evaluation of a low profile cascade aerator
TRANSCRIPT
Mississippi State University Mississippi State University
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Theses and Dissertations Theses and Dissertations
12-15-2007
Evaluation of a low profile cascade aerator Evaluation of a low profile cascade aerator
Chukwukelue Kenneth Monwuba
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EVALUATION OF A LOW PROFILE CASCADE AERATOR
By
Chukwukelue Kenneth Monwuba
A Thesis Submitted to the Faculty of Mississippi State University
in Partial Fulfillment of the Requirements for the Degree of Master of Science
in Civil Engineering in the Department of Civil and Environmental Engineering
Mississippi State, Mississippi
December, 2007
Copyright by
Chukwukelue Kenneth Monwuba
2007
EVALUATION OF A LOW PROFILE CASCADE AERATOR
By
Chukwukelue Kenneth Monwuba
Approved:
_________________________________ _________________________________ Dennis D. Truax James L. Martin Head and Professor of Civil and Professor and Graduate Coordinator Environmental Engineering of the Department of Civil and (Director of Thesis) Environmental Engineering (Committee Member) _________________________________ _________________________________ Benjamin S. Magbanua, Jr. . Roger L. King, Associate Professor of Civil and Associate Dean of Bagley College Environmental Engineering of Engineering (Committee Member)
Name: Chukwukelue Kenneth Monwuba Date of Degree: December 14 2007 Institution: Mississippi State University Major Field: Civil Engineering Major Professor: Dr. Dennis D. Truax Title of Study: EVALUATION OF A LOW PROFILE CASCADE AERATOR Pages in Study: 98 Candidate for Degree of Master of Science
The aeration potential of a low profile cascade aerator was studied under varying
operational conditions in accordance with the ASCE Standard for Measurement of
Oxygen Transfer in Clean Water [ASCE 2-06, 2007]. Operational parameters delved into
included the channel slope (2.50, 4.50 and 6.50); water flow rate (465.75 L/min.m (37.5
gpm/ft), 931.45 L/min.m (75 gpm/ft) and 1397.20 L/min.m (112.5 gpm/ft)); and weir
geometry (rectangular-shaped, inverted T-shaped, W-shaped and inverted Cross shaped
weir). The oxygen transfer coefficient, KLa, was derived by use of a FORTRAN-based
nonlinear regression analysis computer program and served to assess the effectiveness of
various combinations of operational parameters. Statistical tests (ANOVA analysis and
main plot, interactive plot) were performed on the results to determine the optimal
operating conditions. It was discovered that the combination of the inverted Cross shaped
weir and flow rates of 1397.20 L/min.m (112.5 gpm/ft) produced the highest reaeration
rates for all slope considered. On the other hand, the W-shaped weir produced better
reaeration values at lower flows of 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m
(75 gpm/ft) for the range of channel slopes examined.
These effects can be respectively attributed to the strong turbulent mixing
generated by the plunging nappe flow and recirculating air vortices, which apparently led
to substantial air entrainment in the water mass.
ii
DEDICATION
This project write up is whole-heartedly dedicated to the Almighty God, to my
parents, Mr. & Mrs. Monwuba for their moral, spiritual and financial support in the long
road leading to this day and also my brother, Nnamdi and sisters, Ada and Uche for being
there all the time through phone calls and emails despite the distance from home.
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ACKNOWLEDGMENTS
I would like to express my heart-felt gratitude to a number of people, who
contributed to the successful completion of this thesis.
Firstly, I am immensely grateful to Dr. Dennis D. Truax, my thesis director,
advisor and friend, for his priceless contributions, experience, directives that enabled me
to successfully carry out this project. My gratitude also goes to Mr. Joe Ivy, Ayan, Chris
and A.J for their technical support and encouraging words.
Furthermore, a warm thank you goes to Tom and Linda for providing the
experimental aerator model used for this research. I also owe my sincere appreciation to
my professors, family, friends and colleagues for various forms of assistance while
undertaking this degree.
Finally, to the BIG man behind all these, my unquantifiable gratitude goes to the
Almighty God, my reason for existence and without whose assistance nothing is possible.
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TABLE OF CONTENTS
Page
DEDICATION ............................................................................................................. ii
ACKNOWLEDGMENTS ........................................................................................... iii
LIST OF TABLES ....................................................................................................... vi
LIST OF FIGURES ..................................................................................................... vii
CHAPTER
I. INTRODUCTION ........................................................................................... 1
Brief History on Cascade Aerators ...................................................... 2 Focus of Research ................................................................................ 4
II. BACKGROUND ............................................................................................. 5
Review of Earlier Researches .............................................................. 5 Oxygen Transfer Process “Two-Film” Theory of Gas Absorption ..... 8 Flow Regimes in Cascade Aerators ..................................................... 13 Mechanisms of Entrainment of Air Bubbles in Cascade Aerators ...... 15 Air Entrainment in Nappe Flow Regime ............................................. 16 Air Entrainment in Skimming Flow Regime ....................................... 17 Aeration Equipment Performance ........................................................ 18 Measurement of Oxygen Transfer in Clean Water ............................. 19
III. METHODOLOGY .......................................................................................... 22
Objective of Study ............................................................................... 22 Description of Low Profile Cascade Aerator Model ........................... 22 Design Geometry for Weirs ................................................................. 25 Three Slope Variation .......................................................................... 27 Flow Rates Calibration ........................................................................ 27 Application of Sodium Sulphite and Cobalt Chloride ......................... 29 Water Quality ....................................................................................... 31 Dissolved Oxygen (DO) Measurements .............................................. 32 Test Procedure ..................................................................................... 34 KLa Estimation: Nonlinear Regression Method ................................... 34
v
IV. RESULTS AND DISCUSSION ...................................................................... 38
General Observations ........................................................................... 38 Channel Slope 2.50 ............................................................................... 39 Channel Slope 4.50 ............................................................................... 43 Channel Slope 6.50 ............................................................................... 44
Interaction between Channel Slope, Flow Rates, Weir Geometry and Oxygen Transfer Coefficient………. ...................................... 46
V. CONCLUSIONS AND RECOMMENDATIONS .......................................... 55
REFERENCES ............................................................................................................ 61
APPENDIX A DO PROFILE GRAPH ................................................................................... 63
B NON-LINEAR REGRESSION PARAMETER ESTIMATES ...................... 82
C MINITAB® OUTPUT .................................................................................... 89
vi
LIST OF TABLES TABLE Page 4.1 KLa Non-Linear Regression Estimates for Channel Slope 2.50 .................... 39 4.2 KLa Non-Linear Regression Estimates for Channel Slope 4.50 .................... 43 4.3 KLa Non-Linear Regression Estimates for Channel Slope 6.50 .................... 44 4.4 One-Way ANOVA ........................................................................................ 49 4.5 Two-Way ANOVA ....................................................................................... 51 4.6 Two-Way ANOVA for Weir Geometry ........................................................ 52
4.7 Balance (Three-Way) ANOVA ..................................................................... 53 B.1 Results for Evaluation of Channel Slope 2.50 ............................................... 83 B.2 Results for Evaluation of Channel Slope 2.50 ............................................... 85 B.3 Results for Evaluation of Channel Slope 2.50 ............................................... 87
vii
LIST OF FIGURES FIGURE Page 2.1 Elemental Control Volume ............................................................................ 8
2.2 Lewis and Witman’s “Two-Film Theory” .................................................... 10 2.3 Nappe Flow Regime with Fully-Developed Hydraulic Jump ....................... 14 2.4 Skimming Flow Regime with Stable Cavity Recirculation .......................... 15
2.5 Flow Aeration in Nappe Flow Regime with Fully-Developed Hydraulic jump… ..................................................................................... 16 2.6 Flow Aeration in Skimming Flow Regime ................................................... 18 3.1 Schematic Diagram of a Low Profile Cascade Aerator Model ..................... 23 3.2 Front View of Model Aerator with DO Probe (Channel Slope 4.50) ............ 24
3.3 Side View of Model Aerator with DO Probe ................................................ 25 3.4 Rectangular-shaped Weir .............................................................................. 26 3.5 Inverted T-shaped Weir ................................................................................. 26
3.6 W-shaped Weir .............................................................................................. 26 3.7 Inverted Cross shaped Weir ........................................................................... 26 3.8 Equally Spaced Velocity Measurements ....................................................... 28 3.9 Nessler Tube Test to Determine Level of Complete Mixing ........................ 31
viii
4.1 Schematic Front View of Flow over Cross Weir .......................................... 40 4.2 Schematic Front View of Flow over W Weir ................................................ 41 4.3 Schematic Front View of Single Layer Flow over Cross weir ...................... 41 4.4 Main Effect Plot (data means) for KLa .......................................................... 47 4.5 Interaction Plot (data means) for KLa ............................................................ 48 A.1 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg. ............................ 64 A.2 DO Profile: T. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg. ................................ 64
A.3 DO Profile: W. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg. ............................... 65
A.4 DO Profile: Crs. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg. ............................. 65
A.5 DO Profile: Rec. Weir, Flow 75 gpm/ft, Slope 2.5 deg. ............................... 66
A.6 DO Profile: T. Weir, Flow 75 gpm/ft, Slope 2.5 deg. ................................... 66
A.7 DO Profile: W. Weir, Flow 75 gpm/ft, Slope 2.5 deg. .................................. 67
A.8 DO Profile: Crs. Weir, Flow 75 gpm/ft, Slope 2.5 deg. ................................ 67
A.9 DO Profile: Rec. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg. .......................... 68
A.10 DO Profile: T. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg. .............................. 68
A.11 DO Profile: W. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg. ............................. 69
A.12 DO Profile: Crs. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg. ........................... 69
A.13 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg. ............................ 70
A.14 DO Profile: T. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg. ................................ 70
A.15 DO Profile: W. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg. ............................... 71
A.16 DO Profile: Crs. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg. ............................. 71
A.17 DO Profile: Rec. Weir, Flow 75 gpm/ft, Slope 4.5 deg. ............................... 72
A.18 DO Profile: T. Weir, Flow 75 gpm/ft, Slope 4.5 deg. ................................... 72
ix
A.19 DO Profile: W. Weir, Flow 75 gpm/ft, Slope 4.5 deg. .................................. 73
A.20 DO Profile: Crs. Weir, Flow 75 gpm/ft, Slope 4.5 deg. ................................ 73
A.21 DO Profile: Rec. Weir, Flow 112.5 gpm/ft, Slope 4.5 deg. .......................... 74
A.22 DO Profile: T. Weir, Flow 112.5 gpm/ft, Slope 4.5 deg. .............................. 74
A.23 DO Profile: W. Weir, Flow 112.5 gpm/ft, Slope 4.5 deg. ............................. 75
A.24 DO Profile: Crs. Weir, Flow 112.5 gpm/ft, Slope 4.5 deg. ........................... 75
A.25 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 6.5 deg. ............................ 76
A.26 DO Profile: T. Weir, Flow 37.5 gpm/ft, Slope 6.5 deg. ................................ 76
A.27 DO Profile: W. Weir, Flow 37.5 gpm/ft, Slope 6.5 deg. ............................... 77
A.28 DO Profile: Crs. Weir, Flow 37.5 gpm/ft, Slope 6.5 deg. ............................. 77
A.29 DO Profile: Rec. Weir, Flow 75 gpm/ft, Slope 6.5 deg. ............................... 78
A.30 DO Profile: T. Weir, Flow 75 gpm/ft, Slope 6.5 deg. ................................... 78
A.31 DO Profile: W. Weir, Flow 75 gpm/ft, Slope 6.5 deg. .................................. 79
A.32 DO Profile: Crs. Weir, Flow 75 gpm/ft, Slope 6.5 deg. ................................ 79
A.33 DO Profile: Rec. Weir, Flow 112.5 gpm/ft, Slope 6.5 deg. .......................... 80
A.34 DO Profile: T. Weir, Flow 112.5 gpm/ft, Slope 6.5 deg. .............................. 80
A.35 DO Profile: W. Weir, Flow 112.5 gpm/ft, Slope 6.5 deg. ............................. 81
A.36 DO Profile: Crs. Weir, Flow 112.5 gpm/ft, Slope 6.5 deg. ........................... 81
C.1 Summary of KLa values for Slope 2.50. ......................................................... 96
C.2 Summary of KLa values for Slope 4.50. ......................................................... 97 C.3 Summary of KLa values for Slope 6.50. ......................................................... 98
1
CHAPTER I
INTRODUCTION
Water, water everywhere, not a drop to drink………… Samuel Coleridge.
Water quality and its enhancement are closely linked with the presence of
dissolved oxygen (DO) concentrations; basically serving as a prime indicator of water
quality both for human use and aquatic biota life. Typically low DO contents prevent the
development of aquatic life forms and also might indicate the presences of some form of
pollution associated with excessive wastewater inflows. In general the physical process
by which oxygen is transferred or absorbed from the atmosphere to serve as
replenishment for used up oxygen in water is termed rearation. It involves bringing into
contact the water or the wastewater with oxygen in air and thus dissolving the oxygen in
the water phase.
The most common use of aeration is in the biological treatment of wastewater, to
provide oxygen to aerobic microorganisms; due to the low solubility of oxygen additional
devices are applied to aid the natural aeration process. These aeration devices can be
broadly classified into two groups, diffused and mechanical surface systems, and these
are selected by treatment plants based on function to be performed, type and geometry of
the reactor and cost to install and operate the systems.
2
On the other hand, aeration is not limited to only to biological treatment of
wastewater treatment plants. With the ever increasing stringent requirements being
imposed by National Pollution Discharge Elimination Systems permits for certain
effluent standard and high dissolved oxygen levels, the need for postaeration was
developed. Final effluents from certain wastewater treatment plants need to be reaerated
to significant levels (6-8 mg/l) before being discharged to water-quality-limited stream
sections and to effluent dominated waters (Metcalf and Eddy, 2003). The regulatory
intent is to make sure that low dissolved oxygen levels in the treated wastewater do not
cause any form of depression in oxygen levels in waters of receiving streams.
Cascade aerators are one of the methods currently being used to achieve this
requirement. This is being propagated because of low installation, operational and
maintenance cost, especially if water flow is under gravity. Basically, the cascade
aerators increase dissolved oxygen levels by creating some form of turbulent conditions
where small air bubbles can be transferred into the bulk flow of water.
Brief History on Cascade Aerators
Cascade hydraulic structures or stepped wastewater ways were commonly used to
assist with energy dissipation of flow during the 19th and early 20th century (Chanson,
1995). The world’s oldest stepped spillways are presumably those of the Khosr River
dams (or Ajilah dams), in Iraq (Smith, 1971; Schnitter, 1994). Later the Romans,
Moslem and Spanish civil engineers also incorporated the stepped flow into their dams,
mainly to control flow of water (Chanson, 1994). These technology later spread to the
French and British engineers by the middle of the 17th century, in designing their dam,
3
which helped dissipate energy and prevent scouring. It is worth mentioning some
relatively ancient timber and crib dams with stepped overflows; the North-East part of
America benefited from the experience of Northern European settlers and timber dams
were reported as early as A.D 1600 (Chanson, 1994).
It is only in the 21st century that stepped water overflows became more
pronounced as a means of reaerating oxygen-depleted water. In rivers artificial stepped
cascade and weirs have been introduced to enhance the dissolved oxygen of depleted
streams (Avery and Novak, 1978; Nakasone, 1987). A typical example is the Chatuge
weir built by the Tennessee Valley Authority, a cascade built downstream of the dam.
The series of five aeration step cascade built along the Calumet waterway in Chicago is
another example, assisting to re-oxygenate the polluted canal and also serve as landscape
for leisure parks, combining flow aeration and aesthetics.
Presently cascade aerators serve a wide range of uses, which includes
denitrification or removal of volatile organic compounds (VOCs), removal of chlorine in
treatment of drinking water, elimination or reduction of offensive taste and odour.
Generally stepped cascade aerators are known to be very efficient means of aeration
because of the strong turbulent mixing, the large residence time and the substantial air
bubble entrainment (Toombes and Chanson, 2000).
4
Focus of Research
This research is aimed at evaluating the various parameters that affect the
reaeration process of clean water using a low profile cascade aerator. Investigations will
be undertaken as to the efficiency of this aerator under varying combinations of
operational conditions; these conditions are flow rates from 465.75 L/min.m (37.5
gpm/ft) to 1397.20 L/min.m (112.5 gpm/ft); channel slopes from 2.50 to 6.50 and four
different weir geometries. Evaluations will be done in accordance with procedures
detailed in the ASCE Standards of Measurements of Oxygen Transfer in Clean Water,
(ASCE 2-06, 2007). This standard presents a general methodology for the unsteady-state
evaluation of both diffused-air and mechanical aeration systems.
This low profile cascade aeration system is being selected for investigation
because of high efficiency in entrainment of air bubbles by the simplistic use of natural
gravitational forces through controlled application of velocity, pressure differentials,
weirs, weir spacing, height, and controlled head over weirs, during the aeration process.
An optimal combination of flow, weir design and channel slope will be proposed at the
end of this study. Statistical test (ANOVA) will also be undertaken to determine which
parameters greatly influence aeration rates.
5
CHAPTER II
BACKGROUND
Aeration is simply the introduction of oxygen into a bulk liquid, this process may
occur through natural means, such surface diffusion or be propagated by use of
equipments such as (1) diffusers in a pipe or channel (2) cascading water and (3) surface
turbines or wheels that mix water at the top of basins. Regardless of the mechanism being
employed, the fundamental concepts of the aeration process remain the same. This
chapter will focus on such underlying principles involving oxygen transfer and
measurements.
Review of Earlier Researches
Little material could be found on researches which delved into matters pertaining
to the use of the low profile cascade aerator for postaeration of effluent water. Most of
the researches focused more on the conventional cascade aerator, which though different
from model being investigated, basically operates using the same underlying principle of
turbulent mixing of water while flowing under gravity.
Studies undertaken by Baylar and Emiroglu (2007) for flat and stepped cascade
aerators indicated that water can trap a lot of air when passing through steps, and then
increase oxygen content in the water body, and this advantage becomes more pronounced
in the nappe flow regime. Results further indicated that aeration efficiencies are strongly
6
affected by the type of flow regime, which in turn is a function of the step height, channel
slope and flow rate. Moreover it was demonstrated that aeration efficiency of stepped
aerators increased with increasing channel slope.
Likewise, Chanson (1994) performed a comparative analysis on the variability of
slope on aeration of water and came to the conclusion that aeration increases with
increasing channel slope between 150 and 450 and that an optimum aeration rate is
achieved at slope angles of between 450 and 600 . Any further increase in channel slope
will increase the mean velocity there by reducing the residence time needed for air
entrainment, hence reducing aeration efficiency.
Furthermore, Chanson and Toombes (1997) conducted gas-liquid interface
measurements in a stepped cascade aerator and came to the conclusion that stepped
cascade flows are highly aerated and they are characterized by substantial air-water gas
transfer potential. However these researchers stated that additional information is still
needed to predict more accurately the rate of energy dissipation, the rate of air-water gas
transfer and the re-oxygenation characteristics of stepped cascades.
In research conducted by Nakasone (1987) to show the correlation between
discharge and aeration efficiency, it was concluded that aeration efficiency increases with
increased discharge but eventually begins to decrease. The optimal point for aeration was
found to be at a q of about 235 m3/m.h (2529.5 ft3/ft.h) (where q = discharge per meter
(foot) width of weir). The researcher also confirmed that weir geometry affects aeration
efficiency, by splitting a nappe into separate narrow nappes proved to be more effective,
typically nappe width should be less than 1m (3.3 ft).
7
Further credence has also being lent to the reaerating potential of cascades plants
through experiments done by Aral and Gonullu, (1994). They have shown through a
cascade pilot plant aeration system established in the Fezzan Area of Turkey, a site
having hot climate for all seasons yielded an appreciable reaeration performance with
dissolved oxygen concentration nearing saturation values both for winter and summer
seasons, 6.4 mg/L and 5.6 mg/L respectively.
Pincince (1999) in his research on the “Effects of Multiple Compartments on
Oxygen Transfer in Postaeration Tanks” proposed the use of tanks with a high-length to
width ratio for postaeration, due to optimum efficiency obtained during aeration. Multiple
reareation tanks in series require a lower Standard Oxygen Transfer Rate (SOTR) than a
single reaeration tank. For compartmented tanks, the optimum geometry is obtained when
the SOTR for each tank is equal.
Though not typically in line of reaeration goals; research done by Boyden, et al
(1992), demonstrated that inclined cascade aeration was effective in removing 10
chlorinated volatile organic chemicals (VOCs) from drinking water at liquid loadings of 5
gpm/ft to 15 gpm/ft. Cascade angle of 600 was found most efficacious for compounds
with Henry’s law constant Hp values > 300 atm; compounds with Hp values < 300 atm
were most effectively stripped at yet steeper angles.
From the literature mentioned above, it was be observed that water mass
gravitating over weir or steps has some potential of aerating water due to the turbulence
mixing generated in this process which is also based on the operational conditions of the
particular type of cascade aerator used. As earlier mentioned the low profile aerator being
8
investigated in this study similarly functions through the basic underlining principle of a
traditional cascade aerator however in this case it uses an optimal sloping water-way
fitted with weirs, to achieve its rearation, hence it may not be far-fetched to purport that
the low profile cascade aerator also has the capabilities of aerating, which is the objective
of this paper.
Oxygen Transfer Process: “Two-Film” Theory of Gas Absorption.
Aeration can be described as a mass transfer process, whereby a gaseous
component is absorbed into a liquid phase. This transfer process can be portrayed in the
light of the advection-diffusion equation, which considers transportation by moving water
as well as dispersion through turbulence and molecular diffusion, and biological,
physical, and chemical reaction and interaction of the constituent within the elemental
volume (Kiely, 1997). However the aeration in “clean” water, it is assumed that no
biological, physical, or chemical reactions occur to alter the quantity of oxygen
transferred. Also at the elemental level, mass transfer due to advection and turbulent
diffusion is considered negligible.
Figure 2.1 Elemental Control Volume
9
The transfer of soluble gases into liquid is typically attributed to molecular
diffusion (Metcalf and Eddy, 2003) and as shown in the figure 2.1, applying the mass-
balance approach to the elemental control volume, the transfer of mass to a system can be
modeled as:
xCDr M δδ*−= (2.1)
where:
r = Rate of mass transfer per unit area per unit time, ML-2T-1
DM = Coefficient of molecular diffusion in the x direction, L2T-1
C = Concentration of constituents being transferred, ML-3
x = distance, L
This fundamental theory was first proposed by Lewis and Whitman in 1924
(Metcalf and Eddy, 2003). Based on the assumption that two films exist at the gas-liquid
interface, the rate of absorption of a gas into a liquid is related to the diffusivity across the
film established on each side of the gas-liquid interface. Gas transfer across the film is
proportional to the difference in partial pressure of the gas on either side of the gas film
and vice versa, see figure 2.2. It should also be noted that under steady state conditions,
the rate of mass transfer of gas through the gas film must be equal to the rate transfer
through the liquid film (Metcalf and Eddy, 2003).
10
Figure 2.2 Lewis and Whitman’s “Two-Film Theory”
When Fick’s first law of molecular diffusion is applied to this interface, this
equation is derived:
r = kG(PG – PI) = kL(CI - CL) (2.2)
where:
r = rate of mass transferred per unit area per unit time, ML-2T-1
kG = gas film mass transfer coefficient, T-1
PG = partial pressure of constituent in bulk gas phase, ML-2
PI = partial pressure of constituent at the interface in equilibrium with CI, ML-2
kL = liquid film mass transfer coefficient, L/T
CI = concentration of constituent at the interface in equilibrium with PI, ML-3
CL = concentration of constituent in the bulk liquid phase, ML-3
11
The driving force resulting in transfer in the gas and the liquid phase is the
concentration gradient that exist across the interface; (PG – PI) in gas and (CI-CL) in the
liquid, with coefficients kG and kL respectively. Due to difficulties in quantifying these
coefficients, it is generally appropriate to use the overall coefficients KG and KL,
depending on which films controls the mass transfer process (Metcalf and Eddy, 2003).
Furthermore, if it is assumed that the liquid film controls the mass transfer, based
on Henry’s Law equation 2.3 and 2.4.
PG = HCS (2.3)
PI = HCI (2.4)
where, H is the Henry’s Law constant for the constituent.
This Law states that the weight of any gas that will dissolve in a given volume of
liquid at a constant temperature is directly proportional to the pressure exerted by the gas.
Hence in absorption of a low solubility gas like oxygen in water, since the rate of
diffusion across the liquid film is much lower than that across the gas film, the bulk gas
phase is typically more saturated in comparison with the bulk liquid phase. Therefore it
will be appropriate to define that rate of mass transfer in terms of the overall liquid mass
transfer coefficient, thus:
r = KL(CS – CL) = kG(PG – PI) = kL(CI – CL) (2.5)
where, KL is the overall liquid mass transfer coefficient and CS is the concentration of
constituent at the interface in equilibrium with the partial pressure in the bulk gas phase.
12
Thus combining equations 2.3, 2.4 and 2.5 and assuming diffusion through the
liquid film controls the process, the overall driving force for the mass transfer can be
written as:
(CS – CL) = (CS – CI) + (CI – CL) (2.6)
Further substitution in equation 2.6 (Metcalf and Eddy, 2003) shows that a
relationship between overall liquid and gas phase transfer coefficient can be established
as thus:
CS-CL = r/KL (2.7)
= (CS-CI) + (CI-CL) (2.8)
= (PG-PI)/H + (CI-CL) (2.9)
= r/kGH + r/kL (2.10)
1/KL = 1/kGH + 1/kL (2.11)
When H is high, 1/KL >> 1/KGH and KL ~ kL
1/KL = 1/HKG (2.12)
where: KG = Overall gas mass transfer coefficient and r = KG(PG-PI)
Now in order to estimate the rate of diffusion of a gas into a liquid phase at a
particular time and when considering a unit volume, the rate of transfer r can be defined
as:
rv = KL A/V (CS-Ct) = KLa(CS-Ct) (2.13)
where:
rv = rate of mass transfer per unit volume per unit time, ML-3T-1
KL = volumetric mass transfer coefficient, L-3T-1
13
A = area through which mass is transferred in liquid phase, L2
V = volume in which mass is transferred in liquid phase, L3
a = interfacial area for mass transfer per unit volume (A/V), L-1
CS = concentration in equilibrium with gas as given by Henry’s law =PG/H, ML-3
Ct = concentration in bulk liquid, ML-3
Thus for absorption of gases the change in concentration can be defined in terms
of equation 2.14:
dC/dt = KLa(CS-Ct) (2.14)
Flow Regimes in Cascade Aerators
Air entrainment in cascade flow is greatly influenced by the type of regimes
present in the flow. Basically stepped flows can be classified into two distinct flows
regimes: nappe and skimming flow regimes. A third regime, transition phase is generally
not emphasized.
At low flow rates as water bounces from one step to the next one as a succession
of free-falling nappes; this is called a nappe regime. figure 2.3. In most cases such flows
are characterized by a hydraulic jump as the flow from each step hits the step below.
Generally speaking these flows are found in low discharge or wide steps.
14
Figure 2.3 Nappe Flow Regime with Fully-Developed Hydraulic Jump
On the other hand for narrow steps, steeper slopes or larger discharges, skimming
flows dominate, the water flows down the cascade as a coherent stream, the streamlines
being parallel to the pseudo-bottom formed by the step edges, figure 2.4. Beneath the
pseudo-bottom, recirculating vortices develop filling the zone between the main flow and
steps (Chanson, 1994). The recirculation is maintained through the transmission of shear
stress from the water flowing past the edge of the steps.
15
Figure 2.4 Skimming Flow Regime with Stable Cavity Recirculation
For a range of intermediate discharges, a transition flow regime occurs, easily
identified by stagnation on the horizontal face step, significant splashing and a chaotic
appearance (Baylar and Emiroglu, 2007).
Mechanisms of Entrainment of Air Bubbles in Cascade Aerators
Typically, air entrainment in stepped chute flows are due to turbulent velocities
acting next to the air-water interface, flows are characterized by their strong turbulent
mixing, large residence time and substantial air bubble entrainment. Through this
interface, air is continuously trapped and released and entrainment occurs when both
surface tension and gravity effects can be overcome by the turbulent kinetic energy, that
16
is, this turbulent velocity must be able to subdue bubble rise velocity component and also
surface tension (Chanson, 1994).
Air Entrainment in Nappe Flow Regime
In a nappe flow regime air is entrained by two basic mechanisms. Firstly when the
falling nappe hits a receiving pool of water, air is entrained at the intersection between
the pool and the underside of the jet and this air is drawn from the air cavity beneath the
nappe, hence ventilation of the cavity between the nappe and the vertical step should be
ensured. This type of air entrainment is known as the plunging jet entrainment, figure 2.5,
and the effectiveness of this method is dependent on the jet velocities, with higher
velocities producing more qualitative entrainment process.
Figure 2.5 Flow Aeration in Nappe Flow Regime with Fully-Developed Hydraulic Jump
17
The second method of entrainment is due to the hydraulic jump which takes place
immediately downstream of the impact of the falling nappe, where additional air bubbles
are captured at the toe of the jump (figure 2.5).
Air Entrainment in Skimming Flow Regime
For a skimming flow down a cascade channel, the flow is highly turbulent and
this supports the conditions for free-surface aeration. Pockets of air are usually entrained
along the channel and the region where the free-surface aerated flow occurs is smooth
and glossy. Nevertheless, turbulence is created next to the boundary and as this boundary
layer grows, until it reaches the free surface, the turbulence initiates natural free surface
aeration (figure 2.6) (Chanson, 1994).
Flows in a skimming regime are generally categorized into three; point of
inception; downstream a gradual varied flow layer of both air and water and further
downstream a uniform equilibrium flow region.
18
Figure 2.6 Flow Aeration in Skimming Flow Regime
Aeration Equipment Performance
Generally, oxygen transfer rate measurements are used in comparing the
performance and energy efficiency of oxygenation devices in clean water. Although
slight difference in performance efficiency of the equipment when used in process water,
these differences are dependent on the equipment, how it is applied and nature of the
process water (ASCE 2-06, 2007). Research conducted by Barkdoll and Koduri (2003),
while applying twelve different predictive models for oxygen transfer efficiency to
cascade aerators in four wastewater treatment plants in and around Mississippi; showed
19
that none of the predictive models accurately predicted the oxygen transfer efficiencies of
all the treatment plants. This was attributed to the fact that these predictive equations are
only applicable to the particular hydraulic structure for which the models was developed
thereby accounting for the unique physical properties of the structure or the flow
conditions of application to estimate the oxygen transfer efficiencies. It was concluded
that there was a need for a new more comprehensive equation since existing models were
not developed for stepped cascade aerators.
For these and other reasons, a procedure by which aeration equipment
performance could be evaluated under a set of conditions and results of these evaluations
could be extrapolated with reasonable estimates for real life scenarios was developed by
the American Society of Civil Engineers (ASCE).
Measurement of Oxygen Transfer in Clean Water
Due to the need for a uniform evaluation of aeration devices, the American
Society of Civil Engineers (ASCE) created a committee in January 1977, saddled with
the responsibility of developing standard procedures for determining oxygen transfer
rates. Earlier works aimed at assessing existing aeration equipment and techniques
employed in deriving performances of such equipments in use (ASCE Oxygen Transfer
Standard Committee, 1983).
In 1984, the first standards were incorporated by ASCE based on work by the
1983 committee. Over a series of time these standards have been re-evaluated and
corrected for necessary updates, with the most recent being the ASCE STANDARD,
20
Measurement of Oxygen Transfer in Clean Water, ASCE 2-06, (2007); based on which
all procedures pertaining this research was adhered to.
This present test method is simply based on the removal of oxygen form water by
the means of sodium sulfite in the presence of a catalyst, cobalt chloride. Dissolved
oxygen concentration measurements are then collected periodically throughout the re-
oxygenation process. The data collected are then analyzed to derive the apparent mass
transfer coefficient, KLa and the steady-state DO saturation concentration C*∞; based on
equation 2.15:
C = C*∞ – (C*∞– C0) exp (-KLat) (2.15)
where:
C = DO concentration
C*∞ = determination point value of the steady-state DO saturation concentration
as time approaches infinity.
C0 = DO concentration at time zero
KLa = determination point value of apparent volumetric mass transfer coefficient,
t-1, defined so that
KLa = rate of mass transfer per unit volume / (C*∞– C)
By use of nonlinear regression analysis, equation 2.15 can be used to determine KLa and
C*∞ for each determination point (ASCE 2-06, 2007). The ASCE method of evaluation
has gained wide acceptance and is applicable to both field and laboratory evaluation, used
21
for tank volumes ranging from vessels of a few liters to large tanks over 1 million
gallons.
Specific aspects pertaining to the testing protocol, as detailed by the ASCE 2-06,
(2007) document with the potential to influence the reported output values of this
investigated cascade model, were stringently adhered to and will be further expounded in
succeeding chapter of this document.
22
CHAPTER III
METHODOLOGY
Objective of Study
As earlier stated, the aims and objective of this project is to investigate and
optimize the various factors that affect the reaeration potential of the cascade aerator
model being examined. Influential external factors that will be considered are the water
flow rates, the slope angles and the weir geometry and its effect on oxygen mass transfer
coefficients (KLa) will also be statistically examined using the analysis of variance test
(ANOVA).
The ASCE 2-06 (2007) offers a detailed protocol with respect to experimental
procedures, data collection and analysis, so that a standard uniform methodology could
be applied to all experiments pertaining to aeration in order to yield generally acceptable
results.
Description of Low Profile Cascade Aerator Model
The model being investigated is a cascade only in the sense that it is water
gravitating over stages of weirs. Contrary to traditional cascade models where water falls
steeply from step to step requiring great depth for effectiveness, this modified cascade
aerator simply utilizes optimum sloping waterways fitted with series of turbulence
23
control aeration weirs along the channel. A schematic of a model unit is illustrated as
figure 3.1.
Figure 3.1 Schematic Diagram of a Low Profile Cascade Aerator Model
The model aerator used for this study is made of a 165.1 cm (65 inches) long,
20.32 cm (8 inches wide) and 0.635 cm (¼ inches) thick transparent flexi-plastic inclined
at a fixed slope of 4.50. This channel bed was partitioned into three equal sections by the
three weirs which were placed along its length and was fittedly-enclosed in an open
prismatic Rectangular-shaped tank also made of ¼ inches of flexi-plastic, 152.4 cm (60
inches) long, 20.32 cm (8 inches) wide and 50.8 cm (20 inches) deep, with steel-framed
edges for additional support. All joints were tightly sealed with an acrylic solvent cement
24
sealant to ensure no leakages and this was constantly checked during the course of
experiments to ensure water tight connections. A constant water volume of 58 liters (15.3
gallons) was used for the study. Salinity and total dissolved solids effects were minimized
by using tap water and this was pumped by a ¾ HP centrifugal pump (Hayward® High
Performance pump), which firmly rested on steel plates attached underneath the tank,
(figure 3.2 and 3.3).
Figure 3.2 Front View of Model Aerator with DO Probe (Channel Slope 4.50)
25
Figure 3.3 Side View of Model Aerator with DO Probe.
Design Geometry for Weirs.
Four different types of weirs geometry were used for this study. These weirs were
constructed using 3.81 cm (1.5 inches) by 20.32 cm (8 inches) by 0.635 cm (¼ inch)
thick flexi-plastic strips. Three of each type of weir were constructed and placed at three
equal intervals along the channel bed; (at the tip upstream end of the channel bed, and
one-third and two-thirds the distance from the tip), in order to generate the turbulence
needed for aeration. The four geometries looked at are a Rectangular-shaped weir, an
inverted T-shaped weir, a W-shaped weir and an inverted Cross shaped weir, as
illustrated in figure 3.4 to 3.7. The spacing between the flexi strips in the W-shaped weir
and in the Cross-shaped weir were equal, in order to minimize errors that may arise due
to lack of uniformity.
26
Figure 3.4 Rectangular-shaped Weir
Figure 3.5 Inverted T-shaped Weir
Figure 3.6 W-shaped Weir
Figure 3.7 Inverted Cross shaped Weir
27
Three Slope Variation
Channel bed slopes of 2.50, 4.50 and 6.50 were examined. The fixed angle of the
channel bed was 4.50. The other two angles were determined by applying appropriate
increases in height to the ends of the tank. Needed additions were calculated using basic
Pythagoras theorem and further verified by using plumb lines and protractors. It was
eventually determined that an angle of 6.50 could be achieve by applying shims to give an
increase of 5.33 cm (2.1 inches) to the upstream end of the tank and likewise for an angle
of 2.50.
Flow Rates Calibration
The effects of three flow rates on the oxygen transfer coefficient were evaluated;
these three flow rates were selected based on the capacity of the pump. A maximum flow
of 1397.20 L/min (112.5 gpm/ft) could be obtained from the pump which then served as
the highest flow; the two other flow rates readings 465.75 L/min.m (37.5 gpm/ft) and
931.45 L/min.m (75 gpm/ft) are equally spaced flow rates lower than the highest flow.
The water discharge was calibrated with a FLO-MATETM Model 2000 portable
flowmeter. In order to achieve sufficient data for statistical analysis, it was initially
proposed that five flow rates should be evaluated, however due to the limitations in
acquiring five clearly distinct flow calibrations, through the flowmeter; hence flow rate
was limited to three.
Velocity measurements were taken at three equally spaced positions, figure 3.8
(V1, V2, and V3) across the width of the upstream water discharge unto the channel. An
28
average velocity (V) was then derived which was multiplied by the total flow area (A) to
derived the flow rate (Q).
Figure 3.8 Equally Spaced Velocity Measurements
V = (V1+ V2 + V3)/3 (3.1)
Q = V*A (3.2)
where:
V = average velocity calculated from by flowmeter measurements ft/s
A = water flow area ft2
Q = water discharge ft3/s
Initially it was proposed that flow rates be calculated for each weir geometry,
however upon close calculation and verification, it was concluded that it was unnecessary
because differences in flow velocities were considerably negligible. For instance, the
rectangular-shaped weir produced velocities of 0.202 m/s (0.6633 ft/s); inverted T-shaped
0.201 m/s (0.66 ft/s); W-shaped 0.206 m/s (0.675 ft/s) and inverted Cross shaped 0.207
m/s (0.68 ft/s),at mid flows 931.45 L/min.m (75 gpm/ft) hence flow velocity for the
rectangular weir was adopted for all weirs, since it gave more accurate values.
29
Na2SO3 + ½O2 Na2SO4
Co
The three flow rates, 465.75 L/min.m (37.5 gpm/ft), 931.45 L/min.m (75 gpm/ft)
and 1397.20 L/min.m (112.5 gpm/ft), were obtained by appropriately adjusting the valve
controlling the flow of water until a corresponding stable flow velocity was obtained on
the flowmeter. This was done for all flows to obtain accurate flows.
Application of Sodium Sulphite and Cobalt Chloride.
Sodium sulphite (Na2SO3) was limited to around 4.39 g per test run, in
accordance with ASCE 2-06, (2007) manual, which states that theoretically 7.88 mg/L of
sodium sulphite is needed per 1.0 mg/L of DO concentration. Reagent based sodium
sulphite was also used.
(3.3)
This quantity was sufficient to achieve the depressed DO level of 0.5 mg/L
initially needed before every run.
In order to limit the effect of total dissolved solids and salinity, municipally
supplied tap water was used and total runs were restricted to twelve, after which the test
water was then changed. By limiting total runs to twelve, an approximate total dissolved
solids mass of 52.68 g was ensured, this would result in a TDS concentration of about
908 mg/L in the test water, which is well below the 2,000 mg/L limit set by the ASCE 2-
06, (2007) standards. Such precaution were necessary because it has being reported that
theoretically for every 45.4 kg (100 lb) of sodium sulfite added, 53.1 kg (117 lbs) of
sodium sulphate is formed (USEPA, 1979).
30
ASCE 2-06 (2007) specifies that reagent or technical grade cobalt chloride
CoCl2.6H20 or cobalt sulfate, CoSO4 should be as a catalyst for the sulfite deoxygenation
to achieve a soluble cobalt concentration of between 0.1 mg/L to 0.50 mg/L in the test
water. To achieve this concentration approximately 17.4 mg of reagent based cobalt
chloride was used once for every 58 liters of water tested in this experimental procedure,
this was added prior to the beginning of the system operation.
Generally results from initial tests runs were discarded due to anomalies
associated with stabilization of water chemistry. It is recommended that pre-conditioning
of test water be carried out by mixing it first with sodium sulphite and then aerating to
saturation before starting the test program.
Furthermore in order to ensure adequate dispersion of chemicals in the tank, a
Nessler tube color analysis was carried out in the tank. An equivalent quantity of food
coloring was poured into the tank and then samples were taken every 30 seconds and
compared in 100 ml Nessler tubes in order to determine level of mixing necessary for
complete mixing to occur, see figure 3.9.
31
Figure 3.9 Nessler Tube Test to Determine Level of Complete Mixing
Water Quality
Test water quality must be equivalent to that of potable public water supply
(ASCE 2-06, 2007). This is done to provide some uniformity in source water quality.
However it is known that differences exist between water qualities from various
municipalities. Hence an alternative means of evaluating the oxygen transfer efficiencies
of different systems may be needed.
The use of correction factors α and β is widely accepted and used. The correction
factor, α is used to estimate the KLa in actual system and it is strongly influenced by the
mixing intensity and tank geometry, where:
α = (KLa)WW / (KLa)TW (3.4)
(KLa)WW = oxygen reaeration rate for wastewater
(KLa)TW = oxygen reaeration rate for tap water (reference water)
32
Likewise, the correction factor β is used for evaluating the oxygen transfer rate
based on differences that exist due to constituents such as salts, particulates and surface-
active substances (Metcalf and Eddy, 2003),
β = (CS) WW / (CS) TW (3.5)
(CS) WW = oxygen saturation concentration for wastewater
(CS) TW = oxygen saturation concentration for tap water
Generally the tap water referred to here, is the tap water located at the vicinity of
the wastewater treatment plant, however for water of more consistent characterization,
probably distilled water may be preferred.
Its being reported that values of α vary from 0.3 to 1.2 depending on the type of
aeration equipment while β values range from 0.7 to 0.98 (Metcalf and Eddy, 2003).
Dissolved Oxygen (DO) Measurements
The location of DO probes is in test tanks is generally based on type of aeration
device, size and geometry of the tank and mixing pattern of the tank (ASCE 2-06, 2007).
For this research the DO probe was placed downstream of the channel slope and firmly
secured to minimize movement due to flowing water currents.
DO measurements were taken with the use of a YSI 5010 BOD probe and
recorded with a YSI Model 5100 meter at regular intervals of 10 seconds or 20 seconds,
depending on which time intervals deemed appropriate for the reaeration process. The
probe was submerged at a depth well below the surface of the flowing water at the
downstream end of the channel, in order to achieve appropriate readings and readings
33
were electronically transferred to Excel spreadsheets. The DO meters were also calibrated
daily and, calibration procedures followed those recommended by the manufacturers.
All tests were continued long enough so that the last measured DO values were
equal or close to the 98% of the saturation oxygen value and more than 21 DO values
were recorded equally spaced at approximate equal time intervals from the first to the last
DO values.
Water temperature is known to affect the rate of oxygen transfer into liquid, low
temperatures slow the deoxygenation process and may introduce some error (ASCE 2-06,
2007). It is recommended that temperature that tests runs be carried out at water
temperatures of between “100C and 300C, and as close to 200C as possible”, temperature
outside this range are permissible if approved by engineer-owner-representative. In
addition to this, it is advised that a temperature correction factor, θ, of 1.024 be used to
adjust temperature taken outside stipulated range. During the course of this project
temperature typically varied from 220C to 340C.
It is worthy of note that aeration is not only affected by total dissolved solids and
temperature; alkalinity, chlorine residuals, pH, iron, manganese, total organic carbon,
chemical oxygen demand (COD) cobalt and various surfactants have being reported to
affect oxygen transfer rates, but no clear relationship have being determined to establish
the extent. These effects were not measured or taken into consideration while undertaking
this paper. In addition minute quantities of oil contaminants have also being known to
have effects on oxygen transfer rates.
34
Test Procedure
At the beginning of each test run, the tank was filled with tap water to a measured
volume of 58 liters (15.3 gal). Prior to starting to the flow in the channel, the DO probe is
set in place, centrally positioned above the downstream end of the channel, after which
already measured appropriate quantity of deoxygenating chemicals, cobalt chloride and
sodium sulphate concentration was added to the test water.
The desired flow rate is then started; while monitoring the DO meter, as soon as
the DO level is at or below 0.5 mg/L, measurements are then taken at periodic intervals.
This test is carried out three times for a particular flow rate, slope angle and weir
geometry. Results are attached in the appendix.
KLa Estimation: Nonlinear Regression Method
Recorded dissolved oxygen concentration and its corresponding time are used in
estimating mass transfer coefficient KLa, typically the characteristic plot of the obtained
data is a curvilinear graph, which may prove a little difficult in determination of data.
Hence numerical models are generally the preferred means of data estimation.
The general form of oxygen transfer is based on these equations:
W = dC / dt = KLa (C∞* - C) (3.6)
Where:
W = dC / dt = transfer rate per unit volume
KLa = volumetric mass transfer coefficient
C∞* = dissolved oxygen concentration in the liquid phase
C = dissolved oxygen concentration at time t
35
Integrating the above equation and equation initial time t = 0 and concentration C
as C0, further yields the logarithmic equation (3.7) and exponential equation (3.8) below:
ln (C∞* - C) = - ln (C∞* - C0) KLa (t – to) (3.7)
C = C∞* - (C∞* - C0) e - KLa (t – to) (3.8)
where,
C = dissolved oxygen concentration at time t
C∞* = dissolved oxygen concentration in the liquid phase
C0 = dissolved oxygen concentration at time = 0
KLa = volumetric mass transfer coefficient
t = time
Through various application of these equations, it was noticed that the KLa values
obtained from each of this equation differ from each other, therefore no specific model
has being lauded as producing accurate values. Three areas of concern are immediately
identified when trying to fit a mathematical model to a given set of data. The first is
whether the equation being proposed correctly models the system under study. The
second is selecting which bests estimates the parameters of the proposed model and the
third is precision of the selected model (USEPA, 1979).
Using equation 3.6 seems appropriate in analysizing data because no value of C∞*
is required and the model form is linear, however significant inconsistencies have being
observed (USEPA, 1983) even when the data set contains little “noise”. This method is
36
generally not recommended because of lack of accuracy and over shadowing effect of
even the minutest error.
Likewise the logarithmic form (log-deficit approach) of the equation (3.7) is
similar to the linear/differential form but requires the value of C∞* to be given for
analysis. This is seen as a limitation (Boyle et. al., 1974) because values of C∞* vary
depending on field measurements, published values, and assumption. Using this
approach, an increase in selected value of C∞* will invariably cause a decrease in KLa
value for a given data.
Equation 3.8 is typically evaluated using the non-linear regression analysis. The
best estimates of KLa, equilibrium oxygen concentration and initial oxygen concentration
are chosen which then drive the model equation through the prepared DO concentration-
versus-time data points with a minimum residual sum of squares (ASCE 2-06, 2007). The
difference in concentration between a measured DO value at a given time and the DO
value predicted by the model at the same time is known as the residual. This method is
largely preferred by ASCE because there is limited opportunity for bias to be introduced
into the equation, although a drawback is that it is an iterative process and would require
a computer program for such repetitive calculations.
In applying both the log-deficit and non-linear regression method it required that
data be collected over a specific period of time as outlined by the ASCE 2-06 (2007)
instruction manual. Here it is stated that the sulfite added shall depress the DO
concentration to less than 0.5 mg/L at all determination points. It was observed during the
course of the experiments that initial DO readings fluctuated due to the limits of the
37
membrane-based DO method used; hence we deemed it fit to eliminate all of this data as
being equivalent to zero. Therefore we only regressed data that showed a steady positive
increase in DO, which in a couple of cases were of a value greater than 0.5 mg/L,
however it was ensured that DO values greater than 30% of the saturation concentration
were not truncated as stated in the manual (ASCE 2-06, 2007).
38
CHAPTER IV
RESULTS AND DISCUSSIONS
General Observations
The experiments were run following a three-stage sequence starting from the
lowest slope of 2.50 to the highest of 6.50. We also began with lowest flow rates of
465.75 L/min.m (37.5 gpm/ft) and concluded with the highest of 1397.20 L/min.m (112.5
gpm/ft). Attaining an initially DO concentration of 0.5 mg/L for the high slope and high
flow rate conditions proved somewhat difficult because of the rather fast rate of
reaeration resulting from the extremely turbulent flows conditions that occurred in this
setup. It was found that DO values instantly rose as soon pump was started, hence a few
initial DO levels at this stages ranged between 0.5 mg/L to 1.0 mg/L.
On the other hand flows in the lower discharge regime tended to take longer
periods of time to attain the 98% saturation level as required by the ASCE manual, as a
result longer run periods had to be performed. Due to the longer run periods (20 minutes
to 30 minutes), there was an appreciable temperature increase, especially when three
repetitions were made on the same water sample. As earlier stated total dissolved solids
concentration were kept below limits 2000 mg/L by regularly changing water samples
after 12 runs. It was calculated that performing 12 tests would result in an equivalent
increase in the TDS of about 912 mg/L.
39
In all experimental procedures for all three slope stages were relatively consistent
with ASCE 2-06, (2007) manual. A nonlinear regression FORTRAN program developed
here at the department (Brown; 2005) was used to estimate the mass transfer coefficient
data. Appendix A shows the raw data in a graphical form of oxygen increase over time
for all 108 runs performed.
Channel Slope 2.50
It can be observed from the average KLa stated in Table 4.1 that at flow rates of
465.75 L/min.m (37.5 gpm/ft) the W-shaped weir seems to have most favourable
reareation rates (KLa). Likewise for discharges of 931.45 L/min.m (75 gpm/ft), the W-
shaped weir also appeared most advantageous when compared with the rest of the weirs
considered.
Table 4.1 KLa Non-Linear Regression Estimates for Channel Slope 2.50
Flow Rate (gpm/ft)
Average KLa (min-1) For the Specified Weir Geometry
Rec. T W Cross 37.5 0.177 0.195 0.224 0.198 75 0.334 0.354 0.418 0.354
112.5 0.616 0.615 0.812 1.381
On the other hand at flow rates of 1397.20 L/min.m (112.5 gpm/ft) the Cross weir
produced the better reaeration rates in comparison with the W-shaped weir. This higher
KLa can be traced to the additional turbulence generated as a result of increase in flow
rates. This generated an extra nappe plunging flow regime over the upper region of the
Cross weir, which when combined with the lower region flows greatly enhanced air
40
entrainment mechanism see figure 4.1. Similar results were obtained by Nakasone,
(1987) who narrowed the width of his nappe flow regimes invariably increasing
turbulence which then led to an increase in aeration efficiency. At flow rates lower than
283.9L/min (112.5 gpm/ft) this beneficial additional layer could not be generated because
flow rates lower than this are not high enough to drive the water over the upper region of
the Cross weir.
Figure 4.1 Schematic Front View of Flow over Cross Weir
At flow rates of 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m (75 gpm/ft)
for all of the channel slopes examined, the W-shaped weir produced better results. It was
obvserved that the turbulence generated by the more restricted “dual” passage of water
through the “prong” of W-shaped weir (see figure 4.2) exceeded the turbulence created
by the flow over the lower portions of the Cross weir. When compared to the Cross weir,
the W-shaped weir reduces the channel width by 55% in comparison to the Cross’s
reduction of 20%, this reduced flow area may have contributed to an increase in plunging
41
depth of the nappe flow over the weir, thus creating additional turbulence downstream of
the channel bed.
Figure 4.2 Schematic Front View of Flow over W Weir
At these flow rates discharges were not high enough to generate the double layer
plunging nappe flow needed by the Cross shaped weir (figure 4.3), hence the flow was
limited to the lower region of the Cross weir. The W-shaped weir therefore generated
more turbulence, thus its KLa were higher for flow rates of 465.75 L/min.m (37.5 gpm/ft)
and 931.45 L/min.m (75 gpm/ft).
Figure 4.3 Schematic Front View of Single Layer flow over Cross Weir
42
By the calculating the critical velocities for each channel slope, it can be shown
that the super critical velocities occurred on the downstream of the weir, White, (1999).
vc = (gyc)1/2 (4.1)
Where:
vc = critical velocity
g = acceleration due to gravity
yc = critical depth
The critical depth yc can be obtained from equation 4.2:
3/12
2
)(gb
Qyc = (4.2)
Where:
Q = flow rate
b. = width of channel
Critical velocity derived was determined to be 0.589m/s (1.933ft/s), which is
greater than the maximum velocity obtained during flow, hence turbulence occurred on
the downstream side. Furthermore this critical velocity generated a critical depth of about
1.9 cm (0.75 inches) this is less than the low head depth of all weirs which were all 3.8
cm (1.5 inches) in width further confirming that super critical flow was downstream.
The subcritical velocities built up on the upstream of the weir, generated
sufficient depth for the free falling nappe flows to generated large enough turbulence for
entrainment of oxygen in the body of water. As explained before this effect was more
pronounced at lower flow rates 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m (75
43
gpm/ft) for all channel slope, which is most probably why the W-shaped weir dominated
in this flow regimes, because its rather restricted passage water ways forced water depth
to build up on both end before falling down the water ways.
Channel Slope 4.50
In comparison with channel slope of 2.50, all KLa obtained were generally higher
for each respective corresponding flow rates, also linked to the increase in slope angle
which invariably leads to added turbulence to all the flow regimes. Likewise, average
KLa followed the same trends as discussed in channel slope of 2.50, better reaeration rates
were obtained for flow rates of 1397.20 L/min.m (112.5 gpm/ft) using the Cross shaped
weir geometry, see Table 4.2. This effect equally attributed to the extra nappe flow
turbulent regime generated over the upper region of the Cross weir.
Table 4.2 KLa Non-Linear Regression Estimates for Channel Slope 4.50
Flow Rate (gpm/ft)
Average KLa (min-1) For the Specified Weir Geometry
Rec. T W Cross 37.5 0.201 0.214 0.298 0.273 75 0.425 0.425 0.495 0.456
112.5 0.961 0.998 1.065 1.293
Similarly as in the case of channel slope of 2.50, at flow rates of 465.75 L/min.m
(37.5 gpm/ft) and 931.45 L/min.m (75 gpm/ft), it appeared that most favourable
reaeration rates for slope of 4.50 were also obtained from the W-shaped weir.
44
Channel Slope 6.50
Predictably, the highest KLa for all three channel slopes considered were obtained
at this channel slope for all corresponding flow rates. At a combination of this slope angle
and a flow rate of 1397.20 L/min.m (112.5 gpm/ft), using the Cross weir seemingly
appeared to achieve the most optimal reaeration rates for combination of all operational
parameters considered (Table 4.3). As before the W-shaped produced the best reaeration
values for both the 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m (75 gpm/ft) flow
rates.
Table 4.3 KLa Non-Linear Regression Estimates for Channel Slope 6.50
Flow Rate (gpm/ft)
Average KLa (min-1) For the Specified Weir Geometry
Rec. T W Cross 37.5 0.257 0.247 0.276 0.226 75 0.441 0.442 0.569 0.554
112.5 1.780 1.774 1.904 1.977
Based on the earlier discussions we should expect that the inverted T and Cross
weir produce similar KLa at flows of 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m
(75 gpm/ft), since flows here were limited to the lower region of the Cross weir, and
hence it acted as a T-shaped weir. This trend can be observed in their respective KLa for
channel slopes 2.50 and 4.50, though they are not all precisely similar possibly due to
human and experimental errors while running the experiment, they are of some what
roughly close proximity. However as would be seen in Table 4.3 this was not the case for
the flow rates of 931.45 L/min.m (75 gpm/ft) at the slope of 6.50, because at this stage
45
there were intermittent surges of water over the upper regions of the Cross weir, thus
creating additional turbulence in this setup.
As mentioned earlier, in comparison to the other two slope channels investigated,
it can be distinctly noticed that reaeration rates in the channel slope of 6.50 for all four
weir geometries for each respective flow rates are considerable higher than their
corresponding flow rates counterparts in the other two channel slopes. Hence it may be
advisable to operate the low profile cascade aerator at this slope or even a much higher
slope, because better reaeration values are seems to be obtained with increase in channel
slope. Though further analysis may need to be obtained to determine the most optimal
channel slope, because based on literature by Chanson, 1994 reareation process are still
achievable until slopes of between 450 to 600.
On the long run, it appears that the W-shaped weir may be overall the most
beneficial weir. This is because at the highest flow rates of 1397.20 L/min.m (112.5
gpm/ft) where the Cross weir had a distinctly higher reaeration rates in lower slopes; at
this channel slope of 6.50, the difference in KLa between the two weir geometries is rather
negligible and may probably have similar effects. This may be traced to the fact that an
increase in channel slope and flow rates combination may eventually reach a point where
the differences in weir geometry design may have no significant impact on air
entrainment. Therefore, a statistical analysis was under taken to determine if there was a
significant improvement in aeration when the Cross was used.
46
Interaction between Channel Slope, Flow Rates, Weir Geometry
and Oxygen Transfer Coefficient
As part of efforts to delineate which factors play significant roles in the reaeration
a main and interactive effect plot graph was performed on the mean KLa values derived
from one and a combination of the operational parameters.
Firstly a graphical plot of the main effects of the varied operational parameter on
KLa was conducted as displayed in figure 4.4. Isolating the effects of slope channel, it can
be seen that the highest mean oxygen transfer rates are obtained for channel slopes of
6.50, followed by slopes of 4.50, then 2.50, hence it may be safe to say the higher the
channel slope, the better the oxygen transfer rates. Furthermore, if the effects of flow
rates are singled out, from the plot displayed, it is observed that at flow rates of 1397.20
L/min.m (112.5 gpm/ft) highest aeration is achieved.
Finally, in considering the plot showing the effects of the various weir geometries
on the mass transfer coefficient, it is obvious that the Cross shaped weir produced higher
average reaeration rates. Despite this high rates it may be rather hasty to conclude that the
Cross shaped weir are the most influential of all weir type considered, because they are
found to produce better reaeration rates at flow rates of 112.5 gpm/ft, further analysis
may be needed. The rectangular and inverted T-shaped weir appears to produce the same
effect.
47
Mea
n of
KLa
6.54.52.5
1.2
0.9
0.6
0.3
112.575.037.5
WTRec.Crs.
1.2
0.9
0.6
0.3
Slope Flowrates
Weir Config.
Figure 4.4 Main Effects Plot (data means) for KLa
A more detailed analysis of the interactions between the varied parameters and
KLa can be seen in the interaction plot diagram, figure 4.5. Firstly, taking a look at the
slope angle, for all channel slopes the highest aeration rates are obtained for flow rates of
1397.20 L/min.m (112.5 gpm/ft), similarly the Cross shaped weir had the highest
reaeration rates for all channel slopes. It is worth noting that at channel slope of 6.50 and
flow rate of 1397.20 L/min.m (112.5 gpm/ft), aeration rate coefficient for all weir
geometries seem to converge at near equal values. As earlier explained, it may be derived
that at this flow rate and slope angle, difference in weir geometry has negligible impact
on the mass transfer coefficient.
48
Slope
2
1
0
Flowrates
Weir Config.
WTRec.C rs.
112.575.037.5
2
1
0
6.54.52.5
2
1
0
Slope
6.5
2.54.5
Flowrates
112.5
37.575.0
Weir
TW
Config.Crs.Rec.
Figure 4.5 Interaction Plot (data means) for KLa
Secondly, for flow rates of 1397.20 L/min.m (112.5 gpm/ft), KLa peak at channel
slopes of 6.50 and Cross weir geometry, verifying the previous relationship obtained.
Finally for the weir geometries, the Cross weir appeared to be better for flow rates of
1397.20 L/min.m (112.5 gpm/ft) and slope angle of 6.50.
These results indicate that aeration coefficient increases as the flow rates and
slope angle increases, with higher mass transfer coefficient being obtained at this
condition for the Cross shaped weir. The reason for this as discussed earlier, can be
traced to the additional turbulence generated as water flows over the upper and lower
portions of the Cross shaped weir which creates strong mixing of the free falling nappe
49
flow water regime. However it still leaves us in the dark as to which weir is most
influential when all three flow rates and slopes are taken into cognizance.
Further analysis was carried out on the three varied parameters using the One-
way, Two-way and Balanced analysis of variance (ANOVA) procedure of MINITAB®
Student Release 14 (1972-2003 MINITAB® Inc.). Here a 95% (α=0.05) confidence
interval serves as the basis for our computation and the probability (P) that any of the
operational parameters significantly affected reaeration (KLa) could be determined by
comparing both α and P. Here operational or a combination of operational parameters are
deemed as significantly affecting reaeration rates if the probabilities (P values) are less
than α and vice versa.
In the One-way analysis the effects of individual operational parameters were
singled out and examined, results (see Table 4.4) it appears that both flow rates and slope
significantly affects reaeration; because the P values( P=0.000; P=0.003) were less than
α=0.05, P=0.000; P=0.003 respectively. However it was observed that the weir
geometries reportedly had no considerably significant effects on KLa; α=0.05, P=0.635.
Table 4.4 One-Way ANOVA
Parameter F P α=0.05
Slope 6.190 0.003 Flow rates 120.07 0.000 Weir Geo. 0.57 0.635
This analysis clearly indicates that the most significant parameters controlling
aeration in a low profile cascaded aerator are the slope and the flow rate. It is understood
50
that steeper slopes provide better aeration. However, this is a constraint limited by the
desire to minimize this parameter while optimizing aeration. Flow rate is a major
parameter because higher rates of oxygen transfer are obtained as the rate of flow through
an area increases.
Regarding weir geometry, four types were considered and its relationship oxygen
transfer. Lumping them together in this analysis does not allow one to define if one
geometry is significantly better then the others or if there are opportunities to improve
oxygen transfer using different weirs. Therefore, though the above analysis suggests weir
geometry is not all that significant in the process, for a given slope and at a given flow
rate, the analysis is still inconclusive.
Analysis was further undertaken using the Two-way approach; this studied the
effects of the interactions (in pairs), of the three operational parameters considered. It was
identified that the interaction of pairs involving the weir geometry; that is the slope and
weir combinations and flow rates vs. weir combinations, seemingly had no noteworthy
effects on the reaeration rates; (Table 4.5) since P values (P=0.988, P=0.282 respectively)
were greater than α=0.05. Although when considered individually slope and flow rates
appear to influence the reaeration process, a combination with various weir geometries
seems to lessen this effect. On the other hand the combinations of slope and. flow rates
were played significantly greater roles in the reaeration process. (P=0.000). It can be
deduced that discharge and slope angle play a major role in re-aeration using the low
profile cascade aerators.
51
Table 4.5 Two-Way ANOVA
Parameter F P α=0.05
Weir Geo. 0.590 0.621 Slope 5.79 0.004
Interaction 0.07 0.988
Weir Geo. 1.940 0.128 Flow rates 125.11 0.000
Interaction 1.260 0.282
Slope 85.04 0.000 Flow rates 560.72 0.000
Interaction 55.32 0.000 There is a relationship, albeit marginal between the weir geometry and the flow
rate. This suggests that there is a significant difference in the aeration based on weir
geometry when different flow rates are being used. The previous data indicates
specifically that Cross is better at the highest flow studies while the W was better at the
others. However, this analysis could also be suggesting that the “W” and Cross are
simply better then “Rec.” and “T”. Therefore the results are not conclusive at this level.
As expected, flow rate and slope are very significant predictors of reaeration.
Based on the data observations, it can again be concluded that higher flow rates and
slopes are better for reaeration then lower values for either parameter.
Furthermore, in trying to ascertain the degree of influence a particular weir
geometry had over the reaeration rates, a two way ANOVA of on each weir was
52
undertaken. Both the single and combined effect of flow rates and channel slope as it
affects reaeration for a particular weir geometry was evaluated. Apparently the
interaction of the flow rates and channel slopes with the W-shaped weir has a greater
influence on reaeration rates in comparison with the rest of the weirs. This is indicated by
a higher F value (95.16) as detailed in table 4.6. Reaeration derived from the flow of the
Cross weir seems to be largely influenced by a higher flow rate as noticed from its rather
large F value, 2322. This further confirms our earlier discussion that higher flow rates
increases reaeration in Cross shaped weir. Performance by Cross shaped weir
significantly improves as the flow rates increases due to the double layer nappe flow
generated at such high flow rates setup (283.91L/min.m (112.5 gpm/ft) as portrayed in
KLa values obtained from experimental analysis.
Table 4.6 Two Way ANOVA for Weir Geometry
Weir Geo. Rec. T W Cross α=0.05
Parameter F P F P F P F P Slope 112.28 0.000 97.31 0.000 148.71 0.000 107.21 0.000
Flow rates 430.77 0.000 403.16 0.000 825.69 0.000 2322.03 0.000 Interaction 77.14 0.000 71.88 0.000 95.16 0.000 85.13 0.000
For the W-shaped weir it seems that steeper slopes improves reaeration
performance as seen in its high F value 148.71. This further clarifies the increase in KLa
results obtained as channel slope increases from 4.50 to 6.50 Both the rectangular and T-
shaped weir appear to have similar influences on reaeration rates on the low profile
53
cascade aerator model. However statistical analysis shows that there is little advantage to
rectangular weir when compared to the T weir.
An overall investigation was carried out using Balanced (Three) way analysis and
this showed that a combination of all three parameters significantly influence reaeration.
(P=0.000) see figure 4.7.
Table 4.7 Balanced (Three-Way) ANOVA
Parameter F P α=0.05
Slope 438.31 0.000 Flow rates 2890.08 0.000 Weir Geo. 44.92 0.000
Slope*Flow rates 285.12 0.000 Slope*Weir Geo. 5.64 0.000
Flow rates*Weir Geo. 29.18 0.000 Slope*Flow rates*Weir Geo. 7.890 0.000
However, the three-way analysis result may not be a precise representation of
effects, as observed in the unusually high F values, this can be traced to the some what
“limited” data obtained in the course of running this experiments. Typically, the norm for
this type of ANOVA analysis is to ensure that experimental data are derived from at least
six (6) repetitions of test runs, that is at least twice the number of operational
parameters/factors investigated (Montgomery et al, 2003), unless accuracy may be
compromised.
Nevertheless, based on the data obtained, the three-way ANOVA further
corroborates the findings of the two earlier ANOVA analysis and the results of
54
experiments by Baylar, Emiroglu., et al (2007), Chanson,(1994) and Nakasone.,(1987);
that the flow rates and channel slope angle seem to be major players in the aeration
process, since their F-ratios is well into the critical region.
55
CHAPTER V
CONCLUSIONS AND RECOMMENDATIONS
With the ever increasing stringent dissolved oxygen effluent standards and
permits imposed by the National Pollution Discharge Elimination System on various
wastewater treatment plants spread across the United States, there is a growing need for
post-aeration. Some research has been performed on a wide variety of post-aeration
options, but as of now, there has been no general consensus on a particular advantageous
method. Cascade aerators have been proved to be the least costly (Metcalf and Eddy,
2003) most especially if site constraints and hydraulic conditions permit gravity flow.
The purpose of this research was to simulate as closely as possible a full-scale
operation of a low profile cascade aerator, hence a model aerator was fabricated.
Investigation was carried out on three parameters that tend to affect aeration; flow rates
(465.75 L/min.m (37.5 gpm/ft), 931.45 L/min.m (75 gpm/ft), 1397.20 L/min.m (112.5
gpm/ft)), channel slope (2.50, 4.50 and 6.50) and weir geometry (four different geometry).
Evaluation was undertaken in accordance with protocols established in the ASCE
document; “Measurement of Oxygen Transfer in Clean Water (2007)”. This document
offers specific guidance for various aspects of the evaluation process such as de-
oxygenation methodology, data collection and analysis.
56
Based on the results of this investigation, it has been demonstrated that the low
profile cascade aerator is one of the promising avenue of increasing oxygen content in a
water body. As explained in preceding chapters, the nappe flow regime was predominant
in all flows and reaeration is associated with the strong turbulent mixing which occurs as
the water stream plunges downstream along the channel bed. In this flow regime, aeration
is typically linked to two reasons; (1) the effects of the plunging nappe on receiving water
which causes air bubbles to be entrained at the intersection of the jet with the receiving
pool, and (2) the effects of hydraulic jump which immediately takes place after the nappe
plunge at the downstream end of the flow (Chanson, 1994).
Certain observations and recommendations can be deduced from the
experimental analysis
• At a channel slope of 2.50 it appears that in general, the lowest reaeration rates
were obtained when compared to the rest of the slopes studied. Presently the low
cascade aerator is being operated at a channel slope of 4.50, however from results
obtained from this study it can be seen that higher reaeration rates were obtained
at slope of 6.50. Hence it is recommended that the low profile cascade channel
slope should be higher than 4.50 if a significant improvement in aeration operation
is desired. While Chanson (1994) details that reaeration achieves maximum
capability at slopes of 450 to 600, it is noted that the benefit of low profile aerators
would be lost if inclined to this level. Still, it is clear from this effort that minor
increases in slope provide notable increases in aeration and it is suggested that
aerator slopes be increased when specific applications allow.
57
• Similarly, higher reaeration rates are produced with increase in flow rates for all
channel slopes, with highest reaeration being obtained at flow rates of 1397.20
L/min.m (112.5 gpm/ft) for each channel slope. Therefore it may be safe to
recommend that flow rates should be equal to or higher than 1397.20 L/min.m
(112.5 gpm/ft) in order to achieve appreciable increases in reaeration rates.
Further research may be needed to be undertaken to establish an optimal flow
rates, where any increase may not significantly aid the reaeration.
• If the flow rates of 1397.20 L/min.m (112.5 gpm/ft) are to be used for operation
of the low profile cascade aerator for channel slopes of 2.50 and 4.50, it may be
advisable to use the Cross shaped weir, because better reaeration are generally
obtained when it is applied, for example when compared to the next closest
reaeration rates (W-shaped), there is a 70% and 21% increase respectively.
However a minimal increase of 3% for channel slope 6.50 may not
overwhelmingly necessitate a preference for the Cross shaped weir.
• On the other hand if flow rates of 931.45 L/min.m (75 gpm/ft) and 465.75
L/min.m (37.5 gpm/ft) are used, it is preferable to use the W-shaped weir for all
channel slope conditions investigated in this study. As explained in chapter 3
better reaeration are obtained for the W weirs at these flow rates, because flow
rates are not large enough to generate the additional plunging nappe flow over the
upper bar of the Cross weir, which other wise would given it extra turbulence and
hence better reaeration rates.
58
• Furthermore it can be observed that as the channel slope increases the difference
between the least and highest reaeration rates invariably reduces. For example
considering the flow rates of 1397.20 L/min.m (112.5 gpm/ft) for each slope, it
can be observed that the differences between these two values (lowest and highest
KLa values) for slopes of 2.50 and 6.50, reduces from 124% to 11%. As stated
earlier it appears that a combination of an optimal channel slope and flow rates
may exist where differences in weir geometry may have minimal impact on
reaeration rates.
On the long run a balance should be struck between opting for the Cross or the W-
shaped weir based on the operational conditions of the plant. For example if operating at
lower flow rates of 465.75 L/min.m (37.5 gpm/ft) and 931.45 L/min.m (75 gpm/ft) for
the three channel slope type, based on this findings it is recommended that W-shaped
weir be used because as it produces higher reaeration rates.
Additional investigations undertaken using statistical analysis displayed that
reaeration was strongly affected by flow rates and slope angles. The higher the two
parameters, the higher the aeration coefficient, which is in concurrence with findings by
Nakasone, (1987) and Baylar, Emiroglu,, et al (2007). Further investigation is
recommended to obtain an empirical model that could easily depict the relationships that
exist between all the operational parameters involved. This recommendation would serve
to provide results of equipment performance evaluations that are representative of the
practical operating conditions experienced in both pilot and field scale equipment.
59
Another area of recommendation is in this investigation of the effect of tank
geometry on the post-aeration capabilities of the low profile cascade aerator. In this study
no analysis was done to determine the effect of reactor geometry. This might play a role
in the aeration process, for example such as the length to width ratio. Pincince., (1999)
advocates the use of a tank with a high length-to-width ratio, divided into compartment
having the same standard oxygen transfer rate, however this he says is applicable to post-
aeration using mechanical aerators. The effects of side wall friction on flow rates of water
may also be taken in cognizance due to the dragging effect that might occur when
different materials are used.
Typically performance of this aerator will largely depend on the initial dissolved
oxygen, required discharge dissolved oxygen levels, air and water temperatures,
atmospheric humidity, and total dissolved solids concentrations. Other water quality
parameters such as pH, presence of oil, iron, manganese, residual chlorine, chemical
oxygen demand have also be know to affect aeration, though no definite limiting
relationship have been determined to date (ASCE 2-06, 2007). Additional study is
recommended on these influential parameters.
In addition an alternative method for providing the basis for a uniform
comparison of aerator performance may need to be addressed, the alpha and beta
correlation factors being proposed by ASCE seems slightly implausible. This is due to the
fact that differences exist in the drinking water standards used by many pubic water
suppliers. To use these factors in setting clean water evaluations it may be advisable to
60
use a reference water of more consistent characterization regardless of location, for
example distilled water.
Finally it is recommended that a comparative cost analysis be performed on the
various types of post-aeration devices currently in use in the industry; for example,
mechanical or diffused aerators. It might be advantageous to determine which best suits
demand in terms of design, manufacturing, operational and maintenance cost. Further,
the relatively low energy loss, moderate capital cost, and low maintenance cost of the low
profile aerator should position it to be a very competitive approach to aerating treated
wastewater prior to discharge to the environment.
61
REFERENCES American Society of Civil Engineers (ASCE); (2007). “Measurement of Oxygen Transfer
in Clean Water.” ASCE Standard [ASCE/EWRI 2-06] American Society of Civil Engineers, Reston Virginia.
Aral, N. and Gonullu, M.T.; (1994), “Aeration by Conventional Cascades in Arid Weather.” Journal of Environmental Science Health, A29 (9), 1749-59.H.
Baylar, A.; Bagatur, T.; and Emiroglu, M.E.; (2007). “Aeration Efficiency with Nappe Flow over Stepped Cascade.” Water Management 160 Issue WMI, Proceeding of the Institute of Civil Engineers, 43-50.
Barkdoll, D. and Koduri, S.; (2003). “Evaluation of Oxygen Transfer at Stepped Cascade Aerators.” World Water and Environmental Resources Congress June 23-26 2003, Philadelphia, Pennsylvania USA. ASCE Conference Proceedings.
Boyden, Brace H; Banh, Duong T.; Huckaboy, Houston K.; and Fernandes, Joseph B.; (1992). “Using Inclined Cascade Aeration to Strip Chlorinated VOCs From Drinking Water.” Journal of the American Water Works Association 8 (5) 62-69.
Boyle, W.C.; Berthouex, P.M.; and Rooney, T.C.; (1994). “Pitfalls in Parameter Estimation for Oxygen Transfer Data.” Journal of the Environmental Engineering Division, ASCE, 100 (EE2): 391-408, April 1974
Brown, Gregory A.; (2005). “Factors to Consider when Evaluating Horizontal Rotor Aerator Performance” Master of Science Thesis, Dept. of Civil and Environmental Engineering, Mississippi State University.
Chanson, H.; (1994). “Air-Water Interface Area in Self-Aerated Flows.” Water Research 28 (4) 923-929
Chason, H. and Toombes, L.; (1997). “Flow Aeration at Stepped Cascade.” Civil Engineering. Research Reports, Dept. of Civil Engineering, The University of Queensland, Brisbane Queensland 40742 Australia.
Chanson, H.; (1994). “Hydraulic Design of Stepped Cascades, Channels, Weirs and Spillways. “ 1st Edition. Elsevier Science Inc., New York, U.S.A.
Kiely, G.; (1997). “Environmental Engineering.” McGraw-Hill, London, England.
62
Metcalf and Eddy, Inc.; (2003). Edited by George Tchobanoglous, Franklin L. Burton, and H. David Stensel. “Wastewater Engineering, Treatment and Reuse.”McGraw-Hill, New York, NY.
Montgomery, Douglas C. and Runger, George C.; (2003). “Applied Statistics and Probability for Engineers.” 3rd Edition. John Wiley & Sons, Inc, New York, NY.
Nakasone, H.; (1987). “Study of Aeration at Weirs and Cascade.” Journal of Environmental Engineering 113 (1), ASCE Paper No. 21221.
Pincince, Albert B; (1999). “Effect of Multiple Compartments on Oxygen Transfer in Postaeration Tanks” Water Environment Research 71 (6) 1229-34
Tebbutt, T.H.Y.; Issery, I.T.S., and Rasaratnam, S.K.; (1977). “Reaeration Performance of Stepped Cascades.” Journal of the Institution of Water Engineers and Scientists, 31 (4) 285-97
Thacker, N.P.; Katkar, S.L.; and Rudra, A.; (2002). “Evaluation of Mass Transfer Coefficient of Free Fall-Cascade-Aerator.” Environmental Monitoring and Assessment 74 1-9.
United States Environmental Protection Agency (USEPA); (1979). “Proceedings: Workshop Toward an Oxygen Transfer Standard.” EPA-600/9-78-021
United States Environmental Protection Agency (USEPA); (1983). “ Development of Standard Procedures for Evaluating Oxygen Transfer Devices.” EPA-600/2-83-102.
White, F.M.; (1999). “Fluid Mechanics.” 4th Edition. McGraw-Hill United States o America.
63
APPENDIX A
DO PROFILE GRAPHS
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Figure A.1 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg.
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Figure A.3 DO Profile: W. Weir, Flow 37.5 gpm/ft, Slope 2.5 deg.
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Figure A.4 DO Profile: Crs Weir, Flow 37.5 gpm/ft, Slope 2.5 deg.
Run 1 @ 29.01C Run 2 @ 30.55C Run 3 @ 31.8C
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Figure A.5 DO Profile: Rec. Weir, Flow 75 gpm/ft, Slope 2.5 deg.
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Figure A.7 DO Profile: W. Weir, Flow 75 gpm/ft, Slope 2.5 deg.
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Figure A.8 DO Profile: Crs. Weir, Flow 75 gpm/ft, Slope 2.5 deg.
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Figure A.9 DO Profile: Rec. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg.
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Figure A.10 DO Profile: T Weir, Flow 112.5 gpm/ft, Slope 2.5 deg.
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Time, min.
Figure A.11 DO Profile: W Weir, Flow 112.5 gpm/ft, Slope 2.5 deg.
Run 1 @ 25.5C Run 2 @ 26.65C Run 3 @ 27.45C
0.00
1.00
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3.00
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6.00
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8.00
9.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
DO
Con
c., m
g/L
Time, min.
Figure A.12 DO Profile: Crs. Weir, Flow 112.5 gpm/ft, Slope 2.5 deg.
Run 1 @ 24.7C Run 2 @ 25.5C Run 3 @ 26.25C
70
0.00
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2.00
3.00
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9.00
0.0
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5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
DO
Con
c., m
g/L
Time, min.
Figure A.13 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg.
Run 1 @ 26.9C Run 2 @ 26.5C Run 3 @ 27.45C
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
0.0
1.0
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3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
DO
Con
c., m
g/L
Time, min.
Figure A.14 DO Profile: T. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg.
Run 1 @ 25.35C Run 2 @ 28.1C
71
0.00
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4.00
5.00
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8.00
9.00
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8.0
9.0
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11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
DO
Con
c., m
g/L
Time, min.
Figure A.16 DO Profile: Crs. Weir, Flow 37.5 gpm/ft, Slope 4.5 deg.
Run 1 @ 30.35C Run 2 @ 31.05C Run 3 @ 31.6C
72
0.00
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12.0
13.0
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15.0
16.0
17.0
18.0
DO
Con
c., m
g/L
Time, min.
Figure A.17 DO Profile: Rec. Weir, Flow 75 gpm/ft, Slope 4.5 deg.
Run 1 @ 28.2C Run 2 @ 31.2C Run 3 @ 31.95C
0.00
1.00
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11.0
12.0
13.0
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15.0
16.0
17.0
18.0
DO
Con
c., m
g/L
Time, min.
Figure A.18 DO Profile: T Weir, Flow 75 gpm/ft, Slope 4.5 deg.
Run 1 @ 31.95C Run 2 @ 33.9C Run 3 @ 34.0C
73
0.00
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10.0
11.0
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14.0
15.0
16.0
DO
Con
c., m
g/L
Time, min.
Figure A.19 DO Profile: W Weir, Flow 75 gpm/ft, Slope 4.5 deg.
Run 1 @ 23.45C Run 2 @ 25.05C Run 3 @ 26.15C
0.00
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2.00
3.00
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10.0
11.0
12.0
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14.0
15.0
16.0
DO
Con
c., m
g/L
Time, min.
Figure A.20 DO Profile: Crs. Weir, Flow 75 gpm/ft, Slope 4.5 deg.
Run 1 @ 27.4C Run 2 @ 28.7C Run 3 @ 29.8C
74
0.00
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9.0
10.0
11.0
12.0
DO
Con
c., m
g/L
Time, min.
Figure A.21 DO Profile: Rec. Weir, Flow 112.5 gpm/ft, Slope 4.5 deg.
Run 1 @ 30.8C Run 2 @ 31.0C Run 3 @ 31.95C
0.00
1.00
2.00
3.00
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6.00
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8.00
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8.0
9.0
10.0
11.0
12.0
13.0
14.0
DO
Con
c., m
g/L
Time, min.
Figure A.22 DO Profile: T Weir, Flow 112.5 gpm/ft, Slope 4.5 deg.
Run 1 @ 32.2C Run 2 @ 33.55C Run 3 @ 33.2C
75
0.00
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9.00
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5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
DO
Con
c., m
g/L
Time, min.
Figure A.23 DO Profile: W Weir, Flow 112.5 gpm/ft, Slope 4.5 deg.
Run 1 @ 30.2C Run 2 @ 33.4C Run 3 @ 27.3C
0.00
1.00
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8.00
9.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
DO
Con
c., m
g/L
Time, min.
Figure A.24 DO Profile: Crs. Weir, Flow 112.5 gpm/ft, Slope 4.5 deg.
Run 1 @ 26.3C Run 2 @ 25.8C Run 3 @ 27.1C
76
0.00
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9.00
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14.0
15.0
16.0
17.0
18.0
19.0
20.0
DO
Con
c., m
g/L
Time, min.
Figure A.25 DO Profile: Rec. Weir, Flow 37.5 gpm/ft, Slope 6.5 deg.
Run 1 @ 28.1C Run 2 @ 30.55C Run 3 @ 29.4C
0.00
1.00
2.00
3.00
4.00
5.00
6.00
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9.00
0.0
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10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
21.0
22.0
23.0
24.0
DO
Con
c., m
g/L
Time, min.
Figure A.26 DO Profile: T Weir, Flow 37.5 gpm/ft, Slope 6.5 deg.
Run 1 @ 28.7C Run 2 @ 30.05C Run 3 @ 30.3C
77
0.00
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20.0
21.0
22.0
23.0
24.0
25.0
26.0
DO
Con
c., m
g/L
Time, min.
Figure A.27 DO Profile: W Weir, Flow 37.5 gpm/ft, Slope 6.5 deg.
Run 1 @ 31.6C Run 2 @ 32.3C Run 3 @ 32.85C
0.00
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18.0
19.0
20.0
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22.0
23.0
24.0
25.0
26.0
DO
Con
c., m
g/L
Time, min.
Figure A.28 DO Profile: Crs. Weir, Flow 37.5 gpm/ft, Slope 6.5 deg.
Run 1 @ 33.4C Run 2 @ 28.45C Run 3 @ 29.8C
78
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12.0
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16.0
17.0
18.0
DO
Con
c., m
g/L
Time, min.
Figure A.29 DO Profile: Rec. Weir, Flow 75 gpm/ft, Slope 6.5 deg.
Run 1 @ 29.25C Run 2 @ 26.75C Run 3 @ 28.0C
0.00
1.00
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8.00
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10.0
11.0
12.0
13.0
14.0
15.0
16.0
DO
Con
c., m
g/L
Time, min.
Figure A.30 DO Profile: T Weir, Flow 75 gpm/ft, Slope 6.5 deg.
Run 1 @ 28.95C Run 2 @ 29.95C Run 3 @ 30.35C
79
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14.0
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16.0
DO
Con
c., m
g/L
Time, min.
Figure A.31 DO Profile: W Weir, Flow 75 gpm/ft, Slope 6.5 deg.
Run 1 @ 25.55C Run 2 @ 28.6C Run 3 @ 30.7C
0.00
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3.00
4.00
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6.00
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10.0
11.0
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13.0
14.0
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16.0
DO
Con
c., m
g/L
Time, min.
Figure A.32 DO Profile: Crs. Weir, Flow 75 gpm/ft, Slope 6.5 deg.
Run 1 @ 31.4C Run 2 @ 32.05C Run 3 @ 32.65C
80
0.00
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2.00
3.00
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7.00
8.00
0.0
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14.0
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16.0
DO
Con
c., m
g/L
Time, min.
Figure A.33 DO Profile: Rec. Weir, Flow 112.5 gpm/ft, Slope 6.5 deg.
Run 1 @ 28.6C Run 2 @ 29.4C Run 3 @ 30.8C
0.00
1.00
2.00
3.00
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6.00
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11.0
12.0
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14.0
15.0
16.0
DO
Con
c., m
g/L
Time, min.
Figure A.34 DO Profile: T Weir, Flow 112.5 gpm/ft, Slope 6.5 deg.
Run 1 @ 24.55C Run 2 @ 26.1C Run 3 @ 27.55C
81
0.00
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0.0
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3.0
4.0
5.0
6.0
DO
Con
c., m
g/L
Time, min.
Figure A.35 DO Profile: W Weir, Flow 112.5 gpm/ft, Slope 6.5 deg.
Run 1 @ 26.2C Run 2 @ 27.8C Run 3 @ 26.3C
0.00
1.00
2.00
3.00
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6.00
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0.0
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2.0
3.0
4.0
5.0
6.0
DO
Con
c., m
g/L
Time, min.
Figure A.36 DO Profile: Crs. Weir, Flow 112.5 gpm/ft, Slope 6.5 deg.
Run 1 @ 28.15C Run 2 @ 25.3C Run 3 @ 25.8C
82
APPENDIX B
NON-LINEAR REGRESSION PARAMETER ESTIMATES
83
Table B.1 Results for Evaluation of Channel Slope 2.50
Run #
Average Non-Linear Regression Absolute Percent
Water Parameter Estimates Standard Deviation Standard Deviation
Temp, 0C Cs, mg/L Co. mg/L KLa, min-1 Cs, mg/L Co. mg/L KLa, min-1 Cs Co KLa
37.5 gpm/ft Flow Rate
R1 28.45 7.434 0.150 0.182 0.027 0.057 0.003 0.359 37.792 1.637
R2 27.35 7.277 -0.513 0.171 0.007 0.017 0.001 0.092 -3.333 0.423
R3 2.05 6.913 -0.029 0.177 0.009 0.025 0.001 0.128 -87.775 0.668
Average 7.208 -0.131 0.177 0.014 0.033 0.002 7.208 -17.772 7.208
T1 29.85 6.818 -0.076 0.201 0.043 0.128 0.007 0.633 -168.677 3.349
T2 29.7 6.917 0.366 0.184 0.075 0.227 0.011 1.084 61.928 6.209
T3 30.85 6.719 -0.355 0.200 0.028 0.095 0.005 0.415 -26.839 2.298
Average 6.818 -0.022 0.195 0.049 0.150 0.008 7.208 -44.529 7.208
W1 32.25 6.221 -0.008 0.236 0.038 0.187 0.012 0.610 -2499.34 4.464
W2 29.7 7.157 -0.528 0.228 0.008 0.021 0.001 0.115 -4.031 0.532
W3 27.5 7.573 -1.325 0.207 0.202 0.357 0.015 2.671 -26.939 9.143
Average 6.984 -0.620 0.224 0.083 0.189 0.010 7.208 -843.437 7.208
Cross1 29.005 6.797 -1.973 0.192 0.043 0.283 0.013 0.631 -14.364 4.431
Cross2 30.55 6.628 -0.626 0.186 0.033 0.107 0.005 0.500 -17.068 2.576
Cross3 31.8 6.344 -0.737 0.189 0.010 0.036 0.002 0.160 -4.903 0.859
Average 6.590 -1.112 0.189 0.029 0.142 0.006 7.208 -12.112 7.208
75 gpm/ft Flow Rate
R1 27.1 7.704 -0.245 0.372 0.018 0.053 0.005 0.231 -21.673 1.216
R2 27.55 7.261 -0.537 0.322 0.049 0.195 0.013 0.674 -36.279 4.039
R3 29.45 7.021 -0.797 0.309 0.070 0.261 0.017 0.993 -32.781 5.525
Average 7.329 -0.526 0.334 0.045 0.170 0.012 0.633 7.208 3.593
T1 30.45 6.716 -1.680 0.395 0.069 0.364 0.025 1.030 -21.657 6.361
T2 31.7 6.453 -0.936 0.350 0.065 0.325 0.023 1.013 -34.716 6.607
T3 33.3 6.154 -2.361 0.318 0.056 0.415 0.033 0.905 -17.562 6.398
Average 6.441 -1.659 0.354 0.063 0.368 0.027 0.983 0.421 6.455
W1 25.85 8.016 -0.218 0.438 0.017 0.048 0.006 0.218 -21.921 1.085
W2 27.95 7.092 0.052 0.415 0.010 0.033 0.004 0.135 64.084 0.893
W3 29.65 6.801 -1.651 0.401 0.010 0.056 0.004 0.145 -3.368 0.944
Average 7.303 -0.606 0.418 0.012 0.046 0.004 0.166 6.590 6.128
Cross1 31.1 6.449 -0.091 0.343 0.084 0.506 0.042 1.298 -556.436 10.737
Cross2 32.65 6.175 0.064 0.355 0.014 0.078 0.007 0.222 122.973 1.844
Cross3 32.55 6.130 -0.109 0.364 0.034 0.133 0.009 0.561 -121.895 3.499
Average 6.251 -0.045 0.354 0.044 0.239 0.019 0.694 6.590 5.360
84
Table B 1 continued.
Run #
Average Non-Linear Regression Absolute Percent
Water Parameter Estimates Standard Deviation Standard Deviation
Temp, 0C Cs, mg/L Co. mg/L KLa, min-1 Cs, mg/L Co. mg/L KLa, min-1 Cs Co KLa
112.5 gpm/ft Flow Rate
R1 27.1 7.183 -0.758 0.618 0.079 0.296 0.038 1.098 -39.006 6.121
R2 28.3 6.985 -1.364 0.625 0.076 0.384 0.053 1.087 -28.168 6.804
R3 29.45 6.810 -1.078 0.606 0.046 0.196 0.025 0.670 -18.155 3.893
Average 6.993 -1.067 0.616 0.067 0.292 0.039 0.952 -28.443 5.606
T1 28.35 7.049 -0.466 0.626 0.077 0.264 0.033 1.096 -56.733 6.000
T2 29.65 6.796 -0.465 0.616 0.048 0.209 0.029 0.708 -44.962 4.504
T3 30.65 6.589 -0.747 0.604 0.030 0.129 0.017 0.452 -17.327 2.769
Average 6.811 -0.559 0.615 0.052 0.201 0.026 0.752 -39.674 4.424
W1 25.5 7.701 -0.234 0.803 0.032 0.125 0.020 0.414 -53.406 2.523
W2 26.65 7.437 -0.701 0.833 0.063 0.328 0.052 0.853 -46.747 5.867
W3 27.45 7.267 -0.677 0.799 0.055 0.242 0.037 0.751 -35.722 4.683
Average 7.468 -0.537 0.812 0.050 0.231 0.036 0.673 -45.292 4.357
Cross1 24.7 8.091 -2.248 1.321 0.097 0.418 0.072 1.200 -18.611 6.395
Cross2 25.5 7.838 -2.027 1.396 0.049 0.272 0.056 0.621 -13.441 4.006
Cross3 26.25 7.622 -1.058 1.426 0.025 0.145 0.034 0.331 -13.709 2.406
Average 7.850 -1.778 1.381 0.057 0.279 0.054 0.717 -15.253 4.269
85
Table B.2 Results for Evaluation of Channel Slope 4.50
Run #
Average Non-Linear Regression Absolute Percent
Water Parameter Estimates Standard Deviation Standard Deviation
Temp, 0C Cs, mg/L Co. mg/L KLa, min-1 Cs, mg/L Co. mg/L KLa, min-1 Cs Co KLa
37.5 gpm/ft Flow Rate
R1 26.9 7.828 -0.214 0.204 0.030 0.044 0.003 0.377 -20.367 1.401
R2 26.5 10.898 -0.235 0.185 0.930 0.220 0.023 8.534 -93.606 15.674
R3 27.45 8.683 -1.524 0.214 0.576 0.648 0.058 6.639 -42.490 18.367
Average 9.136 -0.658 0.201 0.512 0.304 0.028 5.183 -52.154 11.814
T1 25.35 8.146 -0.195 0.220 0.008 0.014 0.001 0.099 -7.127 0.384
T2 28.1 7.805 -0.207 0.206 0.022 0.029 0.002 0.284 -14.036 0.987
T3 29.8 7.967 0.112 0.218 0.161 0.135 0.013 2.020 120.272 5.882
Average 7.972 -0.096 0.214 0.064 0.059 0.005 0.801 33.036 2.418
W1 30.65 7.228 0.367 0.288 0.061 0.114 0.011 0.844 30.983 3.715
W2 26.35 7.761 0.138 0.295 0.049 0.104 0.009 0.637 75.133 2.890
W3 27.3 7.535 0.074 0.312 0.035 0.089 0.007 0.465 120.188 2.320
Average 7.508 0.193 0.298 0.048 0.102 0.009 0.649 75.435 2.975
Cross1 30.35 7.352 -0.165 0.281 0.068 0.146 0.011 0.922 -88.320 4.075
Cross2 31.05 6.975 0.359 0.265 0.118 0.227 0.021 1.698 63.139 7.791
Cross3 31.6 6.558 -0.396 0.271 0.065 0.224 0.026 0.994 -56.574 5.529
Average 6.962 -0.067 0.273 0.084 0.199 0.019 1.205 -27.252 5.798
75 gpm/ft Flow Rate
R1 28.2 7.728 -0.310 0.408 0.316 0.337 0.026 4.092 -108.766 12.729
R2 31.2 6.107 -0.324 0.420 0.165 0.681 0.111 2.694 -210.147 18.759
R3 31.95 6.534 -0.281 0.446 0.007 0.029 0.003 0.106 -10.503 0.691
Average 6.790 -0.305 0.425 0.163 0.349 0.047 2.298 -109.805 10.727
T1 31.95 6.558 -0.134 0.401 0.012 0.031 0.004 0.189 -23.174 0.952
T2 33.9 6.326 -0.212 0.442 0.029 0.068 0.010 0.459 -31.955 2.186
T3 34 6.165 -0.117 0.432 0.009 0.027 0.004 0.139 -23.006 0.810
Average 6.350 -0.154 0.425 0.017 0.042 0.006 0.262 -26.045 1.316
W1 23.45 8.321 1.871 0.501 0.013 0.055 0.007 0.150 2.937 1.345
W2 25.05 8.005 -1.100 0.478 0.026 0.116 0.010 0.325 -10.524 2.004
W3 26.15 7.689 0.236 0.507 0.012 0.051 0.005 0.150 21.771 1.081
Average 8.005 0.335 0.495 0.017 0.074 0.007 0.209 4.728 1.477
Cross1 27.4 7.397 -0.382 0.450 0.006 0.022 0.002 0.078 -5.844 0.474
Cross2 28.7 7.183 -0.182 0.453 0.013 0.051 0.005 0.182 -27.961 1.139
Cross3 29.8 6.981 -0.439 0.464 0.019 0.074 0.008 0.266 -16.908 1.633
Average 7.187 -0.334 0.456 0.012 0.049 0.005 0.176 -16.904 1.082
86
Table B.2 continued
Run #
Average Non-Linear Regression Absolute Percent
Water Parameter Estimates Standard Deviation Standard Deviation
Temp, 0C Cs, mg/L Co. mg/L KLa, min-1 Cs, mg/L Co. mg/L KLa, min-1 Cs Co KLa
112.5 gpm/ft Flow Rate
R1 30.8 6.842 -0.266 0.947 0.025 0.076 0.016 0.366 -28.480 2.086
R2 31 6.767 -1.118 0.903 0.064 0.380 0.061 0.946 -33.961 6.748
R3 31.95 6.701 -1.065 1.033 0.059 0.427 0.075 0.881 -40.083 7.264
Average 6.770 -0.816 0.961 0.049 0.294 0.051 0.731 -34.175 5.366
T1 32.2 6.639 -1.687 0.812 0.078 0.414 0.052 1.174 -24.509 7.296
T2 33.55 6.521 0.023 0.883 0.101 0.495 0.068 1.552 2141.931 11.577
T3 33.2 6.352 -0.262 0.915 0.037 0.153 0.039 0.583 -58.510 4.240
Average 6.504 -0.642 0.870 0.072 0.354 0.053 1.103 686.304 7.704
W1 30.2 7.306 -3.367 0.998 0.068 0.589 0.089 0.929 -17.503 6.820
W2 33.4 6.369 -0.405 1.124 0.045 0.182 0.062 0.709 -44.940 5.100
W3 27.3 8.042 0.767 1.072 0.038 0.174 0.050 0.469 22.746 3.670
Average 7.239 -1.001 1.065 0.050 0.315 0.067 0.702 -13.232 5.197
Cross1 26.3 7.824 0.456 1.270 0.059 0.245 0.067 0.749 53.732 5.274
Cross2 25.8 7.971 -24.396 1.244 0.038 2.988 0.257 0.476 -12.248 6.054
Cross3 27.1 8.067 -1.191 1.366 0.046 0.213 0.048 0.575 -17.914 3.536
Average 7.954 -8.377 1.293 0.048 1.149 0.124 0.600 7.856 4.955
87
Table B.3 Results for Evaluation of Channel Slope 6.50
Run #
Average Non-Linear Regression Absolute Percent
Water Parameter Estimates Standard Deviation Standard Deviation
Temp, 0C Cs, mg/L Co. mg/L KLa, min-1 Cs, mg/L Co. mg/L KLa, min-1 Cs Co KLa
37.5 gpm/ft Flow Rate
R1 28.1 7.655 -0.240 0.229 0.049 0.071 0.005 0.635 -29.637 2.347
R2 30.55 7.165 -0.179 0.288 0.013 0.032 0.002 0.180 -17.594 0.851
R3 29.4 7.339 -0.697 0.255 0.025 0.059 0.004 0.337 -8.444 1.451
Average 7.386 -0.372 0.257 0.029 0.054 0.004 0.384 -18.558 1.550
T1 28.7 7.055 -0.153 0.233 0.017 0.037 0.003 0.244 -24.456 1.116
T2 30.05 6.918 0.112 0.240 0.021 0.046 0.003 0.298 41.342 1.404
T3 30.3 7.242 0.305 0.270 0.013 0.026 0.002 0.180 8.670 0.811
Average 7.072 0.088 0.247 0.017 0.037 0.003 0.241 8.519 1.111
W1 31.6 6.498 -0.371 0.275 0.029 0.092 0.006 0.450 -24.783 2.366
W2 32.3 6.364 -0.673 0.278 0.035 0.111 0.008 0.545 -16.562 2.778
W3 32.85 6.270 -0.647 0.275 0.025 0.097 0.006 0.406 -15.061 2.316
Average 6.377 -0.564 0.276 0.030 0.100 0.007 0.467 -18.802 2.487
Cross1 33.4 6.138 -0.564 0.257 0.012 0.037 0.003 0.195 -6.601 0.987
Cross2 28.45 7.309 -0.637 0.208 0.080 0.212 0.011 1.089 -33.274 5.073
Cross3 29.8 7.037 -1.080 0.214 0.067 0.156 0.008 0.954 -14.480 3.878
Average 6.828 -0.761 0.226 0.053 0.135 0.007 0.746 -18.118 3.313
75 gpm/ft Flow Rate
R1 29.25 7.698 -0.808 0.440 0.122 0.157 0.022 1.588 -19.484 4.896
R2 26.75 7.645 -0.042 0.431 0.034 0.123 0.012 0.441 -291.964 2.693
R3 28 7.414 -1.191 0.450 0.030 0.126 0.011 0.409 -10.564 2.359
Average 7.586 -0.680 0.441 0.062 0.135 0.015 0.813 -107.337 3.316
T1 28.95 7.434 -1.421 0.427 0.070 0.195 0.017 0.946 -13.753 4.129
T2 29.95 7.099 -1.003 0.432 0.078 0.236 0.023 1.095 -23.537 5.253
T3 30.35 6.948 -0.934 0.468 0.031 0.121 0.013 0.447 -12.944 2.513
Average 7.160 -1.119 0.442 0.060 0.184 0.017 0.829 -16.744 3.965
W1 25.55 7.243 0.098 0.572 0.050 0.256 0.031 0.689 262.053 5.375
W2 28.6 7.713 -0.825 0.578 0.045 0.116 0.018 0.590 -14.054 2.629
W3 30.7 6.987 -1.135 0.558 0.072 0.361 0.038 1.037 -31.793 6.731
Average 7.314 -0.621 0.569 0.056 0.244 0.029 0.772 72.068 4.912
Cross1 31.4 6.788 -0.958 0.542 0.033 0.162 0.017 0.485 -16.904 3.182
Cross2 32.05 6.731 -1.009 0.470 0.062 0.258 0.025 0.921 -25.582 5.365
Cross3 32.65 6.597 -1.762 0.650 0.057 0.345 0.038 0.869 -19.563 5.913
Average 6.705 -1.243 0.554 0.051 0.255 0.027 0.758 -20.683 4.820
88
Table B.3 continued
Run #
Average Non-Linear Regression Absolute Percent
Water Parameter Estimates Standard Deviation Standard Deviation
Temp, 0C Cs, mg/L Co. mg/L KLa, min-1 Cs, mg/L Co. mg/L KLa, min-1 Cs Co KLa
112.5 gpm/ft Flow Rate
R1 28.6 7.415 -9.005 1.885 0.105 2.573 0.323 1.410 -28.578 15.512
R2 29.4 7.227 -7.923 1.744 0.097 2.316 0.312 1.343 -29.233 15.261
R3 30.8 7.028 -6.642 1.712 0.081 1.508 0.202 1.159 -22.700 11.811
Average 7.223 -7.856 1.780 0.094 2.132 0.279 1.304 -26.837 14.195
T1 24.55 8.442 -7.485 1.729 0.082 1.536 0.178 0.970 -20.521 10.291
T2 26.1 8.073 -8.059 1.982 0.069 1.574 0.196 0.855 -19.536 9.868
T3 27.55 7.733 -6.022 1.611 0.072 1.237 0.159 0.937 -20.532 9.840
Average 8.082 -7.189 1.774 0.074 1.449 0.177 0.921 -20.196 10.000
W1 26.2 7.506 -7.835 1.989 0.062 1.670 0.217 0.828 -21.312 10.918
W2 27.8 7.986 -1.357 1.736 0.043 0.268 0.069 0.541 -19.722 3.988
W3 26.3 8.304 -1.306 1.987 0.016 0.119 0.033 0.197 -9.118 1.643
Average 7.932 -3.499 1.904 0.041 0.686 0.106 0.522 -16.717 5.516
Cross1 28.15 7.861 -1.464 1.946 0.014 0.101 0.028 0.181 -6.893 1.446
Cross2 25.3 8.514 -2.472 1.971 0.069 0.497 0.119 0.811 -20.125 6.022
Cross3 25.8 8.335 -1.762 2.013 0.013 0.096 0.025 0.155 -5.423 1.249
Average 8.236 -1.899 1.977 0.032 0.231 0.057 0.382 -10.813 2.906
89
APPENDIX C
MINITAB ® OUTPUT
90
————— 7/29/2007 9:45:28 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. ————— 7/29/2007 9:47:30 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Retrieving project from file: 'C:\Program Files\MINITAB 14 Student\Studnt14\Evaluation of Low Profile Cascade Aerator (Truncated KLa).MPJ' ————— 7/29/2007 9:54:27 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Retrieving project from file: 'C:\Program Files\MINITAB 14 Student\Studnt14\Evaluation of Low Profile Cascade Aerator (Truncated KLa).MPJ' Main Effects Plot (data means) for KLa Interaction Plot (data means) for KLa ————— 7/29/2007 10:37:51 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Retrieving project from file: 'C:\Program Files\MINITAB 14 Student\Studnt14\Evaluation of Low Profile Cascade Aerator (Truncated KLa).MPJ' ANOVA: KLa versus Slope, Flowrates, Weir Geo. Factor Type Levels Values Slope fixed 3 2.5, 4.5, 6.5 Flowrates fixed 3 25, 50, 75 Weir Geo. fixed 4 Cross, Rec., T, W Analysis of Variance for KLa Source DF SS MS F P Slope 2 3.28413 1.64206 438.31 0.000 Flowrates 2 21.65431 10.82716 2890.08 0.000 Weir Geo. 3 0.50481 0.16827 44.92 0.000 Slope*Flowrates 4 4.27262 1.06816 285.12 0.000 Slope*Weir Geo. 6 0.12674 0.02112 5.64 0.000
91
Flowrates*Weir Geo. 6 0.65582 0.10930 29.18 0.000 Slope*Flowrates*Weir Geo. 12 0.35454 0.02954 7.89 0.000 Error 72 0.26973 0.00375 Total 107 31.12270 S = 0.0612071 R-Sq = 99.13% R-Sq(adj) = 98.71% Results for: Worksheet 2 One-way ANOVA: KLa versus Slope Source DF SS MS F P Slope 2 3.284 1.642 6.19 0.003 Error 105 27.839 0.265 Total 107 31.123 S = 0.5149 R-Sq = 10.55% R-Sq(adj) = 8.85% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev -----+---------+---------+---------+---- 2.5 36 0.4724 0.3393 (--------*-------) 4.5 36 0.5814 0.3593 (-------*--------) 6.5 36 0.8846 0.7424 (-------*--------) -----+---------+---------+---------+---- 0.40 0.60 0.80 1.00 Pooled StDev = 0.5149 Results for: Worksheet 3 One-way ANOVA: KLa versus Flowrates Source DF SS MS F P Flowrates 2 21.6543 10.8272 120.07 0.000 Error 105 9.4684 0.0902 Total 107 31.1227 S = 0.3003 R-Sq = 69.58% R-Sq(adj) = 69.00% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ------+---------+---------+---------+--- 25 36 0.2315 0.0397 (--*-) 50 36 0.4389 0.0767 (--*-) 75 36 1.2679 0.5129 (--*--) ------+---------+---------+---------+--- 0.35 0.70 1.05 1.40 Pooled StDev = 0.3003 Results for: Worksheet 4
92
One-way ANOVA: KLa versus Weir Geo. Source DF SS MS F P Weir Geo. 3 0.505 0.168 0.57 0.635 Error 104 30.618 0.294 Total 107 31.123 S = 0.5426 R-Sq = 1.62% R-Sq(adj) = 0.00% Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ------+---------+---------+---------+--- Cross 27 0.7447 0.6178 (-------------*------------) Rec. 27 0.5954 0.5435 (-------------*-------------) T 27 0.5709 0.4833 (-------------*-------------) W 27 0.6735 0.5166 (-------------*-------------) ------+---------+---------+---------+--- 0.45 0.60 0.75 0.90 Pooled StDev = 0.5426 Results for: Worksheet 5 Two-way ANOVA: KLa versus Slope, Flowrates Source DF SS MS F P Slope 2 3.2841 1.6421 85.04 0.000 Flowrates 2 21.6543 10.8272 560.72 0.000 Interaction 4 4.2726 1.0682 55.32 0.000 Error 99 1.9116 0.0193 Total 107 31.1227 S = 0.1390 R-Sq = 93.86% R-Sq(adj) = 93.36% ————— 7/29/2007 11:16:40 PM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Results for: Worksheet 2 Two-way ANOVA: KLa versus Slope, Weir Geo. Source DF SS MS F P Slope 2 3.2841 1.64206 5.79 0.004 Weir Geo. 3 0.5048 0.16827 0.59 0.621 Interaction 6 0.1267 0.02112 0.07 0.998 Error 96 27.2070 0.28341 Total 107 31.1227 S = 0.5324 R-Sq = 12.58% R-Sq(adj) = 2.56% Results for: Worksheet 3
93
Two-way ANOVA: KLa versus Flowrates, Weir Geo. Source DF SS MS F P Flowrates 2 21.6543 10.8272 125.11 0.000 Weir Geo. 3 0.5048 0.1683 1.94 0.128 Interaction 6 0.6558 0.1093 1.26 0.282 Error 96 8.3078 0.0865 Total 107 31.1227 S = 0.2942 R-Sq = 73.31% R-Sq(adj) = 70.25%
————— 8/6/2007 9:38:12 AM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. ————— 8/6/2007 9:44:05 AM ———————————————————— Worksheet size: 10000 cells. Welcome to Minitab, press F1 for help. Retrieving project from file: 'C:\Program Files\MINITAB 14 Student\Studnt14\Evaluation of Low Profile Cascade Aerator (Individual Weir).MPJ' Results for: Worksheet 5 (Crs.) Two-way ANOVA: KLa versus Slope, Flowrates Source DF SS MS F P Slope 2 0.41501 0.20751 107.21 0.000 Flowrates 2 8.98904 4.49452 2322.03 0.000 Interaction 4 0.48521 0.12130 85.13 0.000 Error 18 0.03484 0.00194 Total 26 9.92411 S = 0.04400 R-Sq = 99.65% R-Sq(adj) = 99.49% Results for: Worksheet 4 Two-way ANOVA: KLa versus Slope, Flowrates (W) Source DF SS MS F P Slope 2 0.87927 0.43964 148.71 0.000 Flowrates 2 4.88190 2.44095 825.69 0.000 Interaction 4 1.12527 0.28132 95.16 0.000 Error 18 0.05321 0.00296 Total 26 6.93965
94
S = 0.05437 R-Sq = 99.23% R-Sq(adj) = 98.89% Results for: Worksheet 2 Two-way ANOVA: KLa versus Slope, Flowrates (Rec) Source DF SS MS F P Slope 2 1.21177 0.60589 111.28 0.000 Flowrates 2 4.69063 2.34532 430.77 0.000 Interaction 4 1.67997 0.41999 77.14 0.000 Error 18 0.09800 0.00544 Total 26 7.68037 S = 0.07379 R-Sq = 98.72% R-Sq(adj) = 98.16% Individual 95% CIs For Mean Based on Pooled StDev Slope Mean +---------+---------+---------+--------- 2.5 0.375701 (--*---) 4.5 0.528950 (--*--) 6.5 0.881683 (--*--) +---------+---------+---------+--------- 0.32 0.48 0.64 0.80 Individual 95% CIs For Mean Based on Pooled StDev Flowrates Mean -----+---------+---------+---------+---- 37.5 0.21166 (-*-) 75.0 0.39988 (*-) 112.5 1.17479 (-*-) -----+---------+---------+---------+---- 0.30 0.60 0.90 1.20 Results for: Worksheet 3 Two-way ANOVA: KLa versus Slope, Flowrates (T) Source DF SS MS F P Slope 2 0.90481 0.45240 97.31 0.000 Flowrates 2 3.74855 1.87428 403.16 0.000 Interaction 4 1.33671 0.33418 71.88 0.000 Error 18 0.08368 0.00465 Total 26 6.07376 S = 0.06818 R-Sq = 98.62% R-Sq(adj) = 98.01% Individual 95% CIs For Mean Based on Pooled StDev Slope Mean -------+---------+---------+---------+-- 2.5 0.388274 (--*--)
95
4.5 0.503220 (---*--) 6.5 0.821103 (--*--) -------+---------+---------+---------+-- 0.45 0.60 0.75 0.90 Individual 95% CIs For Mean Based on Pooled StDev Flowrates Mean ---+---------+---------+---------+------ 37.5 0.21892 (-*-) 75.0 0.40720 (-*-) 112.5 1.08648 (*-) ---+---------+---------+---------+------ 0.25 0.50 0.75 1.00
96
1.41.21.00.80.60.40.2
Median
Mean
0.600.550.500.450.400.350.30
A nderson-Darling Normality Test
V ariance 0.11510Skewness 1.64491Kurtosis 2.32912N 36
Minimum 0.17102
A -Squared
1st Q uartile 0.20245Median 0.359233rd Q uartile 0.61707Maximum 1.42594
95% C onfidence Interv al for Mean
0.35761
2.42
0.58719
95% C onfidence Interv al for Median
0.28952 0.48204
95% C onfidence Interv al for StDev
0.27517 0.44255
P-V alue < 0.005
Mean 0.47240StDev 0.33927
95% Confidence Intervals
Figure C1 Summary of KLa Values for Slope 2.50
97
1.20.90.60.3
Median
Mean
0.700.650.600.550.500.450.40
A nderson-Darling Normality Test
V ariance 0.12911Skewness 0.782488Kurtosis -0.763302N 36
Minimum 0.18507
A -Squared
1st Q uartile 0.28292Median 0.448203rd Q uartile 0.91193Maximum 1.36580
95% C onfidence Interv al for Mean
0.45981
2.00
0.70296
95% C onfidence Interv al for Median
0.37775 0.58755
95% C onfidence Interv al for StDev
0.29144 0.46871
P-V alue < 0.005
Mean 0.58138StDev 0.35932
95% Confidence Intervals
Figure C2 Summary of KLa Values for Slope 4.50
98
2.01.51.00.5
Median
Mean
1.21.00.80.60.4
A nderson-Darling Normality Test
V ariance 0.55117Skewness 0.70850Kurtosis -1.42012N 36
Minimum 0.20815
A -Squared
1st Q uartile 0.27469Median 0.468703rd Q uartile 1.73425Maximum 2.08500
95% C onfidence Interv al for Mean
0.63337
4.09
1.13576
95% C onfidence Interv al for Median
0.38992 0.90452
95% C onfidence Interv al for StDev
0.60215 0.96843
P-V alue < 0.005
Mean 0.88457StDev 0.74241
95% Confidence Intervals
Figure C3 Summary of KLa Values for Slope 6.50