Response of a Tropical Reservoir to Bubbler Destratification
Goloka Behari Sahoo1 and David Luketina2
Abstract: A one-dimensional reservoir-bubbler model has been developed to examine the mixing and the change in dissolved oxygen
pattern induced by bubbler operation in a stratified reservoir. The reservoir-bubbler model is applied to a tropical reservoir, the Upper
Peirce Reservoir, Singapore. For this tropical reservoir with low wind speeds, it is found that bubbler operation dominates oxygen transfer
into the reservoir water rather than oxygen transfer from all other sources, including surface reaeration. It is illustrated that selection of
airflow rate per diffuser, air bubble radius, and total number of diffusers are important criteria in bubbler designs. Higher dissolved oxygen
levels in reservoirs are obtained by increasing the bubbler airflow rate that is associated with lower mechanical efficiency 共␩mech兲 than
optimal ␩mech of the bubbler. Determining an appropriate airflow rate is shown to be a tradeoff between increased dissolved oxygen levels
and increased operating costs as airflow rate increases. When the reservoir is close to well mixed, the water quality is usually reasonably
good but the bubbler operates at a very low ␩mech—thus the bubbler should be turned off.
DOI: 10.1061/共ASCE兲0733-9372共2006兲132:7共736兲
CE Database subject headings: Water quality; Stratification; Bubbles; Reservoirs; One-dimensional models; Dissolved oxygen.
Introduction
The vertical thermal stratification observed in most lakes and reservoirs is a natural occurrence, which is often characterized by a
well-mixed surface layer, separated from the deeper hypolimnion
layer by a strong temperature gradient, known as the thermocline.
The thermocline acts as a barrier preventing active exchange
of temperature, dissolved oxygen 共DO兲, and dissolved nutrients
between the reservoir surface and bottom layer. Because of the
biological and biochemical oxygen consumption, a stratified reservoir over a long period cannot prevent the hypolimnion from
becoming anoxic leading to the increased release of undesirable
substances such as nutrients, and iron and manganese from the
sediments of the reservoir 共Kilham and Kilham 1990; Kassim
et al. 1997; McGinnis and Little 2002兲. Moreover, nutrients
originating in local runoff and in the discharges from upstream
treatment plants, and mineralization of biomass within itself
not only induce a permanent stratification 共Wüest et al. 1992;
Schladow and Fisher 1995兲 but also stimulate algal growth causing water quality problems 共Arumugam and Furtado 1980;
Sterner and Grover 1998; Burris et al. 2002兲. In order to suppress
nutrient release from sediments and to ameliorate the reservoir
water quality, oxygen is commonly introduced into the hypolimnion artificially which is combined with artificial mixing
共Wüest et al. 1992; Yang et al. 1993; Burris et al. 2002; McGinnis
and Little 2002; DeMoyer et al. 2003兲.
1
Dept. of Civil and Environmental Engineering, Univ. of California,
Davis, 3108 Engineering III, One Shield Ave., Davis, CA 95616
共corresponding author兲. E-mail: gbsahoo@ucdavis.edu
2
Asian Institute of Technology, School of Civil Engineering, Water
Engineering and Management Program, P.O. Box 4, Klong Luang,
Pathumthani 12120, Thailand.
Note. Discussion open until December 1, 2006. Separate discussions
must be submitted for individual papers. To extend the closing date by
one month, a written request must be filed with the ASCE Managing
Editor. The manuscript for this paper was submitted for review and possible publication on May 24, 2004; approved on October 25, 2005. This
paper is part of the Journal of Environmental Engineering, Vol. 132,
No. 7, July 1, 2006. ©ASCE, ISSN 0733-9372/2006/7-736–746/$25.00.
Artificial destratification of the water column is a common
means of addressing these water quality problems with the most
popular method of destratification being the air bubble diffuser
共McDougall 1978; Schladow 1992, 1993; Asaeda and Imberger
1993; Yang et al. 1993; Schladow and Fisher 1995; Hornewer
et al. 1997; Lindenschmidt and Hamblin 1997; Burns 1998;
McGinnis and Little 1998; Simmons 1998; Johnson et al. 2000;
USGS 2000兲, which is referred to here as a bubbler. Burris et al.
共2002兲 and McGinnis et al. 共2004兲 demonstrated via experiment
that the hypolimnetic oxygenation can be achieved by injecting
oxygen into the hypolimnion using oxygen bubble diffuser without disrupting thermal stratification. Though the use of air or oxygen bubble diffuser is a debatable issue, an air or oxygen bubble
diffuser should be chosen for reservoir water quality management
based on comparative operating costs and total savings from the
waterworks which significantly reduces the amount of chemical
consumption after improvement of the reservoir water quality. In
general, an oxygen bubble diffuser system adds extra cost for
oxygen production, storage, transportation, and safety handling in
addition to operational cost compared to an air bubbler system.
Besides this, an oxygen bubble diffuser system does not dismantle the thermal stratification; thus, the thermocline strongly
inhibits the vertical mixing, and thereby cuts off the flow of DO
from oxygen rich epilimnion to hypolimnion layer. The surface
water in contact with air becomes in equilibrium with the atmospheric oxygen concentration and ceases further oxygen dissolution into the water from the atmosphere. Therefore, the total
amount of gaseous oxygen dissolution from atmosphere into
water is significantly reduced. On the other hand, the overall goal
of the air bubbler is to sufficiently reduce the stratification so that
the water body may completely mix under natural phenomena and
remain well oxygenated throughout 共Johnson et al. 2000兲.
Because DO is transported from water surface to the deeper layer
in the case of a well mixed reservoir/lake, the atmospheric gaseous oxygen dissolves more at the air and water interface. Yang
et al. 共1993兲, Schladow and Fischer 共1995兲, Simmons 共1998兲,
and Burns 共1998兲 demonstrated that the hypolimnetic anoxia in
reservoirs were eliminated by means of artificial destratification
Fig. 1. Outline of Upper Peirce Reservoir showing aeration points 共 兲 and sampling points 共 丢 兲 关after Sahoo 共2002兲兴
using air bubble plumes and the concentrations of phosphates,
ammonical nitrogen, total alkalinity, total organic carbon, iron
and manganese, pH values, and algal populations were reduced
significantly. The air bubbler system successfully operating in
Upper Peirce Reservoir, Singapore for reservoir destratification
and water quality management 关see Yang et al. 共1993兲兴 since from
1990 until now has motivated writers to study the scientific
details of bubbler effect on reservoir destratification in the Upper
Peirce Reservoir.
Fischer et al. 共1979兲 reports that reservoir stratification
depends on wind speed, inflow water temperature, and solar
radiation intensity. A strong stratification is developed for inflow
water temperature much lower than the ambient temperature,
weak wind speed, and intense solar radiation. On the other hand,
strong wind generates a large amount of kinetic energy within the
reservoir leading to reservoir destratification 共Fischer et al. 1979;
Imberger and Patterson 1981兲. Sahoo 共2002兲 demonstrated by
using the surface and bed temperature of nine different reservoirs
and lakes around the world that tropical reservoirs experience
weak stratification compared to temperate and subtropical reservoirs. Moreover, weak wind speed 共0 to −5 ms−1兲 patterns that
occur in tropical reservoir cannot generate sufficient kinetic
energy to break the thermal stratification 共Yang et al. 1993;
Kassim et al. 1997兲. Weak wind speed patterns imply less oxygen
transfer rate at the atmosphere and water interface, thus the only
way to prevent stratification and anoxia is that oxygen must be
supplied by rising bubbles of an aeration system 共Yang et al.
1993; Johnson et al. 2000兲.
Numerical and experimental results described by Asaeda and
Imberger 共1993兲, Schladow 共1992兲, Johnson et al. 共2000兲, and
Sahoo and Luketina 共2003a兲 showed that a single airflow rate
exists for a given stratification at which the mixing efficiency of
the destratification is a maximum. Further, as the stratification
weakens, the airflow rate must be reduced and vice versa if the
bubbler is to be operated at the optimal mechanical efficiency
共␩mech兲. Note that bubbler ␩mech is the ratio between the rate of
change of reservoir potential energy and input compressor energy
关see Sahoo and Luketina 共2003a兲兴. It should be noted that the
energy expended by a variable speed compressor is directly
proportional to the airflow rate 共Sahoo and Luketina 2003a兲. For
the destratification point of view, if the stratification is sufficiently
weak, the accepted wisdom is that the bubbler should be temporarily turned off 共Burns 1998; Simmons 1998兲. However, at the
optimum bubbler ␩mech, the airflow rate is only sufficient to
destratify the reservoir but the airflow rate may be weak to contribute enough DO to meet the biological oxygen demand 共BOD兲,
chemical oxygen demand 共COD兲, and sediment oxygen demand
共SOD兲 of the reservoir. Therefore, in such cases, the DO contribution from the bubbler may become relatively more important
than optimal ␩mech. The present study examines the real time adjustment of the total airflow rate 共i.e., the airflow per diffuser兲
either to maintain the optimum ␩mech or the desired DO level or a
tradeoff between these two.
A one-dimensional reservoir model is developed which incorporates the bubbler model developed by Sahoo and Luketina
共2003a,b, 2005兲. The coupled reservoir-bubbler model is applied
to a tropical reservoir, the Upper Peirce Reservoir, Singapore, to:
1. Estimate the DO transfer 共gain or loss兲 from different sources
共e.g., air bubble, atmosphere, algae, COD, BOD, and SOD兲;
2. Examine the tradeoff between operating at optimum ␩mech
and achieving a desired DO concentration in the reservoir;
and
3. Develop reservoir management strategies for water quality
improvement using bubblers.
Study Area
The Upper Peirce Reservoir shown in Fig. 1 is located at 1° 22⬘
13⬙ N latitude and 103° 47⬘ 36⬙ E longitude, and within the central catchment area at the center of Singapore Islands. The following figures and facts of the Upper Peirce Reservoir and the
bubbler system in operation are taken from Yang et al. 共1993兲.
The Upper Peirce Reservoir, when full, covers 3.20 km2 of
water surface with a maximum depth of about 22 m. The annual
average reservoir depths at the water quality measuring Stations
1–5 共see Fig. 1兲 are 5, 13, 16, 18, and 21 m, respectively. Its main
source of water is the Tebrau River in Johore, Malaysia. Because
industrial waste from Tebrau industrial area flows into the Tebrau
River, the river water always becomes polluted and poses an adverse impact on the reservoir water quality. Prior to the operation
of a bubbler system on May 25, 1990, the reservoir water quality
deteriorated over the years and this caused the Chestnut Avenue
Waterworks to completely shut down for 1 week in May 1990
because of high ammonia content in the raw water. A bubbler
system with an air compressor rated at 720 m3 / h 共i.e., 200 L / s兲
and with a delivery pressure of 2.6 kg/ cm2 共2.6 atm at 20°C兲 was
installed at the draw-off tower in early 1990. Two temporary aeration points located near the draw-off tower were put into operation on May 25, 1990. This was intended to destratify the water
before it was delivered to the waterworks. After aeration, no chlorine was required for removal of ammonia as the ammonia was
almost completely eliminated. Therefore, two permanent aeration
points 共A and B in Fig. 1兲 were installed at the deepest parts of the
main body of the reservoir in June 1990. Points A and B were 100
and 400 m away from the draw-off tower, respectively 共see Fig.
1兲. The two aeration points were 500 m apart and each had a
8.0 m long 50 mm diameter stainless steel Grade 304 pipe as a
diffuser. A total of eight circumferential slits of 20 mm⫻ 5 mm
were made along the length of each diffuser pipe at 1 m intervals.
Each diffuser was sunk into the reservoir at the predetermined
location 共22 m deep兲 using concrete sinkers attached to each end
of the diffuser pipe. The detailed design, and capital, installation
and operation costs of the aeration system can be found in Yang et
al. 共1993兲. In brief, nearly $2.12 and $5.64 million were saved
from chlorine cost from June 1990 to May 1991 and from June
1991 to May 1992, respectively and the total operating cost was
$0.06 million. The installation cost of the aeration system was
nearly $1.35 million.
Data Used
Four data sets of water temperature and DO profile at Station 4 of
the Upper Peirce Reservoir from April 1990 to July 1990 were
extracted from the Yang et al. 共1993兲 paper and used for this
study. Since there is no meteorological station near the Upper
Peirce Reservoir, meteorological data of the Changi Meteorological Station, the only official principal meteorological station near
the Upper Peirce Reservoir, was used in the study. The distance
from the Upper Peirce Reservoir to the Changi Meteorological
Station is about 12 km. The hourly meteorological data: solar
radiation, wind velocity, dry bulb temperature, wet bulb temperature, and relative humidity, and daily sunshine hour data for the
year 1990 at the Changi Meteorological Station were obtained
from Meteorological Department, Government of Singapore and
were used in this study.
Reservoir-Bubbler Model
Background of Bubbler Model
The bubbler aeration technique involves a source of compressed
fresh air being pumped to the bottom of the reservoir and continuously released through a diffuser. The rising air bubbles entrain the ambient water and form an air–water mixture plume. As
the bubbles rise, there is a continuous increase of buoyancy resulting from their volumetric expansion. For a stratified ambient
environment, the entrained air–fluid mixture eventually becomes
heavy compared to the surrounding ambient fluid as the plume
rises, resulting in the centerline velocity of the plume becoming
zero. In more technical terms, the plume detrains all of the entrained water where the downward buoyancy dominates upward
momentum flux. The entrained fluid then sinks to its neutral
Fig. 2. Schematic of Langrangian layer scheme employed in
combined reservoir and bubbler model. Initial density profile 共at left兲
is starting to be modified by entrained water depleting volume of
each of layers up to maximum height of rise to produce final profile
共at right兲. Shaded regions represent layers that are starting to increase
in volume by insertion of entrained water about its level of neutral
buoyancy. Note that insertion occurs below level of maximum rise.
Second plume forms above first, and third plume forms above
second, and immature plume intersecting free surface forces final
detrainment.
buoyancy level before forming a lateral outflow 共Johnson et al.
2000兲. The air bubbles, however, continue to rise and form a new
plume at the point of detrainment. This entrainment and detrainment process, which is referred to here as a cascade, may be
repeated many times until the bubbles reach the surface 关see
Sahoo and Luketina 共2003a兲 for details兴. A schematic of the processes of entrainment and detrainment with an air bubble plume is
shown in Fig. 2. Based on the bubbler concept of McDougall
共1978兲, Asaeda and Imberger 共1993兲, and Schladow 共1992兲;
Sahoo and Luketina 共2003a,b兲 developed a bubbler model that
integrates the differential mass, momentum, and buoyancy conservation equations of bubble plume fluid. The estimated entrainment fluxes, the key predictions of the model, are compared with
the measured data complied by Milgram 共1983兲 for these experiments and his own as shown in Fig. 3. The data cover a range of
water depths from 0.32 to 46.95 m and a range of airflow rates
from 0.21⫻ 10−3 to 590⫻ 10−3 m3 / s. It is found that the model
prediction agrees with the experimental data with determination
coefficient R2 = 0.94. Only two data points in the bottom left corner of Fig. 3 do not fit well on the 1:1 line, where the water
column of the experimental tank was 0.32 m and the corresponding airflow rates were 0.21⫻ 10−3 and 0.59⫻ 10−3 m3 / s, respectively. However, a bubble plume system is not used in cases
where the water depth is less than around 5 m 共Sahoo 2002兲. In
addition to fluid conservation equations, the model integrates the
dissolved and undissolved gas conservation equations of bubble
plume based on assumptions and formulations made by Wüest
et al. 共1992兲, Burris et al. 共2002兲, McGinnis and Little 共1998,
2002兲, and Sahoo and Luketina 共2003b, 2005兲. The model in-
Fig. 3. Comparison of measured experimental and model estimated
entrainment fluxes. R2 refers to correlation coefficient of all measured
and model-estimated values.
cludes the effect of buoyancy on stratification, bubble slip and
bubble expansion, and the effect of bubble radiuses on gas dissolution.
The differential conservation equations 共mass, momentum,
buoyancy, temperature, dissolved solids, algae, and dissolved
and undissolved oxygen and nitrogen兲 are solved in a onedimensional equispaced Langrangian grid using a fourth order
Runge–Kutta scheme. In each time step, the volume of fluid entrained from each layer is computed and removed. The total volume of the entrained water is then inserted back into the layer of
neutral buoyancy. Concurrently, DO of each layer and the amount
of oxygen transferred 共gain or loss兲 from air bubbles into plume
water are computed. Therefore, the total DO of the entrained
water is the total entrained DO from all layers and oxygen and
nitrogen transfer 共loss or gain兲 from air bubbles into the plume
water. Sahoo and Luketina 共2003a,b兲 presented the optimum bubbler design conditions in terms of bubbler operating efficiencies:
␩mech and oxygen dissolution efficiency 共i.e., a ratio between the
rate of change of reservoir DO concentration and the difference of
saturated and initial DO concentration兲 at different air bubble radiuses, stratification strengths, and airflow rate conditions. However, the above model does not include the effects of the external
meteorological forces in the development of thermal stratification
and the subsequent reservoir dynamics, and the oxygen exchanges
at the atmosphere and water interface due to wind.
vertical motions while horizontal variations in density are quickly
relaxed by horizontal advection and convection. Horizontal
exchanges generated by weak temperature gradients are communicated over several kilometers in less than 1 day, suggesting
that the one-dimensional model is suitable for lakes and reservoirs
共Antenucci and Imerito 2000兲. In brief, the reservoir model
assumes that the long wave radiation exchanges, sensible heat
transfer, and the evaporative heat losses all affect only the surface
layer temperature of the reservoir, while only the short wave
radiations effectively penetrate below 1 m or so—thus accounting
for the change in temperature in the deeper part of the reservoir
共Fischer et al. 1979; Imberger and Patterson 1981; Martin and
McCutcheon 1999; Antenucci and Imerito 2000兲. The long wave
radiation exchanges, sensible heat transfer, and the evaporative
heat losses are estimated using the mathematical formulations
and assumptions described in Fischer et al. 共1979兲, Imberger
and Patterson 共1981兲, USEPA 共1995兲, King 共1998兲, Martin and
McCutcheon 共1999兲, and Antenucci and Imerito 共2000兲. The short
wave solar radiations are directly measured.
Imberger and Patterson 共1981兲 and Martin and McCutcheon
共1999兲 reported that there are two useful approaches to quantify
vertical mixing in lakes and reservoirs for one-dimensional layered models. These are 共1兲 the mixed layer model; and 共2兲 the
eddy-diffusivity model. In the present study, the deepening of the
epilimnion is estimated using the mixed layer model described by
Fischer et al. 共1979兲; Imberger and Patterson 共1981兲; and Martin
and McCutcheon 共1999兲. The mixed layer model is the integral
thermocline model which takes into account stirring due to wind
and wave breaking, current shear due to basin scale internal
waves, and convective cooling at the surface. If the deepening is
vigorous enough for the mixed layer to reach the bottom, the
algorithm is complete and control is returned after incrementing
the time step and reinitializing the velocity and energy residual.
Below the thermocline, the vertical mixing of heat is estimated
using the semiempirical eddy-diffusivity model described by
Martin and McCutcheon 共1999兲.
In addition to stirring by winds, the mixing in the hypolimnion
depends on river inflows and reservoir outflow. For the detailed
physics of the effect of inflow and outflow on hypolimnion
mixing, the reader is referred to Fischer et al. 共1979兲 and
Imberger and Patterson 共1981兲 but briefly the river inflow is
inserted at a level where its density matches the reservoir density.
Similarly, water is withdrawn from the layers near to the outlet.
The reservoir model 关see Sahoo 共2002兲 for details兴 is developed
using Langrangian grid and finite difference method to estimate
the change in water temperature and DO concentration in the
reservoir.
Reservoir Model
Simulation of Reservoir Temperature
A one-dimensional reservoir model to simulate the reservoir
dynamics and temperature change due to climatic conditions and
river inflow and outflow is developed using the mathematical
expressions and assumptions of the one-dimensional DYRESM
共Imberger and Patterson 1981兲. The specific reasons of using
the mathematical expressions and assumptions of DYRESM are:
共1兲 it is free of calibration which implied that temporal and spatial
process descriptions are fundamentally correct 共Hamilton and
Schladow 1997兲 and 共2兲 it has been successfully applied to large
number of lakes and reservoirs 共Hamilton and Schladow 1997;
Lindenschmidt and Hamblin 1997; USGS 2000兲. The onedimensional assumption of DYRESM is based on observations
that density stratification usually found in reservoirs inhibits
Simulation of Reservoir Dissolved Oxygen
DYRESM 共Imberger and Patterson 1981兲 does not estimate the
change of DO in reservoir. The reservoir model 共Sahoo 2002兲
simulates DO along with temperature as a transport constituent.
DO in a reservoir is subject to a complex series of interactions
with many different substances. The major sources of oxygen, in
addition to the air bubble diffuser, are
1. Reaeration at the water-atmosphere interface;
2. The dissolved oxygen contained in the incoming flow; and
3. Oxygen produced by photosynthesis during algal growth.
The sinks of dissolved oxygen include
1. Oxygen uptake due to algal respiration;
2. Oxidation of ammonia nitrogen to nitrite nitrogen, COD;
3. Oxidation of nitrite nitrogen to nitrate nitrogen, COD;
4. Carbonaceous BOD decay; and
Table 1. Values Used in Simulation of Dissolved Oxygen in Upper Peirce Reservoir
Symbols
Typical
range
Definition
Source
Reaeration rate, wind dependent 共day−1兲.
King 共1998兲/USEPA 共1995兲
OR
Rate of oxygen production per unit of algal photosynthesis 共mg O/mg algae兲.
1.4–1.8
King 共1998兲
␣3
Rate of oxygen uptake per unit of algae respired 共mg O/mg algae兲
1.6–2.3
King 共1998兲
␣4
Rate of oxygen uptake per unit of ammonia nitrogen oxidation 共mg O/mg N兲.
3.0–4.0
King 共1998兲
␣5
Rate of oxygen uptake per unit of nitrite nitrogen oxidation 共mg O/mg N兲.
1.0–1.14
King 共1998兲
␣6
Rate constant of biological oxidation of ammonia nitrogen 共day−1兲
0.1–1.0
King 共1998兲
␤1
Rate constant of oxidation of nitrite nitrogen 共day−1兲
0.2–1.0
King 共1998兲
␤2
Carbonaceous BOD deoxygenation rate coefficient, temperature dependent 共day−1兲
0.2–0.35
Chapra 共1997兲
DRB
Sediment oxygen demand 共SOD兲 rate, temperature dependent 共g / m2 / day兲.
0.06–2.0
Chapra 共1997兲
DRS
Local specific growth rate of algae, temperature dependent 共day−1兲
1.0–3.0
King 共1998兲
GRA
Local respiration rate of algae, temperature dependent 共day−1兲
0.05–0.50
King 共1998兲
RA
Algal biomass concentration 共numbers/L兲
—
Yang et al.共1993兲
Ac
Concentration of ultimate carbonaceous BOD 共mg/L兲
—
Yang et al.共1993兲
LBOD
Concentration of ammonia nitrogen 共mg N/L兲
—
Yang et al.共1993兲
N1
Concentration of nitrite nitrogen 共mg N/L兲
—
Yang et al.共1993兲
N2
a
From Simmons 共1998兲, 10,000 numbers of algae per liter is approximated to be 3.2 mg/ L
b
Average water quality at Chestnut Avenue Waterworks during June 1989–May 1990 共Yang et al. 1993兲.
5. SOD.
The equation to describe the rate of change of oxygen 共⌬DO兲
during a time step ⌬t within a layer is shown below. Each term
represents a major source or sink of oxygen
⌬DO = 共DOt+⌬t − DOt兲bubbler + 关OR共DOsat − DOsurf兲
atmospheric
+ 共␣3GRA − ␣4RA兲Ac − DRBLBOD − AbDRS/"
algal
− 共␣5␤1N1 + ␣6␤2N2兲兴⌬t
COD
BOD
SOD
共mg/L/day兲
共1兲
where DOsurf 共mg/ L兲 = concentration of dissolved oxygen in the
surface layer of the reservoir; DOsat 共mg/ L兲 = saturation concentration of dissolved oxygen at the local temperature and pressure;
Ab 共m2兲 = plan area of the layer of interest in contact with the bed;
" 共m3兲 = volume of the layer of interest; and other terms OR, ␣3,
␣4, ␣5, ␣6, GRA, RA, Ac, LBOD, DRB, DRS, ␤1, ␤2, N1, and N2 are
defined in Table 1 with their typical values.
The oxygen transfer between the surface water and atmosphere
takes place based on the second term of Eq. 共1兲. Note that atmospheric reaeration OR is wind dependent and only applies at the
surface layer while SOD depends upon the plan area of the bed in
contact with the layer being evaluated. Reader is referred to
USEPA 共1995兲, King 共1998兲, and Sahoo 共2002兲 for the detailed
formulations and assumptions made for the estimation of DOsat
and OR.
Coupling of Reservoir Model and Bubbler Model
The bubbler model was incorporated into the reservoir model.
The reservoir and bubbler model work separately, however, they
interact with each other every hour. The time step for the reservoir
model is 30 min. Every 30 min, the reservoir model estimates the
temperature, DO concentration, and thickness of each layer of the
reservoir due to effects of river inflows and outflows, and climatic
conditions. Every hour, the bubbler model receives the reservoir
profile information 共consisting of DO concentration, temperature,
and thickness of each layer兲 of the reservoir model; estimates
values of DO concentration, temperature, and thickness of each
layer due to bubbler operation; and feeds back information of the
Equations
or value used
Equations
1.43
2.3
3.0
1.00
0.1
0.2
0.35
0.06
1.0
0.5
⬇10,000a,b
2.3b
0.69
0.11b
estimated profile to the reservoir model. Thus, the airflow rate of
the bubbler remains constant for 1 h. However, for the evolution
of different temperature profiles computed by the reservoir model
in the next hour, the airflow rate can be different if the bubbler is
to be operated at the highest possible ␩mech. Therefore, provisions
have been made so that the bubbler airflow rate can be either
constant or updated every hour. In the automatically updating
mode, different airflow rates are examined using the latest
evolved thermal structure of the reservoir. The airflow rate, which
produces the optimum ␩mech, is selected for the next 1 h.
At the beginning, reservoir layers are of equal thickness, i.e.,
25 cm, each having a measured temperature and a DO concentration. Note that water in a layer is assumed well mixed thoroughly,
thus thermal and biochemical properties of water in a layer are the
same. However, the layer thickness of each layer changes due to
the bubbler operation as entrainment and detrainment cause the
layers to contract or expand, respectively. Schladow 共1992兲 reported that the bubbler model produces grid independent results
for a finer grid spacing 共1 cm兲, although considerably larger grid
spacing introduces only a small error. It has been shown in Sahoo
and Luketina 共2003a兲 that a grid spacing of 25 cm produces identical results of Schladow 共1992兲. Therefore, in order to maintain
an adequate resolution for the reservoir model, the layers thicknesses are restructured every hour as follows:
1. A layer, whose thickness becomes less than 50% of its initial
thickness 共i.e., 12.5 cm兲, merges with the lower layer, and
2. A layer, whose thickness becomes more than 200% of its
initial thickness 共i.e., 50 cm兲, splits into two layers.
The vertical movement of layers is accompanied by a thickness
change as the layer plan area changes with the vertical position of
the layer in accordance with the reservoir bathymetry. Mixing in
the surface layer due to wind stirring and surface cooling is modeled by amalgamation of adjacent layers.
Results and Discussions
Simulation without Bubbler System
The water temperature and DO profile on April 17, 1990 was
taken as the initial condition and the parameters of Eq. 共1兲 are
Fig. 4. Reservoir simulation without bubbler system using initial
measured profiles on April 17, 1990, measured profiles on May 25,
1990 for simulation target, and simulated profile of: 共a兲 temperature;
共b兲 dissolved oxygen concentration along depth
adjusted within the range shown in Table 1 so that simulated DO
profile on May 25, 1990 will fit close to the measured profile.
Because the parameters used in Eq. 共1兲 are not known a priori for
the Upper Peirce Reservoir and no experimental data are available
at the study site, the parameters were calibrated within the range
reported by previous researchers 共see Table 1兲. The simulated and
measured water temperature and DO profile on May 25, 1990 are
compared in Fig. 4. The simulated temperature profile is found to
be a good fit to the measured temperature profile. Note that the
annual average river flow rate and water temperature data were
used in the study because of unavailability of time series river
flow rate and water temperature data. The simulated DO profile is
found to fit with the measured DO profile reasonably well for the
model parameters shown in the last column of Table 1. These
parameters were kept constant for the rest of the analysis presented herein.
Simulation with Bubbler
Existing Bubbler System
The temporary bubbler system using 16 diffusers and an airflow
rate of 12.5 L / s per diffuser was put into operation in Upper
Peirce Reservoir on May 25, 1990 共Yang et al. 1993兲. Therefore,
the combined reservoir-bubbler model was run for 40 days 共i.e.,
Fig. 5. Reservoir simulation with bubbler system using initial
profiles on May 25, 1990, measured profiles on June 4, 1990 for
simulation target, and simulated profile of 共a兲 temperature and
共b兲 dissolved oxygen concentration along reservoir depth after
10 days of simulation 共i.e., on June 4, 1990兲. Bubbles system was in
operation for 40 days.
960 h兲 using the temperature and DO profiles on May 25, 1990
as initial condition and using the same operational condition of
the existing system. Due to some uncertainty about the bubble
diameter that the diffuser produces, an average bubble radius
of 4 mm was assumed because the circumferential diffuser slit
is 20 mm⫻ 5 mm 共Yang et al. 1993兲. The simulated water temperature and DO profiles on June 4, 1990 and July 4, 1990 are
compared with the corresponding measured profiles as shown in
Figs. 5 and 6, respectively. The simulated temperature profile in
Fig. 6共a兲 agrees well with the measured values. Though the
simulated temperature in Fig. 5共b兲 overestimates the temperature
values, the deviations are well within 3% of the measured values.
The temperature at the surface is observed to be uniform due to a
mixed layer, which is formed because of wind stirring and surface
cooling. It is observed in both cases that the water temperature
difference between the surface and bottom layer ⌬T 共°C兲 is significantly reduced and the dissolved oxygen concentration of the
hypolimnetic water is significantly increased after 40 days of
Fig. 7. Reservoir behaviors when existing bubbler system is
simulated for 40 days 共i.e., 960 h兲 using existing airflow rate
of 12.5 L / s per diffuser via 16 diffusers. Shown are simulated
mechanical efficiency, ␩mech 共%兲, of bubbler 共thick black line兲 and
temperature difference between top and bottom layer 共thin black
line兲, ⌬T 共°C兲.
Fig. 6. Reservoir simulation with bubbler system using initial
profiles on May 25, 1990, measured profiles on July 4, 1990 for
simulation target, and simulated profile of 共a兲 temperature and
共b兲 dissolved oxygen concentration along reservoir depth after
40 days simulation 共i.e., on July 4, 1990兲. Bubbles system was in
operation for 40 days.
bubbler operation as noted by Yang et al. 共1993兲. In Fig. 5共b兲,
simulated DO values agree well with the values at the upper and
bottom part of the reservoir while the DO values deviate from
the measured values in the middle part of the reservoir. However,
the simulated DO values in Fig. 6共b兲 match closely with the measured values except a few points below the mixed layer and near
the reservoir bed. Possible reasons for these deviations could be:
共1兲 unavailability of distribution of algae, COD, and BOD along
the reservoir depth; 共2兲 unavailability of time series water quality
data of river inflows; and 共3兲 it is shown in Figs. 6共a兲 and 7 that
the reservoir is not fully mixed. Note that the annual average
reservoir water quality parameters given in Yang et al. 共1993兲
were used to predict the reservoir DO. The epilimnion layer
关2 m in Fig. 6共b兲兴 is well mixed and is uniform in DO
共6.5 mg/ L兲. Analyzing the hourly simulated DO profile, it was
found that the neutral buoyancy levels of the plume detrainments
were found to be approximately between 4 and 10 m from the
surface. Therefore, increased DO concentrations were observed
at depths between 5 and 10 m depending on the reservoir temperature profile. Because the reservoir profile after 40 days simulation is not fully mixed, a DO depression was observed between
the epilimnion 共2 m兲 and the average neutral buoyancy level
共5.5 m兲. Another important feature of Fig. 6共b兲 is that the DO
profile of the reservoir is approaching homogeneity after 40 days
of bubbler operation. The average DO values of various sources
and sinks of Eq. 共1兲 are demonstrated in Fig. 9 and existing case
共Symbol E兲. Fig. 9 and the existing case 共E兲 illustrate that the DO
contribution from the bubbler system is more significant than
the wind contribution at the surface due to wave breaking and
stirring.
Wüest et al. 共1992兲 and Sahoo and Luketina 共2003b, 2005兲
showed that DO dissolution from air bubbles is optimum for the
cases of bubble radius 共R兲: 0.80⬍ R 艋 1 mm. The ␩mech of the
existing bubbler system is found to be lower than the optimal
␩mech, mostly being less than 1% 共see Fig. 7兲. This is because a
relatively high constant airflow rate 共i.e., 12.5 L / s per diffuser兲
was applied despite ⌬T 共°C兲 共the temperature difference between
the surface and the bottom layer兲 being very low during some
days 共see Fig. 7兲. Therefore, cases are considered here where the
bubbler is operated at the optimal ␩mech. This means that the
airflow rate adjusts in response to changing ⌬T 共°C兲. For reservoir
management using the bubbler, this can be achieved by introduction of an automatic aeration system which would adjust the airflow rate automatically when the temperature probes suspended in
the reservoir/lake detect critical stratification 共⌬T兲 and ⌬DO
level. The reservoir management using the automatic bubbler system is found in Burns 共1998兲 and Simmons 共1998兲.
Proposed Bubbler System for Reservoir Managements
The performances of seven alternate bubbler designs or scenarios,
proposed in Table 2, were examined for 40 days simulation. The
effects of changes in airflow rate, bubble radius, and the number
of diffusers on bubbler ␩mech, reservoir DO, and ⌬T are compared
in Table 2. The work of Sahoo and Luketina 共2003a兲 suggests that
several hundred diffusers would be required for the bubbler to
operate at or near optimal ␩mech. However, for practical purposes,
a air-bubble-diffuser system having 100/ 150 diffusers is assumed
here. A 1 mm bubble radius is used since Wüest et al. 共1992兲 and
Sahoo and Luketina 共2003b, 2005兲 demonstrated that the bubbler
system would transfer maximum oxygen if it operates with
bubble radius 0.80⬍ R 艋 1 mm, and it is relatively difficult to
produce uniformly R ⬍ 1 mm for practical purposes. In some
scenarios, the airflow rate is fixed; while in others, the optimum
␩mech is evaluated every hour based on the newly evolved
temperature profile and the airflow rate corresponding to the
optimum ␩mech is applied for the next hour. It should be noted that
Table 2. Comparison between Eight Cases
Existing
Bubbler design specification
and its operation efficiency
E
Proposed scenarios for reservoir management strategy
S1
S2
S3
S4
S5
S6
S7
Bubble radius 共mm兲
4.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
Numbers of diffusers
16
16
100
100
100
150
150
150
Variableb
Variablec
Variabled
Fixed
Fixede
Airflow behavior
Fixed
Fixed
Variablea
Average airflow rate 共L/s兲 for 960 h
200
200
18.27
51.58
100.39
150.47
150
133.44
0.49
0.49
3.74
2.02
1.40
1.15
1.07
1.20
Average ␩mech 共%兲
Depth average DO 共mg/L兲 after 40 days simulation
4.36
5.41
4.31
4.33
5.67
5.78
5.91
5.75
1.27
1.43
1.11
0.7
0.68
0.33
0.56
0.49
⌬T 共°C兲 after 40 days simulation
14.34
16.14
12.54
7.91
7.68
3.73
6.33
5.54
N2 共⫻10−5 s−2兲 after 40 days simulation
a
Airflow rate is determined every hour based on the newly evolved temperature profile. The bubbler is run at optimal mechanical efficiency, ␩mech 共%兲.
The bubbler is turned off when the temperature difference between the top and bottom layer, ⌬T 共°C兲 falls below 0.2°C.
b
Airflow rate is determined every hour based on the newly evolved temperature profile. The bubbler is run at optimal mechanical efficiency, ␩mech 共%兲,
however, if the airflow rate falls below 0.5 L/s due to very low ⌬T 共°C兲, the bubbler will be operated at 0.5 L/s. The bubbler will be operated continuously.
c
Airflow rate is determined every hour based on the newly evolved temperature profile. The bubbler is run at optimal mechanical efficiency, ␩mech 共%兲,
however, if the airflow rate falls below 1.0 L/s due to very low ⌬T 共°C兲, the bubbler will be operated at 1.0 L/s. The bubbler will be operated continuously.
d
Same as Variablec . Only the number of diffusers is different.
e
Airflow rate is fixed. However, the bubbler is turned off whenever the ⌬T 共°C兲 falls below 0.2°C.
Scenarios 2, 3, 4, and 5 assume that a variable speed compressor
is available. However, for the case of a constant speed compressor, energy could be saved by turning off the bubbler when the
stratification is weak as noted by Simmons 共1998兲 and Burns
共1998兲. This is examined in Scenario 7 by turning off the bubbler
when ⌬T falls below 0.2 共°C兲. On application of Scenario 7, the
total off hours of the bubbler system is found to be 106 during a
960 h simulation period. Therefore the time average airflow rate
during the simulation is estimated as 133.44 L / s 共Table 2兲.
The temperature and DO profiles for the existing bubbler system and seven scenarios are shown in Fig. 8. The temperature
profiles for the existing case and Scenario 1 are similar though the
temperature only near the reservoir bed is found to be higher
共Fig. 8兲. The ⌬T of Scenario 2 is found to be less than ⌬T of
the existing case. ⌬T is further reduced in Scenarios 3, 4, 5, 6, and
7; and is lowest for Scenario 5 共see Fig. 8 and Table 2兲. The
temperature profiles of Scenarios 4, 5, 6, and 7 are relatively
homogeneous compared to the other four cases.
Sahoo and Luketina 共2003a兲 demonstrated that oxygen transfer
is directly proportional to the airflow rate and inversely proportional to the bubble radius. Since the bubble radius in Scenario 1
共1 mm兲 is smaller than bubble radius of the existing case 共4 mm兲,
the DO profile of Scenario 1 is found to be higher than the existing case. However, the DO profile of Scenario 2 is lower than the
DO profile of Scenario 1 and the existing case because Scenario 2
uses a very low airflow rate. For the same reason, the DO profile
of Scenario 1 is higher than the DO profile of the existing case,
and Scenarios 2 and 3. For Scenarios 4, 5, 6, and 7, the depth
averaged DO values are higher than the depth averaged DO value
of Scenario 1 共Table 2兲; however, the DO profile of the upper half
of the reservoir for Scenario 1 is found to be higher than the DO
profile of the upper half of the reservoir for Scenarios 4, 5, 6,
and 7 共Fig. 8兲. Because the reservoir is relatively well mixed for
Scenarios 4, 5, 6, and 7 than the other four cases, DO profiles of
Scenarios 4, 5, 6, and 7 are also relatively homogeneous compared to the other four cases 共Fig. 8兲. For this reason, though the
bubbler contribution from Scenarios 4, 5, 6, and 7 are much
higher than Scenario 1 as illustrated in Fig. 9, the DO profile of
the upper half of the reservoir for Scenarios 4, 5, 6, and 7 is lower
than the DO profile of Scenario 1.
The ␩mech of the existing case and Scenario 1 are found to be
the same 共Table 2兲. This is expected as Sahoo and Luketina
共2003b兲 demonstrated that the ␩mech is invariant to bubble radius
R in the range 0.67⬍ R ⬍ 5.1 mm. Moreover, the mechanical
efficiencies are lower 共only 0.49%兲 because a relatively high
constant airflow rate is applied during the simulation although
⌬T attains low values at times, i.e., the reservoir is relatively
homogeneous. Since the input energy goes unutilized in a homogeneous case except for adding oxygen to the reservoir, the ␩mech
is reduced. The ␩mech for Scenario 2 is found to be significantly
higher than ␩mech of the existing case and Scenario 1 共see Fig. 8兲
because the bubbler is turned off when ⌬T falls below 0.2 共°C兲
and the airflow is adjusted every hour in response to ⌬T when ⌬T
is greater than 0.2 共°C兲. In Scenarios 3, 4, 5, and 6, the bubbler is
operated continuously even though ⌬T may be very small, i.e.,
the reservoir may be quite homogeneous. The ⌬T is reduced further and the DO levels increase as the total airflow rate increases.
However, the ␩mech is reduced because the bubbler uses the minimum airflow rate even though ⌬T is lower; hence the input energy is unutilized except for adding oxygen to the reservoir. In the
case of Scenario 7, the bubbler is turned off when ⌬T falls below
0.2 共°C兲. For this reason, the ␩mech of Scenario 7 is found to be
higher than Scenarios 5 and 6.
Total DO contribution to the reservoir ambient water from
the various sinks 共BOD, COD, and SOD兲 and sources 共bubbler,
atmosphere, and algae兲 during a 960 h simulation are shown
in Fig. 9, which also shows the time-averaged ␩mech of bubbler
systems for all scenarios. It is seen that in terms of oxygen contribution to the reservoir water, the bubbler dominates nearly
600–1,100 times the atmospheric contribution and 100–300 times
the algal contribution. Because of low wind speed patterns that
occur in Upper Peirce Reservoir, the surface reaeration contribution to reservoir water is found to be low. This means that the
dissolved oxygen concentration in the reservoir can be reasonably
increased only by operating an air-bubbler system at a higher
airflow rate than that associated with optimal ␩mech.
It is clear from Fig. 9 and Table 2 that for all the proposed
scenarios, the bubbler DO contribution increases as airflow rate
increases to around 50 L / s while the ␩mech decreases. When the
airflow rate is increased beyond 50 L / s, the time-averaged ␩mech
Fig. 8. Mixing and DO patterns of reservoir when the bubbler
is operated for 40 days. Shown are simulated 共a兲 temperature and
共b兲 DO concentration profiles of existing case 共thick black line兲,
Scenario 1 共medium black line兲, Scenario 2 共thin black line兲,
and Scenario 3 共thick gray line兲, respectively; and simulated
共c兲 temperature and 共d兲 DO concentration profiles of Scenario 4
共thick black line兲, Scenario 5 共medium black line兲, Scenario 6 共thin
black line兲, and Scenario 7 共thick gray line兲, respectively. Notes on all
scenarios are given in Table 2.
decreases rapidly while the time-averaged DO concentration increases gradually. The existing case has a lower DO than the
proposed 4, 5, 6, and 7 scenarios because the existing case uses a
relatively large bubble radius 共4 mm兲.
Table 2, and Figs. 8 and 9 show that all proposed scenarios
are found to be better than the existing case in terms of ␩mech,
lower airflow rate consumption, and hence higher energy
savings, and higher destratification rate 共i.e., lower ⌬T and
lower reservoir stability frequency N2兲. The stability 共i.e.,
buoyancy兲 frequency N2 is defined as N2 = −共g / ␳r兲共d␳ / dz兲, where
␳r 共kg m−3兲⫽reference density and g⫽9.81 共m s−2兲. However, in
terms of DO contribution, Scenarios 1, 4, 5, 6, and 7 are found to
be better than the existing case. For Scenarios 4, 5, 6, and 7,
the reservoir is relatively homogeneous, and the DO values of
the hypolimnion layer are well above 4 mg/ L. Other important
features of Table 2 and Fig. 9 are that although the total airflow
rate of Scenario 1 is higher than Scenarios 4, 5, 6, and 7 and all
proposed scenarios use a bubble radius of 1 mm, the performance
efficiencies in terms of total DO contribution and overall
destratification of Scenario 1 are lower than those of Scenarios 4,
5, 6, and 7. Schladow 共1992兲 and Sahoo and Luketina 共2003a兲
demonstrated that for a high airflow rate per diffuser compared to
ambient stratification, the bubbler ␩mech and mixing effectiveness
reduce because the plume entrainment rate reduces. Most of the
input energy is wasted making turbulence at the surface as
illustrated in Asaeda and Imberger 共1993兲. Similarly, Sahoo
and Luketina 共2003b兲 showed that oxygen dissolution efficiency
decreases for a high airflow rate compared to ambient stratification, because the air bubbles move faster, thus air bubble contact
time with the ambient water decreases. Besides this, Scenario 1
Fig. 9. Total dissolved oxygen contributed to or consumed from
ambient water for 960 h 共i.e., 24 days兲 of reservoir-bubbler model
simulation for scenarios described in Table 2 and a case without
bubbler system. Positive and negative values represent sources
共bubbler, algae, and atmosphere兲 and sinks 共BOD, COD, and SOD兲,
respectively. Shown are 960 h average mechanical efficiencies, ␩mech
共%兲, 共thick black line with hollow diamond兲 of bubbler systems. E*
and E represent cases without bubbler system and with existing
bubbler system, respectively.
uses a bubbler system with 16 diffusers and an airflow rate of
12.5 L / s per diffuser; thus, the performance efficiency of the
bubbler system is found to be lower. In addition to air bubble
radius and airflow rate per diffuser, selection of the total number
of diffusers of the bubbler system is an important parameter in
bubbler design.
It should be noted that the energy expended by a variable
compressor is directly proportional to the airflow rate 共Sahoo and
Luketina 2003a兲, i.e., the relative operating cost of a compressor
is directly proportional to the airflow rate. Therefore, for a constant speed compressor, Scenario 7 is found to be optimum in
terms of ␩mech and low airflow rate consumption, though the DO
contribution is slightly lower. Although Burns 共1998兲 did not go
through all these analyses, he reported having an air-bubblediffuser system installed with the above mentioned concept. However, for a variable speed compressor, the proposed Scenario 5 is
found to be the most appropriate.
Conclusions
1.
2.
3.
This paper describes a reservoir-bubbler model and examines
the different bubbler design criteria based upon the effects of
bubbler operation on mixing and dissolved oxygen pattern in
the Upper Peirce Reservoir, a tropical reservoir in Singapore,
where a bubbler system is in operation.
It is illustrated that the coupled model can predict the
temperature stratification and dissolved oxygen level in a reservoir with acceptable accuracy. Application of the coupled
reservoir-bubbler model to the reservoir shows that the existing bubbler system installed in the reservoir is not running at
optimal ␩mech.
It is shown that the selections of airflow rate per diffuser,
bubble radius, and total number of diffusers are important
4.
5.
6.
7.
design criteria of a bubbler system. Some scenarios are examined in terms of bubbler ␩mech and total DO contribution.
However, the overall bubbler design depends on the reservoir
size and stratified area of interest, ambient climate, and water
quality of river inflows.
For the tropical reservoir case considered here with low wind
speed patterns when compared to all other sources, including
surface aeration, the bubbler operation dominates oxygen
transfer to the reservoir water. High airflow rates contribute
the most oxygen, however, the operating cost increases as
airflow rate increases. This means that a bubbler should
never be operated at an airflow rate lower than that associated with the optimum ␩mech unless the reservoir is close to
well mixed. When the reservoir is close to being well mixed,
the water quality is usually reasonably good but the bubbler
operates at a very low ␩mech—thus the bubbler should be
turned off.
If only a fixed speed compressor is available with an airflow
rate that is higher than Scenario 7 showed, it is better to turn
off the bubbler when the stratification is weak 共⌬T⬍2°C兲.
This will result in substantial energy savings with only a
small reduction in DO levels.
If improving water quality 共in terms of high DO levels兲 is the
primary objective, then the airflow rate can be determined
using a figure similar to Fig. 9 in order to increase the DO
concentration to a desired level at an appropriate operating
cost. Such figures can be produced using modeling methods
where a bubbler and reservoir model are combined.
The reservoir-bubbler model presented here has not been
validated for other reservoirs. However, the writers believe
that the reservoir-bubbler model may only need little modification to predict the DO and temperature profile for another
reservoir with acceptable accuracy. Also, the writers believe
that no study is complete in itself and there are always scopes
for improvement and the work presented herein will serve as
the basis of further research.
Acknowledgments
The France Government Scholarship awarded to the first writer
is gratefully acknowledged. The writers gratefully acknowledge
the three anonymous reviewers for their valuable comments and
suggestions to improve quality of the paper.
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