EPA-660/2-73-025b
December 1973
Environmental Protection Technology Series
Hypolimnion Aeration with
Commercial Oxygen -
Vol. II - Bubble Plume Gas Transfer
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C. 20460
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and
Monitoring, Environmental Protection Agency, have
been grouped into five series. These five broad
categories were established to facilitate further
development and application of environmental
technology. Elimination of traditional grouping
was consciously planned to foster technology
transfer and a maximum interface in related
fields. The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ENVIRONMENTAL
PROTECTION TECHNOLOGY series. This series
describes research performed to develop and
demonstrate instrumentation, equipment and
methodology to repair or prevent environmental
degradation from point and non-point sources of
pollution. This work provides the new or improved
technology required for the control and treatment
of pollution sources to meet environmental quality
standards.
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EPA-66C/2-73-C25b
December 1973
HYPOLIMNION AERATION
WITH
COMMERCIAL OXYGEN
VOLUME II
BUBBLE PLUME GAS TRANSFER
By
R. E. Speece
George Murfee
The University of Texas at Austin
Project 16080 FYW
Program Element
Project Officer
Lowell E. Leach
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 7^820
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 • Price $1.80
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EPA Review Notice
This report has been reviewed by the Environmental Protection
Agency and approved for publication. Approval does not
signify that the contents necessarily reflect views and
policies of the Environmental Protection Agency, nor does
mention of trade names or commercial products constitute
endorsement or recommendation for use.
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ABSTRACT
Hypolimnion aeration can be a desirable alternative to destratification for
maintenance of good hypolimnion water quality characteristics. Injection
of commercial oxygen can be designed to achieve efficient oxygen absorp-
tion within the hypolimnion, thus maintaining the stratified conditions.
Stratified conditions are very desirable when the cold water resource needs
to be preserved.
A mathematical model was developed for predicting the gas transfer charac-
teristics of a bubble plume within an impoundment. Particular attention was
given to evaluation of the gas transfer coefficient K , as a function of bubble
size. With smaller bubble sizes, the buoyant velocity of the bubbles is
lower, thus prolonging the contact time which tends to increase gas trans-
fer. However, the gas transfer coefficient, K , is a function of bubble
size which tends to counter the beneficial effect of extended contact times.
The net effect is that the fraction of oxygen mass absorbed in a given rise
height can be less for smaller bubbles than for larger ones, depending on
the particular sizes.
Tables were compiled from the calibrated model. These tables predict
the oxygen absorption characteristics which can be expected for various
field situations .
This report was submitted in fulfillment of Project Number 16080 FYW
under the partial sponsorship of the Office of Research and Monitoring,
Environmental Protection Agency.
ui
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CONTENTS
5ection_ Paqe
I CONCLUSIONS }
II RECOMMENDATIONS 3
III INTRODUCTION 5
IV OBJECTIVES OF INVESTIGATION 7
V THEORY OF GAS ABSORPTION 9
VI APPARATUS AND PROCEDURES 23
VJI RESULTS AND DISCUSSIONS 2?
VIII ACKNOWLEDGMENTS 85
IX REFERENCES 87
X LIST OF PUBLICATIONS 89
XI APPENDICES 91
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FIGURES
No. Page
1 RELATIVE RESISTANCE TO GAS TRANSFER OF THE
GAS AND LIQUID FILMS 10
2 LIQUID FILM COEFFICIENT VS DIAMETER 14
3 TERMINAL VELOCITY OF BUBBLES AS A FUNCTION
OF BUBBLE RADIUS 15
4 FLOWCHART 17
5 EXPERIMENTAL SYSTEM 24
6 SPEECE'S MODIFICATION OF BARNHART'S FUNCTION 29
7 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS
VS DEPTH (USING SPEECE'S K FUNCTION) 31
J_i
8 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH
(USING SPEECE'S K FUNCTION) 32
J_i
9 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS
VS DEPTH (USING SPEECE'S K FUNCTION) 33
J_i
10 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH (USING
SPEECE'S K FUNCTION) 34
J_i
11 LIQUID FILM COEFFICIENT VS DIAMETER (MURFEE'S
FUNCTION) 36
12 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS
DEPTH - PURE OXYGEN 37
13 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH - PURE
OXYGEN 38
14 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS
DEPTH - PURE OXYGEN 39
vi
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FIGURES
No. Page
15 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH 40
16 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - PURE OXYGEN 41
17 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH -
PURE OXYGEN 42
18 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - PURE OXYGEN 43
19 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH -
PURE OXYGEN 44
20 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - PURE OXYGEN 45
21 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH -
PURE OXYGEN 46
22 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH -
PURE OXYGEN 47
23 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH 48
24 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH 49
25 RELATIVE VOLUME OF GAS VS DEPTH (FRACTION) 51
26 RELATIVE VOLUME OF GAS VS DEPTH (FRACTION) 52
27 LIQUID FILM COEFFICIENT VS DIAMETER 53
28 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH 54
29 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH -
PURE OXYGEN 55
30 FRACTION OF ORIGINAL AMOUNT OF O VS FRAC-
TION OF INITIAL INJECTION DEPTH 57
vu
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FIGURES
No. Page
31 OXYGEN COMPOSITION OF OFF-GAS VS FRAC-
TION OF INITIAL INJECTION DEPTH 58
32 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH 59
33 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH 60
34 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH 61
35 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS
VS DEPTH 63
36 OXYGEN COMPOSITION OF OFF-GAS VS FRACTION
OF DEPTH 64
37 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH 65
38 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH 66
39 CENTER LINE VELOCITY VS HEIGHT ABOVE DIFFUSER 67
40 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH 68
41 RISE HEIGHT REQUIRED TO ACHIEVE INDICATED AB-
SORPTION EFFICIENCY VS BUBBLE DIAMETER 71
42 NITROGEN IN OFF-GAS VS DEPTH - PURE OXYGEN 77
43 NITROGEN IN OFF-GAS VS DEPTH - PURE OXYGEN 78
44 NITROGEN IN OFF-GAS VS DEPTH - PURE OXYGEN 79
45 NITROGEN IN OFF-GAS VS DEPTH - PURE OXYGEN 80
46 NITROGEN IN OFF-GAS VS DEPTH - AIR 81
viii
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FIGURES
No. Page
47 NITROGEN IN OFF-GAS VS DEPTH - AIR 82
48 NITROGEN IN OFF-GAS VS DEPTH - AIR 83
49 NITROGEN IN OFF-GAS VS DEPTH - AIR 84
50 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - PURE OXYGEN 94
51 RELATIVE VOLUME OF GAS VS DEPTH - PURE
OXYGEN 95
52 FRACTION OF ORIGINAL AMOUNT OF O2 IN OFF-
GAS VS DEPTH - PURE OXYGEN 96
53 RELATIVE VOLUME OF GAS VS DEPTH - PURE OXYGEN 97
54 FRACTION OF ORIGINAL AMOUNT O IN OFF-
GAS VS DEPTH - PURE OXYGEN . 98
55 RELATIVE VOLUME OF GAS VS DEPTH - PURE
OXYGEN 99
56 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - PURE OXYGEN 100
57 RELATIVE VOLUME OF GAS VS DEPTH - PURE OXYGEN 101
58 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - PURE OXYGEN 102
59 RELATIVE VOLUME OF GAS VS DEPTH - PURE OXYGEN 103
60 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - PURE OXYGEN 104
61 RELATIVE VOLUME OF GAS VS DEPTH - PURE OXYGEN 105
62 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS
VS DEPTH - PURE OXYGEN 106
IX
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FIGURES
No.
63 RELATIVE VOLUME OF GAS VS DEPTH - PURE
OXYGEN 107
64 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - AIR 108
65 RELATIVE VOLUME OF GAS VS DEPTH - AIR 109
66 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - AIR 110
67 RELATIVE VOLUME OF GAS VS DEPTH - AIR 111
68 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH -AIR 112
69 RELATIVE VOLUME OF GAS VS DEPTH - AIR 113
70 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH -AIR 114
71 RELATIVE VOLUME OF GAS VS DEPTH - AIR 115
72 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH - AIR 116
73 RELATIVE VOLUME OF GAS VS DEPTH - AIR 117
74 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH -AIR 118
75 RELATIVE VOLUME OF GAS VS DEPTH - AIR 119
76 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-
GAS VS DEPTH -AIR 120
77 RELATIVE VOLUME OF GAS VS DEPTH - AIR 121
x
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TABLES
No. Page
1 SUMMARY OF DATA 28
2 RISE HEIGHTS FOR GIVEN % ABSORPTION,
INJECTION DEPTH, AND INITIAL BUBBLE 72
DIAMETER
XI
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SECTION I
CONCLUSIONS
The concept of in-place hypolimnion aeration by injecting commercial
oxygen bubbles has been validated. The rise height required for efficient
absorption to be achieved within the hypolimnion has been defined. A
relationship between the liquid film coefficient and bubble diameter has
been developed for bubble diameters of approximately 0.2 and 2.0 mm.
This relationship has been verified by use of a computer model and data
obtained in a field study.
A methodology for the design of an in-place hypolimnion aeration system
has been developed which can be of practical value to engineers faced with
the problem of improving the quality of hypolimnetic releases.
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SECTION II
RECOMMENDATIONS
It is recommended that additional studies be conducted to verify inter-
mediate points defining the relationship between the gas transfer coef-
ficient, K , and bubble diameter. A full-scale, well instrumented field
installation needs to be made to demonstrate these laboratory and pilot-
scale studies.
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SECTION III
INTRODUCTION
Stratification of impounded waters causes deleterious changes to occur
in the quality of the hypolimnion waters. If the stratification period is
sufficiently long, an anaerobic condition will result. The dissolved
oxygen in the hypolimnion is depleted due to microbial activity and reaera-
tion will not occur because the hypolimnion is isolated from the atmosphere,
Under these conditions, precipitated iron and manganese will return to
solution, carbon dioxide will accumulate, and hydrogen sulfide will be
produced resulting in taste and odor problems and color. To alleviate these
problems some method of aerating the hypolimnion is called for.
Destratification of the reservoir has been one method used to aerate the
hypolimnion. However, certain drawbacks are associated with this solu-
tion. Large volumes of water must be moved to accomplish the destrati-
fication. The beneficial cold water resource which the hypolimnion waters
represent is destroyed. Algal productivity will be increased due to the re-
turn to the epilimnion of the nutrients which have collected in the hypolim-
nion. The water will be supersaturated with nitrogen causing adverse ef-
fects on trout and salmon if the concentration exceeds 104% of saturation.
Selective withdrawal of water from predetermined depths is another method
which can be used to control the quality of the water discharged below
an impoundment or withdrawn as a water supply. The warm epilimnion
waters containing a high concentration of dissolved oxygen can be with-
drawn and mixed with a chemically low-quality hypolimnetic release and
thereby result in a compromise in the overall quality of the water. How-
ever, certain disadvantages are inherent in the use of this system. The
capital cost and operating cost is high. An operational method must be
employed to insure the release of water of sufficient quality to meet the
downstream use demands. The various levels of release also must be
monitored closely to prevent the accumulation of nutrients in the reser-
voir. It is apparent that in many cases a method must be used which im-
proves the quality of the hypolimnion releases.
Penstock injection of commercial oxygen is another plausible alternative.
Of primary importance, this method involves the least capital expenditure.
Closer control of the dissolved oxygen concentration would be realized
because all of the discharge water must pass through the penstock. The
major disadvantage is that application can only be made during the period
of peaking power production.
-------
Speece (1) has proposed an in-place hypolimnion aeration system whereby
the cold temperature of the hypolimnetic waters is not destroyed while
the dissolved oxygen concentration is increased. Oxygen bubble injection
deep within a reservoir is a desirable method for improvement of the quality
of the water within the hypolimnion for several reasons. First, if the
oxygen bubbles are within certain ranges in size and the depth of injection
is sufficiently deep the bubbles will be completely absorbed before reach-
ing the bottom of the metalimnion and no mixing will occur. With the
thermal stratification maintained, a system of diffusers can be constructed
allowing a build-up of an oxygenated pocket around a municipal or industrial
water supply intake. This will result in quality rectification of the with-
drawn water without aerating the entire hypolimnion. Oxygen gas is a more
feasible gas to use than air because the dissolved nitrogen concentrations
are not increased in the reservoir and more complete absorption of the
total volume of gas injected will be realized, thereby reducing the potential
for mixing to occur between the hypolimnion and the metalimnion for the
cases where the maximum injection depth is relatively shallow.
This report covers several phases of a study directed toward research and
demonstration of the concept of hypolimnion aeration with commercial
oxygen. Laboratory and field experiments were conducted to gather data
with which to calibrate a gas transfer model which could predict gas
absorption characteristics within a bubble plume in an impoundment. Mass
balances were made of the gas in bubble plumes after various rise heights,
both in laboratory columns and in a stratified impoundment. One of the
major considerations was to develop an empirical relationship between the
gas transfer coefficient, K , and bubble diameter. After the gas transfer
model was calibrated with me experimental data, it was used to determine
the sensitivity of the bubble plume absorption characteristics to various
parameters, e.g. dissolved nitrogen in the water, water temperature etc.
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SECTION IV
OBJECTIVES OF INVESTIGATION
The principal objectives of this study were:
1. To investigate the effects of initial bubble size and injection depth
on the mass transfer of oxygen in the field using:
a, A diffuser capable of producing oxygen bubbles with diameters
between 0.2 mm and 0.5 mm.
b. A diffuser capable of producing oxygen bubbles with diameters
between 1.0 mm and 2 .0 mm.
2. To develop a relationship between liquid film coefficient and bubble
diameter based on the data collected in field studies.
3. To develop a methodology for the design of a diffuser system of in-
place hypolimnion aeration.
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SECTION V
THEORY OF GAS ABSORPTION
Gas Mass-Transfer
The absorption rate of a gas into a liquid is basically governed by Pick's
law of diffusion,
dm/dt = DA (dc/dx)
(1)
where:
dm/dt = time rate of mass transfer
D = diffusivity of the gas
A = cross-sectional area across which diffusion
occurs
dc/dx = the concentration gradient
This equation is not directly applicable to an aeration system because of
the turbulent conditions present. As an oxygen bubble rises in water, the
water mass surrounding the bubble is constantly being replaced; hence,
the concentration gradient, dc/dx, will not be allowed to develop due to
insufficient time. The dominant resistance to gas transfer is believed to
occur at the interface between the gas and the liquid. The two film theory
as proposed by Lewis and Whitman (2) in 1924, takes this resistance into
account.
The two film theory assumes that at the interface a film of gas and a film
of liquid is developed. As the gas is transferred, it passes through these
two films by molecular diffusion (Figure 1) . The time rate of mass-transfer
of gas through the gas film must equal the rate through the liquid film and
in turn must equal the rate of diffusion into the liquid. Assuming a steady-
state condition:
where:
dm/dt
D
- D A(dc/dx) = - n A(dc/dx)
9 1
(2)
D
D
1
molecular diffusivity of the gas through the gas film
molecular diffusivity of the gas through the liquid film
eddy or turbulent diffusivity of the gas in the main
body of the liquid.
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GAS
GAS
FILM
MONOLA/ER
RESISTANCE TO
TRANSFER
LIQUID
FILM
LIQUID
Fig . 1 RELATIVE RESISTANCE TO GAS TRANSFER
OF THE GAS AND LIQUID FILMS
10
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Treybal (3) showed that the gas film offers little resistance to mass-
transfer compared to the liquid. Once the gas passes through the two
films it is distributed by eddy or turbulent diffusion in the main body of
liquid. The eddy or turbulent diffusivity, D, is much greater than the
molecular diffusivity of gas through the two films.
Hence, the rate of mass-transfer is controlled by the limiting condition
and
dt L dx
The concentration gradient, dc/dx, is related to the deficiency between
the saturation concentration of the gas in the liquid, C_/ and the concen-
tration of the gas in the liquid, C, .
J-i
T- = CC;-CT <4)
dx S L
Solving this equation with respect to a liquid film thickness, L,
dm -DA(C -CJ (.
jn. = L b L (b)
dt :
Letting L = K , the liquid film coefficient.
L
= KA(C_ -C_) (6)
_ _
dt L o L
From equation 6 it is obvious that the rate of mass-transfer is proportional
to the deficit in concentration of gas in the liquid and the liquid film coef-
ficient.
Higbie (4) argued that the two-film theory was inadequate because of the
assumption of complete saturation of the liquid film and hence a steady-
state process. Higbie states that the liquid film is constantly being replaced,
therefore, the concentration of dissolved gas in the liquid film is equal to
the concentration of dissolved gas in the liquid mass, C , at the time of
replacement. Further, the residence time of the liquid fum at the time of
replacement is insufficient to allow complete saturation of the liquid film.
11
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To account for this unsteady state condition, Higbie (4) proposed the
penetration theory. He defined the liquid film coefficient by the equation,
(7)
where: r = 1/t = rate of renewal of the liquid film.
Equation 7 gives an average value for K based on the assumption that the
liquid mass is quiescent for the time period, t, and then is wholly mixed and
then the process is again repeated.
Dankwertz (5) modified the penetration theory by redefining r as the average
frequency of renewal. The equation for the liquid film coefficient then
becomes:
(8)
Dobbins (6) further modified the liquid film coefficient relation. He main-
tained that the liquid film is continuously being replaced. Dobbins com-
bined the boundary conditions of a liquid film with thickness L and the
Dankwertz K function:
L V Lf C° Vr / L
Dobbins' experiments verified this relationship. However, for an aeration
system above a certain turbulence regime such as injection of gas bubbles
into a liquid, cothJrI//D approaches unity and the value of K approaches
— IHMHMW
r. Dankwertz's modification of the penetration theory is a special case
of the more general function, equation 9.
Bubble Aeration
Eckenfelder (7) stated that oxygen transfer occurs during three phases of
bubble life. At formation the liquid film is continuously being replaced and
results in a higher absorption rate than in the second phase where the bub-
ble is rising. During rise, the rate of mass-transfer is not only a func-
tion of the liquid film coefficient but also the terminal velocity which is a
function primarily of the bubble size. Barnhart (8) has shown how the values
12
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of the liquid film coefficient, K , vary with the bubble diameter (Figure 2) .
The terminal velocity of the bubbles as a function of the bubble diameter
has been reported by the David Taylor Modelling Basin Study (9) (Figure 3) .
The third phase in bubble life occurs when the bubble reaches the surface
and bursts. The generalized equation for these three ph*scT is:
dt ~ LF F LR R LS SS T.'
where: the subscripts F, R, and S denote formation, rising
and surface, respectively.
Subsequently, Calderbank (10) has found that the absorption rate at forma-
tion is less than that in the rising phase. Due to the fact that the time for
mass-transfer at formation is of such short duration together with the lower
absorption rate, the mass-transfer in the formation phase can be considered
negligible .
Liquid Film Coefficient for Nitrogen
It has been found experimentally (11) that the liquid film coefficient for
nitrogen is as follows:
KT(N J - (0.89) K (O ) (ID
LJ Z LJ Z
Temperature Effects on K
The effect of temperature on K has been reported by Eckenfelder (7) .
l_i
K (T) - K (20) 1.028 (T"20) (12)
Mathematical Model to Predict Mass-Transfer
Speece (1) developed a mathematical model to predict gas mass-transfer
from an oxygen bubble injected at various depths into an impoundment. It
13
-------
.04
O
w
.03
o
I— I
{X,
(JH
w
O
u
.02
0
Temp. = 10 C
456
DIAMETER (MM)
10
Fig, 2 k - LIQUID FILM COEFFICIENT VS DIAMETER
Li
-------
Q
2
O
U
w
OS
W
Ou
w
H
50
I I I I I I
en
W
O
>H
H
i— i
O
O
»-]
w
10
Di
U
H
1 I
11 mi
_LL
i i
0.05 O.I
EQUIVALENT RADIUS,
0.5 1.0
CENTIMETERS
4.0
Fig, 3 TERMINAL VELOCITY OF BUBBLES
AS A FUNCTION OF BUBBLE RADIUS
-------
is based on the gas transfer equation:
Equation 13 was incorporated into the model in the form:
AM = KTA (C0 - C_) At
LJ o L,
AM = mass of gas transferred, mg
K = 0.396 mm/sec for bubbles with diam < 1 .2 mm
LJ
K = 0.396 (DIAM/1.2) ' mm/sec for bubbles with diam <
1 .2 mm
2
A = interface area , (mm)
CQ = saturation concentration of the gas in the liquid,
mg/(mm)3
3
CT = actual concentration of the gas in the liquid, mg/(mm)
J_i
t = time interval, seconds.
The model calculated oxygen transfer in the following manner. Initially,
the concentrations of dissolved oxygen and dissolved nitrogen, the tempera-
ture of the water, the initial bubble diameter, and injection depth are set.
The program calculates the mass of oxygen in the bubble, bubble surface
area and the hydrostatic pressure. Next, the dissolved oxygen and dissolved
nitrogen deficits are determined for the respective partial pressures inside
the bubble. The weight of oxygen transferred and the weight of nitrogen
transferred are then calculated. The new gas composition of the bubble was
then determined. The distance the bubble traveled was calculated being a
function of the velocity of rise and time increment, At. The new bubble dia-
meter was determined and the procedure was repeated until the bubble reached
the surface or was 95% absorbed. The model can predict oxygen and nitro-
gen transfer for air bubbles injected into the reservoir as well as for oxygen.
16
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FLOW CHART
'Start
Input:
T, D, Y, O,
N, C, FO, FN
K = Y/2
FC = 1.0 - FN - FO
Tl = 273/273 + T
TO - T(0.0161(T) - 1.61) 10
TN = T(0.0119(T) - 0.87) 10
-6
TC = T(1.204(T) - 106.23) 10
A = 1.0 tY/10.36
V=7T(D)V6 3
MO = (V)(A)(FO)(T1)(1.43)10 ,
MN = (V)(A)(FN)(T1)(1.25)10_3
MC = (V)(A)(FC)(T1)(1.96)10
MO1 = MO
VO = V(FO)
VN = V(FN)
VC = V(FC)
-6
ARE = 7TD
E = 0.125(D - 0.25)
A = Exp(Alog(3V/4-n/r.O-E2)/3)
ARE = (-7>-A2)(2.0 + (1-E2) ( Alog((l+E)/(l-E))/E)
Fig.
17
-------
\
\
X = X + 1
OL = MO/MO1
4
Input: /
Yl = Y /
Df =D /
OL? = OL /
FO1X = FO /
M,
i KT = 1
VEL = 0.244(D)
VEL = (0.176 + (D - 0.72) 10 )/(30 + 156(D - 0.72))
I
DX = 0.006/VEL
DPT = (VEL)(DX)
FO = VO/V
FN = VN/V
FC = VC/V
SO = (A)(FO)(TO)
SN = (A)(FN)(TN)
j SC = (A)(FC)(TC)
(Call KLOZ(D))
K = KLOZ
DM0 = K(ARE)(SO-0)(DX)
MO = MO - DMO
KN = (0.89)(K)
KG =K
DMN = (KN)(ARE)(SN-N)(DX)
DMC = (KC)(ARE)(SC-C)(DX)
Fig.
(continued)
18
-------
MN = MN - DMN
MC = MC - DMC
Y = Y - DPT
/ \
A = 1.0 + Y/10.36
VO = MO/(A) (Tl) (1.43) 10
VN = MN/(A)(T1)(1.25) 10
VC = MC/(A)(T1)(1.96) 10
V = VO + VN + VC
-3 i
-3 1
-3 !
1 D = Exp((Alog(6)(V//r))/3)
ARE = D
E = 0.125(D - 0.25)
A = Exp(Alog(3V/4 1.0-E2)/3)
ARE = ( A)(2.0
Fig. 4 (continued)
19
-------
Output:
Plot Dl vs Yl
Plot DL1 vs Yl
Plot FO1 vs Yl
Subroutine, KLOZ(D):
tartv
KLOZ = 0.555{T2)
KLOZ= (0.213 + 0.156(0)) (T2)
KLOZ= (-0.416 + 0.68(0)) (T2)l-
KLOZ = (-0.024 + 0.120(D)) CT2)
KLOZ = 0.035 (D) (T2)
Return
Fig, 4 (continued)
20
-------
NOTATION FOR FIGURE 4
T = Temperature of the water, °C
D = Initial bubble diameter, mm
Y ~ Injection Depth, m
g
O = Concentration of dissolved oxygen, mg/(mm)
N = Concentration of dissolved nitrogen, mg/(mm)3
C = Concentration of dissolved carbon dioxide, mg/(mm)^
FO = Fraclion of oxygen in the gas bubble
FN - Fraction of nitrogen in the gas bubble
FC = Fraction of carbon dioxide in the gas bubble
A = Pressure, atmospheres
V = Volume of bubble, (mm)^
MO = O2 in bubble, mg
MN = NT2 in bubble, mg
MC = CO2 in bubble, mg
VO = Volume of O2 in bubble, (mm)'-'
VN = Volume of N2 in bubble, (mm)^
VC = Volume of CO2 in bubble, (mm)3
o
SO - Saturation concentration of dissolved oxygen, mg/(mm)
SN = Saturation concentration of dissolved nitrogen, mg/(mm)^
o
SC = Saturation concentration of dissolved carbon dioxide, mg/(mm)
TO = Density of oxygen gas at one atmosphere, mg/(mrn)3
TN = Density of nitrogen gas at one atmosphere,
ARE = Area of bubble, (mm)2
21
-------
OL = Oxygen remaining in bubble, mg
VML ~ Terminal veloeity of bubble, m/si-r
DX = Step interval per iteration, m
DPT = Rise height per step interval, m
DMO = O2 transferred per step interval, mg
DMN = N£ transferred per step interval, mg
DMC = CC>2 transferred per step interval, mg
K = Liquid film coefficient for oxygen, mm/sec
KN = Liquid film coefficient for nitrogen, mm/sec
KL = Liquid film coefficient for carbon dioxide, mm /sec
Ylx = Plotted values of depth, m
Dlx - Plotted values of bubble diameter, mm
OL1X = Plotted values of fraction of initial oxygen remaining in bubble
FO1V = Plotted values of fraction of bubble gas which is oxygen
22
-------
SECTION VI
APPARATUS AND PROCEDURES
Reservoir Bubble Aeration System
The bubble aeration system used in the investigation at the reservoir site
consisted of a polyvinyl chloride diffuser (capable of producing 1.0 -2.0
mm bubbles) , a commercial oxygen cylinder, a pressure regulator, a flow
meter, sheet metal gas collection hood, a sampling gear pump, a wet
test meter, and an Orsat type gas analyzer (Figure 5).
Procedure for Reservoir Study
1. The dissolved oxygen and temperature profile for the injection depth
and each ten foot increment above the injection depth was determined.
A water sample was pumped up from each depth and the dissolved oxygen
was measured by the azide modification of the Winkler method (12).
The temperature was measured by a probe located at the water sample
intake port.
2. The desired oxygen flow rate was established.
3. The off-gas system pump was started.
4. After an equilibrium condition was apparent (steady off-gas flow) the
volume of off-gas was measured over a measured time period.
5. Three gas samples were taken for each test and the percent oxygen pre-
sent was determined on the Orsat gas analyzer.
Lab Bubble Aeration System
The bubble aeration system used in the laboratory portion of the investigation
consisted of essentially the same components as used in the reservoir study
except a ceramic diffuser capable of producing smaller bubbles (between 0.2
mm and 0.50 mm) was used in place of the PVC diffuser.
23
-------
COMPRESSED
OXYGEN
OFF-GAS
GAS COLLECTION
HOOD
DIFFUSER
AERATION AND OFF-GAS COLLECTION
SYSTEM
1
WET
TEST
METER
SAMPLING PORT
WATER TRAP
OFF-GAS MEASURING AND SAMPLING
SYSTEM
Fig. 5 EXPERIMENTAL SYSTEM
24
-------
Procedure for Lab Study
1. Before each run the contents of the lab column were circulated through
the flumes for twenty minutes to allow the water to become saturated
with dissolved oxygen and dissolved nitrogen with respect to air.
2, The dissolved oxygen sample was taken from a depth of 5,0 meters and
measured. The temperature was determined.
3. The rest of the procedure was the same as employed in the reservoir
study.
Pressure Tank Laboratory Studies
One aspect of this project involved construction of a pressure tank four-
teen feet high and thirty inches in diameter. This tank could be pressurized
to a hydrostatic head of 200 feet. Thus, the absorption characteristics of
bubbles injected as deep as 200 feet could be simulated for as much as
fourteen feet of rise.
The column would be pressurized to the desired head and a given mass of
oxygen would be injected. At a given height above the injection point,
the bubbles would be harvested and the composition and mass determined.
The change in mass of oxygen in the off-gas was then correlated with the
increase in dissolved oxygen concentration of the water column.
Absorption characteristics in the laboratory pressure column were correlated
with the field results. Test conditions were more easily controlled in the
laboratory pressure column and test runs could be made more rapidly. In
addition, field studies in Lake Travis were limited to ninety feet depth,
while it was possible to simulate up to 200 feet in the lab.
The laboratory pressure column absorption results were used along with
the field absorption studies to calibrate the oxygen absorption model.
25
-------
SECTION VII
RESULTS AND DISCUSSION
The laboratory and field studies determined the dynamics of bubble mass
and composition with rise height. In this section, the gas transfer pre-
diction model is calibrated by the experimental results. The agreement
between predictions of the calibrated model and actual results is shown.
Then sensitivity of the model to various parameters is illustrated. The
experimental results are summarized in Table 1.
The gas mass-transfer model
The liquid film coefficient, K , has been shown to vary with the bubble
diameter and temperature. Hence, knowing these two values, as well as
the injection depth and depth of gas collection, the results obtained for
the fraction of original oxygen in the off-gas and oxygen composition of
the off-gas were compared to the predicted results. It was found that the
predicted efficiencies of oxygen absorption do not agree with the experi-
mental measurements. Therefore, it was necessary to modify the mathe-
matical function for determining K for bubble diameters less than 2 .2 mm.
Several curves were substituted in the model on a trial and error basis.
Speece's relationship for determining K covering the range of bubble dia-
meters up to 2.2 mm is described as follows:
KL - [(0.041) (D) +(0.096) (D)2] T (14)
where: K = liquid film coefficient, mm/sec
D = diameter, mm
Figure 6 is a graphical representation of this curve up to a 2 .0 mm bubble
diameter. This curve represents an extension of Barnharts curve to the
origin. The diameter, D, is plotted on the abscissa and the liquid film
coefficient, K , is plotted on the ordinate.
i-i
27
-------
to
oo
TABLE 1
Summary of Data
Range of
Bubble Diam .
mm
1.0
1.0
1.0
0.2
0.2
0.2
-2.0
- 2.0
- 2.0
- 0.5
- 0.5
- 0.5
InJ.
12
21
27
8
7
5
Depth,
m.
.1
.2
.3
.5
.7
.0
Collection
Depth, m
3
3
3
0
3
1
.05
.05
.05
.5
.7
.0
0
0
0
0
0
0
Oxygen
Composition
of Off -gas
.63 -
.34 -
.22(3)
.64 -
.70 -
. 68 ~
0.
0.
0.
0.
0.
70(9)*
46(4)
73(9)
77(18)
76(9)
Fraction of
Orig. O Mass
in Off -gas
0.15
0.07
0.55
0.62
0.63
- 0.20(3)
- 0.09(2)
- 0.56(3)
- 0.69(6)
- 0.69(3)
*The numbers in parenthesis following the results denote the number of observations included in the
range of the results.
-------
DO
ID
U
H
£
w
»— i
U
I— I
PL,
PM
W
O
O
.035
.030
.025
.020
.015
Q
I—c
§• .010
i
^
x
.005
0
I I I I I
Temp. = 10 C
I I
.4
.8 1.0 1.2
DIAMETER (MM)
1.4 1.6 1.8 2.0
Fig. 6 k - LIQUID FILM COEFFICIENT VS DIAMETER
Li
-------
A note is necessary on the following graphs in which various parameters
are plotted against the depth. The oxygen is injected at the depth indicated
on the extreme right of the abscissa and rises, to the surface which is indicated
by the extreme left of the abscissa. To trace the changes undergone as the
bubbles rise, the figure should be read from right to left. The lines of the
figure are labeled so as to indicate the initial bubble diameter. It was as-
sumed that the model would be sufficiently verified when the observed re-
sults were within the ranges depicted in each graph.
Figure 7 shows the reduction in the original amount of oxygen as the bubble
rises for the case where the injection depth was 21.2 m. Figure 8 represents
the oxygen composition in the bubble as the bubble rises for the same injec-
tion depth. The initial bubble diameter was believed to be between 1.0 mm
and 2 .0 mm; hence, two lines appear on each graph denoting these two bub-
ble sizes. The values for the fraction of original oxygen in the bubble and
the oxygen composition in the bubble as determined in the field study are
included on the graphs. The data is represented by longitudinal blocks on
each graph at the depth at which the samples were collected. The off-gas
for this injection depth was collected at a depth of 3.05 m. Referring to
Figure 1, the range of observed results for the fraction of original oxygen in
the off-gas was 0.07 - 0.09. These values are plotted on the vertical line
at the 3.05 m depth. For this case Speece's relationship between K and
bubble diameter predicted results comparable to the observed results.
Referring to Figure 8, the experimental values for the oxygen composition of
the off-gas, 34% to 40%, were plotted. As can be seen, in this case, the
model predicted a range of results approximately 15% higher than the range
measured. Based on these two comparisons, it was determined that the K
values were too low to accurately predict the oxygen mass-transfer for
bubbles with diameters in the 1.0 - 2.0 mm range.
Figures 9 and 10 show the reduction in the original amount of oxygen and
oxygen composition in the bubbles for the 8.5m injection depth. The initial
bubble diameter for this run was between 0.2 mm and 0.5 mm. The depth at
which the off-gas was collected was 0.5m. Figure 9 shows the reduction
in the fraction of the original amount of oxygen as the bubble rises. The
range of the experimental values is plotted at the 0.5m depth. Figure 10
shows the oxygen composition versus depth with the experimental observa-
tions plotted on the graph. As can be seen in Figures 9 and 10, Speece's
model predicts better results for oxygen absorption than were measured.
Hence, the K values for the range of bubble diameters between 0.2 mm and
0.5 mm are higher than can be justified by the field studies.
Knowing that Speece's original function for the liquid film coefficient pro-
duces too liberal predictions in the model, a group of straight line approxi-
30
-------
u>
c.c
DO = 9.2 MG/L
TE MP = 12 . 0 C
1, DIAM = 1.0 MM
INJECTION DEPTH
2 , DIAM = 2.0 MM
P-,
8 10 12
DEPTH (M)
Fig. 7 FRACTION OF ORIGINAL AMOUM" OF O IN OFF-GAd VS DEPTH
(USING SPEECEV- k FUNCTION)
LJ
-------
1.00
GO
1X3
DO = 9.2 MG/L
TEMP = 12.0 C
I, DIAM = 1.0 MM
INJECTION DEPTH
2, DIAM = 2.0 MM
14 16 18
8 10 12
DEPTH (M)
Fig. 8 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH (USING SPEECE'S
k FUNCTION)
-------
GO
GO
co 1.0
<
o
P-.
tl-,
O
- .8 —
(M
o
P-.
o
H
1
o
a:
O
PM
O
S
O
I—I
H
u
,4 _
,2 —
DO = 7.9 MG/L
TEMP = 29.0 C
. DIAM = 0.2 MM
INJECTION DEPTH
2, DIAM = 0.5 MM
4 5
DEPTH (M)
Fig, 9 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH
(USING SPEECE'S k FUNCTION)
-------
1.0
co
w
S °-8
1
PL,
0.6
O
P-.
O
CO
O
OH
S
O
u
E
w
O 0.2
0.4
DO = 7.9 UG/L
TEMP = 29.0 C
1, DIAM = 0.2 MM
INJECTION DEPTH
2, DIAM = 0.5 MM
= 8.5 M
4 5
DEPTH (M)
8
Fig. 10 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH (JSING SPEECE'S
k FUNCTION)
LJ
-------
mations were substituted for the K function for bubbles with diameters
less than 2 .2 mm. The K relationship for diameters less than 2 .2 mm
was divided into four sections:
for 0 .0 mm to 0 .3 mm ,
KL = (0.035) (D) (T) (15)
for 0 . 3 mm to 0 . 7 mm ,
K = [(-0.044) +(0.175) (D)] (T) (16)
J_t
for 0. 7 mm to 1.2 mm ,
KL = [(-0.486) + (0.78) (D)] (T) (17)
for 1.2 mm to 2 .2 mm,
K - [(0.323) + (0.105) (D)] (T) (18)
J_i
Figure 11 presents these functions graphically.
Figures 12 through 22 are the graphs for each set of data collected in the
study. The range of observed values are plotted on each graph at the depth
of gas collection. The model with the new K function has been verified by
the field studies. The data in each case falls within an acceptable range as
predicted by the model.
The model has other capabilities that are of interest. The reduction in bub-
ble diameter as the bubble rises can be followed. Figure 23 traces the size
reduction for the 1.0 mm and 2.0 mm bubble injected at 2 1.2 m. Two
processes are responsible for the changes in bubble volume. Cne, the
hydrostatic pressure is being reduced linearly as the bubble rises; hence,
the bubble volume will expand. Two, the processes of gas mass-transfer
are allowing oxygen and nitrogen to be transferred out of or into the bubble.
Figure 24 shows the behavior of the bubble diameter with rise for the 0.2 mm
and 0.5 mm. Notice the diameter remains approximately the same with depth
for bubbles in this range.
35
-------
GJ
CT)
0.4 _
U
w
u
H
S
w
t—t
U
W
O
o
Q
O
0.3
0.2 —
0.1 —
0.2 0.4 0.6
0.8 1.0 1.2 1.4
DIAMETER , D (MM)
1.6 1.8
Fig. 11 LIQUID FILM COEFFICIENT VS DIAMETER
-------
CO
CO
<
O
PH
PH
O
o
PL,
O
O
S
pi
o
P..
o
s
o
1—I
H
o
P-,
1.0
0.8
0.6
0.4
0.2
0
DO = 6.0 MG/L
DN = 15.0 MG/L
1, DIAM = 0.2 MM
DCO2 =25.0 MG/L
2, DIAM = 0.5 MM
1
1.0 1.5 2.0 2.5
DEPTH (M)
3.0
3.5
4.0
4.5
ig. 12 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH
PURE OXYGEN
-------
1.0
oo
00
0.8
0.6
CO
-------
1.0
CO
o
I
PH
O
2
I—I
-------
1.0
0.8
t/5
0.6
O
P-,
o
o
en
O
a.
S
O 0.2
O
^
w
O
DO = 0.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3 4
DEPTH (M)
Fig. 15 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH
-------
1.0
en
<£
o
I
PH
PH
O
O
0.8
o
^ 0.6
C
H
0.4
O
I—f
O 0.2
O
o
I—I
H
0 n
DO = 7.9 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DIAM = 1.0 MM
2, DIAM = 2.0 MM
Fig. 16
12345
DEPTH (M)
FRACTION OF ORIGINAL AMOUNT OF
PURE OXYGEN
IN OFF-GAS VS DEPTH
-------
1.0
0.8
CO
<:
O
O
s
CO
g 0-4
S
O
u
w
0.2
g
0
CL
1,
DO = 7.9 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/L
DIAM = 0.2 MM
2, DIAM = 0.5 MM
345
DEPTH (M)
Fig- 17 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH
-------
1.0
co
<:
o
PH
EM
o
O
0.8
0.6
0.4
DO = 9.6 MG/L
1, DIAM = 1.0 MM
2, DIAM = 2.0 MM
DN = 15.0 MG/L
DCO =25.0 MG/L
u
DEPTH (M)
Pig. 18 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS V3 DEPTH - PURE OXYGEN
£4
-------
CO
<
a
Cu
IX,
O
u.
O
a
o
1.0
0.8
0.6
CO
9 0.4
O
O
w
P 0.2
0
DO = 9.6 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/L
I, DIAM = 0.2 MM
2, DIAM = 0.5 MM
10
DEPTH (M)
Fig. 19 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH
-------
DO = 9.2 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DIAM = 1.0 MM
2 . DIAM = 2.0 MM
8 10 12 14 16 18
DEPTH (M)
Fig. 20 FRACTION OF ORIGINAL AMOUNT OF O£ IN OFF-GAS VS DEPTH - PURE OXYGEN
-------
CT)
CO
I
PJ-.
O
O
fe
O
co
O
a.
O
O
g
1.0
0.9 _
0.8
0.7
0.6
0.4 __
0.2
O 0.1 —
DO = 9.2 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
DIAM = 0.2 MM
2, DIAM = 0.5 MM
8 10 12
DEPTH (M)
Fig. 21 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH
-------
1.0
w
X
o
0.8
CO
<
O
O 0.6 _
IX.
o
O
i—i
w 0-4
O
-------
00
2.0
1.8
1.6
w
m 1.2
CO
w 0.8
H
W
s
<$ 0.6
Q
0.4
0.2
0
1, INITIAL DIAM
2, INITIAL DIAM.
= 1.0 MM
= 2.0 MM
8 10 12
DEPTH (M)
14
16
18
20
Fig. 23 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH
-------
to
0.5 —
0.4
0.3
CQ
03
P
CQ
O 0.2
ctf
w
H
M
IS
Q 0.1
1, INITIAL DIAM = 0.2 MM
2, INITIAL DIAM = 0.5 MM
4 5
DEPTH (M)
Tig. 24 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH
-------
The change in the relative volume of gas at any depth with respect to the
volume injected can also be traced with rise. This can be of interest to
determine the volume of gas which is not absorbed within the hypolimnion
and hence will be responsible for the degree of mixing which will occur
between the hypolimnion and metalimnion. Figures 25 and 26 show the
changes in relative volume for the 21.2 m and 8.5m injection depths,
respectively.
The newly developed K function is compared to Barnhart's function in
Figure 27.
Sensitivity of Model
The sensitivity of the model to the various parameters can be demonstrated.
The variables which are used in the model are the initial bubble diameter,
injection depth, temperature, dissolved oxygen concentration, dissolved
nitrogen concentration, dissolved carbon dioxide concentration, and the
relative slip velocity between the rising bubble and the water mass. For this
example, certain conditions were held in common while each parameter
was investigated separately to show its effect on the model. The common
conditions are as follows:
Initial Bubble Diameter = 0.20 mm
Injection Depth = 40 m
Temperature = 10°C
Dissolved Oxygen = 0 mg/1
Dissolved Nitrogen = 15 mg/1
Dissolved Carbon Dioxide =25 mg/1
Slip Velocity = 0
Initial Bubble Diameter
The sensitivity of the model to the initial bubble diameter is first demon-
strated. The initial bubble diameters which are compared are 0.2, 0.5, 1.0
and 2 .0 mm. Figures 28 and 29 show the reduction in the fraction of the
original amount of oxygen and the oxygen composition of the off-gas for
each bubble diameter. An initial bubble diameter of 2.0 mm results in the
best absorption performance. However, the absorption capabilities of the
other three diameters are not appreciably different from the 2 .0 mm case as
can be seen in Figure 28. Figure 29 shows the reduction in oxygen compo-
sition with rise. More information concerning the absorption efficiency of
different initial bubble diameters is included in the section which follows on
design applications.
50
-------
1.0
en
0.8
O
O 0.6
w
C
£
h—I
H
W
0.4
0.2
1 f
1, DIAM
2 , DIA M
I I
1.0 MM
2.0 MM
I L
0.1 0.2 0.3
0.4 0.5 0.6 0.7 0.8 0.9
DEPTH (FRACTION)
1.0
Fig. 25 RELATIVE VOLUME OF GAS VS DEPTH
-------
en
to
..o IT
0.8
in
S 0.6
fj-c
C
0.4
O
0.2
w
oi
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
DEPTH (FRACTION)
Fig. 26 RELATIVE VOLUME OF GAS VS DEPTH
-------
CJ
0.4
U
W
£> 0.3
E-i
W
i—i
O
t—I
IX,
O 0.2
O
Q
O
0.1
DO
TEMP - 10.0 C
1, = Murfee's Function
2, - Barnhart's Function
I
I
I
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
DIAMETER D (MM)
Fig. 27 LIQUID FILM COEFFICIENT VS DIAMETER, D
-------
1.0
Cn
CO
-------
1.0
Cn
cn
0.6
0.8
CO
-------
Injection Depth
Figures 30 and 31 illustrate the predicted reductions in original oxygen
and oxygen composition for injection depths of 20, 40, 60, and 80 m;
The predictions are plotted against the fraction of the original injection
depth. Notice, on Figure 30, the rise heights associated with any parti-
cular value for the fraction of original amount of oxygen are approximately
the same. For instance, for 30% of the original amount of oxygen the
fraction of the depth for 20, 40, 60, and 80 m is 0.60 , 0 . 80 , 0 . 87 , and
0.90, respectively. The rise height at which 30% of the original amount
is remaining is equal to the fraction of the depth at which 30% is remaining
substracted from 1.0 and multiplied times the injection depth. For example,
20 meters (1-0.6) =8 m; 40 meters (1-0.8) =8 meters etc. For each case
the rise height is approximately 8 m. Notice in Figure 31 that the oxygen
composition of the bubbles for all four injection depths is 88 - 92% of the
total volume at the time when 30% of the original oxygen mass is left.
Temperature
The temperature was set at 10, 20, and 30 C. Figures 32 and 33 show the
absorption of oxygen and the reduction of oxygen in the gas bubbles as a
function of depth. The higher the temperature the greater the absorption
efficiency. This is due to the fact that the liquid film coefficient increases
exponentially with the temperature; whereas, the DC deficit decreases
relatively little at higher temperatures.
Dissolved Oxygen
A dissolved oxygen concentration of 0 mg/1 was compared to one of 10
mg/1 (Figure 34) . The absorption efficiency is approximately the same;
mainly, because the dissolved oxygen saturation concentration, C , is con-
siderably higher than the range of values for dissolved oxygen concentra-
tion which are normally encountered in a body of water. Therefore, the dis-
solved oxygen deficit, C - C , is approximately the same for each case.
For example, at 40 meters theT>G deficit is equal to 373 mg/1 and 363 mg/1
for actual DO concentrations of 0 mg/1 and 10 mg/1, respectively.
Dissolved Nitrogen and Dissolved Carbon Dioxide
The transfer of oxygen from a bubble to a water mass is independent of the
concentrations of nitrogen and carbon dioxide in the water. The composi-
tion of the bubble gas, however, is altered because the nitrogen and/or
carbon dioxide which is stripped will influence the partial pressure of
56
-------
en
CM
o
o
E-i
o
2
<
O
IX,
O
O
>— i
H
O
s
TEMP = 10 C
DIAM = 0.2 MM
1, INJECTION DEPTH = 20 M
2 , INJECTION DEPTH = 40 M
3, INJECTION DEPTH = 60 M
4, INJECTION DEPTH = 80 M
DO = O MG/L
0.4 —
0.2 _
Fig. 30
O.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
DEPTH (FRACTION)
FRACTION OF ORIGINAL AMOUNT OF O2 VS FRACTION OF INITIAL
INJ ECTION DEPTH
-------
1.0
01
CO
CO
TEMP = 10 C
DO = O MG/L
DIAM = 0.2 MM
INJECTION DEPTH
INJECTION DEPTH
INJECTION DEPTH
20 M
40 M
60 M
80
4, INJECTION DEPTH
Fig. 31
0.4 0.5 0.6
DEPTH (FRACTION)
OXYGEN COMPOSITION OF OFF-GAS VS FRACTION OF INITIAL
INJECTION DEPTH
-------
Cn
to
1.0
CO
O
fc 0.8
O
O
O 0.6
O
s
<: 0.4
O
PH
O
s
o
I—I
E-H
u
0.2
T
I I I
DO = O MG/L
DN = 15 MG/L
DC O = 25 MG/L
INJECTION DEPTH = 40 M
DIAM = 0,2 MM
1, TEMP = 10 C
2, TEMP = 20 C
3 TEMP = 30 C
I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
DEPTH (FRACTION)
1.0
Fig. 32 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH (FRACTION)
-------
CD
O
CO
«a:
O
i
PL,
P-i
O
O
O
O
s
pa
S
1.0
0.8
0.6
0.4
0.2
I I I
DO = O MG/L
DN = 15 MG/L
DC O2 =25 MG/L
INJECTION DEPTH = 40 M
DIAM = 0.2 MM
I, TEMP = 10 C
2, TEMP = 20 C
3, TEMP = 30 C
10
15 20
DEPTH (M)
25
30
35
40
Fig. 33 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH
-------
CO
O
O
i—i
O
O
O
1.0
0.8
g 0.6
3 0.4
I—I
a:
O
P-,
O
^
° 0 2
i—i «j • £.
H
O
I, DO - O MG/L
2 , DO = 10 MG/L
10
15 20 25
DEPTH (M)
30
35
Fig. 34 FRACTION OF ORIGINAL AMOUNT OF QZ IN OFF-GAS VS DEPTH
-------
oxygen within the bubble. Figure 35 is a plot of how the fraction of the
original amount of oxygen changes with rise for two dissolved nitrogen
concentrations of 0 mg/1 and 15 mg/1. The reduction in oxygen is not
affected by the changes in dissolved nitrogen. Figure 36 shows the
changes in oxygen composition for the same two dissolved nitrogen con-
centrations. Notice with the dissolved nitrogen set at 0 mg/1 the bubble
is completely absorbed by the time it reaches a depth of 20 meters. The
bubble is not absorbed completely until it reaches a depth of 4 meters when
the concentration of dissolved nitrogen in the water mass is 15 mg/1.
This points up an advantage of using a hypolimnion aeration system. If
the rise of some gas bubbles from the hypolimnion through the metalimnion
can be tolerated, dissolved nitrogen can be stripped out of the hypolimnion
if need be.
Figures 37 and 38 show the behavior for changes in dissolved carbon
dioxide in the water. The saturation concentration for dissolved carbon
dioxide is very low hence, the transfer of carbon dioxide is of a negligible
magnitude. Therefore, the concentration of dissolved carbon dioxide need
not be considered in aeration problems.
Slip Velocity
The computer model assumes zero slip velocity. That is, the velocity with
which a bubble rises is due only to its buoyancy. For 100 per cent slip
velocity, the velocity is due to its buoyancy plus the velocity of the plume
generated by the bubbles. It has been shown by Rayyan (13) that relative
slip velocity is a function of the bubble diameter as well as the injection
rate. Figure 39 shows the predicted center line velocities of plumes generated
by a 2.0 mm bubble for the cases of zero and non-zero slip. Center line
velocity for zero slip is approximately double that for non-zero slip at a
height of 27 meters above the injection depth. Hence, a conservative ap-
proximation of 100 per cent slip would be to double the terminal velocity of
the bubble. Rayyan also showed that for bubbles less than 0.5 mm in
diameter there is no difference between zero and non-zero slip on the rate
of gas transfer. Figure 40 shows the effect of zero and 100 per cent slip
on the reduction in the original amount of oxygen for a 2 .0 mm bubble. As
can be seen, the absorption efficiency is reduced somewhat when 100 per
cent is used. However, the approximation for 100 per cent slip as used in
this calculation is quite crude and a more precise investigation into the
terminal velocity of bubbles in a plume is needed.
The possibility exists that in some cases it may be desirable to reduce
the plume velocity so as to insure that the rate of bubble rise is due to
62
-------
1.0
en
GO
0.8
O
i
O
V—I
O
O
O
g
O °'4
I—I
6
O
O 0.2
u
T
I
1, DN = 0 MG/L
2, DN = 15 MG/L
15 20
DEPTH (M)
25
30
35
Fig. 35 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAo V-l DEPTH
Cj
-------
1.0
0.8
5 0.6
i
o
CM
o
§ °-4
CO
O
PL,
O 0.2
u
2
W
S
I I
1, DN = 0 MG/L
2, DN = 15 MG/L
0.4 0.5 0.6 0.7
DEPTH (FRACTION)
Fig. 36 OXYGEN COMPOSITION OF OFF-GAS VS FRACTION OF DEPTH
-------
en
en
2, DC O = 25 MG/L
ij
15 20
DEPTH (M)
Fig. 37 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH
-------
1.0
en
en
O
8
p.,
o
5
o
CO
O
a.
2
o
u
w
B
8
0.8
0.4
0.2
C
10
1, DC O- = O MG/L
2, DC G = 25 MG/L
15 20
DEPTH (M)
25
30
35
Fig. 38 OXYGEN COMPOSITION OF OFF-GAS VS DEPTI^
-------
25
CT>
0
w
CO
,20
15
10
w
w
w
O .05
o
2.0 = bubble diameter
z = zero slip velocity
s = non zero slip velocity
10 15 20
HEIGHT ABOVE DIFFUSER (M)
25
30
Fig. 39 CENTER LINE VELICITY VS HEIGHT ABOVE DIFFUSER
-------
TO
1, SLIP = 0
2, SLIP = 1
15 20
DEPTH (M)
iq. 40
FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH
-------
buoyancy only. This can be accomplished by installing baffles at an
intermediate height above the diffuser.
Internal Pressure of Small Bubbles
In the calculation of the gas mass-transfer, the saturation concentration
of the gas in the liquid is of considerable importance. It is calculated
by the equation,
C = (A) (FO) (TO) (19)
s
where: A = Pressure in atmospheres
FO = Partial pressure of the gas in the bubble
TO = C of the gas per atmosphere of partial pressure,
sat
A, the pressure in atmospheres is calculated by the equation,
A = 1.0 + D/10.36 (20)
D = Depth in meters
It has been noted that the smaller the bubble, the greater the pressure
of the gas inside as compared to that outside. Therefore, theoretically
the pressure, A, is higher than calculated by equation 15. The pressure
difference for small bubbles, however, can be neglected when using this
model due to the relative magnitudes of pressure involved. For example,
additional increment of pressure is determined by the equation,
P = 4jT/d (21)
where: X = energy per unit area
d = bubble diameter, cm
for oxygen, 2T = 15 . 7 dynes/cm .
For a 0.1 mm bubble, the AP is calculated as follows:
-7
4(15.7 dynes/cm) 9.87 x 10 atm
0 ~ 0.01 cm dynes/cm2
AP = 0.0063 atm
69
-------
This AP is insignificant compared to the hydrostatic pressures of 1 - 4
atmosphere encountered in this study. Therefore, this increased pressure
due to small bubbles was neglected in this study.
Design Applications
A methodology for the design of an in-place hypolimnion diffuser aeration
system has been developed. It is based on the average rise height above
the point of injection to attain a desired per cent of absorption for bubbles
with initial diameters up to 2 .0 mm. The values for the average rise heights
were computed using Speece's mathematical model with a modified K func-
tion. Figure 41 represents a compilation of these values. The rise height
as presented is the average for injection depths of 20, 40, 60, 80 and 160 m.
Table 2 shows the rise height associated with each bubble diameter and
injection depth. The dissolved oxygen, nitrogen and carbon dioxide con-
centrations were 10, 15, and 25 mg./l, respectively. The temperature was
10°C.
The general design procedure for a hypolimnion aeration system is as
follows:
1. The allowable rise height is computed knowing the maximum injection
depth and the depth of the bottom of the metalimnion.
2 . Using Figure 41, the possible combinations of initial bubble diameter
and per cent of absorption can be determined. Notice that in most cases
this will give you two ranges of initial bubble diameter that will insure
a desirable absorption efficiency. Normally, these ranges of values
will be approximately bubble diameters less than 0.3 mm and between
1.0 and 2.0 mm. Generally, the larger initial bubble diameters will be
more economical because the price of diffusers in this range are approxi-
mately one half of those producing the much smaller bubbles. Also,
fewer problems with clogging of the diffusers will be encountered using
the larger bubble size. If, however, a critical situation exists where
mixing between the hypolimnion and metalimnion must be kept to a
minimum, then it may be more beneficial to use the smaller bubbles.
3. Cnce the bubble size has been selected, the injection flow rate, F,
will be a function of the type of diffuser selected. Bubble size pro-
duced by a diffuser is a function primarily of the orifice diameter and
the flow rate.
70
-------
H
ffi
O
I—)
w
K
w
40
30
20
2 10
0
0
1
0.5 1.0 1.5
BUBBLE DIAMETER (mm)
98%
2.0
Fig. 41 RISE HEIGHT REQUIRED TO ACHIEVE INDICATED ABSORPTION
EFFICIENCY VS BUBBLE DIAMETER
71
-------
TABLE 2
Rise Heights for Given % Absorption,
Injection Depth, and Initial Bubble Diameter
%Abs
Im. Depth,
rn
20
40
60
80
160
Av<>
1
20
40
60
80
60
Avg
1
20
40
60
80
60
Avg
i
20
4 0
60
80
60
Avg
1
20
40
(SO
80
60
80
11.
10.
0.
9.
9.
10.
13.
13.
13.
14.
34.
14.
9.
10.
10.
10.
10.
10.
8.
5.
5.
r>.
5.
5.
6.
6.
6.
6.
6.
4
3
9
7
4
1
9
/ 1
o
9
0
3
0
9
6
6
5
5
4
0
0
8
8
8
a
9
7
5
4
3
Rise Height
90 95
16.
13.
13.
12.
12.
13.
21.
22.
22.
21.
22.
16.
16.
16.
16.
15.
16.
a
o
9.
3.
10.
9.
1C.
Q
*-• •
8.
8.
8.
o
o
1
0
7
3
6
-
8
4
1
7
0
9
4
1
0
8
o
2
:•>
i
0
5
0
1
o
8
^7
16.
15.
15.
14.
15.
31.
29.
28.
27.
29.
22.
21.
21.
21.
21.
13.
14.
15.
15.
15.
14.
12.
11.
11.
12.
12.
98
In ilia]
Bubble
Diarn,
mm
7 20. 3
(
o
6
6
-
a
7
8
6
5
-
2
1 1
4
2
6
2
18.
1
1
i
-
-
:•,
3
•>
->
f
i ,
7 .
8.
__
8.
6.
3.
36.
-
v
j
-'
->
2
-
—
0.
0.
<•'.
9.
r'-
--
«)
o
0
5
-
-
-t
2
8
1
-
6
2
•>
9
7
-
0. 2
0. f>
1. 0
5 23.4
4
5
7
9
8
0
o
0
o
2
2
'•>
•.'
*/
- -» .
2.
23.
1
1
t
L
1
i
8.
n ^
8.
'-j.
!^.
o.
a
7
0
2
9
0
9
5
J. 5
2. 0
Avc
6.6
9. 1
12.2
72
-------
4. The amount of supplemental reaeration is determined knowing the volume
of water time period which is oxygen deficient and the extent of this
deficiency.
A = Q (c - C.) (10"6) (22)
eL 1
where: A = Supplemental aeration, Kg/day
0 = Volume of water aerated per day, L/day
C = Desired DC concentration, Mg/L
C = Actual DO concentration, Mg/L
5. Next, the daily requirement of injected oxygen is calculated as follows,
V = A (23)
(X) (p)
where: V = Daily volume of injected oxygen, L/day
A = Supplemental aeration required, Kg/day
X = Per cent absorption expressed as a fraction
p = The density of oxygen at the depth of injection, Kg/1
is calculated by the formula,
P = (1.0+ D ) Atm (Y) ( 273 ) (1 .43 x 1Q~3 Kq/l-atm) (24)
10.36 273 + T
where: D = Injection depth, m
Y = Fraction of O in injected gas
£4
T = Temperature, °C
6. The required area of diffusers is then computed.
N = _V _
F
2
where: N = Area of diffusers required, m
V = Daily volume of injected oxygen, L/day
F = Flow rate per surface area of diffuser, L/day
~1^
73
-------
7. The arrangement of the diffusers, of course, will be determined by
the type of diffuser used. As a general rule, the diffusers should be
separated by a minimum distance of 10 m to minimize interaction of
plumes. However, if the diffusers are arranged in lines, the minimum
distance can be neglected if the diffuser lines are separated by a mini-
mum of 20 meters. Generally speaking, the smaller the allowable rise
height and the more critical the effects of mixing between the hypolim-
nion and the metalimnion, the farther the distance should be separating
the diffuser. At present, there is very little information concerning
the interactive effects of bubble plumes in water. Therefore, a diffuser
system should be designed and built so as to allow for flexibility with
respect to the spacing of the diffusers.
To further clarify the previously outlined design procedure an example is
furnished.
Design Conditions:
3
Release flow = 240 m /sec
Release duration = 4 hours
Withdrawal depth = 20 m
Injection depth = 25 m
Depth of bottom of metalimnion = 10 m
Width of reservoir bottom = 800 m
o
Temp of Hypolimnion = 10 C
Dissolved oxygen = 2 mg/1
Dissolved nitrogen =15 mg/1
Dissolved carbon dioxide = 25 mg/1
Desired dissolved oxygen = 5 mg/1
Calculations:
1. Rise Height = Injection depth - Depth of'bottom of metalimnion
Rise Height = 25m-10m = 15m
2. Referring to Figure 41, with an allowable rise height of 15 m, bubbles
with initial diameter of 1.5 mm will be 95 percent absorbed before
reaching the metalimnion.
74
-------
3. Assume the characteristics of the diffuser are such as to allow the
flow rate per unit area to be 200 1/min-m2 .
F= 2.88 x 105 1/day-m2
4. Required supplemental aeration, A
A = Q(C9 - C ) (ID"6)
3 63
Q = 240 m /sec x 3600 sec/hr x 4 hrs/day = 3.5 x 10 m /uay
C = 5.0 mg/1
£>
C =2.0 mg/1
A = (3.5 x 106)m3day (103 1/m3) (5.0 - 2.0) mg/1 (10~6)
4
A = 1 .05 x 10 kg/day
4
Using a 4 hour period to reaerate this volume, A = 6.3 x 10 kg/day.
5. Required volume of injected gas per day, V, using pure oxygen.
V = A
(X) (o)
A - 6.3 x 10 Kg/day
X = 0.95
f
10.36 273+T
o = (1.0 + D )atm(Y) ( 273 ) (1.43 x 10 3Kg/l-atm)
p - (1.0 + 25 ) (1.0) ( 273 ) (1.43 x 10 3) Kg/1
10.36 273 + T
P = 4.7 x 10~3 Kg/I
V = 6.3 x 104 Kg/day = 1.41x10 I/day
(0.95) (4.7xlO-3 Kg/1)
6. Required diffuser area, N
N = V/F
1 x 107 1/d
2
V = 1.41x10 I/da y
F = 2 .88 I/day - m
7 2
N = 1.41 x 10 I/day = 49 m
2 .88 x 105 1/day-m^
75
-------
A set of reference figures are included in the following section if more
specific information is needed concerning the absorption of oxygen.
Stripping of nitrogen from the hypolimnetic waters may be of importance in
some cases. Figures 42 - 45 show the transfer of nitrogen into and out of
the bubble again for an injection depth of 30 m and using pure oxygen as the
injected gas. The dissolved nitrogen concentration is 15 mg/1. The 2.0
mm bubble is the best example. The mass of nitrogen in the bubble increases
from zero to a maximum of 0.103 mg at a depth of 20 m. This represents
the nitrogen which is stripped out of the hypolimnetic water for a 10 m rise.
As the bubble continues to rise the nitrogen is transferred back into the
water and the mass of nitrogen in the bubble is reduced to .08 mg at the
surface. Figures 46 - 49 show the transfer of nitrogen when air is injected.
As can be seen, air will transfer nitrogen into the water at all depths for
the bubble sizes used.
76
-------
.0001
.0008
.0006 —
w
8
Di
H
h-H
•x-
.0004
.0002
DO - 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
INJECTION DEPTH =30.0 M
TEMP = 15 C
DIAM = 0.2 MM
10 15
DEPTH (M)
25
Fig. 42 NITROGEN IN OFF-GAS VS DEPTH - PURE OXYGEN
-------
.002.S
CO
^
W
s
IX
.0020 _
.0015 __
.0010
.0005 _
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
INJECTION DEPTH =30.0 M
TEMP = 15 C
DIAM = 0.5 MM
10 15
DEPTH (M)
Fig. 43 NITROGEN IN OFF-GAS VS DEPTH - PURE OXYGEN
-------
ID
o
w
8
.016
DO - 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
INJECTION DEPTH = 30.0 M
TEMP = 15 C
DIAM = 1.0 MM
15
DEPTH (M)
Fig. 44 NITROGEN IN OFF-GAS VS DEPTH - PURE OXYGEN
-------
oo
o
w
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/L
INJECTION DEPTH =30.0 M
TEMP = 15 C
DIAM = 2.0 MM
8 -a*-
10 15
DEPTH (M)
25
Tig.
NITROGEN IN OFF-GAS VS DEPTH - PURE OXYGEN
-------
oo
W
8
.0014
.0012
.0010
.0008
.0006
0004
0002
DO :" 10.0 M( ,;/L
DN - 15.0 MG/L •
DC O =25.0 MG/L
INJECTION DEPTH =30.0 M
TEMP ^ 15 C
DIAM = 0.2 MM
I
10 15
DEPTH (M)
25
Fig. 46 NITROGEN IN OFF-GAS VS DEPTH - AIR
-------
.020
.015
M
.010
oo
ro
.005
I
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
INJECTION DEPTH =30.0 M
TEMP = 15 C
DIAM = 0.5 MM
I
10 15
DEPTH (M)
20
25
Fig. 47 NITROGEN IN OFF-GAS VS DEPTH - AIR
-------
.16
.12
CO
CO
g .08
oi
H
I—I
2
.04
DO - 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
INJECTION DEPTH =30.0 M
TEMP = 15 C
DIAM = 1.0 MM
10 15
DEPTH (M)
20
25
Pig. 48 NITROGEN IN OFF-GAS VS DEPTH - AIR
-------
00
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/L
INJECTION DEPTH - 30.0 M
TEMP = 15 C
DIAM = 2.0 MM
15
DEPTH (M)
25
Fig. ^9 NITROGEN IN OFF-GAS VS DEPTH - AIR
-------
SECTION VIII
ACKNOWLEDGMENTS
This study was sponsored by the Office of Research and Monitoring,
Environmental Protection Agency. Grateful appreciation is extended
to Richard Hiller, who was the initial Project Officer and Lowell
Leach, who subsequently served as project officer for the major portion
of the grant. These men took a genuine interest in the project and
whole heartedly supported it. Appreciation is also extended to Dr.
Curtis C. Harlin, Jr. for his support of this project as well as the
general area of river and impoundment aeration.
The University of Texas at Austin staff of Environmental Health Engineering
and Dr. Gus Fruh in particular are gratefully acknowledged for their
consultation and encouragement. The staff and facilities of the Center
for Research in Water Resources are much appreciated.
85
-------
SECTION IX
REFERENCES
1. Speece, R. E., "The Use of Pure Oxygen in River and Impoundment
Aeration," Proceedings 24th Industrial Waste Conference,
Purdue University (1969).
2. Lewis, W. K. and W. E. Whitman, "Principles of Gas Absorption,"
Industrial and Engineering Chemistry, 16, 1215 - 1220 (1924).
3. Treybal, R. C. , Mass Transfer Operations, McGraw-Hill Book Com-
pany, New York, New York (1955).
4. Higbie, R. , "The Rate of Absorption of a Pure Gas into a Still Liquid
During Short Periods of Exposure," Transaction, AICE, 31,
365-389 (1935).
5. Dankwertz, P. V. "Significance of Liquid Film Coefficients in Gas
Absorption," Industrial Engineering Chemistry, 43, 1460 (1951).
6. Dobbins, W. E., "Mechanisms of Gas Absorption by Turbulent Liquids ,"
Advances in Water Research, Proceedings First International
Conference on Water Pollution Research, Pergamon Press Ltd. ,
London, England,_2_, 61 (1964).
7, Eckenfelder, W. W. , Jr. , "Absorption of Oxygen from Air Bubbles in
Water," J5ED, ASCE, 85, 95 (1959).
8. Barnhart, E. T. , "Transfer of Oxygen in Aqueous Solutions," JSED,
ASCE, 95, No. SA3 , 645 - 661 (1969).
9. Rosenberg, B. , "The Drag and Shape of Air Bubbles Moving in Liquids ,"
David Taylor Model Basin, Navy Department Report 727 (Sept. ,
1950).
10. Calderbank, P. H. , and R. P. Patra, "Mass Transfer in the Liquid Phase
During the Formation of Bubbles," Chemical Engineering Science,
1966, 21, 719.
11. Montgomery, J. O. , "Relative Ratio of Nitrogen-to-Oxygen Transfer
Coefficients in Aqueous Solutions, " M. S. Thesis, New Mexico
State University, (March, 1970).
8.7
-------
12 . Standard Methods for the Examination of Water and Wastewater, Amer-
ican Public Health Association, New York, New York, 12th Ed. ,
(1965).
13. Rayyan, Fawzi, "Dynamics of Bubble Plumes Incorporating Mass
Transfer," M. S. Thesis , University of Texas at Austin, (August,
1972).
14. Adamson, A. W. , Physical Chemistry of Surfaces, Interscience Pub-
lishers, New York, New York (1970).
88
-------
SECTION X
LIST OF PUBLICATIONS
One publication, to date, has resulted from this project. It is
entitled "Alternative Considerations in the Oxygenation of Reservoir
Discharges and Rivers" by R. E. Speece, Fawzi Rayyan, George
Murphee. It is a publication in the Conference Proceedings -
Applications of Commerical Oxygen the Water and Wastewater
Systems University of Texas Press (In Press).
No patents resulted from this study.
89
-------
SECTION XI
APPENDICES
91
-------
APPENDIX A
DESIGN FIGURES - O2 and Air
1) Fractional Absorption from Bubbles vs Rise Height
2) Relative Volume in Bubbles vs Rise Height
92
-------
DESIGN FIGURES
The figures in this section can be used as additional material in
the design of hypolimnion aeration systems. The figures which are
included are the fraction of the original amount of oxygen injected
versus depth and the volume of gas remaining at any depth relative
to the volume of gas injected. Bubble diameter and bubble composi-
tion vs injection depth figures are included in the Appendix. These
figures are divided into two sets. The first set is for the case
where pure oxygen is used and the second set is for the use of
air as the injected gas . On each figure, the behavior of four initial
bubble diameters is represented. The four diameters are 0.2, 0.5,
1.0, and 2.0 mm. The injections depths are 8, 16, 24, 32, 48, 64,
and 96 m. The dissolved oxygen, nitrogen, and carbon dioxide
concentrations were set at 10, 15, and 25 mg/1, respectively. The
temperature was set at 15°C. The ' = ' indicates more than one point
is plotted in that space.
93
-------
1.0
CD
CO
DO =10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DIfiM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM =2.0 MM
4.0 5.0
DEPTH (M)
Fig- 50 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH - PURE OX "GEN
-------
to
en
CO
-------
CD
01
1.0
o
I
fc 0-8
O
2
O
s °-6
H
O
-------
1.0
co
ro
O
O
w
2
o
£
i—i
H
0.8
0.6
0.4
0.2
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM 2.0 MM
I
2.0 4.0 6.0 8.0
DEPTH (M)
10.0
12.0
14.0
16.0
Fig. 53 RELATIVE VOLUME OF GAS VS DEPTH - PURE OXYGEN
-------
CD
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
, DIffM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM - 1.0 MM
4, DIAM = 2.0 MM
12
DEPTH (M)
Fig. 54 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH - PURE OXYGEN
-------
LD
(JD
CO
O
PH
o
H
i-J
O
>
w
>
( — l
H
W
fii
DO =10.0 MG/L
DN ^ 15.0 MG/L
DC O =25.0 MG/L
1, DIAM - 0.2 MM
2, DIAM = 0.5 MM
3 , DIAM 1.0 MM
4, DIAM 2.0 MM
0.4
0.2
8 12
DEPTH (M)
Fig.
RELATIVE VOLUME OF GAS VS DEPTPI - PURE OXYGEN
-------
o
o
CO
I I
DO - 10.0 MG/L
DN = 15.0 MG/L
DC CL =25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3 , DIAM = 1.0 MM
4. DIAM = 2.0 MM
15
DEPTH (M)
20
25
30
Fig. 56 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH - PURE OXYGEN
-------
09
O
O
w
D
O
£
i—i
H
W
Di
DO = 10.0 MG/L
DN - 15.0 MG/L
DC O =25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3 , DIAM = 1.0 MM
4, DIAM = 2.0 MM
10
15
DEPTH (M)
Fig. 57 RELATIVE VOLUME OF GAS VS DEPTH - PURE OXYGEN
-------
1.0
o
oo
00
<
O
i
o
2;
I—H
<\
c
o
H
!=>
o
s
-------
o
GO
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/L
I, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM - 1.0 MM
4, DIAM = 2.0 MM
20 25
DEPTH (M)
Fig, 59 RELATIVE VOLUME OF GAS VS DEPTH - PURE OXYGEN
-------
CO
O
PH
C
S
I—I
r
O
55
8
J5
HH
a
8
P-.
O
S
O
»—I
H
u
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
DI£M = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
0.2 _
20 30
DEPTH (M)
60
Fig. 60 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTF! - PURE OXYGEN
-------
o
On
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DLAM = 0.2 MM
2, DIAM = 0.5 MM
3 , DIA M = 1. 0 MM
4, DIAM = 2.0 MM
30
DEPTH (M)
Fig. 61 RELATIVE VOLUME OF GAS VS DEPTFI - PURE OXYGEN
-------
o
CT1
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/L
DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
40 50
DEPTH (M)
Fig. 62 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH - PURE OXYGEN
-------
o
DO - 10 ... IV. G/L
DN = 15.0 MG/L
.0 MG/L
1, DIAV. = 0.2 MM
2, DIAM = 'o.5 MM
3, DIAM -- 1.0 MM
DIAM = 2.0 MM
40 50
DEPTn (M)
Fig. 63 RELATIVE VOLUME OF GAS VS DEPTH - PURE OXYGEN
-------
o
00
o
O
05
O
PM
o
S3
O
>—i
H
U
i.o
0.8
0.6
0.4
0.2
I
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3 , DIAM = 1.0 MM
4, DIAM = 2.0 MM
I
1.0 2.0 3.0 4.0
DEPTH (M)
5.0
6.0
7.0
8.0.
Pig. 64 FRACTION OF ORIGINAL AMOUNT OF Q IN OFF-GAS VS DEPTH - AIR
-------
CO
<:
O
p4
O
1-1
o
H
3
w
1.0
0.8
0.6
0.4
0.2
DO - 10.0 MG/L
DN =15.0 MG/L
DC O = 25.0 MG/L
1, DIKM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM -1.0 MM
4, DIAM =2.0 MM
I
1.0 2.0 3.0 4.0
DEPTH (M)
5.0
6.0
7.0
8.0
Fig. 65 RELATIVE VOLUME OF GAS VS DEPTH - AIR
-------
en
-------
DO = 10. 0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM =0.5 MM
3 , DIAM = 1.0 MM
4, DIAM = 2.0 MM
2.0
4.0 6.0 8.0 10.0
DEPTH (M)
12.0
14.0
16.0
Fig. 67 RELATIVE VOLUME OF GAS VS DEPTH - AIR
-------
CO
-------
1C
l.U
0.8
0.6
w 0.4
G
| 0.2
w
\L
BO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
I, DIAM = 0.2 IV!A,
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM - 2.0 MM
8 12
DEPTH (M)
16
20
24
Fig. 69 RELATIVE VOLUMF -' GAS VS DEPTH - AIP
-------
CO
I
OH
I'.IH
c-
^T~
t'~\
t—l
O
c
c
H
O
i.u
0.8
0.6
0.4
0.2
0
0
T
DO = 10.0 Mi.,/L
DN = 15.0 MG/L
DC C =25.0 Mu/L
I, DIAM = U.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM =2.0
10 15
DEPTH (M)
20
25
30
Fig. 70 FACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTK - AIR
-------
V .
W
Cn
W
M
1.0
0.8
0.2
DN = 15.0 MG/L
DC O =25.0 Mo/I
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM - 2.0 MM
15
DEPTH (M)
rig. 71 RELATIVE VOLUME OF GAS VS DEPTH - AI?
-------
CT1
DO = 10.0 MG/L
DN = 15.0 MG/L
= 25.0 MG/L
1, DI^M = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM - 1.0 MM
4, DIAM = 2.0 MM
20 25
DEPTH (M)
Fig. 72 FRACTION OF ORIGINAL AMOUNT OF Q IN OFF-GAS VS DEPTH - AIR
-------
DO - 10.0 MG/L
DN = 15.0 MG/L
DC O? =25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
20 25
DEPTH (M)
Fig. 73 RELATIVE VOLUME OF GAS VS DEPTH - AIR
-------
1.0
00
CO
IX,
O
£
h-<
o
O
H
55
D
O
2
O
I—I
o
o
C
t—4
H
U
0.8
0.6
0.4
0.2
0
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DDVM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
10
20 30
DEPTH (M)
40
50
60
Fig. 74 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH - AIR
-------
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O - 25.0 MG/L
1, DLAM = 0.2 MM
2, DIAM = 0.5 MM
3 , DIAM = 1.0 MM
4, DIAM = 2.0 MM
30
DEPTH (M)
60
Fig. 75 RELATIVE VOLUME OF GAS VS DEPTH - AIR
-------
1.:
CO
O
cc
<
CJ)
O
8
H
a
I-J
Oi,
O
t^
O
2
O
h— (
H
-.6
0.2
r
i—i
DO = k ., MG/L
DN =15.0 MG/L
DC O2 =25.0 MG/
1, DIAM = , .2 MM
2, DIAM = i-'.S MM
3 , DIA M = 1.. M J\!
'*, DIAM = 2.C MM
I- 20 30 40 SI-
DEPTH (M)
6',
80
90
Fig. 76 FRACTION OF ORIGINAL AMOUNT OF O IN OFF-GAS VS DEPTH - AIR
-------
1.0
DO = 10.0 MG/L
DN =15.0 MG/L
DC O =25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
30 40 50 60
DEPTH (M)
Fig. 77 RELATIVE VOLUME OF GAS VS DEPTH - AIR
-------
APPENDIX B
DESIGN FIGURES - O2 and Air
1) Diameter vs Rise Height
2) 02 Composition vs Rise Height
122
-------
w
2.0
1.8
1.6
1.4
1.2
0:5 1 0
CD l ' U
P
CQ
oi
H 0.6
0.4
0.2
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/L
1, DU?M = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
I
I
1.0 2.0 3.0 4.0 5.0 6.0 7.0
DEPTH (M)
8.0
Fig. 78 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH PURE OXYGFN
-------
to
i.o
0.8
0.4
O 0.6
O
O
t—I
fcj
O
(X
O
(J
w 0.2
g
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O, =25.0 MG/L
1, DD\M =0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
I
1.0 2.0 3.0 4.0 5.0
DEPTH (M)
6.0
7.0
8.0
Fig. 79 OXYGEN COMPOSITION OF OFF- GAS VS DEPTH - PURE OX''GEN
-------
to
Cn
W
t-t
CQ
CQ
£
CQ
O
H
W
P
2.0
1.5
1.0
0.5
0
DO = 10.0 MG/L
DN - 15 .0 MG/L
DC O =25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
6 8
DEPTH (M)
10
12
14
16
Fig. 80 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - PURE OXYGEN
-------
PH
o
CO
O
a,
s
o
o
s
w
O
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O2 = 25.0 MG/L
I, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4( DIAM = 2.0 MM
0.2
6 8
DEPTH (M)
Fig. 81 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH - PURE OXYGEN
-------
a
03
ca
oa
w
H
Q
2.0
1.5
1.0
0.5
0
I I
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
I, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
I
8 12
DEPTH (M)
16
20
24
Fig. 82 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH ^ PURE OXYGEN
-------
1.0
CO
cc
<
O
o
P-.
O
o
o-
t-
6
u
w
O
X
o
0.8
n ,-
O.o
0.2
DO = 10.0 • "G/L
D =15.0 '/G/L
DC O =25.0 --G/T.
I, DljfV = 0.2 ^/TM
2, DIAM = 0.5 MM
3, DIAM = 1.0 VTIV
4 , DIA V = 2 . 0 M
I
12
DEPTH (M)
15
20
24
Fig. 83 OX '"GEN COMPOSITION OF OFF-GAS VS DEPTH - PURE OX ''GEN
-------
ISO
CD
m
-
o
w
D
2.0
1.8
1.6
1.4
1.2
g 1-0
0-8
0.4
0.2
I I
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/I
1, DMM = 0.2 MM
2, DIAM = 0.5 MM
3 , DIAM = 1.0 MM
4, DIAM =2.0 MM
10
15
DEPTH (M)
20
25
30
Fig. 84 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - PURE OX rGEN
-------
GO
o
DO = 10.U MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
A, DIAM = 2.0 MM
g
LO 15
DEPTH (M)
Fig. 85 OX GEN COMPOSITION OF OFF-GAS VS DEPTH - PURE OX GEN
-------
W
CO
DO
CO
O
OS
W
W
2
13
P
2.
1.6
1.2
I
I
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3 , DIAM = 1.0 MM
4, DIAM = 2.0 MM
0.8
0.4
I
10 15 20 25
DEPTH (M)
30
35
40
45
Fig. 86 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - PURE OXYGEN
-------
Go
tx,
O
' -i-i
O
O
t— <
r.^
f — i
CO
O
a,
S
O
c
Vi
w
O
1.0
u.4
C.2
T
T
DO - U.U M, /
Dr«; - l.-.i' MV-/J
DC O2 - 21 .0 M..
I, DIA^ :" v.;.2 Mfv".
2, DiAfy/i ~ i).5 MM
3, DIAM - 1.0 MM
4, DIAM - 2.U MM
I
10 15 2u 25
DEPTH (M)
3U
4U
45
Fig. 87 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH - PURE OXYGEN
-------
CO
CO
„
CQ
CO
-
0
a:
w
Q
2.0
i.b
1.6
1.4
1.2
0.8
0.6
O.i
i.2
0
I 1^
DO = 1U.O MG/L
DN = 15.0 MG/L
DC O = 2;:.0 MG/i
1, DIffM = L'.2 MM
2, DIAM = 0.5 MM
3, DIAM =1.0 MM
4, DIAM = 2.0 MM
10
20 30
DEPT (M)
60
Fig.
DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - PURE OXY(.:EK
-------
1.0
CO
GO
Y
O
(X,
O
V5
CO
O
OH
2
o
u
s
0.8
.2
0
T
DO = U .U MG/L
DN = 15 .U ML-j/L
DC O =25.0 MG/L
1, DI£M = 0.2 MM
2, DIAM = U.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
10
2U
30
DEPTH (M)
Fig. 89 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH - PURE OXYGEN
-------
CO
On
DO - lo.O
DN - 1^.0 Mv,A
DC O = 2b.U Mt-/
1, DIAM - 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
20 30
40 50 60
DIPTH (M)
Fig. 90 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - PURE OXYGEN
-------
1.0
GO
01
DO = 10.0 MG/
DN = 15.0 MG/L
DC O2 =25.0 MG/L
1, DlffM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
40 50 60
DEPTH (M)
Fig. 91 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH - PURE OXYGEN
-------
CO
W
^
OQ
CQ
D
PQ
IJ-,
O
cd
W
H
W
Q
2. u
i 1.5
1.0
o.s
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/I
1, DlffM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
3 4
DEPTH (M)
Fig. 92 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - AIR
-------
CO
oo
8
Pu
2
o
u
I
.20
.16
CO
s
p-l
° .12
8
08
.04
0
H I
DO - 10.0 Mti/I,
DN =15.0 MG/L
DC O = 25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
I
I
345
DEPTH (M)
Fig. 93 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH - AIR
-------
to
CQ
CQ
D
CQ
tM
O
ce!
w
Q
2.0
1.6
1.2
0.4
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DI/TM = 0.2 MM
2, DIAM = 0.5 MM
37 DIAM = 1.0 MM
4, DIAM = 2.0 MM
[X
6 8 10
DEPTH (M)
12
14
16
Fig. 9^ DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - AIR
-------
•tk
c
.20
co
-16
.12
53
O
i— i
g
O .08
PH
s
O
O
J5
w
{5 .04
0
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/L
1, DI/TM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
I
I
6 8
DEPTH (M)
10
12
14
16
Fig. 95 OXYGEN COMPOSITION OF OFF- GAS VS DEPTH - AIR
-------
2.0
1.5
a i.o
CO
DQ
DQ
c
w
a 0.5
Q
0
DO = 10.0 MG/L
DN =15.0 MG/L
DC O =25.0 MG/L
1, DIffM = 0.2 MM
2, DIAM =0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
12
DEPTH (M)
16
20
24
Fig. 96 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - AIR
-------
ND
CO
-------
CO
CQ
CQ
£
00
PM
O
a;
£
w
2.0
1.8
1.6
1.4
0.8
IS °-6
p
0.4
0.2
I
DO = 10.0 MG/L
DN =15.0 MG/L
DC O = 25.0 iVIG/L
1, DIffM = 0.2 MM
2, DIAM =0.5 MM
3, DIAM = 1.0 MM
4, DIAM =2.0 M
10 15
DEPTH (M)
20
25
30
Fig. 98 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - AIR
-------
.20
cn
-------
Cn
2.0
1.8
1.2
w
i—i
CQ
DQ
!=>
03
O 0.8
w
H
Q 0.4
0
I I I
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O = 25.0 MG/L
1, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
10 15 20 25
DEPTH (M)
30
35
40
45
Fig . 100 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - AIR
-------
CD
CO
-------
2.0
1.8
1.6
f 1.4
s
3 1.2
CQ
CQ
S 1.0
O
0.8
w
I 0.6
Q
0.4
0.2
0
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O =25.0 MG/.
1, DI^M = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
10
20
I —
30
DEPTH (M)
40
50
60
Fig. 102 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - AIR
-------
00
CO
-------
to
lu
30 40 50 60 7o
DEPTH (M)
80
Fig. 104 DIAMETER OF BUBBLE AS A FUNCTION OF DEPTH - AIR
-------
.20
en
I
co .16
O
i
o
O
O
co
O
o
u
^
w
.08
.04
DO = 10.0 MG/L
DN = 15.0 MG/L
DC O, = 25.0 MG/L
, DIAM = 0.2 MM
2, DIAM = 0.5 MM
3, DIAM = 1.0 MM
4, DIAM = 2.0 MM
10 20 30 40 50
DEPTH (M)
60
70
80
90
Fig. 105 OXYGEN COMPOSITION OF OFF-GAS VS DEPTH - AIR
-------
SELECTED WATER
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
1. Report No.
w
Hypolimnion Aeration with Commercial Oxygen -
Vol. II - Bubble Plume Gas Transfer
Speece, R.E.; Rayyan, F.; Murfee, G.
f2.
The University of Texas at Austin
Austin, Texas 78712
irj' Organ-
S. Report Date
S. £•" -loimi ,< Org&
------- |