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