Mass Balance

Mass Balance

I like the information a mass balance can provide about a wastewater treatment system. But they can be time-consuming and complicated. Here I show three, two of which are very straight-forward and require minimal inputs to solve. The third mass balance is not truly a mass balance as much as it is a means to simply keep track of what’s going on in the treatment plant.

The first two mass balances shown below are for calculating the return activated sludge (RAS) rate. Even if you don’t want to use the flow rate number generated, you can still use one or the other as a check on your intuitively-based flow rate. In Figure 1 you can see how to do a mass balance around the aeration basin (biological reactor). In Figure 2 you can see how to do a mass balance around the secondary clarifier. For the calculating the RAS flow rate, identified as “R” in Figures 1 and 2, you do need to know the concentration of your mixed liquor suspended solids (MLSS), return sludge suspended solids, and your waste sludge suspended solids, which are often simply equal to the return sludge solids. Finally, Figure 3 shows my “so-called” mass balance that operators find to be both useful and informative. We’ll take a close look at that further down this page.

Figure 1: Mass Balance Around the Aeration Tank

Aeration tank mass balance

Figure 2: Mass Balance Around the Secondary Clarifier


So let’s begin our detailed review of Figure 3. All we are really trying to do here is keep track, on one page, of several key process control parameters. We want to know the loading into and out of each major unit process to see how efficiently they are operating. For the API Separators in Figure 3 a key control variable is the horizontal velocity which we need to maintain at less than 3 feet per second (0.91 meters per second). We are well below that value at 1.13 ft/min so that looks good.

If we know the flow, which we do, and the chemical oxygen demand (COD, mg/L) and the total suspended solids (TSS, mg/L) concentrations we can calculate the pounds of material removed through any given unit process as well as the percent removal. The APIs had a very high COD concentration coming in at 1,035 mg/L so they were getting hit with a lot of oil. The COD leaving the APIs was 325 mg/L resulting in a 68.6% removal rate. This is outstanding for an API and indicates that there must have been a lot of free oil in the wastewater because it was so easily removed. In addition, we had a 28.1% reduction in total suspended solids through the APIs which is good.

The COD leaving the EQ tanks reflects the flow contribution that comes in after the APIs. Since this wastewater plant nitrifies we’re also measuring the pH, alkalinity, ammonia, and nitrate leaving the EQ tanks which is the wastewater that enters the biological reactors. This plant has a two stage aeration system. The wastewater is typically lacking in the critical nutrient phosphorus so the plant feeds phosphoric acid into the effluent from the EQ tanks. This discussion continues below the graphic.

Figure 3: Wastewater System Mass Balance

Wastewater plant simple mass balance

The MLSS concentration in the second stage is higher than we’d like. Keeping the MLSS between 2,800 to 3,400 mg/L works well for this plant. The MLSS is high because their belt filter press (BFP) had been down for maintenance and they had not been able to waste sludge for several days. The combination of the first and second stage bioreactors at this plant is huge with 13.6 million gallons of total volume. So the F:M ratio is typically low at 0.06 but that’s okay. And since the wasting had been off for several days the sludge age has jumped to 47 days. They have some catching up to do and will have to work hard to waste extra sludge.

The solids leaving the secondary clarifiers is excellent at just 7 mg/L. And the low turbidity number correlates well with the low TSS number. The solids removal rate from the EQ tanks to the secondary clarifiers was great at 95.3 percent. Likewise, the COD removal was also very good at 87.5 percent. Obviously, this plant was running very well at the time of my visit.

As stated previously, this plant nitrifies. And we can see that the ammonia concentration has decreased from 15 to 0.09 mg/L, the pH has decreased slightly, the alkalinity has decreased, and the nitrate has increased. All of these numbers are what we would expect from a nitrifying plant and this is shown in the graphic below. Finally, the phosphate concentration in the secondary clarifier effluent is too high at 3.28 mg/L so they can reduce the phosphoric acid feed rate into the EQ effluent. As long as your phosphate concentration is approximately 1.5 mg/L you can be certain that this nutrient is sufficient for the microorganisms. For the record, all the numbers “worked out well” in this exercise but that is not always the case. There are always those days where you find yourself questioning the numbers because one or another data point just doesn’t fit with what you know and expect. Click here for more on nitrification.


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