Improvement on numerical modeling of total dissolved gas dissipation after dam
Introduction
Construction of dams blocks the original flow of river and brings new flow regimes that never existed in natural streams. The total dissolved gas (TDG) supersaturation is one of the most essential problems brought by dam regulation. It would cause fish suffering from gas bubble disease and eventually affect the local riverine eco-environment. This problem was early mentioned in the Columbia River Basin in 1965 (Ebel, 1969), and then observed in numerous rivers due to the construction of dams (Weitkamp et al., 2003; Johnson et al., 2007; Bragg and Johnston, 2016). Large amount of atmospheric gas was entrained and subsequently transported to deep high-pressure regions in the stilling basin, where gas dissolution is enhanced (Geldert et al., 1998). To protect fish from the TDG supersaturation threat, a threshold of 110% for saturation has been set in the water quality standards (US EPA, 1986). Yet the peaking saturation level excessing of 130%, and even 140%, was observed in the plunging region of the tailrace (USACE, 2005; Qu et al., 2011). After being dissolved in the stilling basin with high pressure, the TDG dissipates in the downstream river. As the process of TDG dissipation is extremely slow, high TDG saturation levels may persist for hundreds of kilometers from the source of supersaturation (Feng et al., 2014). Thus, to evaluate the TDG saturation level downstream of the TDG supersaturated source is quite important in realizing river ecological restoration like protecting the fish habitat and aquatic environment.
Several mathematical models were developed to describe the dissipation process of TDG in a river. Perkins and Richmond (2004) derived a two-dimensional depth-averaged model, i.e., MASS2 to simulate the distribution of TDG saturation in shallow rivers. In the studies of Picktt et al. (2004) and Feng (2013), a one-dimensional mathematical model was developed and used to depict the variation of TDG saturation in a river downstream of the source of supersaturation. The description of TDG dissipation process in the above models is based on a first-order kinetics equation (USACE, 2005), in which TDG dissipation is featured as a coefficient (k). Also, some studies have shown that TDG can be analyzed using numerical models and machines learning models. The method of generalized regression neural network (GRNN) and another four data-driven models (high-order response surface method (H-RSM), least squares support vector machine (LSSVM), M5 model tree (M5Tree), and multivariate adaptive regression splines (MARS)) were applied for predicting TDG at Columbia River dams (Heddam, 2017; Keshtegar et al., 2019).
Previous studies have indicated that k is related to many factors, including hydraulic conditions, surface atmospheric conditions, etc. Flow velocity and turbulence intensity accelerate the TDG dissipation process, while water depth decreases the TDG dissipation rate (Qu et al., 2011; Rajib et al., 2019). Negative exponential relationship existed between water temperature and k (Shen et al., 2014). Wind-driven eddies promoted TDG dissipation, and thus led to higher k compared with calm water surface (Huang et al., 2016). An exponential function can be used to quantify the impact of wind on k. Sediment also promotes the TDG dissipation process, for the dissolved gas tends to gather around the sediment surface and then dissipate (Jones et al., 1999; Feng et al., 2012; Rajib et al., 2019). Although there were many factors affecting k, the calculation of the coefficient k is mainly based on flow velocity and water depth, which already reflect more or less other related factors (Picktt et al., 2004; Jha et al., 2010; Feng, 2013).
Several equations have been developed to estimate k in terms of flow velocity and water depth. As the dissipation process of TDG was convinced similar to surface reaeration in previous study, DO reaeration coefficient was directly taken by researchers to approximate k. In the MASS2 model, a DO reaeration equation proposed by Streeter et al. (1936) was used to estimate the TDG dissipation coefficient, taking into account the effects of flow velocity and water depth. While in the model developed by Feng et al. (2013), the DO reaeration equation proposed by O'Connor (1983) considering the effects of wind velocity is also used to estimate k. Nevertheless, the process of supersaturated TDG dissipation and DO reaeration is different (Li et al., 2013). The decay of supersaturated TDG was comparatively slower than DO (Rajib et al., 2016). Therefore, using DO reaeration coefficient to approximate k may induce large error. With the development of TDG saturation monitoring device, a regression formula to estimate the coefficient was proposed considering the effects of flow velocity, water depth and molecular diffusion (Picktt et al., 2004). The formula is further modified by using a comprehensive coefficient to replace the molecular diffusion (Feng, 2013; Ma et al., 2016). However, the equation was fitted by data from specific cases, restricting their applicability.
The objective of this study is to establish a more reasonable and generic equation to estimate k, based on flow velocity and water depth. The performance of the equation was evaluated using the field observations from the Xiangjiaba Reservoir. Comparisons were also made with another two typical equations to demonstrate the rationality and applicability of the developed equation.
Section snippets
Physical experiment for supersaturated TDG dissipation
The physical model for supersaturated TDG dissipation was shown in Fig. 1. The model consisted of two main parts, a supersaturated TDG generating device and an annular dissipation flume. The supersaturated TDG generating device was composed of pressure pot, air compressor, air inlet pipe, water inlet pipe, water outlet pipe, and rotor flowmeters (Fig. 1a). The annular dissipation flume included an annular flume, a nylon propeller, a transmission shaft and a motor (Fig. 1b).
At the beginning of
The simulated region and grid
The testing on the developed equation was based on the case of Xiangjiaba Reservoir in the Jinshajiang River, the upstream of Yangtze River (Fig. 2).
The simulated period was from June 20, 2017 to July 2, 2017, and the simulated region was from the Xiluodu Dam to the Xiangjiaba Dam, covering the 156 km long Xiangjiaba Reservoir. The rectangular grid was 1000 m in the longitudinal direction and 1 m in the vertical direction. The total number of grids was 14, 011 (Fig. S1).
The governing equations of TDG dynamics
The continuity equation
The equation of dissipation coefficient (k) based on experimental results
The dynamics of TDG under different flow conditions were presented in Fig. 3. The value of TDG saturation showed a decreasing trend with time. At the beginning, there was a dramatic decline in TDG saturation. It took a long time for TDG to reach equilibrium saturation. By comparing different scenarios, it was seen that the dissipation of TDG was affected by both water depth and flow velocity, and the dissipation rate increased with flow velocity while decreased with water depth.
To
Discussion
The TDG dissipation coefficient obtained in the present study ranges from 3.408 day−1 to 9.864 day−1. From the 9 different scenarios of hydraulic condition in the experiment, the lowest water depth and the fastest flow velocity led to the highest k value (Table 1). Both experimental results and previous study (Li et al., 2015) showed that k has an increasing trend with flow velocity and a declining trend with water depth. Considering the joint effects of flow velocity and water depth on TDG
Conclusions
In this study, an equation was built for estimation of k value using physical experiments of TDG dissipation. The performance of the developed equation was evaluated through comparison with other two representative equations. It was concluded that using DO reaeration equation to model TDG dissipation would lead to overestimation of TDG saturations, and empirical equations derived from specific field observations are not suitable to model TDG dissipation in significantly different conditions.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the National Key Project for Research and Development Plan (No. 2016YFC0502205), and National Natural Science Foundation of China (No. 51425902).
References (31)
- et al.
A laterally averaged two-dimensional simulation of unsteady supersaturated total dissolved gas in deep reservoir
J. Hydrodyn.
(2013) - et al.
Relationship investigation between the dissipation process of supersaturated total dissolved gas and wind effect
Ecol. Eng.
(2016) - et al.
Bubble nucleation from gas cavities—a review
Adv. Colloid Interf.
(1999) - et al.
Operational regulation of water replenishment to reduce supersaturated total dissolved gas in riverine wetlands
Ecol. Eng.
(2016) - et al.
Experimental study on the impact of temperature on the dissipation process of supersaturated total dissolved gas
J. Environ. Sci.
(2014) - et al.
Total Dissolved Gas and Water Temperature in the Lower Columbia River. Oregon and Washington, Water Year 2015. U.S. Geological Survey Open-File Report 2015–1212
(2016) - et al.
Predictive equation for longitudinal dispersion coefficient
Hydrol. Process.
(2015) Supersaturation of nitrogen in the Columbia River and its effect on salmon and steelhead trout
Fish. Bull.
(1969)The dissipation mechanism for total dissolved gas downstream of high dams and its application
(2013)- et al.
Experimental study on the sediment effect on releasing process of supersaturated total dissolved gas
Adv. Water Sci.
(2012)
Dissipation coefficient of supersaturated total dissolved gas in a one-dimensional longitudinal model
J. Cent. South Univ.
Modeling dissolved gas supersaturation below spillway plunge pools
J. Hydraul. Eng.
Analysis of Spillway Hydrodynamics for Total Dissolved Gas Prediction Downstream of Hydropower Projects with Free, Plunging Spillway Jets
Generalized regression neural network based approach as a new tool for predicting total dissolved gas (TDG) downstream of spillways of dams: a case study of Columbia River Basin dams, USA
Environ. Process.
Refinement of predictive reaeration equations for a typical Indian river
Hydrol. Process.
Cited by (5)
Photodegradation behavior and mechanism of dibutyl phthalate in water under flood discharge atomization
2023, Science of the Total EnvironmentField observation and numerical modelling of supersaturated dissolved gas at river confluence
2022, Ecological ModellingCitation Excerpt :The above analysis indicated that the results of flow-weighted averaging using the inflow supersaturated dissolved gas levels of two or more rivers can be used when accuracy is not required and can roughly meet the requirements. If fine-scale results of supersaturated dissolved gas processes in confluence areas are needed, it was recommended that numerical simulations be used to obtain the supersaturated dissolved gas distribution in the confluence as a method to more accurately analyse the effect of mainstream and tributary interactions on the dissolved gas distribution (Zeng, Mo, and Chen 2020). Using 115% as the safety saturation and statistical the safety zone acreage (Cao et al. 2016) form the confluence to the completed mixed section (YZR-U), which is the safety zone area ratio observed in Fig. 15, the zone acreages are not constant under unsteady conditions during study phase.
Water transparency prediction of plain urban river network: A case study of yangtze river delta in china
2021, Sustainability (Switzerland)
- 1
These authors contributed equally to the paper.