Three graphs and five tables give several examples of the variability between the five-day BOD (BOD5) and chemical oxygen demand (COD) with Tables 4 & 5 adding total organic carbon (TOC) data for further comparison. Here’s the important point to keep in mind as we proceed: The more variable the ratio values, as in, the higher the COD/BOD ratio, the greater the percentage of slowly biodegradable and non-biodegradable material in the sample. And that means the BOD5 test will give a lower value than is truly representative of the oxygen demand in the sample.
The first graph (Figure 1) is a histogram of 1,095 daily composite influent COD/BOD ratios spanning a three-year period from a North American refinery. The histogram has been fit with a distribution using the Monte Carlo simulation program @Risk. From the many distribution options available within @Risk the best fit was a log-logistic distribution that is defined by three parameters: 1) a location parameter (the mean), gamma, 2) a scale parameter, beta, and 3) a shape parameter, alpha. What is not clear from the graph is the range (minimum to maximum values) of the data set. The minimum COD/BOD ratio value was 0.996 and the maximum value was 21.842. The fitted distribution tells us that 88.5% of the COD/BOD ratio values are between 2.38 and 7.36.
Figure 1: COD/BOD Ratio Variability “Complete” Data Set
The data represents an extremely large range and, quite frankly, a range that is suspect. The COD/BOD ratio is always going to be greater than 1.0 because the COD test measures both biodegradable and non-biodegradable organic compounds. The BOD test can only measure the soluble organic compounds that bacteria can consume. So we need to do some data cleaning. But before we edit the data in any way, let’s take a look at a frequency table of the raw data, shown in Table 1.
From Table 1 we can see that 891 of 1,095 sample points (81.4%) had a COD/BOD ratio of less than or equal to 5 and 182 values had a ratio greater than 5 but less than or equal to 10. So almost 98% of the entire data set had a COD/BOD ≤ 10. Let’s drill down deeper into the frequency table by tightening up the step range.
Table 1: COD/BOD Frequency Table
In Table 2 we’ve increased the level of detail in the frequency table, tightening the steps from increments of 5 down to increments of 2. Now we can see that 28 values had a COD/BOD ratio ≤ 2, and we’ll proceed, in a moment, to drop these “extremely low” values from the data set before fitting another probability distribution to the trimmed data. From Table 2 it looks like we may need to remove some values from the high end as well, perhaps all values with a COD/BOD ratio > 8.
Table 2: COD/BOD Frequency Table Expanded
The tricky part of the data editing, data trimming, is in the range of COD/BOD ratios between 2 and 3. Let’s drill down even deeper, making the increments between the data values just 0.1. We’ve done this in Table 3. For now, let me arbitrarily say that the minimum possible COD/BOD ratio value is 2.2. So we are going to drop the 41 lowest values in the data set, values that are ≤ 2.2. And we’re going to remove from the data set the 33 values that have a COD/BOD ratio > 8.
Table 3: COD/BOD Frequency Table Expanded
In Figure 2, we have dropped a total of 74 values (6.8%) from the original data set consisting of 1,095 values. A new probability distribution has been fit to the trimmed data. The fitted distribution has changed from a log-logistic to a gamma distribution. A gamma distribution has two parameters: 1) a shape parameter, alpha and 2) a scale parameter, beta. The fitted distribution tells us that 92.2% of the COD/BOD ratio values are between 2.51 and 6.36.
Figure 2: COD/BOD Ratio Variability “Trimmed” Data Set
There are numerous ways to analyze the data once a probability distribution has been generated. For example, if we wanted to know the likelihood of the COD/BOD ratio falling between a range of 3 and 6 all we have to do is move the delimiters as was done in Figure 3. The probability distribution tells us that 74.4% of the COD/BOD ratio values are likely to be in the range of 3 to 6.
Figure 3: COD/BOD Ratio Variability Being Analyzed
In Tables 4 & 5 below I’ve reproduced data from two different sources (identified in each table) that give you an excellent idea of the variability in the ratios between BOD, COD, and TOC.
Table 4: BOD/COD/TOC Ratio Variability
Table 5: BOD/COD/TOC Ratio Variability