Supersaturated total dissolved gas (TDG) generation in rivers poses great harm to aquatic organisms. In this paper, 30 groups of supersaturated TDG dissipation experiments with aeration were carried out. These results showed that aeration actively promoted the dissipation of supersaturated TDG. The aeration rate decreased by 34.94% from 1.0 m3/h to 5.0 m3/h, the reduced proportion of aeration aperture was 35.51% from 215 mm to 260 mm, whereas the aeration depth increased by 16.93% from 0.4 m to 1.2 m for the TDG dissipation time required, resulting in corresponding the variation of TDG dissipation coefficients were 86.26%, 23.74% and -5.39%, respectively. In general, the effect on TDG dissipation is that the aeration rate is the largest, followed by the aeration aperture, and the aeration depth is the smallest. A quantitative relationship was established between TDG dissipation coefficient and aeration conditions, and followed a power function, while the aeration depth inhibited its dissipation. Moreover, what matters was that a numerical model was presented for predicting the TDG dissipation in Eulerian-Eulerian. When the parameter was β = 10.52, the error between the original experimental data and the simulated of a multiphase TDG dissipation model was 0.2%. The study provides essential scientific data for mitigating the harms of supersaturated TDG.

  • The effect of aeration on supersaturated TDG is analysed.

  • The TDG dissipation coefficient and aeration conditions are established.

  • When the critical TDG source treatment sensitivity parameter β = 10.52, the error between the actual supersaturated TDG dissipation process and the TDG dissipation model is 0.2%, and the experimental data and simulation values are similar.

Hydropower engineering constructed by humans plays a crucially important role in hydropower development, flood control, urban water supply, water storage and shipping safety, which is closely related to numerous river basins with abundant resources (Altinbilek 2002; Jellyman & Harding 2012; Chu et al. 2019; Shi et al. 2019; Paşa et al. 2023). Supersaturation of total dissolved gas (TDG) produced by dam discharge, a sudden rise in water temperature and excess oxygen from plant photosynthesis generation in water have a potentially significant impact on the biodiversity of fish, especially leading to gas bubble disease (GBD) and even death of fish (Ebel 1969; Don & Max 1980; Tan et al. 2006; Evan et al. 2009; Kirk & Wesley 2011; Algera et al. 2022). In recent years, supersaturated TDG has become a potential research topic because of its profound negative impact on the water environment in many places. For example, fish death was found on the downstream water surface of multiple dams in China's Three Gorges Project, high dams in the western region and the Columbia River and its tributary Snake River in the United States (Ebel 1969; Cheng et al. 2005; Jiang et al. 2008; Qin & Li 2008; Politano et al. 2011; Stewart et al. 2015; Wang et al. 2017; Zou et al. 2021).

There are two main ways to mitigate the harm of supersaturated TDG: one is to reduce the generation of supersaturated TDG, and the other is to accelerate the dissipation of supersaturated TDG. The earliest research on measures to mitigate TDG originated from the treatment of low-flow aquaculture water sources, including the siphon method (Colt 1983), packing column method (Politano et al. 2009), activated carbon adsorption (Niu et al. 2015; Huang et al. 2017) and planting aquatic plants (Yuan et al. 2018). Some engineering measures are designed to reduce the generation of supersaturated TDG, such as setting spillway deflectors (Environmental U.S. & Tribe 2004), stepped and baffle spillways (Wang et al. 2019), auxiliary energy dissipation pier (Huang et al. 2021a, 2021b), optimizing discharge structures (Feng et al.2014a) and dispersing discharge (Politano et al. 2012). However, the supersaturated TDG produced by the dam discharge has the characteristics of high saturation, slow dissipation speed, prominent cascade cumulative impact, and significant and sensitive impact on fish biodiversity in the dam downstream area (Li et al. 2009a, 2009b, 2013a, 2013b; Tanner et al. 2010; Feng et al. 2013, 2014a, 2014b). A single TDG mitigation measure can no longer solve the problem of supersaturated TDG hazards in the downstream area of the dam, and multiple mitigation methods should be needed to explore the TDG mitigation measure further.

In the past, aeration was mainly used for water quality treatment, river pollution treatment, environmental pollution treatment, aquaculture and separation of heavy metal pollution in numerous research literatures. Li et al. (2017) and Wang et al. (2013) summarized that micro-nanometer bubbles generated by aeration can degrade different types of organic pollutants, generate efficient free radicals and turbulence, remove solid surface pollutants and restore the water environment. Zhang et al. (2012a, 2012b) and Hong et al. (2011) found that different aeration conditions had a positive effect on removing black and odorous water in rivers. Zhu et al. (2023) and Qiao et al. (2023) found that aeration removed impurities and separated metal ions from wastewater. There is relatively little research on the effect of aeration on supersaturated TDG, where aeration may also be an important measure to slow down the dissipation of supersaturated TDG.

Based on the gas–liquid mass transfer mechanism (Li et al. 2020), aeration positively promoted the dissipation of supersaturated TDG (Ou et al. 2016; Liang et al. 2022; Yao et al. 2022a, 2022b, 2023) and dissolved oxygen (DO) (Chern & Yu 1997, 1999; Chern et al. 2001; Chern & Yang 2003; Huang et al. 2016; Wang et al. 2023), and increased oxygen in aquaculture (Cheng et al. 2013, 2014, 2015) and treated pollutants in rivers (Hong et al. 2011; Zhang et al. 2012a, 2012b). Ou et al. (2016) found that gas flow rate with aeration promoted the dissipation of supersaturated TDG. Huang et al. (2016) established relationships between gas flow rate, aeration depth and DO dissipation coefficient. Wang et al. (2023) found that smaller pinholes with aeration were more effective in promoting the dissipation of supersaturated DO. Zhan found that pinholes with aeration promoted the dissipation of supersaturated TDG. Cheng et al. (2013) found airflow pipe with aeration increased the oxygen content and established a relationship between the oxygen mass transfer coefficient and experimental conditions. Previous researchers were limited to analyzing the effect of aeration on reducing supersaturated TDG, whereas more aeration studies have focused on the transition of oxygen from an unsaturated state to a stable equilibrium state. Therefore, it is necessary to quantitatively analyze the impact of aeration on supersaturated TDG and solve the suppression problem of equipment deceleration.

Furthermore, for the multiphase aeration TDG model and numerical dam discharge TDG model, many researchers' findings were limited to the size of bubbles and their plumes in DO (Cheng et al. 2001, 2008; Fayolle et al. 2007; Xiao et al. 2012a, 2012b, 2014). Qin & Li (2008) found that the supersaturation of dissolved gas downstream of Gezhou Dam led to fish death and proposed a numerical model for supersaturated TDG. Cheng et al. (2009) found that supersaturated DO in the downstream of the Three Gorges Project posed a threat to the survival environment and life of fish and simulated the changes in DO. Politano et al. (2012, 2019) developed a numerical model of TDG changes for dam discharge in the United States. Exploring the application of supersaturated TDG dissipation models in aeration plays a positive role in protecting river ecology and the sustainable development of hydropower engineering.

Taking these results together indicates that the aeration measures to mitigate the harm of supersaturated TDG in the existing high-concentration supersaturated TDG watershed have not been found in the fish habitats. This paper focuses on the quantitative analysis of aeration on supersaturated TDG dissipation, the relationship between aeration conditions and TDG dissipation coefficient and its multiphase model in aeration experiments. The results provide an essential scientific basis for constructing suitable fish habitats with low levels of TDG concentration.

Laboratory instrumentation

The laboratory instrumentation has a TDG dissipation device, which is designed with reference to Yao et al. (2022a, 2022b), and the experimental sketch is shown in Figure 1. The main equipment is a square aeration water tank of 2.0 m in height and 0.4 m in diameter. The aeration distributor is placed at a 0.3 m distance from the column bottom, which contains two microporous aeration distributors with diameters of 215 and 260 mm. The range of the barometer is 1.0~5.0 m3/h. The measuring range of the TGP is 0~600% of saturation with ±1% accuracy.
Figure 1

Experimental setup and sketch.

Figure 1

Experimental setup and sketch.

Close modal

Experimental methods

The basic experimental steps mainly refer to Yao's aeration experiment (Yao et al. 2022a, 2022b). The supersaturated water is produced by the supersaturated TDG generation system and injected into the predetermined height of the circular water tank. And we input the set aeration rate into the supersaturated water and use the TGP meter to start recording the dissipation process of supersaturated TDG until the TDG concentration reaches about 100%, then stop recording and cycle this operation method. There are a total of 30 experiments, as shown in Figure 2.
Figure 2

Experimental conditions for aeration (30 sets of experiments).

Figure 2

Experimental conditions for aeration (30 sets of experiments).

Close modal

Dissipation of supersaturated TDG in aeration-free conditions

In order to study the effect of aeration on supersaturated TDG dissipation, an experiment on supersaturated TDG dissipation without aeration rate was carried out. When the depth of supersaturated water is H = 0.4 m, H = 0.8 m and H = 1.2 m, the time required for supersaturated TDG to dissipate has reached more than 4 h. The dissipation rate is relatively slow, as shown in Figure 3. The dissipation coefficient KTDG,0 is calculated by the first-order dynamic Equation (1) (U.S Army Corps of Engineers 2005) and decreases with the increase of water depth, and the correlation coefficient R2 is greater than 0.983, as shown in Table 1.
(1)
where G is the TDG saturation (%), Geq is the equilibrium saturation of TDG (usually 100%), G0 is the initial TDG concentration (%), KTDG is the dissipation coefficient (h−1), t is the dissipation time (h).
Table 1

Supersaturated TDG dissipation coefficient in different water depth (H/m) under the static condition

Group numberH (m)Q (m3/h)θ (m)R2KTDG,0R2
0.4 – – 0.976 0.00806 ± 0.00 0.995 
0.8 – – 0.976 0.00734 ± 0.00 0.993 
1.2 – – 0.987 0.00636 ± 0.00 0.983 
Group numberH (m)Q (m3/h)θ (m)R2KTDG,0R2
0.4 – – 0.976 0.00806 ± 0.00 0.995 
0.8 – – 0.976 0.00734 ± 0.00 0.993 
1.2 – – 0.987 0.00636 ± 0.00 0.983 
Figure 3

Dissipation process of supersaturated TDG under aeration-free conditions in water depths (H) of 0.4, 0.8 and 1.2 m.

Figure 3

Dissipation process of supersaturated TDG under aeration-free conditions in water depths (H) of 0.4, 0.8 and 1.2 m.

Close modal

Dissipation of supersaturated TDG in aeration

Dissipation process of supersaturated TDG

Figure 4 indicates that aeration can significantly promote the supersaturated TDG dissipation process. Table 2 shows that the time required for supersaturated TDG dissipation is shorter than that required for pinhole aeration, swirling aeration and other mitigation measures, even reaching one to four times. Under the effect of different aeration conditions, supersaturated TDG dissipation appears a sharp decline. When the aeration rate increases from 1.0 to 5.0 m3/h, the average time required for supersaturated TDG dissipation reduction is 34.94%. When the aeration aperture increases from 215 to 260 mm, the average reduction of time required for supersaturated TDG dissipation is 35.51%. When the aeration depth increases from 0.4 to 0.8 m, the average increase of time required for supersaturated TDG release is 16.93%. So, from the average time required for the supersaturated TDG dissipation, it can be seen that the aeration aperture has the greatest effect on the supersaturated TDG dissipation, followed by the aeration rate, and the aeration depth has the smallest effect, that is Tθ > TQ > TH. As shown in Figure 1, the reasons are: (1) The gas–liquid interface is implicated in momentum, heat and mass transfer (Gualtieri & Doria 2012) and the gas flow rate can change the comfort of material surfaces and improve their overall energy performance (Barton et al. 2002; Mohammad et al. 2014). In aeration, a large number of bubbles become more and more with the increase of aeration rate, the supersaturated TDG dissipation process is mainly driven by a certain amount of turbulence generated by the aeration rate in which a large number of bubbles are constantly moving and bubbles in supersaturated water are constantly renewed and rise to the water surface (Chanson 2008). These results can enhance the mass transfer process at the gas–liquid interface and water surface to reduce the supersaturated TDG concentration (Yao et al. 2022a, 2022b). (2) With the increase of aeration depth, a large number of bubbles generated by air compressor conveying gas stagnate in supersaturated water for a relatively long time, resulting in the relative weakening of turbulence intensity caused by bubbles and the reduction of the contact area of gas–liquid interface, which inhibits the dissipation of supersaturation TDG (Brooks 1998; Cheng et al. 2005, 2014; Li et al. 2007). (3) The aeration aperture determines the size of bubbles. Some scholars have shown that a smaller bubble diameter is beneficial for the contact area of the gas–liquid interface and mass transfer between the gas–bubble interface and the water surface (Lehr et al. 2002; Li 2007). The increase of the aeration aperture leads to the increase in the number of bubbles in the same aeration rate, which enhances the mass transfer of supersaturated TDG at the gas–liquid interface (Laakkonen et al. 2007; Prince & Blanch 2010; Ashutosh et al. 2011).
Table 2

Compare the time required for the supersaturated TDG dissipation between microporous aeration and other mitigation measures

ResearchersMitigation measureThe time required for supersaturated TDG dissipation
— Aeration distributor 165~100%/(0.07~0.17)h 
Feng et al. (2012, 2016Sediment 130~105%/(0.18~1.10)h 
Feng et al. (2017)  Water blocking medium 135~(4.1~9.6%)/(6.14~8.17)s 
Liu et al. (2015)  Wind speed 135~115%/(2~4)h 
Ou et al. (2016)  Pinhole aeration 132~105%/(0.22~0.43)h 
Zhang (2021)  Pinhole aeration 140~95%/(0.13~0.53)h 
Yao et al. (2022a, 2022bSwirling aeration 170~100%/(0.13~0.4)h 
Liang et al. (2022)  Pinhole aeration 140~110%/(0.25~0.53)h 
Wang et al. (2023)  Pinhole aeration 170~105%/(0.08~0.18)h 
ResearchersMitigation measureThe time required for supersaturated TDG dissipation
— Aeration distributor 165~100%/(0.07~0.17)h 
Feng et al. (2012, 2016Sediment 130~105%/(0.18~1.10)h 
Feng et al. (2017)  Water blocking medium 135~(4.1~9.6%)/(6.14~8.17)s 
Liu et al. (2015)  Wind speed 135~115%/(2~4)h 
Ou et al. (2016)  Pinhole aeration 132~105%/(0.22~0.43)h 
Zhang (2021)  Pinhole aeration 140~95%/(0.13~0.53)h 
Yao et al. (2022a, 2022bSwirling aeration 170~100%/(0.13~0.4)h 
Liang et al. (2022)  Pinhole aeration 140~110%/(0.25~0.53)h 
Wang et al. (2023)  Pinhole aeration 170~105%/(0.08~0.18)h 
Figure 4

Dissipation process of supersaturated TDG under different aeration rates (Q = (1, 2, 3, 4, 5) m3/h), aeration depth (H = (0.4, 0.8, 1.2) m) and aeration aperture (θ = (215, 260) mm).

Figure 4

Dissipation process of supersaturated TDG under different aeration rates (Q = (1, 2, 3, 4, 5) m3/h), aeration depth (H = (0.4, 0.8, 1.2) m) and aeration aperture (θ = (215, 260) mm).

Close modal

Dissipation coefficient of supersaturated TDG

In order to further study the effect of aeration on supersaturated TDG, a first-order kinetic Equation (1) was introduced to express the dissipation rate of supersaturated TDG (U.S Army Corps of Engineers 2005). The results are shown in Table 3.

Table 3

Supersaturated TDG dissipation coefficient in different aeration depth (H/m) under the aeration conditions

Group numberH (m)θ (mm)Q (m3/h)KTDG (h−1)ψ = KTDG/KTDG,0R2
0.4 215 1.0 0.265 ± 0.00 32.88 0.987 
0.4 215 2.0 0.703 ± 0.02 87.22 0.975 
0.4 215 3.0 1.030 ± 0.06 127.79 0.929 
0.4 215 4.0 1.138 ± 0.06 141.19 0.958 
0.4 215 5.0 1.141 ± 0.03 141.56 0.958 
0.4 260 1.0 0.118 ± 0.00 14.64 0.932 
0.4 260 2.0 0.104 ± 0.01 12.90 0.737 
0.4 260 3.0 0.746 ± 0.06 92.56 0.856 
0.4 260 4.0 0.804 ± 0.02 99.75 0.978 
10 0.4 260 5.0 1.795 ± 0.13 222.70 0.932 
11 0.8 215 1.0 0.235 ± 0.00 32.02 0.994 
12 0.8 215 2.0 0.459 ± 0.00 62.53 0.983 
13 0.8 215 3.0 0.543 ± 0.00 73.98 0.989 
14 0.8 215 4.0 1.102 ± 0.05 150.14 0.959 
15 0.8 215 5.0 1.169 ± 0.05 159.26 0.969 
16 0.8 260 1.0 0.183 ± 0.00 24.93 0.997 
17 0.8 260 2.0 0.594 ± 0.01 80.93 0.992 
18 0.8 260 3.0 0.714 ± 0.02 97.28 0.985 
19 0.8 260 4.0 0.873 ± 0.01 118.94 0.959 
20 0.8 260 5.0 1.225 ± 0.03 166.89 0.986 
21 1.2 215 1.0 0.097 ± 0.00 15.25 0.845 
22 1.2 215 2.0 0.300 ± 0.01 47.17 0.951 
23 1.2 215 3.0 0.308 ± 0.02 48.43 0.881 
24 1.2 215 4.0 0.445 ± 0.02 69.97 0.890 
25 1.2 215 5.0 0.462 ± 0.02 72.64 0.869 
26 1.2 260 1.0 0.273 ± 0.01 42.92 0.968 
27 1.2 260 2.0 0.335 ± 0.02 52.67 0.903 
28 1.2 260 3.0 0.719 ± 0.02 113.05 0.982 
29 1.2 260 4.0 0.763 ± 0.03 119.97 0.968 
30 1.2 260 5.0 0.811 ± 0.05 127.52 0.909 
Group numberH (m)θ (mm)Q (m3/h)KTDG (h−1)ψ = KTDG/KTDG,0R2
0.4 215 1.0 0.265 ± 0.00 32.88 0.987 
0.4 215 2.0 0.703 ± 0.02 87.22 0.975 
0.4 215 3.0 1.030 ± 0.06 127.79 0.929 
0.4 215 4.0 1.138 ± 0.06 141.19 0.958 
0.4 215 5.0 1.141 ± 0.03 141.56 0.958 
0.4 260 1.0 0.118 ± 0.00 14.64 0.932 
0.4 260 2.0 0.104 ± 0.01 12.90 0.737 
0.4 260 3.0 0.746 ± 0.06 92.56 0.856 
0.4 260 4.0 0.804 ± 0.02 99.75 0.978 
10 0.4 260 5.0 1.795 ± 0.13 222.70 0.932 
11 0.8 215 1.0 0.235 ± 0.00 32.02 0.994 
12 0.8 215 2.0 0.459 ± 0.00 62.53 0.983 
13 0.8 215 3.0 0.543 ± 0.00 73.98 0.989 
14 0.8 215 4.0 1.102 ± 0.05 150.14 0.959 
15 0.8 215 5.0 1.169 ± 0.05 159.26 0.969 
16 0.8 260 1.0 0.183 ± 0.00 24.93 0.997 
17 0.8 260 2.0 0.594 ± 0.01 80.93 0.992 
18 0.8 260 3.0 0.714 ± 0.02 97.28 0.985 
19 0.8 260 4.0 0.873 ± 0.01 118.94 0.959 
20 0.8 260 5.0 1.225 ± 0.03 166.89 0.986 
21 1.2 215 1.0 0.097 ± 0.00 15.25 0.845 
22 1.2 215 2.0 0.300 ± 0.01 47.17 0.951 
23 1.2 215 3.0 0.308 ± 0.02 48.43 0.881 
24 1.2 215 4.0 0.445 ± 0.02 69.97 0.890 
25 1.2 215 5.0 0.462 ± 0.02 72.64 0.869 
26 1.2 260 1.0 0.273 ± 0.01 42.92 0.968 
27 1.2 260 2.0 0.335 ± 0.02 52.67 0.903 
28 1.2 260 3.0 0.719 ± 0.02 113.05 0.982 
29 1.2 260 4.0 0.763 ± 0.03 119.97 0.968 
30 1.2 260 5.0 0.811 ± 0.05 127.52 0.909 

Table 3 shows that under aeration conditions, the supersaturated TDG dissipation coefficient is larger than that of pinhole aeration (Ou et al. 2016; Liang et al. 2022) and swirling aeration (Yao et al. 2023). When the aeration rate increases from 1.0 to 5.0 m3/h, the average increase of supersaturated TDG dissipation coefficient is 86.26%. When the aeration depth increases from 0.4 to 0.8 m, the average increase of supersaturated TDG dissipation coefficient is 5.39%. And when the aeration aperture increases from 215 to 260 mm, the average reduction of supersaturated TDG dissipation coefficient is 23.74%. From the average value of supersaturated TDG dissipation coefficient, the effect of aeration rate on supersaturated TDG dissipation coefficient is the largest, followed by the effect of aeration aperture, and the effect of aeration depth is the smallest, that is KQ > Kθ > KH. Therefore, it is further verified that this aeration method can significantly promote supersaturated TDG dissipation.

In addition, the dissipation coefficient of supersaturated TDG varies significantly under different aeration conditions. The dissipation coefficient of supersaturated TDG increases with the increase of aeration rate. When the aeration depth is 0.4 m, the aeration aperture is 260 mm and the aeration rate is 5 m3/h, the maximum supersaturated TDG dissipation coefficient is 1.795 h−1, which is 222.7 times of the supersaturated TDG dissipation coefficient in no aeration. In order to more directly express the effect of aeration on supersaturated TDG dissipation, a relative dissipation coefficient (ψ=KTDG/KTDG,0) which is the ratio of the TDG dissipation coefficient (KTDG) for different aeration to the TDG dissipation coefficient KTDG,0 without aeration is introduced. Then their relationship is shown in Figure 5, and Equation (2) and its correlation is shown in Table 4.
(2)
where β is the relative dissipation coefficient, Q is the aeration rate (m3/h), α1, α2 are fitting parameters.
Table 4

Fitting results of parameters on the relationship of relative dissipation coefficient (β) varying with aeration rate

Parametersθ = 215 mm
θ = 260 mm
0.40.81.20.40.81.2
 51.45 ± 10.69 4.73 ± 3.57 27.54 ± 8.06 34.04 ± 6.27 22.88 ± 4.64 42.10 ± 9.35 
 0.69 ± 0.15 2.37 ± 0.49 1.12 ± 0.21 0.97 ± 0.13 0.75 ± 0.16 0.73 ± 0.16 
 0.947 0.949 0.955 0.976 0.951 0.943 
Parametersθ = 215 mm
θ = 260 mm
0.40.81.20.40.81.2
 51.45 ± 10.69 4.73 ± 3.57 27.54 ± 8.06 34.04 ± 6.27 22.88 ± 4.64 42.10 ± 9.35 
 0.69 ± 0.15 2.37 ± 0.49 1.12 ± 0.21 0.97 ± 0.13 0.75 ± 0.16 0.73 ± 0.16 
 0.947 0.949 0.955 0.976 0.951 0.943 
Figure 5

The relationship between relative dissipation coefficient (β) and aeration rate (Q/m3·h−1).

Figure 5

The relationship between relative dissipation coefficient (β) and aeration rate (Q/m3·h−1).

Close modal

Equation (2) shows a power function relationship. And the water continuously generates strong turbulence during the aeration rate, and the increase of aeration rate causes the increase of water flow velocity gradient in the gas–liquid interface and then leads to the increase of turbulent kinetic energy and its dissipation rate (Geldert et al. 1998; Takemura & Yabe 1998; Shae et al. 2008). This greatly enhances the dissipation rate of supersaturated TDG at the gas–liquid interface, thus increasing in the supersaturated TDG dissipation coefficient (Gresch et al. 2011; Liu et al. 2015).

The effect and quantitative relationship of aeration conditions on the dissipation of supersaturated TDG

Cheng et al. (2013) found that the relationship between the reaeration coefficient and aeration rate did not increase linearly in aeration. It is necessary to analyze further the relationship between aeration rate, aeration depth, aeration aperture and supersaturated TDG dissipation coefficient.

The effect of aeration rate

According to the mathematical analysis software SPSS, the relationship between supersaturated TDG dissipation coefficient and aeration rate is a power function and positive correlation and is fitted in Figure 6. The relationship is expressed in Equation (3), and the fitting parameters are shown in Table 5.
(3)
where KTDG,Q is the supersaturated TDG dissipation (h−1), Q is the aeration rate (m3/h), and α,β are fitting parameters.
Table 5

Fitting results of parameters on the relationship of supersaturated TDG dissipation coefficients (KTDG,Q) varying with aeration rate (Q/m3/h)

Parametersθ = 215 mm
θ = 260 mm
0.40.81.20.40.81.2
 0.440 ± 0.17 0.194 ± 0.11 0.153 ± 0.06 0.1602 ± 0.16 0.222 ± 0.26 0.269 ± 0.12 
 0.668 ± 0.21 1.136 ± 0.33 0.731 ± 0.20 1.152 ± 0.58 0.9484 ± 0.66 0.699 ± 0.24 
 0.948 0.956 0.956 0.879 0.782 0.935 
Parametersθ = 215 mm
θ = 260 mm
0.40.81.20.40.81.2
 0.440 ± 0.17 0.194 ± 0.11 0.153 ± 0.06 0.1602 ± 0.16 0.222 ± 0.26 0.269 ± 0.12 
 0.668 ± 0.21 1.136 ± 0.33 0.731 ± 0.20 1.152 ± 0.58 0.9484 ± 0.66 0.699 ± 0.24 
 0.948 0.956 0.956 0.879 0.782 0.935 
Figure 6

Relationship between the supersaturated TDG dissipation (KTDG,Q) and aeration rate (Q).

Figure 6

Relationship between the supersaturated TDG dissipation (KTDG,Q) and aeration rate (Q).

Close modal

The effect of aeration depth

Figure 7 shows that the supersaturated TDG dissipation coefficient decreases with the increase of aeration depth, because the aeration depth at high water level results in a high pressure, aeration depth makes it difficult for a large number of bubbles to escape from the tension of the gas–liquid interface (Grace 1973; Chesters 1991). According to mathematical regression analysis, the relationship between supersaturated TDG dissipation coefficient and aeration depth is a power function and negative correlation and is obtained as shown in Equation (4) and its optimal parameters are shown in Table 6.
(4)
where KTDG,H is the supersaturated TDG dissipation (h−1), H is the aeration depth (m).
Table 6

Parameter values and correlation coefficients

ParametersValuesCorrelation coefficients
 0.811 1.000 
 0.401 0.687 
 0.4 m – 
ParametersValuesCorrelation coefficients
 0.811 1.000 
 0.401 0.687 
 0.4 m – 
Figure 7

Relationship between the supersaturated TDG dissipation (KTDG,H) and aeration depth (H).

Figure 7

Relationship between the supersaturated TDG dissipation (KTDG,H) and aeration depth (H).

Close modal

The effect of aeration aperture

Figure 8 shows that the supersaturated TDG dissipation coefficient increases with the increase of the aeration aperture. Due to the change of aeration aperture, the average increase of supersaturated TDG dissipation coefficient at the aeration depths of 0.4, 0.8 and 1.2 m is 28.05, 45.57 and 94.71%, respectively. The previous data indicated that larger aeration aperture can promote the supersaturated TDG dissipation and increase the area of gas–liquid interface and its mass transfer effect (Murphy et al. 1998). This element solves a critical problem in that aeration aperture suppresses the dissipation of supersaturated TDG (Ou et al. 2016; Yao et al. 2023). And a relationship between supersaturated TDG dissipation coefficient and aeration aperture is a power function relationship and a positive correlation relationship as shown in Equation (5). Its optimal parameters are shown in Table 7.
(5)
where KTDG,θ is the supersaturated TDG dissipation (h−1) and θ is the aeration aperture (mm).
Table 7

Parameter values and correlation coefficients

ParameterValuesCorrelation coefficients
 0.670 1.000 
 0.357 0.683 
 260 mm – 
ParameterValuesCorrelation coefficients
 0.670 1.000 
 0.357 0.683 
 260 mm – 
Figure 8

Relationship between the supersaturated TDG dissipation (KTDG,θ) and aeration aperture (θ).

Figure 8

Relationship between the supersaturated TDG dissipation (KTDG,θ) and aeration aperture (θ).

Close modal

A quantitative relationship between the dissipation coefficients of supersaturated TDG and aeration conditions

In the aeration experiment, the supersaturated TDG dissipation process is mainly affected by aeration rate, aeration depth and aeration aperture. A quantitative relationship between supersaturated TDG dissipation coefficient and them had been obtained previously, which can further comprehensively establish their relationship graph represented by Equation (6) (Huang et al. 2016; Wang et al. 2023; Yao et al. 2023).
(6)
According to mathematical regression analysis, we obtained the parameters of Equation (6) as shown in Equation (7), and the optimal parameters are shown in Table 8.
(7)
where KTDG is the supersaturated TDG dissipation coefficient (h−1), Q is the aeration rate (m3/h), H is the aeration depth (m) and θ is the aeration aperture (mm).
Table 8

Parameter values and correlation coefficients

ParameterValuesCorrelation coefficients
 1.494 1.000 
 1.093 0.411 
 0.449 0.508 
 0.487 0.510 
 5.0 m3/h – 
 0.4 m – 
 260 mm – 
ParameterValuesCorrelation coefficients
 1.494 1.000 
 1.093 0.411 
 0.449 0.508 
 0.487 0.510 
 5.0 m3/h – 
 0.4 m – 
 260 mm – 

Comparison between experimental data and calculated values

In order to verify the applicability of the quantitative relationship between supersaturated TDG dissipation coefficient and aeration conditions, we used the root mean square value and the absolute average value to obtain the comparison between the experimental data and the calculated value (Li et al. 2013a, 2013b; Cheng et al. 2014, 2015; Alomar et al. 2020), the results are shown in Figure 9 and the error value as shown in Table 9.
(8)
(9)
where RMSE is the root mean square value, AME is the absolute mean value, is the calculated value, is the experimental data.
Table 9

The calculated values of errors

ParametersTDG
RMSE (%)AME (%)
Equation (324.98 18.06 
Equation (438.48 30.72 
Equation (540.38 32.93 
Equation (719.10 12.17 
ParametersTDG
RMSE (%)AME (%)
Equation (324.98 18.06 
Equation (438.48 30.72 
Equation (540.38 32.93 
Equation (719.10 12.17 
Figure 9

Comparison between experimental data and calculated values.

Figure 9

Comparison between experimental data and calculated values.

Close modal

The lower comparison of the experimental data and calculated values shows that the established mathematical model of supersaturated TDG dissipation has particular applicability. It does not need to measure the characteristic dissipation coefficient under specific aeration conditions. However, it can directly predict the dissipation rate of supersaturated TDG in water under this condition by obtaining easily obtained parameters such as aeration rate, aeration depth and aeration aperture. These TDG mass transfer equations have high operability in practical environmental applications.

Based on gas–liquid computational fluid dynamics (CFD) in Eulerian–Eulerian approach (Xia & Sun 2002; Henderson et al. 2007), we compiled the source term (Sc) of TDG transport diffusion equation with self-designed C Language to form a User Defined Function (UDF) file. We selected one of the aeration experiments where Q = 1.0 m3/h, H = 0.8 m, θ = 260 mm, initial TDG concentration (G = 147.4%) and KTDG = 0.183 as a vital model parameter. The supersaturated TDG dissipation model and its essential sensitivity parameters will be obtained, which are used to evaluate the error between the TDG dissipation process in the aeration experiment and the TDG dissipation model in the multiphase model (Cheng et al. 2009; Politano et al. 2009, 2011, 2012; Fu et al. 2010; Huang et al. 2021a, 2021b). Therefore, the calculation of the supersaturated TDG dissipation model includes a mathematical model, turbulent model and TDG transport diffusion equation as follows, and we also consider the effects of buoyancy, pressure, drag, turbulent dispersion and other forces on the supersaturated TDG dissipation (Manninen et al. 1996).

Mathematical model

Mass and momentum conservation equation

Equations (10) and (11) indicate that the material transfer at the gas–liquid interface is controlled by the mass and momentum equations (Drew & Passman 1998).
(10)
(11)
where i is the phase (gas or liquid), is the volume fraction of phase, is the phase density, is the effective density, is the phase velocity, is the correction pressure, is the force of gas and liquid and is the phase effective viscosity.

Effective viscosity of gas–liquid

The effective viscosity of gas and liquid is represented by Equations (12) and (13), which mainly determine the phase viscosity and the phase force in the momentum conservation, which is closed (Hugo et al. 1997).
(12)
(13)
where is the effective viscosity of the liquid phase and is the turbulent viscosity of the liquid phase.

Turbulent model

Κ and ε equation, liquid phase turbulence coefficient

We used the RNG κ-ε turbulence model to turbulence model to describe the turbulence of the liquid phase in an aeration system. The core of the RNG κ-ε turbulence model applies to the turbulence calculation of higher Re number and not only saves the calculation amount but also has good results in engineering applications, expressed by Equations (14)–(16) and their model parameters are shown in Table 10 (Wei et al. 2015; Guo et al. 2017).
(14)
(15)
(16)
where is the density, is the viscosity coefficient.
Table 10

Turbulent model parameters

Parameters
 4.38 0.012 0.085 1.68 0.7179 0.7179 
Parameters
 4.38 0.012 0.085 1.68 0.7179 0.7179 

Gas–liquid interaction forces

Drag force
Drag force is the frictional force generated by the movement of gas–liquid at the interface, as shown in the following equation (Grace 1973; Chesters 1991).
(17)
where is the drag coefficient, . Among them, can be divided into:
Lift of bubbles
The lift of bubbles is caused by the gradient effect of liquid flow velocity, which causes uneven pressure distribution around the bubble and is represented by the following equation (Tominaga & Stathopoulos 2007; Lucas & Tomiyama 2011).
(18)
where CL is the bubble lift coefficient.
Wall lubricating force
Wall lubricating force is the interfacial force that drives bubbles away from the wall due to the gradient of liquid flow velocity near the wall in the aeration system and is represented by the following equation (Ishii 1975; Antal et al. 1991).
(19)
where CW is the wall lubrication force coefficient.
Turbulent dissipation force
Turbulent dissipation force is the interfacial force of bubbles caused by liquid phase turbulence and gas holdup gradient in aeration, as shown in the following equation (Lahey et al. 1993; Li et al. 2009a, 2009b).
(20)
where CTD is the turbulent diffusion coefficient.

TDG transport diffusion equation

The general TDG transport diffusion equation is represented by Equation (21) (Weber & Mannheim 1997; Cheng et al. 2009). The TDG dissipation source treatment in the equation is mainly known for the mass transfer at the gas–liquid interface (SC,G) and the mass transfer at the water free-interface (SC,W).
(21)
where C is the TDG saturation (%), is the molecular diffusion coefficient, is the Schmidt number, is the turbulent diffusion coefficient of gas gas–liquid mixed liquid, is the water flow velocity (m/s).

TDG dissipation source treatment

Some scholars (Politano et al. 2009, 2012, 2019; Qin & Li 2008) have used Equations (22) and (23) to represent gas–liquid interface mass transfer and water free-surface surface mass transfer, which better simulate the distribution of TDG saturation in practical engineering.
(22)
(23)
where KL,B is the gas–liquid interface mass transfer coefficient, KL,S is the water free-surface surface mass transfer coefficient, is the specific surface area of bubbles (mm), is the specific surface area of free water surface (mm), CS is the TDG concentration at atmospheric pressure (100%), Cse is the TDG equilibrium saturation within the bubble at a certain water depth (%).

TDG equilibrium saturation within the bubble

The TDG equilibrium saturation within the bubble is related to the hydrostatic pressure acting on the bubble, and its calculation expression is represented by the following equation (Demoyer et al. 2003).
(24)
where ΔP is the relative pressure of bubbles at depths of water (Pa), γ is the water weight (kg/m3), and h is the water depth (m).

Gas–liquid interfacial mass transfer coefficient and its mass transfer area

The calculation of the gas–liquid interface mass transfer coefficient and its mass transfer area is represented by Equations (25) and (26), respectively (Higbie 1935; Qin & Li 2008). And the distribution of the mass transfer area of bubbles is expressed in the form of the normal distribution function, which improves the traditional uniform particle size distribution and can better simulate the gas concentration distribution in aeration. So, the bubble size conforms to the normal distribution with the mean value μ = 3.0 mm and the standard deviation σ = 0.5, that is μσ (3.0, 0.52).
(25)
(26)
where R is the diameter of the bubble (mm), Pe is the Peclet number (Pe = 2RVr/Dm), Re is the Reynolds number (Re = 2R[(2κ/3)1/2]/Vt), Vr is the bubble rise velocity (m/s), Dm is the molecular diffusivity coefficient (Dm = 2.5*10−9m2/s), Vt is the turbulent diffusion coefficient, β is the TDG source treatment sensitivity parameter.

Water free-surface mass transfer coefficient and its mass transfer area

Equation (27) for the water free-surface mass transfer coefficient is based on the relevant reference (Cheng et al. 2009), and its mass transfer area is represented by Equation (28).
(27)
(28)
where V is the volume of the model (m3), ΔZ is the surface grid size of the model.

Determination of TDG source treatment sensitivity parameters

The TDG source treatment sensitivity parameters were determined through the trial method for β = 7.78, β = 9.48, β = 10.52, β = 11.78 and β = 12.95. And the comparison of the supersaturated TDG dissipation obtained from the TDG source treatment sensitivity parameters with the original experimental data is shown in Figure 10. We see that when β = 10.52, the experimental data and calculated values are relatively similar.
Figure 10

Comparison of the supersaturated TDG dissipation obtained from the TDG source treatment sensitivity parameters with the original experimental data.

Figure 10

Comparison of the supersaturated TDG dissipation obtained from the TDG source treatment sensitivity parameters with the original experimental data.

Close modal

TDG dissipation model in aeration

In order to verify the effect, variation and error of these TDG source treatment sensitivity parameters on the dissipation process of supersaturated TDG, the TDG dissipation model obtained in Eulerian-Eulerian approach is shown in Figure 11. These TDG dissipation models with aeration rate shows that when the parameter is 7.76, 9.48, 10.52, 11.78 and 12.95, respectively, accordingly the concentration variation of supersaturated TDG is 146.7~105.55%, 146.4~105.19%, 147.6~105.12%, 146.3~104.32% and 145.8~103.78%, respectively, and the TDG concentration drop values are 41.15, 41.21, 42.48, 41.98 and 45.02%, respectively. And the difference between the peak concentration value and the initial concentration (G = 147.4%) is 0.7, 1, 0.2, 1.1 and 1.6%, respectively. Therefore, when β = 10.52, this further explains that the experimental data and calculated values are relatively similar, the corresponding difference is 0.2%.
Figure 11

Dissipation process of supersaturated TDG at each parameter.

Figure 11

Dissipation process of supersaturated TDG at each parameter.

Close modal

In order to explore necessary measures to mitigate the harm of supersaturated TDG. Based on the gas–liquid mass transfer mechanism, indoor mechanism experiments and numerical simulation of methods, this paper profoundly aims to investigate the effect of aeration measures on water environments containing high concentrations of supersaturated TDG.

Experimental results indicate that aeration is one of the essential measures to mitigate the harm of supersaturated TDG and plays an active role in the dissipation process of supersaturated TDG and has a significant promoting effect on the gas–liquid interface mass transfer. And the time required for the supersaturated TDG dissipation process decreases with the increase of aeration rate and aeration aperture but is elevated with the increase of aeration depth, that is Tθ > TQ > TH, and TDG dissipation coefficients are elevated with the increase of aeration rate and aeration aperture, but are diminished with the increase of aeration depth, namely that of KQ > Kθ > KH. Compared to the pinhole aeration method, this aeration method's larger aeration aperture has a promoting effect on the dissipation of supersaturated TDG. Besides, the relationship between the relative TDG dissipation coefficient and aeration rate is established, which is a power function and positively correlated. And a crucial quantitative relationship between supersaturated TDG dissipation coefficient and aeration conditions (aeration rate, aeration depth and aeration aperture) is established, that is, the TDG dissipation coefficient is positively correlated with aeration rate and aeration aperture in a power function, and negatively correlated with aeration depth in a power function. Their relative errors are within the controllable range. Moreover, one of the aeration data is selected for numerical simulation. When the critical TDG source treatment sensitivity parameter β = 10.52, the error between the actual supersaturated TDG dissipation process and the TDG dissipation model is 0.2%, and the experimental data and simulation values are close.

This study provides essential scientific data and guiding suggestions for promoting the dissipation of supersaturated TDG and mitigating its harm and also indicates that aeration is likely to be one of the critical mitigating measures for TDG basins with high concentrations of local areas in the future. In future work, we should consider the impact of temperature, salinity, density and dynamic viscosity on supersaturated TDG, and for practical engineering applications, we will actively explore the application of aeration measures in basins with a high concentration of supersaturated TDG.

The article is supported by: National Natural Science Foundation of China (Grant No.51709053) and the Science and Technology Fund of Guizhou Province (No.QKHJ-2019-1117).

Y. Y. conceptualized the whole article, developed the methodology, investigated the article, rendered support in formal analysis, prepared the experiment, wrote the original draft and edited the article. H. Y. brought the resources, supervised the article, rendered support in funding supply, and reviewed the article. Y. W. prepared the experiment.

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

The authors declare there is no conflict.

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