Physical and Hydraulic Physical and Hydraulic Properties of Variably Properties of Variably

Saturated MediaSaturated MediaGoal: Goal:

Retention and movement of fluids Retention and movement of fluids through porous media (not easy)!through porous media (not easy)!

Will introduce the basic physical properties Will introduce the basic physical properties

Get a “feel” for mathematical foundations and the Get a “feel” for mathematical foundations and the physical processesphysical processes

How do you quantitatively describe a How do you quantitatively describe a chunk of wet soil? chunk of wet soil?

Want to describing: Want to describing: how it might dryhow it might dryhow rain falling on it would soak in (how much would run how rain falling on it would soak in (how much would run

off)off)what would happen to it if you spilled some gasoline on what would happen to it if you spilled some gasoline on

it? it?

A set of parameters selected to provide as A set of parameters selected to provide as concisely as possible the greatest insight into the concisely as possible the greatest insight into the response of the media to a range of physical response of the media to a range of physical processes.processes.

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DefinitionsDefinitionsThree constituent Three constituent phases: phases: solidsolidliquidliquidgaseousgaseous

Each phase is an Each phase is an admixture of admixture of compounds. compounds.

Gas

Liquid Solid

VOLUME MASS

V

Vg

Vl

Vs

Mg

l

sM

M M

Gas

Liquid

Solid

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Gaseous phaseGaseous phaseDominated by constituents of atmosphere; NDominated by constituents of atmosphere; N22, O, O22, ,

COCO22, H, H22O vapor etc.O vapor etc.

Respiration: elevated CORespiration: elevated CO22 and CH and CH44

Industrially contaminated sites: organic vapors. Industrially contaminated sites: organic vapors.

Quantify gaseous phase by partial pressures Quantify gaseous phase by partial pressures (temperature dependent)(temperature dependent)

Equilibrium with soluble liquid phases via Henry’s lawEquilibrium with soluble liquid phases via Henry’s law

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Gaseous phase (cont.)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

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Gas phase important in remediationGas phase important in remediationSoil Vapor Extraction (SVE)

Gas is pumped through vadose zone stripping volatile fraction (Henry’s law).

Prediction of flow essential to design remediation

Air SpargingAir 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.

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Air SpargingAir SpargingTwo flow-rates in a 2-dimensional Two flow-rates in a 2-dimensional Chamber packed with sandChamber packed with sand

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Liquid phaseLiquid phase Assume incompressible in vadose (low

pressures).

Interaction other phases: contact angle (solid and gas)capillary pressure (gas)volatility (gas)

We have two primary interestsbulk water movement (agriculture and drinking

water)movement of solutes (contaminants and nutrients)

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Solid phaseSolid phaseSurface area is critical to vadose processesSurface area is critical to vadose processesPermeability to liquid/gas go with the square of Permeability to liquid/gas go with the square of

pore-sizepore-sizeReactive components significant: Clay, organics, Reactive components significant: Clay, organics,

chelates. chelates. What about Goo? What about Goo? Microbes, plants and worms are prevalent and Microbes, plants and worms are prevalent and

important to chemical behavior of the unsaturated important to chemical behavior of the unsaturated zone (not be dealt with much in this class).zone (not be dealt with much in this class).

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Dry bulk DensityDry bulk Density

Dry mass per unit volumeDry mass per unit volume

V = the particular volume usedV = the particular volume useds = solid phase, without fluids = solid phase, without fluidunits: gr/cmunits: gr/cm33; kg/m; kg/m3; (3; (heaven forbid, heaven forbid,

lb./ftlb./ft3 )3 )

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Solid phase densitySolid phase densityUpper limit on Upper limit on vbvb is density of pure mineral is density of pure mineral

Note: Note: ss independent of v ( independent of v (vbvb not so not so cooperative). cooperative). Often reported as specific gravity s, which is the ratio of solid Often reported as specific gravity s, which is the ratio of solid density to that of waterdensity to that of water

s = s = ss//ww [2.3][2.3]

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Solid Phase Density (cont.)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

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Porosity (AKA void fractionPorosity (AKA void fraction ))

Porosity is denoted as nPorosity is denoted as nvv and defined and defined

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What about this annoying v? What about this annoying v? Let’s just run a quick “experiment” with tool Let’s just run a quick “experiment” with tool which measures which measures vsvs for any prescribed v for any prescribed v

Start with the instrument set with v smaller Start with the instrument set with v smaller than any individual grain in the soil. than any individual grain in the soil.

Now, holding the instrument steady, enlarge v Now, holding the instrument steady, enlarge v continuously, all the while recording the values continuously, all the while recording the values of of vbvb..

(Figure 2.3 shows two realizations of such an (Figure 2.3 shows two realizations of such an experiment.)experiment.)

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Bulk density with control volume sizeBulk density with control volume size

As the control volume enlarges, there is no As the control volume enlarges, there is no scale over which density is entirely constant.scale over which density is entirely constant.

Value of all physical parameters in the Value of all physical parameters in the vadose zone are a function of both position vadose zone are a function of both position and sample volume. and sample volume.

Bulk

Dens

ity

Control Volume Size00

s

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We have 2 choicesWe have 2 choices

1) throw up our arms; natural systems are hopelessly 1) throw up our arms; natural systems are hopelessly complexcomplex

2) make some reasonable simplifying assumptions2) make some reasonable simplifying assumptions

For the sake of progress...For the sake of progress...Assume there is some volume, much larger than the grains Assume there is some volume, much larger than the grains

of the porous media, yet smaller than the distance between of the porous media, yet smaller than the distance between dissimilar regions, which provides a representative sample dissimilar regions, which provides a representative sample of our porous media. of our porous media. This volume is the system’s This volume is the system’s Representative Elementary Representative Elementary VolumeVolume (REV). (REV).

Each extensive property defined at point by Each extensive property defined at point by taking v =1 REV about that point.taking v =1 REV about that point.

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

REV 1 1 = 2 +/- for choosen level Boxes 2 with probability P = 1-

for arbitrarily small

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Let’s finish these definitionsLet’s finish these definitionsTotal Bulk Density (solid and liquid phase)Total Bulk Density (solid and liquid phase)

Void Ratio (ratio of pore volume to solid volume)Void Ratio (ratio of pore volume to solid volume)

May relate the void ratio to porosityMay relate the void ratio to porosity

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Water ContentWater ContentEither a mass, volumetric basis, or degree of Either a mass, volumetric basis, or degree of saturation (volumetric more common)saturation (volumetric more common)a. Mass basis (A.K.A. Gravimetric)a. Mass basis (A.K.A. Gravimetric)

b. Volume basisb. Volume basis

c. Degree of saturation.c. Degree of saturation.

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More on Water ContentMore on Water ContentUnits: Units: mass per volume (e.g., gr/cmmass per volume (e.g., gr/cm33))

volume per volume (e.g., cmvolume per volume (e.g., cm33 water/cm water/cm33 media) media)inches of water per foot of depth!inches of water per foot of depth!

The units indicate whether on a volume or mass basis.The units indicate whether on a volume or mass basis.

A few necessary fussy points regarding A few necessary fussy points regarding ss and and oo

Saturation rarely achieved in the vadose zone due toSaturation rarely achieved in the vadose zone due toDead end poresDead end poresWater surrounded poresWater surrounded pores

Alternate terms for soil with standing waterAlternate terms for soil with standing water““Satuated”Satuated”““Satiated”Satiated”““field saturated”field saturated”

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About that “Residual water content”About that “Residual water content”Unless at >200 Unless at >200 ooC for hours, water held in hydrogen bondsC for hours, water held in hydrogen bondsResidual water content a function of the drying processResidual water content a function of the drying processTwo important drying processes for Two important drying processes for oo

gravity drainage = “Field Capacity” gravity drainage = “Field Capacity” fcfc, about -1/3 bar, about -1/3 bar -1/3 bar should be by soil texture-1/3 bar should be by soil texture -1/30 bar for sands -1/30 bar for sands -1 bar for clayey soils -1 bar for clayey soils

plant uptake = permanent wilting point,” plant uptake = permanent wilting point,” pwppwp taken as -15 bar taken as -15 bar Measurement relies on vapor transport of water between pores, and so is necessarily Measurement relies on vapor transport of water between pores, and so is necessarily

slow in achieving equilibrium slow in achieving equilibrium Define the conditions of and there will be a real and measurable residual moisture Define the conditions of and there will be a real and measurable residual moisture

contentcontentIf unsure of the context where the parameter will be used, provide a range of possible If unsure of the context where the parameter will be used, provide a range of possible

valuesvalues

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More on residual water contentMore on residual water contentMeasurement 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

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Typical values of physical propertiesTypical values of physical properties