NC0003468_DRSS CAP Part I_Appx E_Final_20151112

Appendix E
Surface Water Modeling
Methods

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Surface Water Mixing Model Approach
Dan River Steam Station
Overview of Modeling
The relatively simple morphology of receiving waters adjacent to Dan River Steam Station
(DRSS) makes the 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 1Q10, 7Q10, and mean
annual river flows. 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.
The river discharge design flows were combined 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 (cfs); and
Qriver is the upstream river design flow (cfs).
The mixing zone sizes presented in Section 4.2.1 of the 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:
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 the
2L Standards, 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 standards to determine
surface water quality standard (WQS) compliance.
Historical USGS river flow data are available for the Dan River near Wentworth, NC (Gage
#02071000, 1939 to present), which is located approximately 14 miles upstream of the DRSS.
The only major tributary to the Dan River over this section is the Smith River, which enters the
Dan River approximately 3 miles upstream of the DRSS and (USGS Gage #02074000, 1939 to
present). Daily river flow data from these two gages were summed and analyzed to calculate
1Q10, 7Q10, and mean annual design flows for the Dan River at the DRSS.
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);
 When surface water data were reported at the method detection level, half of the method
detection level was used in the mixing model calculations; and
 The analysis is limited by the availability of surface water data used to assign upstream
river COI concentrations.
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 4.2.1 of the CAP Part I report for the acute,
chronic, and human health mixing zone limitations. The 1Q10, 7Q10, and mean annual river
design flows were calculated from the sum of flows at the Dan River near Wentworth and Smith
River, as presented in Table E-1.
Table E-1. Dan River Design Flows
Design Condition Design Flow (cfs)
1Q10 264
7Q10 382
Mean Annual 1,818

For the water quality assessment in the unnamed east tributary, it was assumed that the
upstream low flow was negligible and the resulting surface water concentration was equal to the
groundwater model calculated concentration entering the tributary. There were limited flow
measurements on the east tributary from August 6, 2015 that averaged 0.1 cfs, which indicates
that the mixing model approach taken here is conservative.
3
In addition, dissolved groundwater COI concentrations entering the unnamed east tributary and
unnamed east tributary surface water dissolved COI concentrations are required, which were
determined from observed site monitoring data obtained during the CSA. Table E-2 provides the
applicable NCDEQ or U.S. Environmental Protection Agency surface water quality standards,
which are based on dissolved concentrations for chromium and sulfate and total concentrations
for antimony and cobalt.
Table E-2. Unnamed East Tributary Dissolved COI Concentrations and WQS
COI
Groundwater
Concentration
(µg/L)
Surface Water
Concentration
(µg/L)*
Acute WQS
(µg/L)
Chronic
WQS (µg/L)
Human
Health WQS
(µg/L)
Arsenic 4.66 < 1 / 42.7 340 150 10
Boron 249.3 < 50 / 128 ns ns ns
Total Chromium 17.0 < 1 / 33.6 ns ns ns
Chromium VI 0.009 no data 16 11 ns
Cobalt 0.040 < 1 / < 1 ns ns 4
Sulfate 153,869 5,900 / 23,000 ns ns ns
Thallium 0.004 < 0.2 / < 0.2 ns ns 0.47
Vanadium 0.545 < 0.3 / 1.25 ns ns ns
Notes:
All COIs are shown as dissolved except for total chromium
µg/L = microgram per liter
* – Data from site stations SW-4 / SW-3
ns – no water quality standard

Table E-3 presents the groundwater and surface water data from the Dan River.
Table E-3. Dan River Dissolved COI Concentrations and WQS
COI
Groundwater
Concentration
(µg/L)
Surface Water
Concentration
(µg/L)*
Acute WQS
(µg/L)
Chronic
WQS (µg/L)
Human
Health WQS
(µg/L)
Arsenic 55.4 0.14 340 150 10
Boron 348.8 170 ns ns ns
Total Chromium 14.2 0.59 ns ns ns
Chromium VI 0.972 0.59*** 16 11 ns
Cobalt 1.30 0.32 ns ns 4
Sulfate 57,659 5,000 ns ns ns
Thallium 0.136 0.05** ns ns 0.47
Vanadium 2.61 0.69 ns ns ns
Notes:
All COIs are shown as dissolved except for total chromium
µg/L = microgram per liter
* – Data from upstream site station SW-8
** – Value set to ½ of method detection level (MDL)
*** – Value set equal to total chromium value
ns – no water quality standard

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The groundwater concentrations presented in the Tables E-2 and E-3 are based on model
output from the groundwater model developed for the DRSS. It should be noted that all of the
measured surface water concentrations in the unnamed east tributary and in the Dan River are
less than the associated water quality standard except for one arsenic measurement in the
unnamed east tributary at station SW-3 that is greater than the human health water quality
standard.
In addition, the acute and chronic water quality standards for arsenic and chromium VI use a
water effects ratio (WER) of 1, which expresses the difference between the laboratory-
measured toxicity and toxicity in site water. Measured WERs are typically less than 1 due to
complexing parameters in the site water (e.g., dissolved organic carbon) that reduce the site
toxicity as compared to laboratory measured toxicity for metals. Therefore, use of a WER of 1
provides a conservative assumption in the surface water quality assessment.
Groundwater modeling discussed in Section 4.1 of the CAP Part I report was used to provide
the groundwater flow and COI concentrations into the adjacent receiving waters (unnamed
tributary to the east of the DRSS and the Dan River). Figure E-1 presents the location of the
groundwater model calculated flow inputs into these adjacent receiving waters and Table E-4
presents the total flow along the two flow paths noted in Figure E-1. These groundwater flows
were used to assess the impact on surface water concentrations and compliance with the
applicable water quality standards at the mixing zone boundaries in the unnamed east tributary
and the Dan River.
Table E-4. Model-Calculated Groundwater Flows
Waterbody Groundwater Flow
(ft3/day) (cfs)
Unnamed East Tributary 23,431 0.27
Dan River (Total) 45,129 0.52
Notes:
1. ft3/day = cubic feet per day
2. cfs = cubic feet per second

The values reported in the preceding tables were used to calculate the COI concentrations in
the unnamed east tributary (completely mixed) and in the Dan River at the mixing zone
boundaries for comparison to the applicable water quality standards to assess water quality
compliance of the groundwater discharges from the DRSS.
!
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SW-8
SW-7
SW-6
SW-3
SW-4
±
0 0.1 0.2 0.3 0.4 0.50.05
Miles
Legend
East Trib GW Model Discharge
Dan River GW Model Discharge