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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
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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
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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
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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
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Principle of simulation : for one quadripole
Malmö, 2012
16-17 February
Electrical potential distributionCurrent density
• Evaluation of electrical potential on each electrode
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F3D-Lab Matlab/Comsol tools
Malmö, 2012
16-17 February
Import electrode coordinates Import quadrupoles file
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F3D-Lab Matlab/Comsol tools
Malmö, 2012
16-17 February
Model properties:-Cell size-Current in Amper-Mesh size
Electrode shape
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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
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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
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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
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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
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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
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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
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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
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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