Improvement on numerical modeling of total dissolved gas dissipation after dam

Highlights

• An equation to estimate dissipation coefficient (k) of total dissolved gas (TDG) is proposed.

• The proposed equation outperforms the typical DO reaeration equation and empirical equation.

• DO reaeration equation is not suitable for estimating k values in shallow waters.

• The applicability of empirical equations is mostly restricted to specific conditions.

• The proposed equation is particularly applicable in reservoir-dispatched water with low sediment concentration.

Abstract

Discharge from high dam causes total dissolved gas (TDG) supersaturation, which dissipates slowly along the downstream river and induces fish bubble disease. The dissipation process is closely related to the hydraulic condition. In most TDG prediction models, the hydraulic condition is lumped in a parameter called the dissipation coefficient (k), whose determination usually contains large uncertainty. In this study, the property of k was experimentally investigated under three water depths and three flow velocities. The results demonstrated that the k value increased with v/H ratios. Based on the experimental results, an equation was proposed to calculate k value. The equation was validated by the observed data from field survey in Xiangjiaba Reservoir in the Jinshajiang River, the upstream of Yangtze River. Meanwhile, the proposed equation was compared to two typical equations, a dissolved oxygen (DO) reaeration equation and an empirical equation, using the same datasets. The comparisons indicated that DO reaeration equation was not suitable for k value estimation, particularly under shallow water conditions. The limitation of empirical equation was that the k value was determined by data from a specific case so that was not applicable to other conditions. The proposed equation showed best performance in calculating k value and hence estimating the TDG levels, especially under the condition of low sediment concentration. In addition, the proposed equation was more generically applicable compared to the existing formulas. Our findings could help to draw up governing measures to minimize the risk of supersaturated TDG and achieve river ecological restoration.

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.