Analysis of Oxygen Diffusion Models in Water Aeration SystemsME447/547 Spring 2015Taylor Rice

Background

•Aeration System Types▫Splashing – Rotating paddle systems▫Bubbling – Subsurface gas release systems

•Standard Applications▫Agriculture – Some use in fertilizer

application and growing techniques, soil aeration

▫Aquaculture – Sustaining plant and fish life▫Water treatment – Decarbonization, oxidation

of iron and manganese in wells, bacterial control

Mechanisms•Bubble Effects

▫High surface area with smaller bubbles▫Transfer of O2 and Nitrogen across bubble

membrane•Surface Effects

▫Increased surface area due to ripples on liquid surface

▫Large surface contact with atmospheric air

The Standard Model

•American Society of Civil Engineering (ASCE) standard test procedure▫Developed to test effectiveness of bubble

diffusers in water treatment▫Develops quantities:

Standard Oxygen Transfer Rate (SOTR) Standard Oxygen Transfer Efficiency (SOTE) Standard Aeration Efficiency (SAE)

Development of Standard Model•Two Film Theory (Lewis-Whitman 1923)

▫ Assumed to be Small▫So;

= Mass transfer coefficient [L/T]Concentration of Oxygen at equilibrium within gas phase (steady state) [ML^-3] = Concentration of Oxygen in liquid = Mass transfer flux of oxygen [ML^-2T^-1]

Development of Standard Model Cont.

• Standard Model States:

= Interfacial surface area = Volume of the Liquid body

• Assumes:▫ No bulk motion of fluid▫ No reactions▫ Thin films▫ Small gas mass transfer coefficient () ▫ Completely mixed▫ No change in flux over area

Problems With ASCE Standard Model

•Does not separate bubble and surface diffusion

•Does not account for changes in diffuser depth below the surface

•Analyzes bulk changes in concentration•Does not account for diffusion of other

gases (mainly Nitrogen)•Simplifies or ignores important parameters

for enhancing diffusion:▫Bubble diameter▫Bubble velocity

Problems with ASCE Model Cont.•The ASCE model is functionally useless

for designing aeration systems.•However,

▫ASCE model standardizes testing procedure for aeration systems

▫Gives baseline parameters which evaluate aeration systems effectively: SOTR, SOTE, SAE

The Separated Model•Developed by Connie DeMoyer et al.

(2002)•Separates bubble and surface interactions

for subsurface diffusers.•Indicates where transfer occurs •Gives insight to the effects of important

design parameters•Accurate for differing diffuser depths

(Standard: 3m-5m)

Development of Separated Model• At the free surface:

Where, is the mass transfer rate for liquid surface is the effective water surface area is the free surface oxygen transfer rate (Not a flux!)

• At the bubble interface

Where, is the volumetric bulk mass transfer coefficient (entire liquid volume) is the liquid phase equilibrium oxygen concentration of the bubble is bubble/water oxygen transfer rate

Development of Separated Model Cont.

• Use conservation of mass to combine previous two equations:

To evaluate: is constant for all depths Bubble size/Surface area changes with depth represents a bulk bubble transfer coefficient

to estimate oxygen transfer throughout entire water depth since size change is difficult to measure (assumed constant)

is constant over entire liquid surface

Development of Separated Model Cont.

•Using assumptions listed:

Where, = distance from diffuser = depth from diffuser to water surface=

Determining Parameters

•Transfer rates are dependent on the system▫Typically measured using linear regression

method•Equilibrium concentration, , changes with

depth, but it is possible to evaluate

Evaluating • The following snip from DeMoyer shows the how to evaluate this

quantity:

Results of Separated Model

Figure 1. Fitted vs. Measured DO concentrations (Demoyer et al.)

Results of Separated Model

Figure 2. Oxygen transfer rate from bubbles and free surface for test, scmh(DeMoyer et al.)

Effects on Mass transfer Coefficient

•In this particular study, ranges anywhere from 58% to 82% of .▫Dependent on the concentration gradient.

Gradient in bubble > Gradient at surface•Bubble transfer is dominant but that may

not be the case in other applications.

Table 1. Tabulated results of mass transfer coefficients and

Special Considerations

• Effect of area on transfer coefficient .▫Lakes/Ponds vs. Small Containers

• Turbulent regions▫Velocity considerations▫Mixing

• Bubble Size▫Coarse vs. Fine

• Diffuser Placement• Bubble Velocity• Average parameters

Figure 3. Schematic of bubble aeration system. (Demoyer et al.)

References

• Boyd, Claude E. "Pond Water Aeration Systems." Aquacultural Engineering: 9-40. Print.

• DeMoyer, Connie D, Erica L Schierholz, John S Gulliver, and Steven C Wilhelms. "Impact of Bubble and Free Surface Oxygen Transfer on Diffused Aeration

Systems." Water Research: 1890-904. Print.• McWhirter JR, Hutter JC. Improved oxygen mass transfer

modeling for diffused/subsurface aeration systems. AIChE J 1989;35(9):1527–34.

• Stenstrom, Michael K., Shao-Yuan (Ben) Leu, and Pan Jiang. "Theory to Practice: Oxygen Transfer and the New ASCE Standard." Proc Water Environ Fed Proceedings of the Water Environment Federation (2006): 4838-852. Print.