## Theoretical Considerations

Ammonia nitrogen removal in facultative wastewater stabilization lagoons can occur through the following three processes:

• Gaseous ammonia stripping to the atmosphere

• Ammonia assimilation in algal biomass

• Biological nitrification

The low concentrations of nitrates and nitrites in lagoon effluents indicate that nitrification generally does not account for a significant portion of ammonia nitrogen removal. Ammonia nitrogen assimilation in algal biomass depends on the biological activity in the system and is affected by temperature, organic load, detention time, and wastewater characteristics. The rate of gaseous ammonia losses to the atmosphere depends mainly on the pH value, temperature, and the mixing conditions in the lagoon. Alkaline pH shifts the equilibrium equation NH3 + H2O o NH+ + OH- toward gaseous ammonia, whereas the mixing conditions affect the magnitude of the mass-transfer coefficient. Temperature affects both the equilibrium constant and mass-transfer coefficient.

At low temperatures, when biological activity decreases and the lagoon contents are generally well mixed because of wind effects, ammonia stripping will be the major process for ammonia nitrogen removal in facultative wastewater stabilization lagoons. The ammonia stripping lagoons may be expressed by assuming a first-order reaction (Stratton, 1968, 1969). The mass balance equation will be:

 where V = Volume of the pond (m3). C = Average lagoon contents concentration of (NH+ + NH3) (mg/L as N) t = Time (d). Q = Flow rate (m3/d). C0 = Influent concentration of (NH+ + NH3) (mg/L as N). C = Effluent concentration of (NH+ + NH3) (mg/L as N). k = Mass-transfer coefficient (m/d). A = Surface area of the pond (m3).

The equilibrium equation for ammonia dissociation may be expressed as:

The equilibrium equation for ammonia dissociation may be expressed as:

where Kb is an ammonia dissociation constant.

By modifying Equation 4.26, gaseous ammonia concentration may be expressed as a function of the pH value and total ammonia concentration (NH+ + NH3) as follows:

Assuming steady-state conditions and a completely mixed lagoon where Ce C, Equation 4.28 and Equation 4.29 will yield the following relationship:

C c0

This relationship emphasizes the effect of pH, temperature (pKW and pKb are functions of temperature), and hydraulic loading rate on ammonia nitrogen removal.

Experiments on ammonia stripping conducted by Stratton (1968, 1969) showed that the ammonia loss-rate constant was dependent on the pH value and temperature (°C) as shown in the following relationships:

Ammonia loss rate constant x e1S7(PH-8S) (4.31)

Ammonia loss rate constant x e0.13<T-20) (4.32)

King (1978) reported that only 4% nitrogen removal was achieved by harvesting floating Cladophora fracta from the first lagoon in a series of four receiving secondary effluents. The major nitrogen removal in the lagoons was attributable to ammonia gas stripping. The removal of total nitrogen was described by first-order kinetics using a plug-flow model: Nt = N0e-0 03t, where Nt is the total nitrogen concentration (mg/L), N0 is the initial total nitrogen concentration (mg/L), and t is time (d).

It is well understood that large-scale facultative wastewater stabilization lagoon systems only approach steady-state conditions, and only during windy seasons will well-designed lagoons completely achieve mixed conditions. Moreover, when ammonia removal through biological activity becomes significant or ammonia is released into the contents of the lagoon from anaerobic activity at the bottom of the lagoon, the expressions for ammonia removal in the system must include these factors along with the theoretical consideration of ammonia stripping as shown in Equation 4.30.

In the following text, mathematical relationships for total nitrogen removal based on the performance of three full-scale facultative wastewater stabilization lagoons are developed taking into consideration the theoretical approach and incorporating temperature, pH value, and hydraulic loading rate as variables. Therefore, rather than using the theoretical expression for ammonia nitrogen stripping (Equation 4.30), the following equation is considered for TKN removal in facultative lagoons:

where K is a removal rate coefficient (L/t), and /(pH) is a function of pH.

The K values are considered to be a function of temperature and mixing conditions. For a similar lagoon configuration and climatic region, the K values may be expressed as a function of temperature only. The function of pH, which is considered to be dependent on temperature, affects the pK and pKb values, as well as the biological activity in the lagoon. When the effect of the pH function on ammonia nitrogen stripping was incorporated (Equation 4.33), the pH function was found to be an exponential relationship; the selection of an exponential function to describe the pH function was based on statistical analyses indicating that an exponential relationship best described the data. Also, most reaction rate and temperature relationships are described by exponential functions such as the Van't Hoff-Arrhenius equation; therefore, it is logical to assume that such a relationship would apply in the application of the theoretical equation to a practical problem.