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 

WAHSINGTON, D.C. 20460 

FEBURARY, 2012 

2

PLUME INTERCEPTION BY A STREAM AND CONTAMINANT 

CONCENTRATIONS AT RECEPTOR WELLS LOCATED 

DOWNGRADIENT FROM THE STREAM 

1. INTRODUCTION 

The U.S. Environmental Protection Agency’s Composite Model for Leachate Migration with 

Transformation Products (EPACMTP) was used to predict contaminant concentrations at 

receptor wells located downgradient of the coal combustion residues (CCRs) management sites 

(U.S. EPA, 2003a). 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 were developed to address 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 from 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 procedures were developed for the case of gaining streams (streams receiving baseflow 

from groundwater) only. For losing streams (streams discharging to groundwater), the streams 

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 gradients are not significantly 

impacted by the presence of losing streams. Theoretical details 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 XSW. A receptor well is 

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

>XSW, the well is located downgradient from the surface water body. YB is a constant and 

represents the distance from the plume center line to the plume width at the X = XRW 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. 
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Figure 1.  Plan view and definition of parameters. 

As shown in Figure 2, the depth of the surface water body below the water table is DSW, the 

depth of baseflow that discharges to the surface-water body is DBF, and the saturated thickness of 

the aquifer is B. 

Figure 2.     Cross‐sectional view and definition of parameters. 

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 concentrations at a well downgradient from a traversing surface- water body, which, in 

turn, is downgradient from a WMU. The second procedure was developed to estimate chemical 

z

x

Source Receptor

Well

Flow Direction

B

DSW

Surface water body

River, Creek

Aquifer base

DBF

Surface water body

River

Creek Receptor well

Source

Plume

XSW X‐axis

YB

XRW
4

mass flux removed by the traversing surface-water body. The two procedures are described in 

the following subsections. 

 

2.1 Concentration at Wells Located Downgradient from a Stream

Within the flow domain shown in Figure 1, the total water flux removed by the gaining stream 

(henceforth a surface-water body is referred to as stream) is given by: 

ܳ஻௔௦௘௙௟௢௪ ൌ 2 ܻ஻ ݍ௔஻௦௘௙௟௢௪                 ሺ1ሻ 

Where: 

QBaseflow = total baseflow water flux removed by the stream (L3

/T); 

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

 the flow domain (L2/T); and 

YB = half width of the flow domain (L). 

The aquifer also receives recharge from the infiltration of precipitation within the flow domain 

(USEPA, 2003a). As a result, flow rate per unit width along the X-direction may vary. To 

account for this variation, spatially averaged flow rate per unit width is used. Average flow rate 

per unit width between the stream and the receptor well is given by: 

ݍ஺௩௘௥௔௚௘ி௟௢௪   ൌ

ଵ

௑ೃೈି௑ೄೈ

௥௘௙௜௨஺௤ݍ ׬

௫ୀ௑ೃೈ

௫ୀ௑ೄೈ

݀ݔ           ሺ2ሻ 

where: 

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

baseflow included (L2/T); 

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

included (L2/T);

XSW = distance to the stream from the downgradient edge of the WMU 

(L); and 

XRW = 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: 

ݍே௘௧௙௟௢௪  ൌ ݍ஺௩௘௥௔௚௘௙௟௢௪ െ ݍ௔஻௦௘௙௟௢௪             ሺ3ሻ 

where: 

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

baseflow removed (L2/T). 

The removal of groundwater as baseflow results in changed groundwater flow rate per unit 

width, downgradient from the surface water body, from qAverageflow to qNetflow. It is, however, 

possible to use the same solution to the groundwater flow and contaminant transport equations 

based on qAverageflow by relocating the receptor well from XRW to XRW’, where XRW’ represents an 
5

effective distance at which the concentration under the qNetflow condition between the stream and 

the receptor well is the same as that at XRW under the qAverageflow 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 coefficient 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 using the receptor well distance as the characteristic length, 

indicates that most of the sites in EPACMTP have Peclet numbers varying from 10 to 5,000. 

Based on this assumption, a transformation procedure was developed. In the transformation, 

receptor well location is modified using the equation below: 

ሺܺᇱ

ோௐ െ ܺௌௐ ሻ ൌ   

௤ಲೡ೐ೝೌ೒೐೑೗೚ೢ

௤ಿ೐೟೑೗೚ೢ

ሺܺோௐ െ ܺௌௐ ሻ            ሺ4ሻ 

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

ܺതோௐ   ൌ   

ଵ

ଶ

 ൫ܺோௐ

ᇱ௜ ൅ ܺோௐᇱ௜ିଵ൯                 ሺ5ሻ 

where: 

X’i

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

ݍԢே௘௧௙௟௢௪   ൌ

ଵ

௑തೃೈି௑ೄೈ

௥௘௙௜௨஺௤ݍ ׬

௑ୀ௑തೃೈ

௑ୀ௑ೄೈ ݀ݔ  െ   ݍ௔஻௦௘௙௟௢௪     ሺ6ሻ 

Using X’RW from Equation (5) to obtain average well location, ܺതோௐ, qNetflow is updated to q’Netflow

through Equation (6). Substituting qNetflow by q’Neflow in Equation (4), X’RW and therefore ܺതோௐ 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, 

หܺோௐ

ᇱ௜  െ   ܺோௐᇱ௜ିଵห ൏ Є                     ሺ7ሻ 

where: 

Є ൌ 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 

XRW) is calculated using the solution of the groundwater flow and contaminant transport 

equations at the new well location, X’RW. 

2.2 Mass Flux from Aquifer into a Stream 

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 known. The volumetric groundwater flux depends on the difference between the 
6

stream stage and the hydraulic head in the aquifer. If the hydraulic head in 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 governed 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 estimated 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, DBF, and the 

domain half width, YB. The total mass flux is determined using the baseflow rate and the output 

contaminant concentration from EPACMTP according to the equation below. 

ܯ  ൌ   2  ௤ಳೌೞ೐೑೗೚ೢ

஽ಳಷ

ಳಷ஽ୀ ௭ ݖ ݀ݕ݀ሻݐ ,ݖ ,ݕ ,ௌௐܺൌܺሺܥ ׬ ׬

௭ ୀ଴

௬ୀ௒ಳ

௬ୀ଴ (8) 

where: 

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

C = chemical concentration at ܺൌܺௌௐ (M/L3); 

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

(L); 

XSW = 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, 2003a); and 

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

U.S. EPA, 2003a), positive downward. 

The concentration term, C, is obtained from Equation (4.92) in the EPACMTP Technical 

Background Document (USEPA, 2003a) and baseflow depth which is defined by: 

ܦ஻ி ൌ  

௤ಳೌೞ೐೑೗೚ೢ

௤ಲ೜ೠ೔೑೐ೝ

 (9) ܤ 

where: 

B = saturated thickness of the aquifer 

The baseflow depth, DBF, which is based on the Dupuit approximation (Bear, 1972), is 

considered more accurate than the surface water depth, DSW (Figure 2) for the following reasons: 

(1) baseflow is a measured quantity in gauged streams; (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 steepening of hydraulic gradient before entering the stream. 
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3. References 

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 Background 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, EPA53-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.