CA1040261A - Method and apparatus for investigating earth formations - Google Patents
Method and apparatus for investigating earth formationsInfo
- Publication number
- CA1040261A CA1040261A CA207,193A CA207193A CA1040261A CA 1040261 A CA1040261 A CA 1040261A CA 207193 A CA207193 A CA 207193A CA 1040261 A CA1040261 A CA 1040261A
- Authority
- CA
- Canada
- Prior art keywords
- formations
- attenuation
- dielectric constant
- borehole
- beta
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired
Links
Abstract
METHOD AND APPARATUS FOR INVESTIGATING
EARTH FORMATIONS
ABSTRACT OF THE DISCLOSURE
A method and apparatus for determining the dielectric constant of earth formations surrounding a borehole. Elec-tromagnetic energy is injected into the surrounding forma-tions and received at two locations positioned in spaced relation in the borehole. The phase difference between and attenuation of the signals received at the locations are measured. Finally, the dielectric constant associated with formations surrounding the area between the spaced locations is determined by combining the phase measurement with the attenuation measurement.
EARTH FORMATIONS
ABSTRACT OF THE DISCLOSURE
A method and apparatus for determining the dielectric constant of earth formations surrounding a borehole. Elec-tromagnetic energy is injected into the surrounding forma-tions and received at two locations positioned in spaced relation in the borehole. The phase difference between and attenuation of the signals received at the locations are measured. Finally, the dielectric constant associated with formations surrounding the area between the spaced locations is determined by combining the phase measurement with the attenuation measurement.
Description
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 - , . .. . . . . .
- :
- . - . - . , : .. ..
.. . . . . .
,, , : - .
. ~ - - ,, . ,, - , .. .
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 .
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
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 - , . .. . . . . .
- :
- . - . - . , : .. ..
.. . . . . .
,, , : - .
. ~ - - ,, . ,, - , .. .
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 .
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.
, . . . .
' ~' . ' '
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.
, . . . .
' ~' . ' '
Claims (12)
1. Apparatus for investigating earth formations surrounding a borehole, comprising:
(a) means positionable in a borehole for injecting electromagnetic energy into the surrounding formations;
(b) first and second receiving means positioned in spaced relation in the borehole;
(c) means for measuring the phase difference between signals received at said first and second receiving means;
(d) means for measuring the relative attenuation as between signals received at said first and second receiving means; and (e) means for computing the dielectric constant associated with the formations surrounding the area between the first and second receiving locations by combining the phase measurement with the attenuation measurement.
(a) means positionable in a borehole for injecting electromagnetic energy into the surrounding formations;
(b) first and second receiving means positioned in spaced relation in the borehole;
(c) means for measuring the phase difference between signals received at said first and second receiving means;
(d) means for measuring the relative attenuation as between signals received at said first and second receiving means; and (e) means for computing the dielectric constant associated with the formations surrounding the area between the first and second receiving locations by combining the phase measurement with the attenuation measurement.
2. Apparatus as defined by claim 1 wherein the dielectric constant, .epsilon., of the formations of interest is computed in accordance with the relationship .
where .beta. and .alpha. are, respectively, phase and attenuation con-stants determined by the phase difference measuring means and the attenuation measuring means, .omega. is the angular frequency of the injected electromagnetic energy, and µ is the magnetic permeability of the surrounding formations.
where .beta. and .alpha. are, respectively, phase and attenuation con-stants determined by the phase difference measuring means and the attenuation measuring means, .omega. is the angular frequency of the injected electromagnetic energy, and µ is the magnetic permeability of the surrounding formations.
3. Apparatus as defined by claim 1 wherein said computing means comprises:
(f) means for deriving the quantity, .beta.2, where .beta. is a phase constant determined by the phase difference measuring means;
(g) means for deriving the quantity .alpha.2, where .alpha. is an attenuation constant determined by the attenuation measuring means; and (h) means for deriving the quantity .beta.2 - .alpha.2 which is proportional to the dielectric constant of the formations of interest.
(f) means for deriving the quantity, .beta.2, where .beta. is a phase constant determined by the phase difference measuring means;
(g) means for deriving the quantity .alpha.2, where .alpha. is an attenuation constant determined by the attenuation measuring means; and (h) means for deriving the quantity .beta.2 - .alpha.2 which is proportional to the dielectric constant of the formations of interest.
4. A method of determining the dielectric constant of formations surrounding the borehole, comprising the steps of:
(a) injecting 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 received at said first and second receiving locations; and (e) computing the dielectric constant associated with the formations of interest by combining the phase measurement with the attenuation measurement.
(a) injecting 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 received at said first and second receiving locations; and (e) computing the dielectric constant associated with the formations of interest by combining the phase measurement with the attenuation measurement.
5. The method as defined by claim 4 wherein the step of computing the dielectric constant includes the steps of:
(f) deriving the quantity .beta.2, where .beta. is a phase constant determined from step (c);
(g) deriving the quantity .alpha.2, where .alpha. is an attenuation constant determined from step (d); and (h) deriving the quantity .beta.2 - .alpha.2 which is pro-portional to the dielectric constant of the formations of interest.
(f) deriving the quantity .beta.2, where .beta. is a phase constant determined from step (c);
(g) deriving the quantity .alpha.2, where .alpha. is an attenuation constant determined from step (d); and (h) deriving the quantity .beta.2 - .alpha.2 which is pro-portional to the dielectric constant of the formations of interest.
6. Apparatus for investigating earth formations surrounding a borehole, comprising:
(a) means positionable in a borehole for injecting electromagnetic energy into the surrounding formations;
(b) first and second receiving means positioned in spaced relation in the borehole;
(c) means for measuring the phase difference between signals received at said first and second receiving means;
(d) means for measuring the relative attenuation as between signals received at said first and second receiving means; and (e) means for generating a signal representative of the dielectric constant associated with the formations surrounding the area between the first and second receiving locations by combining the phase measurement with the attenuation measurement.
(a) means positionable in a borehole for injecting electromagnetic energy into the surrounding formations;
(b) first and second receiving means positioned in spaced relation in the borehole;
(c) means for measuring the phase difference between signals received at said first and second receiving means;
(d) means for measuring the relative attenuation as between signals received at said first and second receiving means; and (e) means for generating a signal representative of the dielectric constant associated with the formations surrounding the area between the first and second receiving locations by combining the phase measurement with the attenuation measurement.
7. Apparatus as defined by claim 5 wherein the signal representative of the dielectric constant, .epsilon., of the formations of interest is generated in accordance with the relationship where .beta. and .alpha. are, respectively, phase and attenuation con-stants determined by the phase difference measuring means and the attenuation measuring means, .omega. is the angular frequency of the injected electromagnetic energy, and µ is the magnetic permeability of the surrounding formations.
8. Apparatus as defined by claim 6 wherein said generating means comprises:
(f) means for deriving the quantity .beta.2, where .beta.
is a phase constant determined by the phase difference measuring means;
(g) means for deriving the quantity .alpha.2, where a is an attenuation constant determined by the attenuation measuring means; and (h) means for deriving the quantity .beta.2 - .alpha.2 which is proportional to the dielectric constant of the formations of interest.
(f) means for deriving the quantity .beta.2, where .beta.
is a phase constant determined by the phase difference measuring means;
(g) means for deriving the quantity .alpha.2, where a is an attenuation constant determined by the attenuation measuring means; and (h) means for deriving the quantity .beta.2 - .alpha.2 which is proportional to the dielectric constant of the formations of interest.
9. A method of determining the dielectric constant of formations surrounding the borehole, comprising the steps of:
(a) injecting 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 received at said first and second receiving locations;
and (e) generating a signal representative of the dielectric constant associated with the formations of interest by combining the phase measurement with the attenuation measurement.
(a) injecting 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 received at said first and second receiving locations;
and (e) generating a signal representative of the dielectric constant associated with the formations of interest by combining the phase measurement with the attenuation measurement.
10. The method as defined by claim 9 wherein the step of generating a signal includes the steps of:
(f) deriving the quantity .beta.2, where .beta. is a phase constant determined from step (c);
(g) deriving the quantity .alpha.2, where .alpha. is an attenuation constant determined from step (d); and (h) deriving the quantity .beta.2 - .alpha.2 which is pro-portional to the dielectric constant of the formations of interest.
(f) deriving the quantity .beta.2, where .beta. is a phase constant determined from step (c);
(g) deriving the quantity .alpha.2, where .alpha. is an attenuation constant determined from step (d); and (h) deriving the quantity .beta.2 - .alpha.2 which is pro-portional to the dielectric constant of the formations of interest.
11. A method of determining the dielectric constant of formations surrounding a borehole, comprising the steps of:
(a) deriving a quantity representative of the phase constant 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 attenu-ation measurement.
(a) deriving a quantity representative of the phase constant 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 attenu-ation measurement.
12. A method of determining the dielectric constant of formations surrounding a borehole, comprising the steps of:
(a) deriving a quantity .beta.2, where .beta. is the phase constant associated with the formations at a particular depth of the borehole;
(b) deriving a quantity .alpha.2, where .alpha. is the attenuation constant associated with the formations at the particular depth of the borehole; and (c) computing the quantity .beta.2-.alpha.2 which is proportional to the dielectric constant of the formations at the particular depth.
(a) deriving a quantity .beta.2, where .beta. is the phase constant associated with the formations at a particular depth of the borehole;
(b) deriving a quantity .alpha.2, where .alpha. is the attenuation constant associated with the formations at the particular depth of the borehole; and (c) computing the quantity .beta.2-.alpha.2 which is proportional to the dielectric constant of the formations at the particular depth.
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US39098873A | 1973-08-23 | 1973-08-23 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1040261A true CA1040261A (en) | 1978-10-10 |
Family
ID=23544764
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA207,193A Expired CA1040261A (en) | 1973-08-23 | 1974-08-16 | Method and apparatus for investigating earth formations |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA1040261A (en) |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4553097A (en) * | 1982-09-30 | 1985-11-12 | Schlumberger Technology Corporation | Well logging apparatus and method using transverse magnetic mode |
| US4652829A (en) * | 1984-12-28 | 1987-03-24 | Schlumberger Technology Corp. | Electromagnetic logging apparatus with button antennas for measuring the dielectric constant of formation surrounding a borehole |
| US4689572A (en) * | 1984-12-28 | 1987-08-25 | Schlumberger Technology Corp. | Electromagnetic logging apparatus with slot antennas |
| US4704581A (en) * | 1985-12-28 | 1987-11-03 | Schlumberger Technology Corp. | Electromagnetic logging apparatus using vertical magnetic dipole slot antennas |
| US4857852A (en) * | 1986-06-20 | 1989-08-15 | Schlumberger Technology Corp. | Induction well logging apparatus with transformer coupled phase sensitive detector |
| US6791330B2 (en) | 2002-07-16 | 2004-09-14 | General Electric Company | Well logging tool and method for determining resistivity by using phase difference and/or attenuation measurements |
-
1974
- 1974-08-16 CA CA207,193A patent/CA1040261A/en not_active Expired
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4553097A (en) * | 1982-09-30 | 1985-11-12 | Schlumberger Technology Corporation | Well logging apparatus and method using transverse magnetic mode |
| US4652829A (en) * | 1984-12-28 | 1987-03-24 | Schlumberger Technology Corp. | Electromagnetic logging apparatus with button antennas for measuring the dielectric constant of formation surrounding a borehole |
| US4689572A (en) * | 1984-12-28 | 1987-08-25 | Schlumberger Technology Corp. | Electromagnetic logging apparatus with slot antennas |
| US4704581A (en) * | 1985-12-28 | 1987-11-03 | Schlumberger Technology Corp. | Electromagnetic logging apparatus using vertical magnetic dipole slot antennas |
| US4857852A (en) * | 1986-06-20 | 1989-08-15 | Schlumberger Technology Corp. | Induction well logging apparatus with transformer coupled phase sensitive detector |
| US6791330B2 (en) | 2002-07-16 | 2004-09-14 | General Electric Company | Well logging tool and method for determining resistivity by using phase difference and/or attenuation measurements |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CA1037118A (en) | Method and apparatus for investigating earth formations | |
| US4899112A (en) | Well logging apparatus and method for determining formation resistivity at a shallow and a deep depth | |
| US5345179A (en) | Logging earth formations with electromagnetic energy to determine conductivity and permittivity | |
| US4949045A (en) | Well logging apparatus having a cylindrical housing with antennas formed in recesses and covered with a waterproof rubber layer | |
| US4209747A (en) | Apparatus and method for determination of subsurface permittivity and conductivity | |
| US4185238A (en) | Apparatus and method for determination of subsurface permittivity and conductivity | |
| US3993944A (en) | Movable oil measurement combining dual radio frequency induction and dual induction laterolog measurements | |
| US5544127A (en) | Borehole apparatus and methods for measuring formation velocities as a function of azimuth, and interpretation thereof | |
| US4052662A (en) | Method and apparatus for investigating earth formations utilizing microwave electromagnetic energy | |
| US4302722A (en) | Induction logging utilizing resistive and reactive induced signal components to determine conductivity and coefficient of anisotropy | |
| US7376514B2 (en) | Method for determining properties of earth formations using dielectric permittivity measurements | |
| CA2692555C (en) | A tool for downhole formation evaluation | |
| US5341100A (en) | Electromagnetic wave method and apparatus for downhole measurement of fluid conductivity and hydrocarbon volume during formation testing | |
| US4278941A (en) | High frequency induction log for determining resistivity and dielectric constant of the earth | |
| US5521882A (en) | Measurement of formation characteristics using acoustic borehole tool having sources of different frequencies | |
| US4730161A (en) | Dual frequency well logging system for determining the water resistivity and water saturation of an earth formation | |
| US5168234A (en) | Method and apparatus for measuring azimuthal as well as longitudinal waves in a formation traversed by a borehole | |
| CA1082308A (en) | Method and apparatus for determination for adsorbed fluid in subsurface formations | |
| US5367262A (en) | Advances in high frequency dielectric logging | |
| US4158165A (en) | Apparatus and method for determining subsurface formation properties | |
| CA1040261A (en) | Method and apparatus for investigating earth formations | |
| US4524432A (en) | Measurement of porosity and formation factor using slow compressional waves | |
| US4063151A (en) | Microwave apparatus and method for determination of adsorbed fluid in subsurface formations surrounding a borehole | |
| US4360778A (en) | High frequency induction log for locating formation interfaces | |
| CA1105996A (en) | Apparatus and method for determination of bound water in subsurface formations |