1. Physical and Hydraulic Properties of Variably Saturated Media Goal: Retention and movement of fluids through porous media (not easy)! Will introduce the basic physical properties Get a “feel” for mathematical foundations and the physical processes Goal: Retention and movement of fluids through porous media (not easy)! Will introduce the basic physical properties Get a “feel” for mathematical foundations and the physical processes

2. How do you quantitatively describe a chunk of wet soil? Want to describing:  how it might dry  how rain falling on it would soak in (how much would run off)  what would happen to it if you spilled some gasoline on it? A set of parameters selected to provide as concisely as possible the greatest insight into the response of the media to a range of physical processes. Want to describing:  how it might dry  how rain falling on it would soak in (how much would run off)  what would happen to it if you spilled some gasoline on it? A set of parameters selected to provide as concisely as possible the greatest insight into the response of the media to a range of physical processes.

3. 3 Definitions Three constituent phases:  solid  liquid  gaseous  gaseous Each phase is an admixture of compounds. Three constituent phases:  solid  liquid  gaseous  gaseous Each phase is an admixture of compounds.

4. 4 Gaseous phase  Dominated by constituents of atmosphere; N 2, O 2, CO 2, H 2 O vapor etc.  Respiration: elevated CO 2 and CH 4  Industrially contaminated sites: organic vapors.  Quantify gaseous phase by partial pressures (temperature dependent)  Equilibrium with soluble liquid phases via Henry’s law  Dominated by constituents of atmosphere; N 2, O 2, CO 2, H 2 O vapor etc.  Respiration: elevated CO 2 and CH 4  Industrially contaminated sites: organic vapors.  Quantify gaseous phase by partial pressures (temperature dependent)  Equilibrium with soluble liquid phases via Henry’s law

5. 5 Gaseous phase (cont.)   Transport of gases dominated by diffusion (  2 cm/day). (Diffusion in the liquid phase is  0.02 cm/day.)   Atmospheric pumping (Buckingham, 1904)   Driven by liquid phase movement   Driven by wind and diurnal density (Los Alamos)   Induced mechanically to clean a site   Transport of gases dominated by diffusion (  2 cm/day). (Diffusion in the liquid phase is  0.02 cm/day.)   Atmospheric pumping (Buckingham, 1904)   Driven by liquid phase movement   Driven by wind and diurnal density (Los Alamos)   Induced mechanically to clean a site

6. 6 Gas phase important in remediation   Soil Vapor Extraction (SVE)   Gas is pumped through vadose zone stripping volatile fraction (Henry’s law).   Prediction of flow essential to design remediation   Air Sparging   Air is pumped into aquifers to strip contaminants which will be lifted to the vadose zone, and extracted in gas phase.   Gas movement very complicated due to effects of heterogeneity and fundamental instability of buoyant gas movement in porous media.   Soil Vapor Extraction (SVE)   Gas is pumped through vadose zone stripping volatile fraction (Henry’s law).   Prediction of flow essential to design remediation   Air Sparging   Air is pumped into aquifers to strip contaminants which will be lifted to the vadose zone, and extracted in gas phase.   Gas movement very complicated due to effects of heterogeneity and fundamental instability of buoyant gas movement in porous media.

7. 7 Air Sparging Two flow-rates in a 2-dimensional Chamber packed with sand

8. 8 Liquid phase   Assume incompressible in vadose (low pressures).   Interaction other phases:   contact angle (solid and gas)   capillary pressure (gas)   volatility (gas)   We have two primary interests   bulk water movement (agriculture and drinking water)   movement of solutes (contaminants and nutrients)   Assume incompressible in vadose (low pressures).   Interaction other phases:   contact angle (solid and gas)   capillary pressure (gas)   volatility (gas)   We have two primary interests   bulk water movement (agriculture and drinking water)   movement of solutes (contaminants and nutrients)

9. 9 Solid phase Surface area is critical to vadose processes  Permeability to liquid/gas go with the square of pore-size  Reactive components significant: Clay, organics, chelates. What about Goo?  Microbes, plants and worms are prevalent and important to chemical behavior of the unsaturated zone (not be dealt with much in this class). Surface area is critical to vadose processes  Permeability to liquid/gas go with the square of pore-size  Reactive components significant: Clay, organics, chelates. What about Goo?  Microbes, plants and worms are prevalent and important to chemical behavior of the unsaturated zone (not be dealt with much in this class).

10. 10 Dry bulk Density Dry mass per unit volume  V = the particular volume used  s = solid phase, without fluid  units: gr/cm 3 ; kg/m 3; ( heaven forbid, lb./ft 3 ) Dry mass per unit volume  V = the particular volume used  s = solid phase, without fluid  units: gr/cm 3 ; kg/m 3; ( heaven forbid, lb./ft 3 )

11. 11 Solid phase density Upper limit on  vb is density of pure mineral Note:  s independent of v (  vb not so cooperative). Often reported as specific gravity s, which is the ratio of solid density to that of water s =  s /  w [2.3] Upper limit on  vb is density of pure mineral Note:  s independent of v (  vb not so cooperative). Often reported as specific gravity s, which is the ratio of solid density to that of water s =  s /  w [2.3]

12. 12 Solid Phase Density (cont.) Typical values of specific gravity   2.65 for quartz (commonly assumed for “typical minerals”   2.54 – 2.76 for feldspar (most common mineral in earth’s crust)   2.72 for calcite   5.0 for pyrite.   Not amenable to a universal value   Measured with a pycnometer Typical values of specific gravity   2.65 for quartz (commonly assumed for “typical minerals”   2.54 – 2.76 for feldspar (most common mineral in earth’s crust)   2.72 for calcite   5.0 for pyrite.   Not amenable to a universal value   Measured with a pycnometer

13. 13 Porosity (AKA void fraction) Porosity is denoted as n v and defined

14. 14 What about this annoying v? Let’s just run a quick “experiment” with tool which measures  vs for any prescribed v Let’s just run a quick “experiment” with tool which measures  vs for any prescribed v  Start with the instrument set with v smaller than any individual grain in the soil.  Now, holding the instrument steady, enlarge v continuously, all the while recording the values of  vb. (Figure 2.3 shows two realizations of such an experiment.) Let’s just run a quick “experiment” with tool which measures  vs for any prescribed v Let’s just run a quick “experiment” with tool which measures  vs for any prescribed v  Start with the instrument set with v smaller than any individual grain in the soil.  Now, holding the instrument steady, enlarge v continuously, all the while recording the values of  vb. (Figure 2.3 shows two realizations of such an experiment.)

16. 16 Bulk density with control volume size  As the control volume enlarges, there is no scale over which density is entirely constant.  Value of all physical parameters in the vadose zone are a function of both position and sample volume.  As the control volume enlarges, there is no scale over which density is entirely constant.  Value of all physical parameters in the vadose zone are a function of both position and sample volume.

17. 17 We have 2 choices 1) throw up our arms; natural systems are hopelessly complex 2) make some reasonable simplifying assumptions For the sake of progress...  Assume there is some volume, much larger than the grains of the porous media, yet smaller than the distance between dissimilar regions, which provides a representative sample of our porous media. This volume is the system’s Representative Elementary Volume (REV). 1) throw up our arms; natural systems are hopelessly complex 2) make some reasonable simplifying assumptions For the sake of progress...  Assume there is some volume, much larger than the grains of the porous media, yet smaller than the distance between dissimilar regions, which provides a representative sample of our porous media. This volume is the system’s Representative Elementary Volume (REV).

18. Each extensive property defined at point by taking v =1 REV about that point. We can provide a pseudo-rigorous definition of the REV by looking at two adjacent regions, each of the same volume. For any given parameter describing these parcels, the REV is the volume large enough so that that parameter differs between the two volumes by less than some specified amount (with high probability).

19. 19 Let’s finish these definitions Total Bulk Density (solid and liquid phase) Void Ratio (ratio of pore volume to solid volume) May relate the void ratio to porosity Total Bulk Density (solid and liquid phase) Void Ratio (ratio of pore volume to solid volume) May relate the void ratio to porosity

20. 20 Water Content Either a mass, volumetric basis, or degree of saturation (volumetric more common) a. Mass basis (A.K.A. Gravimetric) b. Volume basis c. Degree of saturation. Either a mass, volumetric basis, or degree of saturation (volumetric more common) a. Mass basis (A.K.A. Gravimetric) b. Volume basis c. Degree of saturation.

21. 21 More on Water Content Units: mass per volume (e.g., gr/cm 3 ) volume per volume (e.g., cm 3 water/cm 3 media) inches of water per foot of depth!  The units indicate whether on a volume or mass basis. A few necessary fussy points regarding  s and  o  Saturation rarely achieved in the vadose zone due to  Dead end pores  Water surrounded pores  Alternate terms for soil with standing water  “Satuated”  “Satiated”  “field saturated” Units: mass per volume (e.g., gr/cm 3 ) volume per volume (e.g., cm 3 water/cm 3 media) inches of water per foot of depth!  The units indicate whether on a volume or mass basis. A few necessary fussy points regarding  s and  o  Saturation rarely achieved in the vadose zone due to  Dead end pores  Water surrounded pores  Alternate terms for soil with standing water  “Satuated”  “Satiated”  “field saturated”

22. 22 About that “Residual water content”  Unless at >200 o C for hours, water held in hydrogen bonds  Residual water content a function of the drying process  Two important drying processes for  o  gravity drainage = “Field Capacity”  fc, about -1/3 bar  -1/3 bar should be by soil texture  -1/30 bar for sands  -1 bar for clayey soils  plant uptake = permanent wilting point,”  pwp taken as -15 bar  Measurement relies on vapor transport of water between pores, and so is necessarily slow in achieving equilibrium  Define the conditions of and there will be a real and measurable residual moisture content  If unsure of the context where the parameter will be used, provide a range of possible values  Unless at >200 o C for hours, water held in hydrogen bonds  Residual water content a function of the drying process  Two important drying processes for  o  gravity drainage = “Field Capacity”  fc, about -1/3 bar  -1/3 bar should be by soil texture  -1/30 bar for sands  -1 bar for clayey soils  plant uptake = permanent wilting point,”  pwp taken as -15 bar  Measurement relies on vapor transport of water between pores, and so is necessarily slow in achieving equilibrium  Define the conditions of and there will be a real and measurable residual moisture content  If unsure of the context where the parameter will be used, provide a range of possible values

23. 23 More on residual water content  Measurement relies on vapor transport of water between pores, and so is necessarily slow in achieving equilibrium.  Define specific definition and there will be a real and measurable residual moisture content, otherwise not very useful  If unsure of the context where the parameter will be used, provide a range of possible values

24. 24 Typical values of physical properties