Formulas

Key Activated Sludge Formulas and Calculations

In order to provide a “scientific” approach to the operation of a biological treatment system, which also depends heavily on the “art” of operation to be successful, a number of process control calculations are available. The biological system equations most often used are the food-to-microorganism or F:M ratio, sludge age, MCRT, which is the same as the solids retention time (SRT), and the sludge volume index or SVI. Some of these equations are calculated a little differently from plant to plant. There’s no real problem with variations in how these activated sludge system calculations are made as long as everyone is calculating them in the same way for a given wastewater plant. What follows are the various calculations for these key biological system process control parameters.

I’m going to use, as an example, the wastewater treatment system at a chemical plant located in the southeast United States. This particular activated sludge wastewater system is an oxidation ditch. Table 1, below, shows the key operating parameters for oxidation ditch biological treatment systems. The ranges provided in Table 1 were derived primarily from experience with municipal oxidation ditch treatment systems. Any given industrial wastewater system may find that they operate outside one or another of these ranges. Given the unique and highly variable composition of industrial wastewater, there is no cause for concern if the industrial plant finds that the optimal performance of their biological treatment systems actually occurs outside any or all of these ranges. Table 1 is used as a starting point and to show the “typical” ranges for which oxidation ditch systems were designed. A simple schematic of the oxidation ditch is shown in Figure 1, below the table.

Table 1: Oxidation Ditch Operating Parameters

Oxidation ditch process control parameters

Figure 1: Oxidation Ditch

Simple oxidation ditch diagram

Measurement of the Organic Strength of the Wastewater

As a point of clarification it should be noted that all municipal wastewater treatment plants use five-day biochemical oxygen demand (BOD5) as a measure of the organic concentration into, and through, the wastewater plant. The BOD5 test measures the oxygen taken up by wastewater during the biological oxidation of the organic matter in the wastewater. But the BOD5 test is a highly unreliable means of determining the amount of organic matter present in water. The test measures only the approximate amount of oxygen that will be required (absorbed or consumed) by a wastewater when it is exposed to air or oxygen for an extended period of time. Toxic substances in the wastewater inhibit or even prevent bacterial growth and, therefore, oxidation of the organic matter. When this happens, the test result is lower than the actual amount of organic matter present would suggest.

The BOD5 test is limited in some applications such as industrial wastewater, which often contains heavy metal ions, cyanides, and other substances toxic to microorganisms. When microorganisms become poisoned by toxic substances, they are unable to oxidize waste, in which case the BOD5 test becomes an ineffective measure of organic pollution.

Most industrial wastewater treatment plants use chemical oxygen demand (COD) or total organic carbon (TOC) rather than the BOD5 test. Due to the length of time required to complete the BOD5 test, results provide historical data only and do not facilitate rapid water quality assessment or optimal process control. The highly variable chemical composition and strength of industrial wastewater requires a much more rapid method for measuring the organic concentration, hence the use of the two hour COD test or the 30 minute TOC analysis. Municipal wastewater plants operate with much greater consistency (less variation) in the strength of the influent organic loading which allows the municipality to wait five days to determine the organic concentration in the plant.

The TOC test can take several minutes to several hours to complete, and information obtained from a TOC analysis is less useful than information obtained from the BOD5 or the COD analysis. The TOC test does not differentiate between compounds with the same number of carbon atoms in different stages of oxidation and will thus produce different oxygen demand results. Because BOD5 and COD tests directly measure the amount of oxygen required to stabilize a waste sample, results reflect the original oxidation state of the chemical pollutants.

COD test results can also be used to estimate the BOD5 results on a given sample. An empirical relationship exists between BOD, COD, and TOC. However, the specific relationship must be established for each sample. Once correlation has been established, the test is useful for monitoring and control. In our example here, without BOD5 data correlated to COD data, the ratios shown in Table 2 below can be used to estimate the relationship between COD, BOD5, and/or TOC. Use Table 2 with caution though. The ratio values shown here are only a guide and may vary significantly from what is actually taking place at your wastewater plant.

The next section will explain the F:M ratio.

Table 2: Correlation Between BOD, COD, and TOC


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