The Importance of Particle Size Distributions to The Characterization of Soils Andy Ward, Ph.D. Caribbean Institute for Meteorology and Hydrology October 25, 2012
Acknowledgments The 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
Background Reliable prediction of multiscale transport behavior needed to support: Environmental remediation Engineered waste repositories Geologic sequestration Oil and gas production Water resources management
A critical need for all application areas is reliable estimation of model parameters, particularly flow and transport properties
Major Challenge Rocks, 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:
Typical Stratification
Interpret current contaminant distributions predict future contaminant migration Manage soil and water resources under changing climate Atypical Stratification
Particle Size Distribution Transcends all Scales
Ice-Age flood deposits in the southern Pasco Basin
Effects Manifested at Multiple Scales
6
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 Architecture Sedimentary Sequences Lithofacies Small-scale heterogeneities
Particle Size Distributions Properties estimated from texture cannot explain transport behavior Measured PSDs mostly multi-modal Size fractions Gravel coatings Rarely log normal
More realistic and unique description using size statistics mean diameter sorting coefficient must account for gravel
Particle Size Classes Boulders Pebbles Very coarse Coarse Medium Fine Very fine
Sand Very coarse Coarse Medium Fine Very fine
Silt Very coarse Coarse Medium Fine Very fine
Clay
Properties Dependent on Particle Size Primary sediment properties are controlled by facies distributions, which in turn are controlled by grain size distributions resulting from the depositional environment
Electrical Properties Dielectric Spectroscopy Surface conductivity Formation Factor Chargeability
Reactive Properties Specific surface area CECpor Spor Reaction Kinetics
Natural Isotope Abundance 40K, 238U, 232Th Gross -ray response
Hydraulic Properties Bulk density Porosity Residual water content Water retention Relative Permeability
Particle Size Distribution
Transport Properties Tortuosity Intrinsic Permeability Dispersivity Formation Factor Thermal Properties Heat Capacity Thermal conductivity
Characterization of Primary Particles Traditional characterization of size of “individual” particles by: Sieving Sedimentation
Soil whose mineral phase is to be characterized is Pretreated to remove organic matter Treated to disperse aggregates Passed 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 Properties
Robust relationships demands a higher level of characterization whole sediments size fractions coatings
4 3 2 1 0 0.01
0.1
1
10
100
1000
3000
Particle Size (µm) C6216/2-29 39'-41' 32mm (Pre sonic) - Average, Thursday, January 08, 2009 3:19:48 PM C6216/2-29 39'-41' 32mm (10min sonic) - Average, Thursday, January 08, 2009 3:46:33 PM C6216/2-29 39'-41' 32mm (Post sonic) - Average, Thursday, January 08, 2009 3:50:32 PM
Particle Size of Coatings on 32 mm Gravel 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
clay
silt 100% 90% 80% 70% 60% 50% 40% 30% 20%
2 µm
Size (mm)
50 µm
10% 0%
Percent Passing
PSDs typically multi-modal Fractions NOT log normal Coatings that affect sorption
Particle Size Distribution
5 Volume (%)
Properties estimated from traditional PSDs often do not explain transport behavior
Paradigm Shift
Heterogeneous Sediment
Grain Subclasses
Identifying such relationships requires a higher level of sediment characterization Whole sediments Size fractions
Characterize mineralogy
x1,1
x1,2
x1,3
x1,4
x2,1
x2,2
x2,3
x2,4
x3,1
x3,2
x3,3
x3,4
x4,1
x4,2
x4,3
x4,4
x5,1
x5,2
x5,3
x5,4
Lithocomponents
Grain Size Classes
CEC, SA, etc
Mass Fraction of Lithocomponents
Sieving
Measure particle size distributions Measure Physico-chemical properties
Mass Fraction, xij, of Size class and Lithocomponents
Conceptual Model for Polydiserse Materials Soils 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:
F ( x1 x2 ) F ( x1 ) F ( x 2 ) PSD of whole sample is then calculated from the distributions of, e.g., 2 components as:
f p1 f1 (1 p1 ) f 2
Challenges to Approach Particle Shape: Assumption of spherical shape Controls arrangement and packing thus mass-volume relationships Individual property as fundamental as size
Sample Size Need PSD of very small samples Requires
precise determination using a rapid and reliable method with a high degree of precision
Mineralogy Affect geochemical properties Transported 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: 0.013000μm Fastest sample analysis available 60 seconds sample-to-sample Rapid change from wet to dry analysis Fully automated, modular sampling systems Easy and cheap to repair even when no technician available provided Home Depot is open
Materials Coarse and fine fractions Silt loam Accusand (.84-.54 mm) Silica beads (4.95 mm) Pebbles (4-5.6 mm)
Binary mixtures Triplicate samples 10% increasing fines Solution-Solid ratio 2:1
Synthetic Groundwater pH = 8.0 [CO3] = 1.05 × 10-3 mol L-1 100 ppb U(VI)
Uranium Sorption Experiments Design Contact times: 0.083, 0.167, 0.33, 0.5, 1, 2, 4, 8, 16, 32, 64, 128, 256 hrs Supernatant separation using 15 minute centrifugation Supernatant filtered (0.25 μm) and analyzed for U and pH
Orbital shaker (116 rpm)
Binary Mixture
Fine End Member
Kinetics 9% Silt + 91% Marbles 51% Silt + 49% Marbles Pebble and Silt end members
Coarse End Member
Sorption on Binary Mixtures Accusand, Marbles, Silt, Pebbles Contact times: 24 hrs, 5 days
Pebble End Member
Analytical Methods Solid Phase Continuous particle size distribution by laser diffraction Surface area measured by N2 gas adsorption Surface area calculated by geometric method:
Quantachrome Autosorb 6B Surface Area and Pore Size Analyzer
n i pi p SAGEO i i i 1 i i d i i ns 1 i i li ns
Surface topography and chemical composition by optical and scanning electron microscopy
Horiba LA-950 laser diffraction analyzer
Laboratory Studies with Model Mixtures Figure 2. Post-sonication Laser Particle Size Distribution of Textures Based on USDA Classification
How Do we Use these Data?
To Describe Particle Size Statistics Folk 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 Median
Md 50
Mean
M
Standard deviation
16 50 84 3
84 16 4
95 5 6.6
84 16 250 95 5 250 284 16 295 5
Skewness
Sk
Kurtosis
95 5 K 2.44(75 25 )
Example Calculation of the Mean Mean
M
16 50 84 3
1. Determine 16, 50and 84
16 = -0.59 50 = 0.35 84 = 1.27 0.59 0.35 1.27 M 3 = 0.34
Texture and Mean Diameter 0.6
0.8
0.5
Silt M ass Fraction
Sand M ass Fraction
1.0 0.9 0.7 0.6
0.4 0.3
0.5 0.4 0.3
0.2
0.2 0.1
0.1
0.0
0 0
0.5
1
1.5
2
0
0.5
dg (mm)
1.5
2
1.5
2
dg (mm) 0.6
0.08 0.07
0.5
M ud M ass Fraction
Clay Mass Fraction
1
0.06
0.4
0.05 0.04
0.3
0.03
0.2
0.02
0.1
0.01 0
0.0
0
0.5
1
dg (mm)
1.5
2
0
0.5
1
dg (mm)
To Understand Depositional Environments Samples 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 beaches Rivers carry wider range of sizes: large particles move in contact with bed; large volume of fine particles in suspension Poorly sorted; rich in fine particles (+ve skewness).
Particle Size and Water-Storage in Alluvium
Particle Size and Porosity Typical sediment made up of Spheres of different sizes Small spheres can fill in pore throats formed by larger spheres Result is a lower porosity
•
n 0.255(1 0.83C ) d C 60 d10
The porosity, b, of a multicomponent mixture may then be calculated as:
b f ( X 1 , X 2 ,, X n ; d p , d p ,, d p ;1 , 2 ,n ) 1
2
n
where Xi is the fractional solid volume of the ith component.
Porosity Predicted from Particle Size Distributions
3
-3
Predeicted Porosity (m m )
0.50
0.45
0.40
0.35
0.30 0.3
0.35
0.4
0.45 3
-3
Measured Porosity (m m )
0.5
Particle Size and Permeability
Hydraulic Properties From Particle Size Distributions Microstructure Characterization grain parameters controlling particle arrangement and packing
Incomplete Mixing Concept Gravel Supported
Matrix Supported
Pore Structure Identify individual particles and arrangement Simulate packing
Extend binary fractional packing concept to the n fractions of the Udden-Wentworth particle-size scale Robust approach for upscaling basic parameters derived from grain size distributions Allows correction for sizes > 2000 micron
Porosity
c
Dispersed mixture
0
min 100
Fines Content by Volume (%) Water Rentention Curve with Unimodal PSD 100000 Measured Data Fitted Params
10000 Pressure Head(cm )
Feasibility established with simple case of binary mixture (coarse + fine)
f
Linear mixture
1000
100
10
1 0
0.1
0.2
0.3 Theta
0.4
0.5
0.6 0.4
Fi = 29.5618 k R 2 = 0.96
0.55
0.4805
s(m3 m-3)
Fredle Index
Hydraulic Properties and Texture
0.2 0.0 0
5e-005
0.0001
0.00015
s = 0.2766 FI -0.0892
0.45
R 2 = 0.67
0.35 0.25
2
0.0
Permeability (mm ) 1.0
0.4
0.6
150
ae (cm)
BC
0.2
Fredle Index ae = 7.0550 FI
100
0.5
BC = 0.9015 FI
0.3863
R 2 = 0.96
0.0 0.0
0.2
R 2 = 0.94
50 0
0.4
0.6
0.0
Fredle Index CEC (meq/100g)
b (g cm-3)
1.8 1.6
b = 1.9401+0.0871 Ln(FI)
1.4
R 2 = 0.74 0.2
Fredle Index
0.2
0.4
0.6
Fredle Index
2.0
0.0
-0.4897
0.4
0.6
20
CEC = 2.3521 FI
-0.3542
R 2 = 0.94 10 0
0.0
0.2
Fredle Index
0.4
0.6
Facies Identifcation Particle Size Distributions Identification of Lithofacies
Clay %
Th/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 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
y = 0.0368x ‐ 0.0661 R² = 0.9432
0
5
10
Th (ppm)
15
Multi-scale Heterogeneity Identification of Lithofacies
34
Transect A-A’ Clay Content
Sorption of Marbles – Accusand
Low but non-zero sorption with standard high SE no change for fines < 40% Nonlinear after 40% Higher sorption in accusand due to: rough surfaces metal-oxide coatings organic matter
0.018 0.016 0.014
U sorbed ug/g
Accusand and marbles are primarily silica No sorption expected
0.020
0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.0
0.2
0.4
0.6
Mass Fraction of Fines
0.8
1.0
Sorption of Pebbles - Silt Loam 0.20
Initial decrease in sorption on the addition of silt loam Likely blocks access to fractures on pebbles
0.16 0.14 U sorbed ug/g
Large amount of U(VI) sorbed by pebbles
0.18
0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.0
Classic v-shaped curve indicative of incomplete mixing
0.4 0.6 Mass Fraction of Fines
0.8
1.0
0.020 0.018 0.016 0.014 U sorbed ug/g
Pebbles sorption inconsistent with current conceptual models negligible surface area no contribution to sorption gravel correction based on linear dilution (zero mixing)
0.2
0.012 0.010 0.008 0.006 0.004
Marbles and Silt Loam
0.002 0.000 0.0
0.2
0.4
0.6
Mass Fraction of Fines
0.8
1.0
Partial Mixing Model
Sorbed Species
Gravel Supported
Matrix Supported
Cf
Zero Mixing
Cc
Incomplete Mixing
Cmin
0
Ideal Mixing
Fines Content by Volume (%)
100
Surface Area vs. Size Statistics
Surface area measurements in mixtures show:
25 (a)
SABET (m2/g)
20
nonmonotonic decrease with increasing D50 decrease with geometric mean diameter, dg Well-behaved decrease as D10 (measure of fines) increases Increase with sorting coefficient
15 10 5 0 1
100
1000
25 (a)
SABET (m2/g)
20
Geometric method assumes smooth spherical particles and not applicable to natural materials
15 10 5 0 1
10
100
1000
Mean Diameter, dg (m)
25
25
(a)
(a)
20
SABET (m2/g)
20
SABET (m2/g)
10
Median Diameter, D50 (m)
15 10
15 10
5
5
0
0 1
10
Sorting Coefficient, g
100
0.1
1
10
D10 (m)
100
1000
Effects of Surface Roughness intercept = internal SA, SAint Slope dependent on roughness, i.e., exta/
(a)
20
SABET (m2/g)
A plot of SA(dg-1) should be linear
Measured
25
15 10 5 0 0
0.05
0.1
0.15
dg ‐1 (m‐1)
Geometric Method
25 (b)
Nonlinear relationship Suggest that SAint and ext both dependent on dg
SAGEXT (m2/g)
indicates SAint > 0 inconsistent with the smooth, nonporous spherical particle assumption
20 15 10 5 0 0
0.05
0.1
0.15
dg ‐1(m‐1)
Component Additivity
25
(d)
20
SACA (m2/g)
Non-zero Intercept
15 10 5 0 0
0.05
0.1
dg‐1(m‐1)
0.15
Comparison of PSD-based SA Methods Geometric Method
Component Additivity Method
25
25 (a)
(d)
R² = 0.5466
20
SACA (m2/g)
SAGEXT (m2/g)
20
R² = 0.9112
15
10
5
15
10 1:1 Line
5
1:1 Line
0
0 0
5
10
15
SABET (m2/g)
20
25
0
5
10
15
SABET (m2/g)
20
25
Conclusions Primary 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
