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Addis Ababa 14.10.2013
Derivation of simple hydrogeological
models created on the basis
of hydrogeological maps, parallel flow
Simple calculations of groundwater flow
in EXCEL, testing of key parameters
Computation of groundwater flow
Ondrej Nol
Addis Ababa 14.10.2013
1. Case problem – introduction to the
hydrogeological problem;
2. Dupuit aassumptions and derivation of governing
equation; Determination of boundary conditions
and resulted equations;
3. Derivation key input data from explanatory notes:
hydraulic heads, hydraulic gradient, hydraulic
conductivity, aquifer base, aquifer thickness and
aquifer width.
Content:
Addis Ababa 14.10.2013
4. Estimations of groundwater volume flowing
through the aquifer for given hydraulic
conductivity, water saturation and aquifer
geometry, Calibration;
5. Comparisons of groundwater flow derived from
different approaches;
6. Discussions, uncertainity;
7. Evaluation of quality.
Computation of groundwater flow
Content:
Addis Ababa 14.10.2013
Addis Ababa 14.10.2013
Asela sheet
Addis Ababa 14.10.2013
Contents
Addis Ababa 14.10.2013
Annexes
Addis Ababa 14.10.2013
Page 18
Addis Ababa 14.10.2013
Asela sheet
Dodola sheet
Addis Ababa 14.10.2013
Weyb River
Addis Ababa 14.10.2013
Weyb River
Addis Ababa 14.10.2013
Direction of ground
water flow
Weyb River
Addis Ababa 14.10.2013
Page 104
Addis Ababa 14.10.2013
Annex No. 1 Borehole inventory (Part 2)
Addis Ababa 14.10.2013
Annex No. 1 Borehole inventory (Part 2)
Addis Ababa 14.10.2013
Width = 5 km
Length = 27 km
Addis Ababa 14.10.2013
For unconfined ground water flow Dupuit developed a
theory that allows for a simple solution based of the
following assumptions:
1) The water table or free surface is only
slightly inclined
2) Streamlines may be considered horizontal
and equipotential lines, vertical
3) Slopes of the free surface and hydraulic
gradient are equal
Dupuit Assumptions:
Computation of groundwater flow
Addis Ababa 14.10.2013
Derivation of the Dupuit Equation - Unconfined Flow
Computation of groundwater flow
0))((
dx
xqd
Addis Ababa 14.10.2013
Derivation of the Dupuit Equation - Unconfined Flow
Computation of groundwater flow
dhxkhqdx )(
cxh
kqx 2
)( 2h(x)
dx
dhkq
Addis Ababa 14.10.2013
Derivation of the Dupuit Equation - Unconfined Flow
Computation of groundwater flow
cxh
kqx 2
)( 2
cH
kq 2
002
1
cH
kqL 2
2
2
22
2
2
2
1 Hk
HkqL
L
HHkq
2
2
2
2
1 h(0)=H1
h(L)=H2
Addis Ababa 14.10.2013
For given one-dimensional
flow yields:
Computation of groundwater flow
k
xqHxh
2)( 2
2
However, this example does not
consider recharge to the aquifer.
Addis Ababa 14.10.2013
Well siting strategy
Inflow hydral. Head H1 is known, no infiltration
Addis Ababa 14.10.2013
Derivation of the Dupuit Equation - Infiltration
Computation of groundwater flow
h(x)dx
dhkq 0
))(( e
dx
xqd
Addis Ababa 14.10.2013
Derivation of the Dupuit Equation - Infiltration
Computation of groundwater flow
0*)( 1 cxexhdx
dhk
0**2
1
2
)(21
22
ccxxexh
k
2
2
1
20 c
Hk
2
2
12
Hkc
02
**2
1
2
2
11
22
2 H
kcLLeH
k LeL
Hk
L
Hkc *
2
1
22
2
1
2
21
02
*2
1
22**
2
1
2
)(2
1
2
1
2
222
HkLe
L
Hk
L
Hkxxe
xhk
2
1
2
1
2
222 *1
**)( HLekL
H
L
Hxx
k
exh
h(0)=H1
h(L)=H2
Addis Ababa 14.10.2013
Derivation of the Dupuit Equation - Infiltration
Computation of groundwater flow
0*)( 1 cxexhdx
dhk Le
L
Hk
L
Hkc *
2
1
22
2
1
2
21
1*)( cxexq
Leqxexq *2
1*)(
Leqc *2
11
Addis Ababa 14.10.2013
-100
0
100
200
300
400
500
600
700
0 3000 6000 9000 12000 15000 18000 21000 24000 27000 30000
GWL
GWL (with infiltration)
Terrain
Addis Ababa 14.10.2013
Page 122
Addis Ababa 14.10.2013
Page 117
Annex No. 2 Chemical
analyses data in mg/l (Part 1)
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