Welcome to
BRE542!
Vadose Zone
Transport
1
Today
Introduction to Course
Related Texts
Definition/importance of Vadose
Zone
Related areas of study
History of Investigation of Vadose
Processes
Relationship to Saturated Media
2
Logistical Issues
BRE 542, Vadose Zone Transport, Fall 2003
Department of Bioengineering
John S. Selker
Telephone: 541-737-6304 email: selkerj@engr.orst.edu
Office hours: MWF 10am-11am, or by appointment
Lab help hours: Monday 4:00-4:45
Websites:
Vadose kits: http://bre.orst.edu/faculty/selker/vadose_teaching.asp
Lectures: http://bre.orst.edu/vzp
How the BRE 542 will be run
•Three exciting lectures/wk
•Numerical simulation project (you don’t need to write code)
Homework largely from experiments
•Experimental and data-based homework.
3
More Logistics ... Grading
• One homework per week given on Monday, due the
following Monday by 5 PM. (1/2 grade).
• One numerical modeling project (presentation plus 7
page paper; 1/6 of grade). Papers are due Dec 5. See
special handout on this component.
• 10 min quizzes will be carried out after each of the 4
chapters, announced 1 week in advance (1/6 of grade).
• Final exam (1/6th of grade). A closed book exam which
covers the most significant concepts presented in the
course.
4
Idiosyncrasies in the professor (the fine print)
Interpretation: 25% of the score of each problem is given
for interpretation of the result (qualitative)
Calculations: Even if you have the right number written
down for the answer, you are only 75% of the way done
unless you have thought about what the results mean.
Late homework is not accepted unless prior arrangements
have been made, as homework is often handed back on
the next class meeting.
The Rules:
Group work: Wonderful, but must list the group of helpers,
and may not simply copy the work of others.
Writing: must be your own work, unless properly cited. If in
doubt, ask me. Plagiarism of written work will result in
failing the course.
5
Course Outline
1. An Introduction to the Vadose Zone (4 lect.)
• History of investigation
• Modern concerns
• Relationship to saturated media
• Primer on soils
2. Physical & Hydraulic Properties Unsaturated Media (8 lect)
• Basic definitions
• Hydrostatics (Surface tension;Characteristic curves; Hysteresis)
• Hydrodynamics in porous media (Darcy's law; Richards equation)
3. Flow of Water in the Vadose Zone (10 lect.)
• The classic solutions (Green & Ampt; Evaporation from Water Table).
• Solution for capillary barriers
• Miller and Miller scaling
• Characterization of soil hydraulic properties
6
Course Outline Continued
4. Solute Transport in the Vadose Zone (5 lect.)
•Processes - Advection, adsorption, diffusion, degradation.
• Advective Diffusive Equation (Linearity, superposition,
solutions).
5. Three-phase flow (2 lect.)
• Surface tension, spreading pressure, layered menisci
• Constitutive relations: Pressure-Saturation-Permeability
• Funicular and residual saturation
• Special problems with continuum assumptions: nonspreading oil.
6. Special Processes (2 lect.)
• Macropore Flow
• Fingered Flow
• Biological considerations
7
The Numerical Component of BRE542
Software Description and Access
 The software is called HYDRUS-2D
 Developed by the staff of the US salinity lab in riverside CA.
 Windows based modules with excellent graphical interface.
 The users manual is very technical
 4:00-4:45 PM help sessions Gilmore annex on Mondays.
 The computer in the upstairs of the annex is set up with new HP
workstations – they rip!
 You may use the computers on a first come first served basis at other
unscheduled times.
 No machines should be left running over night in order to maintain
access for other students.
8
The Numerical Component of BRE542
1. Learning the interface
A.
B.
Clicking through the menus and printing results
Setting up a problem from scratch.
2. Running a simple problem
Draining a profile from saturation to hydrostatic.
3. Project
Rules for numerical homework
 Do all the key strokes for your problem with your own hands, but may talk
to others and watch others do their problems as much as you like.
 Start a problem using the files indicated in the homework (either ones
prepared by me, or new files).
 Only you can enter data in your problem. If you want help from a friend,
they can show you by going through operations on their files.
9
¡El Proyecto!
Project is 1/6 of the grade for the course.
Phase 1. Defining the problem.
a. Due October 3 (15%). 1 or 2 page statement of
problem importance, boundary conditions, and
expected outcome.
b. Due October 13 (15%). Layout of problem in
HYDRUS-2D. Define in detail the full problem to be
solved
Phase 2. Initial simulation results Oct 31 (20%).
Write up (1-3 pg text plus figures).
Phase 3. Presentations. November 24 and 25 (25%).
7:00-9:30 evening donut and coffee evening sessions of
12 minute presentations. Must come to both sessions.
Phase 4. Final submission Dec 5. <10pgs +
figures.
10
Drivers, start
your engines!
11
Disciplinary Context
Related Texts
Definition/importance of
Vadose Zone
Related areas of study
12
HISTORY OF INVESTIGATION
It’s worthwhile to understand the
historical context of the study of
unsaturated flow:
A young field with ongoing conceptual
development
Provides a preview of the topics covered
in the course
13
Evidence of ancient operational
understanding of hydrology
Ancient qanats of Aden
Marib dam in Yemen built in 500 b.c.
and lasting to the beginning of alternate
routes through the orient around 500
a.d. 600 meter face supporting
agriculture for 100,000 people.
600 a.d. Sri Lanka builds a network of
irrigation works that survive to this day.
Yet I know of no evidence that the underlying
quantitative relationships between soil type, pressure
and flow were understood.
14
Review: First quantitative
understanding of saturated flow
Darcy 1856 study of the
aquifers under Dijon;
Introduced the concept of
potential flow
Water moves in direct proportion to:
the gradient of potential energy
the permeability of the media
15
First quantitative application to
unsaturated flow
1870’s Bousinesq extended Darcy’s
law with two approximations (DupiutForcheimer) to deal with drainage and
filling of media.
“Free water surface” problems.
Useful solutions for dikes land
drainage, etc. (all as a footnote
in his book)
Bousinesq
Bousinesq equation is strongly
nonlinear: much tougher to solve!
16
Rigorous foundation for
Darcy’s Law
First encyclopedic source of practical
solutions based on pore-scale
analysis
1899 Slichter “Theory of Flow Through
Porous Media”
Exact solutions for multiple pumped wells
Basis of aquifer testing.
17
Slichter – some of his figures
18
Extension of Darcy’s Law to
Unsaturated Conditions
1907 Buckingham (of Buckingham-pi
fame) Darcy for steady flow with:
Conductivity a function of moisture content
Potential includes capillary pressures
19
Extension of Darcy’s Law
(cont.)
Rule: Folks who write
equations are remembered
for eternity, while the poor
work-a-days who solve them
are quickly forgotten.
d
L
Exception: Green and Ampt,
1911. Key problem of
infiltration.
Modeled as a capillary tubes
which filled in parallel, from dry to
saturation.
Still most widely used infiltration
model.
20
Time passes...time passes
We need a few tools!!
Early 1920’s, W. Gardner’s lab develop the
tensiometer: direct measurement of the capillary
pressure
L.A. Richards extended idea to tension plate:
measure moisture content as a function of
capillary pressure
And then...
1931, Richards derived equation for unsaturated
flow. (p.s. Richards just died in the last 5 years).
21
Moisture contents depends on
history of wetting
Haines (1930) wetting
proceeds as “jumps”
Still largely ignored, but
essential to unsaturated
flow processes.
22
Time passes ... time passes
Turns out that Richards equation is a
bear to solve! Depends on three nonlinear variables: q, y, K
First big break for R’s Eq.
1952, Klute rewrote Richards equation
in terms of moisture content alone
diffusion equation (AKA: Fokker-Plank eq.)
Klute gave solution to 1-D capillary
infiltration
23
Analytical vs. Numerical
Since 1952, more analytical solutions
have been presented, BUT non-linearity
limited to special conditions.
What is the use of Analytical results?
They let you see the implications of the
physical parameters
computers allow solution of individual
problems: tough to generalize
24
Then things took off!
Lots of great stuff in the 50’s and early
60’s
1956: Miller and Miller: relationship of
grain size to fluid properties


60
70
12/20
60
20/30
12/20
50
50
20/30
Scaled Potential

Matric Potential (cm H2O)
80
30/40
40
40/50
30
20
40
30/40
30
40/50
20
10
10
0
0
0
0.2
0.4
0.6
Degree of Saturation
0.8
1
0
0 .2
0 .4
0 .6
0 .8
1
Degree of Saturation
25
More 50’s and 60’s
1957: Philip start to deal with infiltration
(F
ill
in
g hf
Pr
es
su
r
e)
f
(Fraction of Moisture Content)
1962: Poulovassilis: independent
domain model of hysteresis (finally
Haines stuff can be included)
hf+h f
hf
o
0
0
45
he he+h e
he
(Emptying Pressure)
26
1970’s: limitations of the
assumptions
Biggar & Nielson (1970)
 field scale heterogeneity
Hill & Parlange (1972)
fingered flow
Others:
macropores
Kung (1988): Funnel Flow
27
Relationship to saturated media
While the similarity has been very useful,
it is a source of many errors
Main distinctions in three areas.
Capillarity (lateral, upward flow)
Heterogeneity into the temporal domain
Biochemical activity
Diffusion is two orders of magnitude faster
Ample oxygen
Take-home message: be very careful!
28
Similarities:
• Both have governing equations for flow that are
linear in the local potential gradient
• They share similar constitutive media (with
particles ranging from clay to gravel)
Differences
Issue
Conductivity at a
point
Density Effects
Spatial variability
Biological and
chemical activity
Transport
mechanisms
Vadose Zone
A nonlinear function of
moisture content.
Negligible influence for
temperature and solute
based changes.
Saturated Zone
Constant.
Temperature and solute
based density differences can
dominate both static and
dynamic disposition.
Lognormal distribution
Lognormal distribution fixed
and a function of moisture in time.
content and hence time.
Often high in carbon and Typically anoxic with sparse
oxygen, leading to rapid
carbon: comparatively slow
microbial metabolism.
microbial activity.
Advection 0-10 cm/day Advection 0-100 cm/day
Dispersivity 0.5-20 cm
Dispersivity 0.5-20 cm
Diffusion
0.1-.3 cm2/s Diffusion 0.00002 cm2/s
29
Contemporary Concerns with
the Vadose Zone
Water conservation (how to use
minimum water to irrigate crops)
Nutrient storage and transport
Pesticide degradation and movement
Salinity control
Water budget for climatic modeling
Bulk petroleum and organic contaminant
transport (vapor and liquid): Industrial
30
contamination
Example
Suppose that 2,000 liters of some
nasty liquid spilled on a 10 m2 area
above an aquifer that was at a depth
of 10 m. How much makes it to the
aquifer?
31