Reaeration Equations Research Articles

Improvement on numerical modeling of total dissolved gas dissipation after dam

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.

Assessment of Reaeration Equations for River Tungabhadra, Karnataka, India and Generation of the Refined Equation

The ability of a water body to self-purify itself is dependent on its re-aeration rate (Ka). This rate is necessary to calculate the dissolved oxygen content in the waterbody. This rate also depends on some variables that include the stream velocity, stream bed slope, cross section area, water depth, frictional velocity, discharge rate, Froude’s number and a number of other things. For the purpose of this study, thirteen empirical equations are considered when evaluating the performance of the re-aeration rates. This is done with respect to the size of the Tungabhadra river. Observation of the re-aeration rate for this study was done using mass balance approach. The data needed for this was gotten from field investigation data obtained from 288 separate samples (6 different sites) between the period March, 2017 to December, 2018. The performance evaluation of the re-aeration equation was done via the implementation of least square techniques. The following statistical error methods were applied in due course; standard error, normal mean method and mean multiplicative method. The results of the methods are 0.16, -0.0006 and 2.75. The coefficient of correlation for this was 0.91 and by interpretation, it shows an efficient outcome.

Evaluation of re-aeration equations for river Ghataprabha, Karnataka, India and development of refined equation

Stream re-aeration is an extremely important component to enhance the self-purification capacity of streams. To estimate the dissolved oxygen (DO) present in the river, estimation of re-aeration coefficient is mandatory. Normally, the re-aeration coefficient is expressed as a function of several stream variables, such as mean stream velocity, shear stress velocity, bed slope, flow depth and Froude number. Many empirical equations have been developed in the last years. In this work, 13 most popular empirical re-aeration equations, used for re-aeration prediction, have been tested for their applicability in Ghataprabha River system, Karnataka, India, at various locations. Extensive field data were collected during the period March 2008 to February 2009 from seven different sites located in the river to observe re-aeration coefficient using mass balance approach. The performance of re-aeration equations have been evaluated using various error estimations, namely, the standard error (SE), mean multiplicative error (MME), normalized mean error (NME) and correlation statistics. The results show that the predictive equation developed by Jha et al. (Refinement of predictive re-aeration equations for a typical Indian river. Hydrological Process. 2001;15(6):1047–1060), for a typical Indian river, yielded the best agreement with the values of SE, MME, NME and correlation coefficient r. Furthermore, a refined predictive equation has been developed for river Ghataprabha using least-squares algorithm that minimizes the error estimates.

Assessing the Performance of Reaeration Prediction Equations

AbstractThe overall performance of 18 commonly used reaeration rate coefficient prediction equations was evaluated using statistical metrics of prediction accuracy and bias by comparing predicted reaeration coefficients to a database of values measured using gas tracer techniques. Adapting a commonly applied concept, predictive equations were evaluated in discrete regions of the velocity-depth space. Results indicate that rarely is there a single best prediction equation in a given velocity-depth region, rather there usually is a group of statistically indistinguishable top-performing equations. Also, no single reaeration equation performed well over all hydraulic conditions. Prediction equations, which include slope as a variable are more accurate and have lower bias than those that do not. However, even the top-performing equations exhibited large prediction errors of at least 40–50% and exceeded 100% in some regions. This level of error in predicting reaeration rate coefficients will continue to have a...

Comparing the stream re-aeration coefficient estimated from ANN and empirical models / Comparaison d'estimations par un RNA et par des modèles empiriques du coefficient de réaération en cours d'eau

Dissolved oxygen (DO) is one of the most useful indices of river's health and the stream re-aeration coefficient is an important input to computations related to DO. Normally, this coefficient is expressed as a function of several variables, such as mean stream velocity, shear stress velocity, bed slope, flow depth, and Froude number. However, in free surface flows, some of these variables are interrelated, and it is possible to obtain simplified stream re-aeration equations. In recent years, different functional forms have been advanced to represent the re-aeration coefficient for different data sets. In the present study, the artificial neural network (ANN) technique has been applied to estimate the re-aeration coefficient (K 2) using data sets measured at different reaches of the Kali River in India and values obtained from the literature. Observed stream/channel velocity, bed slope, flow depth, cross-sectional area and re-aeration coefficient data were used for the analysis. Different combinations of variables were tested to obtain the re-aeration coefficient using an ANN. The performance of the ANN was compared with other estimation methods. It was found that the re-aeration coefficient estimated by using an ANN was much closer to the observed values as compared with the other techniques.

Reaeration in sewers

The sewer system is a very dynamic system with an abundance of mass transfer processes and transformations. A key process is the mass exchange between the wastewater and the sewer atmosphere. An equation that describes the gas–liquid mass transfer under different hydrodynamic conditions is essential when sewer processes are to be quantified or modelled. In this work, a calibrated reaeration equation is proposed. It is based on the shear Reynolds and the Froude number to correct the increased gas–liquid interface roughness to higher flow rates. The equation was calibrated with previously published data and with new data. This data was obtained with a safe and environmentally friendly gas tracer method for gravity sewers based on the inert gas sulphur hexafluoride (SF 6), a new method for the sewer system. Measurements were conducted in four channels under different conditions. The resulting equation will allow for more accurate simulations of the sewer system. Finally, the effect of reaeration with regard to the oxygen consuming processes for different hydrodynamic conditions is discussed.

Refinement of predictive reaeration equations for a typical Indian river

AbstractDissolved oxygen mass balance has been computed for different reaches of River Kali in western Uttar Pradesh (India) to obtain the reaeration coefficient (K2). A total of 270 field data sets have been collected during the period from March 1999 to February 2000. Eleven most popular predictive equations, used for reaeration prediction and utilizing mean stream velocity, bed slope, flow depth, friction velocity and Froude number, have been tested for their applicability in the River Kali using data generated during field survey. The K2 values computed from these predictive equations have been compared with the K2 values observed from dissolved oxygen balance measurements in the field. The performance of predictive equations have been evaluated using error estimation, namely standard error (SE), normal mean error (NME), mean multiplicative error (MME) and correlation statistics. The equations developed by Smoot and by Cadwallader and McDonnell showed comparatively better results. Moreover, a refined predictive equation has been developed using a least‐squares algorithm for the River Kali that minimizes error estimates and improves correlation between observed and computed reaeration coefficients. Copyright © 2001 John Wiley & Sons, Ltd.

Recalibration of a Reaeration Equation

The atmospheric reaeration prediction equation of Thackston and Krenkel was recalibrated, using additional values of the reaeration coefficient that have been measured since 1969, in addition to the original values. The recalibration corrected a tendency of the original equation to overpredict reaeration coefficients at low Froude numbers. The basic form of the equation was kept intact, but the coefficient involving the Froude number was revised. Accuracy improved in the low Froude number range by 20% and stayed about the same in the remainder of the range.

Closure to “Reaeration Equations Derived from U.S. Geological Survey Database” by Charles S. Melching

Closure to “Reaeration Equations Derived from U.S. Geological Survey Database” by Charles S. Melching

Reaeration Equations Derived from U.S. Geological Survey Database

Reaeration Equations Derived from U.S. Geological Survey Database

Reaeration Equations Derived from U.S. Geological Survey Database

Accurate estimation of the reaeration-rate coefficient (K2) is extremely important for waste-load allocation. Currently, available K2 estimation equations generally yield poor estimates when applied to stream conditions different from those for which the equations were derived because they were derived from small databases composed of potentially highly inaccurate measurements. A large data set of K2 measurements made with tracer-gas methods was compiled from U.S. Geological Survey studies. This compilation included 493 reaches on 166 streams in 23 states. Careful screening to detect and eliminate erroneous measurements reduced the data set to 371 measurements. These measurements were divided into four subgroups on the basis of flow regime (channel control or pool and riffle) and stream scale (discharge greater than or less than 0.556 m3/s). Multiple linear regression in logarithms was applied to relate K2 to 12 stream hydraulic and water-quality characteristics. The resulting best-estimation equations had the form of semiempirical equations that included the rate of energy dissipation and discharge or depth and width as variables. For equation verification, a data set of K2 measurements made with tracer-gas procedures by other agencies was compiled from the literature. This compilation included 127 reaches on at least 24 streams in at least seven states. The standard error of estimate obtained when applying the developed equations to the U.S. Geological Survey data set ranged from 44 to 61%, whereas the standard error of estimate was 78% when applied to the verification data set.

Analysis of Reaeration Equations Using Mean Multiplicative Error

Numerous equations employing depth, velocity, and slope have been developed to estimate the stream reaeration coefficient. These have been evaluated previously using statistics based on differential errors, which are shown to be biased toward underprediction. A new metric, the mean multiplicative error (MME), overcomes this defect and offers other advantages, including identical results for both reaeration and gas transfer coefficients and less sensitivity to extreme errors. It is equal to the geometric mean of the factors, greater than unity, by which the estimates would have to be multiplied or divided to equal the corresponding measurements. With the use of the MME to test 10 selected equations, against a compilation of field measurements based on gas tracers, current equations are shown to be of little value at low slopes, whereas some frequently used equations are shown to have little general value. Slope is found to be an essential component of reaeration equations. Recommendations are made for estimating the reaeration coefficient.

Reaeration Equations and Waste‐Load Allocations

This technical note estimates the possible effects on calculated critical dissolved oxygen deficits of using reaeration equations as compared to measured reaeration rates. Differences between observed and calculated reaeration coefficients can produce changes of about 30 percent in the calculated critical dissolved oxygen deficits. The uncertainty in dissolved oxygen concentrations, due to the use of reaeration equations rather than measured reaeration coefficients, are probably on the order of tenths to one part per million. This technical note deals with the effects of using equations rather than indications of the adequacy of the equations to represent reaeration coefficients.

Predicting Reaeration Rates in Texas Streams

Krypton‐85 was used to measure reaeration coefficients in numerous streams and rivers in Texas with various hydraulic characteristics. Flow rates ranged from 0.027 to 16.0 cms, velocities from 0.009 to 0.87 m/s, and depths from 0.17 to 1.83 m. Using a linear multiple regression technique, the Texas Reaeration Equation was developed for estimating reaeration coefficients in Texas streams and rivers. Statistical and graphical tools were used to evaluate this equation for accuracy and reliability and to determine the limits of its application. The methods of analysis of variance and analysis of residuals were used to evaluate the accuracy of the Texas Reaeration Equation. The 95% confidence intervals of the regression coefficients were also determined. The Texas Reaeration Equation adequately predicted reaeration coefficients in Texas streams and can be reliably applied to streams with depths from 0.2 to 1.0 m and velocities from 0.01 to 0.30 m/s.

A SIMPLIFIED STREAM MODEL OF ACID MINE DRAINAGE EFFECTS1

ABSTRACT: Three methods of modeling acid mine drainage effects are discussed. A net alkalinity routing model is the simplest of these, but can be potentially misleading. It typically overestimates the effect of acid sources on pH by neglecting carbon dioxide transfer to the atmosphere. Inclusion of a simple carbon dioxide transfer function can substantially reduce errors in stream quality prediction. A plug flow reaeration equation, coupled with mass balancing at mixing points in a stream network provides modeling results comparable to those of more complex computerized solutions of chemical equilibrium equations. None of the models accounts for carbonate dissolution or oxidation and hydrolysis of ferrous iron.