Title: Welcome to BAE 558 Fluid Mechanics of Porous Media
1Welcome toBAE 558Fluid Mechanics ofPorous Media
Williams, 2008
http//www.its.uidaho.edu/BAE558 Modified after
Selker, 2000 http//bioe.orst.edu
/vzp/
2Outline - Introduction
- Introduction to Course
- Required and Related Texts
- Definitions Immiscible Fluids, Phase Boundaries,
Vadose Zone - Related Areas of Study
- History of Investigation of Vadose Processes
- Relationship to Saturated Media
3Course Outline
- 1. An Introduction to the Vadose Zone (3-4 lect.)
- History of investigation
- Modern concerns
- Relationship to saturated media
- Primer on soils
-
- 2. Physical Hydraulic Properties of Unsaturated
Media (8 lect.) - Basic definitions
- Hydrostatics (Surface tensionCharacteristic
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
4Course Outline Continued
- 4. Vadose Biogeochemical Processes (6 lect.)
- Kinetics, Thermodynamics, Equilibria
- Biological Processes
- Acid Consumptive Processes (Fluid-Rock
interactions, ARD, etc.) - 5. Solute Transport in the Vadose Zone (6 lect.)
- Processes - Advection, adsorption, diffusion,
degradation. - Advective Diffusive Equation (Linearity,
superposition, solutions). - 6. Heterogeneity in the Vadose Zone (2 lect.)
5Introductions
- Name
- Title/Student Status
- Work/Research Focus at this time
- Barbara will introduce the Engineering Outreach
People later in the semester - Note We will have the emails of all class
participants (who agree) listed on the web so
that students can communicate among themselves -
6Context re Disciplines
- Required and Related Texts
- Definition/importance of Vadose Zone
- Related areas of study
7 8What is a porous medium?
- Definition of porous medium
- Definition of porosity
- Fun question.
9Definition of Porous Medium
- A solid (often called matrix) permeated by
interconnected network of pores (voids) filled
with a fluid (liquid or gas). - Usually both the solid matrix and the pore space
are assume to be continuous.
10Definition of Porosity
11Question
Which of these has the largest porosity?
12HISTORY OF INVESTIGATION
- Its worthwhile to understand the historical
context of the study of unsaturated flow - Variably saturated / vadose zone fluid mechanics
is quite a young field still in conceptual
development - Provides a preview of the topics covered in the
course
13Review 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
14First quantitative application to unsaturated flow
- 1870s Bousinnesq extended Darcys law with two
approximations (Dupuit-Forcheimer) 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) - Bousinnesq equation is strongly nonlinear much
tougher to solve!
15Rigorous foundation for Darcys Law
- First encyclopedic source of practical solutions
based on pore-scale analysis - 1899 Schlichter Theory of Flow Through Porous
Media - Exact solutions for multiple pumped wells
- Basis of aquifer testing.
16Extension of Darcys 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
17Extension of Darcys Law (cont.)
- Rule Folks who write equations are remembered
for eternity, while the poor work-a-days who
solve them are quickly forgotten. - 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.
18Time passes... We need a few tools!!
- Early 1920s, W. Gardners 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. (note Richards just died in late 90s).
19Moisture contents depends on history of wetting
- Haines (1930) wetting proceeds as jumps
- Still largely ignored, but essential to
unsaturated flow processes.
20Time passes ... time passes
- Turns out that Richards equation is a bear to
solve! Depends on three non-linear variables q,
y, K - First big break for Rs 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
21Analytical 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
22Then things took off!
- Lots of great stuff in the 50s and early 60s
- 1956 Miller and Miller relationship of grain
size to fluid properties
23More 50s and 60s
- 1957 Philip start to deal with infiltration
- 1962 Poulovassilis independent domain model of
hysteresis (finally Haines stuff can be included)
241970s to now limitations of the assumptions
- Biggar Nielson (1970)
- field scale heterogeneity
- Hill Parlange (1972)
- fingered flow
- Others
- macropores
- Kung (1988) Funnel Flow
- Stochastics small-scale to large-scale
25Relationship 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!
26Differences
27Contemporary Concerns with the Vadose Zone
- Water conservation (how to use minimum water to
irrigate crops) - Nutrient storage and transport
- Contaminant degradation and movement
- Water budget for climatic modeling
- Bulk petroleum and organic contaminant transport
(vapor and liquid) Industrial contamination