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 = h 1 - h 2

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 to 1 cm/sec Sands to cm/sec Silts to cm/sec Clays to cm/sec

Conditions Darcy’s Law holds for: 1. Saturated flow and unsaturated flow 2. Steady-state and transient flow 3. Flow in aquifers and aquitards 4. Flow in homogeneous and heterogeneous systems 5. Flow in isotropic or anisotropic media 6. 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 area A v voids

Darcy & Seepage Velocity From the Continuity Eqn: Q = A v D = A V V s –Where: Q = flow rate A = total cross-sectional area of material A V = area of voids V s = seepage velocity V D = Darcy velocity

Darcy & Seepage Velocity Therefore: V S = V D ( A/A V ) Multiplying both sides by the length of the medium (L) V S = V D ( AL / A V L ) = V D ( V T / V V ) Where: V T = total volume V V = void volume By Definition, V v / V T = n, the soil porosity Thus V S = V D / n

Equations of Groundwater Flow Description of ground water flow is based on: Darcy’s Law Continuity 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 Mass In - Mass Out = Change in Storage z y Fluid density Steady State mass/area/time

Derivation of 3-D GW Flow Equation from Darcy’s Law Replace V x, V y, and V z with Darcy using K x, K y, and K z Divide out constant , and assume K x = K y = K z = K incompressible fluid, isotropic, homogeneous medium

Permeameters Constant HeadFalling 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 t A = cross-sectional area of the sample L = length of sample h = constant head t = time of flow

Pressure and Elevation Heads - Laboratory Freeze and Cherry,  = pressure head z = elevation head h =  + z = total head

Freeze and Cherry,  = pressure head z = elevation head h = total head Pressure and Elevation Heads - Field

Horizontal and Vertical Head Gradients Freeze and Cherry, 1979.

Two Confined Aquifers with Different Heads Charbeneau, 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 Fluid Flux Heat Flux Mass Flux

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 Standard Aluminum0.05 to 0.2 mg/L Chloride250 mg/L Color15 (color units) Copper1.0 mg/L Corrosivitynoncorrosive Fluoride2.0 mg/L Foaming Agents 0.5 mg/L Iron0.3 mg/L Manganese0.05 mg/L Odor3 threshold odor number pH Silver0.10 mg/L Sulfate250 mg/L Total Dissolved Solids 500 mg/L Zinc5 mg/L

BTEX-Related Compounds

Chlorinated Solvents

Chlorinated Solvents (cont’d)

The Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA), commonly known as Superfund, was enacted by Congress on December 11, 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.SuperfundNational Priorities ListHazard Ranking SystemU.S. Environmental Protection Agency 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