DYNAMIC SLUDGE AGE CALCULATION FOR THE ENVIROSYSTEMS ACTIVATED SLUDGE SIMULATION PROGRAM by David A. Vaccari, Ph.D., P.E. Associate Professor Department of Civil, Environmental, and Coastal Engineering Stevens Institute of Technology Hoboken, NJ 07030 201/420-5570 This is to document the Dynamic Sludge Age (DSA) calculation feature of the Envirosystems Activated Sludge Simulation Program and the standalone FORTRAN and LOTUS programs to compute DSA from data. The traditional sludge age calculation (TSA) was not incorporated into the original version of the simulator because it produces incorrect results with unsteady-state systems. For example, if the waste rate was cut in half, the TSA calculation would predict an immediate doubling in age, so that a sludge could "age" many days in just several minutes. The DSA calculation was developed by Tom Fagedes at the University of Chicago, together with David A. Vaccari at Rutgers University and Jon Longtin of the U. S. E. P. A. at Cincinnati. The formulas Fagedes developed are theoretically exact for computing the average age of a culture that is both growing and being wasted, for unsteady- state situations. The formulation has been published in the jounal "Biotechnology and Bioengineering" v. 27, pp. 695- 703 (1985). Unfortunately, that article has an error in the DSA equations. The correct equations are contained in a more recent article: "Feedback Control of Activated Sludge Waste Rate", Vaccari, et al, Journal of the Water Pollution Control Federation, v60, n11, p 1979-1985 (1988). The "dsa" Command In older versions of the simulator, the program does not compute the DSA until you tell it to with the "dsa" command. Type "dsa" in response to the command prompt, and the program will display the current "DSA COUNT", and prompt for a new one. The DSA COUNT is the number of minutes between updating the DSA calculation. Initially, the count is zero, and the DSA is not computed at all. Changing the DSACOUNT to some number, say 60, causes the program to compute the DSA every 60 minutes. An assumption is made that solids growth and wasting are constant during the count period. This is approximately true, but in general, the smaller the DSACOUNT, the more accurate the calculation will be. However, I have found that in practice, a DSACOUNT of from several hours to one day (1440 minutes) is accurate enough. Newer versions of the simulator, and the free educational version, start up with the dsa feature already initialized, and with DSACOUNT set to 60 minutes. The trend feature will also trend the DSA, just as it does for other variables. Try some experiments: run a simulation with a constant flow (use the fls command) until it is approximately at steady-state, then save (sav command). Now initialize trending for DSA, MASS, WLD, and EBOD. Try different step forcings on the system, one at a time, such as increasing or decreasing influent B. O. D. or flow, or waste flow rate. Observe the effect of each of these on the DSA. The DSA Program A program is included to calculate the DSA separately from the simulation program. It is the file named DSA. EXE. To run it, just type: DSA. The program prompts for three numbers: T, M, and W. T is the time interval at the end of which the DSA is needed. M is the total mass at the end of that time. W is the total mass of solids wasted or lost over the period of time, T. The program then calculates the DSA and the TSA, so you can compare them. Initially, the DSA and the TSA are the same. For example, if the first set of numbers you enter are 1, 100, and 10, (meaning 1 day, 100 pounds of solids in the system, and 10 pounds wasted or lost in the effluent over the past one day) the program will calculate a DSA and TSA of ten days. If you then enter: 1, 100, 5, you will get DSA = 10. 49, TSA = 20. 00. Of course, the sludge hasn't really aged 10 days in one day. The DSA more realistically shows what happened. Consider another example, as shown here: T M W DSA TSA 1 100 10 10.00 10.00 1 110 11 9.09 10.00 1 115 11.5 8.78 10.00 1 118 11.8 8.68 10.00 1 120 12.0 8.66 10.00 5 120 60.0 9.18 10.00 30 120 360. 9.96 10.00 Here is what's happening: For four days, the mass in the system is increasing, but the waste rate is increasing proportionately. This is what would occur in a real plant if the influent BOD increased suddenly, but the influent and waste flow rates remained constant. The TSA stays at ten days because the waste rate is always one-tenth of the total amount of sludge per day. In reality, the average age of the sludge must get younger because there is an increased production of sludge. That is, there is a relatively large amount of "new" sludge present. This will remain so until the production achieves a new equilibrium with the waste rate. Eventually the DSA must return to the steady-state value of ten days, which it clearly is tending to do. Notice that when T is 5, W is 60.0. This means that 60 units of sludge were wasted over the last five days, not 60 units per day. You should enter the total amount of sludge wasted over the time period entered. Play around with the DSA program, and with the "dsa" function of the simulator program. If you have any questions or comments, or any interesting results, let me know. The DSA Worksheet If you have the LOTUS program, you can use the DSA worksheet (DSA.WK1) instead of the DSA program. It works in a similar way, but is easier to use. The worksheet also displays intermediate calculations: K, the net change in system mass, and P, the average rate of solids production over the period T. Other spreadsheet programs such as Excel, QuattroPro, or Lotus 1-2-3 for Windows should be able to read and use the DSA.WK1 file.