## PLUME INTERCEPTION BY A STREAM AND CONTAMINANT

CONCENTRATIONS AT RECEPTOR WELLS LOCATED

DOWNGRADIENT FROM THE STREAM

OFFICE OF RESOURCE CONSERVATION AND RECOVERY (ORCR)

U

. S

. ENVIRONMENTAL PROTECTION AGENCY

WAHSINGTO N , D.C. 20460

FEBURARY , 20122



## PLUME INTERCEPTION BY A STREAM AND CONTAMINANT

CONCENTRATIONS AT RECEPTOR WELLS LOCATED

DOWNGRADIENT FROM THE STR EAM

1

. INTRODUCTION

The U.S. Environm e ntal Protection Agency’s Comp o site Model for Leachate Migration with Transformation Products (EPACMTP) was used to predict contaminant concentrations at receptor wells located downgradien t of the coal combustion residues ( CCR s) management sites (U

. S

. EPA, 2003 a ). The U.S. EPA has not made any changes to the source code of EPACMTP

since its use for the Risk Assessment for the CCRs (U.S. EPA

, 2010). However, new pre

- and

post

- processing modules w ere developed to add ress the public and peer review comments regarding the interception of the plume by a surface

- water body

.

At some of the CCRs sites, a waste management unit (WMU) may be located in an area where the underlying aquifer is traversed by a surface

- water body ( a stream or a river, etc) downgradient from the WMU. At these sites, it is also possible that receptor wells may be located downgradient f rom the traversing surface

- water bodies. In order to determine contaminant concentration at these wells, as well as contaminant mass fluxes that may enter the

surface

- water bodies from the aquifers, two procedures have been developed. These procedures

are described in Section 2 and are used to pre

- process EPACMTP input and post

- process EPACMTP simulation results to take into consideration the interception of a plume by a stream.

The two procedure s w ere developed for the case of gaining stream s (stream s receiving baseflow from groundwater) only. For losing stream s (stream s discharging to groundwater), the stream s receive no contaminants from groundwater and there is no added risk to receptors using the stream waters. In addition, in most hydrogeologic settings, the impact on the ground

- water flow regime tends to be local and the regional groundwater hydraulic gra dients are not significantly impacted by the presence of losing streams. Theoretical de tails of the two procedures are given

in Section 2

.



### 2

. THEORETICAL FORMULATIONS

A waste management unit (WMU) is located upgradient from a surface

- water body (e.g., a creek or a river) which traverses the region in the Y

- direction and is normal to the regional groundwater

flow direction which flows in the X

- direction (Figure 1). The distance between the downgradient edge of the WMU and the upgradient edge of the surface

- water body is X SW

. A receptor well is

located at a distance of X RW from the downgradient edge of the WMU. In the event that X RW

> X SW , the well is l ocated downgradient from the surface water body. Y B is a constant and

represents the distance from the plume center line to the plume width at the X = X RW where

contaminant concentration in the plume is expected to be negligible. It represents the dimension

of one half of the width of the flow and contaminant transport domain along the Y

- direction. Owing to the plume symmetry, only one half of the domain is simulated.3

Figure 1

. Plan view and d efinition of p arameters

.

As shown in Figure 2, t he depth of the surface water body below the water table is D SW , the depth of baseflow that discharges to the surface

- water body is D BF , and the saturated thickness of the aquifer is B

.

Figure 2. Cross

- sectional view and d efinition of p arameters

.

If the surface

- water body is a gaining stream, i.e., receiving baseflow flux from the aquifer, mathematical descriptions of groundwater flow and chemical transport in the aquifer downgradient from the surface

- water body will have to be modified as the stream removes a portion of both water and chemical contaminants from the aquifer. In order to handle these special cases, two procedures were developed. The first procedure was developed to estimate

chemical concentration s at a well downgradient from a traversing surface

- water body , which, in turn, is downgradient from a WMU . The sec ond procedure was developed to estimate chemical Surface water body

River Creek Receptor well

Source Plume

X

- axis X SW YB

X RW4

mass flux removed by th e traversing surface

- water bod y

. The two procedures are described in the following subsections.

2.1 Concentration at Wells Located Downgradient from a Stream

Within the flow domain s hown in Figure 1, the total water flux removed by the gaining s tream (henceforth a surface

- water body is referred to as stream) is given by:

(1)

Where : Q Baseflow = total baseflow water flux removed by the stream (L 3 /T) ;

q Baseflow = total baseflow water flux removed by the stream per unit width of

the flow domain (L 2 /T) ; and

Y B = half width of the flow domain (L )

.

T he aquifer also receives recharge from the infiltration of precipitation within the flow domain (USEPA, 2003 a ) . As a result , flow rate per unit width along the X

- direction may vary. To

account for th is variation, spatially averaged flow rate per unit width is used. A verage flow rate per unit width between the stream and the receptor well is given by:

(2 )

where:

q

Average flow = average aquifer flow rate per unit width of the flow domain with

baseflow included (L 2 /T) ;

q Aquifer = aquifer flow rate per unit width of the flow domain with baseflow

included (L 2 /T) ;
X SW = distance to the stream from the downgradient edge of the WMU

(L ) ; and

X RW = distance to the receptor well from the downgradient edge of the

WMU (L ).

After baseflow loss to the stream , the net aquifer flow rate per unit width (perpendicular to the stream) between the stream and the well is given by:

(3 )

where:

q Net

flow = net aquifer flow rate per unit width of the flow domain with

baseflow removed (L 2 /T)

.

T he removal of groundwater as baseflow results in changed groundwater flow rate per unit width, downgradient from the surface water body , from q Average f low to q

Net f low . It is, however, possible to use the same solution to the groundwater flow and contaminant transport equations

based on q

Averageflow by relocating the receptor well from X RW t o X

RW ’ , where X

RW ’ represents an5

effective distance at which the concentration under the q Netflow condition between the stream and the receptor well is the same as that at X RW under the q

Averagef low condition. The relocation procedure presented below is based on an assumption that the dispersive flux is much smaller than the advective flux. This assumption holds when the Peclet number ([ groundwater velocity* characteristic length ]/ longitudinal dispersion coeffi cient or characteristic length/longitudinal dispersivity) is greater than 10 (Garges and Baehr, 1998). An estimate based on the dispersitivity and receptor well distribution data in the EPACMTP Parameters/Data Background document (US EPA, 2003b), and usin g the receptor well distance as the characteristic length,

indicates that most of the sites in EPACMTP have Peclet number s varying from 10 to 5,000. Based on this assumption, a transformation procedure wa s developed. In the transformation, receptor well location is modified using the equation below:

(4 )

Since q Net

f low is not known a priori , it is necessary to locate X ’ RW iteratively, as follows:

(5 )

where:

X ’i

RW = i

- th iterate of X’ RW with X ’0 RW = X RW

(6 )

Using X ’

RW from Equation (5) to obtain average well location

, , q N et flow is updated to q ’ Netf low through Equation (6). Substituting q Net flow by q ’

Ne flow in Equation (4), X’ RW and therefore in
Equation (5) are updated. The whole process is repeated until the difference between the most

current X ’

RW is sufficiently close to the immediately preceding value. In other words,

(7 )

where:

= acceptable tolerance (a typical value is 0.1 meter)

.

This procedure is used to modify the existing well distance prior to EPACMTP simulations. By relocating the receptor well location to X’ RW from the downgradient edge of the WMU, concentration equivalent to concentration from the actual receptor well (located at the distance of

X RW ) is calculated using the solution of the groundwater flow and contaminant transport equations at the new well lo cation, X’ RW

.

2.2 Mass Flux from Aquifer into a S tream

To predict the mass flux of a contaminant from an aquifer to a stream, the distributions of

contaminant concentration and volumetric groundwater flux along the upgradient edge of the

stream must be kn own . The volumetric groundwater flux depends on the difference between the6

stream stage and the hydraulic head in the aquifer. If the hydraulic head i n the aquifer is higher

than the stream stage , the groundwater from the aquifer will enter the stream as baseflow. When this occurs, the stream is said to be a gaining stream. The procedure below was developed for

the case of a gaining stream only.

The groundwater volumetric flux per unit area of stream bed is govern ed by the difference in groundwater hydraulic head, hydraulic conductivity of streambed, and streambed thickness. In many watersheds, baseflow in terms of volumetric inflow rate per unit length of stream is

available. Assuming that the base flow information is available, mass flux may be e stimated by integrating the product of baseflow flux per unit area and contaminant concentration over the total baseflow area. The total baseflow area is determined by the baseflow depth, D BF , and the domain half width, Y B

. The total mass flux is determi ned using the baseflow rate and the output

contaminant concentration from EPACMTP according to the equation below.

(8)

where:

D BF = baseflow depth (L ) (see Figure 2 and Equation ( 9 ) below )

C = chemical concentration at (M/L 3 ) ;

x = horizontal distance of stream from the downgradient edge of the WMU

(L ) ;

X SW = distance of stream from the downgradient edge of the WMU (L ) ;

y = horizontal distance from the source centroid along the source plane ( L, see

U

. S

. EPA, 2003 a ) ; and

z = vertical distance from the source centroid along the source plane ( L, see

U

. S

. EPA, 2003 a ) , positive downward.

The concentration term, C , is obtained from Equation (4.92) in the EPACMTP Technical Background Document (USEPA, 2003a) and b aseflow depth which is defined by :

(9)

where:

B = saturated thickness of the aquifer

T he baseflow depth, D BF , which is based on the Dupuit approximation (Bear, 1972), is

considered more accurate than the surface water depth, D SW (Figure 2) for the following reasons: ( 1 ) baseflow is a measured quantity in gauged str eams; (2) reference elevations for stream depth are not always known; (3) a reported stream depth for a given stream may not reflect its average depth; and (4) stream depth may not account for the contraction of groundwater flow tube due to localized steep ening of hydraulic gradient before entering the stream.7



### 3

. R eferences

Bear, J

. 1972. Dynamics of Fluids in Porous Media. American Elsevier, New York.

Garges, J. A., and A. L. Baehr

. 1998. Type Curves to Determine the Relative Importance of
Advection and Dispersion of Solute Transport, Ground Water, 36(6):959

- 965.

U

. S

. EPA

. 2003a. EPA’s Composite Model for Leachate Migration with Transformation

Products (EPACMTP) . Technical Backgr ound Document. Office of Solid Waste,
Washington, DC, EPA53

- R

- 03

- 002.

U

. S

. EPA

. 2003b. EPA’s Composite Model for Leachate Migration with Transformation

Products (EPACMTP) . Parameters/Data Background Document. Office of Solid Waste, Washington, DC, EP A53

- R

- 03

- 003

U

. S

. EPA

. 2010. Human and Ecological Risk Assessment of Coal Combustion Wastes. Office

of Resource Conservation and Recovery, Washington, D.C. 20460

.