1 Welcome to BRE542! Vadose Zone Transport

2 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  Introduction to Course  Related Texts  Definition/importance of Vadose Zone  Related areas of study  History of Investigation of Vadose Processes  Relationship to Saturated Media

3 Logistical Issues BRE 542, Vadose Zone Transport, Fall 2003 Department of Bioengineering John S. Selker Telephone: Office hours: MWF 10am-11am, or by appointment Lab help hours: Monday 4:00-4:45 Websites: Vadose kits: Lectures: 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. BRE 542, Vadose Zone Transport, Fall 2003 Department of Bioengineering John S. Selker Telephone: Office hours: MWF 10am-11am, or by appointment Lab help hours: Monday 4:00-4:45 Websites: Vadose kits: Lectures: 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.

4 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. 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.

5 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.   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.

6 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 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

7 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: non- spreading oil. 6.Special Processes (2 lect.) Macropore Flow Fingered Flow Biological considerations 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: non- spreading oil. 6.Special Processes (2 lect.) Macropore Flow Fingered Flow Biological considerations

8 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. 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.

9 The Numerical Component of BRE Learning the interface A.Clicking through the menus and printing results B. 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. 1. Learning the interface A.Clicking through the menus and printing results B. 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.

10 ¡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. 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.

11 Drivers, start your engines!

12 Disciplinary Context   Related Texts   Definition/importance of Vadose Zone   Related areas of study   Related Texts   Definition/importance of Vadose Zone   Related areas of study

13 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 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

14 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.  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.

15 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  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

16 First quantitative application to unsaturated flow  1870’s Bousinesq extended Darcy’s law with two approximations (Dupiut- 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)  Bousinesq equation is strongly nonlinear: much tougher to solve!  1870’s Bousinesq extended Darcy’s law with two approximations (Dupiut- 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)  Bousinesq equation is strongly nonlinear: much tougher to solve! Bousinesq

17 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. 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.

18 Slichter – some of his figures

19 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  1907 Buckingham (of Buckingham-pi fame) Darcy for steady flow with:  Conductivity a function of moisture content  Potential includes capillary pressures

20 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.  Exception: Green and Ampt, Key problem of infiltration.  Exception: Green and Ampt, Key problem of infiltration.  Modeled as a capillary tubes which filled in parallel, from dry to saturation.  Still most widely used infiltration model.  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, Key problem of infiltration.  Exception: Green and Ampt, Key problem of infiltration.  Modeled as a capillary tubes which filled in parallel, from dry to saturation.  Still most widely used infiltration model.

21 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).  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).

22 Moisture contents depends on history of wetting  Haines (1930) wetting proceeds as “jumps”  Haines (1930) wetting proceeds as “jumps”  Still largely ignored, but essential to unsaturated flow processes.  Haines (1930) wetting proceeds as “jumps”  Haines (1930) wetting proceeds as “jumps”  Still largely ignored, but essential to unsaturated flow processes.

23 Time 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 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 Turns out that Richards equation is a bear to solve! Depends on three non- linear 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

24 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  They let you see the implications of the physical parameters  computers allow solution of individual problems: tough to generalize 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  They let you see the implications of the physical parameters  computers allow solution of individual problems: tough to generalize

25 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 Lots of great stuff in the 50’s and early 60’s  1956: Miller and Miller: relationship of grain size to fluid properties

26 More 50’s and 60’s  1957: Philip start to deal with infiltration  1962: Poulovassilis: independent domain model of hysteresis (finally Haines stuff can be included)  1957: Philip start to deal with infiltration  1962: Poulovassilis: independent domain model of hysteresis (finally Haines stuff can be included)

’s: limitations of the assumptions Biggar & Nielson (1970)  field scale heterogeneity Hill & Parlange (1972)  fingered flow Others:  macropores  Kung (1988): Funnel Flow Biggar & Nielson (1970)  field scale heterogeneity Hill & Parlange (1972)  fingered flow Others:  macropores  Kung (1988): Funnel Flow

28 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! 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!

29 Differences

30 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 contamination  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 contamination

31 Example Suppose that 2,000 liters of some nasty liquid spilled on a 10 m 2 area above an aquifer that was at a depth of 10 m. How much makes it to the aquifer?