Hydrogeology Test #2
Factors influencing infiltration
Flow Influences Soil Surface Conductivity Subsurface Conditions Hydrophobicity
Six Flow Influences
Flow head, viscocity, flow chemistry, soil chemistry, soil and water tension, air entrapment.
Homogeneous
Geologic unit has the same properties at all locations.
How do soil properties affect infiltration?
Grain size or soil texture.
What is the most influential factor of the shape of the Water Retention Curve?
Pore-size.
Water Retention Curve
The relationship between negative pressure head and volumetric water content for a sample. As the water content of a soil decreases, pressure head becomes more negative and capillary pressure increases.
Is Pressure Head in the Saturated Zone negative or positive?
The pressure head is *positive* in the saturated zone. ψ > 0.
Characteristics of a permeable boundary:
flow is head independent (specified flux boundary) flow is head dependent (head dependent flux boundary) specific head boundary (constant or fixed head)
A no-flow boundary in a flownet is a...
flow line.
Flow of water in the unsaturated zone is controlled by
hydraulic head, composed of the elevation head and the pressure head.
What is the Pressure Head at the water table?
ψ = 0
LaPlace Equation assumptions
Isotropic, homogeneous, fluid moving in one direction.
Transient
Variable changes over time; described by a form of the diffusion equation.
Calculate the inflow/outflow per year from two rivers 1000m apart and 20m thick. The hydraulic conductivity is 20m/day. The stages of the rivers are 500 and 495m above sea level. Assume elevation is 450m at base. The aquifer is unconfined. (a) What is the hydraulic head of the aquifer at the midpoint? (b) What is the inflow/outflow of the rivers?
(a) h = ROOT ho^2 + (hL^2 + ho^2)(x/L) (b) q = K (ho^2 - hL^2/2L) (c) Q = AREA*q
Practice Question! Calculate the inflow/outflow per year from two rivers 1000m apart and 20m thick. The hydraulic conductivity is 20m/day. The stages of the rivers are 500 and 495m above sea level. The aquifer is confined. (a) What is the Darcy flow velocity? (b) If the reaches of the rivers are 600m long, what is the volume of ground water inflow/outflow per year? (c) If a well were installed in between the two rivers, what would by the hydraulic head before pumping?
(a) q = K (ho-hL/L) (b) Q = AREA*q (c) h = ho + (hL-ho)(x/L)
Basic Concepts of Flow in the Unasturated Zone
- Unsaturated zone pore spaces contain water and soil gasses - Volumetric water content is the ratio of the volume of water to that of the medium
Case Study: Joshua Tree
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For transmissivity = 2500m2/day, storativity = 1.9 x 10-3, and a pumping rate Q = 500m3/day, calculate drawdowns in a confined aquifer for r=10,50,100m at t=150min.
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Numerical models are available for the simulation of water flow in the unsaturated zone. An infiltration experiment was carried out in the farming field to study the potential pesticide contamination of groundwater. The infiltration rate is 10in/hour in a control area. The thicknes of the unsaturated zone is 20 ft. Assuming that a 1-D model will be used for this project, (a) what boundary and initial conditions would you like to specify? (b) What hydraulic parameters do you need in the model? (c) What do saturation and pressure head profiles look like in the unsaturated zone?
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PRACTICE If the aperture of a fracture is 0.001m, (a) what are the permeability and hydraulic conductivity in the fracture? (b) For a network of equally spaced fractures with fracture porosity of 1.0x10-4, calculate the permeability, (c) and hydraulic conductivity of the medium.
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PRACTICE The hydraulic head at a point in a confined aquifer bounded by horizontal formations is 80m and the horizontal hydraulic gradient is 0.03. (a) What is the hydraulic head at 300m downgradient from the point? (b) If the hydraulic conductivity is 20m/day, what is the Darcy velocity?
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Values of drawdown and time in a pumping test are listed in table 9.7. Determine the transmissivity and storativity of a confined aquifer. Both the pumped and observation wells are fully penetrating. A pumping rate of 10,000m3/day is used in the test. The observation well is located 150m away from the pumped well.
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Laws of Thermodynamics (LaPlace)
1. Energy can be neither lost nor gained, it can only change forms. 2. Energy goes from more useful form (mechanical) to less useful form (heat). It is impossible to transfer heat from a colder to a warmer system without changes in the environment.
What are 3 types of differential equations with unknown variables?
1. groundwater flow equation with h (hydraulic head) 2. mass transport equation with C (concentration) 3. energy transport equation with T (temperature)
What is a flownet?
A flownet is a 2-D graphical solution to the LaPlace Equation. Solved after establishing boundary and initial conditions.
What is a cone of depression?
A response to pumping. Usually the assumption of a radial cone is made, however cones are typically distorted due to higher head/recharge near the well.
What is the relationship between hydraulic conductivity and pressure head?
As a soil dries out, an increasingly large negative pressure head means that the mostly air-filled system has a large resistance to flow (or k).
What is the pressure head/moisture content relationship in the Unsaturated Zone?
Both volumetric water content and the unsaturated hydraulic conductivity depend on pressure head, or the capillary pressure.
In a test of a confined aquifer, the pumping rate was 500m3/day. Drawdown/time data were collected at an observation well 300m away. Determine the transmissivity and storativity of the aquifer using the Cooper-Jacob straight-line method.
COOPER-JACOB STRAIGHT LINE METHOD T = 2.3Q/4πΔs S = 2.25Tto/r2 u = r2S/4Tt
Third Type Boundary Conditions
Cauchy (Third Type) relates hydraulic head to a specified water flux at a boundary
Soil Physical Properties
Color Ignition Extrastructural crack Fragipan ID Cementation test Bulk density Pocket pentometer Soil moisture Water table
Measuring Pressure Head: Determining when Irrigation is Required
Deep tensiometer is installed at base of root zone. When tension reading decreases, irrigation should stop. Shallow tensiometer is installed a center of root zone. Indicated when soil is dry, irrigation should start.
First Type Boundary Conditions
Dirichlet (First Type) A value of hydraulic head specified at a boundary.
Causes of Hydrophobicity
Extensive dry periods, Fire changing soils, and organic coating of soil particles.
How does steady flow in a confined aquifer behave in accordance with Darcy's Law?
Head decreases linearly in the direction of flow.
Soil field descriptors:
Horizons, USDA texture, Color, Porosity, Moisture condition, Water table, Saturated hydraulic conductivity, Clay minerals, Other minerals, Odor.
Examples of questions that need answers:
How long will this well produce sufficient water? Will septic tank seepage affect groundwater quality? If the well field produces for 30 years will it affect the nearby streams and springs?
Six Major Hydraulic properties of aquifers
Hydraulic Conductivity K Transmissivity T Specific Yield Sy Specific Retention Sr Specific Storage Ss Storage Coefficient/Storativity S
How are evapotranspiration models useful?
Infiltration/exfiltration models can be used to estimate the water infiltration during the wetting season and evapotranspiration during the drying season.
PRACTICE The aperture of a fracture is 0.001m. The fracture itself is 0.1m wide. If the hydraulic gradient in the fracture is 0.0001, what is the volumetric flow rate in the fracture?
K = Pwgb^2/12u THEN Q=-K(bw)Δh/ΔL
Flow through porous medium is controlled by:
Law of Mass Conservation, and Darcy's Law.
Ward Valley
Low level radioactive waste disposal site (not reactor waste, but medcal and research radioactive waste). Depth to water > 220m
How do we answer hydrogeologic questions?
Model it. Describe reality with a simple mathematical model with limitations and assumptions clearly stated.
Consider a network of parallel fractures with a fracture spacing of 10m and individual fracture apertures of 0.001m. The fracture network is oriented parallel to the direction of flow, and the geological medium is homogeneous. (a) Calculate the permeability, (b) Hydraulic conductivity, (c) Fracture porosity.
N=1/s=0.1(1/m) (a) kf = b^3/12N (b) Kf = Pwgkf/u (c) of = b/s
Second Type Boundary Conditions
Neumann (Second Type) A water flux is specified at a boundary. i.e. a groundwater divide as a no-flow boundary.
Soil Chemical Properties
Organic Matter CEC pH Redox potential Clay minerals Carbonate minerals Soluble salts Iron and manganese
As the water content of a soil decreases:
Pressure head becomes more negative and Capillary Pressure increases.
What is a REV?
Representative Elementary Volume, a volume exhibiting the average properties of a porous medium around a point P.
What is the Water Retention Curve?
Represents the relationship between negative pressure head and volumetric water content for a sample.
Isotropic
Same conditions in all directions (vertical, horizontal).
What is the Golden Rule in practical analysis of ground-water flow?
Start simple and introduce complexities (such as heterogeneity and anisotropy) only where more simple explanations prove wholly inadequate. - Paul Younger
Table 9.1 lists drawdowns measured in 5 observation wells at steady state in a confined aquifer. The well is being pumped at a constant rate of 100m3/day. (a) What is the Transmissivity of the aquifer?
THIEM'S METHOD Plot drawdown versus the logarithm of distance. Draw a best fit line. Two points are chosen to calculate; T = 2.3 Q/2π(s1-s2) log (r2/r1)
The transmissivity and storativity of a confined aquifer are 1000m2/d and 0.00001. An observation well is lovated 500m away from a pumping well. For a pumping period of 220min, calculate (a) the drawdown at the observation well if the discharge rate is 1000m3/day; (b) the pumping rate required to provide a drawdown of 1m at that well after 220min.
THIES SOLUTION (a) u = r2S/4Tt, FIND U ON TABLE, s = (Q/4πT)W(u) (b) Q = 4πTs/w(u)
In a test of a confined aquifer, the pumping rate was 500m3/day. Drawdown/time data were collected at an observation well 300m away. Determine the hydraulic conductivity and storativity of the aquifer.
THIES TYPE-CURVE METHOD T = (Q/4πs)W(u) S = 4Ttu/r2
Fracture Porosity
The Ratio of fracture volume over the matrix volume.
What is wrong with models?
The core of science is not modeling - it is intellectual honesty. We must have our certainties about the world constrained by good evidence and argument.
What is Residual Volumetric Water Content?
The lower limit in water content ( θr ).
Residual Volumetric Water Content
The lower limit in water content.
What is a Groundwater Flow Equation?
The mathematical relationship to describe flow through an aquifer.
What is a "Wetting Front"?
The narrow zone that marks the beginning of elevated water content due to the infiltration event.
Fracture Frequency
The number of fractures per unit length.
What is Hysterisis?
The phenomena exhibited by a system in which the reaction of the system to change is dependent upon its past reaction to change.
Is pressure head in the unsaturated zone negative or positive?
The pressure head is *negative* in the unsaturated zone. ψ < 0
What is Cubic Law?
The volumetric flow in a fracture is a function of the aperture cubed, or cubic law.
Why will water not flow into a borehole dug into a partially saturated formation?
There is a NEGATIVE pressure head
Steady-State
Time is not a factor; describes by a form of the LaPlace equation.
Why measure the water content?
To understand changes in the soil suction with depth. To understand the changes in hydraulic conductivity with the degree of water saturation.
Boundary conditions directly impact:
Transmissivity of an aquifer
What are Dupuit's Assumptions?
Velocity of flow is proportional to tangent of i rather than sine (Darcy); the flow is horizontal and uniform everywhere in a vertical section.
How does volumetric water content in the unsaturated zone relate to porosity?
Volumetric water content is usually less than porosity. 0 < θ < n
Pores in the unsaturated zone contain:
Water and soil gases.
In a water table aquifer bounded on the ends by rivers, the hydraulic conductivity is 50m/day. The hydraulic heads at x=0 and x=1000m are 100m and 90m respectively. (a) Calculate the Darcy velocity at x=0,100,500, and 1000m. (b) Calculate the flow rate in a unit width of an aquifer.
YIELD IN CONFINED
As soil moisture content drops, pressure head...
becomes more NEGATIVE. This is because remaining water tends to be found in smaller voids.
In a water retention curve, changes in storage are dependent on...
material size. Water content changes more for finer grained materials than coarser materials.
What is a Tensiometer?
measures pressure head in unsaturated zones. It consists of ceramic cup, water column or reservoir connected to manometer (or pressure gage or pressure transducer).
Characteristics of impermeable boundaries:
no flow boundary (zero flux) flow swings and runs parallel
What is specific moisture capacity?
the change in moisture content divided by change in pressure head.
In an unconfined aquifer, shape of the water table determines:
the flow distribution.