be much more complex.

Recommended Procedure for Calculating Percent Removal

Because the calculations for Method 2 are much easi er than for Method 3 and the performance of Method 2 and 3 are otherwise fairly similar and usually much better than Method 1, we recommend using Method 2 for calculating percent removal. EPA has previously substituted the

detection limit over two for non

- detects when calculating percent removal. The simulation results provide no reason to modify that approach. Thus, we recommend the following analysis steps:

 

### If most or all influent and effluent measurements can be paired, such as influent and

effluent mea surements from the same day, exclude values that are unpaired. This minimizes the influence of day

- to

- day variation on the results.

 

### Exclude paired data for which the influent is less than the detection limit. Such samples provided little information on per cent removal.

 

### Replace the non

- detects by the detection limit divided by 2.

 

### Calculate the arithmetic average of the influent and effluent measurements, E and I

.

 

### Calculate the percent removal:

P = 1

− E

I

### - 19

-

 

### If desired, calculate the variance of the influent and effluent measurements and their covariance from which the variance of the estimate of percent removal is calculated as follows (N is the number of paired measurements):

VV ( P ) = � E

I � 2 

### � VV ( E )

E 2 

### + VV ( I )

I 2 

### − 2 CCC ( E

, I )

E ∗ I �

N .

 

### If de sired, calculate an approximate 95% confidence interval for the percent removal:

95% C = P ± 1

. 96 � VV ( P )

.

Estimates of percent removal using the different methods

Tables A3 through A6 show estimated percent removal for the Allen and Belews Creek data f or selenate and selenite using the three methods described above. In general, the estimates using Method 2 and 3 are more similar to each other than to the estimate using Method 1. The percent removals calculated using Method 2 and 3 generally are larger than from Method 1; however, there are some exceptions. Approximate confidence intervals are provided for the estimates. Note that when the removal percentages approach 100% any differences between the methods become

difficult to see. The differences in t he methods are apparent when the removal percentages are

much less than 100%.

Table A3

. Estimated percent removal for s elenate at the Allen plant, with 95% confidence intervals using thre e different calculation methods

Substitution

method for

non

- detect Method Treatment

Chemical Precipitation Biological Both (Chem Precip + Bio)

ND=DL 1 0.1% (

- 11.7%, 11.9%) 99.1% (98.8%, 99.4%) 98.4% (96.4%, 100.5%)

2 19.4% (9.2%, 29.6%) 99.8% (99.8%, 99.9%) 99.2% (98.1%, 100.4%)

3 2.6% (

- 25%, 19.9%) 99.9% (99.8%, 99.9%) 99.9% (99.8%, 99.9%)

ND=DL/2 1 0.1% (

- 11.7%, 11.9%) 99.5% (99.4%, 99.7%) 98.7% (96.6%, 100.7%)

2 19.4% (9.2%, 29.6%) 99.9% (99.8%, 99.9%) 99.3% (98.1%, 100.5%)

3 0.3% (

- 32%, 19.6%) 99.9% (99.9%, 99.9%) 99.9% (99.8%, 99.9%)



### Table A4

. Estimated percent removal for s elenate at the Belew s Creek plant, with 95% confidence intervals using thre e different calculation methods

Substitution

method for

non

- detect Method Treatment

Chemical Precipitation Biological Both (Chem Precip + Bio)

ND=DL 1

- 3.3% (

- 16.8%, 10.1%) 98.1% (97.6%, 98.7%) 98.6% (98.3%, 98.9%)

2 16.7% (2.9%, 30.4%) 99.2% (99.0%, 99.5%) 99.4% (99.1%, 99.6%)

3 4.6% (

- 10.4%, 18.4%) 99.2% (99.0%, 99.5%) 99.3% (99.0%, 99.5%)

ND=DL/2 1

- 3.3% (

- 16.8%, 10.1%) 98.7% (98.2%, 99.2%) 99.1% (98.9%, 99.3%)

2 16.7% (2.9%, 30.4%) 99.4% (99.2%, 99.7%) 99.5% (99.3%, 99.7%)

3 3.5% (

- 12.5%, 17.6%) 99.4% (99.2%, 99.6%) 99.5% (99.3%, 99.6%)

### - 20

-

Table A5

. Estimated percent removal for s elen i te at the Allen plant, with 95% confidence intervals using thre e different calculation methods

Substitution

method for

non

- detect Method Treatment

Chemical Precipitation Biological Both (Chem Precip + Bio)

ND=DL 1 61.7% (52.8%, 70.6%) 71.2% (62.1%, 80.2%) 94.0% (90.9%, 97.0%)

2 82.9% (74.9%, 90.9%) 96.1% (93.6%, 98.5%) 99.4% (99.2%, 99.7%)

3 87.8% (81.3%, 91.7%) 93.9% (90.8%, 96.2%) 99.4% (99.0%, 99.6%)

ND=DL/2 1 61.7% (52.8%, 70.7%) 72.6% (63.5%, 81.8%) 94.2% (91.1%, 97.2%)

2 82.9% (74.9%, 90.9%) 96.4% (94.1%, 98.7%) 99.5% (99.2%, 99.7%)

3 87.4% (80.7%, 91.5%) 94.2% (91.3%, 96.4%) 99.4% (99.1%, 99.7%)



### Table A6

. Estimated percent removal for s elen i te at the Belew s Creek plant, with 95% confidence intervals using thre e different calculation methods

Substitution

method for

non

- detect Method Treatment

Chemical Precipitation Biological Both (Chem Precip + Bio)

ND=DL 1 54.6% (46.0%, 63.3%) 92.2% (90.0%, 94.4%) 97.8% (97.3%, 98.4%)

2 72.8% (68.6%, 77%) 96.9% (96.0%, 97.9%) 99.2% (98.9%, 99.4%)

3 73.6% (69.1%, 77.4%) 96.9% (95.9%, 97.6%) 99.2% (98.9%, 99.3%)

ND=DL/2 1 54.6% (46.0%, 63.3%) 93.9% (92.0%, 95.8%) 98.3% (97.8%, 98.8%)

2 72.8% (68.6%, 77%) 97.6% (96.8%, 98.5%) 99.4% (99.2%, 99.5%)

3 73.4% (68.9%, 77.4%) 97.7% (96.9%, 98.3%) 99.4% (99.2%, 99.5%)