derivation of simple hydrogeological models …addis ababa 14.10.2013 derivation of simple...

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


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:


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.


Content:


Asela sheet


Contents


Annexes


Page 18


Asela sheet

Dodola sheet


Weyb River


Direction of ground

water flow

Weyb River


Page 104


Annex No. 1 Borehole inventory (Part 2)


Width = 5 km

Length = 27 km


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:



Derivation of the Dupuit Equation - Unconfined Flow


0))((

dx

xqd




dhxkhqdx )(

cxh

kqx 2

)( 2h(x)

dx

dhkq




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


For given one-dimensional

flow yields:


k

xqHxh

2)( 2

2

However, this example does not

consider recharge to the aquifer.


Well siting strategy

Inflow hydral. Head H1 is known, no infiltration


Derivation of the Dupuit Equation - Infiltration


h(x)dx

dhkq 0

))(( e

dx

xqd




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




0*)( 1 cxexhdx

dhk Le

L

Hk

L

Hkc *

2

1

22

2

1

2

21

1*)( cxexq

Leqxexq *2

1*)(

Leqc *2

11


-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


Page 122


Page 117

Annex No. 2 Chemical

analyses data in mg/l (Part 1)

derivation of simple hydrogeological models …addis ababa 14.10.2013 derivation of simple...

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