Models Describing Carbon and Nitrogen Removal

Carbon Removal

The first model will be discussed in its simplest form, which is typified by the following assumptions:

• The reactor is completely mixed and operated in steady state.

• Oxygen is used only for carbon removal.

• The bacterial growth rate is high compared to its decay rate.

• The concentrations of HCO- and COf- do not change during CO2 production.

• The oxygen/carbon content of bacteria yXO/xC is known and constant.

The balance of substrates takes the form of:

Substrate concentration is measured as dissolved organic carbon (DOC). From Eq. (11.1) we obtain:

Qo where rSc is the rate of carbon (DOC) removal and tR is the retention time.

Is it possible to calculate S by measuring Of and COf concentrations in the effluent air?

The following two equations must be valid:

where rXC is the rate of carbon consumption for bacterial growth (mol L 1 h 1 C), rXO is the rate of oxygen consumption for bacterial growth (mol L-1 h-1 O), rOf is the

respiration rate (mol L-1 h-1 O2), rCOf-C is the rate of carbon consumption for the

formation of CO2 (mol L 1 h 1 C) and rCO2-O is the rate of oxygen consumption for the formation of CO2 (mol L-1 h-1 O).

Our aim is to calculate rSC from the measured rOf. Therefore, we introduce:

inserting Eqs. (11.4) and (11.5) into Eq. (11.3), one obtains:

with the C/O yield of bacteria:

and the true yield coefficient:

rsc rXC and rXO can be replaced and rSC eliminated, giving:

If we know the values of the coefficients YXC/SC (assumed constant) and yx0/xc = yXC/X0, we are able to calculate rSc from the measured rate r02, assuming that bacterial decay, endogenous respiration and nitrification can be neglected.

Carbon Removal and Bacterial Decay

Starting again from the substrate balance in Eq. (11.1), we now have to consider a carbon removal rate rSc which is different from that in Eq. (11.1) as a result of the reduction of bacterial concentration by decay (bacterial death and mass reduction by endogenous respiration). In addition, the oxygen consumption rate is higher than that of Eq. (11.4) due to endogenous respiration. Instead of Eqs. (11.3) and (11.4), we must now write:


where rXc,d is the decay rate of bacteria by bacterial death and endogenous respiration and ro2,e is the rate of endogenous respiration.

Defining a real yield coefficient: Yxc/sc = — (11.14)

and using:

kd from chapter 4 and assuming the same c/o yield of bacteria, the result is:

For the same measured rO2_z = rO2 compared with that of Section 11.2.1, rsc must be lower compared to Eq. (11.9) as a result of bacterial decay kd (death rate and endogenous respiration). rSc can be quite low, particularly for low substrate concentrations (low specific growth rates p), in spite of relatively high oxygen uptake rates.

Carbon Removal and Nitrification Without Bacterial Decay

In addition to the balance of substrate (see Eq. 11.1), we now have to consider the balance of ammonia:

The aim of the following reflections is to replace rSC and rNH4-N with rO2_z. We will learn that we also need to measure rCO2-CZ in addition to rO2_z.

We start with the following equations:

rCO2-N is explained a little later. We will assume that there is complete nitrification without enrichment of NO- (see Chapter 10):

resulting in:

The NH+ needed for the nitrifiers' anabolism is neglected. The pH is stabilized by the addition of HCO3-:

We can assume that CO2 is completely degassed by aeration. Therefore, we can consider:

In Eqs. (11.5), (11.18) and (11.20), the following rates are used: rNH4-O2is the rate of oxygen consumption for the catabolism of nitrification (mol L-1 h-1 O2), rCO2-N is the rate of CO2 formation by neutralization of H+ with HCO- (mol L-1 h-1 C), rCO2-O is the rate of oxygen use forming CO2 (mol L-1 h-1 O) and rCO2-C is the rate of the carbon use forming CO2 (mol L-1 h-1 C).

With the help of Eq. (11.7), we obtain rSC from Eq. (11.3) considering:


and after introduction into Eq. (11.25), we obtain:

SC 9 vo

2 rX


11.3 Models for Optimizing the Activated Sludge Process | 271



By applying Eqs. (11.17) and (11.20), Eq. (11.29) can be written as:


Equations (11.27) and (11.30) are two equations with two unknown parameters rSC and rNH4-N, which can both be solved.

As such methods have only recently become known, balances and waste gas analysis have seldom been used for the process control of activated sludge plants. However, we are convinced that the importance of such methods will increase during the next decades.

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