www.irstea.fr

Pour mieux affirmer ses missions, le Cemagref devient Irstea

R. Clément & S. Moreau

Second workshop on geophysical measurementsin waste managementMalmö, 16-17 February, 2012

Geo-electrical forward Modelling Using Comsol

Multiphysics For Laboratory Simulation

2

Malmö, 2012

16-17 February

Introduction�Before carrying out laboratory survey, metrological evaluation of resistivity device and inversion tools is necessary:

– For resistivity measurement, several parameters can impact the apparent resistivity value at lab-scale:

» Electrodes shape» Electrode position» Surface of electrodes in waste» Size of cell» Impedance effect» Contact resistance

– Geometric factors can be calculated for complex geometry of quadrupoles

– For resistivity Inversion, parameters have to be studied to increase confidence on inversion algorithm

We have selected Comsol Multiphysics

Clement et al., 2011

3

Comsol Multiphysics

Malmö, 2012

16-17 February

The advantage of COMSOL Multiphysics:

� Flexible platform for modelling physical simulation� Design of complex geometries�Combination with Matlab for developing specific tools.

For Electrical Resistivity Tomography

� Electric field distributions can be modelled using full 3D modelling � The potential difference due to injected current can be evaluated� Different resistivity distributions can be tested

4

Principle of Comsol electric current simulation

Malmö, 2012

16-17 February

Use of continuity equation and ohm law’s (stationnary system)

jQJ =⋅∇

Electric insulation on all boundary

0=⋅− Jn

Application of external current density on two electrodes

eJJn =⋅−

jQ Charge density in C.m-3

J Current density in A.m-2

eJ External Current density in A.m-2

eJEJ +⋅= σ

E Electrical field

5

Principle of simulation : for one quadripole

Malmö, 2012

16-17 February

Electrical potential distributionCurrent density

• Evaluation of electrical potential on each electrode

6

F3D-Lab Matlab/Comsol tools

Malmö, 2012

16-17 February

Import electrode coordinates Import quadrupoles file

7

F3D-Lab Matlab/Comsol tools

Malmö, 2012

16-17 February

Model properties:-Cell size-Current in Amper-Mesh size

Electrode shape

8

F3D-Lab Matlab/Comsol tools

Malmö, 2012

16-17 February

Calculating geometric factor for homogenous media (20ohm.m)

• Attribute resistivity distribution• Estimating apparent resistivity for different resistivity distributions:

- homogenous- anisotropic- variable resistivity

9

Malmö, 2012

16-17 February

F3D_lab vers.2.06ParametersModel name:remElectrodes number:16High:170Raduis:75Mesh:5Adapted resistivity:Amper:1Electrode embbed:1.000000e-002Electrodes coordinates1-4.479352e-002 -5.379164e-002 1.568400e-0012 -5.392455e-002 4.463343e-002 1.562000e-0013 4.281484e-002 5.537951e-002 1.564800e-00145.648461e-002 -4.134596e-002 1.562800e-0015 -4.516836e-002 -5.347728e-002 1.166400e-0016 -5.352338e-002 4.511372e-002 1.146800e-0017 4.175414e-002 5.618356e-002 1.151800e-0018 5.636874e-002 -4.150380e-002 1.159000e-0019 -4.572091e-002 -5.300564e-002 6.186000e-00210 -5.457711e-002 4.383308e-002 6.118000e-00211 4.260606e-002 5.554029e-002 6.220000e-00212 5.565916e-002 -4.245066e-002 6.118000e-00213 -4.516836e-002 -5.347728e-002 3.048000e-00214 -5.431846e-002 4.415320e-002 3.036000e-00215 4.218352e-002 5.586189e-002 3.042000e-00216 5.636874e-002 -4.150380e-002 3.048000e-002

A B M N Vm Vn DVmn i 1 13 5 9 -3.531612e+002 3.234354e+002 -6.765966e+002

Example: file with all conditions of the test

Model information

Electrodes coordinates

Quadripole information

10

F3D-Lab Matlab/Comsol tools

Malmö, 2012

16-17 February

Options:

• Save/load configuration

• Combining with hydrodynamical processes with other Comsol tools box

• Analysis of mesh quality and automatic mesh adaptation

• Add option: impedance, contact resistance

11

Result 1: Comparison of geometric factors between measurements and simulation

Malmö, 2012

16-17 February

F3D-lab modeling

Laboratory test cell

variations between -5% and 5%

cell 3cell 4cell 7cell 8

quadrupoles

12

result 2: Comparison between point electrode and complete electrode

Malmö, 2012

16-17 February

electrical potential in V: complete electrode electrical potential in V: point current source

current density: complete electrode current density : point current source

Find an equivalent point positionfor inversion procedure

13

Result 3: Evaluation of inversion process

Malmö, 2012

16-17 February

Bulk resistivity and geometry of numerical laboratory cell

Resistivity in ohm

.m

Resistivity of the cell cylinder

Resistivity of the cylinderInside the cell

Resistivity of the electrodes

14

Result 3: Evaluation of inversion process

Malmö, 2012

16-17 February

• λ = 30 • Z-weight=1• RMS = 3.22 %• Rho min = 23 Ohm.m• Rho max= 133 Ohm.m

Inversions with BERT (Gunther et al; 2007)

• λ = 200 • Z-weight=1• RMS = 2.99 %• Rho min = 23 Ohm.m• Rho max= 129 Ohm.m

• λ = 20 • Z-weight=1•Blocky option• RMS = 3.22 %• Rho min = 23 Ohm.m• Rho max= 101 Ohm.m

15

Conclusions - Perspectives

Malmö, 2012

16-17 February

Field scale modelling is in hand:� Introduction of topography� Introduction of insulating barriers� optimisation of inversion parameters

Modelling of others geophysical methods is imagined (TDEM, EM).

Combination of hydrodynamic modelling and geophysical modelling is studied

Qualification of electrical resistivity measurements in 2D and 3D is available with Comsol Multiphysics to improve the confidence in the geophysical method

Simulation of electric field distributions in insulating and in infinite structure is possible

The optimisation of the different parameters of inversion software could be done