Listen

The production of total dissolved gas (TDG) supersaturation resulting from dam discharges has been identified as a causative factor for gas bubble disease (GBD) or mass mortality in fish. In this study, the mitigation solution for fish refuge in supersaturated TDG water was explored by using microbubbles generated by aeration to enhance supersaturated TDG dissipation. The effects of various aeration factors (aeration intensity, water depth, and aerator size) on the dissipation processes of supersaturated TDG were quantitatively investigated through a series of tests conducted in a static aeration column. The results indicated that the dissipation rates of supersaturated TDG increased as a power function with the factors of aeration intensity and aerator size and decreased as a power function with increasing water depth. A universal prediction model for the dissipation rate of supersaturated TDG in the aeration system was developed based on the dimensional analysis of the comprehensive elements, and the parameters in the model were determined using experimental data. The outcomes of this study can furnish an important theoretical foundation and scientific guidance for the utilization of aeration as a measure to alleviate the adverse impacts of supersaturated TDG on fish.

Listen

  • Conducting the supersaturated TDG dissipation experiment in a fine-bubble aeration column.

  • Investigating the impact of different aeration conditions on supersaturated TDG dissipation behavior.

  • Establishing a correction between the dissipation coefficients and different aeration conditions.

  • Developing a dissipation coefficient prediction model for universal aeration systems.

  • Fish biodiversity preservation in river systems.

aeration conditions, dissipation coefficient, mitigation measure, prediction model, total dissolved gas supersaturation
Listen

Total dissolved gas (TDG) supersaturation occurs when the partial pressure of gases in a solution exceeds the surrounding atmospheric pressure (Colt 1984), and this condition can be produced by diverse natural and artificial factors, for instance, a sudden rise in temperature, strong photosynthesis of algae in the water, and flood discharge in dams (Weitkamp & Katz 1980). In recent decades, with more and more hydropower facilities being constructed and put into operation, TDG supersaturation has received tremendous attention worldwide and has been identified as one of the potential impact factors for limiting the biodiversity in the riverine systems (Pleizier et al. 2020). A vast number of air bubbles are entrained by the water flow during the spill discharge and delivered into the bottom regions of the downstream stilling basin, those entrained air bubbles will be driven to excessive dissolution under the conditions of high hydrostatic pressure and strong turbulence intensity in the stilling basin, resulting in supersaturated TDG generation (Geldert et al. 1998; Li et al. 2009). The recovery rate of TDG in rivers from the supersaturated state to the equilibrium saturated state is very slow under natural conditions. For example, the mean recovery rate is only 4.3% per 100 km over a distance range of 600 km downstream of the Three Gorges Project under an initial TDG percent saturation of 143% (Qu et al. 2011). Fish that have been exposed to supersaturated TDG water for extended periods of time will suffer from gas bubble disease (GBD), which increases the risk of sublethal effects or large-scale mortality (Arntzen et al. 2009; Chen et al. 2012; Wang et al. 2020). To prevent the riverine ecosystem from being damaged by the supersaturated TDG, a threshold frequency of TDG percent saturation of 115% has been set by the USEPA (United States Environmental Protection Agency 2020) in the Water Quality Standard (WQS) as the minimum requirement for the survival of aquatic life.

Reducing TDG production at hydropower plants is a feasible strategy to mitigate the damage to fish and other aquatic organisms from supersaturated TDG, and the relevant measures mainly include engineering or operational solutions. For instance, a previous study reported that installing a flow deflector on the spillway face can decrease the angle of entering the water for plunging flow, which results in minimizing the submergence depth of entrained bubbles and air bubble dissolution in the stilling basin (Orlins & Gulliver 2000). Installing baffle blocks in the stilling basin is another engineering measure for reducing TDG production (Huang et al. 2021). This measure works by redirecting the water flow, which transports entrained bubbles to regions of lower pressure at the water surface. The numerical simulation results show that the maximum reduction in TDG production saturation can be achieved by approximately 20% when the flow deflectors or baffle blocks are installed in the actual hydropower facilities compared with the conditions without those configurations (Wang et al. 2019; Huang et al. 2021). However, the widespread applications of the above engineering methods may be limited to use in low-dam projects since the potential adverse effects of those configurations on the structural safety of high-dam projects are still unclear. Additionally, many operational strategies were proposed by many researchers to reduce TDG production based on the numerical simulation method. For example, a previous study by Politano et al. (2012) proposed that concentrating the discharge flow in one spillway could cause the entrained bubbles to migrate closer to shallower water depths than the conditions of spreading it across multiple spillways, which could obtain a lower TDG production level. To reduce the risk of cumulative effects of TDG supersaturation in cascade reservoirs, Feng et al. (2014) and Ma et al. (2019) suggested using an interval-discharge strategy rather than a continuous-discharge strategy to lower the geographical distribution of high TDG levels in downstream reservoirs. Similarly, Wan et al. (2021) reported that the TDG production level and the detention time of supersaturated TDG in downstream rivers could be effectively decreased by employing the flood pulse discharge patterns. The problem of gas supersaturation in hydroelectric plants cannot be completely eliminated due to the requirements for flood prevention, and the generated TDG has the characteristics of high saturation and a far-reaching impact on the downstream rivers, especially in high-dam projects. Therefore, it is necessary to combine various mitigation strategies to minimize the risk of fish being exposed to supersaturated TDG.

Previous studies demonstrated that fish could detect and avoid the supersaturated TDG on their own (Wang et al. 2015; Pleizier et al. 2020). Based on this, another strategy for mitigating the negative impacts of supersaturated TDG on the riverine systems is to create a lower TDG saturation region in downstream rivers for providing fish with temporary shelter from the supersaturated TDG. The critical problem in this mitigation strategy is obtaining a method that can rapidly accelerate the supersaturated TDG dissipation. Supersaturated TDG dissipation is the gas–liquid mass transfer process with a transition from a supersaturated state to a stable equilibrium state, and the dissipation rate depends on turbulence intention, gas–liquid interface area, and the environmental factors (e.g., temperature and atmospheric pressure) (Shen et al. 2014). Based on the understanding of the dissipation mechanism of supersaturated TDG, some methods have been proposed to accelerate the dissipation process of supersaturated TDG, e.g., decompression degassing, activated carbon adsorption, and low-temperature water mixing (Hargreaves & Tucker 1999; Niu et al. 2015; Kamal et al. 2019). However, it is difficult to use the above approaches to treat the supersaturated TDG in large-scale water bodies due to the low treatment efficiency and high economic costs. It is necessary to explore the methods that can treat the practical supersaturated water with reliable dissipation performance, which is important for the protection of the riverine ecosystem and the sustainable development of hydropower engineering.

Bubbles generated by aeration provide a large interfacial area of gas–liquid contact and a strong turbulence intensity of the water body, which can result in a high mass transfer rate between multiple phases in the system. Aeration technology, with its benefits in operation cost and gas transfer efficiency, has been widely used in various fields, e.g., wastewater treatment, fish farming, and chemical and biological industries, etc. (Cheng et al. 2019; Behnisch et al. 2022; Wang et al. 2022). The relevant studies mainly focused on the mass transfer process of the dissolved gases (e.g., oxygen and carbon dioxide) with a transition from an undersaturated state to a stable equilibrium state. Based on field experiments in the feeder channel downstream of Grand Coulee Dam, Murphy & Lichtwardt (2001) reported that aeration can be used to remove the excess dissolved nitrogen from supersaturated water, with a maximum reduction in TDG saturation of 10% possible at a 124.0% upstream TDG saturation. Subsequently, Ou et al. (2016b) investigated the impact of various aeration operating conditions on the dissipation processes of supersaturated TDG based on a self-made coarse-bubble aeration system and obtained a quantitative relationship between the dissipation rate and the factors of aeration intensity and aeration water depth. Yao et al. (2022) developed this relationship, which extended the effect of the configuration factor for the aeration aperture size on the dissipation rate of supersaturated TDG. Those studies were useful in providing a preliminary understanding of the trend in the removal performance of supersaturated TDG at the different aeration conditions for a given aeration system. However, the results of existing studies are still difficult to directly apply to practical engineering since some important design-related impact factors (e.g., tank geometry, aerator type, and aerator arrangement) were not considered in the obtained relationship.

Comprehensive analysis shows that there are two options for minimizing the negative impacts of supersaturated TDG on fish: lowering TDG production and enhancing supersaturated TDG dissipation. However, the supersaturated problem that occurs in riverine systems cannot be completely avoided through the relevant mitigation measures due to the consideration of dam structural safety and flood control. A high dam with a high-water head and large flow discharge can result in TDG being produced in downstream rivers with the characteristics of high production saturation, a slow dissipation rate, and far-reaching influence. Utilizing the aeration technology to treat the supersaturated TDG in large-scale water bodies is a prospective and feasible solution due to its benefits in operating cost and removal performance. Previous research has obtained an empirical correlation between the dissipation performance of supersaturated TDG and the primary aeration factors, including aeration intensity, aeration water depth, and aeration aperture size. However, the effects of the various configuration factors, such as tank geometry, aerator type, and aeration area, on the dissipation performance of supersaturated TDG also need to be investigated. The present investigation comprehensively examined the dissipation performances of supersaturated TDG under two distinct operating conditions, namely gas flow rate and water depth, and one aerator configuration condition, specifically aerator size. This was achieved through a series of tests conducted in a redesigned fine-bubble aeration system. The study utilized empirical data to analyze and establish a correlation between the dissipation rate and different aeration impact factors.

Listen

Experimental apparatus and materials

Listen
The experimental system consists mainly of a custom-made aeration column, a supersaturated TDG water supply apparatus, and the measurement devices, respectively as given in Figure 1. The aeration column is made of plexiglass and its size of 1.5 m in height and 0.3 m in inner diameter (Dc). The EPDM (ethylene propylene diene terpolymer) fine-bubble aerator with a slit length (ds) of 0.1 mm is installed at 0.05 m from the column bottom. Air is injected into the aerator by supplying from an air compressor (ZBO-12/8, China) and the gas flow rate (Qa) was quantitatively controlled by a gas rotameter (ZBL-10, China) installed on the air supply tube. The supersaturated water with a particular TDG level was supplied from a TDG generator organized by Sichuan University, China (Li et al. 2013) and has been applied in our previous experiments (Ou et al. 2016a, 2016b). The device works by pumping the air and water with a certain proportion into the autoclave and mixing vigorously at high pressure so that the gases were excessively dissolved in water, in which the supersaturated TDG saturation could reach up to 140%. A TDG detector (P4T, Canada) with a 0–200% in measurement range and ±1% in accuracy, and a temperature detector (G95-4PS, China) with an accuracy of ±0.1 °C, were installed at the location of 0.1 m below the water level to collect the data on TDG saturation and water temperature during the aeration process.
Figure 1
A schematic illustration of the current experimental setup.
View largeDownload slide

A schematic illustration of the current experimental setup.

Figure 1
A schematic illustration of the current experimental setup.
View largeDownload slide

A schematic illustration of the current experimental setup.

Close modal

Experimental procedures and conditions

Listen

For each test, the experimental procedure consisted of approximately three steps. First, the supersaturated water with a predetermined TDG saturation was introduced into the aeration column and the water level was maintained at a specific depth. Secondly, the air was injected into the EPDM aerator at a predetermined gas flow rate by controlling the valve located at the position between the air compressor and the gas flowmeter, while the detectors were activated to measure and collect the data on TDG saturation and water temperature in the water. Finally, the test has stopped when the supersaturated TDG in the water had been reduced to the relative equilibrium saturation level (100–105%), and the rationality of the experimental data was verified through post-analysis.

Various aeration conditions, including gas flow rate (Qa), aeration water depth (Ha), and aerator diameter (Da), were carried out to investigate the effect of the operational and configuration factors on the dissipation performance of supersaturated TDG for the fine-bubble aeration system. Detailed information on the experimental conditions is given in Table 1.

Table 1

Experimental conditions setup (36 test cases in total)

Group numberAerator diameter, Da (mm)Water depth, Ha (m)Gas flow rate, Qa (m3·h−1)
1 92 0.5, 1.0 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 
2 215 0.5, 1.0 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 
3 300 0.5, 1.0 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 
Group numberAerator diameter, Da (mm)Water depth, Ha (m)Gas flow rate, Qa (m3·h−1)
1 92 0.5, 1.0 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 
2 215 0.5, 1.0 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 
3 300 0.5, 1.0 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 
View Large

Listen

Obtained findings and dissipation coefficient analysis

Listen
The dissipation processes of the supersaturated TDG under the different conditions in the fine-bubble aeration system are shown in Figure 2 (left). The results showed that the supersaturated TDG dissipation in the fine-bubble aeration system was very fast, and the dissipation rates not only depended on the aeration operating conditions of gas flow rate (Qa) and water depth (Ha) but were also significantly influenced by the configuration condition of aerator diameter (Da). The comparison findings revealed that the mean dissipation time with TDG saturation decreasing from 135 to 105% increased by approximately 30% when Ha increased from 0.5 to 1.0 m. For the condition of Da = 92 mm, the mean dissipation times of different water depths for Qa of 0.5, 1.0, 1.5, 2.0, and 3.0 m3·h−1 were 13.5, 11.5, 10.0, 9.3, 8.8, and 8.0 min, respectively. When the Da was increased to 300 mm, the mean dissipation times for the same cases of Qa decreased by 18.6, 26.0, 19.4, 19.1, 18.6, and 16.4%, respectively. Compared to the coarse-bubble aeration system presented in our previous work (Ou et al. (2016b), the mean dissipation times decreased by approximately 40% with an equal decrement in TDG percent saturation under the same aeration conditions. The findings demonstrated that the treatment efficiency of supersaturated water could be improved by using an aeration system with smaller bubble generation and aerator configurations with larger sizes for the given aeration operating conditions.
Figure 2
Dissipation processes of supersaturated TDG under different conditions (left) and linear fitting (solid lines) for calculating dissipation coefficients (right).
View largeDownload slide

Dissipation processes of supersaturated TDG under different conditions (left) and linear fitting (solid lines) for calculating dissipation coefficients (right).

Figure 2
Dissipation processes of supersaturated TDG under different conditions (left) and linear fitting (solid lines) for calculating dissipation coefficients (right).
View largeDownload slide

Dissipation processes of supersaturated TDG under different conditions (left) and linear fitting (solid lines) for calculating dissipation coefficients (right).

Close modal
To quantitatively estimate the dissipation performance of supersaturated TDG at different aeration conditions in the fine-bubble aeration system, the dissipation coefficients were obtained by using the first-order kinetics reaction equation (Equation (1)) proposed by the U.S. Army Corps of Engineers (2005) to fit the dissipation processes (Figure 2, right). The results showed that the dissipation processes for all experimental conditions were perfectly fitted by Equation (1) with correlation coefficients (R2) of over 0.990. The water temperature (T) for all test cases varied by a certain range (16.0–17.3°C) due to the difference in an experimental environment. To eliminate the contribution of the differences in water temperature on the dissipation rate, a temperature correction formula (Equation (2)) for TDG mass transfer rate was proposed by Shen et al. (2014). This formula was used to normalize the obtained dissipation coefficient.
(1)
(2)
where t is the aeration time (min), G0 is the initial TDG saturation (%), Gt is the TDG saturation (%) with the aeration time of t, Geq is the TDG equilibrium saturation (%) with the value of 100%, k is the dissipation coefficient (h−1), k20 is the dissipation coefficient (h−1) with the water temperature of 20 °C.

Dissipation performances analysis

Listen

Gas flow rate effects on dissipation coefficients

Listen
The normalized dissipation coefficients (k20) for all experimental test cases were obtained based on Equations (1) and (2). The impacts of the Qa on k20 in the fine-bubble aeration system is illustrated in Figure 3. The results showed that k20 increased with the increase of Qa under different conditions of water depth (Ha) and aerator diameter (Da). In the case of Ha = 1 m and Qa = 1.0 m3·h−1, the k20 at aerator sizes of Da = 92, 215, and 300 mm were 11.0, 11.9, and 12.2 h−1, respectively. By increasing the Qa to 2.0 m3·h−1, the k20 for the same configurations of Da was improved by 25.5, 18.5, and 21.7%, respectively. The reason is that the total number of resident bubbles in the water and the degree of water agitation could be greatly increased by increasing the Qa (Gillot et al. 2005), which is beneficial for the improvement of the dissipation rate of supersaturated TDG. In addition, for the same cases of water depth (Ha = 1 m) and aerator diameter (Da = 300 mm), the mean dissipation coefficient for the six studied gas flow rates in the fine-bubble aeration system was greater than 2.1 times that of the coarse-bubble aeration system reported by Ou et al. (2016b). The reason is that the EPDM membrane aerator used in this study has a smaller orifice size and a higher orifice distribution density than that of the pinhole aerator used in the coarse-bubble aeration system (Herrmann et al. 2021), resulting in a smaller generation bubble size and a higher TDG mass transfer rate occurring at the water–bubble interface.
Figure 3
The correlation between the normalized dissipation coefficient (k20) and gas flow rate (Qa) at different conditions of water depths (Ha) and aerator sizes (Da).
View largeDownload slide

The correlation between the normalized dissipation coefficient (k20) and gas flow rate (Qa) at different conditions of water depths (Ha) and aerator sizes (Da).

Figure 3
The correlation between the normalized dissipation coefficient (k20) and gas flow rate (Qa) at different conditions of water depths (Ha) and aerator sizes (Da).
View largeDownload slide

The correlation between the normalized dissipation coefficient (k20) and gas flow rate (Qa) at different conditions of water depths (Ha) and aerator sizes (Da).

Close modal
According to the fitting analysis (solid in Figure 3), the relationship between k20 and Qa for certain conditions of Ha and Da in the fine-bubble aeration system follows the power function relation (Equation (3)). This relationship is similar to that of the results obtained in the coarse-bubble aeration system reported by Ou et al. (2016b). In the fitting processes, the dissipation coefficient in the unaerated (static) state was used with the value of 0.02 h−1 based on Ou et al. (2016b).
(3)
where ɑ and β are the dimensionless parameters and the results are shown in Table 2.
Table 2

The fitting results of the parameters for the correlation between k20 and Qa

ParametersDa = 92 mm
Da = 215 mm
Da = 300 mm
Ha = 0.5 mHa = 1.0 mHa = 0.5 mHa = 1.0 mHa = 0.5 mHa = 1.0 m
α 14.77 12.20 15.58 11.55 17.37 10.91 
β 0.27 0.27 0.26 0.28 0.22 0.30 
R2 0.991 0.989 0.990 0.993 0.977 0.993 
ParametersDa = 92 mm
Da = 215 mm
Da = 300 mm
Ha = 0.5 mHa = 1.0 mHa = 0.5 mHa = 1.0 mHa = 0.5 mHa = 1.0 m
α 14.77 12.20 15.58 11.55 17.37 10.91 
β 0.27 0.27 0.26 0.28 0.22 0.30 
R2 0.991 0.989 0.990 0.993 0.977 0.993 
View Large

Aerator diameter effects on dissipation coefficients

Listen
The impacts of Da on k20 are demonstrated in Figure 4. Herein, in this section the obtained findings revealed that the k20 enhanced with the increase in aerator diameter when Qa and Ha were constant. For different cases of water depth and gas flow rate, the mean dissipation coefficient for the aerator diameter of Da = 300 mm was larger by 12.7 and 6.9% compared with the results of the conditions of Da = 92 mm and Da = 215 mm. For the larger Da cases, smaller bubbles can be generated at the slit under a given gas flow rate due to the lower gas pressure at the single slit (Behnisch et al. 2021, 2022), which results in a higher mass transfer rate in water–bubble interface compared to that of the smaller Da conditions. Moreover, smaller bubbles have a lower rising velocity (Tomiyama et al. 2002), which results in a longer residence time in the water and improves the mass transfer rate of supersaturated TDG at the water–bubble interface. However, the experimental results showed that the dissipation coefficients did not increase in proportionally with the increase in aerator diameter (slit numbers). For example, for the given aeration intensity conditions, the total number of bubbles generated for the configuration of Da = 215 mm was approximately five times greater than that for the configuration of Da = 92 mm, while the ratio of the dissipation coefficient for these two configurations was only 1.05. The reason could be that the situation of a stronger turbulent intensity at the water surface could be formed under the smaller aeration area configurations (Zhang et al. 2017), which could result in a higher mass transfer rate of supersaturated TDG at the water–air interface compared to that of the larger configurations. Changing the configurations of the aerator size (Da) under the given conditions of Qa and Ha can affect the bubble behaviors (number, velocity, and distribution) in the aeration system, which then dominates the dissipation rate of supersaturated TDG.
Figure 4
Effect of Da on k20 at the water depth of Ha = 0.5 m (left) and Ha = 1.0 m (right).
View largeDownload slide

Effect of Da on k20 at the water depth of Ha = 0.5 m (left) and Ha = 1.0 m (right).

Figure 4
Effect of Da on k20 at the water depth of Ha = 0.5 m (left) and Ha = 1.0 m (right).
View largeDownload slide

Effect of Da on k20 at the water depth of Ha = 0.5 m (left) and Ha = 1.0 m (right).

Close modal
Based on the mathematical analysis, the relationship between k20 and Da for different cases of Qa and Ha can be expressed as follows:
(4)
where is the dissipation coefficient (h−1) at the aerator diameter of Di, and λ is the fitting parameter (dimensionless) and was obtained as 0.093 as given in Figure 5.
Figure 5
The correlation between k20 and Da.
View largeDownload slide

The correlation between k20 and Da.

Figure 5
The correlation between k20 and Da.
View largeDownload slide

The correlation between k20 and Da.

Close modal

Water depth effects on dissipation coefficients

Listen

Two water depths with Ha = 0.5 m and Ha = 1.0 m were tested in this study, and the results (Figure 4) showed that k20 increased with the decrease in Ha. For different conditions of Qa and Da, the mean dissipation rates of supersaturated TDG can be improved to 36% when the condition of Ha decreases from 1.0 to 0.5 m. For deeper water depth conditions, a lower TDG concentration difference on both sides of the water and bubbles and a weaker turbulence intensity for the unit water body at a given aeration intensity can be caused, which may reduce the TDG mass transfer rate at the water–bubble and water–air interfaces (Yang et al. 2016).

The correlation between the dissipation coefficient and water depth has been investigated in the coarse-bubble aeration system (Ou et al. 2016b), and their relation presents an inverse proportion function (Equation (5)). Here, the water depth coefficient in Equation (5) was modified by combining with the test data of this study.
(5)
where is the dissipation coefficient (h−1) at the water depth of Hi, ω is the water depth coefficient (dimensionless) and the value was obtained as 0.351 from Figure 6.
Figure 6
The relationship between k20 and Ha.
View largeDownload slide

The relationship between k20 and Ha.

Figure 6
The relationship between k20 and Ha.
View largeDownload slide

The relationship between k20 and Ha.

Close modal

The correlation between the dissipation coefficient and the various conditions

Listen
The findings of the present study revealed that the normalized dissipation coefficients (k20) at a given aeration system are dominated by the impact factors of gas flow rate (Qa), aerator diameter (Da), and water depth (Ha). Its relationship can be described as follows:
(6)
Combined with the basic form of the relationship between the dissipation coefficient and the independent aeration condition established in the previous sections, Equation (6) can be rewritten as follows:
(7)
where a, b, and c are constants, and k0 is a characteristic dissipation coefficient (h−1) at the given conditions for gas flow rate (Qa,0), aerator diameter (Da,0), and water depth (Ha,0).
According to the regression analysis, the constants a, b, and c in Equation (7) were determined as 0.244, 0.095, and −0.443, respectively. By introducing different cases of k0 into Equation (7), the values of k20 for various aeration conditions were calculated. Figure 7 shows the comparison results of k20 between the calculations and measurements. The result revealed that the obtained relationship has good reliability, with the mean relative difference between calculations and measurements being 3.6% for all cases.
Figure 7
The correlation of between measurements and calculations.
View largeDownload slide

The correlation of between measurements and calculations.

Figure 7
The correlation of between measurements and calculations.
View largeDownload slide

The correlation of between measurements and calculations.

Close modal

Discussion on prediction model for dissipation coefficient in aeration system

Listen
Based on analysis of the experimental findings of the current study and the related gas–liquid mass transfer theories, the dissipation rate of supersaturated TDG in the aeration system not only depends on the aerated operation conditions but also is dominated by the geometric characteristics of the aeration system and the liquid properties (Ham et al. 2021). Figure 8 presents the pertinent variables taken into account in the prognostic model utilized to approximate the dissipation coefficient (k) within the aeration system. The interrelation among these variables can be articulated as follows:
(8)
where Ac is the cross-sectional area of the aeration system (m2), Aa is the covered area of the aerator (m2), DT is the diffusion coefficient of the TDG molecule in water (m2·s−1), ds is the orifice diameter or slit length (m), ϕ is the slits/orifice configuration density for the per aerator (m−2), ρ is the liquid density (kg·m−3), μ is the dynamic viscosity of the liquid (Pa·s), σ is the surface tension of the liquid (N·m−1).
Figure 8
Relevant variables affecting TDG mass transfer in the aeration system.
View largeDownload slide

Relevant variables affecting TDG mass transfer in the aeration system.

Figure 8
Relevant variables affecting TDG mass transfer in the aeration system.
View largeDownload slide

Relevant variables affecting TDG mass transfer in the aeration system.

Close modal
Based on dimensional analysis, the independent variables in Equation (8) can be substituted with several dimensionless terms (Cheng et al. 2019; Li & Zeng 2021). Equation (8) can be rewritten as the following expression:
(9)
(10)
(11)
(12)
where ei is the constant, U=Qa/Ac is the superficial gas velocity across the section of Ac (m·s−1), U0 = Qa/(ϕAads2) is the superficial gas velocity across the single orifice/slit (m·s−1), Sh, Re, We are the Sherwood, Reynolds, and Weber numbers, respectively.
The data from this work and relevant studies reported by Ou et al. (2016b) and Yao et al. (2022) are gathered to analyze the constants ei in Equation (9). The details of geometric characteristics of the different aeration tanks and the ranges of the relevant variables involved in Equation (9) are given in Tables 3 and 4. According to the regression analysis, the constants e0, e1, e2, e3, e4, and e5 are obtained as 1,119, 0.323, 0.039, −0.840, 0.112, and −0.413, respectively. Therefore, Equation (9) can be simplified as the following expressions:
(13)
(14)
Table 3

Summary of the relevant aeration experiments on the details of tank geometry

ReferenceTank geometryTank diameter/length × width (mm)Aerator shapeAerator diameter/length × width (mm)Membrane materialOrifice/slit amountOrifice/slit size (μm)
This study Cylindrical 300 Disk 92–300 EPDM 498–5,299 100 
Ou et al. (2016b)  Cylindrical 400 Disk 300 SS 41 400–800 
Yao et al. (2022)  Rectangular 440 × 550 Plate 350 × 350 SS 63 600–900 
ReferenceTank geometryTank diameter/length × width (mm)Aerator shapeAerator diameter/length × width (mm)Membrane materialOrifice/slit amountOrifice/slit size (μm)
This study Cylindrical 300 Disk 92–300 EPDM 498–5,299 100 
Ou et al. (2016b)  Cylindrical 400 Disk 300 SS 41 400–800 
Yao et al. (2022)  Rectangular 440 × 550 Plate 350 × 350 SS 63 600–900 

EPDM, ethylene propylene diene monomer rubber; SS, stainless steel.

View Large
Table 4

Range of the relevant variables used for fitting Equation (9)

VariableQa (m3·h−1)Ha (m)V (10−3·m3)Ac (10−3·m2)Aa (10−3·m2)k (h−1)ReWeAc0.5/HaAa/Acds/Ha (10−4)
Range 0.5–3.0 0.4–3.0 48–377 96–242 6.6–90.0 2.6–17.3 294–18,798 9–88,303 0.12–1.23 0.07–0.73 1–30 
VariableQa (m3·h−1)Ha (m)V (10−3·m3)Ac (10−3·m2)Aa (10−3·m2)k (h−1)ReWeAc0.5/HaAa/Acds/Ha (10−4)
Range 0.5–3.0 0.4–3.0 48–377 96–242 6.6–90.0 2.6–17.3 294–18,798 9–88,303 0.12–1.23 0.07–0.73 1–30 
View Large
The mean relative difference in dissipation coefficients between the measurements and the predictions was 7.5% for all test cases (Figure 9). At a given temperature condition (liquid properties are given), Equation (14) shows that the dissipation coefficient (k) is positively related to the gas flow rate (Qa) and the covered area of the aerator (Aa) but negatively related to the water depth (Ha) and the orifice size (ds), which agrees with the experimental results. This indicates that the established prediction model of the dissipation coefficient in aeration systems is reasonable.
Figure 9
Correlation of k between measurements and predictions.
View largeDownload slide

Correlation of k between measurements and predictions.

Figure 9
Correlation of k between measurements and predictions.
View largeDownload slide

Correlation of k between measurements and predictions.

Close modal

Furthermore, Equation (14) demonstrates a negative correlation between the dissipation coefficient (k) and both the cross-sectional area of the aeration system (Ac) and the orifice configuration density of the aerator (ϕ). The primary mechanism for gas transfer in the aeration system is bubble transfer (Schierholz et al. 2006). Therefore, if the width of the aeration system is increased while maintaining a constant water volume, the TDG transfer rate at the bubble interface will be weakened, resulting in a reduction of the total dissipation rate of supersaturated TDG in the system. For the given aerated operation conditions, lower floating velocities for bubbles and poor liquid mixing can be achieved with higher configurations of orifice density (Liang et al. 2016), which has a negative effect on the improvement of the dissipation efficiency of supersaturated TDG.

The developed model for forecasting the dissipation coefficients of supersaturated TDG in the aeration system (as represented by Equation (13) or Equation (14)) provides valuable insight into comprehending the correlation between the dissipation rate and pertinent geometric and operational factors. It is important to acknowledge that the application of this model is limited to the prediction and assessment of the treatment efficacy of supersaturated TDG in aeration systems where the aerators are arranged at the bottom. The rationale behind this is that the current assessments exhibit a dearth of pertinent information pertaining to the submergence depth of aerators, which also constitutes a primary domain for prospective research.

Listen

Aeration technology has great potential for mitigating the detrimental effects of supersaturated TDG on riverine ecosystems due to its benefits in operational costs and treatment efficiency. However, its practical applications are limited by the insufficient understanding of the correlation between the dissipation performance of supersaturated TDG and the relevant aeration conditions. To investigate this, sequences of experiments were carried out within a microporous aeration system to assess the impact of different operational and structural variables (including aeration intensity, water depth, and aerator size) on the dissipation efficacy of supersaturated TDG. A temperature-normalized dissipation coefficient was adopted to quantify the dissipation performance of supersaturated TDG under the different aeration conditions. The results indicate that the dissipation coefficients exhibited a positive correlation with the factors of aeration intensity and aerator size, following a power function. Conversely, dissipation coefficients demonstrated a negative correlation with water depth, following a power function. A quantifiable relationship between the dissipation coefficients and the aeration parameters (aeration intensity, aerator size, and water depth) was established. This quantitative relationship was developed based on Ou's study Ou et al. (2016b), which extended the effect of the configuration condition for the aerator size on the dissipation coefficient. Although the predictive accuracy of dissipation coefficients in this quantitative relationship is high, its practical application is restricted to scenarios where the geometric parameters of the aeration tank and the characteristic dissipation coefficient are known. Furthermore, a dissipation coefficient prediction model for supersaturated TDG in the universal aeration system was developed through dimensional analysis of the comprehensive elements. The model analysis revealed a negative correlation between the dissipation coefficient and the cross-sectional area of the aeration system, and orifice configuration density of the aerator. The present model is capable of depicting the correlation between the dissipation performances of supersaturated TDG and the pertinent design and operation parameters. This provides a substantial theoretical basis for the application of aeration as a means of dealing with pragmatic issues related to supersaturated TDG.

To enable the research results to be applied in engineering, it is crucial to address two aspects of research in the future. First, to improve the proposed relationship and model for the dissipation coefficient of supersaturated TDG in aeration systems and make it more suitable for practical use, it is important to collect experimental data on the effects of a wider range of aeration factors (e.g., the submergence depth of the aerator and aerator type) and environmental conditions (e.g., water temperature and sediment concentration) on the dissipation processes of supersaturated TDG. Second, to gain a deeper understanding of the gas–liquid multiphase flow behaviors and TDG field features under varying aeration conditions, it is necessary to develop a numerical model that can accurately predict the mass transfer of supersaturated TDG in aerated flows.

Listen

This work is supported by the Key Program of National Natural Science Foundation of China (Grant No. 52039006).

Listen

All relevant data are included in the paper or its Supplementary Information.

Listen

The authors declare there is no conflict.

Arntzen
E. V.
,
Geist
D. R.
,
Murray
K. J.
,
Vavrinec
J.
,
Dawley
E. M.
 &
Schwartz
D. E.
2009
Influence of the hyporheic zone on supersaturated gas exposure to incubating chum salmon
.
North American Journal of Fisheries Management
29
(
6
),
1714
–
1727
.
Google Scholar
Crossref
Search ADS
 
Behnisch
J.
,
Schwarz
M.
,
Trippel
J.
,
Engelhart
M.
 &
Wagner
M.
2022
Oxygen transfer of fine-bubble aeration in activated sludge treating saline industrial wastewater
.
Water
14
(
12
),
1964
.
Google Scholar
Crossref
Search ADS
 
Chen
S. C.
,
Liu
X. Q.
,
Jiang
W.
,
Li
K. F.
,
Du
J.
,
Shen
D. Z.
 &
Gong
Q.
2012
Effects of total dissolved gas supersaturated water on lethality and catalase activity of Chinese sucker (Myxocyprinus asiaticus Bleeker)
.
Journal of Zhejiang University
13
(
10
),
791
–
796
.
Google Scholar
Crossref
Search ADS
PubMed
 
Cheng
X. J.
,
Xie
Y. N.
,
Zhu
D. T.
 &
Xie
J.
2019
Modeling re-oxygenation performance of fine-bubble-diffusing aeration system in aquaculture ponds
.
Aquaculture International
27
(
5
),
1353
–
1368
.
Google Scholar
Crossref
Search ADS
 
Colt
J.
1984
Computation of dissolved gas concentrations in water as functions of temperature, salinity and pressure
.
American Fisheries Society
14
,
277
–
285
.
Special Publication
.
Google Scholar
 
DeMoyer
C. D.
,
Schierholz
E. L.
,
Gulliver
J. S.
 &
Wilhelms
S. C.
2003
Impact of bubble and free surface oxygen transfer on diffused aeration systems
.
Water Research
37
,
1890
–
1904
.
Google Scholar
Crossref
Search ADS
PubMed
 
Feng
J. J.
,
Li
R.
,
Liang
R. F.
 &
Shen
X.
2014
Eco-environmentally friendly operational regulation: an effective strategy to diminish the TDG supersaturation of reservoirs
.
Hydrology and Earth System Sciences
18
(
3
),
1213
–
1223
.
Google Scholar
Crossref
Search ADS
 
Geldert
D. A.
,
Gulliver
J. S.
 &
Wilhelms
S. C.
1998
Modeling dissolved gas supersaturation below spillway plunge pools
.
Journal of Hydraulic Engineering
124
(
5
),
513
–
521
.
Google Scholar
Crossref
Search ADS
 
Gillot
S.
,
Capela-Marsal
S.
,
Roustan
M.
 &
Héduit
A.
2005
Predicting oxygen transfer of fine bubble diffused aeration systems-model issued from dimensional analysis
.
Water Research
39
(
7
),
1379
–
1387
.
Google Scholar
Crossref
Search ADS
PubMed
 
Hargreaves
J. A.
 &
Tucker
C. S.
1999
Design and Construction of Degassing Units for Catfish Hatcheries
.
Southern Regional Aquaculture Center
,
SRAC Publication No. 191
.
Google Scholar
 
Herrmann-Heber
R.
,
Ristau
F.
,
Mohseni
E.
,
Reinecke
S. F.
 &
Hampel
U.
2021
Experimental oxygen mass transfer study of micro-perforated diffusers
.
Energies
14
(
21
),
7268
.
Google Scholar
Crossref
Search ADS
 
Huang
J. P.
,
Li
R.
,
Feng
J. J.
,
Li
Z.
,
Cheng
X. L.
 &
Wang
Z. H.
2021
The application of baffle block in mitigating TDGS of dams with different discharge patterns
.
Ecological Indicators
133
,
108418
.
Google Scholar
Crossref
Search ADS
 
Kamal
R.
,
Zhu
D. Z.
,
Leake
A.
 &
Crossman
J. A.
2019
Dissipation of supersaturated total dissolved gases in the intermediate mixing zone of a regulated river
.
Journal of Environmental Engineering
145
(
2
),
04018135
.
Google Scholar
Crossref
Search ADS
 
Li
R.
,
Li
J.
,
Li
K. F.
,
Deng
Y.
 &
Feng
J. J.
2009
Prediction for supersaturated total dissolved gas in high-dam hydropower projects
.
Science in China Series E: Technological Sciences
52
(
12
),
3661
–
3667
.
Google Scholar
Crossref
Search ADS
 
Li
R.
,
Hodges
B. R.
,
Feng
J. J.
 &
Yong
X. D.
2013
Comparison of supersaturated total dissolved gas dissipation with dissolved oxygen dissipation and reaeration
.
Journal of Environmental Engineering
139
(
3
),
385
–
390
.
Google Scholar
Crossref
Search ADS
 
Liang
X. F.
,
Pan
H.
,
Su
Y. H.
 &
Luo
Z. H.
2016
CFD-PBM approach with modified drag model for the gas-liquid flow in a bubble column
.
Chemical Engineering Research and Design
112
,
88
–
102
.
Google Scholar
Crossref
Search ADS
 
Ma
Q.
,
Li
R.
,
Feng
J. J.
,
Lu
J. Y.
 &
Zhou
Q.
2019
Ecological regulation of cascade hydropower stations to reduce the risk of supersaturated total dissolved gas to fish
.
Journal of Hydro-Environment Research
27
,
102
–
115
.
Google Scholar
Crossref
Search ADS
 
Murphy
A. P.
 &
Lichtwardt
M. A.
2001
Microbubble Treatment of gas Supersaturated Water
.
Desalination and Water Purification R&D Program Report No. 70
.
Niu
J. L.
,
Li
R.
 &
Wang
L. L.
2015
Experimental research on the promotion of supersaturated total dissolved Gas dissipation by the use of activated carbon
.
Nature Environment and Pollution Technology
14
(
2
),
367
–
372
.
Google Scholar
 
Orlins
J. J.
 &
Gulliver
J. S.
2000
Dissolved gas supersaturation downstream of a spillway II: computational model
.
Journal of Hydraulic Research
38
(
2
),
151
–
159
.
Google Scholar
Crossref
Search ADS
 
Ou
Y. M.
,
Li
R.
,
Hodges
B. R.
,
Feng
J. J.
 &
Pu
X. C.
2016a
Impact of temperature on the dissipation process of supersaturated total dissolved gas in flowing water
.
Fresenius Environmental Bulletin
25
(
6
),
1927
–
1934
.
Google Scholar
 
Ou
Y. M.
,
Li
R.
,
Tuo
Y. C.
,
Niu
J. N.
,
Feng
J. J.
 &
Pu
X. C.
2016b
The promotion effect of aeration on the dissipation of supersaturated total dissolved gas
.
Ecological Engineering
95
,
245
–
251
.
Google Scholar
Crossref
Search ADS
 
Pleizier
N. K.
,
Nelson
C.
,
Cooke
S. J.
 &
Brauner
C. J.
2020
Understanding gas bubble trauma in an era of hydropower expansion: how do fish compensate at depth?
Canadian Journal of Fisheries and Aquatic Sciences
77
(
3
),
556
–
563
.
Google Scholar
Crossref
Search ADS
 
Politano
M.
,
Amado
A. A.
,
Bickford
S.
,
Murauskas
J.
 &
Hay
D.
2012
Evaluation of operational strategies to minimize gas supersaturation downstream of a dam
.
Computers & Fluids
68
,
168
–
185
.
Google Scholar
Crossref
Search ADS
 
Qu
L.
,
Li
R.
,
Li
J.
,
Li
K. F.
 &
Deng
Y.
2011
Field observation of total dissolved gas supersaturation of high-dams
.
Science China Technological Sciences
54
(
1
),
156
–
162
.
Google Scholar
Crossref
Search ADS
 
Schierholz
E. L.
,
Gulliver
J. S.
,
Wilhelms
S. C.
 &
Henneman
H. E.
2006
Gas transfer from air diffusers
.
Water Research
40
(
5
),
1018
–
1026
.
Google Scholar
Crossref
Search ADS
PubMed
 
Shen
X.
,
Liu
S. Y.
,
Li
R.
 &
Ou
Y. M.
2014
Experimental study on the impact of temperature on the dissipation process of supersaturated total dissolved gas
.
Journal of Environmental Sciences
26
(
9
),
1874
–
1878
.
Google Scholar
Crossref
Search ADS
 
Tomiyama
A.
,
Tamai
H.
,
Zun
I.
 &
Hosokawa
S.
2002
Transverse migration of single bubbles in simple shear flows
.
Chemical Engineering Science
57
(
11
),
1849
–
1858
.
Google Scholar
Crossref
Search ADS
 
U.S. Army Corps of Engineers
2005
Technical Analysis of TDG Processes
.
US Army Corps of Engineers–Northwest Division, Environmental Resources and Fish Planning offices
.
U.S. Environmental Protection Agency (USEPA)
2020
The EPA's Action on the Revisions to Chapter 173-201A of the Washington Administrative Code Regarding the Total Dissolved Gas Site Specific Criteria for Columbia and Snake Rivers and Other Provisions
.
USEPA
,
Washington, DC, USA
.
Wang
Y. M.
,
Liang
R. F.
,
Tuo
Y. C.
,
Li
K. F.
 &
Hodges
B. R.
2015
Tolerance and avoidance behavior towards gas supersaturation in rock carp Procypris rabaudi with a history of previous exposure
.
North American Journal of Aquaculture
77
(
4
),
478
–
484
.
Google Scholar
Crossref
Search ADS
 
Wang
Y. S.
,
Politano
M.
 &
Weber
L.
2019
Spillway jet regime and total dissolved gas prediction with a multiphase flow model
.
Journal of Hydraulic Research
57
(
1
),
26
–
38
.
Google Scholar
Crossref
Search ADS
 
Wang
Q.
,
Yang
Y. Y.
,
Shen
Q. Y.
,
Chen
X. Y.
,
Li
F. M.
,
Wang
J. X.
,
Zhang
Z. Y.
,
Lei
Z. F.
,
Yuan
T.
 &
Shimizu
K.
2022
Energy saving and rapid establishment of granular microalgae system from tiny microalgae cells: effect of decrease in upflow air velocity under intermittent aeration condition
.
Bioresource Technology
363
,
127860
.
Google Scholar
Crossref
Search ADS
PubMed
 
Weitkamp
D. E.
 &
Katz
M.
1980
A review of dissolved gas supersaturation literature
.
Transactions of the American Fisheries Society
109
(
6
),
659
–
702
.
Google Scholar
Crossref
Search ADS
 
Yang
H. X.
,
Li
R.
,
Liang
R. F.
,
Wei
J.
 &
Zhang
Q.
2016
A parameter analysis of a two-phase flow model for supersaturated total dissolved gas downstream spillways
.
Journal of Hydrodynamics, Series B
28
(
4
),
648
–
657
.
Google Scholar
Crossref
Search ADS
 
© 2023 The Authors
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).