55606704 Hydraulic Modelling 2006

Course Hydraulic Modelling; Granada 2006 by C. Kohfahl

BooksGroundwater in general:Freeze, R. A., Cherry, J. A.: Groundwater. Prentice-Hall, Englewood Cliffs 1979.De Marsily, G.: Quantitative Hydrogeology-Groundwater Hydrology for Engineers. AcademicPress, Orlando 1986.Bear, J.: Hydraulics of Groundwater. McGraw-Hill Series in Water Resources and Environmental Engineering, New York 1979. Bear, J.: Dynamics of Fluids in Porous Media. Dover Publications, New York 1972.Modelling of groundwater flow:Anderson, M. P., Woessner, W. W.: Applied Groundwater Modeling - Simulation of Flowand Advective Transport. Academic Press, San Diego 1992.Chiang, W.-H., Kinzelbach, W., Rausch, R.: Aquifer Simulation Model for Windows -Groundwater flow and transport modeling, an integrated program. Gebrüder Borntraeger,Berlin Stuttgart 1998.Manual of simulator ASM for Windows.Chiang, W.-H., Kinzelbach, W.: 3D-Groundwater modeling with PMWIN: a simulation systemfor modeling groundwater flow and pollution. Springer-Verlag Berlin HeidelbergNew York 2001.Manual of PMWIN 5.0 for windows.Strack, O. D. L.: Groundwater Mechanics. Prentice-Hall, Englewood Cliffs 1989.Focus of analytical solutions for groundwater flow.

Literature


Why modelling?

1. as realization of a conceptual model (tool for understanding)

2. to calculate field data

3. to predict future developments (prognostic purpose)


Classification of models

physical/chemical classificationhydraulic modeling: saturated/unsaturated, one-phase/ multiphase (for example water and oil).transport modeling (dispersion, advection)geochemical modelling (PHREEQC, WATEQ, COTRAM etc.)Combination of the former points

Classification by dimensions1 D 2-D (horizontal, vertical)3-Dquasi 3-D

Classification by algorithm Analytical methodsFinite differences Finite elements


Software

Processing modflowAuthors: Wen-Hsing Chiang +Wolfgang Kinzelbach; interface between MODFLOW; PMPATH, MT3D, PEST and windows in the beginning of the 90th. Modflow versions (without changes in modeling groundwater flow): modflow 83 (Fortran 66)modflow 88 (Fortran 77)modflow 96modflow 2000

MODFLOW :developed by McDonald und Harbaugh (1988) at U. S. Geological Survey.. Why Processing Modflow?-worldwide use-pmwin can be downloaded for free

download Processing modflow, Vers. 5.3: www.pmwin.net/

http://www.pmwin.net/


More software

FEFLOW Finite Element codes

SUTRA density driven flow, saturated-unsaturated flow)

GMS

interface for Finite differences and Finite Element codes

Rockflow

Finite Element code developed for hard rock aquifers

(only flow and transport)

Finite Elements

Finite Differences: Visual Modflow

Analytical solutions: Twodaen


So nowhands on

Processing Modflow


Boundary conditions

Type Name Variable

1st Dirichlet hydraulic head (h)

2nd Neumann flux (q)

3rd Cauchy flux as function of hydraulic gradient

Dirichlet: where measurements of h are available (lakes, boreholes, rivers, shoreline etc.)

Neumann: where measurements of q are available (wells, recharge etc.)

Cauchy:surface water with bad hydraulic contact to groundwater for example river with colmated river-bed


Modflow algorithm for calculation of in/exfiltration:if hgroundwater>hriver: q= Leakage *(hriver – hgroundwater)

if hgroundwater<hriver: q= Leakage *(hriver - hriverbed)

hriver

hgroundwater

colmation

hriverbed

q


Example Cauchy boundary

Calculate the 3rd - boundary flux in cell by hand:

Conductivity of colmation layer: 1e-7 m/svertical thickness of colmation layer: 0.6 mriver head: 107.4 maslgroundwater head: 105 m aslriver bottom: 106 m aslcell length: 100 mcell width: 30 mlength of river in the cell: 180 mwidth of river: 25 m


Some questionsAnswer these questions with (i), (ii) or (iii)

1.) Which type of boundary in PMWIN is applied by defining IBOUND=-1?Dirichlet (i), Neumann (ii) or Cauchy (iii)?

2.) Which type of boundary is a no-flow boundary?Dirichlet (i), Neumann (ii) or Cauchy (iii)?

3.) Which is the default boundary condition in PMWIN?Dirichlet (i), Neumann (ii) or Cauchy (iii)?

4.) Coordinate the following hydrogeological features to its corresponding boundary condition Genil river ( ), Playa lake Fuente de Piedra ( ), Canales reservoir ( ), Mediterranean Sea ( ), springs ( ), Rain ( )


First Example with Processing Modflow

Set up a model to simulate groundwater flow in an aquifer for the following conditions

unconfined aquifer with a vertical thickness of 75 m and hydraulic conductivity of 1e-4 m/s;aquifer top 150 masl); recharge: 40 mm/a

impermeable paleozoic rocks

Miocene marls (recharge = 80 mm/a);

riverriver head: 134 maslriv. bottom 125 maslKf colmation zone: 1e-6 m/svert. thickness colm. zone: 0.7 mwidth of river: 12 m

Lake (124 masl)

5 km

0.5 km

water divide

2 km


Water budget

Calculate the water budget of your model


Applications of Cauchy boundary-General head boundary-

30 km

Problem area = model area?

Granites

Granites

fixed b

ou

nd

ary

L=28 km

Qb = K*A*I= K*A*(hb-h)/L

h

hb


Example General Head boundary in Processing Modflow

42 km

river head =720 m

T = 0.01 sqm /sthickness =10 m

confined, homogeneous and isotropic aquifer

river head =634 m

eastern model boundary(at 2 km from western river)

5km


Flow equation (1-dim)

dydzdtdxqx

qx

x

dxdydzx

hKdxdydz

xxh

Kdxdydz

x

q

t

V x2

2

dxdydzdtmassx

qx

Change of mass = mass outflow – mass inflow

Mass inflow Mass outflow

divide by density and time

dydzdtqx


Recombination of S in flow equation gives

dxdydzdt

dhS

dt

dV

dhdxdydz

dVSs

Introduce specific yield S

dxdydzx

hKdxdydz

t

hS

t

V

2

dt

dhS

z

hKz

y

hKy

x

hKx

2

2

2

2

2

2

In 3 dimensions (with dx=dy=dz=1)


t

hSKKK s

z

hz

y

hy

x

hx

2

2

2

2

2

2

Method of Finite Differences

Example: Simplification of the flow equation to 1 dimension, steady state and homogeneous and isotrope permeabilities

2,1,,1

,1,,,1

20

xxh

2x

h2

x

hhh

xxhh

xhh

jijiji

jijijiji

jijiji hhh ,1,,1 20


jijiji hhh ,1,,1 20 Resolve for hi,j at all points simultaneously

Exercise:

Open iteration_e.xls and see how the Finite difference method can be implemented in excel


Geotechnical applicationFlow Net and (pmwin manual example 6.5.2 Seepage under a Weir)

An impervious weir is partially embedded in a confined aquifer. The aquifer is assumed to be homogeneous with a hydraulic conductivity of the aquifer of 0.0005 m/s and a thickness of 9 m. The effective porosity of the aquifer is 0.15. The boundary conditions are shown in the figure below. Calculate the flow net and the flux through the aquifer for the cases that (1) the aquifer is isotropic and (2) the aquifer is anisotropic with an anisotropy factor of 0.2.

70 m


Partickle TrackingSimulation of advective transport

Application:calculation of isochrones (waterworks, contamination zones)-calculation of capture zone-calculation of flow-paths-calculation of velocitiy-fields along pathlines as for geochemical modeling

Proceeding:1.Calculation of the hydraulic potentials with a groundwater model (steady state ot transient)2.Calculation of particle tracking with the known velocity field of the simulation resultSolution algorithm-Euler algorithm-Runge Kutta-etc.


tvxvt

xv

t

xxxx

y-directionanalog in z-directionProblem: selection of timestep sufficiently small, so that the endpoint of the particle in a certain timestep remains in the same cell.

tvyvt

yv

t

yyyy

Concept of Euler algorithmcalculation of basic vectors in x,y,z directions evaluating the velocity at the startpoint in the cellbasic equation: Darcy q= K*I; v=q/n=K*I/n

x

y

startpoint


So nowcheck pathline options in

Processing Modflow


Example for application of particle tracking

Calculation of water protection areas In Germany for many waterworks water protection zones are defined in which industrial and agricultural activities are more restricted. Three types of protection areas have to be calculated:

Zone I: immediate surroundings of the well (10 m)Zone 2: 50 d-isochroneZone 3 capture zone or 30 a-isochrone

Calculate zone II and III for the following hydrogeologic conditions by particle tracking: steady state conditions


Aquifer Data:homogeneous unconfined aquifer (K = 2*10E-04 m/s)aquifer thickness: 30 m, aquifer top 30 m, bottom 0 m, porosity: 0,2 length and width of model: 3 kmboundaries in the east and west: river with good hydraulic connection to the aquifer,river-heads: east=22 m, west=28 m, distance between rivers 3 km

TasksModel this situation and write out the total balance of all fluxes -Calculate the travel time through the model by hand with the Darcy-equation-Prove your results by starting particles along the west boundary-Complete your model by a water work with 3 evenly distributed wells at 700 meters from the eastern boundary. Qtotal: 6000 m3/d. -Calculate capture zone of wells -Calculate isochrones: 10a, 50 a

Example particle tracking


ikM

QY

f

wellwidth

2

Check the width of your capture zones with analytical formula


Transient groundwater flow

t

hSKKK s

z

hz

y

hy

x

hx

2

2

2

2

2

2

transient conditions

steady state conditions

02

2

2

2

2

2

z

hz

y

hy

x

hx KKK


Examples of transient conditions

almost everything is transient !!

-wells

-recharge

-surface water levels

-springs


Storage coefficient

1 m

1 m

2

3

mm

LwaterS

unconfined aquifer: S = eff. porosityconfined aquifer: S < 1e-3


Storage coefficient in Processing Modflow

specific yield [-]: storage coefficient for unconfined aquifers(equals porosity)

specific storage [1/L]: storage coefficient for confined aquifers normalised to 1 m thickness

storage coefficient [-]: storage coefficient for confined aquifers = specific storage x layer thickness


Aquifer types in Processing modflow

Type 2A layer of this type is partially convertible between confined and unconfined. Confined storage coefficient (specific storage × layer thickness) is used to calculated the rate of change in storage, if the layer is fully saturated, otherwise specific yield will be used. Transmissivity of each cell is constant throughout the simulation. Vertical leakage from above is limited if the layer desaturates.

Type 3A layer of this type is fully convertible between confined and unconfined. Confined storage coefficient (specific storage × layer thickness) is used to calculate the rate of change in storage, if the layer is fully saturated, otherwise specific yield will be used. During a flow simulation, transmissivity of each cell varies with the saturated thickness of the aquifer. Vertical leakage from above is limited if the layer desaturates.


Example Transient modelling-Simulation of a planned open cast mining site-

Your task is to1. construct a steady-state flow model and calculate the necessary

abstraction rate (= inflow into the mining site) for holding the head at 550 m, and

2. use the calculated steady-state head as the initial hydraulic head and calculate the temporal development in the artificial lake for the case that the abstraction within the mining site is turned off.

Data: aquifer length and width = 6 km, aquifer top 650 masl, aquifer bottom 500 masl, Kf =4.e-04, storage coefficient =0.25; northern and southern boundaries are no flow boundaries, western and eastern boundaries are rivers with river heads of 620 and 650 masl respectively. In the final mining phase, the hydraulic head within the mining site (extension=700 x 700 m) must be drawn down at the level of h = 21 m. Afterwards, the mining site will be filled with water to form an artificial lake.


CalibrationFunction and aim of model calibrationComparing and adjusting calculated and measured values by changing flow parameters (for example adjusting measured and calculated hydraulic heads by adapting kf-values of the aquifer)information about reliability of the modelTypes of calibrationsteady statetransientmanualautomatic (Pest, Ucode)calibration parametersin general the most unknown parameters; normally permeabilities and leakage is not known very well; often better information of recharge existsfitted parametershydraulic headsflow directonsflow velocitieswater budget


P2

P1-isoline

: sum of differences between calculated and measured values (has to be minimized)

P1,P2: Calibration parameters


PEST termination criteria:

•relative change of in defined number of iterations•change of parameter value is too small•more than a defined number of iterations without optimation have been done•more than a defined number of iterations have been executed


Question

Do you believe in a model with perfectly fitted hydroisolines?


Calibration example-Estimation of pumping rates for remediation measures-

Hydrogeological data:Dimension of contaminated site = 65 x 65 m, K=3e-04 m/s, specific yield = 0.2,groundwater flow is from west to east with a gradient of 0.005. see pmwin manual chap. 6.4.2

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55606704 Hydraulic Modelling 2006

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