Environmental Forensics: Principles and Applications - Chapter 5 docx

trans-When evaluating contaminant transport models, examine the modeling results bydividing the subsurface into the following discrete zones: 1 the surface paved andunpaved, 2 the soil a

trans-When evaluating contaminant transport models, examine the modeling results bydividing the subsurface into the following discrete zones: (1) the surface (paved andunpaved), (2) the soil and capillary fringe, and (3) the groundwater This division isnecessary because each zone requires different governing assumptions and math-ematics that cumulatively determine the time required for a contaminant to travelfrom the ground surface to groundwater.

The ability to reliably model contaminant transport is directly proportional to therepresentativeness of the input parameters Given uncertainties associated with theseinput parameters, a range of values should be used that produces a range of contami-nant transport probabilities Practical inversion tools now allow for rigorous determi-nation of optimal parameter values and what the data do and do not support A key

theme of this chapter is that a unique solution for contaminant transport models does

not exist (see Figure 5.1)

5.2 LIQUID TRANSPORT

THROUGH PAVEMENT

A frequent inquiry is the determination of whether a solvent migrated through apaved surface such as asphalt, concrete, crushed rock, or compacted soil and, if so,

the time required Ideally, direct measurements are performed to answer this question

by collecting a representative pavement core sample, ponding the liquid of interest,and recording the time required for the liquid to drip from the bottom of the sample.Absent direct measurement, contaminant transport equations are used In order toselect the correct equation(s), identification of the most likely transport mechanism

— such as liquid advection (Darcy flux; see Equation 2.8 in Chapter 2), gas diffusion,liquid diffusion and evaporation — is required

The transport of dense non-aqueous phase liquids (DNAPLs) via liquid tion through pavement is commonly believed to be a rapid process This assumption

advec-is true if the pavement advec-is cracked, allowing unrestricted flow, or if the spill occursover an expansion/control or isolation joint filled with permeable wood, oakum, ortar Expansion joints are placed at the junction of the floor with walls, foundationcolumns, and footings Given the sorptivity of the material used to fill expansionjoints, sampling and testing of these materials are often useful to establish whether

a contaminant was transported into the underlying soil via an expansion joint.Isolation joints are used to separate a concrete slab from other parts of a structure

to permit horizontal and vertical movement of the concrete slab Isolation jointsextend the full depth of the slab and include pre-molded joint fillers (Kosmatak etal., 1988)

In the absence of direct measurements or the presence of cracks or expansionjoints or direct measurements with a pavement core, quantifiable transport variablescan be identified that determine if and when a liquid permeated a paved surface.Variables used in calculating the time required for a liquid to infiltrate through apaved surface include:

FIGURE 5.1 Concept of a unique solution vs a range of probable solutions.

• The temporal nature of the release (steady state or transient)

• The saturated and unsaturated hydraulic conductivity of the pavement

• Physical properties of the contaminant (density, viscosity, vapor pressure)

• Chemical properties of the liquid (pure phase, mixed solvents, or dissolved in water) which affect the evaporation rate

• Liquid thickness and the length of time that the liquid was present on the paved surface

• Volume of the release

• Evaporative flux

• Pavement thickness, porosity, composition and slope

The circumstances of a contaminant release and pavement composition are keyvariables Variables regarding the circumstances of the release include whether theliquid was in contact with the pavement for a sufficient time to allow transportthrough the pavement to occur If the model does not account for evaporation and/

or assumes that the liquid thickness on the pavement is constant, the model willoverestimate the rate of transport If clean-up activities were performed coincidentwith the release (e.g., sawdust, green sand, absorbent socks, crushed clay, etc.) or ifthe spill occurred in a building with forced air, these activities and evaporative losswill compete for the solvent available for transport through the pavement

Noting the physical condition of the paved surface is needed for its incorporationinto the model Such observations would include:

• Is the surface treated with an epoxy coating to prevent corrosion from acid releases (common in plating shops)?

• Was the concrete mixed with an additive to reduce its permeability to chemicals (e.g., addition of Dow Latex No 560 to the concrete)?

• What was the nature of the surface prior to the release (e.g., impregnated with oils and dirt, smooth or pitted, sloped toward a drain, etc.)?

Once this specific information is collected, a conceptual model can be constructed.The saturated hydraulic conductivity or permeability value of the paved surface

is a key variable The terms hydraulic conductivity (K) and permeability (k) are

associated with the ability of a porous media to transmit a fluid While permeabilityand hydraulic conductivity are often used interchangeably, they are not synonymous.Permeability refers to properties associated with the media through which the con-taminant is migrating, such as the distribution of the grain sizes, the sphericity androundness of the grains, and the nature of their packing (Freeze and Cherry, 1979).Fluid properties such as density and viscosity are not included The saturated hydrau-lic conductivity of a material is a measurement of the ability of a fluid to movethrough the material (Lohman et al., 1972) Hydraulic conductivity accounts for fluiddensity and viscosity

The release of a DNAPL compound such as tetrachloroethylene (PCE) (1.63 g/

cm3 at 20∞C) requires that the water-saturated hydraulic conductivity be adjusted to

account for the differences in density and viscosity of PCE relative to water (Pankowand Cherry, 1996) As an example, the saturated hydraulic conductivity of water

through a mature, good-quality concrete is about 10–10 cm/sec (Norton et al., 1931;Whiting et al., 1988) This value is corrected using the following definition ofhydraulic conductivity:

K = krwg/mw (Eq 5.1)where

or in a building with forced air, evaporation is rapid As a consequence, little liquid

is available to initiate movement into the pavement If trichloroethylene accumulates

in a blind concrete sump/neutralization pit or clarifier, the trichloroethylene (TCE)may reside for a sufficient period of time with a significant DNAPL hydraulic head

to allow penetration into concrete

Numerous models are available to calculate the rate of transport of a liquidthrough pavement For saturated flow, a one-dimensional expression for the vertical

TABLE 5.1

Saturated Hydraulic Conductivity of Concrete for Non-Water Liquids

transport of the liquid using Darcy’s Law is available This expression defines thedownward velocity (v) of the liquid as being equal to the downward flux (q) divided

by the porosity of the pavement The downward flux is the saturated hydraulicconductivity multiplied by the vertical gradient Porosity values for paved materialsare measured directly or obtained from the literature This calculation results in avalue in units of length over time that is divided into the pavement thickness toestimate the transport time This approach does not consider the transient nature ofthe spill in which liquid thickness is changed due to evaporative loss

Pavement transport models that use Darcy’s Law assume that the pavement issaturated with liquid prior to the release If the pavement is unsaturated, liquidtransport is dominated by unsaturated flow resulting in contaminant velocities sev-eral times slower than for saturated flow The importance of moisture content onunsaturated hydraulic conductivity relative to saturated flow conditions (100% satu-rated) is shown in Figure 5.2

For unsaturated flow, an equation analogous to Darcy’s equation called the Richard’sequation is used (Richards, 1931) A one-dimensional expression of this equation is

C(∂y/∂t) = ∂/∂z(K∂y/∂z) + ∂K/∂z (Eq 5.3)

where

C = the specific water capacity or change in water content in a unit volume of soil per unit change in the moisture content.

y = suction head (i.e., matric potential).

K = unsaturated hydraulic conductivity.

FIGURE 5.2 Difference between saturated and unsaturated hydraulic conductivity values.

If the pavement is partially or fully water saturated and a hydrophobic fluid such astrichloroethylene is released, the pore water in the pavement will repel the trichloro-ethylene While the extent of repulsion is difficult to quantify, the net result is somedegree of trichloroethylene retardation.

infor-• Vapor density and pressure of the contaminant

• Whether the vapor source is constant or transient above the pavement

• Henry’s Law constant of the contaminant

• Pavement thickness, porosity, and moisture content

• Concentration of the vapor above the pavement

• Concentration of the vapor within and below the pavement prior to the spill

The vapor density of the compound diffusing through the pavement is a key variable.The vapor density is approximately equal to the molecular weight (MW) of thecompound divided by the molecular weight of air (29) The molecular weight of PCE

is about 166 g/mol, so the vapor density is 166/29 = 5.7 Table 5.2 lists vapordensities of common compounds relative to air (Montgomery 1991; Pankow andCherry, 1996)

The value in knowing the vapor density of a volatile compound is that it provides

a qualitative basis to determine if a sufficient period of time has occurred to allowthe vapor to permeate through a paved surface; therefore, the topography of the paved

TABLE 5.2

Vapor Density of Selected Compounds

surface is required to determine if features exist to allow accumulation of the vapor.Vapor degreasers, for example, are often set in a concrete catch basin to capture anyliquid spills While cement catch basins are effective at mitigating liquid spills, theyexacerbate the potential for vapor transport through the concrete because they act as

an accumulator for the solvent vapor The catch basin also minimizes the dilution ofthe vapor with the atmosphere Soil samples collected under degreaser catch basinsare often non-detect for chlorinated solvents while soil vapor concentrations are high

An explanation for this observation is the presence of a vapor cloud in the soil

(Hartman 1999) The significance of vapor clouds is that they migrate through the

subsurface and can potentially contribute to groundwater contamination Using theeffective diffusion coefficient for the compound approximates the transport rate of

a vapor cloud through soil For many vapors, this value is about 0.1 cm2/sec Ageneral approximation is that the soil porosity reduces the gaseous diffusivity by afactor of 10 For many organic vapors, the gaseous diffusion coefficient is approxi-mated as 0.01 cm2/sec A rule-of-thumb calculation for the distance a vapor cloudmoves through soil for many volatile compounds is estimated by Equation 5.4(Hartman, 1997):

Distance = (2)(0.01 cm2/sec ¥ 31,536,000)1/2 = 800 cm = 25 ft (Eq 5.4)

A more rigorous approach to this problem is via a differential equation for theunsteady, diffusive radial flow of vapor from a source (Cohen et al., 1993):

∂2Ca/∂r2 + [1/r(∂Ca/∂r)] = (RaD*)(∂Ca/∂t) (Eq 5.5)where the air-filled porosity (na) is assumed to be constant (see Equation 5.7), Ra isthe soil vapor retardation coefficient, Ca is the computed concentration of the vapor

in air, and r is the source radius The effective diffusion coefficient, D* (for TCE, 3.2

¥ 10–6 m2/sec; for PCE, 0.072 cm2/sec) (Lyman et al., 1982) is equal to:

Ra = 1 + nw/(naKH) + rbKd/(naKH) (Eq 5.7)where nw is the bulk water content, na is the air-filled soil porosity, rb is the soil bulkdensity, Kd is the distribution coefficient, and KH is the dimensionless Henry’s Lawconstant

Numerous vapor transport equations are available to estimate the travel time ofvapor through pavement (Crank, 1985; McCoy and Roltson, 1992) These equationsdescribe specific conditions that best represent the events associated with the vaporrelease Appendix A provides a sample calculation for the vapor transport of PCEthrough a concrete pavement

5.4 CONTAMINANT TRANSPORT IN SOIL

If a liquid has penetrated the pavement, estimated transport times for the contaminantcan be calculated for the second zone (soil) Variables used to perform this calcula-tion include:

• Saturated hydraulic conductivity and porosity of the soil

• Variability of vertical vs lateral hydraulic conductivity

• Presence of lower permeability horizons such as clay

• Fluid properties (density, viscosity, etc.)

• Depth to groundwater

As with contaminant transport through asphalt or concrete, the hydraulic ity of a contaminant (if in pure form) is adjusted using the relationship for intrinsicpermeability For diesel, the conversion is described as:

conductiv-(Kdiesel – Kwater)([mwater/mdiesel][rdiesel/rwater]) (Eq 5.8)Assuming that diesel viscosity is 0.042 cP (water = 0.1 cP) and diesel density is 0.84g/cm3 (water = 1.0 g/cm3), then Equation 5.8 yields an expression that describes thesaturated hydraulic conductivity of diesel through a soil as equal to about 0.20 thevelocity of water; therefore, diesel travels slower than water through this soil Ifdifferences in the viscosity and density of diesel are not considered, the calculatedtransport time using the hydraulic conductivity for water overestimates the rate ofdiesel transport

Numerous equations exist to describe contaminant transport through soil (Ghadiri

et al., 1992; Selim et al., 1998) A common equation for the one-dimensionaltransport of a single component via advection and diffusion in the unsaturated zone

is described by Equation 5.9 (Jury and Roth, 1990; Jury and Sposito, 1985; Jury etal., 1986)

Rl∂Cl/∂t = Du∂2Cl/∂z2 – V∂Cl/∂z – lmRlCl (Eq 5.9)where

Rl = liquid retardation coefficient.

Cl = pore water concentration in the vadose zone.

Du = effective diffusion coefficient.

lm = decay constant.

V = infiltration rate.

The retardation coefficient (Rl) is estimated by:

Rl = rbuKdu + qm + (fm + qm) KH (Eq 5.10)where

r bu = soil bulk density.

Kdu = distribution coefficient for the contaminant of interest.

qm = soil moisture content.

fm = soil porosity.

KH = Henry’s Law constant for the contaminant of interest.

The distribution coefficient (Kdu) of the contaminant of interest can be estimated via:

Kdu = 0.6 foc,u Kow (Eq 5.11)where

foc,u = fraction of organic carbon in the soil.

Kow = octanol-partition coefficient of the contaminant of interest.

The degradation rate constant can be estimated by Equation 5.12:

where T1/2m is the degradation half-life of the contaminant of interest The effective

diffusion coefficient is

Du = tL DLM + KHtG DGM (Eq 5.13)where

t L = soil tortuosity to water diffusion.

DLM = molecular diffusion coefficient in water.

t G = soil tortuosity to air diffusion.

DGM = molecular diffusion coefficient in air.

The tortuosity associated with the diffusion of a compound in water and air isdescribed by Equation 5.14 (Millington and Quirk, 1959):

tL = qm10/3/fm2 and tG = (fm – qm)10/3/fm2 (Eq 5.14)For a non-aqueous phase liquid (NAPL), the NAPL velocity (nu) for the verticalmigration via a constant rate release is approximated by Equation 5.15 (Parker,1989):

nu = (rro kro Kn)/(hrofa S) (Eq 5.15)where

r ro = specific gravity of the NAPL.

kro = relative permeability of the NAPL.

K n = vertical saturated hydraulic conductivity to water.

h ro = the light non-aqueous phase liquid (LNAPL)-water viscosity ratio.

fa = the initial air-filled porosity of the soil.

S = the effective NAPL saturation behind the infiltration front.

The travel time for the LNAPL to move through the unsaturated zone is thereforeequal to the distance from the source to the water table divided by the NAPL velocity(nu).

A question that arises in environmental litigation is when did the contaminationenter the groundwater? This question is answered by using Darcy’s Law An example

is the release of diesel from an underground storage tank If the diesel flows throughmore than one soil type, a transport rate through each soil horizon is required Inputvariables include the saturated hydraulic conductivity of the soil, soil porosity, andthe hydraulic gradient for each horizon Assuming a knowledge of the underlyingsoils (pea gravel and mixed sands) and the saturated hydraulic conductivity of thesesoils between the tank bottom and the groundwater table (ª24.5 ft) and that Darcy’s

Law is valid, Table 5.3 is an example of the tabulated results The total travel timefor the release of diesel into the soil is about 225 days An issue regarding the results

in Table 5.3 is that it offers a unique solution A more defensible approach is the use

of a range of input parameter values (primarily the saturated hydraulic conductivityvalue) (Morrison, 1998)

A novel approach for identifying when a DNAPL has been released into a permeability layer of base of an aquifer has been reported (Parker and Cherry, 1995).Soil cores collected at discrete distances from the DNAPL provide the basis foridentifying the concentration of the dissolved contaminant Diffusion calculations arethen employed to estimate the length of time that diffusion has occurred and thereforethe time since the DNAPL was immobilized Assumptions include the premise thatlow-permeability layers of silt and clay underlying the perched DNAPLs havesufficient porosity to allow, without advection, migration of the dissolved constitu-ents into the soils via molecular diffusion and that the location of the DNAPL isprecisely known

low-5.4.1 C HALLENGES TO C ONTAMINANT

T RANSPORT M ODELS FOR S OIL

Transport mechanisms and pathways exist that are rarely included in contaminanttransport models Artificial examples include dry wells, foundation borings, utilitytrenches, sewer or stormwater backfill, cisterns, and septic lines Natural preferentialpathways include high-permeability soils, mechanical disturbance, and cosolventtransport Table 5.4 lists some of these pathways and common computer modelvariables along with their impact on contaminant transport

5.4.2 C OLLOIDAL T RANSPORT

Colloidal transport is a mechanism by which a hydrophobic compound preferentiallysorbs to a colloid particle in water and is transported to depth Colloids are generallyregarded as materials up to 10 mm (10–6 m) in size Colloids exist as suspendedorganic and inorganic matter in soil or aquifers In sandy aquifers, the predominant

colloids that are mobile range in size from about 0.1 to 10 mm The importance of

colloidal particles on contaminant mobility diminishes as the octanol-water partitioncoefficient (Kow) decreases

The mass of contaminants associated with colloids may be significant In a study

of PCBs and polycyclic aromatic hydrocarbons associated with different size tions of groundwater colloids underlying an abandoned landfill, over two thirds ofthe total amount of contaminants were associated with colloids greater than 1.3 nm(1 nm = 10–9 m) (Villholth, 1999) Another example is the transport of polycyclicaromatic hydrocarbons via colloidal transport, which was examined in two creosote-contaminated aquifers on Zealand island in Denmark The mobile colloids weredominated by clay, iron oxides, iron sulfides, and quartz particles The researchersconcluded that the sorption was associated with the organic content of the colloids.Creosote-associated contaminants were also found to be associated primarily withcolloids that were larger than 100 nm These findings indicate that colloid-facilitatedtransport of polycyclic aromatic hydrocarbons exists and may be significant Thistransport mechanism is rarely included in a soil or groundwater transport model

frac-5.4.3 P REFERENTIAL P ATHWAYS

Preferential pathways provide a means for dissolved and precipitated phase meric species and hydrophobic compounds to be adsorbed to colloids and to berapidly introduced at depth Preferential flow pathways include natural and artificialfeatures such as worm channels, decayed root channels (Plate 5.1*), soil fractures,swelling and shrinking clays, insect burrows, dry wells (Plate 5.2*), open cisterns,septic lines, macropores, and highly permeable soil layers The significance ofpreferential flow is that the actual travel time of a compound to the water table is

poly-TABLE 5.3

Summary of Transport Calculations for Individual Soil Layers

K water Thickness K diesela Vb Travel

a Kdiesel – Kwater ( m water / m diesel )( r diesel / r water ), where m water = 0.01 cP and r water = 1.0 g/cm 3 and

m diesel and r diesel = 0.042 cP and 0.84 g/cm 3 , respectively.

b Porosity = 0.30 and dH/dL = 1.0.

* Plates 5.1 and 5.2 appear at the end of the chapter.

order of minutes or hours rather than days or months (Barcelona and Morrison,1988).

The term “preferential flow” encompasses a range of processes with similarconsequences for contaminant transport The term implies that infiltrating liquiddoes not have sufficient time to equilibrate with the slowly moving water residing

TABLE 5.4

Variables of Contaminant Transport in Soil and their Impact on

Contaminant Velocity

Soil Variables

Impacting Transport Comments and Impacts

Soil porosity Changes in soil porosity can result in multiple velocities with depth

through the soil column Coarse-grained materials tend to have a higher porosity than fine-grained materials The porosity of dense crystalline rocks, tight shales, caliche, and unweathered limestone may range from less than 0.01 to 0.10.

Volume of release Impacts whether saturated or unsaturated flow dominates, the time

required for residual saturation to occur, and the degree of contaminant spreading.

Saturated vs unsaturated flow Unsaturated flow is slower than saturated flow (see Figure 5.2).

Moisture content with depth determines the hydraulic gradient and therefore the rate of transport in unsaturated flow conditions.

velocity and the geometry of the contaminant plume.

thickness, presence of

cracks, presence or absence

of surface coatings

and/or expansion joints.

surface area and thickness

Changes in soil redox and/or pH Increases or decreases the depth of penetration of otherwise

low-mobility contaminants, such as metals.

in the soil (Jarvis, 1998) Preferential flow includes the following transport cesses: finger flow (also viscous flow) (Bisdom et al., 1993; Glass and Nicholl,1996), funnel flow (Diment and Watson, 1985; Hill and Parlange, 1972; Kung,1990a,b; Philip, 1975), and macropore flow (Bouma, 1981; Morrison and Lowry,1990; White, 1985).

pro-Finger flow (also dissolution fingering) is initiated by small- and large-scaleheterogeneities in soil such as a textural interface between a coarse-textured sand thatunderlies a silt (Fishman, 1998; Miller et al., 1998) The term “finger flow” refers tothe splitting of an otherwise uniform flow pattern into fingers These fingers areassociated with soil air compression encountered where a finer soil overlies a coarseand dry sand layer The contact interface between the contaminant and the water inthe capillary fringe results in an instability (see Plate 5.3*) The spacing and fre-quency of these fingers are difficult to predict, although they are at the centimeterscale and are sensitive to the initial water content (Imhoff et al., 1996; Ritsema andDekker, 1995; Wei and Ortoleva, 1990)

Numerical simulations of fingering suggest that transverse dispersion is a cant impact on the formation and anatomy of fingers Aspects of the fingeringphenomenon that introduce uncertainty when modeling contaminants such as NAPLsinclude (Miller et al., 1998):

signifi-• The effect of dispersion

• The impact of heterogeneity on porous media properties and residual NAPL saturation

• The validity of fingering when a NAPL solution is flushed with chemical agents such as surfactants and alcohols

• Incorporation of the impacts of fingering on NAPL phase mass transfer models when the model is discretized at scales larger than the centimeter scale

Funnel flow occurs in soils with lenses and admixtures of particle sizes For asaturated soil, the most coarse sand fraction is the preferred flow region; for unsat-urated flow, finer textured materials are more conductive Examination of texturaldescriptions on boring logs and contaminant concentration depth profiles can provideinsight to determine if contaminant transport via funnel flow is a viable transportmechanism

A macropore is a continuous soil pore that is significantly larger than the granular or inter-aggregate soil pores (micropores) In general, a macropore is oneorder of magnitude greater in dimension than the indigenous soil micropores While

inter-a minter-acropore minter-ay constitute only 0.001 to 0.05% of the totinter-al soil volume, it minter-ayconduct a majority of an infiltrating liquid

Plate 5.4* illustrates the impact of liquid transport via macropores in a mature soil

in the United Kingdom Hydrated gypsum was ponded on the ground surface anddrained into the underlying soil via macropores The gypsum then dehydrated,leaving the macropore channels clearly visible

* Plates 5.3 and 5.4 appear at the end of the chapter.

5.4.4 C OSOLVENT T RANSPORT

Hydrophobic compounds are generally considered to be immobile in the soil profile,due primarily to their low water solubility and their tendency to be adsorbed by clay,organic matter, and mineral surfaces (Odermatt et al., 1993) Soil contaminanttransport models tend to predict low velocities for these compounds Cosolvation ofthese compounds with a fluid can introduce these contaminants at depth, but thisphenomenon is rarely included in contaminant transport models Contaminants such

as polychlorinated biphenyls (PCBs) or DDT can be re-mobilized by the preferentialdissolution of the PCBs into a solvent released into the same soil column (Morrisonand Newell, 1999) A variation of this scenario is the preferential dissolution of animmobile chemical into a solvent prior to its release (e.g., PCBs dissolved in adielectric fluid)

A similar transport mechanism occurs when a contaminant sorbed by a soil iswashed with a liquid that re-mobilizes the compound An example is the presence ofcopper bound in soil under a leaking neutralization pit Low pH wastewaters leakingthrough an expansion joint and contacting the precipitated copper will remobilize andtransport the copper with the low pH wastewaters to depth until the acidic wastewaterand copper solution is buffered and the copper re-precipitates at a lower depth

5.5 CONTAMINANT TRANSPORT

IN GROUNDWATER

In environmental litigation, groundwater models are usually used in a predictive,interpretative, or generic application Predictive models forecast the future of someaction and require calibration Interpretative models are used to study aquifer andcontaminant dynamics Generic models are used to analyze flow in hypotheticalsystems, such as for regulatory purposes

The transport of a contaminant in groundwater is controlled by the aquiferparameters (advective model) and by physical and chemical processes that aresimulated in the contaminant transport portion of the model The advective portion

of a contaminant transport model requires measured groundwater elevations Theprimary hydraulic forces in an advective model are the main driving forces, naturaltransient forces, and manmade transient forces An example of an advective model

is MODFLOW Since its release by the U.S Geological Survey in the early 1980s,MODFLOW has become the international standard code for three-dimensional,finite-difference groundwater flow modeling (McDonald and Harbaugh, 1988).Mass transport models such as MT3D (Modular Transport Three-Dimensional)are coupled to an advective model such as MODFLOW to simulate the three-dimensional advection, dispersion, and chemical transformations of contaminants(Zeng, 1993, 1994) MT3D is available commercially and in the public domain (theU.S Environmental Protection Agency provided partial support for the development

of MT3D)

The selection of a model is made in large part by identifying the primaryprocesses controlling contaminant transport that the user intends to simulate Theseprocesses include aquifer physical parameters, the initial contaminant concentra-tions, physical processes, chemical attenuation, and biological attenuation Figures5.3 and 5.4 summarize the impact of these hydraulic, physical, chemical, and biologi-cal processes on contaminant transport in groundwater (Szecsody, 1992) If themodel intends to simulate any or all of these processes, the value assigned and theaccuracy of the number should be fully evaluated.

The developmental progression of a model used for contaminant transport cludes the following steps:

in-• Identification of the goal of the modeling

• Creation of a conceptual model

• Selection of the governing equations and computer code

• Adjustment of the conceptual model for modeling

• Model calibration with field measurements

• Sensitivity analysis to establish the effect of input parameters variations on model output

• Model verification via calibrated of parameter values and stresses

• Performance of computer simulations or runs to predict future events

FIGURE 5.3 Effects of aquifer physical parameters on contaminant transport.

• Post-auditing to test the reliability of the simulations by comparing simulated results with new acquired field measurements

• Model calibrations to reflect changes in the post-audit step

5.5.1 T YPES OF G ROUNDWATER M ODELS

Three types of groundwater models are physical or scale models, analog, andmathematical models Physical or scale models include physical experiments usingboxes filled with a representative media into which fluids are introduced Analogmodels use materials such as electrical circuits to represent a groundwater system.While popular prior to the advent of personal computing, they are seldom used.Mathematical models are divided into three types: analytical, numerical, and analyticelement and contain the following components:

• Definition of the site boundary conditions

• Equation(s) describing the contaminant mass balance within the modeled boundary

FIGURE 5.4 Effects of physical, chemical, and biological processes on contaminant transport.

• Equations that relate contaminant flux to relevant variables

• Equation(s) that describe the contaminant and hydrogeological conditions at an initial time

• Equation(s) that describe the interaction of the contaminant within the prescribed boundary conditions

Analytic element models are adaptations of established analytical techniqueswhereby several analytic functions are solved simultaneously Analytical models useclosed-form equations or solutions to the partial differential equations governinggroundwater flow (Bear 1979; Van Genuchten and Alves, 1982) An analyticalmodel is easily solved This simplification is a limitation, as aquifer homogeneity,isotropy, and an infinite horizontal extent are assumed For complex hydrogeologicalsettings, they are usually inadequate

A numerical flow model solves partial differential equations governing flow atdiscrete points or nodes within a groundwater system Numerical models requireelaborate computational methods to solve flow equations at a discrete set of pointswithin an aquifer(s) Examples include:

character-• Integrated finite-difference models

Numerical models can be converted to a format amenable to visualization Becausethe physical properties at each point in the model can be varied, numerical methodscan solve flow problems in complex hydrogeological systems Features such asbiodegradation, radioactive decay, sources, and sinks can be included in themodel

Analytic element models combine aspects of analytical and numerical models Aset of simultaneous equations with an equal number of unknowns are solved usingnumerical techniques, while analytic functions are superimposed onto a particularsite feature, such as a river or pumping groundwater well An advantage of ananalytic element model is that a small portion of the site can be intensively modeled

or multiple aquifer systems can be examined Most analytic element models areproprietary

Groundwater models can provide greater understanding of a flow system andcontaminant transport Groundwater models are commonly encountered in insurancecoverage cases, in litigation to demonstrate that a potentially responsible party hascontributed to the contamination of a Superfund site, and to illustrate long-termimpacts of an unremediated contaminant plume over time The following is a briefoutline of the use of groundwater modeling and its application in environmentallitigation For a further understanding, numerous texts on groundwater modeling areavailable (Freeze and Cherry, 1979; Zeng and Bennett, 1995)

The foundation of groundwater modeling is the advection-dispersion equation.Governing assumptions are that the porous medium is homogeneous and isotropic,the medium is saturated with a fluid, and Darcy’s Law is valid If these assumptionsare violated, the applicability or precision of the model in predicting contaminantflow is compromised to some degree.

The selection of the contaminant transport model that is appropriate for theparticular site is important and should be carefully considered when evaluating acontaminant groundwater model If the conceptual model does not represent therelevant flow and contaminant transport phenomena, the subsequent modeling effort

is wasted This is not to say that misuses may not occur during any phase of themodeling process Common misuses and mistakes associated with modeling include(Bear et al., 1992; Mercer, 1991):

1 Improper conceptualization of a groundwater model relative to the site — for example, selection of a three-dimensional model when a two-dimensional model is sufficient can lead to complications in the modeling effort Incorrect assumptions concerning the significant contaminant processes, such as contaminant transport, which are then incorporated into the model can magnify the inaccuracy of the model Disregarding the importance of retardation of a chemical or discounting the impact of biological transformations are other examples.

2 Selection of an inappropriate computer code for solving the problem — it is not uncommon for a consultant to select a computer code that is too versatile or powerful for the site and the availability of input parameters.

3 Improper model applications usually results in the selection of improper values for modeling Examples include the misrepresentation of aquitards in a multi-level system or identifying and modeling contaminant transport in a series of aquifers which are actually one hydraulically connected aquifer.

4 Misinterpretation of modeling results occurs if mass balance is not achieved or if calibration of the modeling results with field data is not performed The end result

of the model is the ability to simulate contaminant transport based on actual field measurements.

5 Uncertainty is posed by the inability to accurately model various sinks (irrigation wells, spring discharge, etc.) and sources (rivers, lakes, temporal irrigation, or watering, etc.) over time that impact model precision.

Inappropriate model selection is one of the most common shortcomings It isuseful to direct the expert witness to prepare a table describing the model and thencompare it to the site Differences in the capabilities of two computer models aresummarized in Table 5.5

The SWIFT model permits a great deal more model complexity and flexibilitythan does the QUICKFLOW model This is because the two models address thegroundwater flow systems in different ways The analytical element modelQUICKFLOW uses hand-derived analytical solutions which are then incorporatedinto the program These analytical solutions are derived for simplified flow situa-tions; otherwise, the mathematics become too difficult to solve The numerical modelSWIFT permits greater complexity because the flow and transport equations aresolved by computer code

5.5.2 S ELECTION OF B OUNDARY C ONDITIONS ,

G RIDS , AND M ASS L OADING R ATES

Boundary conditions are required whenever a computer model is created For aprogram such as MODFLOW, general head boundaries are used to define the lateralboundary conditions that define the flux of water recharge or discharge along theseboundaries The boundary conditions are a function of the hydraulic conductivity,groundwater flow gradient, and the absolute difference in water level elevationsbetween the block elements located on the lateral boundaries with locations locatedoutside of the model grid

Common specified boundary conditions include no-flow, specified flux, andfixed head boundaries While model boundary conditions are fixed and cannot bechanged during a single simulation, they can be adjusted between simulations It isconceptually undesirable to alter the boundary flux conditions to assist in calibration

of each stress period vs accounting for these differences by adjustments in dynamicfeatures such as pumping wells or recharge of surface water bodies located within thegrid The impact of a model boundary can be examined if all model input files andsoftware are available to reproduce the modeling result using different boundaryconditions

Grid selection is important For numerical models, finite difference and finiteelement grids are used, while block-centered and mesh-centered grids are used forfinite element grids Finite element grids are generally more versatile than finitedifference grids For a finite difference model, examine the grid density to ascertainwhether the data support finer mesh nodes or whether higher grid densities areselected in areas of interest but which contain insufficient data to warrant a highergrid density

TABLE 5.5

Comparison of SWIFT III and QUICKFLOW Computer Models

of contaminants

elements)

time