NUMERICAL MODELING OF HYPOLIMNETIC OXYGENATION BY ELECTROLYSIS OF WATER

Transcription

1 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... S679 NUMERICAL MODELING OF HYPOLIMNETIC OXYGENATION BY ELECTROLYSIS OF WATER by Nenad M. JAĆIMOVIĆ a, Takashi HOSODA b, Ho-Don PARK c, and Marko V. IVETIĆ a a Department of Hydraulic and Environmental Enineerin, Faculty of Civil Enineerin, University of Belrade, Belrade, Serbia b Kyoto University, Kyoto, Japan c Shinshu University, Matsumoto, Japan Oriinal scientific paper The paper presents a novel method for hypolimnetic oxyenation by electrolysis of ater. The performance of the method is investiated by the laboratory and the field experiment. The laboratory experiment is conducted in a 90 L vessel, hile the field experiment is conducted at the lake Bia in Japan. In order to provide a better insiht into involved processes, a numerical model for simulation of bubble flo is developed ith consideration of as compressibility and oxyen dissolution. The model simultaneously solves 3-D volume averaed to-fluid overnin equations. Developed model is firstly verified by simulation of bubble flo experiments, reported in the literature, here ood qualitative areement beteen measured and simulated results is observed. In the second part, the model is applied for simulation of conducted ater electrolysis experiments. The model reproduced the observed oxyen concentration dynamics reasonably ell. Key ords: eutrophication, electrolysis, oxyenation, numerical model Introduction Eutrofication is a natural process of primary production increase in lakes, hich may lead to severe deterioration of ater quality [1-3]. These processes are sinificantly affected by thermal stratification [4-6], due to formation of density and temperature structure consistin of relatively homoeneous surface ater layer hich is separated from the deep hypolimnion zone by a layer ith the stron temperature radient, referenced as metalimnion. The metalimnion has effective role of barrier that prevents exchane of dissolved oxyen (DO) from the surface layer. Due to excessive release of nutrients by human activities, this process is sinificantly accelerated and, in extreme cases, to anoxic conditions [7-9]. Lo levels of DO have extremely neative consequences on ecoloical status, as ell as on drinkin ater treatment process in the case of ater supply reservoirs [10]. This includes production of hydroen sulfide and ammonia, and may lead to reactivation of heavy metals and nutrients from the sediment [11, 12]. * Correspondin author, nacimovic@hikom.rf.b.ac.rs

2 S680 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... One of available lake restoration strateies is hypolimnetic oxyenation, ith idea to replenish the DO by aeration, hile preservin the thermal stratification [13-19]. Gafsi et al. [16] concluded that aeration by oxyen has sinificant advantaes in comparison ith aeration by air. In this case, very efficient oxyen transfer can be achieved. In this paper e propose a novel technoloy, hich includes electrolysis of ater at the lake bottom, ith oxyen dissolution and possible hydroen harvestin for further enery purposes. For simulation of the processes associated ith the proposed technoloy, a numerical model for bubble flo simulation is developed, ith the consideration of as compressibility and oxyen dissolution. The model has the aim to provide a better insiht into the processes related ith oxyen bubble production and its dissolution in the ater. The model solves 3-D volume-averaed, to-fluid overnin equations. The developed model is verified by simulation of bubble flo experiments, previously reported in the literature. Different flo confiurations are tested: in hich quasi-steady state is achieved, and here steady conditions can not develop. In the second part, the model is applied for simulation of the conditions achieved in the electrolysis laboratory and field experiments conducted in this study. This is a ne approach aimed at providin the oxyen directly from the ater. Experimental study The experimental study of electrolysis effects on DO rehabilitation has been performed in the laboratory (at the Shinshu University) and in the field conditions. The laboratory set-up consisted of the 90 L transparent vessel, ith 56.6 cm ater depth. The electrolysis apparatus (7.0 cm in heiht) consists of seven pairs of platinum plates (20 7 cm), placed at the middle of the vessel bottom. Direct current of 2.3 A is applied, and transient DO concentrations are measured at different levels, in the center of horizontal plane section. Control levels are at 25 cm, 35 cm, and 45 cm from the vessel bottom. The as phase (hydroen and oxyen) is uniformly produced at the 7.5 cm above the bottom, at the horizontal area cm. The volume of produced oxyen by electrolysis is calculated from the Faraday s la: 24.8L/mol 2.3A L/s As/mol hich, expressed per minute at 1.05 atm pressure, ives L/min. The volume of produced hydroen may be considered as double of this value. After imposin the current throuh the electrolysis setup, a stream of hydroen and oxyen bubbles, due to buoyancy, starts to flo upard. This stream entrains the surroundin ater phase, hich causes circulation of the ater, fi. 1. The electrolysis produced the sinificant increase of DO concentrations, hile the induced ater circulation enhanced its dispersion. As a result, relatively uniform DO distribution is observed ithin the vessel, reachin the DO limit in nearly 8 hours (from initial 2 m/l to final 13.5 m/l). The field experiment has been conducted at the lake Bia in Japan by the Lake Bia Environmental Research Center, Shia Prefectural Government. Installation consisted of the plexilas box ith dimensions cm. The box bottom as open and the top of the box as partially closed ith the to 17 3 cm openins at the top cover. Three electrolysis devices ere placed at the box bottom, in the middle of the box lenth, fi. 2. The purpose of the box as to attenuate lateral currents and to accelerate the experiment by reducin the volume of influenced ater.

3 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... S681 Fiure 1. Experimental set-up for electrolysis experiment in the laboratory (for color imae see ournal ebsite) The ater column as relatively homoeneous reardin the temperature distribution (14.5 C). Other ater quality parameters ere observed as follos: ph = 5.8, Cond = = 18.5 ms/m, Turb = 6.1 NTU, TDS = 0.12 /L and oxidation reduction potential ORP = 89 mv. Durin the experiment, the hydroen bubbles ere captured ith the plastic covers and removed from the box by pipes. The ater depth at the experiment site as 10 m. The DO concentration as measured 38 cm belo the box cover (Horiba W-23XD monitorin system), at the middle of the smaller vertical all, 2.5 cm from the all. The direct current of 7.71, 7.91, and 8.05 A as imposed on three devices respectively. Takin into account ater pressure at 10 m of ater column, calculated total oxyen production as L/min. After imposin the current, the DO concentration as continually observed. The recorded increase of DO concentration as approximately linear ith the time. After 87 minutes, the DO concentration increased from initial 0.4 m/l to 6.4 m/l. Outline of the numerical model Several approaches have been proposed in the literature for bubble plumes modelin. The most often applied are models based on 1-D, transversally interated equations and self-similar solutions [17-21]. They provide a simple and robust tool for estimation of mechanical efficiency (mixin rate) and oxyen transfer, if considered. Naturally, such models can not account for possible crossflo effects and oxyen transfer by lo level aeration. Bernard et al. [22] proposed relatively simple 3-D sinle-phase model ith the implementation of turbulence effects. In their model, authors idealized the bubble plume as a cylindrical volume ithin hich all bubbles remain and rise vertically by the assumed slip velocity. As authors pointed out, the model is not applicable in the stratified environment, due to uniform bubble column approximation. To phase models [23-26] provide a better insiht into the effectiveness of the applied aeration technoloy. Here, several approaches are possible for couplin the as and ater phases: (1) Eulerian-Eulerian (EE), (2) Eulerian-Laranian (EL), here as bubbles are treated as Laranian markers, and (3) Interface trackin method, in hich a numerical method has to be applied for trackin of the boundary beteen to phases. The ell knon Volume of Fluid (VOF) [27] method may be considered as a representative for this approach. In the pioneerin ork of multidimensional, to phase modelin of bubble plumes, Sokolichin and Eienberer [23] considered EE and EL methods, and concluded that EL app-

4 S682 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... (a) (b) Fiure 2. (a) Schematic representation of the field experiment; (b) Three electrolysis devices installed at the box bottom (for color imae see ournal ebsite) roach potentially have advantaes in lare scale eometry. Hoever, a detailed computational comparison [28] revealed that EE based models provide similar results as EL models in terms of accuracy of averae flo quantities. Fraa et al. [26] proposed recently an advanced lare-eddy simulation (LES)-based EL model for simulation of bubble plume dynamics hich is applied to the simulation of laboratory experiments. They concluded that bubble-induced turbulence eneration may play an important role and should be further investiated. Hoever, the real scale application of the model, e.. for hypolimnetic aeration of stratified lakes, is not discussed. In this study a to-phase EE model is proposed, based on the volume-averaed Raynolds-averaed Navier-Stokes equations (VARANS). Considerin compressibility of the as phase, and the mass transfer beteen the phases, continuity equations for the as and the ater phase can be obtained by the volume averain (e.. [29]): V t t x V x G G (1) (2) 1 (3) here subscripts and denote as and ater phase, respectively, x is the Cartesian coordinate, t is the time, is the phase density, is the phase content, V is the component of velocity vector and G is the mass transfer beteen to phases, per unit time and volume. It is assumed that density of the as phase comply ith the ideal as la: p m (4) RT here p is the as pressure, m is the as molar mass, T is the absolute temperature, and R is the as constant (= LatmK 1 mol 1 ).

5 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... S683 Dissolution of oxyen into the ater phase is modeled as a first-order process, proposed by Wuest [18]: G K A H p DO (5) here K is the mass transfer coefficient, A is the as-ater surface area, H is the dimensional Henry s constant, and DO is the dissolved oxyen. Durin the buoyancy-forced flo of bubbles, their size is chanin due to pressure chane, as ell as due to dissolution. In order to model this chane, a number of bubbles is updated at each time step by solution of the folloin advection equation: N b t NbV x here N b is the number of bubbles per unit volume. Bubble diameter is calculated from the as content and number of bubbles, and it is utilized to calculate the dra force and as-ater surface area throuh hich the oxyen mass transfer occurs. Volume averaed momentum equations can be formulated as: V V V t i x i 0 p x i V ViV p 1 i i i F i 1 i t x x x in hich i is the component of ravitational acceleration, i is the shear stress, includin viscous and turbulent effects, and F is the momentum interaction term [29]. The latter is modeled considerin three components: F F (6) (7) (8) Fd Fam Fl (9) here F d is the dra force, F am is the added mass force, and F l is the lift force. These forces are calculated as follos: F d 2 b 1 d Cd V V V V 2 4 (10) DV DV F am Cv Dt Dt (11) l v ( V V V (12) F C ) here C d is the dra coefficient, d b is the bubble diameter, C v is the coefficient, and is the diverence operator. The dra coefficient is calculated as a function of Reynolds and Eotvos numbers [30]: Eo Re,, 24 C d max (13) Re 3 Eo 4

6 S684 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... Presented overnin equations are discretized by finite volumes ith staered arranement of flo variables. Pressure and velocity fields, at each time step, are calculated usin the Hihly Simplified Marker and Cell (HSMAC) method [31], ith application of Adams-Bashforth scheme for time interation of convective and viscous terms in momentum equations. For solution of continuity eqs. (1) and (2), as ell as eq. (6), a hiher order approach is utilized by linear interpolation of variables and application of TVD limiters [32], in order to prevent oscillations and to minimize numerical dispersion effects. Sokolichin and Eienberer [33] analyzed applicability of the standard k- turbulence model for simulation of bubble plumes. The simulation of experiments conducted in laboratory vessels revealed very ood qualitative and acceptable quantitative predictions; in spite the fact that bubble induced turbulence as not considered. They emphasized the sensitivity of results to the approximation of the convective terms in the model formulation. Buscalia, et al. [25] arued that the to-phase, bubble induced turbulence closure is still far from the clear resolution, althouh some authors have proposed corrections to the k-equations to account this effect. Recent studies reveal that bubbles induce sinificant turbulence of anisotropic nature, even at lo Reynolds numbers [34]. In this study, e applied a non-linear k-turbulence model [35]. No corrections for bubble induced turbulence are included: 2 k 3 1 uu i tsi ki t C Si Si (14) 2 k t C (15) k ku ui t k uu i t x x x k x 2 u ui t C1 uu i C2 t x k x k x x S i ui x u x i (16) (17) (18a) u u 1 i u u r ur u i ur ur S1i, S2i, S3i xr xr 2 xi xr x x (18b) r xi x here uu is the Reynolds stress, k the turbulent kinetic enery, the dissipation rate, and i t the eddy viscosity coefficient. The model coefficient C is a function of strain and rotation parameters, as described ith model parameters in the reference [35]. For simulation of DO dissolution/transport in the ater, an additional DO transport equation has to be solved: DO t x here D is the effective dispersion coefficient. DO DOV D G x x (19)

7 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... S685 Electrolysis produces hydroen and oxyen in the 2:1 molar ratio. In the laboratory experiment simulated in this study, hydroen is not removed after bubble-up at the cathode, and therefore, it affects flo and distribution of oxyen bubbles, as ell as DO distribution. In order to track hydroen and oxyen number of bubbles, eq. (6) is solved separately. Since the size of hydroen and oxyen bubbles is not the same, for calculation of the momentum interaction term in eqs. (7) and (8), the volume-eihted representative diameter is calculated from available volumetric contents: do2 O2 dh H db (20) here d is the representative bubble diameter, α b O2 and α H are volumetric contents of oxyen and hydroen, respectively, d O2 is the oxyen bubble diameter and d H is the bubble diameter of hydroen. Model validation Simulation of air-flo/distribution durin its constant rate inection As an addition to already reported simulation results [36], the model performance reardin flo and air distribution is validated by application to another reported experiments [37], conducted in a flat bubble column 50 cm ide, 200 cm hih, and 8 cm thick. Air sparer as centered at the bottom, throuh hich different air inection flo rates ere applied in different experiments. The ater level in the column is also varied for different experiments. Bubble plumes ere visually observed throuh transparent column alls. In addition, a Laser Doppler Anemometer as used to measure velocity manitudes of the ater phase in the midplane of column depth (4 cm from the alls), at reular rid points (10 cm or 20 cm apart). In the first case, the experiment ith 100 cm ater depth is simulated. Air flo rate is 1.0 L/min. Simulation domain is discretized by calculation cells, and simulation time step of s is adopted. The air bubble diameter is taken as uniform in the plume, 4 mm as averae observed durin experiments [37]. In this case, it is reported that no steady flo conditions could be established. Periodic flo ith to staered ros of vortices movin donard as observed, due to hich the bubble plume also periodically bends. This behavior is reproduced ell by numerical model. Fiure 3 shos the bubble at one time section. Left fiures sho observed bubble plume, hile middle and riht fiures sho calculated air distribution and velocity vectors of the ater phase. The model reproduced the dynamics of bubble plume bendin very ell. In the second case, the experiment ith ater level at 50 cm from the bottom is chosen. Air-flo rate is 2.0 L/min. Simulation domain is discretized by cells, and simulation time step of s is adopted aain. Dependin on the start-up conditions, the authors reported formation of a sinle vortex, near the center of the flo domain, in the clockise or counter clockise direction. Quantitative comparison of simulated and measured velocities for quasi-steady conditions is shon in fi. 4. Good overall areement of the developed flo field can be observed. The flo is characterized by a sinle, almost centrally placed, vortex ith near stanant ater in the top and bottom riht corners. Simulation of the laboratory electrolysis experiment For the numerical simulation of the laboratory experiment conducted in this study, the domain is discretized by rectanular cells ith 5 5cm rid size in the horizontal plane,

8 S686 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... Fiure 3. Comparison of observed and simulated bubble plumes for to time sections at 1 L/min air flo rate Fiure 4. Comparison of observed and simulated velocity mid-profile for steady conditions at 2 L/min air-flo rate; (a) reported ater phase velocities (after [37]), (b) simulation results and varyin size in vertical direction: from 5 cm at the bottom, to 1.2 cm at the ater surface. The total volume of ater is 90.6 L. The startin diameter of the as bubbles is assumed as 0.1 mm. Consequently, mass transfer coefficient in eq. (5) is taken as m/s. This coefficient depends on bubble size, hoever, in this study it is taken as a constant, assumin that bubble size does not chane sinificantly. Prior the electrolysis, measured DO concentrations ere 0 m/l at 25 cm, m/l at 35 cm, and m/l at 45 cm from the bottom. After the start of electrolysis, recorded values shoed that DO increased very fast at 35 cm and 45 cm levels. After 2 minutes, measured DO concentration as 2.96 m/l at 35 cm, and 3.78 m/l at 45 cm. Such a lare increase of DO in a short period of time, after start of electrolysis, could not be resolved by model described by eq. (5). Therefore, in the simulation described here, a uniform initial DO concentration of 2.0 m/l as applied. This is the reason for discrepancy beteen measured and calculated DO in the early stae of experiment. The areement in the later stae is ood, as shon in fi. 5. Fiure 5. Comparison of simulated and calculated DO values; (a) at 25 cm, (b) at 35 cm, and (c) at 45 cm, from the bottom center

9 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... S687 Experimental results indicate and numerical simulation confirmed intensive mixin due to induced ater circulation, resultin in uniform distribution of the DO. That is the reason the fi. 5 contains only one line representin the simulation results. The size of released bubbles certainly has the influence on the dynamics of the DO increase. This is not a linear correlation, since the mass transfer coefficient is also function of the bubble diameter. The effect of the bubble size on DO increase in the simulated experiment is shon in fi. 6, for the first 100 minutes after the start of electrolysis. A sinificant difference beteen simulations can be observed. All three computations are conducted ith the same mass transfer coefficient. In reality, the difference is probably less pronounced than shon here, due to the increase of the mass transfer coefficient ith increase of bubble diameter. Fiure 6. Simulation of DO increase at 25 cm from the bottom center, as a function of the size of released oxyen bubbles Simulation of the electrolysis field experiment The simulated flo domain is the box itself and surroundin ater, 60 cm around the box in the horizontal directions and the ater column above the box up to the ater surface (9 m). The molar volume of oxyen, at this pressure, is taken as 11.2 L/mol. Startin bubble diameter, as ell as mass transfer coefficient is taken the same as in the simulation of the laboratory experiment. Hoever, the Henry s constant is multiplied by 2, since 10 m of ater column represents approximately an additional atmosphere of pressure. The initial DO concentration in the hole domain as imposed as 0.4 m/l. The experimental box is discretized by rectanular cells varyin in size, from cm near the alls up to cm. The experiment is utilized to compare the standard k- turbulence model ith the here presented the non-linear k- model. The non-linear k- models are attractive for the computations of flos influenced by anisotropy of the turbulence [34]. Therefore, it as interestin to analyze the difference in the case of the eak bubble plume flo, as in the case of electrolysis experiments presented here. The same mesh, boundary and initial conditions ere applied for both calculations. Calculated DO concentrations, at the location of the measurement probe, durin the experiment are shon in fi. 7. The numerical model revealed the circulation flo pattern similar as in the laboratory experiment, hich produces relatively uniform DO distribution, ith slihtly hiher concentrations above the electrolysis plates and near the side alls of the box. It can be seen that DO concentrations increase approximately linearly and that both

10 S688 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... models reproduce the dynamics relatively ell. Unfortunately, the experiment did not last enouh to reach the limit value of DO concentration. The linear k-model produced slihtly hiher concentrations throuhout the simulation time in comparison ith the non-linear one. Fiure 8 compares calculated turbulent kinetic enery at the middle profile, at the level of the probe and at the to time sections. It is expected to obtain the hihest values in the reion of stronest chanes in liquid velocities [32]. While the distribution of the kinetic enery of turbulence is very similar, the non-linear k-model produced hiher values of the eddy viscosity, ith the difference reachin the 50% Measured Linear k E NonLin k E DO (m/l) Time (min) Fiure 7. Comparison of measured and calculated DO concentrations at the location of the probe durin the experiment (a) (b) Fiure 8. Comparison of the standard and the non-linear k- model results; (a) turbulence kinetic enery horizontal profiles at the level of the DO probe, (b) Eddy viscosity at the same profiles. The lenth is presented as non-dimensional, by dividin the distance from the vertical all ith the box lenth Conclusions In this paper e propose electrolysis as a novel hypolimnetic oxyenation tool. Due to the small bubble diameter produced, it shoed to be very effective reardin dissolution of oxyen. If combined ith hydroen harvestin for enery purposes, it may even be economically viable. Hoever, its applicability requires further experimental and modelin ork to be

11 Ja}imovi}, N. M., et al.: Numerical Modellin of Hypolimnetic Oxyenation by... S689 done. In that respect, a 3-D numerical model for simulation of bubble plumes for DO recovery has been developed. Model is validated by simulation of bubble plume experiments reported in the literature, as ell as on conducted electrolysis experiments. Considerin natural complexity of simulated processes and a number of adopted approximations in mathematical description, it can be concluded that developed model reproduced experiments of DO recovery reasonably ell. The model experiments revealed sinificant sensitivity of DO recovery efficiency to initial bubble size. Therefore, additional research efforts are required to determine the initial bubble size of electrolysis and possible influence of physicochemical conditions. In reard of utilized turbulence model, it can be concluded that both models produced the similar DO concentration dynamics. References [1] Wetzel, R. G., Limnoloy, W. B. Saunders Company, Philadephia, Penn., USA, 1975 [2] Codd, G. A., Cyanobacterial Тoxins, the Perception of Water Quality, and the Prioritisation of Eutrophication control, Ecoloical Enineerin, 16 (2000), 1, pp [3] Cao, H. S., et al., Eutrophication and Alal Blooms in Channel Type Reservois: a Novel Enclosure Experiment by Chanin Liht Intensity, J. Environ. Sci., 23 (2011), 10, pp [4] Elci, S., Effects of Thermal Stratification and Mixin on Reservoir Water Quality, Limnoloy, 9 (2008), 2, pp [5] Ranel-Peraza, J., et al., Modelin Approach for Characterizin Thermal Stratification and Assessin Water Quality for a Lare Tropical Reservoir, Lakes & Reservoirs: Research & Manaement, 17 (2012), 2, pp [6] Ma, W. X., et al., Study of the Application of the Water-Liftin Aerators to Improve the Water Quality of a Stratified, Eutrophicated Reservoir, Ecoloical Enineerin, 83 (2015), Oct., pp [7] Jones, R. A., Lee, G. F., Recent Advances in Assessin Impact of Phosphorus Loads on Eutrophication- Related Water Quality, Water Research, 16 (1982), 5, pp [8] Smith, V. H., et al., Eutrophication: Impact of Excess Nutrient Inputs on Freshater, Marine, and Terrestrial Ecosystems, Environmental Pollution, 100 (1999), 1-3, pp [9] Sylvan, J. B., et al., Eutrophication-Induced Phosphorus Limitation in the Mississippi River Plume: Evidence from Fast Repetition Rate Fluorometry, Limnoloy and Oceanoraphy, 56 (2007), 6, pp [10] McGinnis, D. F., Little, J. C., Predictin Diffused-Bubble Oxyen Transfer Rate Usin the Discrete- Bubble Model, Water Research, 36 (2002), 18, pp [11] Beutel, M. W., et al., Effects of Aerobic and Anaerobic Conditions on P, N, Fe, Mn and H Accumulation in Waters Overlayin Profundal Sediments of an Olio-Mesotrophic Lake, Water Research, 42 (2008), 8-9, pp [12] Bryant, L. D., et al., Solvin the Problem at the Source: Controllin Mn Release at the Sediment-Water Interface via Hypolimnetic Oxyenation, Water Resources, 45 (2011), 19, pp [13] Little, J. C., Hypolimnetic Aerators: Predictin Oxyen Transfer and Hydrodynamics, Water Research, 29 (1995), 11, pp [14] Janczak, J., Koalik, A., Assessment of the Efficiency of Artificial Aeration in the Restoration of Lake Goplo, Limnoloical Revie, 1 (2001), 3-4, pp [15] McGinnis, D. F., et al., Interaction Beteen a Bubble Plume and the Near Field in a Stratified Lake, Water Resources Research, 40 (2004), 10, pp. W W [16] Gafsi, M., et al., Comparative Studies of the Different Mechanical Oxyenation Systems Used in the Restoration of Lakes and Reservoirs, J. of Food, Aricalture & Environment, 7 (2009), 2, pp [17] Schlado, S. G., Bubble Plume Dynamics in a Stratified Medium and the Implications for Water Quality Amelioration in Lakes, Water Resour. Res., 28 (1992), 2, pp [18] Wuest, A., et al., Bubble Plume Modelin for Lake Restoration, Water Resour. Res., 28 (1992.), 12, pp [19] Sahoo, G. B., Luketina, D., Modelin of Bubble Plume Desin and Oxyen Transfer for Reservoir Restoration, Water Research, 37 (2003), 2, pp

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