NC0004961_RBSS CAP Part I_Appx E_Final_20151116

Appendix E
Surface Water Modeling
Methods

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Surface Water Mixing Model Approach
Riverbend Steam Station
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) was 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:
ܦܨ ൌ
ொ೒ೢାொೝ೔ೡ೐ೝ
ொ೒ೢ

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 4.2.1 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:
ܥ௦௪ ൌ ሺ஽ிିଵሻൈ஼ೝ೔ೡ೐ೝ ା஼೒ೢ
஽ி
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:
ܥ௦௪ ൌ ொ೒ೢൈ஼೒ೢାொೝ೔ೡ೐ೝ ൈ஼ೝ೔ೡ೐ೝ
ொ೒ೢାொೝ೔ೡ೐ೝ

where: Qgw is discharge rate from the groundwater model (cfs);
Cgw is the groundwater model concentration entering the river (µg/L);
Qriver is the upstream river design flow (cfs); and
Criver is the upstream (background) river concentration (µg/L).
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For each groundwater COI that discharges to surface waters at a concentration exceeding its
applicable groundwater quality standard or criteria (as outlined in Section 1.9.2), 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 (WQS) 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 ten 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; and
 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 low river design flows for the
fraction of the river as specified in Section 4.2.1 for the acute, chronic, water supply and human
health mixing zone limitations. The calculated 1Q10, 7Q10, and mean annual river design flows
used for the Catawba River near the RBSS site are provided in Table E-1.
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Table E-1. Catawba River Design Flows
Design Condition Catawba River Design Flow (cfs)
1Q10 121
7Q10 229
Mean Annual 2,622
Notes:
1. cfs = cubic feet per second
Limited surface water quality data are available in the Catawba River 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 method detection limits
(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 was used to provide the
groundwater flow and COI concentrations into the adjacent receiving waters (Catawba River
and East Basin). Figure E-1 presents the location of the groundwater model calculated flow
inputs into these adjacent receiving waters, and Table E-2 presents the total groundwater flow
along the two flow boundaries noted on Figure E-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 the Catawba River and East Basin.
Table E-2. Model-Calculated Groundwater Flows
Waterbody Groundwater Flow
(ft3/day) (cfs)
Catawba River Upstream 5,376 0.062
East Basin 4,196 0.049
Catawba River Total 9,572 0.111
Notes:
1. ft3/day = cubic feet per day
2. cfs = cubic feet per second

Total loading of groundwater COIs to the Catawba River at the RBSS site includes direct
loading to the Catawba River, local loading to the East Basin, and local loading to an unnamed
tributary that discharges to the East Basin. As noted in Section 4.2.2, concentrations of COIs
from the groundwater model already met applicable water quality standards or criteria at the
discharge locations of groundwater to surface receiving waters, so further dispersion and
dilution of COIs within the Catawba River was not required. Nevertheless, representative mixing
zone dilution calculations for the Catawba River were performed to show expected COI
concentrations at the edges of the surface water mixing zones. Table E-3 provides flux-
weighted average COI concentrations in groundwater discharging to the Catawba River
adjacent to the RBSS site, as well as assigned upstream surface water concentrations. These
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values were used in the mixing zone dilution calculations presented in Section 4.2.2. Table E-3
also lists for comparison the surface water quality standards or criteria applicable to each COI.
Table E-3. Catawba River Dissolved COI Concentrations and WQS
COI
Groundwater
Concentration
(µg/L)
Surface Water
Concentration
(µg/L)*
Acute WQS
(µg/L)
Chronic
WQS (µg/L)
HH / WS
WQS (µg/L)
Antimony 1.20 0.25 ns ns 640 / 5.6
Total Chromium 0.28 0.50 ns ns ns / ns
Sulfate 45,524 500 ns ns ns / 250,000
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. HH / WS – human health / water supply
4. ns – no water quality standard

Mixing zone calculations for the East Basin first required performing mixing zone calculations for
COI loads to the Catawba River upstream of the inflow channel to the East Basin. For this
assessment, inflow to the East Basin was assumed to be 10% of the river design flow for the
Catawba River. Bear in mind, however, that concentrations of groundwater COIs at locations of
discharge to the East Basin (and its associated unnamed stream) already met applicable water
quality standards or criteria, so further dispersion and dilution within the East Basin was not
actually required. Table E-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 4.2.2. Table E-4 also lists for comparison the surface water
quality standards or criteria applicable to each COI.
Table E-4. East Basin Dissolved COI Concentrations & WQS
COI
Groundwater
Concentration
(µg/L)
Surface Water
Concentration
(µg/L)*
Acute WQS
(µg/L)
Chronic
WQS (µg/L)
HH / WS
WQS (µg/L)
Antimony 1.72 0.25 ns ns 640 / 5.6
Total Chromium 0.28 0.50 ns ns ns / ns
Sulfate 33,486 530 ns ns ns / 250,000
Notes:
1. All COIs are shown as dissolved except for total chromium
2. * – Mixing-zone concentrations from upstream loading to the Catawba River
3. HH / WS – human health / water supply
4. ns – no water quality standard

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S-8
278.0
277.5
Source: Esri, DigitalGlobe, GeoEye, Earthstar Geographics,
CNES/Airbus DS, USDA, USGS, AEX, Getmapping, Aerogrid, IGN,
IGP, swisstopo, and the GIS User Community
±
Legend
East Basin GW Model Discharge
Main River GW Model Discharge
0 0.25 0.5 0.75 10.125
Miles