Note: Descriptions are shown in the official language in which they were submitted.
l~P'~
BACKGROUND OF THE INVENTION
This invention relates to the investigation of earth
formations with electromagnetic energy and, more particularly
to a method and apparatus for determining the dielectric
properties of subsurface formations by passing electromag-
netic energy therethrough. The subject matter of this
application is related to subject matter in a copending
Canadian application No. 207,191, entitled "METHOD AND
APPARATUS FOR INVESTIGATING EARTH FORMATIONS," filed of
even date herewith and assigned to the same assignee as the
present invention.
There have been previously proposed various techniques
for measuring the dielectric constant or electric permitti-
vity of subsurface formations. Prior investigators have
recognized that the dielectric constant of the different
materials of earth formations vary widely (e.g. 2.2 for oil,
7.5 for limestone and 80 for water) and that the measurement
of dielectric properties therefore holds promise of being a
useful means of formation evaluation. As an illustration,
if the lithology and degree of water saturation of a parti-
cular formation are determined from conventional well logging
techniques, it is recognized that porosity should be deter-
minable if the dielectric constant of the material could be
measured. Similarly, if the lithology and porosity were
given as "knowns", information as to the degree of water
saturation would be obtainable by measuring the dielectric
constant of the formation.
~, , .
~` 2
.. . . , ; ~ .
~: : . . . . .
.: . - . ~.. . ~ ' -
.. . - ,~ .
; . . : ~,
4CJ~
Pre~iously proposed instruments for the logging of'
dielectric constants in a borehole have not achieved hoped-for
success for a variety of reasons. To understand the
difficulties which have been encountered by investigators it
is helpful to examine momentarily the general nature of the
dielectric constant of a lossy material which can be expressed
as a complex quantity of the form
~ * = ~ + ~
The real part ~' in this equation represents the "true"
dielectric constant of the material in lossless form; i.e.,
the measure of displacement currents for a particular
electric field in the material if it were lossless. The
imaginary part " represents the "loss factor" of the
material; i.e., the losses due to conduction and relaxation
effects. Most previous efforts have been concerned with
determining the value of ~' for a particular portion of sub-
surface formation. However, subsurface formation materials
have appreciable conductivity and thus a significant loss
factor ~" which is often greater in magnitude than '-
Since loss factor is necessarily measured to some extent when
attempting to measure ~', the attainment of accurate values
of ~' has been largely frustrated by the presence of a
significant loss factor.
The U.S. patent 3,551,797 of Gouilloud et al
issued December 29, 1970 teaches a technique wherein high
frequency electromagnetic energy is emitted into a formation.
The r,esultant propagated electromagnetic waves are measured
to determine
.
.,, ~ ~ .
properties o~ the formation through which the waves have
passed. The patent disclosure is largely concerned with
determining formation conductivity which is achieved by
indirectly measuring the "skin depth" of the traversed !~
formation. It is instructive as background herein to
examine the theory underlylng the skin depth measurement of
that patent which is described briefly as follows: The
magnetic field strength Hz at a distance z, for large values
of z from a transmitter, is expressed in Gouilloud et al as t
z (l+j)
Hz = HOe
,
where e is the natural logarithm base, H is the magnetic
field strength at the transmitter, and ~ the skin depth
defined as ~,
~ 2)
where ~ is the radian frequency of the transmitter signal,
~ is the magnetic permeability of the formation, generally
considered a constant, and ~ is the conductivity of the
formation. (A similar equation could be set forth to express
the electric field.) Equation ~1) indicates that the
electromagnetic field is attenuated and phase shifted as the
distance term z increases; i.e., as the electromagnetic
energy propagates through the formations. The degree of
.,
phase shift is expressed by the term -j~ and the degree of
attenuation expressed by the term ~ ~S The composite term
~(l+j) is defined as the propagation cons~ant, the term
1 bein~ the attenuation constant and the term j~l being the
phase constant.
In the Gouilloud et al patent, the attenuation
constant and the phase constant are indicated as having the
same magnitude and, consequently, skin depth can be
determined from either attenuatior. measure~ents or phase
measuremen~. The attenuation calculation involves the
measurement of the amplitude of the electro~agnetic energy
,
at receiving locations spaced a distance AQ apart in the
formation. The amplitudes at the t~;o receiving locatlons,
designated Al and A2, are used to calculate the skin depth
~ in accordance with the relationship
- A2 ~ ~Q
_ - e
- .
Alternately, the phase difference between the two receiving
- locations, designated as ~, is used to calculate skin depth
- in accordance with the relationship
~ = AQ
Knowing ~, the conductivity of the formation, ~, is
determined from equation (2).
The described technique of Gouilloud et al is
predicated on the substalltial equality of the attenuation
and phase constants of the electroragnetic energy. ~his
_7_
~' '' . ' ' '' ' - ~ '. ~
l()~OZ~il !
assumption holds whcnever
a >>1
t~) E .
where E is the dlelectric constant of the material through
which the wave is propagating. The term a known as the
(~
"loss tangent", is the ratio of a quantity that relates to
lossy conduction currents (a) with respect to a quantity that
relates to displacement currents (~f). (Note that the loss
tangent, a measure of relative conauction losses, contributes
to the loss factor term ~" introduced above.) Thus, if a is
substantial, and the operating frequency relatively low, the
propagation constant of the electromagnetic wave has little
dependence upon the material's true dielectric constant.
This is evidenced by equation (2) (which does not depend
upon dielectric constant) and the subsequent Gouilloud et a]. t
expression for propagation constant, 1(1+;)- ,
As was initially stated, p.ast attempts at determin-
ing true dielectric constant have met little success. It is
an object of the present invention to utilize a propagating
electromagnetic wave type of technique to determine the true
dielectric constant of a subsurface formation under investiga-
tion.
U~l
SUMMAR~ OF THE INVENTION
One aspect of the present invention is directed to
an appara~us for investigating earth formations surrounding
a borehole. Means positionable in the borehole are provided
for in~ecting electromagnetic energy into the surrounding
formations. ~irst and second receiving means are positioned
in spaced relation in the borehole. Means are provided for
measuring the phase difference between the signals received
at the first and second receiving means. Further means are
provided for measuring the relative attenuation as between
the signals received at the first and second receiving means.
Finally, means are provided for computing the dielectric
constant associated with formations surrounding the area
between the first and second receiving locations by combining
the phase measurement with the attenuation measurement.
Another aspect of the invention is directed to a
method of determining the dielectric constant of formations
surrounding the borehole, comprising the steps of: (a) in~ecting
electromagnetic energy into the surrounding formations;
(b) receiving energy signals at first and second receiving
locations; (c) measuring the phase difference between the
signals received at said first and second receiving locations,
(d) measuring the relative attenuation as between signals
rece~ved at said first and second receiving locations; and
(e3 computing the dielectric constant associated with the
formations of interest by combining the phase measurement
with the attenuation measurement.
Still another aspect of the invention is directed
to a method of determining the dielectric constant of
formations surrounding a borehole, comprising the steps of:
(a) deriving a quantity representative of the phase content
- ~ _7_ -
,
.~ . : . . .
- - : - .
of the formations at a particular depth of the borehole; (b)
deriving a quantity representative of the attenuation constant
of the formations at the particular depth of the borehole; and
(c) computing the dielectric constant associated with the
formations at the particular depth by combining the phase
measurement with the attenuation measurement.
A further aspect of the invention is directed to a
method of determining the dielectric constant of formations
surrounding a borehole, comprising the steps of: (a) deriving
a quantity ~2, where ~ is the phase constant associated
with the formations at a particular depth of the borehole;
(b) deriving a quantity a2, where ~is the attentuation constant
associated with the formations at the particular depth of the
borehole, and (c) computing the quantity ~2-a~ which is
proportional to the dielectric constant of the formations at
the particular depth.
In a preferred embodiment of the invention, the
dielectric constant, , is computed in accordance with the
relationship
= ~32 e,2
where ~ and ~ are, respectively, the phase and attenuation
constants determined by the phase difference measuring means
and the attenuation measuring means, ~Jis the angular
frequency of the electromagnetic energy, and ~ is the magnetic
permeability of the surrounding formations.
.
' ' , ' " ' ;
- ~, ' .
1~)4(~
Purther features and advantages of the invention
will become more readily apparent from the following
detailed description when taken in conjunction with the
accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FTG. 1 is a schematic xepresentation, partially
in block diagram form, of an embodiment of the invention.
FIG. 2 is a block diagram of the amplitude
comparator of FIG. 1. .
FIG. 3 is a block diagram of the computing
module of FIG. 1.
- DESCRIPTION OF THE PREFERRED EMBODIMENT
~ ,
Consider a plane electromagnetic wave propagating
in a lossy medium. The propagation constant of the wave can
15 be expressed by
Y = ~ ~ 1 1 + j ~ (3)
where ~ is the dielectric constant of the medium, ~ the
magnetic permeability, ~ the conductivity, and ~ the radian
frequency of the wave. In a case where the loss tangent
term, ~ , is much greater than unity, the propagation con-
stant reduces approximately to the term set forth above in
the Bac~ground.
,, ,
: -
- - . . ,
- . . - , . .
.
.. . ~; :
~ U~
For relatively large valucs of ~, tllc term
~ is not inordinately large and the propagation constant
will depend to a significant extent on the mcdium's
dielectric constant, ~. It is helpful to represent the
propagation constant y as ilaving a real part ~ and an
imaginary part ~, so we have
~ = ~ + j ~
where ~ is associated with wave attenuation of loss. (`~ote
- that the propagation constant is used in the wave equation
in the form eiY~ so the real part of the propagation con-
stant becomes the imaginary part of the exponent and vice
versa.) Squaring equations (3) and (4) and equating the real
parts of each gives
~2 _ ~2 = ~~2 (5)
Solving equation (5) for gives
~2 _ 2 (6)
In the present invention, the dielectric constant
of subsurface formations is determined using equation (6).
~he ~ and a of equation (6) are calculated from subsurface
measurements, ~ being determined from a phase measurement
and ~ from an attenuation mcasurement.
Referring to FIG. 1, there is shown a representa-
tive embodiment of an apparatus constructed in accordance
with the present invention for investigating subsurface
' -' ~
. . . .
1i~4(~Zf~l
formations 31 traversed by a borchole 32. The boreholc
32 is typically filled with a drilling fluid or drilling
mud which contains finely divided solids in suspension.
The investigatin~ apparatus or logging device 30 is sus-
pended in the borehole 32 on an armored cable 33, the length
of which substantially determines the relative depth of the
device 30. The cable length is controlled by suitablc means
at the surface such as a drum and winch mechanism-(not shown).
The logqing device 30 includes a coil array com- !
prising a transmitter coil T and two recei~er coils Rl and ¦.
- R2. The intermediate point between the receiver coils
and R2 is a distance Ltr from the transmitter coil T and the
two receiver coils are spaced a distance L apart. The loggin~ !
device 30 also includes a fluid-tight electronic cartridge
lS 40 which houses the downhole electronic circuitry, a block
diagram of this circuitry being shown in the dotted area
also designated h O .
The circuitry 40 includes an oscillator 41 which
energizes the transmitter T to emit electromagnetic energy
for propagation through the formations 31. The receivers
Rl and R2 have voltages induced therein that are proportional
to the energy of the propagating electromagnetic wave at
their respective positions. The path of the wave portion
which propagates through the formation and is ultimately
received by the two receivers is represented in simplified
form by the arrows designated A, B, C, D and E. The energy
received at Rl travels the path A-B-D while the energy
-10-
- , . .. . . . . .
- :
- . - . - . , : .. ..
.. . . . . .
,, , : - .
. ~ - - ,, . ,, - , .. .
1(140Z61
received at R2 travels tlle path A-B-C-E. Since the dis-
tances D and E are substantially equal, the difference in
pathlengths is ~he len~th of arrow C, or, approximately the
distance between the receivers, L. Accordingly, the
utilized differentlal receiver arrangement allows investi-
gation of the portion of the formation lying approximately
opposite the separation between Rl and R2. The nature of
the propagating waves, the effects of reflection of the
wave off beddin~ boundaries, and techniques for dealing
with these phenomena are disclosed in considerable detail
in the patent of Gouilloud et al; and the disclosure of
that patent is incorporated by reference herein. The present
invention is concerned with a particu ar advance in propa-
gation logging, and previously developed techni~ues, ~hile
highly advantageous in the context of this invention, will
- be described only to the extent necessary for an understand-
ing of the present invention.
The outputs of receivers Rl and R2 are coupled to
a pair of amplifiers 42 and 43. The amplifiers are preferably
matched so that any drift in the amplifiers, due to environ-
mental factors such as temperature, will have an equal effect
on both amplifiers, and therefore substantially cancel out
because of the differential receiver arrangaMent. The
signals from amplifiers 42 and 43 are applied to a phase
detector circuit 44 and to an amplitude comparator 45. The
output of phase detector 44 is a signal which is proportional
to the phase difference ~ between the signals received at
- ., . ~ . .
~ , , , ~ . -
:, - .. ,, . ~. , ,: ., -
,. .. . . . .
1~14()2~ ~
Rl and R2, and thus proportional to ~ in accoraance with
~ = ~ . The output of amplitude comparator 45 is a si~nal
level which is proportional to the attentuation constant a.
A convenient comparator circuit 45 for obtaining
an output proportional to ~ is shown in FIG. 2. The signals
from amplifiers 42 and 43 are respectively applied to
logarithmic amplifiers 55 and 56 whose outputs are applied
to a difference amplifier 57 which yields a signal level
proportional to ~. This can be visualized by representing
the amplitude of the wave energy re,ceived at Rl as Ae az ' ¦'
where ~ is an amplitude constant and z is the distance
separating T and Rl. It follows that the amplitude of the
wave energy received at R2 is Ae ( ), where L is the
distance,separating the receivers Rl and R2. The ratio
of the wave amplitudes at the two receivers is therefore
Ae ~(z~L), = e-aL
Ae~~Z
The log of the ratio of wave amplitudes is therefore pro-
portional to a. It ~ill be appreciated that the circuit
45 of FIG. 2 accomplishes the same Mathematical result by
taking the difference of the logs of the wave amplitudes.
The outputs of the phase detector circuit 44 and
the amplitude comparison circuit 45 are transmitted to the
surface over the conductor pair 44A and 45A (FIG. 1) which
in actuality pass through the armored cable 33. Typically,'
these signals are D.C. levels which are stepped-up by
_ 1 ~_
- , . ., ' ~
- .. ~.. , . .... ~ .. . . - ........ .............. . .
1~40Z~l
amplification before transmission t:o the surface.
At the surface of the earth the siynals on lin~s
44A and 44B are applied to a computin~ module 35 which
com?utes the value of the dielectric constant in accordance
with equation (6). The cornputed dielectric constant is
recorded by a recorder 95 that is conventionally driven as
a function of borehole depth by mechanical coupling to a
rotating wiheel 96. The ~heel 96 is coupled to the cable 33
and rotates in synchronism therewith so as to move as a
- 10 function of borehole depth. Thus, the dielectrlc constant
is recorded as a function of borehole depth by the recorder
31.
FIG. 3 is a block diagram of the computing module
85 which receives the signals on lines 44A and 45A that are
indicative of measured values of ~ and a, respectively.
The signals are first applied to variable gain amplifiers
86 and 87 which can be utilized for calibration. The
amplifier outputs are fed to conventional sqaure law circuits
88 and 89 which produce signals proportional to ~2 and ~2.
These signals are applied to a difference amplifier 90 which
produces an output proportional to ~2-a2. From equation (6),
it is clear that this output is a measure of , since ~ is
essentially a constant and ~ is a selected fixed value.
The referenced patent of Gouilloud et al describes
in detail the practical considerations of transmitter-
receiver spacings, and that description ~enerally applies to
the present invention. In the preferred embodiment of the
invention, the spacin~ Ltr is selected to facilitate
investigation of the "invaded zone" which surrounds the mud-
cake in the borehole. ~s is well known, the invadcd zone
-13
.
1~4()2t;1
contains fluids from the mud which filter through the
mudcake into the surrounding formations. The depth of
invasion of this zone generally varies from about an inch .
or so to a few feet depending upon such factors of the
plasterincJ qualities of the mud and the lithology of the
formations. The knowledge of the dielectric constant of
the invaded zone can be gainfully utilized in conjunction
with other data to determine formation parameters such as
porosity or litholo~y. ~o achieve substantial investigation
of the invaded zone, the receivers should be placed far
enough away from the transmitter such that the electromagentic
wave propagating through the mud column is not a significant
factor (by virtue of its attenuation in the relatively lossy
mud) and yet close enough to the transmitters such that the
wave does not spread into the noninvaded zone to an exten~
that would impair the measurements. In the case where it
is desired to attempt to investigate the noninvaded zone,
Ltr should be made accordingly longer.
The spacing L between receivers Rl and R2 should
be sufficiently small to allow determination of the phase
measurement without ambiguity and sufficiently long to give
adequate resolution for both the phase and attenuation
measurements. The frequency of operation should be selected
high enough such that, for a maximum expected values of a
and minimum expected values of , the term a would not be
w~
inordinately greater than unity. ~hen this condition is
met, meaningful computations can be made in accordance with
equation (6) as was described above.
.
- . - - - - , : . .
- . . ' . . - ,: ' '
l~OZ~l .
1 The foregoing has describcd a parti.cular
2 embodiment, but it will be appreciated that variations
3 are available ~i.thin the spirit and scope of the invention.
4 For example, transmitting and receiving electro~es that
are responsive to the electric field portion of the .
6 electromagnetic wave could be substituted for the-magnetic-
7 ally sellsitive coils of FIG. 1. This version of transmitteI-
8 receiver setup is also described in the referenced Gouilloud
9 et al patent.
, . . . .
' ~' . ' '
