SUBSURFACE DIELECTRIC LOGGING BASED ON BOREHOLE RADAR
Sixin LIU and Motoyuki SATO
Center for Northeast Asian Studies, Tohoku University Sendai, 980-8576, Japan
[email protected] 1. Introduction
There are many kinds of borehole electromagnetic logging that have been applied in various industrial fields by now, such as oil exploration, nuclear waste disposal, and other civil and environmental engineering. Generally, they can be divided into two categories according to their detecting principle.
The first category, which includes induction log, electromagnetic propagation log et al, operates
in single or dual frequencies and measures direct coupling wave related to near field. The measurement can be thought as a volume average of surround formation. For example, EPT (electromagnetic propagation tool), which operates only at 1.1 GHz, measures the phase delay and attenuation of an electromagnetic wave. These parameters are related to the dielectric characteristic very near the borehole [1]. In oil exploration, for instance, the electrical conductivity is the most important in evaluating the water saturation in both porous and fracture formation when the formation water is of salinity. While the dielectric permittivity, primarily a function of the water content, is independent of the salinity. These allow EPT the measurement of the water-bearing characteristic of the surround media even in saline shaly-sand.
The second category, the borehole radar, mainly measures scattering wave in the time domain. Its
interest is mainly of the reflecting body or surface [2]. Two antennae are employed in this kind of system, one is used to transmit an EM pulse, and the other is used to receive the signal including the direct coupling wave and the scattering wave, where the scattering component is of mainly interest. A radar profile along the borehole can be acquired using these scattering signals in the time domain.
Fig. 1 Borehole Radar system configuration. Fig. 2 Antenna arrangement (a) and detecting range (b).
Borehole radar generally operates in granite or other hard rocks. However, when the rock or the soil is very conductive, the scattered wave cannot clearly be measured, due to high attenuation in material. Even in this situation, the direct-coupled component is normally very clean. In this report, we introduce a new technique that uses the direct component of the borehole radar measurement for dielectric logging.
2. Borehole radar system
We have developed a borehole radar system based on a network analyzer [3][4]. This system, which is a stepped frequency system as shown in Fig. 1, can measure both direct coupling wave and scattering field related to far field simultaneously in wide frequency range. Both transmitting antenna and receiving antenna are put in a down-hole sonde. As the sonde moves along a borehole axis, electromagnetic signal corresponding to that depth can be measured. Not only the radar profile around the borehole, but also the relative dielectric permittivity and the conductivity of in situ formation can be acquired.
3. Signal processing As an antenna transmits a signal along borehole axis direction, approximately, the receiving
signal by the receiver in the borehole can be expressed as:
jkzeEE −= 0 (1)
where, z is the separation between the transmitter and the receiver, αβ jk −= is the wave number in which α is an attenuation constant, β is a phase constant. E0 is a transfer function between the transmitter and the receiver, which is a complex amplitude having a frequency dependency. This signal is determined by E0 which is affected by the physical property of the medium between two antennae. The attenuation constant and the phase constant that are related to the physical property of around medium cannot be obtained without knowing E0.
There are some methods to reduce the effect of E0. A way, which can be called “two runs” with different separation between two antennae, was chosen. In this study, actually, during the first run, the antenna separation is 1.0m and during the second run, the separation is 1.6m as shown in Fig. 2(a).
The signal of two runs are formulated as following:
101
jkzeEE −= (2)
202
jkzeEE −= (3)
where, z1 and z2 are the separations between the two receiving antennae. The ratio of two signals ER , which is not affected by the antenna transfer function E0, can be obtained as:
φβα ∆−∆−∆−∆− ==== jE
zjzzjkE eReee
E
ER
1
2 (4)
where 12 zzz −=∆ . The electromagnetic field of the first run is mainly affected by the medium within a small range as shown in Fig. 2(b) and the electromagnetic field of the second run is affected mainly by the medium of a larger range. Therefore, ER is determined only by the differential medium between two measurements. The differential phase between two antennae is z∆=∆ βφ , the amplitude ratio is ze ∆−α . The attenuation constant and the phase constant can be rewritten by using
ER as:
z
RE
∆−=
lnα (5)
z∆∆= φβ (6)
Using Eqs. (5), (6) and
ωµσµεω jk −= 22 (7)
where ω is an angular frequency, µ is a magnetic permeability, the relative dielectric permittivityε and the conductivity σ can be calculated as:
2
22
µωαβε −= (8)
µωαβσ 2= (9)
4. Field Experiment
Field experiments were carried out at Kamaishi mine, Japan, and the data were processed using the method described above. The amplitude spectrum and the phase of certain depth are shown in Figs. 3(a) and 3(b), respectively. The attenuation constant is stable between 20 to 100MHz as shown in Fig. 3(c), while phase constant seems stable in all frequency range as shown in Fig. 3(d). Both the relative permittivity shown in Fig. 3(e) and the conductivity shown in Fig. 3(f) have a frequency dependency. The relative permittivity and the conductivity at 50 MHz, 60 MHz, 70 MHz, 80 MHz, 90 MHz of all depths were calculated as shown in Fig. 4. The permittivity and the conductivity of different frequencies have correspondence in this range.
Fig. 3 (a) Amplitude spectrum of two signals, (b) phase spectrum of two signals, (c) attenuation constant, (d) phase constant, (e) relative permittivity, (f) conductivity of certain depth. 5. Discussion
For the purpose of comparison, the frequency domain signals were changed into the time domain by using inverse Fourier transform. A radar profile as shown in Fig. 5 was obtained using these time domain data. Fracture zones found at about 6m, 18m show good correspondence to the dielectric characteristic calculation above.
The exact detectable range or radial detectable depth of radar measurement is rather difficult to
compute, it depends on both the wavelength of electromagnetic wave and the separation between the transmitter and the receiver. it may be approximated by the skin depth.
5 0 2 0 0
- 5 0
- 4 0
- 3 0
- 2 0
- 1 0
am
pli
tud
e(d
B)
F r e q u e n c y ( M H z )( a ) A m p l i t u d e s p e c t r u m
1 . 0 m s e p a r a t i o n1 . 6 m s e p a r a t i o n
5 0 2 0 0
- 2
0
2
ph
as
e(r
ad
ian
)
F r e q u e n c y ( M H z )( b ) P h a s e s p e c t r u m
1 . 0 m s e p a r a t i o n1 . 6 m s e p a r a t i o n
5 0 2 0 0
0
0 . 5
1
1 . 5
2
Alp
ha
(dB
/m)
F r e q u e n c y ( M H z )( c ) A t t e n u a t i o n c o n s t a n t
5 0 2 0 0
0
5
1 0
1 5
Be
ta(r
ad
ian
/m))
F r e q u e n c y ( M H z )( d ) P h a s e c o n s t a n t
5 0 2 0 00
1 0
2 0
3 0
4 0
5 0
Re
lati
ve
pe
rmit
tiv
ity
F r e q u e n c y ( M H z )( e ) R e l a t i v e p e r m i t t i v i t y
5 0 2 0 00
0 . 0 2
0 . 0 4
Co
nd
uc
tiv
ity
(s/m
)
F r e q u e n c y ( M H z )( f ) C o n d u c t i v i t y
It is a kind of approximation to calculate attenuation and phase change using the presented method since an exact analytical solution is difficult to obtain for this kind of antenna system. The calculated relative permittivity and conductivity are about 10=rε and 02.0=σ (S/m) which are close to 87 −=rε and 001.0<σ (S/m) calculated from other method [4]. However, the difference can be resulted from that the detecting range is different for the directing wave and the scattering wave. Additionally, the water-filling borehole affects the measurement although the measurement of “two runs” has some effect to reduce this effect. This effect should be compensated during the data processing. It is suggested to calibrate this radar system in different type of rocks. Frequency dispersion at high frequencies should also be considered.
6. Conclusion
Borehole radar provides us an approach to measure dielectric characteristic of in situ formation. This method can be applied to detect the geological target and evaluate the geological characteristic around a borehole. The measurement of “two runs” has an advantage over simultaneous measurement with two receiving antennae, because it is possible to reduce the mutual coupling between two receivers. The measurement in wide frequency range can be made and the signal in good frequency range can be chosen to process because maybe different range is fitted for different types of formation. Fig. 4 Relative permittivity and conductivity Fig. 5 Radar profile along borehole
of all depth obtained by presented (Kamaishi KR-4). method (Kamaishi KR-4).
Reference [1] O. Serra, Fundamentals of well-log interpretation, Amsterdam: Elsevier, 1984. [2] E.Sandberg, O.Olsson, and L.Falk, “Combined interpretation of Fracture Zone in Crystaline Rock
Using Single-hole, Crosshole Tomography and Directional Borehole-Radar Data,” The Log Analyst, Vol. 32, pp. 108-119, March-April, 1991.
[3] Motoyuki Sato, Kohei Hamano and Katsuto Nakasuta, “Polarimetric Crack Imaging by Borehole Radar,” in Proc. of the 4th SEGJ International Symposium, Tokyo, Japan, December 1998, pp.277-282.
[4] Takashi Miwa, Motoyuki Sato and Hiroaki Niitsuma, “Subsurface Fracture Measurement with Polarimetric Borehole Radar,” IEEE Trans. on Geosci. and Remote Sensing, Vol. 37, pp. 828-837, March 1999.
0 5 10 15 20
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Relative permittivity
Dep
th(m
)
50MHz60MHz70MHz80MHz90MHz
0.02 0.04 0.06 0.08 0.1
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Conductivity(s/m)
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