How to Design a Biological Wastewater Treatment Process

Davide Dionisi’s worked example demonstrates how sustainable wastewater treatment design can balance environmental protection, energy efficiency, and operating costs

THE AIM of biological wastewater treatment processes is to remove the biodegradable organic matter from municipal or commercial wastewater streams so that they can be safely discharged into the receiving water body (eg river or sea).

In biological wastewater treatment, microorganisms grow on the organic matter from human waste, distilleries or other businesses converting it into new microorganisms, CO2, and water. These processes bring large environmental benefits but also consume large amounts of energy. Therefore their design needs to be optimised to maximise both environmental protection and sustainability. In this article we will cover the design of the activated sludge process, which is one of the most common processes for biological wastewater treatment. Most of the design concepts illustrated here can apply, however, to other process configurations.

Process description and assumptions

In its basic configuration (see Figure 1) the activated sludge process is made of two tanks: the biological reactor and the settling tank. The biological reactor receives the influent wastewater stream, usually after it has passed through the primary treatments (eg screens and primary settling tanks). In the biological reactor, the microorganisms carry out the biological reactions that remove the organic matter (substrate) from the liquid phase. The aim of the settling tank is to separate the suspended solids, ie the microorganisms, from the treated effluent. The clarified effluent is sent to the final or tertiary treatments (eg disinfection) while the settled microorganisms are recycled back to the reactor. From the bottom of the settling tank, a stream of settled microorganisms is also removed, to control the microorganisms’ concentration in the reactor. This stream is often sent to anaerobic digestion, where the microorganisms are converted to methane for energy generation.

When designing an activated sludge process, I recommend you assume that the feed is composed only of readily biodegradable substrates and that the settling tank operates without any biomass losses with the clarified effluent. You should also assume that the substrate concentration is expressed as COD (chemical oxygen demand).

Use the following notation:

S₀ (kgCOD/m³) = substrate concentration in the influent wastewater
S (kgCOD/m³) = substrate concentration in the biological reactor
X (kg/m³) = biomass concentration in the biological reactor
X_R (kg/m³) = biomass concentration at the bottom of settling tank
Q (m³/day) = flow rate of the influent wastewater
Q_R (m³/day) = flow rate of the recycle stream
Q_W (m³/day) = waste sludge flow rate
V (m³) = volume of the biological reactor

The model of the biological processes occurring in this system assumes that two processes occur in the biological reactor: biomass growth on the substrate and endogenous metabolism. Biomass growth is the multiplication of microorganisms, which occurs when microorganisms remove the external substrate from the liquid phase. Endogenous metabolism includes all the processes (not yet entirely understood) which cause a reduction in the concentration of microorganisms, eg self-oxidation, death, and predation. Both biomass growth and endogenous metabolism involves the consumption of dissolved oxygen.

The kinetic model to use in this section is the well-known Monod model where the rate of biomass growth is given by:

The rate of endogenous metabolism is assumed to be given by:

where the negative sign is due to the fact that microorganisms are consumed in this process.

As a consequence of these assumptions on the kinetics of the process, the rate of substrate removal is given by:

In the numerical examples in this article, you should use the following values of the kinetic parameters:

Mass balances and design

Designing the activated sludge process means finding the values of all the variables that characterise it. You know the characteristics of the feed, ie Q and S₀, and the kinetic parameters m_max, K_S, b, and Y_X/S. The process will be designed when you have calculated the values of the remaining variables, ie V, Q_R, S, X, X_R, Q_W. So, in total, you need to calculate the values of six variables.

These variables are linked by three mass balances, the mass balances for the biomass in the reactor, the biomass in the whole system, and the substrate in the reactor. These mass balances are shown below.

Balance for the biomass in the reactor:

Balance for the substrate in the reactor:

Balance for the biomass in the whole system (reactor + settling tank):

These three equations can be rearranged after the introduction and definition of recycle ratio (R), hydraulic residence time (HRT), and solids residence time (SRT):

R is the ratio between the recycle and influent flow rates. The HRT is the “nominal” residence time of the liquid phase in the biological reactor, where the specification “nominal” accounts for the fact that the actual flow rate going through the reactor is Q+Q_R, rather than just Q. The SRT is the residence time of the microorganisms in the system, and is calculated as the mass of microorganisms in the reactor divided by the mass flow rate of microorganisms leaving the system.

By introducing R, HRT, and SRT, and after some rearrangements, the three design equations become:

Equations (10) through (12) are the design equations for the activated sludge process. To solve these equations, you need to choose the values of SRT, HRT, and R and then calculate S, X, and X_R. Equations (10) through (12) represent a system of three equations in three unknowns (S, X, and X_R) that can be solved easily.

Once the equations are solved, you know the values of SRT, HRT, R, S, X, and X_R. From these values you can immediately calculate the other variables; the volume of the reactor, which follows immediately from the definition of HRT, equation (8), and the required sludge waste flow rate, which is obtained by combining equations (8) and (9):

Once all the variables that characterise the process have been calculated, the sludge production and the oxygen consumption can also be calculated. The sludge production is important because the produced sludge can be a resource (if it is used for energy recovery using anaerobic digestion) or a liability (if it is treated and disposed of) for the plant. The oxygen consumption by the microorganisms represents one of the main operating costs of the plant and therefore needs to be minimised, if possible.

The sludge production in the activated sludge process is simply given by:

and per unit of influent flow rate:

The oxygen consumption rate by microorganisms can be calculated using the COD balance on the whole system:

The COD balance used in the equation represents an electron balance across the entire system. It indicates that the total electrons removable by oxygen from the organic substrate in the inlet wastewater (proportional to the feed COD) are either retained in the produced microorganisms or removed by oxygen.

In equation (16) the factor 1.42 that multiplies the sludge production is needed to convert the biomass concentration in COD units. The oxygen consumption per unit of influent flow rate is:

Note that, from the COD balance in the whole process, which has been used to derive equation (16), it follows that, for a given influent flow rate and composition and for a given extent of substrate removal, the sum of the oxygen consumed and biomass produced (converted into COD units) is constant and cannot be altered by changing any design or kinetic parameters:

Equation (18) is particularly important considering that usually, for well-designed and well operated processes, S<<S₀  and so Q(S₀-S) ≅ QS₀ . Therefore, equation (18) shows that, for a well-designed process, the sum of oxygen consumption and biomass production only depends on the flow rate and composition of the influent stream.

In summary, the activated sludge process for carbon removal, in its simplest version of one biological reactor followed by a settling tank, can be designed by specifying the values of the solids residence time (SRT), the hydraulic residence time (HRT), and the recycle ratio from the settling tank to the reactor (R). Once these three variables have been specified, and assuming appropriate rate equations for microbial growth, endogenous metabolism, and substrate removal, the values of all the variables that characterise the process can be calculated by solving the system of mass balance equations.