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The Importance of Particle Size Distributions to The Characterization of Soils
Andy Ward, Ph.D.
Caribbean Institute for Meteorology and Hydrology
October 25, 2012
AcknowledgmentsThe U.S. Department of Energy for funding through the Remediation and Closure Science and Science Focus Area Projects.
Kathryn Draper, formerly of the Pacific Northwest National lab, who performed most of the measurements as part of her M.Sc research
Gary Rawson, Technologies North America Inc, perhaps the only sales person I have ever trusted
BackgroundReliable prediction of multi-scale transport behavior needed to support:
Environmental remediationEngineered waste repositoriesGeologic sequestrationOil and gas productionWater resources management
A critical need for all application areas is reliable estimation of model parameters, particularly flow and transport properties
Major ChallengeRocks, soils and sediments are naturally heterogeneous
Known to control near-surface and subsurface contaminant distributions
Knowledge of flow and transport (energy, mass) properties and how they vary in space (and time) to:
Interpret current contaminant distributionspredict future contaminant migrationManage soil and water resources under changing climate
Typical Stratification
Atypical Stratification
Particle Size Distribution Transcends all Scales
Ice-Age flood deposits in the southern Pasco Basin
6
Effects Manifested at Multiple Scales
Why Measure Particle Size Distributions?Particle size is a fundamental property of any sediment, soil or dust deposit
can provide important clues to nature and provenance
It influences a variety of other properties
Can be defined across a hierarchy of scales
Stratigraphic ArchitectureSedimentary SequencesLithofaciesSmall-scale heterogeneities
Particle Size DistributionsProperties estimated from texture cannot explain transport behavior
Measured PSDs mostly multi-modal
Size fractions Gravel coatingsRarely log normal
More realistic and unique description using size statistics
mean diametersorting coefficientmust account for gravel
BouldersPebbles
Very coarseCoarseMediumFineVery fine
SandVery coarseCoarseMediumFineVery fine
SiltVery coarseCoarseMediumFineVery fine
Clay
Particle Size Classes
Primary sediment properties are controlled by facies distributions, which in turn are controlled by grain size distributions resulting from the depositional environment
Reactive PropertiesSpecific surface areaCECporSporReaction Kinetics
Thermal PropertiesHeat CapacityThermal conductivity
Electrical PropertiesDielectric SpectroscopySurface conductivityFormation FactorChargeability
Transport PropertiesTortuosityIntrinsic PermeabilityDispersivityFormation Factor
Particle Size Distribution
Natural Isotope Abundance 40K, 238U, 232ThGross -ray response Hydraulic Properties
Bulk densityPorosityResidual water contentWater retentionRelative Permeability
Properties Dependent on Particle Size
Characterization of Primary ParticlesTraditional characterization of size of “individual” particles by:
SievingSedimentation
Soil whose mineral phase is to be characterized is
Pretreated to remove organic matterTreated to disperse aggregatesPassed through series of sieves with specified openings (smallest is 0.05 mm)Sizes of remaining dispersed separates characterized indirectly by sedimentation (based on Stokes’ Law)
Challenges in Estimating PropertiesProperties estimated from traditional PSDs often do not explain transport behavior
PSDs typically multi-modalFractions NOT log normalCoatings that affect sorption
Robust relationships demands a higher level of characterization
whole sedimentssize fractionscoatings
Particle Size Distribution
0.01 0.1 1 10 100 1000 3000 Particle Size (µm)
0
1
2
3
4
5
Vol
ume
(%)
C6216/2-29 39'-41' 32mm (Pre sonic) - Average, Thursday, January 08, 2009 3:19:48 PMC6216/2-29 39'-41' 32mm (10min sonic) - Average, Thursday, January 08, 2009 3:46:33 PMC6216/2-29 39'-41' 32mm (Post sonic) - Average, Thursday, January 08, 2009 3:50:32 PM
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Perc
ent P
assi
ng
Size (mm)
C5213 3-30 6.5'-8'C6216 2-29 39'-41'C6213 2.5'-5'C6212 2-28 47'-49'C6216 2-29 30-33
siltclay
2 µm 50 µm
Particle Size of Coatings on 32 mm Gravel
Paradigm ShiftIdentifying such relationships requires a higher level of sediment characterization
Whole sedimentsSize fractions
Measure particle size distributions
Measure Physico-chemical properties
CEC, SA, etc
Characterize mineralogy
Mass Fraction, xij, of Size class and LithocomponentsHeterogeneous
Sediment
Gra
in S
ize
Cla
sses
Lithocomponents
Mass Fraction of LithocomponentsGrain
Sub-classes
x1,1
x2,1
x3,1
x4,1
x5,1
Sieving
x1,2
x2,2
x3,2
x4,2
x5,2
x1,3
x2,3
x3,3
x4,3
x5,3
x1,4
x2,4
x3,4
x4,4
x5,4
Mass Fraction, xij, of Size class and LithocomponentsHeterogeneous
Sediment
Gra
in S
ize
Cla
sses
Lithocomponents
Mass Fraction of LithocomponentsGrain
Sub-classes
x1,1
x2,1
x3,1
x4,1
x5,1
Sieving
x1,2
x2,2
x3,2
x4,2
x5,2
x1,3
x2,3
x3,3
x4,3
x5,3
x1,4
x2,4
x3,4
x4,4
x5,4
HeterogeneousSediment
Gra
in S
ize
Cla
sses
Lithocomponents
Mass Fraction of LithocomponentsGrain
Sub-classes
x1,1
x2,1
x3,1
x4,1
x5,1
Sieving
x1,2
x2,2
x3,2
x4,2
x5,2
x1,3
x2,3
x3,3
x4,3
x5,3
x1,4
x2,4
x3,4
x4,4
x5,4
Conceptual Model for Polydiserse MaterialsSoils are linear systems that obey the additivity principle
For all linear systems F(x) = y, where x is a stimulus and y is a response, the superposition of stimuli yields a superposition of the respective responses:
PSD of whole sample is then calculated from the distributions of, e.g., 2 components as:
)()()( 2121 xFxFxxF
2111 )1( fpfpf
Challenges to ApproachParticle Shape:
Assumption of spherical shapeControls arrangement and packing thus mass-volume relationshipsIndividual property as fundamental as size
Sample SizeNeed PSD of very small samples
Requires precise determination using a rapid and reliable method with a high degree of precision
MineralogyAffect geochemical propertiesTransported aggregates are often polymineralic
Accounting for Mineralogy
Figure 1.5: Mineralogy of Yukon River Sediment as a function of grain size for (a) fine material, and (b) coarse material (after Matthews, 2007).
Solution to Most of My Problems
Horiba LA 950 Particle Size Analyzer
Widest Range Available: 0.01-3000μmFastest sample analysis available60 seconds sample-to-sampleRapid change from wet to dry analysisFully automated, modular sampling systemsEasy and cheap to repair even when no technician available provided Home Depot is open
MaterialsCoarse and fine fractions
Silt loam Accusand (.84-.54 mm) Silica beads (4.95 mm) Pebbles (4-5.6 mm)
Binary mixturesTriplicate samples10% increasing finesSolution-Solid ratio 2:1
Synthetic GroundwaterpH = 8.0[CO3] = 1.05 × 10-3 mol L-1
100 ppb U(VI)
DesignContact times: 0.083, 0.167, 0.33, 0.5, 1, 2, 4, 8, 16, 32, 64, 128, 256 hrsSupernatant separation using 15 minute centrifugationSupernatant filtered (0.25 μm) and analyzed for U and pH
Kinetics9% Silt + 91% Marbles51% Silt + 49% MarblesPebble and Silt end members
Sorption on Binary MixturesAccusand, Marbles, Silt, PebblesContact times: 24 hrs, 5 days
Uranium Sorption ExperimentsOrbital shaker (116 rpm)
Binary Mixture
Fine End Member
Pebble End Member
Coarse End Member
Analytical MethodsSolid Phase
Continuous particle size distribution by laser diffractionSurface area measuredby N2 gas adsorption Surface area calculatedby geometric method:
Surface topography and chemical composition by optical and scanning electron microscopy
n
nsi iii
iins
i iii
iiGEO l
pd
pSA11
QuantachromeAutosorb 6BSurface Area and Pore Size Analyzer
Horiba LA-950 laser diffraction analyzer
Laboratory Studies with Model MixturesFigure 2. Post-sonication Laser Particle Size Distribution of Textures Based on USDA Classification
How Do we Use these Data?
To Describe Particle Size StatisticsFolk and Ward (1957) introduced the Graphic Method to estimate the various statistical parameters describing a grain size distribution using only percentiles taken from cumulative frequency
50Md Median
16 50 84
3M
Mean
6.645951684
Standard deviation
595
50595
1684
501684
22
22
SkSkewness
2575
595
(44.2
KKurtosis
)
16 50 84
3M
Mean
1. Determine 16, 50and 84
16 = -0.5950 = 0.35
84 = 1.27
0.59 0.35 1.273
M
= 0.34
Example Calculation of the Mean
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 0.5 1 1.5 2dg (mm)
Clay
Mass Fractio
n
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5 2dg (mm)
Silt M
ass Frac
tion
0.00.10.20.30.40.50.60.70.80.91.0
0 0.5 1 1.5 2dg (mm)
Sand
Mas
s Frac
tion
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.5 1 1.5 2dg (mm)
Mud
Mas
s Frac
tion
Texture and Mean Diameter
To Understand Depositional EnvironmentsSamples collected from rivers and beaches (lake and ocean)
Skewness plotted against Sorting Coefficient
Beach sands better sorted and with more common coarse tail skewness than river sands
Reflects difference in processes acting on rivers and beachesRivers carry wider range of sizes: large particles move in contact with bed; large volume of fine particles in suspensionPoorly sorted; rich in fine particles (+ve skewness).
Particle Size and Water-Storage in Alluvium
Particle Size and PorosityTypical sediment made up of Spheres of different sizes
Small spheres can fill in pore throats formed by larger spheresResult is a lower porosity
• The porosity, b, of a multicomponent mixture may then be calculated as:
10
60
)83.01(255.0
ddC
n C
),,;,,,;,,,( 2121 21 npppnb ndddXXXf
where Xi is the fractional solid volume of the ithcomponent.
0.30
0.35
0.40
0.45
0.50
0.3 0.35 0.4 0.45 0.5
Measured Porosity (m3 m-3)
Pred
eict
ed P
oros
ity (m
3 m-3
)
Porosity Predicted from Particle Size Distributions
Particle Size and Permeability
Hydraulic Properties From Particle Size DistributionsMicrostructure Characterization
grain parameters controlling particle arrangement and packing
Pore StructureIdentify individual particles and arrangementSimulate packing
Feasibility established with simple case of binary mixture (coarse + fine)
Extend binary fractional packing concept to the n fractions of the Udden-Wentworth particle-size scaleRobust approach for upscaling basic parameters derived from grain size distributionsAllows correction for sizes > 2000 micron
Fines Content by Volume (%)0
min
100
f
Gravel Supported Matrix Supported
c
Poro
sity
Linear mixture
Dispersed mixture
Fines Content by Volume (%)0
min
100
f
Gravel Supported Matrix Supported
c
Poro
sity
Linear mixture
Dispersed mixture
Incomplete Mixing Concept
Water Rentention Curve with Unimodal PSD
1
10
100
1000
10000
100000
0 0.1 0.2 0.3 0.4 0.5
Theta
Pres
sure
Hea
d(cm
)
Measured Data
Fitted Params
0 5e-005 0.0001 0.00015Permeability (mm2)
0.0
0.2
0.4
0.6
Fred
le In
dex
0.0 0.2 0.4 0.6Fredle Index
0.25
0.35
0.45
0.55
s(m3 m
-3)
0.0 0.2 0.4 0.6Fredle Index
0.0
0.5
1.0
B
C
0.0 0.2 0.4 0.6Fredle Index
0
50
100
150
ae
(cm
)
0.0 0.2 0.4 0.6Fredle Index
1.4
1.6
1.8
2.0
b (g
cm
-3)
0.0 0.2 0.4 0.6Fredle Index
0
10
20C
EC (m
eq/1
00g)
Fi = 29.5618 k 0.4805
R2 = 0.96s = 0.2766 FI-0.0892
R2 = 0.67
BC = 0.9015 FI 0.3863
R2 = 0.96
ae = 7.0550 FI -0.4897
R2 = 0.94
b = 1.9401+0.0871 Ln(FI)
R2 = 0.74
CEC = 2.3521 FI -0.3542
R2 = 0.94
Hydraulic Properties and Texture
Facies Identifcation Particle Size Distributions
Identification of LithofaciesTh/K expresses relative K enrichment as indicator of clay mineral species and useful for distinguishing architectural elements (e.g. Coarse vs. fine) grain parameters controlling particle arrangement and packing
y = 0.0368x ‐ 0.0661R² = 0.9432
0%5%
10%15%20%25%30%35%40%45%
0 5 10 15
Clay %
Th (ppm)
Identification of Lithofacies
34
Multi-scale Heterogeneity
Transect A-A’ Clay Content
Sorption of Marbles – AccusandAccusand and marbles are primarily silica
No sorption expected
Low but non-zero sorption with standard high SE
no change for fines < 40%Nonlinear after 40%
Higher sorption in accusanddue to:
rough surfacesmetal-oxide coatingsorganic matter
0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.020
0.0 0.2 0.4 0.6 0.8 1.0
U so
rbed
ug/
g
Mass Fraction of Fines
Sorption of Pebbles - Silt LoamLarge amount of U(VI) sorbed by pebbles
Initial decrease in sorption on the addition of silt loam
Likely blocks access to fractures on pebbles
Classic v-shaped curve indicative of incomplete mixing
Pebbles sorption inconsistent with current conceptual models
negligible surface areano contribution to sorptiongravel correction based on linear dilution (zero mixing) 0.000
0.0020.0040.0060.0080.0100.0120.0140.0160.0180.020
0.0 0.2 0.4 0.6 0.8 1.0
U s
orbe
d ug
/g
Mass Fraction of Fines
Marbles and Silt Loam
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.0 0.2 0.4 0.6 0.8 1.0
U s
orbe
d ug
/g
Mass Fraction of Fines
Partial Mixing Model
Fines Content by Volume (%)0 100
Gravel Supported Matrix Supported
Sorb
edSp
ecie
s
Ideal Mixing
Zero Mixing
Incomplete MixingcC
minC
fC
Surface Area vs. Size StatisticsSurface area measurements in mixtures show:
nonmonotonic decrease with increasing D50
decrease with geometric mean diameter, dg
Well-behaved decrease as D10(measure of fines) increasesIncrease with sorting coefficient
Geometric method assumes smooth spherical particles and not applicable to natural materials
0
5
10
15
20
25
1 10 100 1000
SABE
T (m
2 /g)
Median Diameter, D50 (m)
(a)
0
5
10
15
20
25
0.1 1 10 100 1000
SABE
T (m
2 /g)
D10 (m)
(a)
0
5
10
15
20
25
1 10 100
SABE
T (m
2 /g)
Sorting Coefficient, g
(a)
0
5
10
15
20
25
1 10 100 1000
SABE
T (m
2 /g)
Mean Diameter, dg (m)
(a)
Effects of Surface RoughnessA plot of SA(dg
-1) should be linear
intercept = internal SA, SAint
Slope dependent on roughness, i.e., exta/
Non-zero Interceptindicates SAint > 0inconsistent with the smooth, nonporous spherical particle assumption
Nonlinear relationshipSuggest that SAint and extboth dependent on dg
0
5
10
15
20
25
0 0.05 0.1 0.15
SABE
T (m
2 /g)
dg ‐1 (m‐1)
(a)
0
5
10
15
20
25
0 0.05 0.1 0.15
SAGE
XT (m
2 /g)
dg ‐1(m‐1)
(b)
0
5
10
15
20
25
0 0.05 0.1 0.15
SACA
(m2 /g)
dg‐1(m‐1)
(d)
Measured
Geometric Method
Component Additivity
R² = 0.5466
0
5
10
15
20
25
0 5 10 15 20 25
SAGEXT (m
2 /g)
SABET (m2/g)
(a)
1:1 Line
R² = 0.9112
0
5
10
15
20
25
0 5 10 15 20 25SA
CA (m
2 /g)
SABET (m2/g)
(d)
1:1 Line
Geometric Method Component Additivity Method
Comparison of PSD-based SA Methods
ConclusionsPrimary properties of sedimentary structures are largely controlled by the distribution of facies, which is in turn controlled by the depositional environment and grain size distributions
Particle size is a fundamental property of any sediment, soil or dust deposit
Shape and mineralogy can be assumed fixed for a depositional environment
High resolution particle size distributions of < 3000 micron sediments and application of the principle of superposition allows accurate estimation of critical properties
Data most easily obtained with the Horiba LA-950
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