(QD) is a Microsoft Excel spreadsheet application of “An Analytical Model For
Multidimensional Transport of a Decaying Contaminant Species”, by P.A. Domenico, Journal of
Hydrology, 91 (1987), pp 49-58. QD solves the following equation with two modifications to be discussed
erfc x vt
erf y Y
x erf y Y
x erf z Z
x erf z Z
( , , , ) ( )exp
C(x,y,z,t) = the concentration of the contaminant at location x, y, z from the source at time t.
= source concentration - the highest concentration of the contaminant in the groundwater at the source.
dispersivity in the x direction.
= dispersivity in the y direction .
= dispersivity in the z direction.
k= hydraulic conductivity.
i = hydraulic gradient
n = porosity (entered as a decimal fraction - (i.e. .25)
v = specific discharge. (ki/n)
1st order decay constant.
= width of source area.
= depth of source area.
x, y, z - these are the spatial coordinates in the horizontal, transverse and vertical directions, respectively,
that define the point or points where concentration information is desired.
t - this is time since the plume source started moving
In QD this equation has been modified in two ways.
First, “v” has been modified to include a retardation factor defined as 1+ (KOC*foc*p
KOC = the organic carbon partition coefficient
foc = fraction of organic carbon expressed as a decimal percent
= the dry bulk density of the aquifer matrix.
Secondly, the term “Z/2” in the last two error function terms of the equation have been replaced by “Z” as
described by Domenico (1987), page 53, to account for dispersion in the vertical axis in only the downward
direction, as would occur with contaminants at the water table in a thick uniform aquifer and the source
geometry for which this application is designed.
IBM Compatible PC
Windows 3.1 or later
Microsoft Excel 5.0 or later - with Analysis Tool Pack running. (On menu bar, click Tools, AddIns,
Intel 486 or better processor recommended.
GENERAL APPLICATION INFORMATION
Quick Domenico (QD) calculates the concentration of contaminant species at any point and time
downgradient of a source area of known size and strength. The kinds of contaminants for which QD is
intended are dissolved organic contaminants whose fate and transport can be described or influenced by
first order decay and reaction with organic carbon in the soil. The model allows for first order decay,
retardation and three-dimensional dispersion, which will be discussed below. In addition, QD calculates
the concentrations in a two dimensional 5x10 grid whose length and width are set by the user. The output
of the grid is plotted on an Excel chart each time any element of the input data is changed. This allows
users to see almost immediately the effects of changes in input data.
Upon selection and input of the final input parameters, the output can be printed on any Windows
compatible printer using a pre-set print area.
QD is based on the Domenico analytical model referenced above. The major limitation of any analytical
groundwater transport model is that steady, uniform, one dimensional groundwater flow is assumed.
Consequently, only a single value of any one of the 20 or so flow and transport parameters required by the
model are allowed at any one time. Therefore the model should not be used where any of these parameters
vary significantly in direction or magnitude over the model domain. Further, QD uses physical properties
of the soil such as dry bulk density and fraction organic carbon that are difficult to relate to or determine for
fractured bedrock aquifers. Therefore QD should be used with caution in these environments. QD is
primarily intended for use in unconsolidated (soil) aquifers with reasonably uniform physical and
QD is primarily intended for use with dissolved organic compounds that may react with organic carbon in
the soil and/or may be subject to biodegradation or reaction that can be described by 1st order decay. The
first order decay constant (lambda) can be set to zero where evidence of biodegradation of the compound or
its decay rate is questionable. (e.g. MTBE). QD does not simulate the transformation of parent compounds
into daughter compounds (e.g. TCE to DCE). QD considers compounds individually and assumes no
reaction between compounds.
Despite these many limitations, the Domenico model has been successfully applied as a screening model to
actual data from contaminated sites. In addition, QD has application as a “conceptual” model where
hypothetical or “worst case” conditions are investigated. By using conservative input assumptions, QD may
be useful in Pennsylvania’s Land Recycling Program in providing quantitative support to qualitative fate
and transport analyses based solely on professional experience or opinion at sites which do appear to justify
the time, expense and data requirements associated with more rigorous numerical modeling efforts.
The cells in the spreadsheet have been color coded to assist in use and understanding.
Light Green - these cells allow or require the user to enter data.
Light Yellow - these cells are locked and calculated by the spreadsheet.
Other Colors - these cells are used for labels and other information not critical to use of the application.
Where input requires a certain unit of measurement, it has been indicated. Because the spreadsheet contains
internal formulas that depend on the units of the input data, use of improper units may result in spurious
results. However, concentrations may be entered in any unit and the output will be in that unit. If units
different from mg/l are used, the user should note that on the output.
Cell-By-Cell Description -
The following section discusses the information that is input cell by cell. The discussion will emphasize
conservative selection of parameters where appropriate.
Enter project name
Enter the date that application was prepared.
Enter name of person or firm preparing application.
Enter name of contaminant.
Source Concentration in mg/l - QD allows one source concentration that is applied to the entire
width and thickness dimensions of the source. The source is presumed to be continuous, which
makes QD inherently conservative with respect to concentration at sites where sources have been
removed or remediated. The highest concentration in the groundwater determined from the site
characterization is usually entered, but can be adjusted within reasonable limits for model
Distance to Location of Concern (x) (in feet) – This is the distance from the source along the
plume centerline where a point concentration may be desired. Currently, the sole purpose of this
cell is to transfer the cell content to cell A18.
Longitudinal Dispersivity - (Ax) - dispersion parallel to the direction of groundwater flow and
Transverse Dispersivity - (Ay) - dispersion perpendicular to the direction of groundwater flow and
parallel to the water table.
Vertical Dispersivity - (Az) - dispersion perpendicular to the direction of groundwater flow and
water table. In QD, only vertical dispersion downward below the water table is considered.
These parameters are dispersion terms that describe the extent to which contaminants spread out
from the source into areas that cannot be accounted for by advective transport alone. Initially these
parameters are often estimated, using rules of thumb, and then adjusted in order to calibrate a
model to better fit actual field conditions. Several relationships have been proposed for initial
estimates of Ax, Ay, and Az.
Ax = X/10 where X is the distance a contaminant has traveled by advective transport (i.e. velocity
Ay = Ax/10
Az = Ax/20 to Ax/100. In general, it is recommended for to a very small vertical dispersion of
.001, unless there is vertical monitoring can reliably justify a larger number. This essentially
converts QD to a two-dimensional transport model. Because of the way QD is set up, a vertical
dispersion of zero cannot be used. A value of about .0001 is suggested for initial uncalibrated or
) - this is the first order decay constant. It is determined by dividing .693 by the
half-life of the compound (in days). The value can be calculated for stable* or shrinking plumes
and selected by trial and error to existing data for expanding plumes. Dispersivity values and
lambda are the two most important calibration terms available in this application. QD is very
sensitive to the lambda term. Users should not rely on published values. Published values are
often estimates based on idealized lab or bench scale conditions or derived in other ways. Further,
lambda can vary from site to site for the same compound because subsurface conditions favorable
to biodegradation vary from site to site. For compounds that are not biodegradable or at sites
where biodegradation is not occurring use a lambda of zero.
* See Buscheck, T. E. and Alcantar, C. M., 1995, Regression Techniques and Analytical Solutions
to Demonstrate Intrinsic Bioremediation , In Hinchee, R. E., Wilson, J. T. and Downey, D. C.
(Eds.), Intrinsic Bioremediation, pp. 109-116.
Source Width (ft) - enter the maximum width of the area of contaminated soils that have been
impacted, or the maximum width of free product or smear zone of contamination measured
perpendicular to the direction of groundwater flow. Data should be based on and justified by site
characterization data. Because one concentration rarely characterizes the entire source width of a
plume, source width can be adjusted somewhat and serve as a calibration parameter.
Source Thickness - typically this is the thickness of contaminated soils below the water table that
contribute contamination to the water table plus the water table fluctuation that creates a smear
zone. Average water table fluctuation can be used as an estimate of the smear zone at sites with
Hydraulic Conductivity (k)(ft/day) - the hydraulic conductivity of a geologic material is a measure
of it’s ability to transmit water. The hydraulic conductivity is determined from pumping or slug
tests using standard ASTM or other methods described in numerous hydrogeology textbooks. QD
allows only one hydraulic conductivity measurement to be input.
Hydraulic Gradient (ft/ft)- this is the slope of the water table in the direction of ground water flow.
QD assumes horizontal flow and a uniform hydraulic gradient. Hydraulic gradient of the water
table should be measured at each site. A minimum of three wells drilled to the same depth into the
geologic formation is required to measure the hydraulic gradient.
Porosity - (decimal fraction- e.g. .25) - porosity is the ratio of volume of void space in a geologic
material to the total volume of material. Porosity can be determined by sending soil samples to a
laboratory or, if the texture of the material is uniform and well described, by estimating the value
of textbooks. The lower the porosity, the faster groundwater moves through the void space for a
given value of ‘k’ and hydraulic gradient.
Soil Bulk Density -(p
) - this is the dry weight of a sample divided by its total volume in an
undisturbed state. QD is not particularly sensitive to this parameter. Samples can be sent to a lab
for measurement. The equation p
= 2.65* (1-porosity) can also be used to estimate soil bulk
KOC - this is the organic carbon partition coefficient and is chemical specific. During formulation
of the Act 2 regulations, the Department went to considerable time and expense, using outside
expertise, to develop the most
up to-date KOC values. These are provided in Appendix A, Table
5, of the Act 2 regulations. Use these KOC values unless the KOC value is determined for the
Fraction Organic Carbon (foc) - (decimal fraction) - this is the organic carbon content of the soil.
A soil laboratory using ASTM methods can determine this value. Samples for organic carbon
should be taken from the same soil horizon in which the contaminant occurs, but from an area that
has not been impacted. One/half of one per cent (.005) is a commonly estimated value.
Retardation - the spreadsheet calculates this value automatically. It is defined as 1+
Velocity (V) - (ft/day) – this is rate of contaminant flow. The spreadsheet calculates this value
automatically from the previous inputs.
This cell is automatically filled by transferring the content in cell B7. The value is repeated here
simply to facilitate the view of the x, y and z coordinates for which the spreadsheet calculates a
point solution in cell A22.
‘y’ (ft)- this is the ‘y’ coordinate (horizontal distance perpendicular to the plume centerline) for
which a single point solution is desired. For a solution on the centerline of the plume
downgradient from the source, ‘y’ would be set equal to zero. Both positive or negative values
may be entered, however, because QD provides a symmetrical solution, there is no difference in
the values obtained.
‘z’ (ft) - this is the ‘z’ coordinate in the vertical axis perpendicular to the ‘x’ and ‘y’ location. For
most applications this should be left at zero since this value will yield the highest concentration,
which is at the water table in this configuration of the Domenico model. If the concentration of a
point below the water table is desired, the depth can be entered here. The value entered in this cell
will also determine the depth below the water table that concentrations are calculated and
displayed in the 5 x 10 grid.
‘t’ - (days) - this is the time (in days), after a contaminant began moving in the groundwater away
from the source, for which a solution is desired. By adjusting the spreadsheet with the scroll bars
so that both the grid, graphic chart and time can be seen at the same time on the screen, adjusting
the time progressively upward provides a graphical way to determine at what time steady state is
reached for the particular set of input conditions. The time a source has been active is one of the
most important parameters in any model, and often one of the hardest to pin down. Historical
records and analysis is usually the best source for reasonable values.
these cells are where the user sets the grid dimensions for the 5 by 10 grid that appears in
. The grid dimensions form the window through which the plume is viewed and
the locations where concentrations are calculated. By setting length at 500 ft and width at 50 feet,
for example, the grid would cover a length of 500 feet from the source and a width of 50 feet on
either side of the source origin. Concentrations in the plume are calculated increments of
length/10, and width/ 2. By changing grid sizes, the user will very quickly see how grid
dimensions and the locations where calculations are made is affected.
These cells contain the source concentration calculated for the specific location and time
A18 through D18.
These cells contain the output for the grid nodes defined by the grid dimensions input in
C26 and C27.
The output from the grid is automatically displayed in a Microsoft Excel chart located
above the grid.