Retardation Factors for Selected Organic Compounds

Material Retardation Factor (Rd)

Chloride 1

Chloroform 3

Tetrachloroethylene 9

Toluene 3

Dichlorobenzene 14

Styrene 31

Chlorobenzene 35

(PCBs) are effectively removed by most soils. Highly soluble compounds such as chloroform, benzene, and toluene are removed less efficiently by even highly organic soils. Because volatilization and biodegradation are not necessarily dependent on soil type, the removal of organic compounds via these methods tends to be more uniform from site to site. Table 3.1 presents retardation factors for a number of organic compounds, as estimated from several literature sources (Bedient et al., 1983; Danel, 1953; Roberts et al., 1980).

3.1.2 Movement of Pollutants

The movement or migration of pollutants with the groundwater is controlled by the factors discussed in the previous section. This might be a concern for ponds and other aquatic systems as well as when utilizing the slow rate (SR) and rapid infiltration land treatment concepts. Figure 3.1 illustrates the subsurface zone of

RI basin

RI basin

Zone Influance Wetlands
FIGURE 3.1 Subsurface zone of influence for SAT basin.
Rapid Infiltration Basin
FIGURE 3.2 Nomograph for estimating pollutant travel.

influence for a rapid infiltration basin system or a treatment pond where significant seepage is allowed. It is frequently necessary to determine the concentration of a pollutant in the groundwater plume at a selected distance downgradient of the source. Alternatively, it may be desired to determine the distance at which a given concentration will occur at a given time or the time at which a given concentration will reach a particular point. Figure 3.2 is a nomograph that can be used to estimate these factors on the centerline of the downgradient plume (USEPA, 1985). The dispersion and retardation factors discussed above are included in the solution. Data required for use of the nomograph include:

Aquifer thickness, z (m)

Seepage velocity, v (m/d)

Dispersivity factors ax and ay (m)

Retardation factor Rd for the contaminant of concern

Volumetric water flow rate, Q (m3/d)

Pollutant concentration at the source, C0 (mg/L)

Background concentration in groundwater, Cb (mg/L)

Mass flow rate of contaminant QC0 (kg/d)

Use of the nomograph requires calculation of three scale factors:

Qd = (16.02)(n)(z)[Dx )( Dy )] (3.9)

The procedure is best illustrated with an example. Example 3.1

Determine the nitrate concentration in the centerline of the plume, 600 m down-gradient of a rapid infiltration system, 2 years after system startup. Data: aquifer thickness = 5 m; porosity = 0.35; seepage velocity = 0.45 m/d; dispersivity, ax = 32 m, ay = 6 m; volumetric flow rate = 90 m3/d; nitrate concentration in percolate = 20 mg/L; and nitrate concentration in background groundwater = 4 mg/L.


1. The downgradient volumetric flow rate combines the natural background flow plus the additional water introduced by the SAT system. To be conservative, assume for this calculation that the total nitrate at the origin of the plume is equal to the specified 20 mg/L. The residual concentration determined with the nomograph is then added to the 4-mg/L background concentration to determine the total downgradient concentration at the point of concern. Experience has shown that nitrate tends to be a conservative substance when the percolate has passed the active root zone in the soil, so for this case assume that the retardation factor Rd is equal to 1.

2. Determine the dispersion coefficients:

Dx = (ax)(v) = (32)(0.45) = 14.4 m2/d Dy = (ay)(v) = (6)(0.45) = 2.7 m2/d

3. Calculate the scale factors:

XD = DJv = 14.4/0.45 = 32 m tD = Rd(Dx)/(v)2 = 1(14.4)/(0.45)2

Qd = (16.02)(n)(z)[(Dx)(Dy)]1/2

= (16.02)(0.35)(5)[(14.4)(2.7)]1/2 = 174.8 kg/d v

4. Determine the mass flow rate of the contaminant:

(Q)(C0) = (90 m3/d)(20 mg/L)/(1000 g/kg) = 1.8 kg/d

5. Determine the entry parameters for the nomograph:

Xd 32

- = 10.3 use — = 10 curve tn 71 tn

Qd 174.8

6. Enter the nomograph on the x/xD axis with the value of 18.8, draw a vertical line to intersect with the t/tD curve = 10. From that point, project a line horizontally to the A-A axis. Locate the calculated value 0.01 on the B-B axis and connect this with the previously determined point on the A-A axis. Extend this line to the C-C axis and read the concentration of concern, which is about 0.4 mg/L.

7. After 2 years, the nitrate concentration at a point 600 m downgradient is the sum of the nomograph value and the background concentration, or 4.4 mg/L.

Calculations must be repeated for each contaminant using the appropriate retardation factor. The nomograph can also be used to estimate the distance at which a given concentration will occur in a given time. The upper line on the figure is the "steady-state" curve for very long time periods and, as shown in Example 3.2, can be used to evaluate conditions when equilibrium is reached.

Example 3.2

Using the data in Example 3.1, determine the distance downgradient where the groundwater in the plume will satisfy the U.S. Environmental Protection Agency (EPA) limits for nitrate in drinking-water supplies (10 mg/L).


1. Assuming a 4-mg/L background value, the plume concentration at the point of concern could be as much as 6 mg/L. Locate 6 mg/L on the C-C axis.

2. Connect the point on the C-C axis with the value 0.01 on the B-B axis (as determined in Example 3.1). Extend this line to the A-A axis. Project a horizontal line from this point to intersect the steady-state line. Project a vertical line downward to the x/xD axis and read the value x/xD = 60.

3. Calculate distance x using the previously determined value for xD:

3.1.3 Groundwater Mounding

Groundwater mounding is illustrated schematically in Figure 3.1. The percolate flow in the unsaturated zone is essentially vertical and controlled by Kv. If a groundwater table, impeding layer, or barrier exists at depth, a horizontal component is introduced and flow is controlled by a combination of Kv and Kh within the groundwater mound. At the margins of the mound and beyond, the flow is typically lateral, and Kh controls.

The capability for lateral flow away from the source will determine the extent of mounding that will occur. The zone available for lateral flow includes the underground aquifer plus whatever additional elevation is considered acceptable for the particular project design. Excessive mounding will inhibit infiltration in a SAT system. As a result, the capillary fringe above the groundwater mound should never be closer than about 0.6 m (2 ft) to the infiltration surfaces in soil aquifer treatment (SAT) basins. This will correspond to a water table depth of about 1 to 2 m (3 to 7 ft), depending on the soil texture.

In many cases, the percolate or plume from a SAT system will emerge as base flow in adjacent surface waters, so it may be necessary to estimate the position of the groundwater table between the source and the point of emergence. Such an analysis will reveal if seeps or springs are likely to develop in the intervening terrain. In addition, some regulatory agencies require a specific residence time in the soil to protect adjacent surface waters, so it may be necessary to calculate the travel time from the source to the expected point of emergence. Equation 3.10 can be used to estimate the saturated thickness of the water table at any point downgradient of the source (USEPA, 1984). Typically, the calculation is repeated for a number of locations, and the results are converted to an elevation and plotted on maps and profiles to identify potential problem areas:

where h = Saturated thickness of the unconfined aquifer at the point of concern (ft; m).

h0 = Saturated thickness of the unconfined aquifer at the source (ft; m).

d = Lateral distance from the source to the point of concern (ft; m).

Kh = Effective horizontal permeability of the soil system, mid (ft/d).

Qi = Lateral discharge from the unconfined aquifer system per unit width of

the flow system (ft3/d-ft; m3/d-m):

where di = Distance to the seepage face or outlet point (ft; m). h = Saturated thickness of the unconfined aquifer at the outlet point (ft; m).

The travel time for lateral flow is a function of the hydraulic gradient, the distance traveled, the Kh, and the porosity of the soil as defined by Equation 3.12:

tD =(Kh )(h0- h) (3'12)

where tD = Travel time for lateral flow from source to the point of emergence in surface waters (ft; m). Kh = Effective horizontal permeability of the soil system (ft/d; m/d). h0, hi = Saturated thickness of the unconfined aquifer at the source and the outlet point, respectively (ft; m). di = Distance to the seepage face or outlet point (ft; m). n = Porosity, as a decimal fraction.

A simplified graphical method for determining groundwater mounding uses the procedure developed by Glover (1961) and summarized by Bianchi and Muckel (1970). The method is valid for square or rectangular basins that lie above level, fairly thick, homogeneous aquifers of assumed infinite extent; however, the behavior of circular basins can be adequately approximated by assuming a square of equal area. When groundwater mounding becomes a critical project issue, further analysis using the Hantush method (Bauman, 1965) is recommended. Further complications arise with sloped water tables or impeding subsurface layers that induce "perched" mounds or due to the presence of a nearby outlet point. References by Brock (1976), Kahn and Kirkham (1976), and USEPA (1981) are suggested for these conditions. The simplified method involves the graphical determination of several factors from Figure 3.3, Figure 3.4, Figure 3.5, or Figure 3.6, depending on whether the basin is square or rectangular.

It is necessary to calculate the values of W/(4at)05 and Rt as defined in Equations 3.13 to 3.15:

12 = dimensionless scale factor (3.13)

where W is the width of the recharge basin (ft; m), and

FIGURE 3.3 Groundwater mounding curve for center of a square recharge basin. where

Kh = Effective horizontal permeability of the aquifer (ft/d; m/d).

h0 = Original saturated thickness of the aquifer beneath the center of the recharge area (ft; m). Ys = Specific yield of the soil (use Figure 2.5 or 2.6 to determine) (ft3/ft3; m3/m3).

FIGURE 3.3 Groundwater mounding curve for center of a square recharge basin. where

Kh = Effective horizontal permeability of the aquifer (ft/d; m/d).

h0 = Original saturated thickness of the aquifer beneath the center of the recharge area (ft; m). Ys = Specific yield of the soil (use Figure 2.5 or 2.6 to determine) (ft3/ft3; m3/m3).

FIGURE 3.4 Groundwater mounding curves for center of a rectangle recharge area with different ratios of length (L) to width (W).
Retardation Basin

FIGURE 3.5 Rise and horizontal spread of a groundwater mound below a square recharge area.

FIGURE 3.5 Rise and horizontal spread of a groundwater mound below a square recharge area.


R = (I)/(Ys) (ft/d; m/d), where I is the infiltration rate or volume of water infiltrated per unit area of soil surface (ft3/ft2-d; m3/m2/d). t = Period of infiltration, d.

Enter either Figure 3.3 or 3.4 with the calculated value of W/(4(at)1/2 to determine the value for the ratio hm/(R)(t), where hm is the rise at the center of the mound. Use the previously calculated value for (R)(t) to solve for hm. Figure 3.5 (for square areas) and Figure 3.6 (for rectangular areas, where L = 2W) can be used

FIGURE 3.6 Rise and horizontal spread of a groudwater mound below a rectangular recharge area with a length equal to twice its width.

to estimate the depth of the mound at various distances from the center of the recharge area. The procedures involved are best illustrated with a design example.

Example 3.3

Determine the height and horizontal spread of a groundwater mound beneath a circular SAT basin 30 m in diameter. The original aquifer thickness is 4 m, and Kh as determined in the field is 1.25 m/d. The top of the original groundwater table is 6 m below the design infiltration surface of the constructed basin. The design infiltration rate will be 0.3 m/d and the wastewater application period will be 3 days in every cycle (3 days of flooding, 10 days for percolation and drying; see Chapter 8 for details).


1. Determine the size of an equivalent area square basin:

Then the width (W) of an equivalent square basin is (706.5)1/2 = 26.5 m.

2. Use Figure 2.5 to determine specific yield (Ys):

Kh = 1.25 m/d = 5.21 cm/hr Ys = 0.14

3. Determine the scale factors:

Ys 0.14

(4at)1/2 [(4)(35.7)(3)]1/2 0 3

( R)(t ) = (2)(3) = 6 m 4. Use Figure 3.3 to determine the factor hm/(R)(t):

hm = (0.68)(R)(f) = (0.68)(2)(3) = 4.08 m

5. The original groundwater table is 6 m below the infiltration surface. The calculated rise of 4.08 m would bring the top of the mound within 2 m of the basin infiltration surface. As discussed previously, this is just adequate to maintain design infiltration rates. The design might consider a shorter (say, 2-day) flooding period, as discussed in Chapter 8, to reduce the potential for mounding somewhat.

6. Use Figure 3.5 to determine the lateral spread of the mound. Use the curve for W/(4(at)1/2 with the previously calculated value of 1.28, enter the graph with selected values of x/W (where x is the lateral distance of concern), and read values of hm/(R)(t). Find the depth to the top of the mound 10 m from the centerline of basin:

Enter the x/W axis with this value, project up to W/(4at)l1/2 = 1.28, then read 0.58 on the hm/(R)(t) axis:

The depth to the mound at the 10-m point is 6 m - 3.48 m = 2.52 m. Similarly, at x = 13 m, the depth to the mound is 3.72 m, and at x = 26 m the depth to the mound is 5.6 m. This indicates that the water level is almost back to the normal groundwater level at a lateral distance about equal to two times the basin width. Changing the application schedule to 2 days instead of 3 would reduce the peak water level to about 3 m below the infiltration surface of the basin.

The procedure demonstrated in Example 3.3 is valid for a single basin; however, as described in Chapter 8, SAT systems typically include multiple basins that are loaded sequentially, and it is not appropriate to do the mounding calculation by assuming that the entire treatment area is uniformly loaded at the design hydraulic loading rate. In many situations, this will result in the erroneous conclusion that mounding will interfere with system operation.

It is necessary first to calculate the rise in the mound beneath a single basin during the flooding period. When hydraulic loading stops at time t, a uniform hypothetical discharge is assumed starting at t and continuing for the balance of the rest period. The algebraic sum of these two mound heights then approximates the mound shape just prior to the start of the next flooding period. Because adjacent basins may be flooded during this same period, it is also necessary to determine the lateral extent of their mounds and then add any increment from these sources to determine the total mound height beneath the basin of concern. The procedure is illustrated by Example 3.4.

Example 3.4

Determine the groundwater mound height beneath a SAT basin at the end of the operational cycle. Assume that the basin is square, 26.5 m on a side, and is one in a set of four arranged in a row (26.5 m wide by 106 m long). Assume the same site conditions as in Example 3.3. Also assume that flooding commences in one of the adjacent basins as soon as the rest period for the basin of concern begins. The operational cycle is 2 days flood, 12 days rest.


1. The maximum rise beneath the basin of concern would be the same as calculated in Example 3.3 with 2-day flooding: hm = 3.00 m.

2. The influence from the next 2 days of flooding in the adjacent basin would be about equal to the mound rise at the 26-m point calculated in Example 3.3, or 0.4 m. All the other basins are beyond the zone of influence, so the maximum potential rise beneath the basin of concern is (3.00) + (0.4) = 3.4 m. The mound will actually not rise that high, because during the 2 days the adjacent basin is being flooded the first basin is draining. However, for the purposes of this calculation, assume that the mound will rise the entire 3.4 m above the static groundwater table.

3. The R value for this "uniform" discharge will be the same as that calculated in Example 3.2, but t will now be 12 days: (R)(t) = (2)(12) = 24 m/d.

4. Calculate a new W/(4at)1/2, as the "new" time is 12 days:

W/(4at)1/2 = 26.5/[(4)(35.7)(12)]1/2 = 0.62

5. Use Figure 3.3 to determine "hm"/(R)(t) = 0.30: "hm" = (24)(0.3) = 7.2 m. This is the hypothetical drop in the mound that could occur during the 10-day rest period; however, the water level cannot actually drop below the static groundwater table, so the maximum possible drop would be 3.4 m. This indicates that the mound would dissipate well before the start of the next flooding cycle. Assuming that the drop occurs at a uniform rate of 0.72 m/d, the 3.4-m mound will be gone in 4.7 days.

In cases where the groundwater mounding analysis indicates potential interference with system operation, several corrective options are available. As described in Chapter 8, the flooding and drying cycles can be adjusted or the layout of the basin sets rearranged into a configuration with less inter-basin interference. The final option is to underdrain the site to control mound development physically.

Underdrainage may also be required to control shallow or seasonal natural groundwater levels when they might interfere with the operation of either a land or aquatic treatment system. Underdrains are also sometimes used to recover the treated water beneath land treatment systems for beneficial use or discharge elsewhere.

3.1.4 Underdrainage

In order to be effective, drainage or water recovery elements must either be at or within the natural groundwater table or just above some other flow barrier. When drains can be installed at depths of 5 m (16 ft) or less, underdrains are more effective and less costly than a series of wells. It is possible using modern techniques to install semiflexible plastic drain pipe enclosed in a geotextile membrane by means of a single machine that cuts and then closes the trench.

In some cases, underdrains are a project necessity to control a shallow ground-water table so the site can be developed for wastewater treatment. Such drains, if effective for groundwater control, will also collect the treated percolate from a land treatment operation. The collected water must be discharged, so the use of underdrains in this case converts the project to a surface-water discharge system unless the water is otherwise used or disposed of. In a few situations, drains have been installed to control a seasonally high water table. This type of system may

Hydraulic loading rote Lw + P


Soil surface

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