LDEQ’s RECAP

Domenico and Summer’s Models

DOMENICO MODEL

The Domenico groundwater model is used to calculate a dilution and attenuation factor (DF or DAF) associated with SoilGW2 , SoilGW3 , GW2 , and GW3 values

DF or DAF is the source concentration of a constituent divided by its down gradient concentration

DF or DAF > 1 If DF or DAF = 1 then no dilution and/or attenuation

Domenico Model

FIGURE I-1

SCHEMATIC DESCRIPTION OF DOMENICO’S MODEL

Impacted Area

Leachate

v Sd

z

y

x

SECTION

PLAN

v Sw

Source Area(Contaminated Groundwater)

Source Area(Contaminated Groundwater)

Csi

Csi

Sw

B

Infiltration Rate

Ground Surface

L

L

MO-1 Domenico ModelSoilGW2 & 3 and GW2 & 3

Default assumptions:Equation accounts ONLY for dilutionPlume is allowed to expand infinitely

laterally in 2 directions vertically in 1 direction

Planar plume size is based onSw is 1/2 acre site - 148 ft by 148 ftSd depths vary from 5 to 20 feet

Two pieces of data are needed to determine a DF from the table:

x - shortest downgradient distance from source to exposure point

Sd - vertical depth of plume

MO-1 Domenico Model

Determination of Sd - vertical depth of plume

METHOD 1:

Sd: depth of plume at initial conditions

Sd = hadv + hdisp

= advective flow + dispersive flow

Sd can not be greater than the aquifer thickness-B

METHOD 1 cont.

Sd = hadv + hdisp

hadv = B[1-exp((-I*L)/(B*Dv)

hdisp = (2* z*L)(0.5)

B: aquifer thickness = 10 ft

I: infiltration rate = 0.33 ft/yr

L: length of source = 148 ft

Dv : groundwater transport velocity = 30 ft/yr

z : vertical dispersivity = L/200 = 148/200

Sd = 1.5 + 14.8 = 16.3 > B Therefore, Sd = 10 ft

The thickness of the impacted permeable zone shall be used as the Sd if the thickness of groundwater plume is unknown

Determination of Sd - vertical depth of plume

METHOD 2:

MO-1 DF Table Values given in tables in Appendix I

X Sd

<5 6-10 11-15 16-20 0-50 1.5 1 1 1 51-100 2.6 1.5 1.2 1.1 101-150 4.1 2.1 1.6 1.3 151-250 8.4 4.3 3 2.3 251-500 29 15 9.8 7.4 501-750 63 32 21 16 751-1000 111 57 37 28 1001-1250 173 86 58 43 1251-1500 248 124 83 62 1501-1750 337 169 113 84 1751-2000 440 220 147 110

If Sd is greater than 20 feet then a site-specific DAF shall be calculated under MO-2 or MO-3

If the distance from the source is greater than 2000 feet, then: (1) the DF for 2000 feet may be used under MO-1; or (2) a site-specific DAF may be calculated under MO-2 or MO-3

MO-1 Domenico Model

MO-2 Domenico Model

Equation can account for dilution and attenuation

Attenuation must be based on site-specific data (NO TEXT BOOK VALUES)

Plume is allowed to expand infinitely in the 2 lateral directions

Plume vertical depth is limited to the aquifer thickness and must be accounted for in the equation

P. WJ1-1 & 2(1) The plume's vertical depth is or is assumed to bethe full thickness of the groundwater stratum. Therefore,spreading in the vertical direction is ignored and the Erf termcontaining Sd is removed from the Domenico model.

Model equation when Sd = H: (Csi/Cxi)= DAF =1/[EXP(X/(2*Ax) * (1-SQRT(1+(4*Yi*Ax*Ri/v))))

* Erf(Sw/(4*SQRT(Ay*X)))] = 8.776 (dimensionless)

(2) The plume's vertical depth is less than the full thickness of the groundwater stratum. The distance over whichvertical spreading can occur is limited to the thickness of thegroundwater stratum. The horizontal distance over which verticalspreading can occur is approximated by Xp = ((H-Sd) 2̂)/Az.

Xp equation:2.5 (ft) = Xp = (H-Sd) 2̂/Az

2000 (ft) = X = distance downgradient from source

Model equation when X < or = Xp:(Csi/Cxi)= DAF =1/[EXP(X/(2*Ax) * (1-SQRT(1+(4*Yi*Ax*Ri/v))))

* Erf(Sw/(4*SQRT(Ay*X))) * Erf(Sd/(2*SQRT(Az*X)))] = 440 (dimensionless)

Model equation when X > Xp:(Csi/Cxi)= DAF =1/[EXP(X/(2*Ax) * (1-SQRT(1+(4*Yi*Ax*Ri/v))))

* Erf(Sw/(4*SQRT(Ay*X))) * Erf(Sd/(2*SQRT(Az*Xp)))] = 16.86 (dimensionless)

MO-2 Domenico Model cont.

If the POE is within the boundary of plume use given form of equation - Fig. J-1

This means the “x” value, the distance from the source to the POE, is much less than the groundwater transport velocity multiplied by the time since the spill

(x << v * t)

If the POE is in front of plume x > v * t then equation must be modified and time t adjusted to account for maximum COC at point x (see model reference)

This is a judgment call. Looking for maximum contaminant concentration at the point x.

Summers Model

The Summers model is used under MO-2 to calculate a site-specific dilution factor for a COC in soil water as it moves from the soil column into the adjacent groundwater (Appendix K)

DFSummers = chemical concentration in soil leachate divided by the chemical concentration in the adjacent groundwater = Cl / Csi

Under MO-1 a DF of 20 is used

SUMMERS MODEL

FIGURE J-1

SCHEMATIC DESCRIPTION OF DOMENICO’S MODEL

Impacted Area

Leachate

v Sd

z

y

x

SECTION

PLAN

v Sw

Source Area(Contaminated Groundwater)

Source Area(Contaminated Groundwater)

Csi

Csi

Sw

B

Infiltration Rate

Ground Surface

L

L

MO-2 Summers Model DAFSummers = Cl / Csi = (Qp + Qa) / Qp

= (I * Sw * L + Dv * Sd* Sw) / (I * Sw * L)

= (0.33*148*148 + 30*10*148) / (0.33*148*148) = 7 Qp volumetric flow of infiltration into aquifer

I: infiltration rate

Sw : width of impacted area perpendicular to GW flow direction

L: length of impacted area parallel to GW flow direction

Qa volumetric flow rate of groundwater

Dv : darcy GW velocity

Sd : thickness of GW plume

Estimation of Sd

Sd = Thickness of impacted groundwater within permeable zone

Un-impacted groundwater

10’

15’

Impacted groundwater5’

Sd = 5’

Estimation of Sd

Sd = Thickness of permeable zone if thickness is not known or if the zone is not

impacted

Un-impacted groundwater

10’

15’

Sd = 15’