Numerical modeling of the electromagnetic coupling effects for phase error correction in EIT borehole measurement Y Zhao 1, E Zimmermann 1, J A Huisman.

Numerical modeling of the electromagnetic coupling effects for phase error correction

in EIT borehole measurementY Zhao1, E Zimmermann1, J A Huisman2, A Treichel2, B Wolters1, S van Waasen1, A Kemna3

1Central Institute ZEA-2 – Electronic Systems, Forschungszentrum Jülich GmbH, Germany2Institute of Bio- and Geosciences (IBG-3), Forschungszentrum Jülich GmbH, Germany

3Department of Geodynamics and Geophysics , University of Bonn, Germany

Yulong Zhao

Dipl.- Ing.

ZEA-2 Electronic Systems

Forschungszentrum Jülich

Tel: +49 2461 614323

Email: [email protected]

• Introduction

• Objective of this work

• Inductive coupling effect

• Capacitive coupling effect

• Results

• Summary

Overview

Introduction

iel surf surf| | e ( ) i ( )

--- -----

pore fluid matrix

clay particle

cation

anion anion

cation--- ----- +-„membrane“ polarizationelectrical

double layer

• Spectral induced Polarization (SIP) of soils and rocks

• Description by complex, frequency-dependent electrical conductivity

• Textual, hydraulic, and geochemical properties of soils and rocks could be characterized with SIP

1peak ~

2~ r0.001 0.01 0.1 1 10 100 1000 100000

10

20

30

-5

-10

-15

-20

-25

Frequency (Hz)

r(Wm)

(mrad)

r

frequency [Hz]

ampl

itude

[Ωm

]

phas

e [m

rad]

(Kemna 2011)

• Electrical Impedance Tomography (EIT) = SIP + imaging

f1

logflogf

imaging at diverse frequencies

EIT SIP

(Kemna 2011)

f2

f3

Introduction

• Accurate EIT-measurement for high frequencies with small phase error in field measurements

10-3

10-2

10-1

100

101

102

103

104

105

10-4

10-3

10-2

10-1

Frequenz f in [Hz]

Ph

ase

in

[ra

d]

B75 5 mB75 6.5 m

B75 7.5 m

B75 9 m

B75 10 mB75 11 m

Measured phase spectra of sediment samples from Krauthausen, Germany

loess

middle gravel

middle sand

fine gravel

middle gravel

sand, gravel, clay

fine sand

clay

aqu

ifer

0.02

0.002

10 Hz 10 kHz

Objective of this work

• Starting situation and objective

EIT40• 40 channels• <1 mrad phase accuracy at 1kHz

in laboratory measurementUI01

Gen.

M01

UI04

M10

SampleADC

I

U

I

U

UI37

UI40

I

U

I

U

CM

E33

I

U

I

U

E40

BC5

E01

I

U

I

U

E08

BC1

C

C

C

C

EIT40 - borehole measurement system• correction of the phase errors due to

inductive and capacitive effects from the cable for field application

Objective of this work

shielding of cable shielding of wires

: amplifier

ring electrodes

: relay switched to electrode

: relay switched to amplifier

GND

16.2 cm

wire 1

wire 2

wire 3

wire 4

E1 E2 E3 E4

Objective of this work• Simplified circuit diagram of electrode modules

𝐿II , I=𝜇0𝑙2𝜋

ln𝑟14 𝑟23

𝑟13𝑟 24

=𝐿𝐼 , 𝐼𝐼=𝑀

mutual inductance:

measured impedance:

𝑈𝑀 (𝜔 )𝐼 𝐼 (𝜔)

=𝑍𝑀=𝑍𝑜 (𝜔 )+ 𝑗𝜔 𝑀(𝜔)

: wire pair I/ loop I (current injection)

:wire pair II/ loop II(voltage measurement)

: injection current: magnetic field line

1

2 4

3r13

r24

r14

r 23

II

𝑼 𝑰𝑰

B

• Inductive coupling between two wire pairs

Inductive coupling effect

EIT40

GND

wire 1 to 8

ring electrode

short-circuit linemulticore cable

The mutual impedance between the single current wire and the single potential wire instead of the wire pairs will be measured!

Inductive coupling effect

• The pole-pole calibration measurement

C1 C2 P

1 0 2, 3, 4, 5, 6, 7, 8

2 0 1, 3, 4, 5, 6, 7, 8

3 0 1, 2, 4, 5, 6, 7, 8

… …

8 0 1, 2, 3, 4, 5, 6, 7

example:

Z1234 = Z123-Z124 = (Z13 – Z23) – (Z14 – Z24)

C1 C2 P1 P2 1 2 3 4

Z fn=[[ ] 𝑍 1,2

𝑍 2,1 [ ]⋯

𝑍1,7 𝑍1,8

𝑍2,7 𝑍2,8

⋮ ⋱ ⋮𝑍 7,1 𝑍 7,2

𝑍 8,1 𝑍 8,2

⋯ [ ] 𝑍7,8

𝑍8,7 [ ]]

Z f 1=[[ ] 𝑍1,2

𝑍2,1 [ ]⋯

𝑍1,7 𝑍 1,8

𝑍2,7 𝑍 2,8

⋮ ⋱ ⋮𝑍7,1 𝑍7,2

𝑍8,1 𝑍8,2

⋯ [ ] 𝑍 7,8

𝑍8,7 [ ]]

⋱

⋱• The pole-pole matrix

Inductive coupling effect

electrodes

insulatorel. conductive shielding

soil

currents in the soil

i

i

+u

-u

wires

: parasitic current

: injection current

: capacitor

R1R2

The capacitance between the shield and the environment is calculated with:

PVC as insulator

The relative permittivity εr of PVC materials is also frequency-dependent. C* fitting with Cole-Cole is

necessary

𝜀∗=𝜀0−𝜀∞

1+( 𝑗 𝜔𝜏0)1−𝛼 +𝜀∞

Capacitive coupling effect

• Calculation of the admittance matrix and the transfer impedance due to the capacitive effect

A

B

M

N

: electrodes: C at cable: C at rod: C at bottom

2D- mesh of the rain barrel with integrated capacitances

For the whole admittance matrix: [𝑌 𝐺 ]= [𝑌 𝑆 ]+ [𝑌 𝐶𝑛 ,𝑛 ][𝑌 𝐺 ] [𝑈 ]=𝐼From

𝑌 𝐶𝑛,𝑛= 𝑗 𝜔𝐶𝑛 ,𝑛

∗

𝑍𝑀 ,𝑁=𝑈𝑀 ,𝑁 /𝐼

test measurement in a rain barrel with borehole logging tool

For each node with C:

• comparison of Z, Zcr and Zc (Zcr = Z - jωM, ZC: modeled Z)

Results of the correction procedures

101

102

103

104

105

22.5

23

23.5

24real 1 4 2 3

real(Z

) in

[W]

ZZcrZc

101

102

103

104

105

-1

0

1

2

im(Z

) in

[W]

ZZcrZc

101

102

103

104

105

-0.05

0

0.05

frequency in [Hz]

phase

(Z)

in [ra

d]

ZZcrZc

at 10 kHz, Δϕ= 0.8 mrad

• The first field demonstration (1D inversion at 1kHz)

-15 -10 -5 0 5 10-9

-8

-7

-6

-5

-4

-3

-2

angle(r) in [mrad]

dept

h in

[m

]

(r) original(r) ind. corr.(r) +cap. corr

0 100 200 300 400 500-9

-8

-7

-6

-5

-4

-3

-2

real(r) in [Wm]

dept

h in

[m

]

|r| original|r| ind. corr.|r| +cap. corr

z = -9.7 m

z = -2.5 m

borehole with slices

z = 0 m

z = -2.7 m

water

• A high phase accuracy of 0.8 mrad at 10 kHz in the test

measurements has been obtained

• The correction procedures were successfully applied in real

field measurements

• The same accuracy was achieved with the new pole-pole

calibration

Summary

Outlook

• Correction procedures for field measurements in two

boreholes

Thank you for your attention!

References

About SIP or EIT:

Kemna et al. 2000 Complex resistivity tomography for environmental applications Chem. Eng. J. vol 77 pp 11 – 8

Binley et al. 2005 Relationship between spectral induced polarization and hydraulic properties of saturated and unsaturated sandstone Water Resour. Res. vol 41 p W12417

About the instruments:

Zimmermann et al. 2008 EIT measurement system with high phase accuracy for the imaging of spectral induced polarization properties of soils and sediments Meas. Sci. Technol. vol 19 p 094010

About the modeling and phase error correction:

Zimmermann 2010 Phasengenaue Impedanzspektroskopie und -tomographie für geophysikalische Anwendungen (phD thesis.) Rheinischen Friedrich-Wilhelms-Universität Bonn

Zhao et al. 2013 Broadband EIT borehole measurements with high phase accuracy using numerical corrections of electromagnetic coupling effects Measurement Science and Technology vol 24 p 085005