Oil Spill Simulation near The Red Sea Coast using The Random Walk Technique. http://www.petroenvironment.com/

1. Oil Spill Simulation near
The Red Sea Coast using
The Random Walk
Technique
Amro M. Elfeki
King Abdulaziz University

2. Outline
• Problem Statement and Study Area.
• Objectives.
• Methodology.
• Data Collection.
• First order analysis of the problem in 1D.
• Brief Description of the GW-Transport Model (RandomWalkTechnique).
• Oil Spill andTransport Scenarios
• Simulation Results .
• Summary and Conclusions.
• Recommendations.

3. Problem Statement (Study Area)
• EIA study of Oil Spill from Fuel Supply Facility near the Red Sea Coast
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s tin g (m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)

4. Objectives
The objective of this study is developing groundwater flow
and transport models to study and simulate pollution fate
due to oil spill in a Fuel Supply Facility near red sea coast.

5. Tank Shape (Oil Spill Source)
Example of HFO Tank.

6. Methodology
• Data Collection.
• 2D-Mapping of Groundwater Elevations (Using SURFER).
• Estimation of Groundwater Fluxes.
• Estimation of GroundwaterVelocities.
• Analytical Check andTesting of 1D Profile.
• Simulation of Oil Spill by “GW-Transport Model” Elfeki
(1996).
• This model is based on the random walk theory and has
been tested and applied for real case studies that has
been published in international peer reviewed journals.

7. Data Collection
- Aquifer parameters,
- Groundwater Elevations,
- Transport Parameters,
- Tanks Dimensions, and
- Oil Characteristics.

8. Input Parameters for The Study
Parameter Value
Average aquifer thickness, H, 15 m.
- Groundwater table elevations at
selected boreholes.
measured from baseline study
Average aquifer hydraulic conductivity, K, 8.64 m/day.
Average aquifer effective porosity, n, 0.3 [-]
- Bulk Soil dry density, γ, 1.6 g/cm3
Biodegradation coefficient, λ, 0.0001 day-1
Partitioning coefficient, Kd, 0.15 cm3
/g.
Longitudinal dispersivity, αL where, Lp is plume length.
Transversal dispersivity αT = (0.1-0.2) αL
Oil density 7.2 Ib/gallon
HFO Settling Tank volume (FFO-HF-T-02
A/B)
12,200 M3
HFO Tank volume ( FFO-HF-T-02 A/B/C) 72,000 M3
ALC Tank volume ( FFO-HF-T-02 A/B) 29,000 M3
2.414
103.28 0.83 log in feet
3.28
p
L p
L
Lα
  
= ×   ÷
   (Xu and Eckstein, 1995)

9. Mapping Groundwater Elevations
Construct a water
table elevation
map using
Kriging
technique in
SURFER
software.
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7

10. 1D-GWE Profile
Comparison of
groundwater
profile data
with
theoretical
profile for
unconfined
aquifers
“Good
Agreement”
( )2 2
1 22
1( )
h h
h x h x
L
−
= −

11. Groundwater Fluxes andVelocities
x
y
h
q K
x
h
q K
y
∂
=−
∂
∂
=−
∂
Where,
qx is Darcy’s flux in x-direction [L/T],
qy is Darcy’s flux in y-direction [L/T],
K is the hydraulic conductivity [L/T], and,
h is the hydraulic head.
x
y
K h
v
n x
K h
v
n y
∂
=−
∂
∂
=−
∂
Groundwater Fluxes
Groundwater Velocities
where, n is the effective porosity

12. TravelTime Calculations (1D Case)
( )
( )
3
2 2
1 22 3
1 12
2 2
1 2
4
3
h hn
t h h
Lh h
K
L
 
 −  ÷= − −  ÷ −     ÷
 ÷
 
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s tin g (m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)

13. Oil Spill Simulation “GW-Transport”
1
x y xx xy yx yy
f
C C C C C C C
v v D D D D C
t R x y x x y y x y
λ
    ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂
= + − + − + − ÷   ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂    
where C is the concentration of the contaminant at time, t at location (x, y),
vx and vy are the average groundwater flow velocity components in the x and y
directions respectively,
Dxx, Dyy, Dxy, Dyx are the components of the hydrodynamic dispersion tensor,
that is given by,
The governing equation of the model is
( ) ( )*
- i j
mL L Tij ij
V V
D V D
V
α δ α α= + +
δij is the delta function,
αL is the longitudinal dispersivity,
αT is the lateral dispersivity,
Rf is the retardation factor, and
λ is the decay coefficient.

14. RandomWalk Solution ofThe Model
Equation
( ) ( ) ( )( ) ( )( ) ( )( )
1
2
2t t tt t t t t   +∇×   +∆ = + ∆ + ∆p p pp p V X D X D X ZX X
where, Xp (t+Δt) is the new position
vector for particle p, Xp (t) is the old
position vector of the particle p, Z is
a vector of statistically independent
normal random numbers with zero
mean and unit variance, and Δt is the
time step in calculations.

15. The Concept of RandomWalk
15

16. Random Walk Model Testing
16
2 2
/( )
( , , )
4 4
( - - ( -) )
exp -
4 4
o
l x t x
o ox
l x t x
HMC x y t
t tV V
x t yVX Y
t tV V
ε
=
π πα α
 
+ 
α α 
( )0
/ ( )
( )
1 ( ( () )
exp
( ) ( )
o
x l t
t 2 2
o ox
l x t x
HMC x,y,t =
4 V
x - - t y -VX Y- + d
t 4 t 4 tV V
•
ε
π α α
 − τ
τ 
− τ − τ − τα α 
∫
16

17. Adsorption and Biodegradation
1 d
f b
K
R
n
ρ= +
where, Kd is the partitioning coefficient, and ρb is the bulk density of the aquifer material
Adsorption is modelled by a retardation factor which is
calculated by,
Biodegradation or decay is modelled by a decay coefficient, λ and is
implemented in the particle model as,
( ) (0)exp( )p pM t M tλ= −
where, Mp (t) is the mass per particle at time t, and Mp(0) is the initial mass
per particle at time.

18. Transport Scenarios
• Advection-dispersion transport.
• Advection-dispersion-adsorption transport.
• Advection-dispersion-adsorption-decay transport.

19. Snapshots of plume simulation of the oil spill from
settling tank “B” after 1, 25 and 50 years
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
0 . 0 E + 0 0 0
1 . 0 E + 0 0 6
1 . 0 E + 0 0 8
1 . 0 E + 0 0 9
C o n c e n t r a t io n
( m g / L )
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
P lu m e a t T im e = 1 Y E A R
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
P lu m e a t T im e = 2 5 Y E A R S
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
P lu m e a t T im e = 5 0 Y E A R S
4 2 9 5 0 0 4 3 0 0 0 0 4 3 0 5 0 0 4 3 1 0 0 0 4 3 1 5 0 0 4 3 2 0 0 0 4 3 2 5 0 0
E a s t in g ( m )
2 6 4 3 0 0 0
2 6 4 3 5 0 0
2 6 4 4 0 0 0
Northing(m)
1
2
3
4
5
7
A d v e c t io n + D is p e r s io n A d v e c t io n + D is p e r s io n + A d s o r p t io n A d v e c t io n + D is p e r s io n + A d s o r p t io n + B io - D e g r a d a t io n

20. Summary and Conclusions
• Groundwater flow and transport modelling have been performed for the EIA Study on oil spill from Fuel
Supply Facilities.
• A 2D GW-Transport Model (Elfeki, 1996) has been implemented to study the fate of the oil spill from Fuel
Supply Facilities.
• The model is based on a random walk theory and has been proved to be powerful in modelling
contaminant transport in groundwater (Many applications available in the literature).
• Three transport scenarios have been considered namely: (1) advection and dispersion, (2) advection,
dispersion and adsorption, and (3) advection, dispersion, adsorption and natural attenuation.
• It has been shown that under the first scenario the plume reaches the sea in almost 50 year if it has been
gone undetected, while in case of the second scenario, the plume will take longer to reach the sea may be
about 90 years due to retardation process that takes place due to adsorption mechanisms. In the third
scenario, the plume will undergo bio-degradation process, which would never reach the sea because the
rate of transport is very small with respect to the biodegradation rate.

21. Recomendations
Based on the above mentioned results and conclusions, it is
recommended to have a monitoring system from the
available wells at the site to check every 6 month the
quality of the groundwater to have early detection of
contaminant plumes if oil spill takes place accidentally.