Lower Bull Run River Dye Studies

Table of Contents

- Dye Study June 16, 1999

- Dye Study August 5, 1999

Two dye studies were performed on the Lower Bull Run River in the summer of 1999. The first was on June 16, the second on August 5. The intention of these studies was to determine the travel times and dispersion coefficients for various stretches of the river at different flow rates. The physical characteristics of the river that are determined from these studies will be used as boundary conditions in the CE-QUAL-W2 Version 3 model.

Bull Run River Dye Study June 16, 1999

Two liters of a Rhodamine WT 20% dye solution (500 grams) was released into the river just below (200 ft) the diversion pool of Bull Run Reservoir #2 at 9:21 a.m. Water samples were taken from four downstream sites. These sites and the point of dye injection are shown in Figure 1. Table 1 shows the names of these sample stations and their distance downstream of the dye injection point.

Figure 1. Dye Study Monitoring Locations, June 16, 1999

Sample Site | Code | Distance Downstream m (ft.)
Dye Injection Point | INJ | 0 (0)
Below Plunge Pool | SPP | 579.4 (1901)
Route 14 Bridge | USGS | 2639.4 (8660)
Larson’s Bridge | LARB | 4232.6 (13,887)
Bowman’s Bridge | BOWB | 6501.8 (21,332)

Table 1. Dye Study Release and Sample Sites

River discharge measurements were taken every 15 minutes at USGS gage station #14140000 located just downstream of the Route 14 Bridge throughout the duration of the test. The measured flow ranged between 112 and 100 cfs (3.171 and 2.831 m3/s) with an average flow of 103.7 cfs (2.936 m3/s).

Each water sample consisted of two 25 ml glass vials filled with river water. The samples were then analyzed at Bureau of Waterworks Water Quality Laboratory. The concentration of dye was determined using a Turner Fluorometer Model #112. The minimum detection limit for these water samples was 1.0 mg/L. Continuous Fluorometer readings were also taken in the field at the USGS station. The results of the analysis are in Appendix C. A graphical display of the observed concentration data is found in Figure 2. Concentration measurements noted in Figure 2 for station SPP were taken from the left side of the river facing downstream.

Figure 2. Dye Study Field Data

Velocity Calculations

The velocity of the river was found by measuring the travel time of the peak concentration of the dye plume and dividing this by the travel distance. The calculated velocities are shown in Table 2.

Station to Station | Velocity m/s (ft/s) |  | INJ to Station | Velocity m/s (ft/s)
INJ-SPP | 0.136 (0.446) |  | INJ-SPP | 0.136 (0.446)
SPP-USGS | 0.230 (0.755) |  | INJ-USGS | 0.200 (0.656)
USGS-LARB | 0.266 (0.873) |  | INJ-LARB | 0.220 (0.722)
LARB-BOWB | 0.189 (0.620) |  | INJ-BOWB | 0.208 (0.682)

Table 2. Average River Velocities

River Cross-Sectional Area

The effective cross-sectional area of the river was found by dividing the flow rate by the velocity. The average flow rate measured at the USGS gauging station was used for this calculation. The calculated areas are shown in Table 3.

Station to Station | Area m2 (ft2) |  | INJ to Station | Area m2 (ft2)
INJ-SPP | 21.6 (232) |  | INJ-SPP | 21.6 (232)
SPP-USGS | 12.7 (137) |  | INJ-USGS | 14.7 (158)
USGS-LARB | 11.1 (119) |  | INJ-LARB | 13.3 (143)
LARB-BOWB | 15.5 (167) |  | INJ-BOWB | 14.1 (152)

Table 3. Average River Cross-sectional Area

Conservation of Mass

The loss coefficient (k) was calculated by integrating the observed Concentration vs. Time curve at each sample point and multiplying this by the flow rate. This gave the mass of dye that passed each station. These values are shown in Table 4.

Station | Mass (g)
INJ | 400
SPP | 333.9
USGS | 251.1
LARB | 230.2
BOWB | Undetermined

Table 4. Observed Mass

The loss coefficient takes into account dye that became trapped in "dead zones" where river current is slow, and dye that adhered to rocks and sediments. The loss coefficient was calculated from Equation

( 1 ).

| ( 1 )

The calculated values are in Table 5. The mass of dye that passed the Bowman’s Bridge station was not determined because not enough samples were collected at this location.

Station to Station | k-values (s-1) |  | INJ to Station | k-values (s-1)
INJ-SPP | 4.24E-05 |  | INJ-SPP | 4.24E-05
SPP-USGS | 3.19E-05 |  | INJ-USGS | 3.53E-05
USGS-LARB | 1.44E-05 |  | INJ-LARB | 2.88E-05

Table 5. Loss Coefficients

Estimation of EL

The dispersion coefficient (EL) was estimated using three different methods: decay in peak concentration, Method of Moments, and by solving for EL in Equation ( 3 ) at each data point.

The advection-diffusion equation describes the concentration distribution of dye, Equation ( 2 ).

| ( 2 )

A one-dimensional river model with an instantaneous plane source of dye was used to describe the Bull Run River. This assumes that the dye is fully mixed in the cross-section, the velocity is constant, and that the cross-sectional area of the river is constant. Equation ( 3 ) is the solution to the differential equation that describes these conditions.

| ( 3 )

C = Concentration of dye (g/m3)

M = Initial mass of dye = 500 g

A = Cross-sectional area of the river (m2)

EL= Longitudinal dispersion coefficient (m2/s)

t = Time after dye release (s)

x = Downstream distance from release point (m)

U = Velocity of the river (m/s)

k = Dye loss coefficient (s-1)

Decay in Peak Concentration

When the peak concentration of the dye plume reached a sample station, the distance from the point of dye injection x, was equal to the velocity of the river U, multiplied by the time from the dye release t. This causes Equation ( 3 ) to simplify to:

| ( 4 )

This equation can be evaluated for EL at each of the sample stations. The results are shown in Table 6. The dispersion coefficient at the Bowman’s Bridge station was calculated using k from INJ-LARB because k at Bowman’s Bridge is undefined due to the lack of sample data.

Reach | EL (m2/s)
INJ-SPP | 1.85
INJ-USGS | 7.24
INJ-LARB | 8.96
INJ-BOWB | 4.84

Table 6. Dispersion Coefficient (Decay of Peak Concentration Method)

Method of Moments

The Method of Moments uses Equation ( 5 ) to estimate the dispersion coefficient:

| ( 5 )

This describes the distribution of the dye plume about the center of mass of the plume. st2 is estimated using the field data by:

| ( 6 )

This method cannot be used at the Bowman Bridge Station because not enough data was collected to describe the distribution of the entire dye plume. Table 7 shows the calculated st2terms. Table 8 shows the values of the dispersion coefficient.

Station | st2 (s2)
INJ | 0
SPP | 672,314
USGS | 3,071,815
LARB | 5,445,091

Table 7. Sigma t Squared (Method of Moments)

Reach | EL (m2/s)
INJ-SPP | 1.46
INJ-USGS | 4.65
INJ-LARB | 6.89

Table 8. Dispersion Coefficient (Method of Moments)

Evaluation of EL at Each Data Point

At each data point, Equation ( 3 ) was written for that point and also for the peak concentration at that station, Equation ( 4 ). The equation for the data point was divided by the equation for the peak concentration to give Equation ( 7 ).

| ( 7 )

Equation ( 7 ) was evaluated for EL.

| ( 8 )

Equation ( 8 ) was used to find a value for the dispersion coefficient for each field sample. The results of this analysis are shown in Figure 3. The apparent increase in the dispersion coefficient after the peak of the plume passes occurred because dye that had been trapped in low-velocity areas upstream of the sample station was slowly being released back into the main flow. This caused observed dye concentrations to be higher after the peak passed than they were before the peak passed the sample station. This resulted in the dye plume being more "stretched out" upstream which results in greater values of EL. Table 9 shows the range of values for the dispersion coefficient. For the Bowman’s Bridge site, no information was available for the plume after the peak concentration passed.

Samples that are taken too close to the peak do not accurately describe the plume distribution about the peak. Because the exact location of the peak of the dye plume is unknown, calculations of EL are made only for samples with concentrations less than 80% of the observed peak concentration.

Figure 3. Results of Dispersion Coefficient Evaluation

Reach | Range EL (m2/s)
INJ-SPP | 0-4
INJ-USGS | 2-11
INJ-LARB | 3.5-13
INJ-BOWB | 3.5-4.5

Table 9. Dispersion Coefficient (Evaluation at Each Data Point)

An advantage to this analysis is that the area of the river is not needed to find EL. It also uses information from many data points while the "Decay in Peak Concentration" analysis uses only one sample at each station. The dispersion coefficient can also be found at the Bowman’s Bridge station (using k from INJ-LARB) while there was not enough data to find EL at Bowman’s bridge using the "Method of Moments".

Comparison of Analytical 1-D Model to Observed Data

Average values for river cross-sectional area, velocity, and dye loss coefficient from the dye injection point to Bowman’s Bridge were inserted into Equation ( 3 ). The calculated value for the average dispersion coefficient using the third method (Evaluation of EL at Each Data Point) was also used in the equation. The calculated concentration values were then compared with the field data. The values used in the model are shown in Table 10.

Figure 4. Comparison of Model to Observed Data

Variable | Value
Cross-Sectional Area | 14.09 m2 (151.6 ft2)
River Velocity | 0.208 m/s (0.682)
Decay Coefficient | 2.88E-05 s-1
Dispersion Coefficient | 4.00 m2/s

Table 10. Model Variables

This 1-D model gives a good first approximation to the observed data. There are several reasons why the model fits the data better at the down stream sample locations as opposed to the Plunge Pool location. The average river velocity between the Injection Point and the Plunge Pool sample location was 0.136 m/s. This value is only 65% of the value used in the 1-D model. This is the reason that the model predicted an earlier arrival time for the dye plume. The effective cross-sectional area in the plunge pool was about 1.5 times larger than the average value determined for the entire river. This causes the concentrations in the 1-D model to be greater than the observed dye concentrations at the Plunge Pool sample location.

These field data will later be used to calibrate the Bull Run River water quality model which is an unsteady, variable area, 2-D hydrodynamic and water quality model.

Bull Run River Dye Study August 5, 1999

A second dye study was conducted on the Bull Run River on August 5, 1999. Rhodamine WT 20% dye solution was released at four different locations on the river and samples were taken downstream. The sample sites and points of injection are shown in Figure 5. Table 11 shows the locations, times, and mass of dye in each of the releases.

Figure 5. Dye Releases and Monitoring Locations, August 5, 1999

Location | Time | Volume 20% Dye Solution | Dye Mass
Bowman’s Bridge | 8:36 am | 200 ml | 40 g
Between Diversion and Beaver Pool | 11:12 am | 500 ml | 100 g
100 ft. downstream of USGS gage | 11:45 am | 500 ml | 100 g
100 ft. downstream of spillway crest | 12:15 pm | 170 ml | 34 g

Table 11. Dye Study Release Sites

River discharge measurements were taken every 15 minutes at USGS gage station #14140000 located just downstream of the Route 14 Bridge throughout the duration of the test. The measured flow on August 5 ranged between 11.74 and 208.3 cfs (0.3324 and 5.898 m3/s) and is shown in Figure 6. These gage readings were used to estimate the flow at other locations on the river.

Figure 6. Measured Flow at USGS Station August 5, 1999

Each water sample consisted of a 25 ml glass vial filled with river water. The samples were then analyzed at Bureau of Waterworks Water Quality Laboratory. The concentration of dye was determined using a Turner Fluorometer Model #112. The minimum detection limit for these water samples was 1.0 mg/L. Continuous Fluorometer readings were also taken in the field at the USGS station. The results of the analysis and the field Fluorometer readings are in Appendix D.

The dispersion coefficient (EL) was estimated using three different methods: decay in peak concentration, Method of Moments, and by solving for EL in Equation ( 3 ) at each data point. Similar methods for computing EL were used for this dye study as for the June 16 event.

Dye Release 1

The USGS gage (which is 2.4 miles (3862 m) upstream from Bowman’s Bridge) recorded flows between 206 and 211 cfs (5.83 and 5.97 m3/s) from 4:30 am to 7:00 am. It was assumed that tributaries between USGS and Bowman’s Bridge increase the flow. Therefore an estimated flow of 225 cfs (6.37 m3/s) was used in all calculations for Dye Release 1.

Samples were taken approximately 200 feet (60 m) upstream of the Bull Run Powerhouse at the County Bridge (COUB) site. This resulted in a distance of 1404 meters (4607 feet) between the release and sample locations. Figure 7 shows the sample concentrations, and the time after the dye was released.

Figure 7. Field Data for Dye Release 1

The velocity of the river was found by measuring the travel time of the peak concentration of the dye plume and dividing this by the travel distance. The effective cross-sectional area of the river was found by dividing the estimated flow rate by the calculated velocity. The loss coefficient (k) was calculated by integrating the observed Concentration vs. Time curve at the sample point and multiplying this by the flow rate. This gave the approximate mass of dye that passed the sample site. The loss coefficient takes into account dye that became trapped in "dead zones" where river current is slow and dye that adhered to rocks and sediments. The loss coefficient was found using Equation ( 1 ).

Because the sampling at COUB caught the entire dye plume, each of the three methods described above for estimating the dispersion coefficient was used for this dye release. Table 12 shows the calculated velocity, effective area, and dye loss coefficients for this dye release and also the results from the Decay in Peak Concentration and Method of Moments EL analyses. The results obtained by directly solving for EL are shown in Figure 8.

Parameter | Value
Velocity | 0.433 m/s (1.42 ft/s)
Cross-sectional Area | 14.7 m2 (158 ft2)
Dye Loss Coefficient (k) | 1.09 E-5 s-1
EL (Decay in Peak) | 12.5 m2/s
EL (Method of Moments) | 7.3 m2/s
EL (directly Solve) | 3.5 – 15.0 m2/s

Table 12. River Parameters for Dye Release 1

Figure 8. Dispersion Coefficient Evaluation for Dye Release 1 Using Equation ( 8 )

Dye Release 2

At the time of dye release the recorded flow at the USGS site was 18.92 cfs (0.5358 m3/s). Throughout the day, the flow at USGS slowly decreased to 14.51 cfs (0.4109 m3/s). This flow is used in the calculations for the second dye release because the USGS is so far downstream of the point of release.

Samples were taken at two points downstream: above the spillway pool (ASP) and below the spillway pool (SPP). The ASP site was 322 m (1060 feet) and the SPP site 885 m (2900 feet) downstream of the injection point. Figure 9 shows the sample concentrations for each site, and the time after the release of dye. Sampling at ASP captured most of the plume, but sampling stopped at SPP before the plume was captured. At SPP the plume is very dispersed at the peak suggesting that the plunge pool is acting like a stirred reactor rather than a plug flow with dispersion reactor. The maximum recorded concentration was 6.7 mg/L. However, samples that were within 90% of this value were taken over a period of 70 minutes.

Figure 9. Field Data for Dye Release 2

The velocity and cross-sectional area were estimated using the procedure in Dye Release 1. The dye loss coefficient could not be found at either sample location. At ASP the Concentration vs. Time curve was integrated. A dye mass of 114.6 grams is calculated. This is greater than the mass of dye released (100 g). There are several possible reasons for this. The flow rate may have been lower than 14.51 cfs (0.4109 m3/s), there may have been a mistake in measuring the amount of dye to be released, or errors in the analysis of the samples may have occurred. At SPP, not enough of the plume was sampled to determine the mass of dye passing the sample site. For use in calculations, values of 4.24 E-5 s-1 (the k value that was calculated in the June dye study for this part of the river) and 0 are used for this stretch of river. This lack of data at SPP means that the Method of Moments can not be used at SPP, and only the first five samples can be used to solve for EL directly.

Since data taken at SPP were reflective of a plug flow with dispersion reactor followed by a well-mixed tank, analyses using the EL calculation techniques outlined above are not that useful. These data will be used with the Bull Run River model to compare model predictions to data.

The results of Dye Release 2 are shown in Table 13 and Figure 10. The lack of data at SPP, the uncertainty regarding the flow rate, and the inability to calculate k results in a great deal of uncertainty in the calculations. For example, in the Decay of Peak method for calculating EL the two values for k give very different results at SPP. Also note that the EL values that are shown in Figure 10 are for the leading edge of the plume. There was not enough data collected to calculate values for the tail.

Parameter | ASP Values | SPP Values
k = 0 | k = 4.25E-5 | k = 0 | k = 4.25E-5
Velocity | 0.094 m/s (0.31 ft/s) | 0.094 m/s (0.31 ft/s) | 0.046 m/s (0.16 ft/s) | 0.046 m/s (0.16 ft/s)
Cross-sectional Area | 4.4 m2 (47 ft2) | 4.4 m2 (47 ft2) | 8.9 m2 (96 ft2) | 8.9 m2 (96 ft2)
EL (Decay in Peak) | 2.61 m2/s | 1.95 m2/s | 18.5 m2/s | 3.7 m2/s
EL (Method of Moments) | 2.50 m2/s | 2.50 m2/s | NA | NA
EL (directly Solve) | 0.4 – 7.3 | 0.4 – 5.3 | 0.7 – 1.0 | 0.6 – 0.8

Table 13. River Parameters for Dye Release 2

Figure 10. Dispersion Coefficient Evaluation for Dye Release 2 Using Equation ( 8 )

Dye Release 3

The dye was released at the USGS station at the same time that a flow reading was taken at USGS (18.92 cfs (0.5358 m3/s)). Samples were taken at Larson’s Bridge, 1563 m (5128 feet) downstream. Figure 11 shows the sample concentrations and the time from release. This shows that most of the plume was captured by the sampling.

Figure 11. Field Data for Dye Release 3

All parameters at this site were calculated using the same methods as Dye Release 1. The results are shown in Table 14 and Figure 12.

Parameter | Value
Velocity | 0.130 m/s (0.427 ft/s)
Cross-sectional Area | 4.1 m2 (44 ft2)
Dye Loss Coefficient (k) | 2.2 E-5 s-1
EL (Decay in Peak) | 3.9 m2/s
EL (Method of Moments) | 2.5 m2/s
EL (directly Solve) | 1.0 – 6.0 m2/s

Table 14. River Parameters for Dye Release 3

Figure 12. Dispersion Coefficient Evaluation for Dye Release 3 Using Equation ( 8 )

Samples were also taken at Bowman’s Bridge for this dye release. However, the laboratory analysis of the samples indicated that each sample had concentrations less than 1 mg/L.

Dye Release 4

Samples for the fourth dye release were taken at the USGS station. In total, 56 samples were taken. However, only the final 11 samples contained concentrations over 1.0 mg/L of dye. The recorded flow during the time interval when sample concentrations were at least 1.0 mg/L was constant at 15.53 cfs (0.4398 m3/s), and the distance between the release and sampling was 1724 meters (5656 feet). Sample concentrations and time from release are shown in Figure 13. It is clear that the peak of the dye plume was not captured by the samples.

Figure 13. Field Data for Dye Release 4

In order to determine parameters for this dye release, values for velocity, dye loss coefficient, and EL were inserted into Equation ( 3 ). Values for k were chosen, then the velocity and EL were varied in an attempt to fit a curve to the sample data. The sample concentrations (black squares) and resulting curves are shown in Figure 14.

Figure 14. Sample Data and Fitted Curves for Dye Release 4

Table 15 shows the range of values that was obtained by matching the data. It should be noted that the values for EL and k match only the leading edge of the plume while in the other dye releases, data from the tail of the plume was used which tends to increase EL and decrease k.

Parameter | Range of Values
Velocity | 0.068 – 0.079 m/s (0.22 – 0.26 ft/s)
Cross-sectional Area | 6.5 – 5.6 m2 (70 – 60 ft2)
Dye Loss Coefficient | 0 – 5.6E-5 s-1
EL | 1.8 – 0.6 m2/s

Table 15. River Parameters for Dye Release 4

Comparison of Analytical 1-D Model to Observed Data

The parameters that were calculated in each of the dye releases were inserted into Equation ( 3 ). Values of EL and k were adjusted in each instance to obtain the best fit with the sample data. The parameters and results for Releases 1-3 are shown in Table 16 and Figure 15. The results for Release 4 are given in the previous section.

The models matched the observed data with varying degrees of success in each dye release. The model works well when the river velocity is relatively high. When velocity is low the model does not work as well. In this study the velocity is found by observing how long it takes for the peak of the dye plume to reach a sample site. In the Plunge Pool the velocity of the river is very low when the flow rate is low. In this case, much of the transport of the dye is due to dispersion. The method used to find river velocity probably gives values that are higher than the actual velocity, and the effect of dispersion is probably underestimated.

The lack of data at some sample sites also made it difficult to determine the travel time of the dye plume. Not having information about the tail of the plume makes it hard to determine the dispersion coefficient with accuracy.

Parameter | Release 1 | Release 2 (ASP) | Release 2 (SPP) | Release 3
Mass of Dye | 40 g | 100 g | 100 g | 100 g
Velocity | 0.433 m/s (1.42 ft/s) | 0.094 m/s (0.308 ft/s) | 0.046 m/s (0.151 ft/s) | 0.130 m/s (0.427 ft/s)
Cross-sectional Area | 14.7 m2 (158 ft2) | 4.4 m2 (47 ft2) | 8.9 m2 (96 ft2) | 4.1 m2 (44 ft2)
Dye Loss Coefficient (k) | 1.1 E-5 s-1 | 4.3 E-5 s-1 | 8.0 E-5 s-1 | 2.2 E-5 s-1
EL | 7.5 m2/s | 1.2 m2/s | 0.6 m2/s | 2.5 m2/s

Table 16. Model Parameters

Figure 15. Comparison of Model to Observed Data

Comparison of Dispersion Coefficient Analysis Results to Previous Studies

Several equations are available to estimate the dispersion coefficient of a river based on its physical characteristics. Equation ( 9 ) was developed by Fischer et al. (1979) and Equation ( 10 ) was developed by McQuivey and Keefer (1974). These equations are accurate to within plus or minus half an order of magnitude.

| ( 9 )

| ( 10 )

U = River Velocity (m/s)

B = River Width (m)

H = River Height (m)

g = Gravity (m/s2)

S = Slope (m/m)

Q = Flow (m3/s)

These equations were solved using average values for the Lower Bull Run River. Equation ( 9 ) returned values in the range of 0.28 – 1.3 m2/s. Equation ( 10 ) gave 0.074 – 1.9 m2/s. The results of the dispersion coefficient analysis gave values of EL in the range of 1 –10 m2/s. Fischer et al. (1979) also observed dispersion coefficient values for rivers with similar average velocities. Table 17 shows these observed EL values.

River | Velocity (m/s) | EL (m2/s)
Copper Creek, VA | 0.16 | 3.0
Powell River, TN | 0.15 | 9.3
Clinch River, VA | 0.21 | 8.1

Table 17. Historical Dispersion Coefficient Data for Similar Rivers