Relevance of Intra-Particle Diffusion in Modelling ...

Relevance of Intra-Particle Diffusion in

Modelling Hydrocarbon Transport

through Dual-Porosity Porous Media in

the Absence and Presence of Particles

Dr. Stephane Ngueleu, Prof. Peter Grathwohl, Prof. Olaf Cirpka

Kananaskis, April 22, 2015

Outline

► Introduction

► Objectives

► Materials and Methods

► Results and Discussion

► Conclusions

Introduction

(Citizen Journalist Exchange, 2013)

(The Canadian Press, 2012)

Introduction

(Energy Resources Conservation Board, 2013)

Introduction

(Energy Resources Conservation Board, 2013)

Introduction

(Energy Resources Conservation Board, 2013)

Introduction

Medium type

Flow rate

Oilmass

Processes

Oil

Introduction

Sorption

and

intra-particle diffusion

Initial state Final state

Initial state

Advection

Diffusion

Dispersion

Compound

Followed path lines

Mean path line

Aquifer material

Final state

Initial state Final stateInitial state Final state

Sorption

Diffusion

Pollutant

Particle

Inter-particle pore

Intra-particle pore

Aquifer

particle/grain

Inter-pore

Intra-pore

Introduction

Organic particles (size ≤ 10 µm) released from soils

and tailings ponds to aquifers.

!

(Figure from en.wikibooks.org)

Thin and mature fine tailings

(approx. size < 44 µm)

(Figure from www.gardguide.com)

Objectives

Understand through model-based analysis:

Hydrocarbon transport in saturated dual-porosity

porous media

Organic particle transport and its influence on

hydrocarbon transport

Materials and Methods

• Porous medium: natural soil with the structure of a

clayey sand, grain size up to 2 mm.

Laboratory experiments

Organic carbon content

[weight%]

Particle density

[g cm-3]

CaCO3

[weight%]

0.25 2.84 0.7

)( OCf

Materials and Methods

• Organic particles: natural lignite (brown coal)

weight%.5.60OCf

Fine particlesd50 = 0.8 µm

Filtered particles

Based on the size: dissolved

organic carbon (DOC)

d50 ≤ 0.45 µm

d50 : median diameter based on the number of particles

Materials and Methods

• Lindane (gamma-hexachlorocyclohexane):

very hydrophobic in water.

Materials and Methods

Lindane

(contaminant)

Lignite

(Organic particle)

Clayey soil

(porous medium)

• Sorption behaviour of lindane through batch

sorption experiments

Materials and Methods• Transport simulation through column experiments

Po

rou

s

med

ium

Length:

15 cm

Diameter:

2.4 cm

0.05 mL min-1

Materials and Methods

Injection phase Elution phase

Lindane alone

in 0 to 60 mmol L-1 NaCl

0 to 60 mmol L-1 NaCl

Lindane and organic particles

in 0 to 60 mmol L-1 NaCl

0 to 60 mmol L-1 NaCl

!(Figure from en.wikibooks.org)

Materials and Methods

• Transport of lindane alone:

One-dimensional transport modelling

- Model with kinetic sorption

- Model with equilibrium sorption and intra-particle diffusion

• Transport of lignite particles: Model with straining and

attachment

Attachment

Straining

Particles

Aquifer

matrix

• Simultaneous transport of lindane and lignite particles

Results and Discussion

Equilibrium sorption of lindane

• Clayey soil:

- Linear distribution coefficient (Kd): 3.38 ± 0.16

- Low sorption!

1Lkg

Linear model

CKS d

Results and Discussion

• Lignite:

- Freundlich distribution coefficient (KFr): 707 ± 18

- Freundlich exponent (1/nFr): 0.72 ± 0.02

- High sorption!

11/n1/n1kgLmg FrFr

Freundlich model

Frn

FrCKS1

Results and Discussion Column experiments

1 pore volume4 pore volumes8 pore volumes12 pore volumes

Injection stopped

16 pore volumes20 pore volumes

• Spatial concentration profile of lindane alone

X [cm]

Results and Discussion

Ionic strength reduction (60 to 6 mmol L-1 NaCl) did not cause soil particle

mobilization.

5.0n

Porosity

4.0 mn

1.0imn

Dual-

porosity

Kinetic sorption

Equilibrium

sorption and

intra-particle

diffusion

• Effluent chloride and lindane concentrations

Results and Discussion

• Effluent lindane and organic particle concentrations

Travel time of lindane reduced by 25% with lignite particles < 0.45 µm.

Fine lignite particles were completely retained in the porous medium.

Lindane with

filtered particles or DOC

(d50 < 0.45 µm)

d50 < 0.45 µm

Lindane with

filtered particles or DOC

(d50 < 0.45 µm)

Lindane with

filtered particles or DOC

(d50 < 0.45 µm)

Lindane with

fine particles

(d50 = 0.8 µm)

Lindane without

particles

d50 < 0.45 µm

Lindane with

filtered particles or DOC

(d50 < 0.45 µm)

Results and Discussion

• Hydraulic conductivity (K) and flow field

𝟏𝟎−𝟕

𝟏𝟎−𝟓

K [m s-1]

Extension to 2-D transport

Hydraulic gradient

𝛻ℎ ≈ 0.005

Results and Discussion

• Separate transport of organic particles and

lindane (kinetic sorption)

Contamination time [day] ½

Concentration of organic particles [mg L-1] 12

Concentration of lindane [mg L-1] 5

Results and Discussion

Particles, 5 days Particles, 1 month

Lindane, 5 days C/CinLindane, 1 month

Results and Discussion

Particles, 6 months Particles, 1 year

Lindane, 6 months C/CinLindane, 1 year

Results and Discussion

• Transport of lindane alone with equilibrium sorption

and intra-particle diffusion

Z [m

]

Results and Discussion

Z [m

]

Z [m

]

Inter-particle porosity

Intra-particle porosity

X [m]

Results and Discussion

Lindane, 5 days Lindane, 1 month

Lindane, 6 months Lindane, 1 year

Conclusions

Organic particles < 0.45 µm (DOC) enhanced

contaminant transport.

Organic particles > 0.45 µm were strongly retained,

leading to retarded contaminant transport.

Lindane transport was represented best when accounting

for intra-particle diffusion.

Conclusions

Long term contamination can be an indication of back

diffusion from intra-particle pores to inter-particle pores,

not an indication of new contamination.

Pollutant

Particle

Inter-particle pore

Intra-particle pore

Aquifer

particle/grain

Inter-pore

Intra-pore

Pollutant

Particle

Inter-particle pore

Intra-particle pore

Aquifer

particle/grain

Inter-pore

Intra-pore

Supplementary Information

(Roy and Dzombak, 1997)

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