GEOS 4430/5310 Lecture Notes: AquiferProperties

Dr. T. Brikowski

Fall 2016

0file:aquifer properties.tex,v (1.21), printed September 27, 2016

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Introduction

Some physical, mathematical and geologic background needed tobe able to quantify groundwater movement

1. a review of energy balance, to allow quantification of thedriving force for fluid flow

2. a brief review of quantitative sedimentology, to allow fordescription of (sedimentary) rocks, and their ability totransmit fluids

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Work and Energy

I Recall that work is equal to the product of the net forceexerted and the distance over which the force moves

W︸︷︷︸Work (

ML2

T2 )

= F︸︷︷︸Force (

MLT2 )

· D︸︷︷︸Distance (L)

(1)

I Work is done when moving any object in a gravitational field(e.g. water), pressurizing a gas or fluid, etc.

I Recall that force is the mass times the acceleration of a body(Newton’s 2nd Law)

F = m︸︷︷︸mass (M)

· a︸︷︷︸acceleration

LT2

(2)

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Units for Work and Energy

Table 1: Comparison of SI and English units for work and energy. Noteespecially that kilograms and pounds are not equivalent parameters,despite common usage (OK as long as ~g is constant).

Parameter SI English

Length m ft

Time sec sec

Mass kg slug

Force kg·msec2

= Newton pound

Pressure Pascal = Newtonm2

lbft2

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Porosity

I The sub-surface void space that holds groundwater is porosity

I the basic definition of porosity is the ratio of void space(volume) to total volume

n% = 100 · Vv

V= void volume

total volume (3)

I In the laboratory soil/rock (effective) porosity is most simplydetermined by:

1. measuring the original volume of sample2. drying the sample to remove unbound water3. submerging dried sample in a known volume of water until

saturated4. the void volume (Vv ) is the difference between the original

water volume minus that remaining after the saturated sampleis removed

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Porosity (cont.)

I Total porosity is generally computed using:

n% = 100 ·[

1 − ρbρd

](4)

I ρb is the bulk density of the solids (i.e. dried mass overoriginal volume, often assumed to be 2650 kg

m3 )I ρd is the particle density (dried mass over particle volume,

determined by water displacement test)

I these two measures can differ dramatically depending on rocktype

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Classification of Sediments

I Soils and lithified sediments are initially classified by grain size(Figs. 1–2)

I grain size distribution is measured by stacked sieves for coarsefraction, hydrometer for fine fraction (relies on Stoke’s Law)

I Most environmental studies will characterize soils, standardsoil classification is the Unified Soil Classification System (Fig.5), and Wikipedia summary

I Table 3.3 of Fetter (2001) gives useful field tests that helpdistinguish the ratio of clay to silt (Fig. 6). Note that organiccontent is generally determined by reaction with hydrogenperoxide.

I Grain size distribution ultimately determines the permeabilityof the rock. This is quantified using diagrams (Fig. 3), and by

I effective grain size - the size corresponding to the 10% line on(Fig. 3)

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Classification of Sediments (cont.)

I uniformity coefficient - a direct measure of the sorting given by

Cu =d60

d10

I For modeling purposes, porosity is often estimated fromtabulated averages (Fig. 4)

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Scales for Grain Size

Figure 1: Commonly applied grain size scales for field characterization ofsediments, after Dietrich, J. T. Dutro, and Foose (Datasheet 17-2,1982).

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Estimating Grain Size

Figure 2: Grain size estimation chart, after Dietrich, J. T. Dutro, andFoose (Datasheet 16-1, 1982).

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Grain Size Distribution Curves

Figure 3: Grain Size Distribution Curves, after (Fig. 3.4, Fetter, 2001).

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Typical Porosity Ranges

Figure 4: Typical porosity ranges for sediments, after (Table 3.4, Fetter,2001). The form and electric charge on clay particles causes poorpacking, making porosity of clays high.

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Unified Soil Classification System

Figure 5: Unified Soil Classification System, after Dietrich, J. T. Dutro,and Foose (Datasheet 26.1, 1982).

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ASTM Standard D2488 for Soil Description

Figure 6: ASTM Standard D2488 for Soil Description, after (Table 3.3,Fetter, 2001). “Toughness” is the consistency of the soil near the plasticlimit.

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Geotechnical Properties of Soil

Often want to know soil strength as affected by water content. Ingeneral these are termed the Atterberg Limits, which seek to definethe boundaries between liquid, plastic, semi-solid and solid states.

I Liquid Limit (LL):I The water content corresponding to an arbitrary limit between

the liquid and plastic states of consistence of a soilI The water content at which a pat of soil, cut by a

standard-sized groove, will flow together for a distance of 12mm under the impact of 25 blows in a standard liquid-limitapparatus (see also lab class procedure)

I Plastic Limit (PL):I The water content corresponding to an arbitrary limit between

the plastic and the semisolid states of consistence of a soil.I The water content at which a soil will just begin to crumble

when rolled into a thread approximately 3 mm in diameter

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Geotechnical Properties of Soil (cont.)

I Plasticity Index (PI): is given by PI = LL− PL, highly plastic(high PI) soils tend to be clay rich and expansive (all thatwater has to go somewhere!). Very important in foundationstability (e.g. Fig. 10)

I Note water (moisture) content is obtained by measuringoriginal sample volume (Vtotal) and mass (Mwet), then dryingit and obtaining dry mass Mdry . Then volumetric moisturecontent (saturation)

θ =

(Mwet−Mdry)ρwater

Vtotal=

Vwater

Vtotal(5)

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Geotechnical Origin of Group Names

Figure 7: USCS Group Names vs. geotechnical properties. Silty soils plotto lower left, clay-rich soils to upper right. “A” line separates inorganicclays above from organic clays and silty soils. After British StandardsInstitute Standard for Site Investigations (BS 5930).

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Mineralogical Origin of Group Names

Figure 8: Mineralogic controls on geotechnical properties. After KSlandslide hazard example.

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USCS Classification Chart

Figure 9: Unified soil classification system chart, from Virginia DOT.

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PI Map, Upper Trinity Watershed

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LakeLavon

5

43

2

1

Denton

Dallas

DecaturMcKinney

Rockwall

Jacksboro

Fort Worth

Gainesville

Weatherford

0 10 20 30 40 505Kilometers¹

+U Basin Outlet (Trinity R. at Rosser)

+U USGS HCDN Stations

\ Cities

Rivers

Subbasin boundary

Soil Parameters

Plasticity Index

Water

Stable (5-15)

Moderately Swelling (15-20)

Swelling Clay (20-50)

Trinity

San Jacinto

Figure 10: Plasticity Index, Upper Trinity River watershed (Fig. 1,Brikowski, 2015).

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Hydrologic Observations

I Modern quantitative observations began with Henri Darcy in1856, analyzing flow in sand-filled pipes (filters) for a cityfountain (central water supply)

I Head: Darcy noted that discharge (water mass percross-sectional area per time) increased with increasing heightdifference between ends of the pipe. We’ll call this “headdifference” or hydraulic gradient.

I Hydraulic Conductivity: also noted differing linear relationshipsbetween hydraulic gradient and discharge depending on thematerial (Fig. 11). We’ll call the slope of these linesHydraulic Conductivity, a material property of the aquifer.

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Darcy Results

Figure 11: Darcy experimental results, after (Fig. 3.13, Fetter, 2001).

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Hydraulic Conductivity

I depends on both aquifer (intrinsic permeability) and fluid(density and viscosity) properties

I can be related to mean grain size in sediments by the formula(Shepherd method, 1989)

K︸︷︷︸Hydraulic Conductivity

= C︸︷︷︸shape factor

· d j50︸︷︷︸

mean grain size (mm)

where 1 ≥ j ≥ 2 (Fig. 12)

I Tabulated ranges are often used in modeling and initialanalysis of well testing (Fig. 13)

I note the Hazen method (1911) is also popular, and uses theformula

K = C︸︷︷︸shape factor

·d 210

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Conductivity vs. Mean Grain Size

Figure 12: Hydraulic Conductivity vs. Mean Grain Size, after (Fig. 3.15,Fetter, 2001). “Textural maturity” essentially refers to sorting/uniformitycoefficient, and this is effectively a graphical version of the ShepherdMethod.

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Conductivity vs. Mean Grain Size (cont.)

25

Typical Values of Conductivity and Permeability

Figure 13: Typical Values of Conductivity and Permeability, after (Tbl.3.7, Fetter, 2001). See also lithology correlation.

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Groundwater Features

Water in the ground is found in three general zones (Fig. 14):

I Vadose, or unsaturated zone, saturation <1, pore pressureΨ < Patmospheric)

I Saturated zone, saturation = 1, pore pressureΨ > Patmospheric

I Capillary zone, lies above the water table (the line at whichΨ = Patmospheric, saturation =1, Ψ < Patmospheric)

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Groundwater Zones

Figure 14: Groundwater zones, after (Fig. 3.18, Fetter, 2001).

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Water Table Features

I A sloping water table indicates water is flowing (Fig. 15)

I Groundwater discharges at topographic (and water table)low-spots

I The water table generally has the same shape as thetopography, modified by the location of water source/sinksand distrtibution of permeability (see Introductory LectureNotes)

I Water typically flows away from topo highs and toward topolows

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Example Potentiometric Maps

Figure 15: Example Potentiometric Maps, after (Fig. 3.24, Fetter, 2001).

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References

Brikowski, T. H. (2015). “Multi-parameter runoff elasticity as a tool for watersupply management: An example from North Texas, USA”. In: HydrologicProcesses 29.7, pp. 1746–1756. doi: 10.1002/hyp.10297. url:http://onlinelibrary.wiley.com/doi/10.1002/hyp.10297/abstract.

Dietrich, R. V., Jr. J. T. Dutro, and R. M. Foose (1982). AGI Data Sheets forgeology in the field, laboratory, and office. 2nd. Falls Church, VA: AmericanGeological Institute. isbn: 0-913312-38-X.

Fetter, C. W. (2001). Applied Hydrogeology. 4th. Supplemental websitehttp://www.appliedhydrogeology.info. Upper Saddle River, NJ:Prentice Hall, p. 598. isbn: 0-13-088239-9. url:https://www.pearsonhighered.com/program/Fetter-Applied-

Hydrogeology-4th-Edition/PGM163763.html.

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