Tool to Predict TDG for the Columbia River Basin

The authors propose a simplified method for determining total dissolved gas (TDG) uptake at hydropower facilities on the Mid-Columbia River. This work constitutes a significant contribution to a much larger effort aimed at improving real-time optimized scheduling of hydropower systems with respect to TDG constraint and control.

By Boualem Hadjerioua, Marcela Politano, Scott DeNeale, Merlynn D. Bender and Alejandro Castro

Boualem Hadjerioua, PhD, is deputy water power program manager and senior research engineer with Oak Ridge National Laboratory. Marcela Politano, PhD, is a research engineer with IIHR — Hydroscience & Engineering. Scott DeNeale is a water resources engineer in the Environmental Sciences Division of ORNL. Merlynn Bender is a hydraulic engineer and modeler with the U.S. Department of Interior’s Bureau of Reclamation. Alejandro Castro, PhD, is a research assistant scientist with IIHR — Hydroscience & Engineering.

This article has been evaluated and edited in accordance with reviews conducted by two or more professionals who have relevant expertise. These peer reviewers judge manuscripts for technical accuracy, usefulness, and overall importance within the hydroelectric industry.

Total dissolved gas (TDG) supersaturation can cause gas bubble trauma in fish, resulting in injury or mortality. TDG supersaturation became evident in the Columbia River Basin (CRB) in the Pacific Northwest of the U.S. in the 1960s.¹ The effect of TDG supersaturation depends on TDG levels, exposure time, fish life stage and swimming depth.2,3

TDG production is a complex process. The energy in spillway flows introduces bubbles and creates waves and sprays. When bubbles are carried to deep, high-pressure regions in the stilling basin, solubility increases and air is transferred from the bubbles to the water. TDG production is affected by the amount of air entrained in the spillway and during plunging of spillway flows, breakup and coalescence of entrained bubbles, and mass transfer between bubbles and water. TDG distribution downstream of dams is strongly coupled with the hydrodynamics in the tailrace and river downstream. A lateral gradient of TDG is frequently observed in tailraces due to the location of the spillway or operation of the dam.

More than 50 dams throughout the CRB are managed for irrigation, hydropower production, flood control, navigation and fish passage, which frequently results in spillway releases. Dam operations are constrained by state and federal water quality criteria, which balance the benefits of spillway operations designed to pass Endangered Species Act (ESA)-listed fish with the degradation to water quality as defined by TDG supersaturation. In the 1970s, the U.S. Environmental Protection Agency (EPA), under Section 303(d) of the Clean Water Act, established a criterion not to exceed the TDG supersaturation level of 110%.

The states of Washington and Oregon have adopted standards for TDG supersaturation on the Columbia and Snake rivers. With oversight by Oak Ridge National Laboratory (ORNL) for the U.S. Department of Energy (DOE), TDG modeling experts from the U.S. Army Corps of Engineers (USACE) and U.S. Department of Interior’s Bureau of Reclamation and IIHR at the University of Iowa are developing a method for predicting and managing TDG at the Columbia and Snake river dams.⁴ A system-wide real-time data-driven approach should meet the needs to summarize the findings from operational and structural TDG abatement programs conducted throughout the CRB and to develop a prediction model that pools data collected at projects. A generalized TDG exchange model can be tuned to specific projects and coupled with water regulation models to formulate optimal daily water regulation schedules.

The major issues regarding predicting TDG during spillway releases are air entrainment and the effect of water entrained from the powerhouse into the spillway region. Spillway jets may significantly change the tailrace flow pattern because they attract water toward the spillway region, a phenomena called water entrainment. This entrainment increases the amount of water in the aerated zone, resulting in more supersaturated water and modified downstream mixing.

SYSTDG is a real-time tool developed to provide support to spill management throughout the CRB.5″>href=”mailto:CRB.@5″>CRB.5 The SYSTDG model uses empirical equations that relate TDG production to unit spill and tailwater depth. In contrast, the model developed in this study mathematically incorporates the main physical processes including air entrainment, bubble dissolution and TDG transport.

Methodology

Many models require calibration with data collected at a particular site. Site-specific characteristics that may impact TDG exchange include structural features of the spillway and stilling basin, such as spillway flow deflectors, stilling basin and tailrace channel depths, training walls, baffle blocks and end sills, and spillway gate geometry.

There are no generalized predictive tools readily available and applicable to assessing the effects of hydro operations on downstream TDG minimization and/or reduction. A generalized empirical approach could be used as a supplemental tool in daily hydropower operations or long-term planning scenarios to predict and assess TDG levels in a simplified fashion.

TDG in the tailrace was modeled three ways: control vlume at the aerated zone (top), air entrainment at the plunging point in bay n (middle) and at depth Hb (bottom).

The uniqueness of this research is its classification of structural, operational and environmental parameters in the development of a predictive generalized TDG exchange formulation. Operational and environmental parameters involve stilling basin channel depth, total head, spill volume and pattern, powerhouse flow, background TDG pressure, water temperature, and local barometric pressure. Structural properties involve spillway geometry and incorporation of spillway flow deflectors, training walls, endsill and baffle blocks, training walls, and proximity of powerhouse flows. Different ranges of the main parameters associated with the highest response to TDG levels are to be established; classifications based on combinations of these main parameters are then developed. While tradeoffs may exist in such a simplified tool, it is important to conserve predictive accuracy such that it can still be regarded as a viable alternative for predicting TDG.

Dams in the CRB employ a variety of spill bay, powerhouse, and plunge pool configurations ideal for model calibration and development. In addition, a system-wide approach is needed because elevated TDG levels produced by projects on the upper Columbia River affect TDG levels at projects down river. A challenge associated with system-wide TDG analysis is collection of data from projects operated by independent organizations. USACE, Reclamation and multiple local utilities play a role in managing the water resources of the CRB.

Hourly data for eight CRB dams were collected from the USACE Northwestern Division’s Dataquery system and Historical Water Quality Reports (HWQR) database. The data include measurements of TDG, water temperature, and headwater and tailwater elevations, as well as flow and energy measurements at the dams.

Hourly unit spill operational data are needed to fully model TDG exchange. This information is especially important for projects that employ outlet works conduits in conjunction with traditional spill bays, such as Grand Coulee. The use of outlet works conduits can greatly influence air bubble entrainment depth.

Available data for Grand Coulee did not specify which gates and conduits were open or the flow rate through individual gates. Using total spill (available from the USACE databases) in conjunction with the outlet works rating curve and headwater elevation, it is possible to calculate unit spill for the majority of spill scenarios. Chelan County Public Utility District provided unit spill operation data for Rocky Reach and Rock Island dams.

Model development

Equations to predict TDG downstream of a hydropower facility were developed based on the main physical processes involved in TDG production and downstream mixing, including air entrainment during the plunge of spill water in the tailrace, bubble dissolution, and entrainment of powerhouse water into the spillway region. The independent variables included in the equations are: tailwater depth, powerhouse flowrate, spillway flowrate, unit spill, project head, and environmental variables (atmospheric pressure and temperature).

Air entrainment
The model is based on three assumptions:

Most air entrainment occurs in the tailrace at the plunging region and entrainment along the spillway face can be considered negligible;
The energy available for air entrainment is a function of project head and unit spillway flow;
Bubbles in a spillbay are entrained at a maximum depth of Hnb; and
Bubbles are entrained with a monodisperse size distribution.

Mathematical model
TDG in a tailrace near the dam is modeled by applying mass and momentum balances to a control volume that extends downstream of the impingement point to the end of the aerated zone (see Figure 1). TDG concentration is defined as:

Equation 1
TDG = C / Catm
where:

C is the concentration of dissolved gas or solubility; and
Catm is the gas concentration in equilibrium at atmospheric pressure.

Following are the six assumptions that are used when modeling TDG:

Negligible mass transfer at the free surface. Mass transfer between bubbles and liquid is a more efficient process than mass transfer at the free surface and it can therefore be neglected in the aerated zone.
Vertical TDG distribution is accounted for by considering streamwise transport of TDG.
A one-dimensional model for the average TDG at a given location downstream of the spill is formally obtained by averaging the two-dimensional TDG profile in the depth coordinate.
Velocity and therefore transport in the vertical direction is assumed to be negligible. Only transport downstream is considered.
Turbulent mixing is neglected when considering the transport of bubbles. As a consequence bubbles are confined to the aerated zone.
TDG dilution by powerhouse flows occurs downstream of the aerated zone.

Because the mean flow in the vertical direction is zero, the 2D concentration is transported according to:

Equation 2
where:

U is the streamwise velocity; and
S (x,z) is the TDG source by bubble dissolution, which is a function of the difference between TDG at equilibrium and local TDG. TDG at equilibrium is calculated following the Henry’s law considering the effect of the temperature on the Henry coefficient. Total gas dissolution increases with the gas volume fraction, which depends on air entrainment modeled considering unit spill and project head.

Streamwise velocity
Velocity in a spillway bay before the plunging of spillway jets in the tailrace can be calculated assuming zero loss. The velocity in the tailrace is then calculated considering that part of the kinetic energy contained in the spillway jets is lost both during the plunge into the tailwater pool and at the bottom of the tailrace.

TDG concentration downstream of the aerated zone
TDG measurements are usually collected downstream of the dam where mixing with powerhouse flows has occurred. Assuming full mixing, TDG concentration is:

Equation 3
where:

C0 is forebay TDG;
HT is the tailrace depth;
Hb is the bubble depth;

Qs is spill;
Qp is the powerhouse flow; and
C1 and C2 are model parameters related to water entrainment that are a function of the dam geometry and depend on the spillway and powerhouse configurations.

Description of dams
Project operational data were available for three dams on the Mid-Columbia River: Grand Coulee, Rocky Reach and Rock Island. Analysis of operational and field data, as well as implementation of the proposed model, was performed using the computing environment MATLAB.

Analysis of TDG data from Rocky Reach Dam from 2008 to 2012 demonstrates mean TDG uptake was about -0.4%. Average net TDG uptake when the dam was spilling is about 0.3%. Because TDG production at Rocky Reach is insignificant, data for this dam were not used to validate the model.

Rock Island comprises a complex spillway with 31 spillway gates, a first powerhouse with 11 units and a second powerhouse with 8 units. A deflector was installed in spillway bay 16 to reduce TDG production. Tailrace bathymetry is complex and ranges in elevation from about 580 feet near bays 21 to 23 to about 520 feet near bay 1.6

Plant operations, temperature, pressure, forebay and tailwater elevations, and TDG field data from April 2008 to Sepember 2012 at one-hour intervals were provided by Chelan County PUD. Two fixed monitoring stations collected TDG and temperature data at Rock Island Dam from April through autumn as part of the TDG monitoring system.

Grand Coulee Dam is comprised of a spillway, two powerplants on the left and right sides of the spillway, and a third powerplant located almost parallel to the right abutment. Two water quality monitoring stations collect TDG and temperature data at Grand Coulee. Station FDRW measures TDG in the forebay and GCGW measures TDG in the river 6 miles downstream of the dam. Tailwater and forebay elevations are found at www.nwdwc.usace.army.mil/tmt/wq/historical.

Operators tend to use the regulating outlet below a forebay elevation of 1265.5 feet and the drum gates above 1266.5 eeft. In addition, when drum gates are used, spill is uniform in all 11 gates.

Total dissolved gas

Figure 2 on page 56 shows TDG in the forebay and tailrace of Rock Island Dam. There is a direct relationship between increased spill flow and higher tailrace TDG. Both the forebay and tailrace TDG levels were higher in 2011 than in other years.

Figure 3 shows TDG measured in the forebay and tailrace of Grand Coulee Dam. Water released in the spillway plunges into the roller bucket energy dissipater, increasing tailwater TDG concentration. Elevated values of TDG were measured in 2011 when the ratio of spill to river flow was larger than the rest of the analyzed years.

Model application

The capability of the model to represent TDG downstream of a dam was tested using field data. Data collected at Grand Coulee and Rock Island dams were filtered to remove outliers. Only events with spill and TDG concentration in the tailrace larger than those measured in the forebay were considered.

Rock Island Dam
A nonlinear regression model was used to obtain the eight model parameters that minimize the error between predictions and field data collected at Rock Island in 2010. After calibration, the model was validated using data collected in 2008, 2009, 2011 and 2012.

The coefficient of determination R2 was used to evaluate the capability of the model to reproduce the measured TDG:

Equation 4

The second term in the equation represents the proportion of the variation that is unexplained by the model. The R2 coefficient for all data from 2008 to 2012 was 0.9626, indicating very good agreement between measurements and predictions. Figure 4 on page 62 compares TDG predicted and measured.

Grand Coulee Dam
Because the number and location of regulating outlets are unknown, operations with only drum gates were analyzed. Only events with TDG concentration in the tailrace larger than those in the forebay were analyzed and used to compare against model results.

Model parameters determined for Rock Island Dam were demonstrated to over-predict TDG at Grand Coulee Dam. Only the two most important parameters, C1 and C2, were recalibrated using 2010 data for the Grand Coulee results. These parameters are related to the maximum depth bubbles can travel in the tailrace and the vertical distribution of the gas volume fraction. The model was then validated comparing model predictions against TDG and net TDG uptake collected in 2008, 2011 and 2012. Only a few days were observed with spill and positive TDG uptake during years prior to 2008 and in 2009 and therefore these years were not useful for model comparison.

Fit of the proposed model is shown in Figure 5 (page 62). The R2 coefficient for 2008 to 2012 was 0.9197, indicating a good agreement between field data and model predictions. The coefficient of determination of the model for 2012 is significantly lower than in the other years. With the selected parameters, the model over-predicts the measured TDG most of the time in 2012. Data in this year are only available during the summer for conditions with elevated powerhouse and spillway flows. These results, together with those obtained for Rock Island Dam, seem to indicate that the model should be improved for extreme powerhouse or spillway operations.

Conclusions and future directions

The aim of this study was to demonstrate that a simplified model based on physical mechanisms rather than on empirical correlations can capture the main TDG trends observed downstream of a hydropower facility. The model reproduced the net TDG uptake measured in the tailraces and captured the observed TDG variation with spillway and powerhouse flowrates. The largest differences between predictions and measurements occurred for extreme spillway or powerhouse flow rates and proportions thereof, likely due to over-simplification of the water entrainment model. Numerical modeling of the hydrodynamics in the tailrace or velocity field data can guide the development of a more comprehensive water entrainment model.

To improve and further generalize the model for application to other dams, it is necessary to include all important processes and geometric characteristics that affect air and water entrainment. Future development work should focus on:

Inclusion of mass transfer at the free surface to predict TDG routing from a dam tailrace to a downstream forebay.
Understanding the effect of the spillway deflectors on the maximum penetration depth of the bubbles and vertical gas distribution. TDG field data along with a deflector performance curve can be used to understand the effect of spillway jet regimes on these parameters.
Development of advanced mathematical models to represent air entrainment as a function of turbulence. This is expected to significantly improve model generalization.
Development of a simple turbulence model, which is needed for air entrainment modeling and also to improve prediction of bubble/liquid mass transfer.
Improvement of water entrainment models based on numerical or velocity field data.

Proposed future work includes the following tasks:

Model development for the five remaining projects on the Mid-Columbia River (preliminary calibration and validation has been completed).
Implementation of the predictive developed TDG equations into RiverWare, a real-time scheduling tool developed by CADSWES, Colorado State University.
Verification, simulation and optimization of the real-time scheduling tool.
Quantification of the added value of the optimization real-time scheduling tool.

Notes

1Ebel, W.J., “Supersaturation of Nitrogen in the Columbia River and its Effect on Salmon and Steelhead Trout,” United States National Marine Fisheries Service Fishery Bulletin 68, 1969, pages 1-11.

2Weitkamp, D.E., and M. Katz, “A Review of Dissolved Gas Supersaturation Literature,” Transactions of the American Fisheries Society, Volume 109, 1980, pages 659-702.

3Bouck, G.R., “Etiology of Gas Bubble Disease,” Transactions of the American Fisheries Society, Volume 109, 1980, pages 505-516.

4Pasha, M.F.K., et al, “Prediction of Total Dissolved Gas (TDG) at Hydropower Dams throughout the Columbia River Basin (CRB) — Challenges and Proposed Methodology,” Proceedings of HydroVision International 2012, PennWell Corp., Tulsa, Okla., 2012.

5Schneider, M.L., SYSTDG Primer, CE-ERDC, US Army Engineer Research and Development Center, Vicksburg, Miss., 2003.

6Frantz, W., “2012 Gas Abatement Annual Report, Rocky Reach and Rock Island Hydroelectric Projects FERC No. 2145 and 943,” Chelan County Public Utility District, 2012.

Reference

Hadjerioua, Boualem, et al, “Predicting Total Dissolved Gas (TDG) for the Mid-Columbia River System,” Proceedings of HydroVision International 2014, PennWell Corp., Tulsa, Okla., 2014.

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