Science in China Series E: Technological Sciences

© 2009 SCIENCE IN CHINA PRESS

Citation: Li R, Li J, Li K F, et al. Prediction for supersaturated total dissolved gas in high-dam hydropower projects. Sci China Ser E-Tech Sci, 2009, 52(12): 3661−3667, doi: 10.1007/s11431-009-0337-4

www.scichina.com tech.scichina.com

www.springerlink.com

Prediction for supersaturated total dissolved gas in high-dam hydropower projects

LI Ran, LI Jia†, LI KeFeng, DENG Yun & FENG JingJie State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

The supersaturated total dissolved gas (TDG) generated during high dam spills may cause gas bubble disease for fish and ultimately endanger their existence. As more and more high-dam hydropower projects have been constructed in China, the environmental assessment of the supersaturated TDG is becoming more and more important. It is of great importance for quantitative impact assessment of the supersaturated TDG of high dams and for the construction of ecological friendly high-dam hydropower projects. Based on the conceptual summarization of the TDG production process, the TDG prediction model for high-dam projects, in which the ski-jump energy dissipation is adopted, is developed in the paper. The model is validated by field data and employed in the TDG prediction of a high-dam hydro-power project to be built in southwest China.

high dam, ski-jump energy dissipation, total dissolved gas, supersaturation

1 Introduction

The supersaturation of total dissolved gas (TDG) may cause gas bubble disease for fish and ultimately endan-ger their existence. Therefore the problem of supersatu-ration of TDG becomes one of the main adverse impacts of the high-dam hydropower projects. With the devel-opment of the western region and the implementation of “West-East Power Transmission Strategy” in China, a group of high-dam hydropower projects, such as Zi- pingpu, Xiluodu, Xiangjiaba and Jinping, have been constructed or under construction, and also a great number of high dams with the height of more than 200 m, such as Shuangjiangkou and Baihetan, are to be con-structed. Due to the unique climate and geography, aquatic organisms in the western rivers of China are rich and characterized by a high degree of endemic species. The problem of the supersaturated TDG caused by the spillway discharge will become more and more promi-nent in China. As there is little field observation and quantitative TDG prediction model for high-dam hydropower project, the environmental impact assess-ment and its abasement study are affected and

hampered seriously. The research about the TDG supersaturation was ini-

tiated in the United States. The study focused mainly on the effects of the supersaturated TDG resulting from spill discharge of the hydraulic engineering in Columbia River and Snake River, which caused damages to the Salmon and other rare and precious fisheries[1,2]. The research involved fish impact investigation, TDG pro-duction and dissipation process, abatement measures and so on. The prediction method for the oversaturated TDG covers empirical formula, one-phase model and two- phase model[3,4]. However, all the results have been ob- tained from middle-head or low-head hydraulic projects, the heads of which are less than 50 m and the underflow energy dissipation is employed. As the ski-jump energy dissipation is usually adopted in high-dam projects with the height of more than 100 m or even 200 m, the TDG generation process is different from that of low or mid-dle head projects. Therefore the earlier research results Received May 8, 2009; accepted July 19, 2009 doi: 10.1007/s11431-009-0337-4 †Corresponding author (email: lijia@scu.edu.cn) Supported by the National Natural Science Foundation of China (Grant No. 50579043) and the Open Foundation of the State Key Laboratory of Hydraulics and Mountain River Engineering (Grant No. 0604)

3662 Li R et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3661-3667

cannot be applied directly in high dams in China. In 1980s, the problem of the supersaturated TDG and

its negative effect on fish was realized in China during the early operation of Gezhouba hydropower project. A preliminary investigation was carried out by Water Re-sources Protection Bureau of Yangtze River of China in 1983. In recent years, the problem of the supersaturated TDG caught the attention of researchers again as more and more hydropower stations have been under opera-tion or construction[5,6]. It shows that there exits empiri-cal relationship between TDG level and discharge rate, but the relationship is varied with projects and it is dif-ficult to develop a general empirical formula suitable for all projects. With the development of numerical simula-tion technology, some researchers began to study the TDG prediction by employing the numerical simulation technology. As there is lack of knowledge on air-water interface mass transfer, some coefficients in the numeri-cal simulation are difficult to determine. Also there are some convergence and economy difficulties in the two- phase flow numerical simulation for the whole discharge process of high-dam projects. As such, although the TDG prediction model for high-dam project is of great practical significance and theoretical value, there is cur-rently no satisfactory model of this kind being reported.

2 Development of TDG prediction model The previous study on the dissolution process of gases shows that temperature, salinity and pressure are the main factors affecting the dissolubility, while the inter-face area and turbulent intensity affect the dissolution rate[7]. For the discharge flow with large amount of air bubbles and high turbulence intensity, the temperature and salinity are relatively stable. In such a case, the dis-solubility of bubbles, which indicates the TDG satura-tion level, is determined mainly by the hydrodynamic

pressure and the water depth, which represents the hy-drostatic pressure. Therefore the prediction model to be developed in the following will take the water depth and the hydro-pressure as the main dependent variables.

The scour hole and the plunge pool are two kinds of energy dissipation structures employed by high-dam projects (see Figure 1). When the jet is far from dam, the scour hole formed naturally is employed to dissipate the flood energy. While the dropping location of the jet is close to the dam, a plunge pool and a second dam have to be constructed for energy dissipation. Because of the difference in energy dissipation inside the scour hole and the plunge pool, the production of the supersaturated TDG and its prediction model are specific. The models for the scour hole and the plunge pool are to be illus-trated individually below. 2.1 TDG model for the scour hole The TDG generation process of the supersaturated TDG and its affecting factors were analyzed by the U.S. Army Corps of Engineers in 2005[8]. It was assumed th the spills experienced a rapid absorption of gases inside the stilling basin where the air content, depth of flow, flow velocity and turbulence intensity were generally high. As the flows moved out into the tailrace channel, the net mass transfer reversed and component gases were stripped from the water column as the entrained air rose and was vented back to the atmosphere. According to the mechanism analysis, the production of the super-saturated TDG can be summarized into two conceptual stages. The first conceptual stage is the oversaturation process of gases in high-pressure aerated flow inside the scour hole, where the averaged percentage TDG level is G1 and the oversaturation percentage level is Δ G1. The second stage is the instantaneous dissipation process of the oversaturated TDG for the sharp decrease of pressure and water depth when it moves out of the scour hole,

Figure 1 Sketch of ski-jump energy dissipation structure.

Li R et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3661-3667 3663

where the averaged percentage of TDG level in the end is Gd and the percentage oversaturation level is ΔGd.

The pressure in the scour hole is usually lower than 10 atmospheric pressure. It is showed that the dissolu-bility of air is proportional to the pressure under such pressure condition[5]. Thus on the first conceptual stage, the oversaturation level in the scour hole, ΔG1, is as-sumed to be approximately proportional to the averaged pressure, PΔ . The relationship is expressed as follows:

1 eq0

= PG GPΔ

Δ , (1)

where ΔP is the averaged relative pressure in the scour hole (kPa); P0 is the local atmospheric pressure (kPa); Geq denotes the percentage of TDG equilibrium concen-tration at the local atmospheric pressure (%).

Except in some local areas, the hydrodynamic pres-sure in the scour hole along the water depth is in linear distribution approximately[6,9]. The equation can be written as follows:

1 1 eq0

1=2

dPG G

Pφ

ΔΔ , (2)

where Δ dP is the averaged pressure on the bottom of the scour hole (kPa), which can be determined according to the relative criterion, standard and physical model,

1φ denotes the correction coefficient. On the second conceptual stage, the oversaturation

level ΔGd at the end of the second stage is related to the averaged oversaturation level in scour hole, ΔG1, the averaged water depth in scour hole, hd, and the averaged water depth downstream the scour hole, hr. According to the research result on TDG dissipation process of the U.S. Army Corps of Engineers, the dissipated process is defined as first-order kinematics:

eqd = ( )dG k G Gt

− − , (3)

where the coefficient k is proportional to 3 2 power of the water depth: 3 2( )k f h−= . (4) From eqs. (3) and (4), it can be reduced as follows:

3 20= exp ( )eG G f h−⎡ ⎤Δ Δ −⎣ ⎦ , (5)

where ΔG0 represents the original TDG saturation level and ΔGe denotes the TDG saturation level in the end.

According to eq. (5), the instantaneous dissipation process of the oversaturated TDG at the outlet of the scour hole can be expressed as 3 2

1= exp ( )d rG G f h −⎡ ⎤Δ Δ −⎣ ⎦ . (6)

Taking into account the effects of the scour hole depth of hd, the nondimensionless factors hr/hd and kd are intro-duced and the following equation can be obtained:

3 2

1= exp dd d

r

hG G k

h

⎡ ⎤⎛ ⎞⎢ ⎥Δ Δ − ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

. (7)

Substituting eq. (2) into (7), we obtain

3 2

eq 1 eq0

1= exp2

d dd d

r

P hG G G k

P hφ

⎡ ⎤⎛ ⎞Δ ⎢ ⎥+ − ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

. (8)

Eq. (8) is the supersaturated TDG prediction model for the scour hole.

2.2 TDG model for the plunge pool

Similar to the analysis of the scour hole, the generation of the supersaturated TDG for the plunge pool can be summarized into two stages also. The first stage is the oversaturation process of gases in high-pressure aerated flow in the plunge pool. The second stage is the instan-taneous dissipation process of the oversaturated TDG for the sharp decrease of pressure and water depth when it moves out of the plunge pool. By taking the same analy-sis method with that of the scour hole, the TDG model for plunge pool is developed as follows:

3 2

eq 2 eq0

1 exp2

k kk k

t

P hG G G k

P hφ

⎡ ⎤⎛ ⎞Δ ⎢ ⎥= + − ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

, (9)

where Gk represents the TDG saturation level in percent downstream the plunge pool, Δ kP is the averaged pressure on the bottom of the plunge pool (kPa), which can be determined according to the relative criterion, standard and physical model, 2φ is the correction coef-ficient, kk represents the TDG release factor near the second dam, hk denotes the height of the second dam, and ht denotes the water depth above the second dam. The models for scour hole (eq. (8)) and plunge pool (eq. (9)) have rather similar forms, both of which are related with pressure and water depth. However because of the difference in energy dissipation characteristics in scour hole and in plunge pool, the pressure and water depth will be different under the same spill rate, resulting in different TDG saturation levels.

3664 Li R et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3661-3667

3 Model validation and parameter cali- bration

The preceding TDG prediction models were validated by field observation data of the high dams. Sponsored by the National Natural Science Foundation of China, TDG field observation of the existing high dams in China, such as Three Gorges, Ertan and Manwan, was conducted by Sichuan University during 2006 to 2008. The locations of the projects are illustrated in Figure 2. Features of the projects are shown in Table 1.

The TDG pressure in water was measured by YSI52 TGP probe made by YSI Company. The TDG saturation level in percent was obtained by dividing the TDG pressure with local atmospheric pressure. The observed sections were tried to be located near the outlet of the scour hole or the plunge as far as possible. However, limited by topography conditions, some observed sec-tions had to be located far away from the scour hole or the plunge pool, such as Ertan and Three Georges. The location of the observed sections and the measurement of TDG in the projects are shown in Table 2.

The TDG level at the downstream of each observed project was observed to be supersaturated. The highest TDG level observed was shown to be located at down-stream of the Three Gorges dam, which is about 143%.

The maximum TDG level of each project is listed in Table 2.

The TDG models for the scour hole and the plunge pool were calibrated by the observed results. The hy-drodynamic pressure at the bottom of the energy dissi-pation structure of each project was needed in the cali-bration. It was determined according to the experimental research by physical model and the design results of the energy dissipation structure of each project. The mixing model was employed to consider the entrance of the powerhouse tail water when the powerhouse was running during observation. The calibrated results for the models of the scour hole and the plunge pool are listed in Tables 3 and 4 individually. The comparison between the computed results by the model and the ob-served data is shown in Figure 3.

For the model of scour hole, the correction coefficient

1φ is calibrated to be 0.40—0.55 and the TDG dissipa-tion coefficient kd near the outlet of scour hole is cali-brated to be 0.1—0.2. For the model of plunge pool, the correction coefficient 2φ is calibrated to be 0.43—0.56 and the TDG dissipation coefficient kk near the outlet of scour hole is calibrated to be 0.08—0.12.

The difference of TDG level in percent between the computed results and the observed data is less than

Figure 2 Locations of the field observation projects.

Table 1 Features of the high-dam projects for TDG field observation

No. Project River Dam type Maximum dam

height (m) Release structure

1 Ertan Yalong River concrete hyperbolic arch dam 240 surface, middle and bottom discharge orifice, discharge tunnel

2 Zipingpu Minjiang River concrete deck rock-filled dam 156 discharge tunnel, spillway

3 Manwan Lancang River concrete gravity dam 132 surface and middle discharge orifice, discharge tunnel

4 Three Gorges Yangze River concrete gravity dam 185 surface and bottom discharge orifice

Li R et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3661-3667 3665

Table 2 Measurement of TDG of high-dam hydropower projects

No. Project Location of the observed sections Maximum TDG level (%) Occurrence time

1 Ertan 3000 m downstream the dam 140.0 2007-07-27

2 Zipingpu outlet of the scour hole 130.6 2006-12-28

3 Manwan outlet of the scour and plunge pool 124.0 2008-07-31

4 Three Gorges 4000 m downstream the dam 143.0 2007-07-10

Table 3 TDG calibrated results for scour hole model

Case No. Project Discharge rate (m3/s)

Power flow (m3/s)

Correction coefficientφ1

Dissipationcoefficient kd

Observed TDGlevel (%)

Computed TDG level (%)

Difference between computed and observed (%)

1 Ertan 3700 1809 0.50 0.20 140.0 138.1 −1.9

2 Ertan 1850 1263 0.48 0.15 134.1 130.1 −4.0

3 Ertan 2220 1263 0.40 0.20 121.6 126.6 5.0

4 Zipingpu 170 0 0.46 0.15 107.1 107.5 0.4

5 Zipingpu 310 0 0.47 0.15 111.0 113.7 2.7

0 6 7

Zipingpu Manwan

340 880 2304

0.48 0.55

0.15 0.10

114.9 120.0

115.7 115.6

0.8 −4.4

8 Manwan 540 1968 0.55 0.10 116.0 113.6 −2.4

Table 4 TDG calibrated results for plunge pool model

Case No. Project Discharge Rate (m3/s)

Power flow (m3/s)

Correctioncoefficientφ2

Dissipation coefficientkk

Observed TDG level (%)

Computed TDG level (%)

Difference between computed and observed (%)

1 Ertan 2400 1809 0.475 0.08 127.2 122.5 −4.7

2 Ertan 800 1809 0.429 0.08 122.6 118.1 −4.5

3 Manwan 1810 1927 0.562 0.08 124.0 120.5 −3.5

Figure 3 Comparison between computed results and observed data. (a) Scour hole; (b) plunge pool.

5.0%. Analysis shows that the error of the TDG predic-tion model is acceptable and the models can be used to predict supersaturated TDG at the downstream of high- dam projects.

4 Model error analysis

The field observation data was employed directly in the model calibration. Limited by the observation condition,

some observed sections were located far from the dam. The representation of the observed data relates with the model error.

Based on the conceptual summarization of the pro-duction process of the supersaturated TDG, the correc-tion coefficients of 1φ and 2φ are introduced into the models individually. The release factors of kd and kk are introduced to represent the instantaneous dissipation

3666 Li R et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3661-3667

process of oversaturated TDG for the sharp decrease of pressure and water depth when it moves out of the plunge pool and the scour hole. More thorough research and field observation should be made in order to deter-mine the factors more accurately in the future.

At present, both empirical formula recommended by design criterion or standard and physical model may be employed to determine the hydrodynamic pressure and water depth inside and downstream of the scour hole. For large spill rate of high dams, empirical formula may cause many errors, and then physical model must be employed simultaneously. Therefore, to avoid the re-sulting error in TDG prediction, more accurate results of the hydraulic design for energy dissipation should be adopted as much as possible.

5 TDG prediction for a high-dam hydro- power project in Southwest China

One high-dam hydropower project is to be built in Southwest China. The maximum height of the dam is 289.0 m. Its release structure consists of in-dam and in-bank release structures. The in-dam release structure consists of 6 surface discharge orifices, 7 bottom dis-charge orifices, with the plunge pool and second dam as its energy dissipation structure. The in-bank release structure consists of 3 discharge tunnels.

To evaluate the environmental risk of TDG super-saturation and to study about further abasement meas-ures, the supersaturated TDG under different discharge cases is predicted by employing the preceding TDG models developed in the paper. All the prediction cases are listed in Table 5. The parameters in the models of discharge tunnel and orifice are determined according to the preceding calibrated results by field observed data

and the discharge characteristics of the project. The value of parameters and the resulting TDG level are shown in Table 5.

The predicted results show that the TDG supersatura-tion phenomenon appears when the project spills due to its high water head and large flow rate. The maximum TDG level predicted is 143.8% when there is only one discharge tunnel operated. It tells that the problem of TDG supersaturation exists when the project is put into operation in the future.

It also shows that the TDG level varies with the dis-charge pattern. The TDG level is the lowest when the bottom orifice is under operation and that of the surface orifice is the second, while the TDG level of the dis-charge tunnel is the highest. To minimize the effects of the supersaturated TDG, it is suggested to discharge from the bottom orifice first and avoid discharging from the tunnel as far as possible.

6 Conclusions and future work

Two prediction models for the supersaturated TDG of scour hole and plunge pool of high-dam projects were developed in this study with the method of theoretical analysis and field observation. The models were em-ployed in the TDG prediction of a high-dam hydropower project to be built in Southwest China. Flood discharge characteristics such as water depth and pressure were taken into account in the model. As the variables are also important characteristic variables to be determined in the energy dissipation design of the project, the application range of the models are extended. The model is a part of pioneering research work in the environmental risk as-sessment of the supersaturated TDG downstream of high dams. It is important to evaluate the environmental

Table 5 Predicted TDG results downstream the high dam

Case No. Release mode Discharge rate (m3/s)

Correction coefficient 1φ

Dissipation coefficient dk

Correction coefficient 2φ

Dissipation coefficient kk

Predicted TDG level (％)

1 single surface orifice 11468 − − 0.495 0.08 140.0

2 single bottom orifice 10689 − − 0.473 0.08 135.0

3 single discharge tunnel 3703 0.46 0.2 − − 143.8

Li R et al. Sci China Ser E-Tech Sci | Dec. 2009 | vol. 52 | no. 12 | 3661-3667 3667

impact of the high dam project objectively. The supersaturated TDG problem is a difficult and

sophisticated problem which involves a two-phase flow and many complex influencing factors. The mechanism study about supersaturated TDG production process is

still ongoing, and the field observation on high dams is inadequate. Further improvement of the prediction model developed in the paper and its further application in the practical high dam projects will continue as more data are available.

1 Orlins J J, Gulliver J S. Dissolved gas supersaturation downstream of

a spillway Ⅱ: Computational model. J Hydraul Res, 2000, 38 (2): 151⎯159

2 Politano M, Carrica P, Turan C, et al. A multidimensional two-phase flow model for the total dissolved gas downstream of spillways. J Hydraul Res, 2007, 45(2):165⎯177

3 Huang H Q. Computational model of total dissolved gas downstream of a spillway. Doctoral Dissertation. Iowa: University of Iowa, 2002

4 Dai H C, Wang L L, Gao J Z, et al. Numerical simulation of two-phase

turbulent flow in hydraulic and hydropower engineering. Sci China

Ser E-Tech Sci, 2007, 50 (Suppl I): 79⎯89

5 Tan D C. Research on the lethal effect of the dissolved gas super-

saturation result from There Gorges project to fish (in Chinese). The

Master Thesis. Chongqing: Southwest University, 2006

6 Jiang L. Study on total dissolve gas supersaturation in downstream of

high dam (in Chinese). Doctoral Dissertation, Chengdu: Sichuan

University, 2008

7 Li R, Luo L. Study on the effect of hydrodynamic characteristics on

reaeration process. J Environ Sci, 2002, 14(3): 393⎯398

8 US Army Corps of Engineers. Technical Analysis of TDG Processes.

US Army Corps of Engineers —Northwest Division, Environmental

Resources and Fish Planning Offices, 2005

9 Diao M J. Numerical simulation and experiment study on flood dis-

charge and energy dissipation of high dam (in Chinese). Doctoral

Dissertation. Chengdu: Sichuan University, 2004