NC0004961_7. RBSS CAP Part 2_Appx D_FINAL_20160212

Appendix D
Surface Water Mixing
Model Approach

This page intentionally left blank
Surface Water Mixing Model Approach
Riverbend Steam Station Ash Basin

Overview of Modeling
The relatively simple morphology of the receiving waters adjacent to Riverbend Steam Station
(RBSS) makes this site amenable to the Mixing Model Approach. For this approach, river flow
data from the U.S. Geological Survey (USGS) were analyzed to determine upstream river
design flows and assess compliance with North Carolina Department of Environmental Quality
(NCDEQ) surface water quality standards, including determination of applicable low river flow
statistics.
The river design flows were used along with groundwater model discharge results to calculate
effluent dilution factors using the following equation:
𝐷𝐷𝐷𝐷=𝑄𝑄𝑔𝑔𝑔𝑔+𝑄𝑄𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑄𝑄𝑔𝑔𝑔𝑔
where: DF is the groundwater dilution factor;
Qgw is discharge rate from the groundwater model (cubic feet per second [cfs]);
and
Qriver is the upstream river design flow (cfs).
The mixing zone sizes presented in Section 4.2 of the Corrective Action Plan (CAP) Part I
Report for the different water quality standards were used in this equation to determine the
appropriate dilution factor to assess compliance with the applicable water quality standards. The
applicable dilution factor was then used with the groundwater model concentration and
upstream concentration for the constituent of interest (COI) to determine the resulting surface
water concentration at the edge of the mixing zone, using the following equation:
𝐶𝐶𝑠𝑠𝑠𝑠=(𝐷𝐷𝐷𝐷−1)×𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟+𝐶𝐶𝑔𝑔𝑔𝑔𝐷𝐷𝐷𝐷
where: Csw is the surface water concentration at the edge of the mixing zone (µg/L);
Cgw is the groundwater model concentration entering the river (µg/L);
Criver is the upstream (background) river concentration (µg/L); and
DF is the groundwater dilution factor.
Alternately, the resulting surface water concentration can be calculated using the following mass
balance equation:
𝐶𝐶𝑠𝑠𝑠𝑠=𝑄𝑄𝑔𝑔𝑔𝑔×𝐶𝐶𝑔𝑔𝑔𝑔+𝑄𝑄𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟×𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑄𝑄𝑔𝑔𝑔𝑔+𝑄𝑄𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
where: Qgw is discharge rate from the groundwater model (cfs);
Cgw is the groundwater model concentration entering the river (µg/L);
Surface Water Mixing Model Approach
Riverbend Steam Station Ash Basin

2
Qriver is the upstream river design flow (cfs); and
Criver is the upstream (background) river concentration (µg/L).

For each groundwater COI that discharges to surface waters at a concentration exceeding its
applicable groundwater quality standard or criteria, the appropriate dilution factor and upstream
(background) concentration were applied to determine the surface water concentration at the
edge of the applicable mixing zone. This concentration was then compared to the applicable
water quality standard or criteria to determine surface water quality standard compliance.
Historical river flow data were available for the Catawba River at Catawba, North Carolina
(USGS #02142500, from 1896 to 1962 with gaps from 1900 to 1935), which is located
approximately 34 miles upstream of the RBSS site. Flows prior to 1935 appear to have been
unregulated and would not have been representative of present day conditions and were not
used. Daily river flow data from this gage for 1935 to 1962 were analyzed to calculate the 1Q10,
7Q10 and mean annual river design flows for the Catawba River at Catawba, North Carolina.
The 1Q10 flow is the annual minimum 1-day average flow that occurs once in 10 years; the
7Q10 flow is the annual minimum 7-day average flow that occurs once in ten years; and the
mean annual flow is the long-term average annual flow based on complete annual flow records.
These river design flows were scaled up using a drainage area ratio to account for additional
drainage from minor tributaries between the USGS gage location and the RBSS site. Drainage
area ratios where developed using information from the USGS StreamStats web application
(http://water.usgs.gov/osw/streamstats/).
Key Assumptions and Limitations for Each Model
The key model assumptions and limitations include, but are not limited to, the following:
• Groundwater flow mixing in the receiving water occurs over the entire cross-section of
the mixing zone area (e.g., over 10% of the river width for the acute water quality
assessment).
• COI transformations are not represented in the analysis (i.e., all COIs are treated as
conservative substances without any decay).
• The analysis is limited by the availability of surface water data used to assign upstream
river COI concentrations.
• When surface water data were not available, or when surface water data were reported
at the method detection limit (MDL), half of the MDL was used in the mixing model
calculations.
• The analysis is limited by the availability of contemporary USGS gage data to develop
low river design flow statistics (i.e., 1Q10, 7Q10, and annual mean).
Mixing Model Development
The mixing model approach requires the assignment of upstream critical river design flows for
the fraction of the river as specified in Section 4.2 of the CAP Part I Report for the acute,
chronic, water supply, and human health mixing zone limitations. The calculated 1Q10, 7Q10,
Surface Water Mixing Model Approach
Riverbend Steam Station Ash Basin

3
and mean annual river design flows used for the Mountain Island Lake portion of the Catawba
River near the RBSS site are provided in Table 1.
Table 1 Catawba River Design Flows
Design Condition Catawba River Design Flow (cfs)
1Q10 121
7Q10 229
Mean Annual 2,622

Limited surface water quality data are available in Mountain Island Lake at the RBSS site;
however, two National Pollutant Discharge Elimination System (NPDES) water quality
monitoring stations sampled by Duke Energy are located nearby, one just upstream and one
just downstream from the RBSS site. For those COIs sampled, upstream concentrations for
dilution calculations are based on the maximum concentration reported at the NPDES station
278.0 from February 2011 to February 2015. If the upstream concentrations were reported at
the MDL, then the concentrations used for the dilution calculations were equivalent to half of the
MDL for each COI.
The RBSS groundwater modeling discussed in Section 4.1 of the CAP Part 1 Report was used
to provide the groundwater flow and COI concentrations into the adjacent receiving waters
(Mountain Island Lake and East Basin). Figure 1 presents the location of the groundwater model
calculated flow inputs into these adjacent receiving waters, and Table 2 presents the total
groundwater flow along the two flow boundaries noted on Figure 1. These groundwater flows
were used to assess the impact on surface water concentrations and compliance with the
applicable water quality standards or criteria at the mixing zone boundaries in Mountain Island
Lake and East Basin.
Table 2 Model-Calculated Groundwater Flows
Waterbody Groundwater Flow
(ft3/day) (cfs)
Catawba River Upstream 15,910 0.184
East Basin 16,192 0.187
Catawba River Total 32,102 0.372
Notes:
1. ft3/day = cubic feet per day

Total loading of groundwater COIs to Mountain Island Lake at the RBSS site includes direct
loading to Mountain Island Lake, local loading to the East Basin, and local loading to an
unnamed tributary that discharges to the East Basin. Table 3 provides total flux-weighted
average COI concentrations in groundwater discharging to Mountain Island Lake adjacent to the
RBSS site, as well as assigned upstream surface water concentrations. These values were
used in the mixing zone dilution calculations presented in CAP Part 1, Section 4.2. Table 3 also
lists for comparison the surface water quality standards or criteria applicable to each COI.
Surface Water Mixing Model Approach
Riverbend Steam Station Ash Basin

4
Table 3 Catawba River Dissolved COI Concentrations and Water Quality Standards
COI
Groundwater
Concentration
(µg/L)
Surface Water
Concentration
(µg/L)*
Acute WQS
(µg/L)
Chronic
WQS (µg/L)
HH / WS
WQS (µg/L)
Antimony 1.03 0.25 ns ns 640 / 5.6
Arsenic 1.00 0.25 340 150 10 / 10
Boron 108 25 ns ns ns / ns
Total chromium 4.96 0.50 ns ns ns / ns
Hexavalent chromium 2.95 0.50 16 11 ns / ns
Cobalt 6.06 0.25 ns ns 4 / 3
Sulfate 25,106 500 ns ns ns / 250,000
Thallium 0.212 0.05 ns ns 0.47 / 0.24
Vanadium 1.11 0.50 ns ns ns / ns
Notes:
1. All COIs are shown as dissolved except for total chromium
2. * – data from upstream NPDES station 278.0 (maximum total recoverable) or ½ MDL
3. WQS = water quality standards
4. HH / WS = Human Health / Water Supply (15A NCAC 02B .0211, 15A NCAC 02B .0216, effective
January 1, 2015
5. ns – no water quality standard

Mixing zone calculations for the East Basin first required performing mixing zone calculations for
COI loads to Mountain Island Lake upstream of the inflow channel to the East Basin. These
mixing zone concentrations served as upstream surface water concentrations entering the
inflow channel. Table 4 provides flux-weighted average COI concentrations in groundwater
discharging to the East Basin, as well as calculated upstream surface water concentrations
entering through the inflow channel. These values were used in the mixing zone dilution
calculations presented in Section 4.2. Table 4 also lists for comparison the surface water quality
standards or criteria applicable to each COI.
Surface Water Mixing Model Approach
Riverbend Steam Station Ash Basin

5
Table 4 East Basin Dissolved COI Concentrations and Water Quality Standards
COI
Groundwater
Concentration
(µg/L)
Surface Water
Concentration
(µg/L)*
Acute WQS
(µg/L)
Chronic
WQS (µg/L)
HH / WS
WQS (µg/L)
Antimony 1.07 0.251 ns ns 640 / 5.6
Arsenic 1.00 0.261 340 150 10 / 10
Boron 132 25 ns ns ns / ns
Total chromium 4.97 0.500 ns ns ns / ns
Hexavalent
chromium 0.067 0.581 16 11 ns / ns
Cobalt 6.90 0.258 ns ns 4 / 3
Sulfate 25,208 539 ns ns ns / 250,000
Thallium 0.200 0.050 ns ns 0.47 / 0.24
Vanadium 1.20 0.500 ns ns ns / ns
Notes:
1. All COIs are shown as dissolved except for total chromium
2. * – mixing-zone concentrations from upstream loading to Mountain Island Lake
3. WQS = water quality standards
4. HH / WS = Human Health / Water Supply (15A NCAC 02B .0211, 15A NCAC 02B .0216, effective
January 1, 2015
5. ns – no water quality standard

In Tables 3 and 4, the aquatic life water quality standards for arsenic and hexavalent chromium
assume a water effects ratio of 1, which expresses the difference between toxicity measured in
a laboratory and toxicity in site water. Site-measured water effects ratios are typically less than
1 due to complexing parameters in the site water (e.g., dissolved organic carbon) that reduces
site toxicity as compared to laboratory measured toxicity for metals. Thus, using a water effects
ratio of 1 provides a conservative assumption in the surface water quality assessment for these
COIs.

Surface Water Mixing Model Approach
Riverbend Steam Station Ash Basin

6

Figure 1 RBSS Groundwater Model Flow Locations and Surface Water Stations