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
Oil
Oil
mass
Medium type
Flow rate
Processes
Introduction
Sorption
Sorption
and
intra-particle diffusion
Advection
Initial state
Initial state
Final state
Diffusion
Diffusion
Initial state
Initial state
Dispersion
Final state
Final state
Final state
Pollutant
Aquifer
Particle
particle/grain
Inter-particle pore
Inter-pore
Intra-particle pore
Intra-pore
Introduction
Organic particles (size ≤ 10 µm) released from soils
and tailings ponds to aquifers.
Thin and mature fine tailings
(approx. size < 44 µm)
!
(Figure from en.wikibooks.org)
(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
 Laboratory experiments
• Porous medium: natural soil with the structure of a
clayey sand, grain size up to 2 mm.
Organic carbon content
( f OC ) [weight%]
0.25
Particle density CaCO3
[g cm-3]
[weight%]
2.84
0.7
Materials and Methods
• Organic particles: natural lignite (brown coal)
f OC  60.5 weight%.
Fine particles
d50 = 0.8 µm
Filtered particles
d50 ≤ 0.45 µm
Based on the size: dissolved
organic carbon (DOC)
d50 : median diameter based on the number of particles
Materials and Methods
• Lindane (gamma-hexachlorocyclohexane):
very hydrophobic in water.
Materials and Methods
• Sorption behaviour of lindane through batch
sorption experiments
Clayey soil
(porous medium)
Lindane
(contaminant)
Lignite
(Organic particle)
Materials and Methods
Porous
medium
• Transport simulation through column experiments
Length:
15 cm
Diameter:
2.4 cm
0.05 mL min-1
Materials and Methods
Injection phase
Lindane alone
in 0 to 60 mmol L-1 NaCl
Elution phase
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
 One-dimensional transport modelling
• Transport of lindane alone:
- Model with kinetic sorption
- Model with equilibrium sorption and intra-particle diffusion
• Transport of lignite particles: Model with straining and
attachment
Aquifer
matrix
Straining
Attachment
Particles
• Simultaneous transport of lindane and lignite particles
Results and Discussion
 Equilibrium sorption of lindane
• Clayey soil:
- Linear distribution coefficient (Kd): 3.38 ± 0.16 Lkg 1
- Low sorption!
S  KdC
Linear model
Results and Discussion
• Lignite:
- Freundlich distribution coefficient (KFr): 707 ± 18 mg11/n L1/n kg 1
Fr
- Freundlich exponent (1/nFr): 0.72 ± 0.02
- High sorption!
S  K Fr C
1 nFr
Freundlich model
Fr
Results and Discussion
 Column experiments
• Spatial concentration profile of lindane alone
12
16
20
1 pore
4
8
pore volumes
volume
volumes
Injection stopped
X [cm]
Results and Discussion
• Effluent chloride and lindane concentrations
Kinetic sorption
Equilibrium
sorption and
intra-particle
diffusion
Porosity
n  0 .5
nm  0.4
nim  0.1
Dualporosity
 Ionic strength reduction (60 to 6 mmol L-1 NaCl) did not cause soil particle
mobilization.
Results and Discussion
• Effluent lindane and organic particle concentrations
d50 < 0.45 µm
Lindane without
particles
Lindane with
fine particles
(d50 = 0.8 µm)
Lindane with
filtered particles or DOC
(d50 < 0.45 µm)
 Fine lignite particles were completely retained in the porous medium.
 Travel time of lindane reduced by 25% with lignite particles < 0.45 µm.
Results and Discussion
 Extension to 2-D transport
• Hydraulic conductivity (K) and flow field
𝟏𝟎−𝟓
K [m s-1]
𝟏𝟎−𝟕
Hydraulic gradient
𝛻ℎ ≈ 0.005
Results and Discussion
• Separate transport of organic particles and
lindane (kinetic sorption)
Contamination time [day]
Concentration of organic particles [mg L-1]
½
12
Concentration of lindane [mg L-1]
5
Results and Discussion
Particles, 5 days
Particles, 1 month
Lindane, 5 days
Lindane, 1 month
C/Cin
Results and Discussion
Particles, 6 months
Particles, 1 year
Lindane, 6 months
Lindane, 1 year
C/Cin
Results and Discussion
Z [m]
• Transport of lindane alone with equilibrium sorption
and intra-particle diffusion
Z [m]
Z [m]
Results and Discussion
Intra-particle porosity
Inter-particle porosity
X [m]
Results and Discussion
Lindane, 5 days
Lindane, 1 month
Lindane, 6 months
Lindane, 1 year
Conclusions
 Lindane transport was represented best when accounting
for intra-particle diffusion.
 Organic particles > 0.45 µm were strongly retained,
leading to retarded contaminant transport.
 Organic particles < 0.45 µm (DOC) enhanced
contaminant transport.
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
Pollutant
Aquifer
Particle
particle/grain
Aquifer
Particle
particle/grain
Inter-particle pore
Inter-pore
Intra-particle pore
Intra-pore
Inter-particle pore
Inter-pore
Intra-particle pore
Intra-pore
Supplementary Information
(Roy and Dzombak, 1997)
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