VI EIEC, Chiclana, Spain An hp Fourier Finite Element (FFE) Framework with Electromagnetics and Multiphysics Applications D. Pardo, C. Torres-Verd´ ın, L.E. Garc´ ıa-Castillo, M. Paszynski, M.J. Nam October 23, 2008 Basque Center for Applied Mathematics (BCAM) Promoting Technological Advances Through Mathematics
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VI EIEC, Chiclana, Spain
An hp Fourier Finite Element (FFE) Framework withElectromagnetics and Multiphysics Applications
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo,M. Paszynski, M.J. Nam
October 23, 2008
Basque Center for Applied Mathematics (BCAM)Promoting Technological Advances Through Mathematics
OVERVIEW
1. Motivation: Waveguide Design and Oil-IndustryApplications.
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
FOURIER FINITE ELEMENT METHOD
A Self-Adaptive Goal-Oriented hp-FEMOptimal 2D Grid
(Through Casing Resistivity Problem)
p=1
p=2
p=3
p=4
p=5
p=6
p=7
p=8
ddd
We vary locally the element sizeh and the polynomial order ofapproximation p throughout thegrid.
Optimal grids are automaticallygenerated by the computer.
The self-adaptive goal-orientedhp-FEM provides exponentialconvergence rates in terms ofthe CPU time vs. the error ina user prescribed quantity ofinterest.
Basque Center for Applied Mathematics (BCAM)13
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
MULTIPHYSICS FRAMEWORK
Final hp-grid and solution
Basque Center for Applied Mathematics (BCAM)18
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem I: UNIFORM FORMATION
1 Ohm−m
z=0 mz=50 mTX(HED)
Basque Center for Applied Mathematics (BCAM)19
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem I: UNIFORM FORMATION — 0.25 Hz —
0 2000 4000 6000 8000 1000010
−17
10−16
10−15
10−14
10−13
10−12
10−11
10−10
10−9
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
Uniform Material, 0.25 Hz
1 MODE5 MODES9 MODESEXACT
0 2000 4000 6000 8000 10000−600
−500
−400
−300
−200
−100
0
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
Uniform Material, 0.25 Hz
1 MODE5 MODES9 MODESEXACT
Basque Center for Applied Mathematics (BCAM)20
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem I: UNIFORM FORMATION — 0.75 Hz —
0 2000 4000 6000 8000 1000010
−20
10−18
10−16
10−14
10−12
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
Uniform Material, 0.75 Hz
1 MODE5 MODES9 MODESEXACT
0 2000 4000 6000 8000 10000−1000
−900
−800
−700
−600
−500
−400
−300
−200
−100
0
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
Uniform Material, 0.75 Hz
1 MODE5 MODES9 MODESEXACT
Basque Center for Applied Mathematics (BCAM)21
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem I: UNIFORM FORMATION — 1.25 Hz —
0 2000 4000 6000 8000 1000010
−22
10−20
10−18
10−16
10−14
10−12
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
Uniform Material, 1.25 Hz
1 MODE5 MODES9 MODESEXACT
0 2000 4000 6000 8000 10000−1400
−1200
−1000
−800
−600
−400
−200
0
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
Uniform Material, 1.25 Hz
1 MODE5 MODES9 MODESEXACT
Basque Center for Applied Mathematics (BCAM)22
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem II: CSEM SCENARIO WITHOUT OIL
1 Ohm−m
0.3 Ohm−m
z=0 m
z=1000 m
z=50 m
10 Ohm−m
TX(HED)
6
Basque Center for Applied Mathematics (BCAM)23
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem II: WITHOUT OIL — 0.25 Hz —
0 2000 4000 6000 8000 1000010
−17
10−16
10−15
10−14
10−13
10−12
10−11
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
Without Oil, 0.25 Hz
1 MODE5 MODES9 MODESEXACT
0 2000 4000 6000 8000 10000−600
−500
−400
−300
−200
−100
0
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
Without Oil, 0.25 Hz
1 MODE5 MODES9 MODESEXACT
Basque Center for Applied Mathematics (BCAM)24
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem II: WITHOUT OIL — 0.75 Hz —
0 2000 4000 6000 8000 1000010
−20
10−18
10−16
10−14
10−12
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
Without Oil, 0.75 Hz
1 MODE5 MODES9 MODESEXACT
0 2000 4000 6000 8000 10000−800
−700
−600
−500
−400
−300
−200
−100
0
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
Without Oil, 0.75 Hz
1 MODE5 MODES9 MODESEXACT
Basque Center for Applied Mathematics (BCAM)25
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem II: WITHOUT OIL — 1.25 Hz —
0 2000 4000 6000 8000 1000010
−20
10−18
10−16
10−14
10−12
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
Without Oil, 1.25 Hz
1 MODE5 MODES9 MODESEXACT
0 2000 4000 6000 8000 10000−900
−800
−700
−600
−500
−400
−300
−200
−100
0
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
Without Oil, 1.25 Hz
1 MODE5 MODES9 MODESEXACT
Basque Center for Applied Mathematics (BCAM)26
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem III: CSEM SCENARIO WITH OIL
1 Ohm−m
1 Ohm−m
0.3 Ohm−m
100 Ohm−m
z=0 m
z=1000 m
z=−1000 m
z=−1100 m
z=50 m
10 Ohm−m6
TX(HED)
Basque Center for Applied Mathematics (BCAM)27
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem III: WITH OIL — 0.25 Hz —
0 2000 4000 6000 8000 1000010
−15
10−14
10−13
10−12
10−11
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
With Oil, 0.25 Hz
1 MODE5 MODES9 MODESEXACT
0 2000 4000 6000 8000 10000−180
−160
−140
−120
−100
−80
−60
−40
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
With Oil, 0.25 Hz
1 MODE5 MODES9 MODESEXACT
Basque Center for Applied Mathematics (BCAM)28
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem III: WITH OIL — 0.75 Hz —
0 2000 4000 6000 8000 1000010
−16
10−15
10−14
10−13
10−12
10−11
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
With Oil, 0.75 Hz
1 MODE5 MODES9 MODESEXACT
0 2000 4000 6000 8000 10000−350
−300
−250
−200
−150
−100
−50
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
With Oil, 0.75 Hz
1 MODE5 MODES9 MODESEXACT
Basque Center for Applied Mathematics (BCAM)29
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Model Problem III: WITH OIL — 1.25 Hz —
0 2000 4000 6000 8000 1000010
−17
10−16
10−15
10−14
10−13
10−12
10−11
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
With Oil, 1.25 Hz
1 MODE5 MODES9 MODESEXACT
0 2000 4000 6000 8000 10000−450
−400
−350
−300
−250
−200
−150
−100
−50
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
With Oil, 1.25 Hz
1 MODE5 MODES9 MODESEXACT
Basque Center for Applied Mathematics (BCAM)30
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
NO OIL
1 Ohm−m
0.3 Ohm−m
z=0 m
z=1000 m
z=50 m
10 Ohm−m
TX(HED)
6
Basque Center for Applied Mathematics (BCAM)31
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
INFINITE LAYER OF OIL
1 Ohm−m
1 Ohm−m
0.3 Ohm−m
100 Ohm−m
z=0 m
z=1000 m
z=−1000 m
z=−1100 m
z=50 m
10 Ohm−m6
TX(HED)
Basque Center for Applied Mathematics (BCAM)32
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
FINITE LAYER OF OIL
1 Ohm−m
0.3 Ohm−m
z=0 m
z=1000 m
z=−1000 m
z=−1100 m
z=50 m
100 Ohm−m
x=2000 m x=5000 m
1 Ohm−m 1 Ohm−m
10 Ohm−m6
TX(HED)
1 Ohm−m
Basque Center for Applied Mathematics (BCAM)33
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
FINITE LAYER OF OIL + ANISOTROPY
0.3 Ohm−m
z=0 m
z=1000 m
z=−1000 m
z=−1100 m
z=50 m
100 Ohm−m
x=2000 m x=5000 m
10 Ohm−m6
TX(HED)
1 Ohm−m
3 Ohm−m
1 Ohm−m
3 Ohm−m
3 Ohm−m 3 Ohm−m
1 Ohm−m 1 Ohm−m
Basque Center for Applied Mathematics (BCAM)34
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Comparison — 0.25 Hz —
0 2000 4000 6000 8000 1000010
−15
10−14
10−13
10−12
10−11
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
0.25 Hz
NO OILINFINITE LAYER OILFINITE LAYER OILANISOTROPY
0 2000 4000 6000 8000 10000−250
−200
−150
−100
−50
0
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
0.25 Hz
NO OILINFINITE LAYER OILFINITE LAYER OILANISOTROPY
The finite layer of oil is clearly identified, and it is different fr om thesolution for the infinite layer of oil. To consider anisotropy is e ssential.
Basque Center for Applied Mathematics (BCAM)35
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Comparison — 0.75 Hz —
0 2000 4000 6000 8000 1000010
−16
10−15
10−14
10−13
10−12
10−11
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
0.75 Hz
NO OILINFINITE LAYER OILFINITE LAYER OILANISOTROPY
0 2000 4000 6000 8000 10000−450
−400
−350
−300
−250
−200
−150
−100
−50
0
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
0.75 Hz
NO OILINFINITE LAYER OILFINITE LAYER OILANISOTROPY
As we increase the frequency, the effect of oil becomes morelocalized.
Basque Center for Applied Mathematics (BCAM)36
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM
Comparison — 1.25 Hz —
0 2000 4000 6000 8000 1000010
−18
10−17
10−16
10−15
10−14
10−13
10−12
10−11
10−10
Am
plitu
de o
f Ele
ctric
Fie
ld (
V/(
A m
2 )
Horizontal Distance between TX and RX (m)
1.25 Hz
NO OILINFINITE LAYER OILFINITE LAYER OILANISOTROPY
0 2000 4000 6000 8000 10000−600
−500
−400
−300
−200
−100
0
Pha
se o
f Ele
ctric
Fie
ld (
degr
ees)
Horizontal Distance between TX and RX (m)
1.25 Hz
NO OILINFINITE LAYER OILFINITE LAYER OILANISOTROPY
As we increase the frequency, the effect of oil becomes morelocalized.
Basque Center for Applied Mathematics (BCAM)37
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM0.75 Hz (FINITE LAYER OF OIL)
TX: x = 0 m ; RX: x = 2000 m.
Basque Center for Applied Mathematics (BCAM)38
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM0.75 Hz (FINITE LAYER OF OIL)
TX: x = 0 m ; RX: x = 5000 m.
Basque Center for Applied Mathematics (BCAM)39
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 2D MARINE CSEM0.75 Hz (FINITE LAYER OF OIL)
TX: x = 0 m ; RX: x = 8000 m.
Basque Center for Applied Mathematics (BCAM)40
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Model Problem
0.05 m
mΩ .
0.2
5 m
1.0
m
150 kHz (Wireline)
Fiber Glass Mandrel
Mandrel Radius: 0.04 m
105
Finite SizeLoop Antenna
mΩ .
mΩ .
mΩ .
mΩ .
mΩ .
mΩ .
mΩ .
mΩ .20
mΩ .30mΩ .50
Oil−Based M
ud (1000 m)
1.5 m
Ω
.
0.5 m0.65 m
3 m
SHALE
SAND
SANDSAND
SAND
OIL
SHALE
3
200.05
0.1
100
1
1
4 m
Anisotropy (10:1)
Anisotropy (10:1)
Anisotropy (10:1)
Anisotropy (8:1)
Basque Center for Applied Mathematics (BCAM)41
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Verification
Logging Instrument in a Homogeneous Formation
10−2
100
102
−6
−4
−2
0
2
4
6
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−0.02 −0.01 0Imag Part (V/m)
1 1
Basque Center for Applied Mathematics (BCAM)43
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Verification
Logging Instrument in a Homogeneous Formation
10−2
100
102
−6
−4
−2
0
2
4
6
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
13
13
Basque Center for Applied Mathematics (BCAM)43
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Verification
Logging Instrument in a Homogeneous Formation
10−2
100
102
−6
−4
−2
0
2
4
6
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
135
135
Basque Center for Applied Mathematics (BCAM)43
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Verification
Logging Instrument in a Homogeneous Formation
10−2
100
102
−6
−4
−2
0
2
4
6
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
1359
1359
Basque Center for Applied Mathematics (BCAM)43
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Verification
Logging Instrument in a Homogeneous Formation
10−2
100
102
−6
−4
−2
0
2
4
6
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
135913
135913
Basque Center for Applied Mathematics (BCAM)43
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Dip Angle
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
0 degrees30 degrees60 degrees
0 degrees30 degrees60 degrees
Basque Center for Applied Mathematics (BCAM)44
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Dip Angle + Invasion
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
0 degrees30 degrees60 degrees
0 degrees30 degrees60 degrees
INVASION
NO INVASION
Basque Center for Applied Mathematics (BCAM)45
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Dip Angle + Anisotropy
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
0 degrees30 degrees60 degrees
0 degrees30 degrees60 degrees
VERT. ρ
HORIZ. ρ
Basque Center for Applied Mathematics (BCAM)46
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Dip Angle + Invasion + Anisotropy
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
0 degrees30 degrees60 degrees
0 degrees30 degrees60 degrees
INVASION
NO INVASION
VERT. ρ
HORIZ. ρ
Basque Center for Applied Mathematics (BCAM)47
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
60-Degree Deviated Well
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
NO INV.NO INV + ANI.INVINV + ANI
NO INV.NO INV + ANI.INVINV + ANI
INVASION
NO INVASION
VERT. ρ
HORIZ. ρ
Basque Center for Applied Mathematics (BCAM)48
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Vertical Well with 0.03 m Eccentricity
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−2 −1 0 1
x 10−3
Wireline, 150 Khz
Real Part (V/m)
−3 −2 −1 0
x 10−3Imag Part (V/m)
NO INV.NO INV + ECC.INVINV + ECC
NO INV.NO INV + ECC.INVINV + ECC
INVASION
NO INVASION
Basque Center for Applied Mathematics (BCAM)49
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Model Problem and Verification
Ω . mµr
µr
Ω . m
0.25
m
0.15 m
0.05 m0.1 m
0.7
m
Magnetic Buffer:
=10000=10000ρ
Metallic Mandrel:ρ =10
−5
=50
Loop AntennaFinite Size
1 3 5 7 910
−2
10−1
100
101
102
LWD PROBLEM (30 degrees)
Number of Fourier Modes
Re
lative
Err
or
(in
%)
Basque Center for Applied Mathematics (BCAM)50
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Dip Angle
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−0.4 −0.2 0 0.2
LWD, 2 Mhz
Real Part (V/m)
−0.4 −0.2 0 0.2Imag Part (V/m)
0 degrees30 degrees60 degrees
0 degrees30 degrees60 degrees
Basque Center for Applied Mathematics (BCAM)51
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Dip Angle + Invasion
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−0.4 −0.2 0 0.2
LWD, 2 Mhz
Real Part (V/m)
−0.4 −0.2 0 0.2Imag Part (V/m)
0 degrees30 degrees60 degrees
0 degrees30 degrees60 degrees
INVASION
NO INVASION
Basque Center for Applied Mathematics (BCAM)52
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Dip Angle + Anisotropy
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−0.4 −0.2 0 0.2
LWD, 2 Mhz
Real Part (V/m)
−0.4 −0.2 0 0.2Imag Part (V/m)
0 degrees30 degrees60 degrees
0 degrees30 degrees60 degrees
VERT. ρ
HORIZ. ρ
Basque Center for Applied Mathematics (BCAM)53
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
Dip Angle + Invasion + Anisotropy
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−0.4 −0.2 0 0.2
LWD, 2 Mhz
Real Part (V/m)
−0.4 −0.2 0 0.2Imag Part (V/m)
0 degrees30 degrees60 degrees
0 degrees30 degrees60 degrees
INVASION
NO INVASION
VERT. ρ
HORIZ. ρ
Basque Center for Applied Mathematics (BCAM)54
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
RESULTS: 3D RESISTIVITY LOGGING
60-Degree Deviated Well
10−2
100
102
−6
−4
−2
0
2
4
6
8
10
Resistivity (Ω−m)−0.4 −0.2 0 0.2
LWD, 2 Mhz
Real Part (V/m)
−0.4 −0.2 0 0.2Imag Part (V/m)
NO INV.NO INV + ANI.INVINV + ANI
NO INV.NO INV + ANI.INVINV + ANI
INVASION
NO INVASION
VERT. ρ
HORIZ. ρ
Basque Center for Applied Mathematics (BCAM)55
For more info, visit: www.ices.utexas.edu/ ∼pardo
D. Pardo, C. Torres-Verdın, L.E. Garcıa-Castillo, M. Pasz ynski, M. J. Nam 23 Oct 2008
CONCLUSIONS AND FUTURE WORK
• A Fourier-Finite-Element method provides a suitable formulation forsimulation of resistivity geophysical applications.
• Goal-oriented refinements are essential in marine CSEM geophysi calapplications due to the dissipative nature of the earth.
• A parallel implementation based on a shared domain-decompositi on issimple and provides additional performance for a moderate num ber ofprocessors.
• We are developing a multiphysics framework for the joint-inversi on ofmultiphysics measurements.
• We are looking for Ph.D. students and postdoctoral fellows to furthe rdevelop this software and work on the joint-inversion of multiphysi csmeasurements.