**By Gary L. Rogers**

** Summary**: For many applications, aeration is a process that makes practical sense. Before using aeration, however, it’s crucial to identify the importance of oxygen transfer rates and how they affect aeration’s overall effectiveness. Aeration theory and a few key factors of the process are discussed here.

Water quality management can be vitally important for many applications, particularly wastewater treatment, lake and reservoir management, aquaculture, environmental management, biofiltration and water treatment. A key water quality parameter common to each is dissolved oxygen. As a result, aeration can be critical in maintaining good water quality conditions for all of these processes.

**Various uses of aeration**

Aeration is widely used in wastewater treatment in the biodegredation of waste constituents.^{7,12} Oxygen is used to degrade carbonaceous (biological oxygen demand [BOD]) as well as nitrogenous (ammonia) components of the waste stream. Other applications of aeration include control of odor by oxidizing sulfides and other reduced compounds, as well as oxidation of iron and manganese.

Environmental consultants use aeration in air stripping systems and in unit processes for removal of petroleum compounds (BTEX) and volatile organic contaminants that are degraded chemically or biologically using aeration. These processes are used for groundwater and surface water remediation and treatment of various hazardous wastes.

In aquaculture, oxygen depletion can be a serious problem especially with intensive applications. High density production of the cultured species requires high feed application rates that can result in accumulation of wastes and uneaten food. They also lead to high concentrations of dissolved plant nutrients in the water and, consequently, dense growths of planktonic algae. These conditions alone can exert an unbalanced demand on a pond’s oxygen reserves, and dissolved oxygen levels can fall to lethal levels for the cultured fish or crustaceans if corrective action isn’t taken. In addition, catastrophic declines sometimes occur due to massive algae die‑offs. These oxygen depletions can cause partial or complete mortality of the cultured species—and a substantial loss to the grower.^{6,9,10,11}

Aeration is also used in water treatment processes, dechlorination and other applications. In each case described above, the first step in design of an aeration system is to determine total oxygen required—generally in kilograms of oxygen per hour (kg O^{2}/hr). Once the oxygen requirement is known, design is similar for most applications. The following section describes the theory behind oxygen transfer. This information is needed to properly size aeration systems for various applications.

**Aeration theory**

There are several theories proposed for the mechanism of oxygen transfer in water. These theories are widely used in modeling oxygen transfer kinetics. Interestingly, the simpler forms have proven effective in aeration design yielding results close to more complex models and usually provide equivalent predictions of oxygen transfer.

The rate of gas movement into a liquid is described by Fick’s first law. The relationship describes the rate of mass transfer as directly proportional to the concentration gradient. It’s expressed as:

** Equation 1**.

dm/dt = D

_{m}A dC/dt

In the equation, dm/dt is the mass transfer rate in grams per second (g/sec), D

_{m}is the molecular diffusion constant (or coefficient) of the gas in square centimeters per second (cm

^{2}/sec), A is the area through which transfer occurs (cm

^{2}), and dC/dt is the concentration gradient of the gas.

One of the earliest models for gas transfer suggests two laminar films of gas and liquid exist at the interface of two phases. The model is referred to as the “two-film model,” or Lewis and Whitman model after its original presenters. Gas moves through the liquid film by molecular diffusion and is distributed in the liquid by turbulent diffusion. The two-film model for oxygen transfer describes the rate of transfer by the following:

**.**

*Equation 2*dm/dt/A = D

_{m}× (C

_{s}-C) / L

_{f}

In this equation, dm/dt/A is the rate of transfer per unit area, C

_{s}is the saturation concentration of gas, L

_{f}is the thickness of liquid film, and C is the gas concentration. The model is based on a stable laminar film at the interface requiring tranquil flow conditions. These conditions are rarely found in the field, yet Equation 2 has been employed widely to effectively describe oxygen transfer and aeration design for many applications.

The basic model for oxygen transfer used for sizing aeration systems is based on the Lewis and Whitman model. The following equations present the model in differential form and exponential form:

*.*

**Equation 3**dC/dt = K

_{L}a (C

_{s}-C)

Equation 4.

C = C

_{s}– (C

_{s}– C

_{O}) exp (-K

_{L}a × t)

In these equations, C is the dissolved oxygen (DO) concentration in milligrams per liter (mg/L), C

_{S}is the equilibrium concentration of DO attained as time approaches infinity, C

_{O}is the DO concentration at time zero, and K

_{L}a is the mass transfer or re-aeration coefficient (hr

^{‑1}) defined as the rate of mass transfer per unit volume divided by the concentration differential gradient (C

_{S}– C

_{O}), and t is time (hr).

**Factors on rate of solution**

Several factors affect the rate of solution of oxygen in water. Downing and Truesdale^{8} discussed many of these factors including the degree of agitation, effects of temperature, and the concentration of soluble and insoluble contaminants. The effect of wind action on re-aeration rate has been considered by Banks and Herrera.^{4}

There are many water quality parameters that affect saturation concentrations of dissolved gases. Table 1 presents a summary of dissolved oxygen saturation concentrations based on temperature and salinity. For further information regarding saturation values, see Standard Methods.^{1}

**Standard tests in tank**

Performance of aeration devices may be compared based on evaluation of re-aeration rates from tests completed in clean water. Results are then converted to standard conditions. This procedure was prepared by the American Society of Civil Engineers subcommittee on oxygen transfer standards.^{2,3,5} The standard aeration test includes guidelines on basic geometry, analytical methods for dissolved oxygen measurement, test procedure and data analysis.

Dissolved oxygen measurements may be made using DO meters and probes or by wet chemistry methods using titration of water samples collected throughout the test. In most cases, DO probes are used.

Prior to each oxygen transfer test, cobalt chloride (CoCl_{2}) is added to the tank and mixed to produce a soluble cobalt concentration between 0.10 mg/L and 0.50 mg/L in the test tank. Next, sodium sulfite (Na_{2}SO_{3}) is dissolved and added to the tank (approximately 8 mg/L sodium sulfite per 1 mg/L DO concentration). With the addition of the dissolved sodium sulfite solution, the DO level is reduced below 0.50 mg/L in the test tank.

Once the dissolved oxygen level has stabilized near zero, the aeration device is started and the rate of increase in dissolved oxygen is measured. The experimental run is terminated when the DO levels reach at least 95 percent of saturation. Information must be recorded on the physical test configuration, meteorological conditions, power consumption and water quality, as well as the dissolved oxygen data. The re-aeration results of a typical aeration test are shown in Figure 1.

**Standard oxygen transfer rate**

The data collected from the oxygen transfer experiments may be analyzed by the mass transfer model to estimate the mass transfer coefficient, K_{L}a, and the saturation concentration, C_{S}.

The oxygen transfer capacity of the various aeration systems may be compared using the rate of oxygen transfer predicted using this model. The comparisons are for standard conditions (zero dissolved oxygen, 20°C temperature, and 1.0 atmosphere of pressure).

The SOTR can be calculated by first correcting K_{L}a and C_{S} to standard conditions using the values determined in the mass transfer model. Equations 5 and 6 are used to convert these values to standard conditions. The value of SOTR is calculated using Equation 7.

**Equation 5.**

K_{L}a 20 = K_{L}a θ ^{(20 ‑ T)}

* Equation 6*.

C

_{S20}= C

_{S}(l/t Ω)

*.*

**Equation 7**SOTR = V × K

_{L}a

_{20}× C

_{S 20}

In these equations, K_{L}a 20 is the value of K_{L}a corrected to 20 °C, θ is the empirical temperature correction factor (generally equal to 1.024), C_{S} _{20} is the value of C corrected to 20 °C and standard barometric pressure of 1.0 atmosphere, t is the temperature correction factor, V is the pressure correction factor, and T is the water temperature during the test (°C). SOTR is measured in kilograms per hour (kg/hr). V is the volume of water in the test tank (L).

**Oxygen transfer rate**

The oxygen transfer rate (OTR) for field conditions won’t be the same as that predicted at standard (SOTR) conditions. The field oxygen transfer rate may be estimated using the following equation:

**Equation 8.**

OTR = SOTR θ^{(T-20)} α(β C_{s} – C)/C_{20}

In this equation, OTR is the field oxygen transfer rate (kg O_{2}/hr), α is the correction for K_{L}a in process water, β is the correction for dissolved oxygen saturation in process water, and θ is the correction for temperature.

Table 2 presents a summary of field oxygen transfer rates applicable to aquaculture. The factor obtained from the table is multiplied by the SOTR to obtain the field oxygen transfer rate (kg/hr). Table 2 was prepared based on freshwater conditions at sea level using an α of 0.92, β of 0.98, and θ of 1.024. Similar tables may be prepared for applications other than aquaculture.

**Conclusion**

Maintaining adequate dissolved oxygen concentrations can be vitally important in many applications. A better understanding of aeration theory is needed for proper sizing and design of aeration systems.

**References**

- APHA, AWWA, WEF, Standard Methods for the
*Examination of Water and Wastewater*, 18^{th}Edition, 1992. - ASCE Oxygen Transfer Standards Committee, “Development of Standard Procedures for Evaluating Oxygen Transfer Devices,” EPA‑600/2‑83‑102, American Society of Civil Engineers, New York, 1983.
- ASCE Oxygen Transfer Standards Committee, “A Standard for the Measurement of Oxygen Transfer in Clean Water,” ASCE, 1984.
- Banks, R.B., and F.F. Herrera, “Effect of Wind and Rain on Surface Re-aeration,”
*Journal of Environmental Engineering*, ASCE, EE3:489-504, 1977. - Brown, L.C., and C.R. Baillod, “Modeling and Interpreting Oxygen Transfer Data,” ASCE, Vol. 108, No. EE4, 1982.
- Colt, J.E., and G. Tchobanoglous, “Design of Aeration Systems for Aquaculture,” Bioengineering Symposium for Fish Culture (FCS Pub. 1); 138‑148, American Fisheries Society, 1981.
- Crites, R., and G. Tchobanoglous, “Small and Decentralized Wastewater Management Systems,” McGraw Hill, 1998.
- Downing, A.L., and G.A. Truesdale, “Some factors affecting the rate of solution of oxygen in water,”
*Journal of Applied Chemistry*, 5, 570-81, 1955. - Madenjian, C.P., G.L. Rogers and A.W. Fast, “Estimation of Whole Pond Respiration Rate,”
*Canadian Journal of Fisheries and Aquatic Sciences*, 47; 682-686, 1990. - Rogers, G.L., and A.W. Fast, “Aeration and Circulation for Effective Aquaculture Pond Management,”
*Aquacultural Engineering*, 8; 349-355, 1988. - Rogers, G.L., C.P. Madenjian and A.W. Fast, “Estimation of Oxygen Transfer Rates for Mechanical Aerators in Brackishwater Aquaculture Ponds,”
*Journal of Applied Aquaculture*, Vol 1(2); 63-77, 1991. - WPCF, “Aeration Manual of Practice,” FD-13, ASCE and Water Pollution Control Federation (now WEF), 1988.

*About the author*

*Gary L. Rogers, Ph.D., is a civil engineer with Aquatic Eco-Systems Inc., of Apopka, Fla. He provides technical support for wastewater and environmental products. Dr. Rogers has over 20 years experience with aeration equipment applications in aquaculture, environmental consulting, lake and reservoir water quality management, and wastewater treatment. He can be contacted at (407) 886-3939, (407) 886-6787 or email: [email protected]*