International Conference on The Marine Environment of The Red Sea, Jeddah, Saudi Arabia. 2014.

1. Modeling Saltwater Intrusion
along Jeddah Coast Using
Multiple Spreadsheets
By
Amro M. M. Elfeki1,2 & Jarbou A. Bahrawi1
1 Department of Hydrology and Water Resources Management,
Faculty of Meteorology, Environment and Arid Land Agriculture,
King Abdulaziz University
2 Faculty of Engineering Mansoura University, Egypt

2. Outlines
• Objectives.
• Study Area.
• Data Collection.
• Conceptual Model.
• Mathematical Formulation.
• Numerical Model Based on IFD Scheme.
• Multiple Spreadsheets used in the Model.
• Testing and Results.
• Conclusions.

3. Objectives
• The current research is a modeling study and simulations of saltwater
intrusion along Jeddah city coast using multiple spreadsheets.
The reason for using spreadsheets:
1. It simplicity.
2. Well known to every scientist and engineer.
3. It has a rich library with built-in-functions with equation solvers.
4. It performs fast calculations.
5. It has a user friendly graphical interface.
6. It can produce animated graphs.

4. Spreadsheet Modeling
• This study is an extension of the spreadsheet Model called “GWMAP”
developed by the authors:

5. Study Area
• AL-Sefry, S. A. and Z. Sen, (2006) Groundwater rise problem and risk evaluation in major cities of arid lands- Jeddah case in Kingdom of Saudi Arabia, Water
Resources Management, 20: 91-108.

6. Data Collection
• Aquifer Thickness.
• Permeability of the Aquifer.
• Sewage Discharge.
• Topography.
Ref.: Alquhtani, M.B. and W.M. Shehata (2003) Vulnerability map of the
groundwater rise in Jeddah, Saudi Arabia: 12 Asian regional conf. on the
soil mechanics and geotechnical engineering, 4-8 August, 2003, Singapore,
Chapter 3-3, pp: 357.
Study Area

7. Data Collection (cont.)
Leakage from water supply systems 191,000m3/day
Infiltration from cesspools 89,250m3/day
Recharge from rainfall 0.001014m/day
Excess landscape irrigation 26,300m3/day
Subsurface inflow 33,000m3/day
AL-Sefry, S. A. and Z. Sen, (2006) Groundwater rise problem and risk evaluation in major cities of arid lands- Jeddah case in Kingdom of Saudi Arabia, Water Resources
Management, 20: 91-108.
Basamed, A. (2002) Hydrochemical study and bacteriological effect on groundwater in the northern part of Jeddah district, M.Sc. Thesis, Faculty of Earth Sciences, King Abdulaziz
University, Jeddah, Saudi Arabia.
Alquhtani, M.B. and W.M. Shehata (2003) Vulnerability map of the groundwater rise in Jeddah, Saudi Arabia: 12 Asian regional conf. on the soil mechanics and geotechnical
engineering, 4-8 August, 2003, Singapore, Chapter 3-3, pp: 357.

8. Conceptual Model

9. Mathematical Model
Fresh Water Model
Salt Water Model
   
   
1: at the interface
0
2 : after the interface toe
0
f f
f f
f f
f f
Zone
h h
K h K h R E W
x x y y
Zone
h h
K h Z K h Z R E W
x x y y
 

     
              

     
              
f s f
approximation
(1 )
= /( )
f s
Geyben Herzberg
h h  
   

  


10. Finite Difference Model
 
1 1
1 1 1 1, ,
, , , ,2 2
2 2 2 2
1, 1,2 2
1 1
1 1 1 1, ,
, , , ,2 2
2 2 2 2
, 1 , 12 2
.
, , ,
. .
. .
f f
f fi j i j
i j i j i j i j
i j i j
f fi j i j
i j i j i j i j
f fi j i j
i j
i j i j i j
K h Z K h Z
h h
x y
K h Z K h Z
h h
y y
W
R E R L B T h
x y
 
   
 
 
   
 
   
    
   
 
   
    
    
 
      
 










jiji
ji
KK
K
,,1
,
2
1
11
2
1
, 1, ,
2
0.5f f fi j i j i j
h h h 
   
 jiji
ji
ZZZ ,,1
,
2
1 5.0  


11. Groundwater Levels (m) on Spreadsheet

12. Graphical Representation of GWL Map

13. Permeability Spatial Distribution on
Spreadsheet (m/day)

14. Sewage Discharge (L/day/person)

15. Boundary Conditions
1 1 1.8 2.2 2.2 2 1 1 0 6 11 16 20 25 28 32 40 40 40 40 40
43
43
40
49
43
37
37
49
49
49
49
46
46
41
38
34
31
28
0.25 0 0 1 2 4 8 13 17 22 26

16. Evaporation From Groundwater Sheet (m/day)
0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0 0 0
0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0 0 0
0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0 0.009 0.009
0 0 0 0 0 0 0.009 0.009 0.009 0.009 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0.009 0.009 0.009 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0.009 0.009 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0 0 0.009 0.009 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.009 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.009 0 0 0.009 0.009 0.009 0.009 0.009 0.009 0.009 0.009

17. Aquifer Bedrock Bathymetry
0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10
0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10
0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10
0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10 -10
0 0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10 -10
0 0 0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10 -10
0 0 0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10
0 0 0 0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10
0 0 0 0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10
0 0 0 0 0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10 -10 -10
0 0 0 0 0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10
0 0 0 0 0 0 0 0 0 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10
0 0 0 0 0 0 0 0 0 -25 -25 -10 -10 -10 -10 -10 -25 -25 -25 -25 -25 -25 -25 -25 -10
0 0 0 0 0 0 0 0 0 0 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -25 -25 -10
0 0 0 0 0 0 0 0 0 0 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -25 -25 -10
0 0 0 0 0 0 0 0 0 0 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -10 -25 -10 -10
0 0 0 0 0 0 0 0 0 0 -10 -10 -10 -10 -10 -10 -10 -10 -10 -25 -25 -25 -25 -10 -10
0 0 0 0 0 0 0 0 0 0 0 -10 -10 -10 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10
0 0 0 0 0 0 0 0 0 0 0 -10 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10 -10
0 0 0 0 0 0 0 0 0 0 0 -10 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10
0 0 0 0 0 0 0 0 0 0 0 -10 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -25 -10
0 0 0 0 0 0 0 0 0 0 0 -25 -25 -25 -25 -20 -20 -25 -25 -25 -25 -25 -10 -10 -10
0 0 0 0 0 0 0 0 0 0 0 -25 -25 -25 -20 -20 -20 -20 -25 -25 -25 -25 -10 -10 -10
0 0 0 0 0 0 0 0 0 0 0 -25 -25 -25 -20 -20 -20 -20 -25 -25 -25 -25 -10 -10 -10
0 0 0 0 0 0 0 0 0 0 0 -25 -25 -25 -20 -20 -20 -20 -20 -25 -25 -25 -25 -10 -10

18. Formulation of the Model Equation on
Spreadsheet

19.  
1 1
1 1 1 1, ,
, , , ,2 2
2 2 2 2
1, 1,2 2
1
1 1 1 1 1,
, , , , ,2
2 2 2 2 2
, 1 , 12 2
.
, , ,
. .
. .
f fi j i j
i j i j i j i j
f fi j i j
f i j
i j i j i j i j i j
f fi j i j
i j
i j i j f i j
K h Z K h Z
h h
x y
K h Z K h Z
h h
y y
W
R E R L B T h
x y
 
   
 

    
 
   
    
   
 
   
    
    
 
      
 
1
,
2
1, ,
1
, 1, ,
2
1 1, ,
,
2
2
1 1
0.5
0.5
i j
i j i j
f f fi j i j i j
i j i j
i j
K
K K
h h h
Z Z Z


 



 
 
  
   
   
1
switch
2
2
2
3
3
3
4
4
4
6
5
11
8 9
5 7
10
6
7
8
9
10
11

20. Excel Solver by Iteration

21. Spreadsheet Model Testing by Analytical
Solution
   
2 2
1 22
1( )
h h R
h x h x L x x
L K

   

22. Comparison of Fresh water Lens:
Numerical vs Analytical

23. Comparison of
Water Table
Elevations
A: Observations
B: Model Results

26. W= .5
m/day

27. Conclusions
• The results have shown that multiple spreadsheet modeling approach
are powerful, flexible, and a user-friendly tool in the simulation of
saltwater intrusion.
• The simulation is performed with one cell equation which is copied
on the entire region without performing sophisticated programming.
• The results are well presented with the built in graphical interface in
2D and 3D.
• Results can be converted to GIS softwares to be presented on base
maps.