Oil Spill Simulation near The Red Sea

Coast using The Random Walk

Technique Amro M. Elfeki

King Abdulaziz University

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 (Random Walk

Technique). • Oil Spill and Transport Scenarios • Simulation Results .• Summary and Conclusions.• Recommendations.

Problem Statement (Study Area) • EIA study of Oil Spill from Fuel Supply Facility near the Red

Sea Coast

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

No

rth

ing

(m

)

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.

Tank Shape (Oil Spill Source)

Example of HFO Tank.

Methodology • Data Collection.• 2D-Mapping of Groundwater Elevations (Using

SURFER).• Estimation of Groundwater Fluxes.• Estimation of Groundwater Velocities.• Analytical Check and Testing 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.

Data Collection

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

Input Parameters for The StudyParameter 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/gallonHFO 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

pL p

LL

(Xu and Eckstein, 1995)

Mapping Groundwater Elevations

Construct a water table elevation map using Kriging technique in SURFER software.

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

1D-GWE Profile

Comparison of groundwater profile data with theoretical profile for unconfined aquifers

“Good Agreement”

2 21 22

1( )h h

h x h xL

Groundwater Fluxes and Velocities

x

y

hq Kxhq Ky

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 hvn xK hvn y

Groundwater Fluxes

Groundwater Velocities

where, n is the effective porosity

Travel Time Calculations (1D Case)

3

2 21 22 3

1 122 21 2

4

3

h hnt h hLh h

KL

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

No

rth

ing

(m

)

Oil Spill Simulation “GW-Transport”

1x y xx xy yx yy

f

C C C C C C Cv v D D D D Ct R x y x x y y x y

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 jmL L Tij ij

V VD V D

V

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.

Random Walk Solution of The Model Equation

122t 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.

The Concept of Random Walk

15

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

0

/ ( )( )

1 ( ( () )exp( ) ( )

o

x l t

t 2 2o ox

l x t x

HMC x, y,t = 4 V

x - - t y -VX Y - + d t 4 t 4 tV V

16

Adsorption and Biodegradation

1 df b

KRn

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 t

where, Mp (t) is the mass per particle at time t, and Mp(0) is the initial mass per particle at time.

Transport Scenarios

• Advection-dispersion transport.• Advection-dispersion-adsorption transport.• Advection-dispersion-adsorption-decay

transport.

Snapshots of plume simulation of the oil spill from settling tank “B” after 1, 25 and

50 years

429500 430000 430500 431000 431500 432000 432500

E asting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

0.0E+000

1.0E+006

1.0E+008

1.0E+009

C oncentration (mg/L)

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

Plum e at T im e = 1 YE AR

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

429500 430000 430500 431000 431500 432000 432500

E asting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

Plum e at T im e = 25 YEAR S

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

429500 430000 430500 431000 431500 432000 432500

E asting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

Plum e at T ime = 50 YEA R S

429500 430000 430500 431000 431500 432000 432500

Easting (m )

2643000

2643500

2644000

Nor

thin

g (m

) 1

2

3

4

5

7

Advection+Dispersion Advection+D ispersion+A dsorption A dvection+D ispersion+Adsorption+ B io-Degradation

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.

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.