modeling saltwater intrusion along jeddah coast using multiple spreadsheets

Modeling Saltwater Intrusion along

Jeddah Coast Using Multiple

SpreadsheetsBy

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 University2 Faculty of Engineering Mansoura University, Egypt

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.

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.

Spreadsheet Modeling• This study is an extension of the spreadsheet Model called “GWMAP”

developed by the authors:

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.

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

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.

Conceptual Model

Mathematical Model

Fresh Water Model

Salt Water Model

1: at the interface

0

2 : after the interface toe

0

f ff f

f ff f

Zone

h hK h K h R E Wx x y yZone

h hK h Z K h Z R E Wx x y y

f s f

approximation(1 )

= /( )f s

Geyben Herzbergh h

Finite Difference Model

1 11 1 1 1, ,, , , ,2 22 2 2 21, 1,2 2

1 11 1 1 1, ,, , , ,2 22 2 2 2, 1 , 12 2

., , ,

. .

. .

f f

f fi j i ji j i j i j i j

i j i j

f fi j i ji j i j i j i j

f fi j i j

i ji j i j i j

K h Z K h Zh h

x y

K h Z K h Zh h

y yW

R E R L B T hx y

jiji

ji

KK

K

,,1

,21

112

1, 1, ,2

0.5f f fi j i j i jh h h

jijijiZZZ ,,1,

21 5.0

Groundwater Levels (m) on Spreadsheet

Graphical Representation of GWL Map

Permeability Spatial Distribution on Spreadsheet

(m/day)

Sewage Discharge (L/day/person)

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

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

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

Formulation of the Model Equation on Spreadsheet

1 11 1 1 1, ,, , , ,2 22 2 2 21, 1,2 2

11 1 1 1 1,, , , , ,22 2 2 2 2, 1 , 12 2

., , ,

. .

. .

f fi j i ji j i j i j i j

f fi j i j

f i ji j i j i j i j i j

f fi j i j

i ji j i j f i j

K h Z K h Zh h

x y

K h Z K h Zh h

y yW

R E R L B T hx 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 ji j

K

K K

h h h

Z Z Z

1switch

2

2

2

3

3

3

4

4

4

6

5

11

8 9

5 7

10

67

8

910

11

Excel Solver by Iteration

Spreadsheet Model Testing by Analytical Solution

2 2

1 221( )

h h Rh x h x L x xL K

Comparison of Fresh water Lens: Numerical vs Analytical

Comparison of Water Table Elevations

A: Observations

B: Model Results

W= .5 m/day

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.