Introduction to Ground Water Contamination

CIVE 7332

Lecture 2

Darcy allows an estimate of: • the velocity or flow rate moving within the aquifer• the average time of travel from the head of the

aquifer to a point located downstream

Darcy’s Law

• Darcy’s law provides an accurate description of the flow of ground water in almost all hydrogeologic environments.

Who Was Darcy? Henry Philibert Gaspard Darcy was born June 10, 1803 in

Dijon, France.

Admitted to the French School of Bridges and Roads in Paris, part of the Corps of Bridges and Roads. After graduation, he was eventually assigned by the Corps to a position in Dijon.

In 1828, Darcy designed a 12.7 km system of aqueducts to supply the city of Dijon with surface water. The system included 28,000 m of pressurized surface lines and required no pumps or filters.

Made important contributions to flow and friction loss in pipes, created an improved pitot tube design, and was the first to postulate the existance of a boundary layer in fluid flow.

In 1856, carried out experiments while researching sand filters that lead to Darcy’s Law.

Died unexpectedly January 3, 1858 from pneumonia during a trip to Paris.

Darcy’s Legacy

Place Darcy, Dijon, France.

Flow in Aquifers

Darcy’s Experiment (1856):

Flow rate determined by Head loss dh = h1 - h2

Darcy’s Law

• Henri Darcy established empirically that the flux of water through a permeable formation is proportional to the distance between top and bottom of the soil column.

• The constant of proportionality is called the hydraulic conductivity (K).

• V = Q/A, V – ∆h, and V 1/∆L

Darcy’s Law

V = – K (∆h/∆L) and since

Q = VA (A = total area)

Q = – KA (dh/dL)

Hydraulic Conductivity

• K represents a measure of the ability for

flow through porous media:

• Gravels - 0.1 to 1 cm/sec

• Sands - 10-2 to 10-3 cm/sec

• Silts - 10-4 to 10-5 cm/sec

• Clays - 10-7 to 10-9 cm/sec

Conditions• Darcy’s Law holds for:

1. Saturated flow and unsaturated flow2. Steady-state and transient flow3. Flow in aquifers and aquitards4. Flow in homogeneous and heterogeneous systems5. Flow in isotropic or anisotropic media6. Flow in rocks and granular media

Darcy Velocity

• V is the specific discharge (Darcy velocity).

• (–) indicates that V occurs in the direction of

the decreasing head.

• Specific discharge has units of velocity.

• The specific discharge is a macroscopic

concept, and is easily measured. It should be

noted that Darcy’s velocity is different ….

Darcy Velocity

• ...from the microscopic velocities associated with the actual paths if individual particles of water as they wind their way through the grains of sand.

• The microscopic velocities are real, but are probably impossible to measure.

Darcy & Seepage Velocity• Darcy velocity is a fictitious velocity

since it assumes that flow occurs across the entire cross-section of the soil sample. Flow actually takes place only through interconnected pore channels.

A = total areaAv voids

Darcy & Seepage Velocity

• From the Continuity Eqn:

• Q = A vD = AV Vs

– Where:Q = flow rate

A = total cross-sectional area of        material

AV = area

of voids Vs

= seepage velocityVD = Darcy velocity

Darcy & Seepage Velocity• Therefore: VS = VD ( A/AV)

• Multiplying both sides by the length of the medium (L)

VS = VD ( AL / AVL ) = VD ( VT / VV )

• Where:VT = total volume

VV = void volume

• By Definition, Vv / VT = n, the soil porosity

• Thus VS = VD / n

Equations of Groundwater Flow

• Description of ground water flow is based on:Darcy’s LawContinuity Equation - describes conservation of fluid mass during flow through a porous

medium; results in a partial differential equation of flow.

• Laplace’s Eqn - most important in math

Derivation of 3-D GW Flow Equation from Darcy’s Law

x

Vx y

Vy z

Vz 0

Mass In - Mass Out = Change in Storage

Vx x

Vx

Vx

z

y

Fluid density

SteadyState

mass/area/time

Derivation of 3-D GW Flow Equation from Darcy’s Law

x

Kx

h

x

y

Ky

h

y

z

Kz

h

z

0

Replace Vx, Vy, and Vz with Darcy using Kx, Ky, and Kz

Divide out constant , and assume Kx= Ky= Kz = K

2h

x 2 2h

y 2 2h

z2 0

2h 0 called Laplace Eqn.

incompressiblefluid, isotropic,homogeneousmedium

Permeameters

Constant Head Falling Head

Constant head Permeameter• Apply Darcy’s Law to find K:

V/t = Q = KA(h/L)or:

K = (VL) / (Ath)• Where:

V = volume flowing in time tA = cross-sectional area of the sampleL = length of sampleh = constant head

• t = time of flow

Pressure and Elevation Heads - Laboratory

Freeze and Cherry, 1979.

= pressure headz = elevation headh = + z = total head

Freeze and Cherry, 1979.

= pressure headz = elevation headh = total head

Pressure and Elevation Heads - Field

Horizontal and Vertical Head Gradients

Freeze and Cherry, 1979.

Two Confined Aquifers with Different Heads

Charbeneau, 2000.

Groundwater will tend to flow from the top aquifer to the bottom aquifer.

(Assuming that horizontal distance between piezometers is small)

Hydraulic Head is a Potential Field

Hubbert (1940): potential – a physical quantity, capable of measurement at every point in a flow system, whose properties are such that flow always occurs from regions in which the quantity has a higher values of those in which it has lower, regardless of the direction in space.

Potential fields and associated physical laws:

Head (Darcy’s Law)

Temperature (Fourier’s Law) Conduction of heat in solids

Concentration (Fick’s Law) Diffusion of chemicals dx

dCDJ

dx

dTkF

dx

dhKq

m

FluidFlux

HeatFlux

MassFlux

Horizontal and Vertical Head Gradients

Freeze and Cherry, 1979.

Potentiometric Surface – Dakota Sandstone

Domenico and Schwartz, 1992.

Drinking Water Standards

Maximum Contaminant Level (MCL)• Microorganisms• Disinfectants• Disinfection by-products• Inorganic chemicals• Organic chemicals• Radionuclides

Primary Standards

List of National Secondary Drinking Water Regulations

Contaminant Secondary StandardAluminum 0.05 to 0.2 mg/LChloride 250 mg/LColor 15 (color units)Copper 1.0 mg/LCorrosivity noncorrosiveFluoride 2.0 mg/LFoaming Agents

0.5 mg/L

Iron 0.3 mg/LManganese 0.05 mg/LOdor 3 threshold odor numberpH 6.5-8.5Silver 0.10 mg/LSulfate 250 mg/L

Total Dissolved Solids

500 mg/L

Zinc 5 mg/L

BTEX-Related Compounds

Benzene

Toluene

Xylene, ortho

Xylene, meta

Xylene, para

Ethyl benzene

Name Structure

CH3

CH3

CH3

CH3

CH3

CH3

CH3

CH3CH2

MolecularWeight

Solubility in Water

Soil-Water Partition Coefficient

78.11

92.1

106.17

106.17

106.17

106.17

1780 mg/L

500 mg/L

170 mg/L

150 mg/L

97

242

363

622

173 mg/L

200 mg/L

182

331

Chlorinated Solvents

C C

H H

Cl

HVinyl chloride (chloroethene)

Gas used in the manufacture of polyvinyl chloride. End product of microbial degradation of chlorinated ethenes.

C C

H H

H

Cl

H

H

Liquid used to manufacture tetraethyl lead. Degradation product of chlorinated ethanes.

Chloroethane

C

H

Cl

Cl

ClTrichloromethane (chloroform)

Liquid used in manufacture of anesthetics, pharmaceuticals, fluorocarbon refrigerants and plasics. Used as solvent and insecticide. Formed from methane when chlorinating drinking water.

C C

H H

H

Cl

H

Cl

Liquid used to manufacture vinyl chloride. Degradation product of trichloroethane.

1,2-Dichloroethane

Name Structure Uses and Other Sources

Chlorinated Solvents (cont’d)

Cl

Cl

Chemical intermediate. Solvent. Fumigant and insecticide. Used for industrial odor control. Found in sewage form odor control chemicals used in toilets.

o-Dichlorobenzene (1,2-dichlorobenzene)

C C

H

ClCl

Cl

Solvent used in dry cleaning and metal degreasing. Organic synthesis. Degradation product of tetrachloroethene.

Trichloroethene (Trichloroethylene)

C C

ClCl

Cl Cl

Solvent used in dry cleaning and metal degreasing. Used to remove soot from industrial boilers. Used in manufacture of paint removers and printing inks.

Tetrachloroethene (perchloroethene) (perchloroethylene)

C C

H H

H C

H

H

Br Br Cl

Soil fumigant to kill nematodes. Intermediate in organic synthesis.

1,2-Dibromo-3-chloropropane (DBCP)

Name Structure Uses and Other Sources

The Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), commonly known as Superfund, was enacted by Congress on December 11, 1980. This law created a tax on the chemical and petroleum industries and provided broad Federal authority to respond directly to releases or threatened releases of hazardous substances that may endanger public health or the environment. Over 5 years, $1.6 billion was collected, and the tax went to a trust fund for cleaning up abandoned or uncontrolled hazardous waste sites. Superfund National Priorities List (NPL) sites are the most serious uncontrolled or abandoned hazardous waste sites that have been identified for possible long-term remedial action under Superfund. The list is based primarily on the score a site receives from the Hazard Ranking System. The U.S. Environmental Protection Agency (EPA) is required to update the NPL at least once a year. A site must be on the NPL to receive money from Superfund for long-term remedial action. Long-term remedial action is defined as action that stops or substantially reduces a release or threat of a release of hazardous substances, where such a threat is serious but not an immediate threat to public health.

The EPA administers the Superfund program in cooperation with individual States and tribal governments.

Source: EPA website

Superfund - CERCLA

Triangle – proposed (2)Circle – approved (43)Square – deleted (9)

National Priorities List Sites in Texas (Superfund)

The NPL is the list of national priorities among the known releases or threatened releases of hazardous substances, pollutants, or contaminants throughout the United States and its territories