Date: September 28, 2015 Memo 6-14

To: Ron Jordan, EPA

From: John Rogers, Luke Smith

Subject: Relationship Between ORP and Analytes

Introduction

Discussion in a Babcock and Wilcox Technical Report1 referenced by EPA (herein referred to as 

BW), suggests that oxidation reduction potential (ORP) may affect the portion of the selenium 

that is presented as selenate versus selenite. BW explored how “swings” in values of ORP 

generally affected trends in several analytes, including selenate and selenite. BW concluded that 

selenate ions increase and selenite ions decrease as ORP increases. This conclusion is 

underscored by Figure 3 in BW, which plots selenate and selenite against ORP.

There are several limitations of BW. BW makes general conclusions without backing them up 

using a hypothesis test. BW includes trend lines to support their conclusion without describing 

the trend lines or the method used to generate them. BW claims that selenite decreases with 

ORP, but shows a trend line that increases with ORP for large values of ORP. Finally, all of these 

values come from only one plant, so there is no way to assess plant-to-plant variability. 

In this memo we examine the relationship between ORP and selenate and selenite concentrations 

in wastewater and how this relationship changes across plants. We first explore the relationship 

between ORP and the analytes. We then take a model-based approach that allows us to test if 

ORP affects selenate and selenite. Finally, we examine how these relationships change across 

plants. 

Data

 

For this analysis we used data provided by Duke Energy for the Allen, Belews Creek and Cliffside 

plants, which have 2, 4, and 1 absorbers respectively. Summary statistics by plant and absorber

are in Table 1. 

 1

Brown, S. R., R. F. DeVault, M. Gadgil, D. B. Johnson, S. P. Ulbricht, and P. J. Williams. Optimization and 

Process Control of Air Quality Control Systems for Improved WFGD Oxidation Chemistry and Effluent 

Composition for Wastewater Treatment. Tech. no. BR-1902. Barberton, OH: Babcock & Wilcox Generation 

Group, 2013. Print.
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Table 1: Summary statistics of selenate and selenite by plant and absorber. Selenate and selenite 

are measured in μg/L.

Plant/Absorber N Date Range

Selenate 

Mean

Selenate 

Range

Selenite 

Mean

Selenite 

Range

Allen 1 55 05/28/2012 – 09/12/2013 787 (23,4800) 255 (1, 4170)

Allen 3 105 05/23/2011 – 10/22/2013 686 (6, 4800) 268 (0, 4170)

Belews Creek 1A 65 08/29/2012 – 11/28/2013 96 (1, 1010) 173 (1, 1280)

Belews Creek 1B 64 08/29/2012 – 11/11/2013 97 (1, 1010) 173 (1, 1280)

Belews Creek 2A 71 08/29/2012 – 11/28/2013 91 (1, 1010) 193 (1, 1450)

Belews Creek 2B 43 08/29/2012 – 06/04/2013 118 (29, 1010) 130 (9, 367)

Cliffside 24 06/21/2012 – 10/16/2012 322 (26, 750) 141 (1, 972)

Table 1 shows that the sample size and date of collection varies considerably by plant. Selenate 

occurs in smaller concentrations at the Belews Creek plants, while selenite occurs in larger 

concentrations at the Belews Creek plants. 

Methods

We want to see if there is any relationship between ORP and selenate and selenite, and the 

percentage of selenium that is selenate. BW claimed that when ORP is above roughly 300 mV, 

selenium shifts forms to become selenate. Looking at the percentage of selenate can help examine 

the joint response of these two analytes to ORP. To investigate this we plotted the raw data and 

percent selenate vs. ORP, and these plots are shown Figures 1 – 7 in Appendix 1. 

Figures 1 – 7 show an uneven or non-existent relationship between ORP and the analytes. 

Identifying overall trends is difficult, and plotting the data on the measurement scale obscures the 

small values. To further investigate this relationship we plotted the data on the log scale in 

Figures 8-14 in Appendix 2. Figures 8 -14 show a clearer relationship between the log of the 

analytes and ORP. 

Here we outline the statistical models used in our analyses. We begin by regressing the log 

concentration of analyte (selenate or selenite) on ORP by plant and absorber. Linear regression 

assumes the magnitude of the variation around the line is relatively constant. By predicting the 

log-transformed selenate and selenite concentrations versus ORP using a linear function we 

achieve three objectives: 1) all predicted concentrations are greater than zero; 2) all functions have 

the same linear form making comparisons between plants easier; and 3) the magnitude of the 

variation around the regression line is relatively constant.

In our second model we look at how the percentage of selenium that is selenate changes as a 

function of ORP. We are interested in seeing if the relationship between both analytes and ORP 

can be simplified further. At least at some plants, the concentrations are consistent with this 

hypothesis in that the selenate concentration increases and the selenite concentration decreases as 
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ORP increases and the sum of the selenate and selenite concentrations is relatively constant. Thus, 

EPA may be interested in the fraction (or percentage) of selenium that is present as selenate as a 

function of ORP. This is a reduction in information that enables the relationship between both 

analytes and ORP to be captured through one analysis. To avoid predicting fractions of selenium 

that are less than zero or greater than one we use a logit transformation, which is standard 

statistical practice. For a percentage p, the logit = log(p / (1 – p)). 

Finally, we want to know how ORP affects the analytes across all plants. We fit a regression 

model with separate regression effects for each plant and each absorber within plant. This mixed 

model enables us to construct an overall regression effect that is a weighted average of the 

individual regression effects at each plant. 

Results

We begin with the linear relationship between ORP and the log of selenate (log selenate), the log 

of selenite (log selenite), and the log of the percentage of selenate in selenium (logit). Selenate 

tends to increase with ORP and selenite tends to decrease with ORP. Therefore, modeling the 

logit allows us to focus on one relationship that captures the increase in selenate and the decrease 

in selenite. 

We performed linear regressions of log selenate, log selenite, and logit on ORP for each absorber 

within the Allen, Belews Creek and Cliffside plants. The results of the log selenate regressions are 

presented in Table 2.

Table 2: Regression effects of ORP on log selenate by plant and absorber. Statistical significance 

at the 0.05 level is indicated by *.

Plant/Absorber Slope Estimate p-value R-squared

Allen 1 0.41 < 0.001* 0.22

Allen 3 0.53 < 0.001* 0.52

Belews Creek 1A -0.03 0.816 < 0.01

Belews Creek 1B 0.32 < 0.001* 0.20

Belews Creek 2A 0.34 0.021* 0.08

Belews Creek 2B -0.05 0.830 < 0.01

Cliffside 0.21 0.021* 0.22

 

The slope estimate in Table 2 represents the expected increase in log selenate due to a 100 mV

increase in ORP. The p-value in Table 2 represents the probability of a slope estimate as extreme 

or more extreme than our observed data given there is no linear relationship between log selenate 

and ORP. Low p-values indicate that if there is no linear relationship between log selenate and 

ORP, then the probability of the observed data occurring is unlikely. The R-squared value 

represents the proportion of information in log selenate explained by ORP. R-squared values 

close to one represent high proportions of explained information. 

Table 2 shows that at 5 of the 7 plant/absorber combinations ORP had a statistically significant 

effect on log selenate. The slope estimates for log selenate are positive for all statistically 

significant regression effects across plant and absorber within plant. In contrast, the slope 
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estimates for log selenite are negative for all statistically significant regression effects across plant

and absorber within plant, as shown in Table 3. Table 3 shows that at 4 of the 7 plant/absorber 

combinations ORP had a statistically significant effect on log selenite.

Table 3: Regression effects of ORP*100 on log selenite by plant and absorber. Statistical 

significance at the 0.05 level is indicated by *.

Plant/Absorber Slope Estimate p-value R-squared

Allen 1 -0.74 < 0.001* 0.25

Allen 3 -0.94 < 0.001* 0.64

Belews Creek 1A 0.18 0.353 0.01

Belews Creek 1B -0.28 0.032* 0.07

Belews Creek 2A 0.13 0.569 < 0.01

Belews Creek 2B 0.36 0.317 0.02

Cliffside -1.26 < 0.001* 0.74

This leads us to the effects of ORP on the logit. Table 4 shows that the effect of ORP on the 

logit is positive for all statistically significant effects. Further, R-squared is generally highest for 

the logit in comparison to log selenate and log selenite, indicating that the logit best captures the 

effect of ORP. The 4 statistically significant effects in Table 4 are the same as in Table 3. ORP is 

statistically significant for the same plants across analyte, excepting Belews Creek 2B. There is a 

loss of information in using the logit and selenate regression is weak to begin with, so it is not 

surprising that we don’t have significance for selenite or the logit. 

Table 4: Regression effects of ORP*100 on the logit by plant and absorber. Statistical significance 

at the 0.05 level is indicated by *.

Plant/Absorber Slope Estimate p-value R-squared

Allen 1 1.15 < 0.001* 0.31

Allen 3 1.48 < 0.001* 0.72

Belews Creek 1A -0.21 0.355 0.01

Belews Creek 1B 0.60 < 0.001* 0.24

Belews Creek 2A 0.21 0.431 0.01

Belews Creek 2B -0.41 0.407 0.02

Cliffside 1.47 < 0.001* 0.77

Plots of the regressions are shown in Appendix 2. The plots of selenate and selenite are labeled 

using the observed concentration units using a log axis. 

An assessment of the consistency of the relationships across plants can be based on a visual 

inspection of the plots, a comparison of the slope estimates in the tables above or a formal 

statistical test. However, any conclusions are limited by the small number of plants for which we 

have data. 

We fit a mixed linear model to estimate the overall (average) ORP slope across all plants assuming 

the Allen, Belews Creek, and Cliffside plants were representative of all plants EPA is interested in 

and assuming that there may be different slopes and intercepts in different plants and absorbers 

(this corresponds to treating plant and absorber intercept and slope differences as random 
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effects). Table 5 shows the overall slope estimate, 95% confidence interval, and p-value for the 

overall effect of ORP. 

Table 5: Overall ORP*100 slopes predicting log selenate, log selenite, and logit. Statistical 

significance at the 0.05 level is indicated by *.

Analyte

Overall 

Estimate

95% Confidence 

Interval p-value

Log Selenate 0.3379 ( 0.0034, 0. 6723) 0.049*

Log Selenite -0.695 ( -0.02142, 0. 7522) 0.172

Logit .018 ( -0.534, 02.571) 0.106

Roughly speaking, the overall slope estimate represents the mean of all linear ORP effects across 

all plants, including those not in our data. That is, if we were to collect data on a new plant not in 

our current data, the overall estimate represents our best guess for the linear relationship between 

ORP and the analyte at the new plant. This parameter interpretation comes from using a mixed 

effects regression model. 

For selenate the effect of ORP is positive and barely statistically significant (p-value of 0.049). 

The confidence intervals for the overall effects of ORP on selenite and the logit contain zero and 

are not statistically significant. The overall slope estimates in Table 5 are weighted averages of the 

slope estimates at each plant. Log selenate is statistically significant while the others are not 

because the variability in the slope estimates at each plant is smaller for log selenate than it is for 

log selenite and the logit. We only have 3 plants for constructing this overall estimate, so 

additional plants could easily push log selenate into not being statistically significant or push log 

selenite or the logit into statistical significance. 

Although these data are consistent with the hypothesis that selenate concentrations increase and 

selenite concentrations decrease as ORP increases, based on the p-values, we cannot rule out the 

alternative hypothesis that there is no relationship between selenate, selenite, and ORP.

Conclusions

In this memo we have examined the relationship between ORP and the analytes selenate and 

selenite. We found some evidence at a few absorbers that ORP is linearly related to the analytes. 

Most of the R-squared values are low. While the mean of the log analytes often appears to change 

linearly with ORP, there is still considerable variability along the line unexplained by our model. 

There is a statistically significant relationship only for some absorbers, but not for others. Where 

we found a statistically significant relationship, there is a substantial amount of unexplained 

variability in the model. A model that incorporated pH and other important variables could offer 

considerable improvement. 

The mixed linear model provides estimates of the variance of the random effects. From these, we 

conclude that differences in the intercept and slope between different absorbers at the same plant 

are small enough to be ignored. As a result, the analysis might combine the data across absorbers, 
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fitting one slope per plant. Thus, for future analyses, we suggest predicting the log-transformed 

selenate and selenite concentrations (or logit) as a linear function of ORP at each plant. This 

analysis suggests that pooling the data from all absorbers at the same plant is reasonable, but this 

assumption would be good to test with future data.

BW asserts that selenate increases and selenite decreases as ORP increases, stating that at ORP 

levels below about 300 mV the selenium will predominantly exist as selenite, and when ORP is 

above about 300 mV the selenium will shift form to selenate. BW makes general conclusions 

without backing them up using any form of statistical analysis, such as modeling techniques or 

hypothesis testing. BW includes trend lines to support their conclusion without describing the 

trend lines or the method used to generate them. We did not find convincing evidence of this for 

the data at Allen, Belews Creek, and Cliffside plants. As noted above, ORP was found to have a 

statistically significant effect on the log-transformed analytes at only some of the absorbers, but 

not at others. Furthermore, the R-squared values for most of the regression lines are low, which 

indicates that the models for the relationships between the analytes and ORP are not particularly 

good. In addition, contrary to the BW assertion, we found that selenate can be present as a 

substantial fraction of the total selenium at both high and low ORPs (i.e., above and below about 

300 mV). We also found that selenite can similarly be present as a substantial fraction of the total 

selenium at both high and low ORPs.
Appendix 1

Figure 1: Plots of selenate, selenite, and the proportion of selenium that is selenate against ORP at 

the Allen plant using absorber 1.
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Figure 2: Plots of selenate, selenite, and the proportion of selenium that is selenate against ORP at 

the Allen plant using absorber 3.
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Figure 3: Plots of selenate, selenite, and the proportion of selenium that is selenate against ORP at 

the Belews Creek plant using absorber 1A.
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Figure 4: Plots of selenate, selenite, and the proportion of selenium that is selenate against ORP at 

the Belews Creek plant using absorber 1B.
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Figure 5: Plots of selenate, selenite, and the proportion of selenium that is selenate against ORP at 

the Belews Creek plant using absorber 2A.
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Figure 6: Plots of selenate, selenite, and the proportion of selenium that is selenate against ORP at 

the Belews Creek plant using absorber 2B.
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Figure 7: Plots of selenate, selenite, and the proportion of selenium that is selenate against ORP at 

the Cliffside plant.
Appendix 2

Figure 8: Regressions of log selenate, log selenite, and logit on ORP at the Allen plant using 

absorber 1. The logit corresponds to the proportion of selenium that is selenate.
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Figure 9: Regressions of log selenate, log selenite, and logit on ORP at the Allen plant using 

absorber 3. The logit corresponds to the proportion of selenium that is selenate.
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Figure 10: Regressions of log selenate, log selenite, and logit on ORP at the Belews Creek plant 

using absorber 1A. The logit corresponds to the proportion of selenium that is selenate.
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Figure 11: Regressions of log selenate, log selenite, and logit on ORP at the Belews Creek plant 

using absorber 1B. The logit corresponds to the proportion of selenium that is selenate.
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Figure 12: Regressions of log selenate, log selenite, and logit on ORP at the Belews Creek plant 

using absorber 2A. The logit corresponds to the proportion of selenium that is selenate.
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Figure 13: Regressions of log selenate, log selenite, and logit on ORP at the Belews Creek plant 

using absorber 2B. The logit corresponds to the proportion of selenium that is selenate.
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Figure 14: Regressions of log selenate, log selenite, and logit on ORP at the Cliffside plant. The 

logit corresponds to the proportion of selenium that is selenate.