Note: Descriptions are shown in the official language in which they were submitted.
WO 95/24663 2 1 8 5 0 2 9
5 A BOREHOLE MEASUREMENT SYSTEM EMPLOYING
ELECTROMAGNETIC WAVE PROPAGATION
FIELD OF THE INVENTION
This invention is directed toward the determination of
10 geophysical pdldlll~ of earth fommations penetrated by a borehole. The
invention is more particularly directed toward the determination of
geophysical properties from measures of electromagnetic properties of earth
rur",d~ions in the vicinity of a borehole either during the drilling of the
borehole or subsequent to the drilling of the borehole.
BACKGROUND OF THE ART
A measure of geopl,,/~i.al pard",~er~ of earth formations
pell~l,dlæd by a borehole, as a function of depth within the borehole, is
commonly referred to in the oii and gas industry as a "well log". The first well20 log was measured or "run" in 1927 and consisted of a measure of the
:"uu~ldneOUS potential (SP) properties of earth formation p~"~l,dlæd by the
well borehole. The log was run after the borehole was drilled using a
borehole instrument operating on an electrical wireline. The wireline served
as a means of conveying the borehole instrument or "logging tool" along the
25 borehole and also as an electrical path for l~dll~",illi"g da~a from sensors
within the borehole instrument to the surface of the earth. During the
intervening decades, the wireline well iogging art has grown in sùpl,i~ aliu~
and complexity, employing electromagnetic, acoustic, nuclear and
",e~l,anicdl te~:l",olo~ s to determine geophysical parameters of interest.
30 Probably the most important geophysical pa,el",~ ~r~ to the producer of
hy~i,u~ d,b~lls are the hy~i,u~a,~u" (or water) saturation of the fommation, theporosity of the formation, and the permeability of the fommation. These
pa~dlll~ are, in tum, used to detemmine (a) if hy ilùcdl~u" is present in the
W095/24663 2 1 8 5 029 ~ q
formation, (b) how much hydrocarbon is present, and (c) the ease in which
the h~d~v~,a~60ll can be extracted or "produced~ from the formation.
During the past two decades well logs of increasing complexity
and sO~II;vti~.a~ have been measured while drilling the borehole. The
advantages of measultS",e~ .h' drilling (MWD) logs are well known in
the art. Cl~vl,u,,,ay,,etic, nuclear and acoustic techniques have been
employed in MWD systems which are ap~,uavl,;"g the accuracy and
precision of their wireline counterparts.
Cl.vl~v~ag~etic induction techniques have been used for a
1û number of years in wireline and MWD logging ope,dliu,1s to detemmine the
resistivity and other electromagnetic parameters of earth formations
penetrated by a borehole. One or more lldllsl~ within a borehole
induction logging instrument induce an -" "dli"g voltage into the borehole
and the earth formation in the vicinity of the instrument. The all, " lriQs and
phases of the signals produced by these r" ."dli"g el0ullulllayll~ fields
are measured by one or more receivers within the borehole instrument.
Resistivity and other el~ ,u",ay"~ properties are computed from the basic
amplitude and phase measurements. Using the basic premises that
~urlllaliulls saturated with h~v~a~u~) are more resistive than formation
2û saturated with saline water, the presence and amount of hydrocarbon "in
place" is d~t,r",i"~d.
The accuracy and precision of hydrocarbon measures
computed from measures of formation resistivity are controlled by the
accuracy and precision of the underlying resistivity measurements. Error in
resistivity measurements, whether wireline or MWD, arise in prior art systems
from a number of sources. These sources of error are discussed briefly
under the fûllowing vdlt gOI ie-.
1. INSTRUMENT CALIBRATION
3û In prior art systems borehole instruments or logging tools, both
wireline and MWD, are typically calibrated at the well site (or in the
l WO95/24663 2 ~ 8 5 0 2 9 .~11. 3'
laboratory) using an "air-hang" ~ I ~.dliol~ operation, during which the
lldns",illul and receiver antennas of the logging tool are utilized to transmit
and receive electromagnetic signals which propagate through the
dl".o~llert: around the tool. These air-hang calibration ~,e,dliùlls provide
5 no data whatsoever about the operation of the tool once it is run into the
wellbore and operated in the wellbore env;,ul""e"l. Calibration values
obtained during the air-hang may not apply for the wellbore env;,u"",~"l, or
the logging tool may go out of calibration once it is run into the wellbore.
Prior art borehole instruments typicaliy include a collside,diJI~
10 number of analog electrical and electronic components in both the
lrdns",illi"g and receiving circuits, which tend to introduce an error
C~lll,uulltelll when subjected to changes in temperature. This type ûf error
culllluùll~:lll is typically identified as a "themmal drift" error cu"")U,~"I. In prior
art devices, this thermal drift error component introduces substantial
15 inaccuracies in measurements, which can reduce the overall accuracy of the
logging instrument.
Many prior art MWD logging tools claim to be able to provide
some indication of the size and shape of the borehole, during uperdlk~lls
which are generally characterized as "calipering" operations. Such
2û calipering ope,dliùl~s depend upon the ability to detect slight changes in the
amplitude attenuation or phase shift in the logging measurements which is
attributable to changes in the borehole size. A variety of factors are taken
into account during calipering operations, including the diameter of the
logging tool, the resistivity of the drilling fluid or "mud", the diameter of
25 invasion of the drilling mud into the formation, the resistivity of the formation
and drilling mud in the invaded zone, and the resistivity of the fommation for
uninvaded portions of the formation. C ' ' ~ errors and thermal drift error
components, along with the other inaccuracies inherent in utilizing such a
large number of variables typically dwarf the changes in resistivity of the
30 borehole, and render prior art borehole calipering u,uerd~ions techniques
essentially ",edl,;"yl~ss.
W095/24663 2 1 85 029
Another problem typically encountered during logging
operations is ~lldt:silable magnetic field mutual coupling which may occur
between two or more receiving antennas. Viewed broadly, the magnetic
mutual coupling between receivers can be co,)siJt:,t,d a loss of ill~UlllldliUIIattributable to the magnetic i, ' .a~ of the receivers, and which can be
cu"siJe":d to be an error c~"".o~"l. More particularly, mutual coupling
arises when a plu~Jaga~;~lg eleul,u",a,u~ field generates a current in a
particular receiver, and the current which is generated in a particular receiveritself generates a i-,u~,dgdli"~ el~:~,l,u,,,dg,,~li.; field which is combined with
the primary or "illle:lluyalilly" ele-.l,u",a~u",~ field to influence the amount of
current gen3rated in one or more adjacent receiving antennas.
In summary, some of the principal technical problems
~cs~ tPd with borehole instruments and particularly MWD logging tools
include~ the inability to obtain a meaningful and accurate calibration, (2)
the difficulty of obtaining the calibration, (3) the inability to detemmine when a
tool goes out of calibration during logging u,UeldliOlls~ (4) the ~,ulloiJerdi~le
impact on accuracy of thermal drift error ~ulll,uù~ 111o, (5) the inability to
obtain accurate borehoie caliber data utilizing a logging tool, principally due
to the combined effect of error c~"" on~"tO ~o~ d with the variables
utilized to derive borehole caliper data, and (6) the effects of undesired
magnetic field mutual coupling between receiving antenna in a logging
apparatus.
2. SERIAL PROCESSING OF MEASURED DATA
As l"e"liol1ed previously amplitude and phase measurements
are used to compute the resistivity and other ele.;l,u",au~,lt,li~, properties of
the formation and borehole in the vicinity of the borehole logging instrument.
It is rather common practice to use two or more lldl ,O,,,ill,:l-receiver pairs with
different spacings along the axis of the borehole. It is also quite common
practice to operate one or more ll~ lllitl~lo at different frequencies. Both
practices are directed toward obtaining electromagnetic measurements of
1~ W0 95/24663 2 1 8 5 0 2 9
differing radial depths of investigation into the formation, near borehole and
borehole regions. These measurements are then combined to obtain
resistivity measurements which have been corrected for adverse
environmental ~ol1ù;tiùl1s such as lulll~ations invaded by drilling fluid,
5 formations of limited vertical thickness, the diameter of the borehole, the
resistivity and other ele-;l,u",aull~lk, properties of the driiling fluid, and the
like. The e~i.u~ lldl co"~u~iu"~ are performed sequentially or "serially"
in the prior art. Serial eml;.u,lm~llldl correction tends to propagate error
~soci~t~od with each correction thereby Illd,~ 9 the error ags~ d with
1û the env;,u,l",c~"'l'y corrected resistivity measurement.
It is known in the art that measurements made at different
llall~ r receiver spacings and at different frequencies exhibit different
vertical resolutions. Prior art has matched the vertical resolutions using
various convolution and deconvolution techniques prior to co",L.i"i"g
multiple measurements. This is, again, referred to in the art as serial data
p,~uue~bi"~. U.S. Patent 4,6û9,873 to Percy T. Cox, et al teaches the use of a
wireline logging system culll~liaillg at least three lldllSlllill~l coils and atleast two receiver coils to determine resistivity and dieiectric constant of a
subsurface formation adjacent to a drilling fluid invaded zone. The
2û llal1s",ill~,s are operated at a single frequency of 3û MHz. Amplitude and phase measurements are made and serial prucessi"g of the data is
employed. At relatively low llall~lllill~l frequencies, serial processing
introduces only negligible errors. At higher l,dns",ill~, frequencies in the 2
MHz range or higher, vertical resolution is affected not only by the physical
dlldl~gelllc:lll of the l~dn~",;tler receiver c~llll.illdliol~s, but also si~u",i~i~al,lly
by the electromagnetic properties of the borehole envi,u"",t",~ and the
formation. The functional dt:p~l~d~"ce of vertical resolution and lldllSlllill~lfrequency is ad,l,c:ss~d in the pll ' 'i ~ "2-MHz Flu,ua~dliull Resistivity
Modeling in Invaded Thin Beds", W. Hal Meyer, The LogAnalyst, July-August
1993, p.33 and "Inversion of 2 MHz P,ùpagdliul~ Resistivity Logs'`, W. H.
Meyer, SPWLA 33rd Annual Logging Symposium, Paper H, June 14-17,
W0 95/24663 2 1 8 5 0 2 9 . ~
1992. Stated another way, prior art serial ,~"u~ g of data can introduce
significant error at l,d,~:,l,,illel- frequencies in the range of 2 MHz and higher.
In order to obtain accurate and precise pdldlll~llh, d~'~,.lllilldlio~)s at these
frequencies, it is necessary to compute the parameters of interest and to
5 make the required c~n~1iu, Is, including co,l~:utiùns for the effects of differing
vertical resoiutions, simultaneously.
3. BOREHOLE PARAMETER DETERMINATIONS
The prior art correction of resistivity measurements for the
10 adverse effects of env;,urllllt~ d~ co,le~iliuns, and in particular for borehole
conditions, has been discussed briefly in the previous section. In order to
make valid ~,o"t~ ls for borehole conditions, it is usually necessary to
know the borehole or near borehole conditions which include borehole
diameter, the el~;llu",au"~ properties of the drilling fluid, the degree of
15 invasion of the drilling fluid, and the like.
Borehole and near borehole parameters also provide other
extremely useful ill~ulllldliu11. As an example, the drilling fluid invasion
profile is indicative of the p~ y of the fommation. As a further example,
the physical properties of the borehole such as rugosity and ellipticity can be
20 related to the Illec.llal,i~al properties of the rock matrix and to the
effectiveness of the drilling operation. A hl,oul~d~ of rock matrix properties
is extremely useful in specifying subsequent c~lll,ult,liull activities such as
possible fracturing and even pel~u,dti,lg programs. As a still further example,
a hllu./l~ge of borehole conditions can often be used to increase efficiency
25 of the borehole drilling operation such as modifying drilling pa,d",~ , to
increase bit penetration rates. Prior art has ~Id.lili~ll "y viewed borehole
parameters as sources of error or Dnoise" in desired formation
measurements. Efforts to quantify borehole pa,d""~ ra have, in general,
been pursued only to the extent required to obtain ,t,aso"a~l~ COII~uliulla to
30 the fommation pdrd"l~ ,a which have been ~,ol1sid~ltd the "signal".
WOg5/24663 21 85029 r~
4. QUANTIFICATION OF ERRORS
Error in resistivity or other electromagnetic properties of the
fotmation, near borehoie and borehole pard",~ can arise from many
sources. As discussed previously, instrument calibration is a major source of
5 error in prior art devices. In addition, algorithms or "models" used to convert
raw amplitude attenuation and/or phase shift measurements into the desired
formation and borehole paldlll_t~.a of interest can introduce error in certain
borehole and fommation conditions. Errors of both types can be GGIll,uel~sdlcd
for properly only if error is first clearly identified and quantified. Prior art10 systems have not been directed to the i.le"lili~,dlioll and qual,li~i.,dlioll of
error, especially in real time. Error analysis, if performed at all, is usually
perfommed by the analyst long after the well has been logged.
5. ADDITIONAL SOURCES OF ERROR
In addhion to the above sources of error, fullJdlll~ tdl problems
exist in the conversion of measures of resistivity into measures of
hydrocarbon saturation. As ,,,e,,liun~d previously, fommation resistivity has
historically been the primary pard",_~. of interest in MWD and wireline
logging since it is used to delineate lljJIu~dllJolls from saline waters.
2û Resistivity measurements can not be used to delineate hyJIu~dl~ulls from
relatively fresh waters due to a lack of contrast in the re~i-t:vitic-i of the two
fluids. HyJIu~idr~oli and water, whether saline of fresh, exhibit different
dielectric constants. A simultaneous measure of fommation dielectric constant
and formation resistivity has been used in wireline logging to delineate
25 between hydrocarbon and water (fresh or saline) saturated f~illldliul1s. This technique has not, however, been used in MWD logs.
SUMMARY OF THE INVENTION
The invention is directed toward the measure or "logging" of
30 eleu~,u",dy"~ i properties of earth formation penetrated by a borehole.
Electromagnetic wave propagdliol1 techniques are used to determine
.
WO 95114663 2 ~ 8 5 0 2 9
parameters of interest of the formation and borehole in the Yicinity of a
borehole instrument. The borehole instrument contains one or more
transmitter-receiver pairs operating at one or more frequencies. The
borehole instrument is preferably conveyed along the borehole by means of
5 a drill string. The invention is, therefore, primarily directed toward MWD
Opt:ldLiUl1s but is also applicable to wireline logging. Measures of amplitude
attenuation and phase shift are preferably l,dns",ill~d to the surface for
processing and l~d~a~u~ dliul1 into pdrd",~l~,a of interest using a model of
the response of the logging instrument and suitable computing means.
1û Alternately, the l,d,~a~u""d~iol- of the amplitude and phase measurements
can be made with processing means contained within the borehole
instruments, and the parameters of interest are l,dna",illt,d to the surface, orstored within the borehole instnument for subsequent retrieval at the surface.
One objective of the invention is to provide a logging system
15 which yields accurate and precise measures of amplitude attenuation and
phase shift of el~.;llu",ay"~ , radiation induced within the formation by the
lldl~alllill~l elements of the borehole instnument. This, in tum, results in more
accurate and precise formation and borehole paldlll~ a of interest which
are computed from the basic amplitude and phase measurements using the
2û instrument response model. More ~re~ " "y, the downhole instrument
utilizes digital circuitry which minimizes enrors resulting from thermal drift of
the el~,l,ul~ics of the system. In addition, calibration of the system before,
during and after logging is improved thereby further reducing equipment
related type error. The system also corrects for mutual coupling of receiver
25 antennas within the borehole instrument thereby further reducing systematic
error in the basic amplitude and phase measurements and the pdldlll~ of
interest computed therefrom. These features, in c~lllbi~)dli~l1, are not offeredin prior art systems.
Another objectiv~ of the invention is the reduction of error in the
3û determined parameters of interest resulting from en\,i,u"",l,"ldl co,,~u~;ulls.
Simultaneous or Uparallel'', rather than serial, data ,u,ucesai"g methods are
WO 95/24663 2 1 85
used to transform the basic amplitude attenuation and phase shift
measurements into fommation and borehole pdldlllt~ of interest. Parallel
data p,oces:,i"g reduces the p~upagdlioll of error ~so~ t~d with the
cor,~ulioll of data for individual env;.u"n,er,ldl parameters. Serial
5 p~u~e~illg is widely used in prior art MWD and wireline logging systems.
Yet another objective of the invention is the ~t:l~llllilldliOIl of
borehole as well as formation parameters of interest. Such borehole
parameters can be used as indicators of the overall efficiency of the drilling
program. In addition, measured borehole parameters such as borehole
10 rugosity, caliper and ellipticity can be used to estimate ".e~,l,dl~ical properties
of the pe,~l,dl~d formation which, in turn, can be used as designed
pald"...~ in future well cu",ult:tioli programs. Accurate dt~ ldliu~s of
borehole pard",el~,~ result in more accurate and precise correction of
formation pdld~ la for ~ i.ullllldllldl borehole conditions. Prior MWD and
1~ wireline systems have directed little effort to the specific d~ ",i"dliun and use of borehole pa~dl,lc~
Still another objective of the invention is the provision of means
for identifying and quantifying total error ~c~ou;~l~d with parameters of
interest. Such dt:l~llllil~dliolls can be used to assign a quality factor to the2û logged pal..",~l~r~ as well as serve as an indicator of equipment or
instrument response model problems in certain formation and borehole
conditions. Such extensive error indication systems are not available in prior
art systems.
A still further objective of the invention is to measure
25 simultaneously the resistivity, dielectric constant and the porosity of the
formation in the vicinity of the well bore. A measure of formation dielectric
constant is needed to delineate llydlu~dllJull bearing zones from fresh water
or low salinity water bearing zones. Simultaneous measures of resistivity,
dielectric constant and porosity are not known to have been made with a
30 MWD logging system.
W095124663 2 1 85029 14
Additional objectives, features and advantages will become
apparent in the detailed i~eaeli~liol) of the invention and appended drawings
which follow.
BRIEF DESCRIPTION OF THE DRAWINGS
So that the manner in which the above cited features,
advantages and objects of the present invention are attained and can be
understood in detail, a more particular description of the invention, briefly
siJllllllari~ed above, may be had by reference to the a~ Jodilllelllb thereof
which are illustrated in the appended drawings. It is noted, however, that the
appended drawings illustrate only typical ellliJO~ ellts of this invention and
are therefore not to be col~si.lG-red limiting of its scope, for the invention may
admit to other equally effective e" ,i~oili" lel ,ts.
Fig. 1 depicts the invention in a measurement-while-drilling
el " boi ii " lel , t,
Fig. 2 illustrates a more detailed view of ~IdllbllliLlel~ receiver and a
control circuit siliJasselllt~ly of the borehole instmment portion of the system;
Fig. 3 is a block diagram view of the ~,dns,,,issiull and reception
systems of the logging-while-drilling apparatus of the present invention;
Fig. 4 is an electrical schematic of the receiving circuits of the block
diagram of Fig. 3;
Fig. 5 is a block diagram view of the ni~",e,ic~:ly controlled oscillators
of the block diagram of Fig, 3;
Fig. 6 is a block diagram view of the digital signal processor of the
block diagram of Fig. 3;
Figs. 7A, 7B, and 7C, are high level flowchart le~lesellIclliOlls of tool
operation in accordance with the preferred embodiment of the present
invention;
Fig. 8 is a high level flowchai-t le~ Seilldliull of a digital calibration
operation in 2CGuldc~ .i3 with the present invention;
~ W095124663 218502~ 9 14
Fig. 9 is a graphical depiction of the amplitude, frequency, and phase
shift data derived through a digital calibration operation;
Figs. 10A, 10B, and 10C yldpllibally depict a variety of comparison
o,U~IdtiOl~s which can be pe,lul",ed utilizing data derived from a digital
5 ~ "` d~ion operation;
Fig. 11 is a simplified block diagram view of circuit and data
plUCeSSi"y Cb'lll,Oull~ b which can be utilized to measure the undesired
mutual coupling between particular antennas;
Fig. 12 is an equivalent electrical circuit for the circuit of Fig. 11;
Fig 13 is a block diagram of the technique for ~I;.Ili,)d~illg mutual
coupling;
Fig. 14 is a detailed electrical schematic of the block diagram of Fig
13;
Figs. 15A, 15B, 15C, 16A, 16B, and 16C depict types of
15 measurements obtained with the circuit of Fig. 14;
Fig. 17 is a flowchart ,~,u,_s~"ldtibn of the technique of bl;",i,ldli"g the
corrupting influence of mutual coupling and antenna draft;
Fig. 18 illustrates measured amplitude and phase ~ ,th/' ~ across
a relatively thin formation bounded by fbr",dlibns of essentially infinite
20 vertical extent;
Fig. 19 is a graphical depiction of an algorithm for serially correcting
apparent resistivity for the effects of invasion of the drilling fluid;
Figs 20A and 20B are graphical depictions of alyulitl"":, for serially
correcting phase and amplitude resistivity measurements, respectively, for
25 the effects of finite bed thickness;
Fig. 21 yld~JI)ib~lly illustrates the i"l~,b!ep~"d~,lce of apparent phase
and amplitude resistivity, true formation resistivity, and instrument-borehole
ecb~"., ibily for a borehole fluid of resistivity of 20 ohm meters;
Fig. 22 yld,UIlib~"y illustrates the i~ b~,ue~)d~l)ce of apparent phase
30 and amplitude resistivity, true formation resistivity, and instrument-borehole
ecb~"l,ibity for a borehole fluid of resistivity of 0.2 ohm meters;
1 1
W095/24G63 - 2 1 8 5 0 2 9 r~
Fig. 23 shows apparent resistivity logs dt:~""i"ed at four lld~
frequencies and recorded as a function of depth within a well borehole;
Fig. 24 shows apparent dielectric constant logs determined at four
lldllalllill~r frequencies and recorded as a function of depth within a well
5 borehole;
Fig. 25 illustrates the variation of measured relative dielectric constant
and conductivity as a function of IICII~:~I "illt:r frequency;
Fig. 26 depicts a plot of cornputed variations in dielectric constant as a
function of l~d":,",ill~r frequency and a C~ ,ua~ l of IlleOlt~ .dl values with
10 measured values at four different lldl)~ el frequencies;
Figs. 27A and 27B illustrate the variation of the real portion of
effective dielectric constant and the real portion of effective formation
conductivity as a function of water resistivity, at various fommation porosities;
and
Fig. 28 is a graph which depicts how amplitude attenuation and phase
shift measurements can be used to determine borehole diameter.
wo ss/24663 2 18 5 0 2 9 r~ Q14
DETAILED DESCRIPTION OF THE PRt,~t~RE,J EMBODIMENT
The invention employed in a MWD environment is illustrated in
a very general manner in Fig. 1. Elements shown in Fig. 1 will be discussed
in detail in subsequent sections of this disclosure. The drill bit 31 is attached
5 to borehole instrument 36 which, in the MWD ~,llluoJi,,,t,,,l, is preferably ametallic drill collar which, in turn, is mounted on the wellbore drill string 37.
This assembly is shown suspended in a wellbore 34 which penetrates the
earth formation 32. A means for rotating the drill string 37 is identified by the
numeral 40. The drill string 37 and the borehole instrument 36 are axially
10 hollow such that drilling fluid or "mud" may be pumped clu...,.._ J there
through and out ports of the drill bit 31 and retumed to the surface by way of
the drill string-borehole annulus identified as 34a. The mud circulation
system, including mud pumps at the surface, are not shown. It is well known
in the art that the mud provides a means for returning drill bit cuttings to the15 surface, cools and lubricates the drill bit 31b, and provides II~lUbldli~
pressure to contain intemal pressures of t(JlllldliUllb pe~ by the drill bit
31. Four ~Idllbllli~ r antenna coils of one or more turns are identified by the
numerals 207, 209, 205, and 203. The axes of the coils are coincident with
the axis of the borehole instrument 36. The coils are eleul,i: "y insulated
20 from and slightiy recessed within the outer diameter of the drill collar thereby
G~ pli:.illg integral elements of the collar assembly. Two receiver antenna
coils are identified by the numerals 213 and 211. The g~u",~t,i~s of these
coils are quite similar to the geometries of the lldllblllill~:r coils and againcomprise integral elements of the borehole instrument 36. Transmitter coils
2~ are preferably arranged Sy.ll",t,l,i1~.11y on either side of the midpoint between
receiver coils 213 and 211. Power sources and control circuitry for the
lldllblllillt:lb and receivers are indicated schematically as a suuass~,,,L,ly
201 of the borehole instrument 36 for purposes of discussion. In
~IIluo.li~ l of the invention as a MWD device, the control circuits are
30 preferably located within pressure and fluid tight c~",ua,l",~"lb within the
wall of the borehole instrument 36 which is preferably a drill collar. Data
13
21 85029
W0 95/24663 . ~ 14
recorded by the receivers can be either l,dn:""illt:d in real time to the surface
using drilling fluid pulsing means (not shown) or " Il..~ly can be recorded
with recording means downhole (not shown) for later retrieYal. For the real
time data l,dn~l,,;ssiol1 embodiment, signals from the receivers are
5 transmitted to the surface by a path means generically denoted by the
numeral 46, llclll:~fe~ d to a CPU for p,u~es~ g and correlated with depths
from a drill collar depth indicator 43, and output to recorder 44 which
displays the computed pdldlll~ of interest as a function of depth at which
the input measurements were made. A model 4~ of the response of the
1û L~dll:,",il~ receiver pai~s, in varying borehole and formation conditions, isprovided to convert amplitude attenuation and phase shifts measured by the
receiver elements into formation and borehole parameters of interest. The
model is preferably based derived from theoretical calculations of the
responses of the lldl)allli~ receiver pairs, and also derived from measured
15 ~ OI~S~S of the l~d"s"~ r-receiver pairs in known test formation and
borehole conditions. The model can alternately be stored within memory
(not shown) of the CPIJ 42. An altemate ~",Lodi",el,l of the invention
comprises a processor unit (not shown), with response model stored within,
mounted within the drill collar 36 to perform data p~oces:ii"g downhole.
20 Memory capacity is usually limited in MWD borehole instruments. In order to
most effectively utilize memory capacity, it is often desirable to process
measured data downhole and store processed results rather than the more
voluminous measured data.
Various elements, features and methods of the invention will be
25 discussed in detail in ~he following sections. It should be recalled the
although the preferred t:",~odi",~:"l of the invention is MWD logging, the
invention can be z" lld~ly embodied for wireline ligging or any logging
operation involving the conveying of a measuring instrument along a
borehole.
14
~ W095/24663 2185029
1. THE BOREHOLE INSTRUMENT
The borehole logging instrument 36, preferably a drill collar,
.i~"".lisi"g the lldl~ receiver coil anray is shown in greater detail in
Fig. 2. The two receiver coils are denoted by the numerals 213 and 211.
Transmitter coils 207 and 209 are longitudinally spaced distances 23 and
21 r~ue~ cly, from the midpoint 25 between the receiver coils 213 and
211. The l,d"~",ill~r coils 205 and 203 are likewise longitudinally spaced
distances 23 and 21, l~pe~ cly from the midpoint 25. Again power
sources and control circuitry for the llall~ , and receivers are shown
schematically as a subsection 201 of the borehole instrument 36. In the
preferred e",bodi",~"l the circuitry, which will be described in detail in the
next section, is contained within pressure and tight c~",part",~"t~ within the
wall of the borehole instrument 36. The symmetrical spacing pattern of
lld~ r:, and receivers about a point 25 midway between receivers 213
and 211 is preferred but not a necessary condition for the elll~odi",~, ll of the
invention.
1.1 T~ ci ~n ~nd Rece~tiQn Systems
Fig. 3 provides a block diagram view of the exemplary logging
instrument or tool~ 36 with the su~a,s~",L,ly 201, illustrated previously in
Fig. 2 and constructed in acc~,ddl1c~ with the present invention. Logging
tool subassembly 201 includes upper lldlls",illt:rs 203, 205 lower
lldll::~lll"' .a 207 209, and i, ",edidl~ series resonant receiving antennas
2~ 211, 213. Central processor 215 is preferably a ",i~,uprucessor device
which is utilized to could~lldl~ the operation of the cu",pol1e,ll:, of logging
tool 36 and su~ass~",~ly 201, to record and process the data obtained from
measurements made by intermediate series resonant receiving antennas
211 213 and to interact with a mud pulse telemetry data lldll!;lll;O~iOII
system (not shown) preferably carried in the adjoining drill collar member.
Processor 217 is provided and dedicated for the control of numerically
2 1 g5~2~
WO 95124663 I ~ ,5.. '~
controlled oscillator 223. Processor 219 is provided and dedicated for the
control of numerically controlied oscillator 225. Central processor 215
communicates with processors 217, 219 via data buses 241, 243
respectively Numerically controlled oscillators 223 225 are adapted to
5 receive a binary command signal as an input and to produce an analog
output having particular frequency, phase, and amplitude attributes. The
frequency phase, and amplitude attributes are d~t~""i"ed at least in part by
the command signals applied from processor 217, 219 to the input of
numerically controlled oscillators 223, 225 and the data contained in
10 various registers within numerically controlled c- :b 223 225.
Numerically controlled OS- illdlul~ 223, 225 provide the analog signal to
~Idllbll ,9 circuits 227 229 ,t:b,ce~ cly. The c~""uu"~"t~ which make up
transmitting circuits 227, 229 will be described in greater detail in
col~neulioll with a technique of the present invention of quantifying the
15 ~" ~desildbl~ magnetic field mutual coupling between particular antennas.
Receiving antennas 211 213 communicate through analog
receiving circuit 231 witl1 the first and second data input channels of a digital
signal processor 221. The digital signal processor 221 receives data at the
first and second inputs after it is converted from analog form to digital fomm by
20 analog-to-digital converters 220, 222, and records the data elements in a
circular memory buffer. Central processor 215 pulls data from the buffers in
a IJl ~:bCI iL,ed and ,u, ~dt:l~l " ,i"ed manner in order to sample the current which
is generated in receiving antennas 211 213 in response to the p~uuaydliull
of ele~l,ui,,aylletic signal through the adjoining formation. As is
25 conventional the resistivity of the formation surrounding the logging tool 36and sul,asse",bly 201 may be d~lt,l",; ,ed by either (1) d~l~lllli,l;,lg the
amplitude attenuation of an ele~:t,u",ay"~ wave ulupau~; l9 through the
formation adjoining receiving antenna 211 and receiving antenna 213 or
(2) by d~l~lll,i,l;,lg the phase shift between the ~ u~ay~etic signal
30 ,~u~ aydlillg through the forma~ion adjoining receiving antenna 211 and
16
-
W095/2.1663 2 1 8 ~ 0 2 9
213, or from both. These measurements comprise a relative measurement
of the amplitude attenuation and a relative measure of the phase shift.
The present invention also allows other tecl)":., les for
quantifying the elevl,u",ay"~il, field which ulvpaydl~s through the formation
5 surrounding logging tool 36. Since precise control can be obtained with the
present invention over the frequency, phase, and amplitude of the
ele_l,u",ay"t,li~ wave generated by l,an:,", ,9 antennas 203, 205, 207,
and 209, the present invention allows the measurement of the absolute
amplitude attenuation of el~.,t,u",dy"eli~ signal between any particular
~Idll::~ll "" ,g antenna 203, 205, 207, and 209 and any particular receiving
antenna 211, 213. Furthemmore, the logging tool 36 of the present invention
allows for the absolute measurement of the phase shift of an electromagnetic
signal between any particular l,dns", ,9 Qntenna 203, 205, 207, 209
and any particular receiving antenna 211, 213. Prior art devices do not
15 allow such optional techniques for d~,t~,.lll;lli,~g amplitude attenuation and
phase shift, since prior art devices are unable to determine easily and
precisely the frequency, phase, and amplitude of a signal generated at any
particular ~l~llall ' 19 antenna.
The operation of numerically controlled oscillators 223, 225 is
20 clocked by the output of reference clock 237, which is preferably 12 MHz.
The operation of receiving circuit 231 is controlled by the output of
numerically controlled oscillator 231, which is also clocked by the output of
the reference clock 237, which is 12 MHz. Thus, a clocking pulse is
provided to numerically controlled oscillator 223, 225 at a frequency
25 identical to that which is provided to numerically controlled oscillator 223,which e:,~dl,l;~l~es the operating frequency of receiving circuit 231. Digital
signal processor 221 is clocked by the output of divide-by circuit 239, and
thus samples the output of receiving circuit 231 at a particular frequency
which is much less than that utilized to energize lldll~lllill~ antennas 203,
30 205, 207 and 209.
17
WO 95/24663 2 1 8 5 0 2 9 ~ 4
Numerically controlled oscillator 233 produces a phase-locked
sine-wave signal with a center frequency of 1.995 MHz, that is used as a
local osciliator signal by a receiving circuit (not shown) located in the wall of
the logging tool 36.
Reference is now made to Fig. 4. The overall function of the
circuitry depicted in block diagram and schematic fomn in Fig. 4 is to respond
to the local oscillator signal and one of the two receiver coil output signals to
produce a receiver phase output signal relative to the llallalllil~ and a
receiver amplitude output signal. A conventional pre-amp circuit generally
indicated at 271 responds to the receiver pick-up signal and its output is
applied to a mixer circuit ~lldll9elllt~ generally indicated at 273. Mixer
circuit alldl)~e~ 273 includes an integrated circuit 275 that suitably is
ill,pl~",t:" ~ by an integrated circuit manufactured and sold by Motorola and
other c..",~-d"i~s under the ~esiy" , MC 1596.
Because the frequency of the pick-up signal and the local
oscillator signals are phase-locked to a common frequency reference and
differ by 6 KHz, the i"l~""edidl~ frequency (IF) produced by mixer circuit
a"dl~ger"e~,l 273 is at 6 Kl1z. A band pass tuning circuit a~d~ ulll
generally indicated at 277 passes the 6 KHz IF signal to an amplifier circuit
arrangement generally indicated at 279. An active band pass filter circuit
al,a,1n~l"e"l generally indicated at 281 provides further band pass filtering
and provides a signal t~ an analog-to-digital converter, which supplies a
digital input to a particular input channel of digital signal processor 221 (of
Fig. 3).
Fig. 5 is a block diagram view of the n~",eri~:'y controlled
oscillators 223, 225, 233 of Fig. 3. Since the numerically-controlled
oscillators are identical, only m,"~e,ically controlled oscillator 223 will be
discussed and described. In the preferred embodiment of the present
invention, numerically-controlled oscillator 223 C~ uliaes a CMOS, DDS
modulator manufactured by Analog Devices of Norwood, Massachuseffs,
which is identified by Model No. AD7008. The nu",er;-~'ly controlled
18
W0 9!i/24663 2 1 8 5 0 2 9 ~ 14
oscillator 223 includes a thirty-two bit phase accumulator 301, a sine and
cosine look-up table 303, and a ten-bit digital to analog converter 305.
Clock input 307 is provided to receive a clocking signal from a device which
is external to the numerically-controlled oscillator 223. The particular
5 nu~ dl!y controlled oscillator of the present invention is adapted to accept
clock rates as high as 20 MHz to 50 MHz, but can ac~ u"""ù.ldl~ much lower
clock rates. The device purports to have a frequency accuracy which can be
controlled to one part in four billion. NUIII~I jG~IIY controlled oscillator 223includes a thirty-two bit serial register 309 which receives serial data at
10 serial data input pin 311, which is clocked into the register in ac.o,~allce
with a clock signal which is supplied to serial clock input 313. A thirty-two bit
parallel register 313 is also provided which receives parallel binary data
from MPU interface 315. Data bus 317 includes sixteen digital input pins
identified as D0 through D15. The chip select pin 321 is utilized when writing
15 to the parallel register 313. The write pin 319 is also utilized when writing to
the parallel register 309. The transfer control address bus 323 is utilized to
determine the source and de:,li"dliol, registers that are used during a
transfer. A source register can be either the parallel assembly register 313
or the serial assembiy register 309. The '~ ~i Idlio~- register can be any one
20 of the following registers: the command register 325, the FREQ0 register
327, the FREQ1 register 329, the phase register 331, the IQMOD register
333. The command register is written to only through the parallel assembly
register 313. The contents of the command register detenmine the operating
state of the nu",e,ic..lly controlled oscillator 223. In the preferred device
25 utilized in the present invention, the command register is a four bit register.
The content of this register d~l~""i"es the operating state of the numerically-
controlled oscillator. Table 1 provides an overview of the possible operating
states of the nu",~lic~lly controlled oscillator 223 which is utilized in the
present invention. During iogging o,uerdliulls~ the logging apparatus of the
30 present invention is ~,uy,~l"""ed to provide co"""al1d, from ~u~ss~ra
215, 217, 219 (of Fig. 6) with eight-bit COIllllldlnl:i, SO the "CR0" bit is 0.
19
WO 95124663 2 1 8 ~ 0 2 9
Nommal operation is desired, so the "CR1" bit is 0. In the present invention,
amplitude modulation is bypassed, so the "CR2" bit is 0. In the present
invention, the s~ l"u"i~el logic is enabled, so the ~CR3" bit is 0. The
FREQ0 register 327 defines the output frequency of the numerically-
controlled oscillator 223, when the FSELECT pin is 1, as a fraction of the
frequency of the clock signal applied to clock pin 307. The FREQ1 register
329 defines the output frequency of the nul"èlic~ controlled oscillator 223,
when FSELECT equals 1, as a frequency of the clock signal applied to clock
pin 307. The contents of the phase register 331 are added to the output of
the phase accumulator 301. The IQMOD register 333 is not utilized in the
present invention.
The o~e,dliol1s which can be performed with the registers by
supplying command signals to transfer control address bus 323 are set forth
in tabular form in Tables 2 and 3. Three basic operations can be performed.
The contents of the parallel assembly register 313 can be lldll:,~lled to
command register 325; the contents of the parallel assembly register can be
lldll~el~ed to a selected destination register, in acconldnce with the
de~li"dliol1s identified in Table 3; and the contents of the serial assembly
register 309 can be lld~ lled to a selected de:,ti,ldLiu~ register.
The load register pin 335 is utilized in conjunction with the
transfer control address bus 323 to control loading of intemal registers from
either the parallel or serial assembly registers 309, 313. The test pin 337 is
utilized only for factory testing. The reset pin 339 is utilized to reset the
registers. The reset pin in particular is utilized to clear the command register325 and all the modulation registers to 0. The current output pins 341, 343
are utilized to supply an " lldlill9 current to a selected end device. In the
particular é~llJodi~ l of the present invention, only one of these outputs is
utilized for a particular l~ d~ 19 antenna, since one current is the
c~r", ' llelll of the other current. The c~",,,~e,)sdliol- pin 342 is utilized to
Culll,uel,sdlt, for the intemal reference amplifier. The voltage reference pin
WO 95/24663 2 1 8 5 0 2 9
343 can be utilized to override an intemal voltage reference, if required. The
full-scale adjust pin 345 d~lt,l"i"es the magnitude of the full scale current atoutput pins 341, 343. The ground pin 347 provides a ground reference,
while the positive power supply pin provides power for the analog
co",l,ol,e"l:, within numerically-controlled oscillator 323. The frequency
select pin 351 controls frequency registers FREQ0 register 327 and FREQ1
register 329, by dt~ ,i"il lg which register is used in the phase accumulator
301 by c~"l,~ " ,y multiplexer 353. The contents of phase register 331 is
added to the output of phase accumulator 301 at sumer 355. The IQMOD
registers 333 are provided to allow for either quadrature amplitude
modulation or amplitude modulation, so the sine and cosine outputs of look-
up table 303 are added together at sumer 357, and are unaffected by the
IQMOD registers 333. The output of sumer 357 is provided to digital-to-
analog converter 305, which creates an analog signal having a frequency
which cull~:,pol,ds to either the contents of the FREQ0 register 327 or the
FREQ1 register 329, a phase which is dt:l~""i"ed by the output of sumer
355 which is provided as an input to look-up table 303, and an amplitude
which is dt:Lt:""i"ed by full scale control 359 which is set by full scale adjust
pin 345 and reference voltage pin 343. Therefore, the numerically-
controlled oscillator of Fig. 5 can provide an analog output having a precise
frequency attribute, phase attribute, and amplitude attribute. Since the
device is extremely accurate, it is possible to provide a driving current for the
lldilslllillillg antennas 203, 205, 207, 209 of Fig. 3 which is controlled
precisely. In the preferred ~,,ILod,,,,t~ of the present invention, one of
lldll:~lll"" ,g antennas 203, 205 is operated at 400 KHz, while the other of
llall~lll"" ,g antennas 203, 205 is operated at 2 MHz. The same is true for
antennas 207, 209, with one being operated at 400 KHz and the other
being operated at 2 MHz. However, the p,ucessol~ 215, 217, 219 can be
pluylalllllled to provide any particular frequencies for the lldl1slllillillg
antennas. This will be used to good advantage as will be described below in
co",~e~.t~ 1 with a calibration routine.
21
WO95/24663 2 1 8 5 029 1~ 4
In operation, a command signal is supplied to the FSELECT pin
351 to determine which frequency will be utilized for el1e,yi~;"g a particular
lld"~"~ g antenna. The FREQ0 register 327 and FREQ1 register 329 may
be preloaded with two particular frequencies (such as 400 KHz and 2 MHz).
5 The binary signal applied to the FSELECT pin 351 ~ ""i"es the operation
of multiplexer 363, which supplies the contents of either FREQ0 register 327
or FREQ1 register 329 of the input of phase accumulator 301. Phase
accumulator 301 accumulates a phase step on each clock cycle. The value
of the phase step d~ .",i"es how many clock cycles are required for the
10 phase accumulator to count two 1~ radians, that is, one cycle of the output
frequency. The output frequency is dt l~""i"ed by the phase step multiplied
by the frequency of the signal applied to the clock input pin 307 divided by
232. In practice, the phase accumulator 301 is cleared, then loaded with the
output of multiplexer 353. Then, a p,~dtlri"ed time interval is allowed to
15 pass, during which the signal applied to clock input pin 307 steps the outputof phase accumulator 301 through an i"~ ",~"~ 'y increasing phase for the
particular frequency. In other words, phase accumulator steps from 0 phase
to 180 for a particular frequency. At any time, the output of phase
accumulator 301 may be altered by a phase offset which is supplied by
20 phase register 331. Phase register 331 may be loaded in response to
COIllllldlld::~ from pluCeSSOla 215, 217, 219. The phase value is supplied as
input to look-up table 303, which converts the output of the phase
accumulator 301 (and any desired offset) into a digital bit stream which is
se,l~ c of an analog signal. This digital bit stream is supplied as an
25 input to the 10-bit digital-to-analog converter 305 which also receives
amplitude i,,~r,,,dliu,, from full scale control 359. The digital-to-analog
converter 305 supplies an analog output with a particular frequency
attribute, phase attribute, and amplitude attribute. For example, an output of 2MHz, with 15- of phase, and a particular peak amplitude current may be
30 provided as an input to a particular lldllallliltillg antenna.
22
W0 95/24663 2 1 8 5 0 2 9 P~ ,,5, .
Fig. 6 is a block diagram view of the digital signal processor
221 of Fig. 3. In the preferred t""l,odi",e"l of the present invention, digital
signal processor 221 col"u,i~es a DSP ~ uco~puter manufactured by
Analog Devices of Norwood Massachusetts, which is identified as Model No.
5 ADSP-2101. This is a single-chip ~ uco~ uuter which is utilized for high-
speed numeric p,ucessi"g ,s. Its base architecture 379 is a fully
c~ Jdlibl~ superset of the ADSP-2100 instruction set. The base architecture
includes three independent computational units: shifter 371,
multiplier/accumulator 373, and arithmetic and logic unit (ALU) 375.
10 Program sequencer 369 supports a variety of operations including
col. 'il 1al jumps, subroutine calls and returns in a single cycle. Data
address generator 367 includes two address gel-eldlu,:,. Digital signal
processor 221 includes serial port 381 which includes two input channels:
input channel 383, and input channel 385. Timer 387 provides timing
15 signals for the data ul-~c~ssillg operation and receives as an input a clock
signal from divide-by circuit 239 (of Fig. 3). Extemal address bus 289 and
external data bus 391 allow digital communication between digital signal
processor 221 and central processor 315 of Fig. 3. Memory 393 includes
program memory 395 and data memory 397. As is typical with digital signal
20 ,u,ucesso,:, data memory 397 defines at least two circular buffers A~So~
with serial ports 383 385 which are designed to receive asy ,~l"u"ous
digital data, and store it i"d_rill l~ or for a pl~ ""i"ed time interval. The
digital signal processor 221 receives digital inputs at channel inputs 383
385 from an analog-to-digital converter such as is depicted in the circuit of
25 Fig. 4. The receiving circuit of Fig. 4 receives a current which is
rts~"ldlive of the response of a particular receiving antenna 211 213 to
el~.t,u,,,ay,,tlic radiation p,~.aydli"g through the borehole. This electrical
signal is p~u- t~ssed through the circuit ~ uol~ ts of Fig. 4 and is provided
as an input to digital signal processor 221. In the preferred 6IIILodilllt:lll of
30 the present invention, receiving antenna 211 is identified with a particular
input channel of digital processor 221 while receiving antenna 213 is
23
-
W095/24663 2 1 8502q P~,l/ll.. ,". 1 --
identified v~ith the other input channel of digital signal processor 221.
Central processor 215 (of Fig. 3) utilizes external address bus 389 and
external data bus 391 to address a particular input channel and read digital
data into central processor 215 for p~u~ es~ g. In the preferred t""L,od~",~"l
of the present invention, digital signal processor 221 can sample data from
receiving antennas 211, 213 at a very high sampling rate which can be
read periodically by central processor 215 which p,uc~sses the data to
determine the amplitude attenuation and phase shift of the el~,u,,,ay,,~lic
signal which is Pll-r _ ~ through the borehole. One particular routine for
1 û calculating amplitude attenuation and phase shift is set forth in greater detail
herebelow, in co,,,,e~;liùll with a discussion of the error CdllC611dliull feature
of the present invention. In broad overview, central processor 215 can pull a
selected amount of data from each channel of digital signal processor 221,
and from that data calculate the amplitude attenuation and phase shift of the
electrûmagnetic wave as it propagates through the wellbore and past
receiving antenna 211 and receiving antenna 213. In the preferred
embodiment of the present invention, an upper l,d~l:,",itlt,r transmits an
interrogating ele~ llul"ay"etic signal of a particular frequency which
~,u,uaydl~S downward past receiving antennas 211, 213. Then, a particular
2û one of lower lldll::~lllillillg antennas 207, 209 propagate an interrogating
~le~l,u,,,aylle~ signal upward. Measurements from receiving circuit 231 are
stored in the input channels of digital signal processor 221, and read by
central processor 215 in a manner which al~ows for the calculation of
amplitude attenuation and phase shift.
Another important feature of the present invention arises from
the fact that a precise el1eryi~i"g current can be utilized to energize a
particular one of llall:,lllillillg antennas 2û3, 2û5, 2û7, 209. This will
establish the frequency attribute, phase attribute, and amplitude attribute of
the el~_L-u",ay"etic illl~llugdlilly signal. Therefore, a single receiving
3û antenna can be utilized to make the measurement of the el~l,u,,,au,,~lic
uydlillg signal as it passes through the wellbore. The amplitude and
24
W095/24663 2 1 8 5 0 2 9 r~l,. 1
phase of that i"l~"., ,g signal can be recorded in memory, and compared
with values in memory for the tllelyi~;,lg current. This allows a single
receiving antenna to be used to provide an accurate measure o~ amplitude
attenuation between that particular receiving antenna and the particular
5 I-d"~",iLIi"g antenna, and the phase shift of the i" ,u, ,g signal between
the l,di,~",illi"g antenna and the receiving antenna. Of cûurse, the amplitude
attenuation and phase shift of the el~:t,u,~,ay"~lk, i~ ùyAlillg signal as it
passes through the fommation is indicative of the resistivity of the wellbore
and surrounding fommation
1û Figs. 7A, 7B, and 7C provide high level flowchart
represer,ldliol~s of logging ope,dliul,s performed in accoldance with the
preferred ~ bù~i",e"l of the present invention. Fig. 7A depicts logic steps
which are performed by central processor 215. Fig. 7B represents
op~ldliol1s controlled by processors 217, 219. Fig. 7C depicts operdliù"s
15 controlled by digital signal processor 221 and central processor 215. The
lldnalllibsio~1 operdli~l)a begin at block 401. Processor 215 performs a
calibration operation upon receiving antennas 211, 213, as will be
discussed in greater detail elsewhere in this .1" 'i~ ,. After the calibration
Up~ld~iOIls are perfommed central processor 215 instructs processor 217 to
2û energize 11dll:illl;llill9 antenna 203 with a 400 KHz current. Then, in
ac~on~d"ce with block 407, central processor 215 instructs processor 219
to energize lldll:,lllillillg antenna 209 with a 4ûO KHz current. Next, central
p,uce:,sor 215 instructs processor 217 to energize l,d":,",illi~g antenna
205 with a 2 MHz current, in acc~ldal1ce with block 409. Then, in
25 occurrence with block 411, central processor 215 instructs processor 219 to
energize l,d":,",illi.,g antenna 207 with a 2 MHz current. The process stops
at block 413. In actual practice, I,d"~",i~aiol) ope,dliùns will be perfomned
continuously over ~,~dt,li"ed intervals.
Fig. 7B depicts the control operdlio~,s performed by p~ucessor:~
30 217, 219 to cause numerically controlled oscillators 223, 225 to energize
particular lldnalll :,. The process begins at block 415. It continues at
WO95/24663 2 1 8 5 0 2 9 1~1,.
block 417, wherein the processor 217 or219 clears the registers in
numerically controlled oscillators 223 or225 by providing the a~ ,u,ulJ,idle
instruction. Then, in acco"~dnce with block 419, processor 217 or219
loads a ule:del~lllli"ed value to the FREQ0 register and the FREQ1 register.
5 These values detemmine the frequency of the e~ ,uj~;"g current which is
supplied to a particular ll~"a",i~ti"g antenna. Then, in accu,~d"~.~ with block
421, processor 217 or219 loads a pr~d~le"" ,ed phase value to the
phase register of numerically controlled oscillator 223 or 225. Processor
217 or 219 then provides a binary comnnand to the FSELECT input pin of
10 numerically controlled oscillator 223 or 225 to select a particular frequencyof operation. Then, in ac~.u,dal1~ with block 425, a particular time interval isallowed to pass. This time interval d~t~""i,)es how many cycles of energizing
current are applied to a particular lld~ lillg antenna. The process ends at
software block 427. Typically, each time processor 217 or 219 is instructed
15 by central processor 215 to energize a particular lldll:~lllillillg antenna, the
steps of Fig. 7B are performed.
Fig. 7C depicts in flowchart for the reception Op~ldliolis. The
process begins at block 429. The process continues at block 431, wherein
the current within receiving antennas 211, 213 are sampled by receiving
20 circuit 231. Then, in a-,co~al-c~ with block 433, these samples are loaded
to the a,~luUlidl~ input channels 283, 285 of digital signal processor 221.
In ac~old~,~ce with block 435, central processor 215 fetches selected
samples from the memory buffers ~.so~ 1 with the digital signal processor
input channels. In acc~,.ld,-ce with block 437, optionally, samples may be
25 modified to offset for error cu" ,,uu, ,~"ts due to "", "' dliUI 1" of the antenna,
which will be described in greater detail elsewhere in this r, ~ . Next,
in accolddi~ce with software block 439, the digital samples may be digitally
filter with either a low-pass digital filter, high-pass digital filter, or a bandpass
digital filter. Alternatively, the samples can be averaged over p,~dt,li"ed
30 intervals to provide stability to the samples and eliminate the influence of
spurious or erroneous samples. Next, in accu,dal~ce with block 441, the
26
W0 95124663 2 1 8 5 0 2 9
amplitude attenuation and phase shift are calculated, as is described
elsewhere in this i~.~ 1. Finally, the process ends at block 443.
1.2 Antc~ lihr~ rl O~er~ti~ s
The invention provides seYeral novel caiibration features of the
receiver antennas. The utilization of ",i_,v~.r_ceb_o,b and numerically
controlled oscillators (see Fig. 3) in the present invention allows for very
precise cali._,dLiul~ measurements to be made of the l~dnb",;~ n and
reception of the i,l~"u ~_:i. I9 signal either outside the borehole, or preferably
in the borehole during logging operations. This is ac_o,l-~,l;sl~ed by having a
calibration program resident in memory of pr_cebsol:, 217, 219, or in central
processor 215, which causes a nu",t~ 'ly controlled oscillator to step or
sweep through a particular frequency range. This is acco",,~ ed by
sequentially providing a command signal from ~,ocesso,b 217 219 to
1~ numerically controlled oscillators 223, 225 which ebla!~ l1es a frequency
for the energizing current which is supplied to a particular lldl1b~l ,g
antenna. a,~ , a command is supplied from plucessolb 217, 219 to
numerically controlled oscillators 223 225 to establish the phase
characteristic of the signal. In practice, the frequency sweep should include
a fairly wide range of frequencies. Normal reception operdliol~s are
conducted while a particular l,anb",iller is swept through a range of
frequencies. The data is recorded and provides a combined measure of the
response of the l,dnb."itli"g antenna and receiving antenna.
In the preferred e,~lbo i;",e"L of the present invention each
2~ llal l~ ;l ,g antenna coil is swept through a p,~ ",i"ed frequency range
while the receiving antennas are sampled. The result is eight sets of data
one for each possible lldilblllil~ ceiver ~u~ illdtiull, which quantifies the
operating condition of the particular lldllblllit.i.lg antenna and the particular
receiving antenna. Malfunctions in a particular receiving antenna or
lldllblllilt;.lg antenna can be d~.t~i.",i"ed by co""ua,ibul~s between the eightdata sets. For example, with reference to Fig. 3, supposing that l~a"b~,itli"g
27
W0 95/24663 2 1 8 S 0 2 9
antenna 203 is damaged or out of calibration. The data set which
establishes the operating condition of lldll:~lll'" 19 antenna 203 and
receiving antenna 211 can be compared with the data set which eald~ es
the operating conditions of l-di,a",illi"g antenna 203 and receiving antenna
5 213 to determine that l,~n:"";lli"g antenna 203, and not a particular
receiving antenna, is damaged or out of calibration. The id~ dliu~1 of a
damaged or uncalibrated antenna is an important diagnostic tool. It can be
utilized during logging op~,dlior,s to drop one or more of the l,d"a",illi"y or
receiving antennas out of the normal operating cycle, once it has been
10 detected that it is damaged, in order to maintain high quality logging
i"~u""dlion. All~l~la';~cly, the calibration data can be used in post-logging
o~ liùl ,s to modify, interpret, or manipulate the log3ing data to correct for
intervals of measurement during which a particular lldi,s,,,illi,,g antenna was
damaged or fell out of calibration.
Fig. 8 pr~vides a high level flowchart representation of
'' -dliul1 op~,dlions, which of course is set forth in the context of the
flowcha~ts of Figs. 7A, 7B, and 7C. The process begins at block 445. The
process continues at block 447, wherein the calibration operation is initiated
by central processor 215. Then, in acculdance with block 449, a particular
20 lldllal"itlillg antenna is selected; in acco,danc~ with block 451, a particular
receiving antenna is selected. The calibration up~ldliùlls will be pe,rur",ecl
utilizing this particular llallalll ,9 antenna and this particular receiving
antenna. The resulti~g data will provide ill~UlllldliUI1 about the operating
condition of both of these antennas. In acco,-lance with block 453, an
25 ~l1eryi~dlion frequency is set. This is accor,lr' 'led by providing an
ap,ur~,p~idl~ command to numerically controlled oscillator 223. Then, in
accordance with block 455, the l,d"a",illi,\g antenna is energized. In
accordance with block 457, the receiving antenna is sampled, and the data
is stored in memory. At block 459, one or rnore of the ~,ucessu,:a detemmine
30 whether all the frequencies have been swept through. If not, the process
continues at block 453, wherein the el1eryi~dliol~ frequency is set, once
28
WO 9~il24663 2 1 8 5 û 2 9 . ~I/L _ 14
again, at a higher frequency than the previous frequency utilized. However, if
it is d~ ,lilled block 459 that all frequencies haYe been used, the process
ends at block 461. In the preferred ~Illbo.li,ll~, a particular frequency
range is stepped through in ill.;l~ > of fractional portions of 1 Hertz. For
5 practical purposes, the calibration operation can be col~sidelt:d to be a
sweep through all frequencies within a plt:d~l~llllill~cl frequency range. The
data that is recorded in memory can be analyzed in a manner discussed
below to assess the operating condition of the ~Iclh:,lllitl;ng antenna and the
receiving antenna.
Fig. 9 provides a depiction of an example of the type of data
that can be acquired during a calibration operation. Of course, during
logging operations, the data will not be recorded or depicted in graphical
fonm. Instead, a data array will be defined which includes il,f~i,llalic,l~ about
the amplitude and phase attribute of the receiving antenna's response at a
15 particular frequency. The graphical depiction in Fig. 9 is provided for
purposes of exposition. In the view of Fig. 9, the amplitude of the response of
the llall~l, ,g and receiving antenna is depicted by curve 463. In Fig. 9,
the phase of the response of the ~ alllulli"g and receiving antenna is
depicted by curve 465. In order to determine when malfunctioning is
20 occurring, it is necessary that a normal operating condition be
p,~ bli~,lled. This should be done with regard to a range of ~r~e~ le
operating conditions. The graph of Fig. g depicts nonmal operation over a
range of 300 KHz to 3.3 MHz. In the view of Fig. 9, peaks 467, 469, 471,
473 define two resonant frequencies for the l~ ",illillg and receiving
25 antennas, with l~s~ ,c~s occurring at 400 KHz and 2 MHz, since the
particular antennas utilized to generate this calibration graph were resonant
at both 400 KHz and 2 MHz. From the illtUllllClliu~ contained in the
measurements made when the tool is operating nommally, pdlCllllL~t~ can be
e:,labl;..lled to alert of malfunctioning. Figs. 10A, 10B, and 10C graphically
30 depict three techniques for detecting antenna malfunction. The first
technique for detecting antenna malfunction is depicted in Fig. 10A wherein
29
,
W0 95114663 2 1 8 5 0 2 9
peak 475 is r~ at~lk~ e of either an amplitude or phase peak for norrnal
oueldliul~s~ In contrast, psak 477, which is y~ ,dled as a result of
calibration operations during logging, indicates to the operator that a shift inthe resonant frequency has occurred. A range of ~,-c~rl '~le resonant
5 frequencies can be established. If the measurement falls outside an
a.,~uldbl~ range, a d~ lll;,ldt~ can be made that either the l,d" ""illi"g
antenna or the receiving antenna is malfunctioning. Fig. ~OB depicts
another technique for detecting malfunctioning antennas. Peak 479
,~p~ "t~. normal U,~J~ldliUIls, while peak 481 ~yr~s~ a measurement
10 made during logging. The antenna Q for the actual measurement differs
~iy"i~i~d"lly from the antenna Q of the normal operating state. A change in
the antenna Q can thus be used to indicate malfunctioning.
1.3 Correction for Changes in Antenna l",ueddl-ce and Antenna Mutual
1 S Couplin~
When an interrogating signal is receiveGI at the receiver
antenna, the electrical pa,d",c~ which quantify the signal, phase and
dll, "' Irie, are functions not only of the desired signal from the lldllalllillt~l,
but are also functions of the antenna i",~e~dl~ce. Antenna i~",o~dd,~ce can
20 change during tool operation as a function of temperature and pressure.
Since this funGtional forrn of this change may not be known a priori, the
present invention devises a method to measure the effects of these functional
changes upon the desired signal.
Fig. 11 provides an electrical scl)er"dli~ depiction of an
25 equivalent circuit which depicts the r~lationship between antenna
i"",~dd"ce and an antenna transfer function. This can be utilized to explain
the pald",~:lc";, which aflect the i",~-edd,~ce of a receiver in a logging tool. In
this eleGtrical schematic, the i"",e.ldnce of a receiving circuit is identified as
Rr. The voltage Ejn across the receiver circuit input ,t"~,~s~"l:, the receiving30 antenna~s response to the measurement of the ,~"" ~l ,9 el~-;l,u",ay"etic
field. Zin ,~ s~.,ts the illl~ddi~Ge of the receiving antenna as seen from
3û
WO9S/24663 2 1 &5029 1~ "7~14
the receiver ~le~ .,r,i.,s. The impedance includes Rant which is the resistive
COIIl~,o~l~lll of the receiving antenna, Ca which is the capacitive component
of the receiving antenna, and La which is the inductive cor"pol~e"l of the
receiving antenna. This equivalent circuit is mutually ",ay"dli~ally coupled
to the steel drill collar logging tool suL,dsst Il~L,ly RSub~ the surrounding
fommation Rformation~ and the lldll~ . The sub is ess~, " lly a resistive
cor"po,~"~ which is mutually coupled through inductive c.""~ one"l Ls to the
receiving antenna denoted by the mutual coupling Mat. The fommation is
esse"li~a"y a resistive cor"pol~e"l which is coupled magnetically to the
10 receiving antenna through inductor Lfvia mutual inductance Mat. The
voltage induced in the receiving antenna from the lldll~ is the desired
signal, and the effect of the fommation, sub, and antenna i",yedd~lc~ upon the
measurement of this voltage are variabies for which this invention accounts.
The ll~ r is ess~ dlly a voltage source which is coupled to the
15 receiving through inductor Lt. The circuit of Fig. 11 can be reduced to the
circuit depicted in Fig. 12, with the impedances of the antenna, the
s~bass~,.-bly, the fommation, and the llal)~lllill~l l~.l~a~ d respectively as:
Zantenna, Zsub, Zformation, and Zt- Et is the equivalent voitage source in the
receiver circuit due to the l,d":""ill~r. A current I is induced to flow through20 this equivalent circuit by voltage source Et. As is depicted in Fig. 12, a
voltage Ejn is developed across the receiving circuitry as a result of this
current flow. The combined effect on the antenna of i",pedal,ce of the
antenna, the drill collar su~a~ l"bly, the formation, and the lldl~:~lllitl~l isl~,ul~s~ d in this view as Zin- The i",~ dl~ce of the receiving antenna,
25 along with the impedances introduced through normal operation and
undesired mutual coupling make up the i""ueJdllce Zin, as is set forth
herebelow:
(1 ) Zin = Zantenna + Zsub + Z fommation + Zt
The transfer i""~edd,.~ for the antenna is represented as:
31
WO 95/24663 2 1 8 5 0 2 9
(2) Rr + Zantenna + Zsub + Zfommation + Zt = - Et / l
This transfer i",l.eddnce states that the total current within the
equivalent circuit of Fig. 12 ts a function of the voltage of the lldl,a",ili;"g5 antenna Et, and all the i""~edd"ces of the circuit of Fig. 12. The current can also be stated as a function of Ejn and Rr, as:
(3) 1 = - Ein / Rr
~0
The transfer function for the antenna can be dc~ lli"ed from
these l~ldliu~ ll;,us in ~c~,~,dal~ with equation (4):
~4) Transfer Function = Et / Ein
=(Rr + Zantenna + Zsub + Zfommation +Zt) / Rr
Combining equation (1~ with equation (4) yields:
(5) Transfer function = Et / Ein = (Rr + Zin) / Rr
2û
Note that the transfer function is a simple function of the
receiver i"",e~dilce Rr and the measured antenna input i",,ueddllce Zin-
ln the present invention, the particular technique utilized tûmeasure Zin is a conventional "network analysis method.- In accol.ldn.,~
25 with this ~echnique, a reflection coefficient p is obtained by meaâuring the
ratio of an incident wave to the reflected wave. Typically, a directional
coupler or bridge is used to detect the reflected signal, and a network
analyzer is used to supply and measure the signals. In the present invention,
the numerically controlled oscillator can serve the functions of the network
3û analyzer, since its output attributes (frequency, phase, and amplitude) can be
precisely controlled, and further since the actual output is measured over a
predetermined frequency interval. Directional couplers ar~ devices which
32
W0 95/24663 2 ~ 8 5 0 2 ~ 4
are used to separate or sample the traveling ~le~;t,ulllayll,:lk, wave moving inone direction on a l,dn:""is~ion line while remaining virtually unaffected by
the traveling ele.;l,~,r"ay"~k, wave moving in the opposite direGtion. Thus,
they are typically utilized in analyzing power lldl~ iOI) lines and the like
5 They are frequently used in culllbilldliull with power splitters which receive an input, and provide two equal outputs. In the present invention, both
.lional couplers and power splitters are utilized to derive the
measurements which are utilized in the c~;.llilldliu~ of the undesired effects of
mutual coupling between receiving antennas.
The reflection co~r~i.. i~"l is derived from the voltage of the
signal reflected from the antenna and the voltage of the signal going into the
antenna, in a.,c~r id~ with the foliowing equation:
(6) p = reflection .,c~r~i,;i~"l = (voltage of signal reflected from
1 5 antenna)
+ (voltage of signal going into the antenna)
Furthermore, the i,l",~ ial,ce of the antenna can be derived
from the reflection coefficient and the i",,ue id~,ce of the directional coupler ZO
20 in accor~idnce with equation (7) as:
(7) Zin = ((p + 1) Zo) / (p - 1)
Equations (5) and (7) can be combined to determine the transfer
25 function Et/Em in temms of Rr (the illlpe idll~C7 of the receiver circuit, which is
known), Zo (the i,,,f,edc,nce of the directional coupler, which is also known),
and p (the reflection coefficient, which an be calculated from a measurement
of the incident signal and a measurement of the reflected signal) as follows in
equation (~).
- (8) Et/Em = (Rr + ((p + 1)/(p-1))Zo) / Rr
.
33
W0 95124663 2 1 8 5 0 2 9
From this transfer function tlle voltage induced into the receiving antenna by
the transmitter Et may be dc,~,,,,i,,ed by simply multiplying the receiver
voltagQ by the transfer function: Et = Em~EtlEm) corrected by Zantenna
5 Zsub and Zt
Fig. 13 provides a block diagram view of the c~"",one"l:,
which interact in the measurement process to eliminate the influence of
undesired magnetic field mutual coupling between receiving antennas. Fig.
14 is a more detailed view of the c~"",o,)~"~ which cooperate together to
10 make this analysis possible.
With ref~rence first to Fig. 13 directional coupler 501,
directional coupler 503 and numerically controlled oscillator 509 are
especially provided to allow for the measurements which can be utilized to
eliminate the effects of ~"de~i,d~le magnetic field mutual coupling between
15 receiving antennas 211 213. As will be described in c~""~ i;al, with Fig.
14, directional couplers 501, 503 are switched in and out of the circuit
depending upon whether normal reception ope,dliolls are desired, or
whether a mutual coupling c~l~bld~ l operation is required. Receiver
circuits 505 507 are identical to the receiver circuit depicted in Fig. 4 and
20 described above. This receiver circult has a ~I,an~ resistance Rr for
receiver 505 and Rr for receiver 507. These resistance values are about 50
ohms. The di~liul~al coupler 501 in Fig. 14 by provides at least 60dB
isolation between forward and backward traveling signals. Receiving
antennas 211 213 have an effective i",pedd"ce Of Zin. which mat change
25 with temperature and pressure. Digltal signal processor 221 generates, or
passes along, commands to numerically controlled oscillator 509 to provide
an energizing signal which may be directed through either directional
coupler 501 to receiving antenna 211 or through directional coupler 502 to
receiving antenna 213. A certain portion of the e~,e,yi~i"g signal is
30 accepted by receiving antenna 211 or213 and a portion is reflected back
through directional coupler 501 to receiver 505 or through directional
34
i W095/24663 2185029
coupler 503 to receiver 507. The reflected signals are ,u,ucesDed by digital
signal processor 221, and passed to central processor 215. Digital signal
processor 221 may simply provide a circular memory buffer for the storage of
data, which is then pe,iùdi~l'y fetched by central processor 215 for further
5 I-,uceDsi"g. This activity is l,:;Vlt:s~ by the 'data out' bus of Fig. 13 . In the preferred embûdiment of the present invention, each of receiving
antennas 211, 213 is analyzed separately.
In broad overview, in the present invention, the technique for
correcting a measurement made with a particular receiving antenna for the
lû (corrupting) error c~",pone"l due to u"desi,dbl~ magnetic field mutual
coupling is a~i~ù,,,~,liDlled by making the following measurements over a
pr~d~i"ed frequency interval (such as 100 Hertz to 6 MH~): direct an
~l1 Iyi,i"g signal to a particular receiving antenna, and measure with
precision the amplitude and phase attributes of the incident wave; measure
15 with precision the reflected wave which reflects off of the receiving antennaand back through a directional coupler; calculate the reflection cOe:~iui~ p
from the measurements of the incident wave and reflected wave; utilize the
calculated value of reflection coemcient p, and the known i""~e.ld,lce ZO of
the directional coupler, to calculate the input illl~edd~ Zin for the particular20 receiving antenna; utilize Zin and the known ~or fixed) i,n~.e~dn.,~ of the
receiver circuit Rr to calculate the transfer function for that particular antenna.
Note that this dt:l~llllil,~tiv,, is made for all operating frequencies of interest.
With specific regard to the preferred ~",I,oui",~ of the present invention,
measurements will need to be made for 400 KHz and for 2 MHz, since these
25 are the two operating frequencies are utilized during logging opeldliolIs.
Note that, in accordance with equation (5), the transfer function provides a
measure of the ratio of the voltage generated in the receiving antenna as a
consequence of an illl~ gdlillg electromagnetic signal (Et) and the voltage
detected at the input of the reception circuit (Ejn). In other words, the transfer
30 function at a particular frequency equals Et + Ejn. This transfer function may
be applied to measurements made during logging o~,dlk,ns to eliminate
W0 95/24663 2 1 ~ 5 ~ 2 9 ~
the influence of the corruption in the detected voltage (Ejn) which is due to
magnetic field mutual coupling and thermal (and other) drifts in antenna
response. This correction may be a..Gu,,,,ul;~l,ed by merely multiplying a
detected signal (Ejn) times the transfer function value for the receiving
5 antenna at the illle:lluydi;vl~ frequency which is sensing the illlellugdlillg signal. In this manner, the measurement is corrected to supply an
uncorrupted signal Et for further IJIuCQSaillg In the preferred ~IllI,odi",6"l of
the present invention, the ",all,~",ali.ial Op~ldliUI~s which eliminate the
corrupting influence of the ull~e~;ldblt magnetic field mutual coupling occur
1 û in either digital signal processor 221 or central processor 215.
In other words for each measurement made by receiving
antenna 211 digital signal processor 221 (or central processor 215)
aulGIlld~iu. lly fetches a value recorded in memory for the transfer function ofreceiving antenna 211 at the particular frequency of the i,,~rlu~dlillg signal
15 which is being utilized. The measurement made utilizing receiving antenna
211 is multiplied by the transfer function value; the resulting product is a
measurement value which is corrected for the corrupting influence of
u~ bildble magnetic field mutual coupling between receiving antenna 211
and receiving antenna 213. Conversely when reCQiving antenna 213 is
20 utilized to measure an i,,lG-r,uydlillg elecl,ur,,aylltllic field, digital signal
processor 221 (or central processor 215) fetches the transfer function value
for the particular frequency of the i"~ .,u~ ,9 field and then multiples that
value times the measurement obtained from receiving antenna 213. The
product is the measurement made with receiving antenna 213 which has
25 been corrected for the corrupting influence of ullde:,ildble magnetic field
mutual coupling between receiving antenna 213 and receiving antenna
211. The details of operation are set forth below in the desc,iulivll in
cc,l,,,euliv,, with Fig. 14.
With reference now to the view of Fig. 14 receiving antenna
3û 211 is depicted as being optionally connected through directional coupler
501 to receiver circuit 505 and digital signal processor 221. Receiving
36
W0 95/24663 2 1 8 5 0 2 9 r~
antenna 213 is likewise depicted as being optionally coupled through
iul1al coupler 503 to receiver circuit 507 and digital signal processor
221. Receiving antennas 211, 213 are optionally coupled to the output of
numerically controlled oscillator 509 through power splitters 519, 521, and
5 523. Attenuators 511, 513, 515, and 517 are provided at selected
positions within the circuit for load balancing purposes. Preferably, each
attenuator provides a 60dB load. In the circuit of Fig. 14, four switches are
provided: switch S1, switch S2, switch S3, and switch S4. Each of these
switches is under the control of digital signal processor 221 and/or central
10 processor 215 (of Fig. 6). Switches S1, S3 are three-positioned switches,
while switches S2, S4 are two-position switches. Each switch is under the
binary control of a particular output pin of digital signal processor 221.
Changes in the binary condition of the output pin of digital signal processor
221 will toggle switches S2, S4 between open and closed positions, while
15 switches S1, S3 are toggled between the three positions.
Fig. 14 will now be utilized to describe six basic measurement
V~,e,dl;v,ls which underlie and allow the technique of the present invention of
C'illlilld~ the undesired eflects of magnetic field mutual coupling between
receiving antennas and phase drift due to high wellbore temperatures or
20 pressures.
Step 1: in this step, switch S1 is set in position number two,
switch S2 is closed, switch S3 is placed in position number one, and switch
S4 is left open. Nu",e,i..ally controlled oscillator 509 is coupled to receivingantenna 213 through switch S2 to allow an electromagnetic propagating
25 wave to pass between receiving antenna 213 and receiving antenna 211.
Also, in this particular configuration, receiver circuit 507 is co""e~ d to
receive and monitor the output of numerically controlled oscillator 509
through power splitter 523 and impedance 513 while receiving antenna
213 is energized. Additionally, receiving circuit 505 is col~"e~ ,d to monitor
30 the signal originating from receiving antenna 211 in response to the
37
WO 95/2-1663 2 1 8 5 0 2 9
ele,:t,.,",~yl,etic wave which travels from receiving antenna 213 to receiving
antenna 211.
~ 2: this step is performed simultaneously with Step 1.
Receiving circuit 505 is coupled through switch S3 through receiving
5 antenna 211 and monitors the response of receiving antenna 211 to the
,"la~"t~ic propagating wave which is generated at receiving antenna
213 (which is operating as a lldl~:~lllitl~l) and received at receiving antenna
211 (which is operating as a receiver). In Step 2 all the switch positions are
identical to those positions of Step 1.
The rQsult of the simultaneous pelfulllldllce of these ope,d~ions
it that channel 1 of digital signal processor 221 records data from recQiving
antenna 211 through receiver circuit 505 while channel 2 of digital signal
processor 221 records the output of numerically controlled oscillator 509
through receiver circuit 507. In the preferred embodiment of the present
15 invention numerically controlled oscillator 509 is cu,,,,,,al~ded by digital
signal processor 221 to step through a p~ed~l~""i"ed range of frequencies.
The data accumulated on channel 1 and channel 2 of digital signal
processor 221 thus defines two data sets: one which records the energizing
signals supplied to receiving antenna 213 (the "incident signal~) which is
20 operated as a lldll~ r~ and another which records the response of
receiving antenna 211 to that energizing signal.
Fig. 1 5A provides a graphical depiction of data which is
recorded on channel 2 of digital signal processor 221, with curve 601
providing a view of the amplitude of the output of the numerically controlled
25 oscillator over the ~ dt,ri"ed frequency range Of f1 to f2 and with curve 601providing a record of the phase attributes of the output of the numerically
controlled oscillator 509 for the range of frequencies from f1 to f2. Together,
these values for amplitude and phase provide a measurQ of the 4incident
signal". Fig. 15B provides an exemplary view of the type of data which can
30 be recorded on channel 1 of digital signal processor 221 with curve 605
Sellldli~le of the amplitude response of receiving antenna 211 to the
38
~ WO9!i/24663 2185029
energizing el~l,v",as~"elic wave provided by receiving antenna 213, over
the prt,d~i"ed range of frequencies of fl to f2, and with curve 607 providing
dliUI I about the amplitude response of receiving antenna 211 over the
same range of frequencies. The i,,fv,,,,d~iv,, contained in Fig. 15B is similar
5 to that contained in Fig. 9, but provides i"rvl",dlion about the operating
condition of receiving antennas 211, 213. The type of data analysis which
is discussed above in cu,,,,eulion with Figs. 9,10A, 10B, and 10C can be
perfommed upon the receiver-to-receiver profile. In other words, the signal
recorded on channel 1 provides a measure of the combined response of
10 receiving antenna 211 (operating as a llall:,llli~lc:l) and receiving antenna213 (operating as a receiver) in Cvlllvilldlivll with the impact of the boreholeand formation on the signal l~d",",;~s;~n. Data sets can be created for
l~dn:"";ssion in one direction (receiving antenna 213 operating as a
l,dns", 'er, and receiving antenna 211 operating as a receiver) as well as
15 the other direction (receiving antenna 211 operating as a l~d"-;",ill~r, and
receiving antenna 213 operating as Q receiver). The data sets dsser"vled
for these operations can be compared with profiies developed in the
laboratory for normal operation. Changes or shifts in resonant frequency,
antenna Q, or the amplitude of response at a particular frequency can
20 provide important ill~Ulllldliol1 about whether the receiving antennas 211,
213 are operating as desired, or whether they are damaged or out of
C&IlL~l dliUIl.
Step 3: in this step, switch 1 is set in position three, and switch
2 is closed. The positions of switch S3 and switch S4 are are open and are
25 unimportant for this operation. In this operation, numerically controlled
oscillator 509 directs an i"lt:r,uyclli"g signal through power splitter 519,
power splitter 523, and switch 3 toward directional coupler 503 and
receiving antenna 213. A portion of the t:"t"yi~;"g signal is accepted by
receiving antenna 213, and It:pl~s~"l~ the "incident signal", while a portion
30 is rejected by receiving antenna 213 and ,t,,vl~St:rll:, the "reflected signal."
The reflected signal is directed through attenuator 511 and switch S1 to
39
W0 95/24663 2 1 8 5 0 2 9 ~ 4
receiver circuit 507. Preferably numerically controlled oscillator 509 is
stepped through a ~ .",i"ed frequency range and receiver circuit 507
monitors the reflected signal over the particular frequency range and ports
the data into channel two of digital signal processor 221. Fig. 15C provides
a graphic depiction of the type of data which is recorded in channel two of
digital signal processor 52 with curve 609 representative of the amplitude
attributes of the reflected signal and curve 611 ,t~ ,s~" :c of the phase
attributes of the reflected signal.
In steps 4s 5 and 6 the process is reversed, with receiving
antenna 211 serving as the lldllblllil~illg antenna. This provides ill~ulllldliùfrom a different point of view.
Step 4: in this step, switch S3 is set in position two switch S4 is
closed switch S1 is set in position one, and switch S2 is left open. In this
configuration, numerically controlled oscillator 509 may be stepped through
a ,ul~dt~ ed frequency range and receiver circuit 505 can record the
amplitude and phase of the output of numerically controlled oscillator 509
(the "incident signal"), and provide this to channel one of digital signal
processor 221. Fig. 16A provides a view of the type of amplitude 613 and
phase 615 data which may be recorded during this operation.
Ste~ 5: This step is perfommed simultaneously with step 4. With
the same particular switching configuration of Step 1 receiving antenna 211
is supplied with an ~e~yi~i"g signal, causing an ele~.l,u,,,ay~ ic wave to
propagate toward receiving antenna 213. Receiving antenna 213 responds
to the p~upaydlillg ele.~l,u,,,ayll~liu- signal and this response is monitored by
receiver circuit 507 and recorded on channel two of digital signal processor
221. Fig. 19B yldUI ' ~Iy depicts the amplitude response curve 617 and
the phase response curve 619, both over the prt:dt,l~,l"i"ed frequency
range.
Step 6: in this step, switch S3 is set in position three switch S4
is closed switch S1 is set in position 1 and switch S2 is left open. In this
particular switching configuration, the energizing signal provided by
WO 95124663 2 1 8 5 0 2 9 r~ g! ~
numerically controlled oscillator 509 is directed toward receiving antenna
211. A portion of the ~"~ i"g signal is accepted by receiving antenna
211, and a portion is reflected. The reflected portion is routed through
attenuator 517 and switch S3, where it monitored by receiver circuit 505,
5 and recorded to channel one of digital signal processor 221. Fig. 16C
provides 8 graphical depiction of the data sets which are maintained in
channel one of digital signal processor 221 in graphic fomm.
In the preferred ~ iJo.li~ of the present invention, the data
from these O,UeIdI;OI~5 are arranged in data arrays, to allow for the use of
10 conventional data manipulation ope,dli~ns in order to detect or identify
particular attributes of the data set, such as maximum responsiveness,
minimum ,~:,,uo"siv~,1ess, rates of change of the data, and the relative
position of particular data attributes. Diagnostic UUtlldliUlls can be perfommedutilizing these data sets. For example, the l~:~,uùl~SeS recorded in data sets
15 co"~:.pol~di"y to the illru""dli~ll displayed in graphical fomm in Figs. 15A
and 1 6A may be compared. Since the numerically controlled oscillator 509
has "phase coherency," the amplitude and phase measurements of the data
sets of Figs. 15A and 16A should be identical. The failure to find similarity,
or the discovery of dissimilarity, can serve to diagnose a variety of
20 ",e~l,a,1icdl problems, including broken switches, a malfunctioning receiver,or other co",uu~ "l failure. For an alternative example, the data sets which
are visually l~plt~s6"1~d in Figs. 15B and 16B may be compared. The
curves of Figs. 15B and 16B should be identical, since they represent the
combined response of the receiving antennas and the borehole region
25 illl~""edidl~ the receiving antennas.
Fig. 17 is a flowchart depiction of the preferred technique of the
present invention for correcting for the undesired corrupting influence of (1)
magnetic field mutual coup~ing between receiving antennas, and (2) any drift
in antenna response. The process begins at flowchart block 615. In block
30 653, a particular lldll~ is energized with a current having a particular
frequency to generate an eleul,u",dg,~ field which ,ulUUaydL~s through the
41
WO95/24663 2 1 85029
borehole, and which is detected at recoivers 211, 213, in acco,ddl,c~ with
software block 655. Then, in acc~n~allce with software block 657, digital
signal processor 221 or central processor 215 fetch transfer function values
for the particular operating frequencies for (a) the mutual coupiing impact of
receiving antenna 211 on receiving antenna 213, and (b) the mutual
coupling impact of receiving antenna 213 on receiving antenna 211. Then,
in accoldarlce with software block 659, the transfer function value of the
impact of receiving antenna 211 on receiving antenna 213 is applied to the
measurements made with receiv~ng antenna 213. Then, the transform value
for the impact of receiving antenna 213 on receiving antenna 211 is applied
to the measurements made with receiving antenna 2 11. Then, in
ac~,o,~d"ce with software block 661, resistivity values for the fommation are
calculated using the corrected measurements, and the process ends at block
663. Thesa Cpt:ld~iù~)s are performed for every measurement made during
logging operations. The transfer functions .~so~ d with ~Idl-blllibsiol1
operation frequencies of 400 KHz are utilized to correct for mutual coupling
and thermal error c~ll,UUIl~llLb present during 400 KHz logging u,ue,d~i~l,s~
while the transfer functions A.~.,U~ t. d with 2 MHz are utilized to correct forthe influence of mutual coupling and drift Colll,uu116111s during 2 MHz
~Idllblllibsion ope~dli-~"s.
1 .4 Log~ing CAI~ At~ S
The following section illustrates how the present invention is
used to derive an accurate measure of the amplitude attenuation and the
phase shift of the i"~ rluydlillg ele.;l,u",ay" signal which travels through
the borehole and surrounding formation. The r~ ' ~sl,i~ between these
amplitude and phase measurements, and their l~ldliù~blli~u to the resistivity
of the material, will also be illustrated. It should be t~,uilasi~:d that the
resulting measure of resistivi~y contains a contribution from the borehole as
well as the fommation and is not, therefore, a "final" resistivity answer in thecontext of previous discussion. It is also e",,ul,asi d that a borehole
42
~/ WO 95/24663 2 ~ 8 5 0 2 9 ~ .,51. 1
instnument Cu~ ibillg two ~d~ lllitl~1 7 and two receivers is used to iilustratedata ~J~u~es:7illg methods. The derivation of resistivity of the formation,
resistivity of the borehole, ~;lldla~:t~ of the fommation and borehole, and
data ,ulucesai"g using a borehole instrument co",pri:,i"g four l
5 and two receivers will all be discussed in subsequent sections.
First, consider four t,d,l~"litl~r-to-receiver signals:
(Transmitter 1 [X1] to Receiver 1 [R1]): A1 1 ei01 l
(Transmitter 1 [X1 ] to Receiver 2 [R2]): A12 ei012
1û (Transmitter2[X2]toReceiver1 [R1]): A21 ei02l
(Trdnsmitter 2 [X2] to Receiver 2 [R2]): A22 ei022
The measured dll~ ' IrlR5 are made up of:
(9) Amn =xmRnatmn
where Xm - llal Iblllill~ output variation
Rn = receiver sensitivity variation
atmn = true amplitude (lldl~:~lllitl~l M to receiver N);
2û
and the measured phases are made up of:
(1 û) 0mn = 0Xm + 0Rn + 0tmn
25 where 0Xm = lldllalll~ phase (output) variation
0Rn = receiver phase variation
0tmn = true phase (I~ dl l~ l M to receiver N)
The foregoing general equations cor~ olld to the following
3û more specific equations:
~ .
43
W0 9~/24663 2 1 8 5 0 2 q ~ 2~14
All =Xl Rl atl1
A12=X1 R2at12
A21 = X2 Rl at21
A22 = X2 R2 at22
5 011 = 0X1 + 0R1 + 0t1~ -
012=0X1 +0R2+0t12
021 =0X2+0R1 +0t21
022=0X2+0R2+0t22
Taking ration of the various transmitter-to-receiver signals
produces the following:
For Transmitter 1
(Al2ei0l2lAllei011)= (Al2lAll)ei(0l2-011)
and for Transmitter 2:
(A21 el021 / A22 ei022) = (A21 / A22)e i(021 - 022)
20 Multiplying the above equations and taking the square root gives:
(1 1 ) [(A1 2A21 / A11 A22)]112 exp (i (a 12 l a~ 1 0 l 1-022)/2)
Slldiul,l~u~ia,d algebraic manlpulation of equations (9) through (11) yields:
(12) [(at12at21/atllat22)]1l2exp(i(0~i2~k~ 0t22)l2)
because all the system variables drop out of the measurement.
Therefore, by using two transmitters and two receivers,
3û systematic variables can be removed from both the attenuation (amplitude)
and from the phase velocity (phase difference) terms.
44
~ W0 95/24663 2 1 ~ 5 ~ 2 9 r~
Within the context of the preferred ~ bodi~ of this invention,
in which a sampled data ~ ues:~i"9 means produces a signal as a function
of formation resistivity based on phase-representing signals, the following
anaiysis d~lllul)~lldl~s certain matter relevant to the stability feature.
Consider two consecutive samples: Sample A and Sample B.
During Sample A, a first l~dri:,", ,~ coil is energized to cause a wave to
propagate through the formation in a direction such that the wave passes a
first receiving coil (R1), and later passes a second receiving coil (R2), and
induces each receiver coil to produce a signal. During Sample B, a second
10 lldn:,,tli"g coil is energized to cause a wave to propagate through the
fommation in a direction such that the wave passes a second receiving coil
(R2), and later passes the first receiving coil (R1~, and induces each receiver
coil to produce a signal~
Let 0MR2A represent the measured phase of the signal
produced by receiver coil R2 during Sample A; let 0MR1A represent the
measured phase of the signal produced by receiver coil R1 during Sample A;
let 0MR1B represent the measured phase of the signal produced by receiver
coil R1 during Sample B; and let 0MR2B represent the measured phase of
the signal produced by receiver coil R2 during Sample B.
The ~MR2A signal depends on the phase of the wave at the
location of R2, and in general, has an error component attributable to various
phase shifts including those introduced by the tuned receiver coil, cabling
from the receiver coil to the receiver, and the receiver itself. Let 0TR2A
represent the true phase of the wave at the location or R2 during Sample A,
and let 0R2E represent the error c~,,,pull~ so introduced.
(13) 0MR2A = 0TR2A + 0R2E
Similarly, the 0MR1A signal depends on the phase of the wave
at the location or Rl, and in general, has its own error cullluùllerlt~ Let
W0 95/24663 ` 2 1 8 5 0 2 9 ~ u~
0TR1A represent the true phase of the wave at the location of R1 during
Sample A, and let 0R1E represent the error Cul"~,ù~ so introduced.
(14) 0MR1A = 0TR1A + 0R1E
During Sample A, the 0MR1A signal and the 0MR2A are
simultaneously ~Iu~,essed tû produce a DeltaA signal that Ic,l,lt,s~,li, the
difference in phase between these two signals (i.e., 0MR~a - 0MR2A).
1û (15) DeltaA=(0TR2A-0TR1A)+(0R2E-0R1E)
The col"pol~e"l of the DeltaA signal It,pl~s~"li"g the true
phase difference (0TR2A - 0TR1A) is a function of the resistivity of the
fommation in the region between the two receiver coils. Let F(Rapp) represent
this c~",,u~"~"l.
(16) DeltaA = F(Rapp) + (0R2E - 0R1 E)
Similarly, during Sample B, the 0MR2B signal and the 0MR1B
are simultaneously processed to produce a DeltaB signal that It~ 5t~ the
2û difference in phase between these two signals (i.e., 0MR2B - 0MR1B).
(17) 0MRt B = 0TR1 B + 0R1 E
(~ 8) 0MR2B = 0TR2B + 0R2E
(19) DeUaB = (0TR1 B - 0TR2B) + (0R1 E - 0R2E)
The co",uoll~"l of the DeltaB signal ,~p~s~"li"g the true
phase difference (0TRlB - 0TR2B) is a function of the resistivity of the
fommation in the region between the two receiver coils; i.e., U equals F(Rapp)~
3û (21 ) DeltaB = f(Rapp) + (0R1 E - 0R2E)
46
W095124663 21~5[~29 r~ 4
The Delta A signal is recorded so that it can be retrieved and
processed with the Delta B signal.
By adding Equations (19) and ~20~, it follows that:
5 DeltaA + DeltaB = 2 ~ F(Rapp) + 0R2E - 0R1 E - 0R2E + 0R 1 E, and
(21) F(Rapp) = 1/2 ~ (DeltaA + DeltaB)
In other words, a computed signal ~ s~"li"g the sum of the
10 consecutive samples is a function of formation resistivity, and error
COlllpOI~ such as 0R1E and 0R2E do not introduce errors into this
computed signal.
2. PARALLEL PROCESSING OF MEASURED DATA
As discussed briefly is a previous section, it is desirable to
transform signals measured by the one or more receivers into parameters of
interest using simultaneously using "parallel" plucessi,-g. Consider again
the four ~rdl1SIl ~ tWO receiver embodiment of the borehole logging
instrument shown in Fig, 2. The near spacing dn between l-dn:,,,,ill~l and
20 receiver array is denoted by the numeral 23 and the far spacing df is
denoted by the numeral 21. Both the near spacing distances 23 and far
spacing distances 21 are measured with respect to the midpoint 25 between
the receivers 213 and 211. Point 25 is commonly referred to as the
"measure point" of the borehole instrument. For lldl~ frequency ~1 the
25 phases of the signal detected at receivers 213 and 211 resulting from the
sequential l,~,~s",;~siol1 from l,al1s",i~l~rs 209 and 205 are combined
alg~b,di~ r to obtain Rp,n,1. More s, " 'Iy, a first phase shift computed
from the difference in the responses of receivers 213 and 211 resulting from
the activation of transmitter 207 is algebraically averaged with a second
30 phase shift computed from the difference in the ,~ .ol~ses of receivers 213
and 211 resulting from the activation of the lldll~ r 205 to yield Rp,n,1-
47
W0 95124663 2 1 8 5 ~ 2 9 r~
The dll, '~ RS of these receiv2d signals are simultaneously measured andcombined yielding Ra,n,1. More :,I,eci~ 'ly, a first amplitude attenuation is
computed from the ratio of the responses of receivers 213 and 211 resulting
from the activation of l,dll:,",iller 207 is alyel,,di-;~l'y averaged with the ratio
5 of the ,tl:,~Jùllses of receivers 213 and 211 resulting from the activation oflld~lSlllillt:r 205 to yield Ra,n,1. Again for a lldll~lllillt:l frequency ~1, the
phase of the signals received at receivers 213 and 211 resulting from the
sequential l~dll;,",;.,sion from lldll~ ; 209 and 203 are combined
dlgeL, "y in a similar manner to obtain Rp,f,1. The amplitudes of these
10 signals are likewise simultaneously measured and combined in a similar
manner yielding Ra,f,1. The above sequence is repeated with a second
l frequency ~2 yielding Rp,n,2, Ra,n,2, Rp,f,2 and Ra,f,2. The end
result is eight apparent resistivity measurements cu",,u,i:,i"g amplitude and
phase shift measured at two l,dl1s", r-receiver spacings and at two
15 l,d,~s",ill~r frequencies.
Fig. 18 illustrates hypothetical measurements of resistivity
across a thin formaticn bed denoted by the numeral 51 using a single
lldl~s",i~ and two receivers. This bed of vertical extent 56 is bounded on
either side by formation of essc:~l "y infinite vertical extent identified by the
20 numeral 61. In the example, the vertical extent 56 of bed 51 is 4.0 feet. Thetrue resistivity of the bed is 10 ohm meters as illustrated by curve 50 and the
bed is invaded to a depth of dj = 60 inches. With the resistivity of the invadedzone RXO = 2.0 ohm meters as illustrated by curve 52. The resistivity of the
surrounding or shoulder fomnation, RSHOULDER = 0~5 ohm meters, is illustrated
25 by curve 60. The shoulder ~u,,,, ,s are not invaded by the drilling fluids.
Curves 53 and 54 illustrate the apparent phase and amplitude resistivities
measured across the bed boundaries at a tldll:~lllillt~l frequency of ~1 = 2
MHz. Using previously defined nu",t")cldlure, curve 53 is computed from
the difference of the two receivers and is denoted by Rp,f,1 and curve 54 is
30 calculated from the ratio of the two receivers and is denoted by Ra,f,1.
Similar curves are generated at a second frequency ~2 but are not shown.
48
WO ~5124663 2 1 8 5 0 2 9 p_l/L _. 1
It can be seen that the maximum or peak values of curves 53 and 54 within
zone 51, denoted by the numerals 58 and 57"~:,pe~ti./cly, are 2.23 and
2.07 ohm meters, respectively. Both apparent resistivity measurements
diverge greatly from the actual or true resistivity of Rt = 10 ohm meters. Fig.
5 19 is a graphical l~.n:s~ liol~ of an algorithm for correcting apparent
resistivity measurements made at a frequency of 2 MHz for the effects of
invasion in t.,r",dliv"s of infinite vertical extent. The algorithm was derived
using ll,ev,~ al lld";""illt,l receiver array calculations well known in the art.
Using values for dj = 60 inches, Rxo = 2.0 ohm meters and the maximum
10 phase and amplitude values of 2.23 and 2.07 ohm meters, I~_r "~ly~ the
resulting "-;v"~ d" value for true resistivity, RCor = 2.09 ohm meters, still
exhibiting significant divergence from the actual bed resistivity value of 10.0
ohm meters, Bed boundary cor,~ are applied to the maximum phase
and amplitude resistivity measurements 58 and 57 using correction
15 algorithm derived from theoretical l,a"s",illt:r receiver response calculations
well known in the art and depicted graphically in Figs 20A and 20~,
respectively, using a bed thickness of 4.0 feet. Ra denotes apparent
resistivity measurement in using the charts. These corrected values are then
serially corrected for invasion, again using the synthetic data depicted
20 Jldplli~ "y in Fig. 18. After applying both bed boundary col,~,lio"s and
invasion c~ .tiv, ,s ssrially, the resulting "cor,~ d" value for true resistivity
is RCor = 5.2 ohm meters which still exhibits significant deviation from the true
resistivity value of 10.0 ohm meters~ It is apparent that serially c~r,~:-;li.)ns for
the l,y,,vll,~ al example at a frequency of 2 MHz is totally inadequate.
25 Similarly, the same sequence of corrections using .~o-,~spoll.li"g amplitude
and phase resistivjties made at a~2 = 400 MHz can also be shown to be
totally inR~leql)^'~ Serially Co..~;tio,ls for additional pdldll.~t~ (not shown)such as borehole diameters, resistivity of the drilling fluid, dielectric effects
and formation anisotropy also yield inadequate co~ ;liol,s at either
30 lldl~ l frequency for true resistivity.
49
WO 95/24663 2 ~ 8 5 ~ 2 9 r~~ 9~ 14
The current invention utilizes the eight previously defined
measurements of apparent resistivity along with the cu",,u,~ e~ c model of
the response of the borehole instrument in a variety of formation and
borehole conditions to simultaneously detemmine formation and borehole
5 parameters of interest. The process is generally defined by the matrix
equation:
(22) [R] = rr1 X Pq
10 where [R] jS a 1 x 8 matrix ~I,,t,se~ g eight measures of apparent resistivity
at multiple frequencies and lldll:~lllilltsr spacings as defined previously, and[X] is a 1 x 8 matrix It~ a~l ,Y 8 pa~d~ esrb of interest to be ~ ""i"ed.
For the example being cullsi~ d, Rt, RXO, RSHOULDER~ dj and the thickness
of the zone 56 are included as elements of the matrix [X]. [Tl is an 8 x 8
15 transfomm matrix based upon the cu,,,p,t:lle,,~ e model of the borehole
instrument response in a variety of borehole and formation conditions,
examples of which are shown ylclpllic~:ly in Fig.s ~9, 20A, and 20B. As an
example, [rl comprises the response functions for the borehole instrument
across bed boundaries, the ,t"~pu"aes characteristics as a function of
20 invasion, and response functions for all other borehole and formation
pard,,,~le,x discussed previously in this disclosure. The values of the
elements of rl 1 will depend upon resistivity and will, therefore, depend upon
the matrices [X] and [R]. As a result of this functional d~p~lld~l-c~, equation
(22) is not a simple linear matrix equation. US. Pat. No. 5,144,245 to M. M.
25 Wisler, assigned to the assignee of this disclosure, describes such a model
and is hereby entered by reference. A non-linear regression scheme is used
to invert the equation (22) yielding
(23) [~q = [T] x [R]
-
WO 95124663 2 t 8 5 0 2 9 p~ ~",~ ~
where IT'] is the inversion of the response matrix lTl. The matrices on the
right hand side of eguation (23) are therefore either ~p,~s~,ldlive of
measured quantities ([R]) or are known from II,eortlliual calculations ([T']).
Solving equation for [X], which includes Rt as an element, a corrected value
5 of Rt = 10 ohm meters is obtained for the l,yputl,~,tival example shown in Fig.
18. The fact that sets for two lldl ,:""itl~r frequencies are used in the present
invention contributes to the convergence of the measured and tnue formation
resistivities when compared to the previous computations using only
measurements at 2 MHz. Equally important in the conversion is that the
10 current invention employs simultaneous inversion of the measurements at
multiple frequencies and multiple spacings. The errors introduced at higher
frequencies resulting from serial pruces:,i"y are thus avoided.
3. DETERMINATION OF BOREHOLE PARAMETERS
Previous discussions defined the uses of measured borehole
and near borehole pa,a",~ . The drilling fluid invasion profile is indicative
of the pel" ~"'y of the fommation. In addition, physical properties of the
borehole such as nugosity and ellipticity can be related to the Ille~,llà~liVdl
properties of the rock matrix and to the effectiveness of the borehole drilling
20 operation using the preferred MWD ~Illbou'i~ l of the invention. Further,
hl IO~ edge of rock matrix properties is extremely useful in specifying
subsequent co,,,ul~lio,, activities such as possible fracturing and even
pe,ru,dli"g programs. Finally, a kl ~.k,Jye of the condition of the borehole,
the drilling program can often be modified to increase efficiency such as
25 modifying drilling pd,d",~ a to increase bit pe,l~l, , rates.
Referring again to Fig, 2, the transmitters are activated
sequentially at a first frequency, The phase shift and amplitude attenuation
of the induced el~,l,u"laull~; signals are measured at each receiver, with
respect to the lldll:~lllill~l outputs as previously described, yielding sixteen30 basic signal measurements (Eight amplitude attenuation and eight phase
shift measurements). The procedure is then repeated at a second lle~
.
51
W095/24663 2~5a29
frequency yielding an additional eight measurements of amplitude
attenuation and eight measurements of phase shift. A total of thirty two
ullcor,t:~,lt,d "raw" measurements are therefore obtained for each cycle of
lld":,",itlel activations as the borehole instrument 36 is conveyed along the
borehole 34. Each phase shift and amplitude attenuation, being ~ o"~lt,d
by means previously ",t:"~iu,led, is greatly affected by the borehole and the
near borehole environs. These raw measurements are used, therefore, to
determine borehole ~:I,ard~,lt:li:,l;.,:, such as borehole diameter, nugosity and
ecce"l,i~;;ly as well as providing means for correcting apparent resistivity
measurements for these borehole effects. Stated another way the invention
not only provides fommation resistivity measurements corrected for perturbing
effects of the borehole as previously described, but also provides means for
quantifying these corrections thereby providing useful i~rullllalioll on the
physical properties of the borehole. These borehole properties, in turn, can
be related to such pardl"~ as ",e.:l,a"i~,al properties of the rock matrix,
shallow invasion profiles, and the effectiveness of the drilling program. The
vertical resolution of the thirty two measurements are, in general, different
and vary from measurement to measurement when borehole conditions are
rapidly varying with respect to the l,d"~",ill~r-receiver array spacings 21 and
23. It is necessary to apply deconvolution techniques in order to ~match" the
vertical resolution of all sixteen measurements prior to combining these data
using means previously mentioned. Resolution matching is not an
illdt~ ld~"l data ~.,uce~i"y step as is often the case in prior art, but is an
integral step in the calculation of all pa,d",~t~l:, of interest.
It should be understood that other l,dns",il~r-receiver-
operating frequency cG,,,u;,,alions can be utiiized. As an example, two
lldl)~lllillt:l:~ and four receivers with the lldr,s",ill~r:, operating at two
frequencies will also yield tllirty two raw measurements. Expanding the
variability concept even further, an array of one receiver, operating at two
frequencies, and eight receivers will also yield a total of thirty two raw
measurements of amplitude and phase, as will one receiver and one
52
-
WO 95/24663 2 t 8 5 0 2 q r~
I-dlls",itldr operating at sixteen frequencies. The llall:,lll r-receiver
frequency C~llluilldliull can also be varied to yield a raw measurement total
greater than or less than thirty two with a corresponding increase or
decrease in the number of parameters of interest that can be uniquely
5 d~ I " ,i"ed.
Referring again to Fig. 2, the lldll~ lillt,la 209, 207, 205 and
203 are activated sequentially at a given frequency O1. The phase and
amplitude of the induced elel,l,u",dy,~ . signal are measured at each
receiver l.a,1s",itldr pair thereby yielding a total of eight measurements of
U dll, 'il Jrles and eight measurements of phase which will be identified as Aj
and Pj, respectively, where (i = 1,...,8). The procedure is then repeated at a
second l,d..a",ill~l frequency 2 yielding an additional eight measurements
of amplitude and eight measurements of phase which will be identified as Aj
and Pj, ,t:~,ue,,tiicly, where (i = 9,...,16). The above defined cycle is repeated
15 as the borehole instrument is conveyed along the borehole. In summary,
thirty two pdldlllt~ are measured as a function of instrument depth within
the borehole.
The p~uce~illg of measured data can best be visualized by
matrix operation wherein the previously defined sixteen raw amplitude and
20 sixteen raw phase measurements are multiplied by a non-square matrix
which lldl1~UIlll5 these thirty two measurements into the parameters of
interest. The pa~d~ L~ of interest can be selected and varied by a user,
and can include traditional fommation evaluation related paldllltSlt:la such as
resistivity and dielectric constant as well as near borehole paldll,~,t~l~ such
25 as the radial extent of invasion of the formation by drilling fluid and the
resistivity of the invaded zone. Furthemmore, borehole pclldll.~ such as
borehole diameter, dCC~Illli~ily and ellipticity can be quantified as well as the
resistivity of the fluid contained within the borehole. The number of
pdldlll~,t~ of interest must be limited to thirty two or less in the preferred
30 e:lllbodi",t",l. In an alternate ~IllLodi,,,t,,,l, the number of parameters of
interest can be greater than the number of raw data measurements. This
53
2 1 85029
wo gsl24663
condition yields an ~"d~ le""i"ed set of equations requiring that initial
estimates be supplied for the number of pal~ of interest exceeding the
number of raw data measurements. Rey~t~ssioll techniques are then used to
minimize the di~ uallcy between tool response predicted by the model and
5 the set of measured raw data. The preferred ~:lllbo-li",~"l employing thirty
- two measured parameters will directed to toward the measurement of
borehole and near borehole pdla~ ,. For purposes of illustration it will
be assumed that five borehole or near borehole parameters are to be
d~lt,r",i"ed. These will be denoted Bn where n = 1,.... 5. The matrix
10 operation is written as
(24) rTl x [M] = [B]
where
B~
(25) [B] =
_B5
A,
(26) [M]= A~6
.P~
_P16 _
54
WO 95/24663 2 1 8 5 0 2 9 r~
and
T,~, T, 2 Tl 32
5 (27) rTl =
T5, T5 2 T5 32
The matrix [~ is a transform which ~ lCJS~IIta a cu",~ bi,/e model of the
borehole instrument response with the borehole, near borehole, and
formation conditions being variables. Since the elements Tj,j are predicted
10 by the model, the borehole pdldlll~ la to be d~,~,""i"ed, Bn (n=1,....,5), can
be c~lr~ tPd directly from the measured parameters rt~pl~selll~d by the
matrix [M]. Using the formalism of equation (24), it is essential that the modell~pl~sv"l~d by [Tj yield pdldlll~lt71a of interest (the "unknowns") as a function
of the downhole instrument response (the measured quantities).
1~ Jian-Qun Wu and Macmillian M. Wisler (~Effects of Ccc~" i"g
MWD Tool on [ICvll~ dy,l~tiV Resistivity Measurements", SPWLA, 31st
Annual Logging Symposium, June 24-27, 1990) disclose a method for
calculating the eflects of a borehole logging tool being ecve,,lt,,,vd in a
borehole upon resistivity measurements and is hereby entered by reference.
As an example of this work, Fig. 2~ illustrates the variations of apparent
resistivity 75a computed from phase shift measurements (denoted by curves
74) and amplitude ratio measurements (denoted by curve 76) resistivities,
as a function of logging instrument-borehole eccv"lli~;ily, for true fommation
resistivity 70 of 0.2, 2.0 and 20 ohm meters and with a borehole fluid
resistivity 72 of 20 ohm meters. The lldllalllill~l frequency is 2 MHz. A
similar plot is shown in Fig. 22 for a borehole fluid resistivity of 0.2 ohm
meters and all other pard",~ ra remaining the same. In these examples,
functional r~ldliollalli~Ja have been developed which yield apparent resistivity
WO9~/24663 2 1 85029 .~ 14
values 75a that will be measured by the borehole instrument 36 (the
measured quantities) as a function of true fommation resistivity 70 borehole
'h~itir~ 72, and ecc~,lt,i~ y 75b, which are the "unknown" quantities to
be d~""i"ed with means and methods of this invention. The responses are
computed using a model developed around basic ~le~ l,u",as~"~ . wave
u~uuaudliùl~ principles using borehole geometry. The calculations have been
verified exueli",t:"'.J:y. J.-Q. Wu, M. M. Wisler and J. F. Towle (UEffects of
Arbitrarily Shaped Boreholes and Invasion on Plupa~dliol1 Resistivity
Measurements in Drilling Horizontal Wells~, Progress in [le~,ui,,ayllt~lic
Research Symposfum, Pasadena California July 14 1993) likewise
discloses means for clc~ r",' ,i"g the measured response of borehole
instnuments in temms of circular and non circular invasion profiles and also in
terms of instrument eccd"l,icily within the borehole. Again measured
quantities are expressed in temms of unknown pa,d".~ of interest. Stated
another way the cited reference discloses means for calculating the for~vard
problem which if incorporated in the corllpl~llellsi~/e model the current
invention would cast the matrix equation (24) in the reverse direction yielding
equation (28)
(28) ~T'] x [B] = [M]
where
T,', T, 2 Tl 5
(29) [~]= -
T' T' ~'
3æl 32,2 32,5_
The solution of equation (29) ~or [B] requires a regression scheme which is in
general non-linear. That is values of the pdldll~ of interest namely the
elements of [B] are iterated until the elements of [M] calculated from equation
56
W0 95124663 2 t 8 5 ~ 29 r~"-a
(29) converge upon the actual measured values Aj and Pj (i = 1 ...,16). It is
again ~IIl,ul~d~ dd that the other borehole and near borehole pald~ a are
included in the model. Such additional pdldll~ la might include borehole
diameter and resistivity of the invaded zones. Those pdldllll:lt~ detailed in
5 Figs. 21 and 22 are presented as examples to illustrate the concepts of the
data p,ùces:.i"g method. The additional ,I,a,dult,riali~;s of the response of
the downhole instrument, obtained by Illd~ llldli~ al modeling are likewise
i, I~ ul u~, ' as elements of the matrix [Tl.
10 4. DETERMINATION OF ERRORS ASSOCIATED WITH PARAMETERS
OF INTEREST
The current invention provides means and methods for
dt,l~r",i ,i"g error which can be re~ated to uncertainty A~.soi;-lPd with
measured pdldlll~ of interest. Again the user of the i"~.",dlion, or log
15 "analyst", selects the pdldllltll~ . of interest which might include the resistivity
(or conductivity) of the fommation, the dielectric constant of the formation, orperhaps the degree to which drilling fluids invade the fommation in the vicinityof the borehole. As ",t:"liu"ed previously the analyst's primary interests are
usually the dt,l~r". ~dlion of the hy~uia~bul1 saturation porosity and
20 pe",--' ' y of the ~u,,~dliuns penetrated by the borehole. It is highly
desirable to make such measurements while drilling or soon after the driliing
of the well borehole so that critical economic decisions c~ncel" ,9 the
amount and producibility of h~,~,u~arL,ul~s in place can be made. Based
upon this ill~ulllldliol) the well will either be Cu~lu'~ t~d or dban.lo~)ed. The
25 accuracy and precision of measured pard",~ , selected to make such
critical decisions are also of prime i",poltal1c~. The error measurements
provided by the invention can also be used to indicate equipment
malfunctions of both the electrical and ",eil,al~i"al types. Although prior art
teaches means and methods of measuring a wide range of geophysical
30 parameters using electromagnetic techniques, little if any emphasis is
placed upon dt~ ll";,l;,lg the quality of the measurements. Usually the
57
W095/24663 : 2 1 85~29
analyst can only rely on past e~ "ce in assigning, at best, qualitative
estimates of the quality of the measurements obtained from the borehole
instrument and ~ ' -d system. Any error analysis is usually performed
long after the measurements are made and usually not at the well site.
5 Stated another way, prior art does not provide means and methods for
cl~lt ""i"i"g the quality of electromagnetic based geophysical measurements
in real-time or near real-time, although real-time or near real-time economic
and op~,u~io~al decisions are made based upon these measurements. This
is especially true in electromagnetic type measurements of formation
10 resistivity which weighs so heavily in the decision to complete or abandon
the well. The invention provides this very ill~ulllldliul1 by providing means
and methods for measuring geopl,;_;_al pard",~ selected by the analyst
and simultaneously yielding quantitative measurements of the quality or error
~ccO.; ~ with the measurements of the selected pa,d",~tt"~.
Referring again to the ~IllLodi,,,~,,l of the invention shown in
Fig. 2, llc l~:,lllillt l:, are dctivated sequentially at a first frequency. The phase
and amplitude of the induced ele~,ln,",au"~ signal are measured yielding
four measurements of amplitude and four measurement of phase at each of
the two receivers. The procedure is repeated at a second l,~"",
20 frequency yielding an additional four measurements of amplitude and four
measurements of phase at each of the two receivers. Each sequence as
described therefore yields thirty two i".l~pel~d~"l, raw measurements. The
measurement sequence is continuously repeated as the instrument is
conveyed along the borehole. The previously discussed ,,ldll,elllativa
2~ model, which is based upon f~llddlll~llldl el~,l,ulllay"~; wave propagation
properties, describes the Ille~l~ti.,dl response of the borehole instrument as
a function of numerous formation and borehole parameters. Such
parameters again include formation resistivity, invasion parameters,
formation bed boundary effects, borehole conditions and the like. In this
30 embodiment of the invsntion, the model contains fewer than thirty two
variable pald"le~ while the borehole instnument yields thirty two measured
58
2~ 85029
WO 9S/24663 . .~
pala~ Lt~lO as described previously. The system of unknown pald~ .O is
therefore ~over dt~l~""i"ed in the sense that there is more measured
paral"~ O than variable or unknown pa,a"~ lO to be ~c,l~l",;"ed it
should be noted that other transmitter-receiver-operating frequency
5 cull,b;,ldlio~s can be utilized as discussed previously. The number of
selected pa,a",~l~,O of interest must, however always be less than the
number of raw data measurements so that the resulting system of equations
is over d~l~"~,i"ed.
Non-linear inversion techniques are used to determine the set
10 of selected unknown para",~ltrs which through the Illdlllt~llldli~dl model,
predicts a tool response which most closely matches the thirty two measured
raw data points. The predicted tool ,~Opol7ses and the measured tool
responses will exhibit no dioul~ual ,~ ies only if (a) there is no error A~.SO~:. ,t~ d
with the measured data and (b) if the model ,t,pr~Ot"lO without error the
15 response of the instrument in every encountered borehole and formation
condition. This is because there are more measured data points than
unknown variable pdldlllet~lO in the model. Any degree of non-c~"lul",dllce
or ~ ioll~alcll~ of the model data and the measured data is a measure of
inaccuracy of either the data or the model or both the data and the model. In
20 all cases the .1~ ~.",i"dd non-c~"fu""d"ce is treated as a quality indicator for
the d~lt,r",i"ed pard~elts~O of in$erest. In other words, an uncertainty is
attached to each parameter selected by the analyst based upon the
goodneOO of fit between the model and the measured data.
Referring again to Fig. 2, I,anO",~ O 209, 207 205 and 203
25 are activated sequentially at a first frequency ~1. The phase and amplitude
of the induced el~ u~ayllt~ signal is measured at the receiver nearest to
each activated l,a":.",illt:r thereby yielding four measurements of amplitude
and four measurements of phase shift. These measured parameters will
again be identified as Aj and Pi ,~Ope"lil~ 'y, where (i = 1 ... 4). The
30 procedures is repeated at a Oecond frequency ~2 yielding an additional four
measurements of amplitude and four measurements of phase identified
59
W0 95/24663 2 1 8 5 0 2 9 ~ 14
hereafter as Aj and Pi"~t~,ue~,t;~cly, where (i = 5,...,8). The entire procedureis then repeated for the rec~iver farthest from each activated lldllblll-'' .
yielding values of Aj and Pj where (i = 9,...,16). In summary, a total count of
thirty two pardrllelelb is measured by the borehole instrument 36 during
5 each cycle as it is conveyed along the borehole 34. The above combined
procedure of lldllbllliltillg at frequencies ~1 and ~2. and recording received
signals is repeated sequentially as the instrument is conveyed along the
borehole.
Fdldlllel~ of interest related to the fommation, near borehole,
10 and borehole are selected by the analyst. These paldlllelelb might include
fommation resistivity, formation dielectric constant, radius of invasion of the
drilling fluid, resistivity of the drilling fluid and perhaps the diameter of the
borehole. The selected number of pdldlllelel:~ must be less than thirty two so
that the system of equations described in the following section is over
15 d~lellllilled thereby pemmitti~g uncertainty associated with the selected
paldlllelelb to be delellllilled~ For purposes of illustration, it will be assumed
that the analyst selects n paldlll~ to be d~erlllilled~ where n is less than
thirty two.
The p,ucesbi"g of the data to obtain the pdlaillelelb of interest
20 and the delellllilldli~ll of unc~rtainty ~cs~ d with these pdldlllelelb can
best be described using matrix notation. The system is written as
(30) rT~ x [M] = [Xl
25 where
Tl, T, 2 Tl 32
(31) [~
Tm I Tm~2 Tm,32_
W0 95124663 2 1 8 5 0 2 9
Al
Al6
(32) [M]= p
p
16 _
and
X
(33) [X] =
Xm
The matrix [T] ~ svlll~ the theoretical response of the
borehole instrument calculated using dV,l~rUplidlV electromagnetic modeling
techniques for a broad range of formation and borehole co~ iuils~ the
10 matrix [M] ,~v,~s~"l:, the thirty two raw data points measured by the borehole
instrument, and the matrix [X] ~,vl~se"l~ the formation and borehole
pa~d",~ , selected by the analyst to be de'~.",i"ed. Although the solution
of the matrix equation (30) to attain the desired parGI"t~ r" ,~ur~s~"l~d by
the vector [X] is viewed as linear in this case the element of the matrix [Tl can
15 be dt,p~lldt~lll upon the elements of [X]. The solution of equation (30) will therefore, require a non-linear regression solution such as a ridge
" :yl ~ siv~.
Once equation (30) has been solved for [X] an inverse matrix
operation is pe,lu""ed to generate a synthetic matrix of the measured
20 quantities denoted as [M~]. That is
(34) [T'] x [X] = [M ]
61
W0 951~4663 2 ~ 8 5 0 2 9 ~ s ~ 14
where
Tl'l Tl~2 Tl~m~
) [T]= -
T32 I T32.2 T32,m _
and
, _
A,
Al6
(36) [M'] = p,
P'
The mismatch between the measured pald",~lt,r:,, [M], and the syntheticvalues of the measured parameters [M'] is a measure of quality of the
15 pdldlIIt~ Sr::. of interest,[X]. If
(37) [M ] Y [M]
then there is little uncertainty A~.soc;~d with the computed values [X]
20 indicating that the quality of the measured data [M] and the model
_yl~ lllillg the response of the instrument rrl are both good. If, however,
62
1~ W09!i/24663 2 1 8 5 0 2 9 ~ 9! .1
(38) [M'] ~ [M]
it can be concluded that either the mea~sured data [M] are of poor quality (due
to tool function, calibration error or the like), or the model of the tool response
rt~ se~led by [T] is inadequate for the conditions encountered, or both
co~ s have occurred. ~ ,i",i~dliùn of calibration, thermal drift and
antenna mutual coupling errors have been discussed previously. It has been
d~lt"",i"ed that in many cases, the response model is also quite reliable and
error in the modei is only a minor contributor to the observed enror. It follows,
therefore, that when [M'] ~ [M], the source of the observed error can not be
identified. The degree of mismatch of [M'] and [M] is indicative of the
magnitude of the uncehtainty or error in the computed pald,l,~ of interest,
[X]. Non-linear regression techniques suitable for ~ 'icn in this
invention are described in the pll' ' 1 "Inversion of 2 MHz Plupdydli
Resistivity Logs~ by W. H. Meyer, SPWLA 33rd Annual Logging Symposium,
June 14-17, 1992, Paper H.
5. FORMATION PARAMETERS OF INTEREST
The llall:~fullllcLIiul~ of ray data measured by the sensors into
apparent resistivities of the formation, near borehole and borehole environs
has been discussed in previous sections. The determination of error
AC~O~ d with these quantities has also been liccllcse~l In addition,
previous discussions encompassed the general concepts of converting
25 apparent ~ k,th~it;~.~, and other elelluh,ay"e~ properties into pdrdllltSlel~from which aend" ill'..llldliùl~, such as h~dlucdll,ùl, saturation and porosity of
the formation, is derived, Finally, basic problems As~ociAtPd with the
d~k,lll,;,~dliol~ of hydrocarbon saturation from resistivity measurements
alone, in the presence of low salinity or fresh waters, has also been
3û addressed. The following section is devoted to the conversion of tool
measurements, whose accuracy and precision have been d~ rl"i"ed and
63
W0 95/24663 2 1 8 5 0 2 9
optimized using previously discussed methods, into "end" pdldrl~lc~ which
include ll~,uculLlull saturation and porosity.
5.1 A Review of Physical Principles
Phase shiff and attenuation measurements in the low MHz
frequency range are dd~lldl::lll upon only three el~_l,u",ay"_t;. properties
- and the manner in which these three properties are combined and spatially
distributed near the borehole lldll~lllitlel and receiver assembly. The three
properties that control, as an example, the propagation of a 2 MHz
eleu~,u,,,dy,,~Li~ wave are (1) magnetic p~""~ ' "'~y, (2) conductivity, and (3)dielectric permittivity. The primary pa,c.",~ of interest is conductivity (or
resistivity) since this is the primary parameter used in hyd,uca,~u" saturation
calculations if the connate water is saline. In order to relate the measured
phase shift and attenuation measurements made with the borehole
instrument to conductivity, assumptions must be made col1cel"i"g the
magnetic pemmeability and dielectric pt"",ilti~; y of the fommation.
Magnetic perlll ~'"ly is defined as the ability of magnetic
dipoles in the fommation to align themselves with an external field. Minerals
and fluids commonly found in sed~",~"ldly earth ~ulllldliulls do not exhibit
significant magnetic permeability. In computing resistivities from
measurements of amplitude and phase measurements from a device
operating in the mid KHz to low MHz frequency range, minimal error is
introduced in assuming a value of magnetic pe",i~a' ""y to be equal to that
of ~ree space, or 1.25 x 10-61 lellly~/ll.~.~
Conductivity is defined as the ability of a material to conduct an
electric charge, while dielectric permittivity is defined as the ability of a
material to store an electrical charge. Dielectric pe""''"~ily is usually
expressed in temms of relative dielectric constant, Efi which is the dielectric
permittivity E of the substance in question divided by the dielectric pemmittivity
in free space, fo= 8.854 x 10-12.
Attention is now turned to dielectric pemmittivity and the physical
principles behind the effects of this parameter upon attenuation and phase
64
WO 95/24663 2 1 8 5 0 2 9 r~
signals measured in a borehole ~ i,ullllldl~. In se " ll~lllary formations,
dielectric pe""il~i~ri.y arises from the ability of electric dipoles to align
themselves with an a':_."a~i"g ~ ,u",ay"~ field induced by the borehole
instnument. Water molecuies will be used for purposes of discussion. There
5 are three pl,e"ul"~a contributing to rin a porous earth formation. The first
contribution is the rotation of dipolar water molecules. The water molecule
has a slight positive charge on the side to which are bound the two hydrogen
atoms, and a corl~a,uolldil,9 negative charge on the side of the molecule
opposite to the bound hydrogen atoms. In the presence of an applied
10 electric field, the water molecule will rotate to align the positive and negative
poles of the molecule with the applied electric field. In an alt~" ,9 current
(AC) field such as that produced by the borehole instrument, the water
molecule will rotate back and forth as the polarity of the applied field
alternates. During the time period in which the water molecule is in actual
15 rotation seeking to align with the applied field, the l"ù.v~,."e"l of the charge
It~plt:btll~ts electrical charges moving in phase with the applied field and aretherefore carrying current and contributing to the co",posile formation
conductivity. Once aligned with the field, the polarized water molecules
represent fixed or stored charges and thereby contribute to the formation
20 permittivity until the polarity of the r" llalillg applied field is reversed. At
this time, the water molecules again rotate contributing again to co",,uo:,ilt:
fommation conductivity. This sequence, of course, repeats with the cycling of
the applied AC field. Ions disso~ved in the formation pore water are a second
contributor to r in that they will also be set in motion by the applied AC field
25 and migrate in the direction of the field until they encounter a physical
obstruction such as a rock grain forming the boundary of the pore space.
Once the ions abut the pore boundary and begin to accumulate, they
likewise become fixed or "stored" charges thereby contributing to the
formation dielectric permittivity as described by M. A. Sherman, "A Model for
3û the Frequency Dt~ db"~,e of the Dielectric Permittivity of Rock", The Log
Analyst, Vol. 29, No. 5, September-October, 1988. Cations attached to cation
W0 95124663 2 1 8 5 0 2 9 ~ 4
exchange sites on the surface of certain clay minerals are a third contributor
to r in that they can also move under the influence of an applied AC field.
The movement of cations between various exchange sites produces effects
similar to those of free ions in the pore water.
C~", ' Ig the issue of dielectric effects is the fact that er
values are dependent uporl the frequency of the applied field. At low
frequencies, dielectric constants can be quite high since the water molecules
can easily rotate and align themselves with the field before the polarity of thefield reverses. Similarly, dissolved ions can migrate to the boundary of the
pore space and accumulate against the pore wall long before the polarity of
the field reverses. Likewise, the ~u~.ll~ of cations can be completed prior
to the reversal of the field polarity. Therefore, at low frequencies, water
molecules, dissolved ions and cations spend most of their time in a fixed
oli~,,Ldlivl1 or position and only a smal~ fraction of the time moving during any
given cycle of the applied AC ele~;l,u,,,~ly,,~lic field. At high frequencies,
however, the polarity of the applied field will reverse before the three types of
mobile charges come to rest. In this situation, the mobile charges spend
most of their time moving in phase with the external electromagnetic field
thereby increasing the conductivity and resulting in a lower dielectric
constant. The phenomena of changing dielectric and conductivity values
with frequency is known as dispersion. The frequency at which the rotating
molecules or mobile ions can no longer keep pace with the oscillating field is
known as the "Itlla~dlioll frequency~. The relaxation frequency, relative
dielectric constant Sfi and conductivity (J will depend upon various factors
such as porosity, mean pore size, the resistivity of the water Rw, and shale
mineralogy as described in the praviously cited reference by Shemman.
J. C. Sims, P. T. Cox and R. S. Simpson, "Complex Dielectric
l"l~",r~ldlion of 20 MH~ Ele~;l,u,,,ay,.~i'iv Logs", Paper SPE 15486, 61 st
Annual Technical Conferencs and Exhibition of the Society of Petroleum
Engineers, October 5-B, 1g86, teaches the use of a mixing formula to
interpret dielectric log data, but measurements made at only one frequency
66
~ WO 95/24663 2 1 8 5 0 2 9 p~,l/L--
are employed. U. S. Pat. No. 3,891,916 to R. A. Meador et al teach the use of
two frequencies, both much higher than 2 MHz, to detenmine dielectric
constant. Meador et al, however, teach the use of amplitude measurements
to determine dielectric constant and resistivity and do not address the
5 problem of dielectric dispersion using two frequencies with both amplitude
and phase measurements. U.S. Pat. No. 5,144,245 to M. M. Wisler discloses
the use of the Complex Refractive Index Model (CRIM) as a means for
correcting resistivity measurements for dielectric effects where the resistivityamplitude and phase data are taken at a single frequency. K. S. Cole and R.
10 H. Cole, "Dispersion and Absorption in Dielectrics", Jouma/ of Chemical
Physics, Vol. 9. P 341 (1941) disclose a model for dielectric dispersion which
can be used as a mixing model in a sor"~...l,dl similar to the previously
"ced CRIM model and could be used as an element in the ~II,I,o.li",."l
of the current invention. There are many other mixing and dispersion models
15 that might also be used.
This brief review of pertinent basic physical principles will assist
in fully disclosing the means and methods of the invention and advances of
the current invention over prior art.
Recall that a major objective of invention is directed toward the
20 accurate measure of the conductivity (or resistivity) of earth fommation
penetrated by a borehole. As discussed previously, formation resistivity
combined with fommation porosity and connate water resistivity can be used
to compute fonmation hy~ llJul1 saturation of a porous formation. The
invention is further directed toward the determination of the dielectric
25 constant of the formation. This measurement is used to correct resistivity
measurements made at certain frequencies for the adverse effects of the
dielectric permittivity of the formation. The invention is directed still further
toward the Llt~ ldliOI~ of the volume fraction of the formation saturated
with water. This measurement, when combined with an i,~depe,~de,~l
30 measure such as a neutron porosity measurement which responds to total
formation liquid (water plus liquid hydrocarbon), can be used to determine
67
W0 95/14663 2 1 8 5 0 2 9 ~
hydrocarbon saturation of the formation in either fresh or saline water
environments. Hydrocarbon saturation can not be determined using
resistivity measurements only in fresh water env;,ul""c:"l:, since the
resistivity of fresh water and I l,rdlu~;d,Lùl) exhibits little contrast.
5.2 Theor~ti~ cic
Solutions to Maxwell's equations in ll~",oyelleous lossy media
dre a function of a factor commonly referred to as the IJ~u~aycl~ constant or
wave number, defined h~rein as "h", which contains conductivity, dielectric
10 constant and magnetic pel" ~~' "'y temms. A plane wave solution will have
the form
(39) V = Ceikx
1 5 where
V = a field variable;
C = a constant
e = the naperian log base
i = the square root of -1;
x = the distance traveled; and
(40) k= [ ~oluro~r)+(io~olur~)]
where:
~llo = the magnetic pt"" - ' "'y of free space;
~r = the relative p~" " ~ ~ ' ~y (which is 1.0 for free space
and most earth materials);
o = the electric pemlittivity of free space;
~r = the relative dielectric constant (which is 1.0 in free
space);
68
.
WO 9~/24663 2 1 8 5 0 2 ~ w 14
= the angular frequency of the applied field; and
~J = the conductivity which is the inverse of resistivity.
the temm k can be rewritten in temms of a relative complex dielectric constant,
5 r which includes the effect of dielectric constant and conductivity, as
(41) k=ko~
where
ko = the wave number in free space;
~r= l; and
,= [r +i~(-l/~o)]
We now assume a model of the earth fommation wherein there
are two layers of different pr,pd~dlio" constants kand differing complex
relative dielectric constants r with the first region spanning (1 - 0) units of
length and the second region spanning 0 units of length A plane wave
incident on the layers and passing through the layers without reflection will
20 have the form
(42) eik~eik~ )=e~lk,o+k,(l_O)l
The effective propagation constant for this model, keff, is therefore
(43) keff= ko~ = = ko [~;~ ~ + ~;~ )]
Equation (5) is solved for the equivalent relative dielectric constant to obtain
(44) ~ff = c 1~ + c ~ ) + 2(1
69
wo9s/24663 2 1 85029 ~", l.1
C~l,sideli"3 all of the aboYe It:ldliOl~b~ Js ieading to equation (44), it is
apparent that the effective real relative dielectric constant is therefore
corrupted by the imaginary parts of the relative dielectric constants of the two5 regions and likewise the effective conductivity is cornupted by the real parts of
the relative dielectric constants. The model is now further related to actual
earth ~UlllldliUllb. The first region is equated to connate water filling the pore
space of the rock matrix with the water fractional volume being 0 of the total
formation volume. The second region is equated to the rock matrix with the
1û rock matrix fractional volume being (1 - 0) of the total fommation volume.
Expanding equation (44) to illustrate real and imaginary co",,.~on~"lb and
d~siu~"dli"~ temms with respect to the above fommation model yields
(45)
15 E~+i~cf~ 2W+2~ Ew+i~JwICi))Em +(1--~b )m
where the subscripts w and m designate pard",~l~lb ~o~ ;-.S~ ~i with the
water and rock CUlll,UO~ lllb of the fommation, Itla~ k/Oly~ Note that ~J m is
equal to zero. If measurements are made at two known frequencies
2û 0 = 6~ )2~ equation ~45) yields two il,dep~l,de,ll complex equations.
Because both real and imaginary parts of these equations must be equal,
measurements at two frequencies actually yield four illd~pl:lld~lll equations.
The dielectric constant of water, w~ is i"dd,uel1delll of the salinity of the
water thus is a known quantity. The two frequencies are ul~dl:Lellllilled thus
25 are known. The quantities eff and ~ eff are measured. The four
i,,de,u~l~d~,ll equations can, therefore, be used to solve for the remaining
three unknown quantities, namely the porosity 0, the conductivity of the water
~JW and the dielectric constant of the rock Em. ~t is noted that a plurality of
lldl1blllill~r-receiver-operating frequency colllLillalions can be used in
3û e",L,o ii",~"la of the invention as long as the chosen cu",L)i~ 1 yields fourindependent equations relating ~ eff and eff to ~w, m and 0. It should
WO95/24663 2~85~29 ~ J
also be noted that the dielectric constant of the rock matrix and the dielectricconstant of any h~d~ucar~ù~ contained within the pore space of the rock are
essentially equal and the conductivity of each is esse,' "y zero. The
computed quantity 0 is therefore the fraction of water within the fommation and
5 not necessarily the effective porosity of the formation in the sense commonly
used in the art. In order to obtain effective fommation porosity, it is necessary
to combine the "water filled" porosity yielded by the present invention with a
second il~ pt:lld~"l measure of formation porosity which responds to the
total fluid filled porosity. An example of such a second measurement would
10 be a thermal neutron "porosity" measurement which responds to the
hydrogen content of the formation. Since most hydrogen in earth formation
resides in the pore space rather than the rock matrix and since the response
is essentially the same for both water and liquid h~-llu~ dlb~lls the neutron
porosity measurement yields total liquid porosity.
5.3 Logging EY~rnple
Attention is directed to Fig. 23 which illustrates logs of
resistivity which is the inverse of conductivity, measured at four different
lld~ frequencies as a function of depth, in feet, within a borehole. The
2û measurements were made in a test well in which the ~l~d,a~ ,lk ~ of the
ru,l"dliol~s are well known from numerous studies of well log and core data
as referenced in "C~"")a,i~o,1 of MWD Wireline and Core Data from a
Borehole Test Facility" Paper SPE 22735 p~uceau~ y:~ of the Society of
Petroleum Engineers 66th Annual Conference and Exhlbition, pp 741-754,
25 (1991). These "logs" of resistivity clearly illustrate the effects of dispersion
effects as a function of the frequency of the induced ele. l,u",ay.,t:~ic field.Attention will be focused on the zones denoted by the numerals 840 and
844 which are shales and the low pemmeability limestone zone denoted by
the numeral 846. Zone 842 is a pt""ea~le sandstone and is therefore
30 invaded by the drilling fluid. Radial invasion combined with differing depthsof inve:.ligdliolls for the measurements at different frequencies mask the
71
2 l 85029
W095124663 r~". .
di~.e,:,iol~ effects. Zon~ 842 will therefore be ignored in this discussion.
Curves 850, 852, 854 and 856 represent resistivities measured at
frequencies of 1100 MHz, 200 MHz, 25 MHz and 2 MHz, respectively.
Knowing that zones 840, 844, and 846 are radially homogeneous (that is,
non-invaded by the drilling fluid), it is concluded that the observed dispersionis due to dielectric effects. Fig. 24 illùstrates relative dielectric constant
measurement over the same formation zones of interest but at different
frequencies where curves 870, 872, 874 and 876 represent measurements
at 1100 MHz, 200 MHz, 25 MHz, and 2 MHz, respectively. Dielectric
dispersion is again quite apparent. The pl~el~o"lt:~la of both dielectric and
conductivity (or resistivity) dispersion and their d~,elld~"cy upon the
frequency of the induced field has been discussed in a ~ e or
conceptual sense in a previous section. The ~JIIt:ll-nllella can be quantified
as illustrated in Fig. 25 which illustrates generalized theoretical di~" e,~iu,lplots for a clean sandstone formation. The dielectric dispersion curve 860
illustrates that in general ~rdecreases as frequency increases. Conversely,
the conduction curve 862 illustrates that conductive dispersion increases
with increasing frequency. Both curves 860 and 862 also clearly illustrate
frequency ranges at which interfacial relaxation and molecular relaxation
occur. To assess whether the variations in the relative dielectric constant r
observed in the logs of Fig. 24 are indeed consistent with dispersion effects,
the four values Of ~r depicted by curves 870, 872, 874 and 876 at a depth
of 1660 feet in the limestone formation 846 were compared in Fig. 26 to a
dispersion curve 880 based upon published (M. R. Taherain et al, "Dielectric
Response of Water-Saturated Rocks", Geophys~cs, Vol. 55, No. 12,
December 1990) dielectric measurements made on limestone core samples
with matrix and connate water resistivities very similar to the limestone of
formation 846. The su,l,t"i",~osed data points 881, 882, 883, and 884 are
average readings of the curves 876, 874, 872, and 870 taken at a depth of
1660 feet in zone 846"~ e~ 1y. The good ay,~:ts"lt",i between the core-
derived dispersion curve and the log derived measurements from these two
72
2 1 85029
WO 95/24663 . ., ~ . . J
carbonate ~ur,,,dlic,l~s suggest that the .~"ces between the various E~
values from the log sre indeed due to dispersion. Col,sid~,i"g Figs. 23, 24,
25 and 26 in col" :.~alion it is apparent that any model which
simultaneously extracts .I;v,u.er~iol~ corrected resistivity and dielectric
5 constant values from measurements of phase difference and amplitude ratio
at varying frequencies must quantitatively include the frequency of the
induced ~ l,u",ayl~ v field.
Recall that one of the basic objectives of the invention is to
determine conductivity (or resistivity) of the formation which is free of
1 û dispersion effects. A second objective is to detenmine the dielectric constant
of the fommation which again, is free of dispersion effects. A third objective is
to determine effective water filled porosity of the formation which when
combined with i"d~uel~d~"l measurements of total liquid filled porosity, can
be used to determine the hydrocarbon saturation of the formation. A
15 theoretical Complex Refractive Index Model (CRIM) has been developed
which relates rto true fommation resistivity and meets the previously stated
objectives of the invention. The development of the model begins with the
solutions to Maxwells equations in ho",og~"eous lossy media are a function
of a factor CGIl~ l,ly referred to as the propagation constant or wave
20 number, defined herein as "ka, which contains conductivity dielectric
constant and magnetic p~""~r~' ~y terms. Restating, for co",,ul~ ess
Equation (39) for a plane wave solution yields
(39) V = Ceikx
where
V = a field variable;
C = a constant
e = the naperian log base
3û i = the square root of 1;
x = the distance traveled; and
73
W095/~4663 2 1 8 5 02 9 .~
(40) k = [( o2~uo~ur~o~r ) + (~ o~r ~5)]
where:
c = the speed of light = 2.999 108 (,,,~l~r~lse~u,,d);
,llo= the magnetic p~,,l, ' "~y of free space = 4 x 10-7;
,Ll ,= the relative p~"" ~ y (which is 1.0 for free space and
most earth materials);
= the electric permittivity of free space = (1/ /l oC2 )= 8.864
1 X 1 o-1 2;
r = the relative dielectric constant (which is 1.0 in free space);
= the anguiar frequency of the applied field; and
~ = the conductivity.
The term k can be rewritten in tenns of a relative complex dielectric constant,
which includes the effect of dielectric constant and conductivity, as
(41) k= ko
where
ko = the wave number in free space;
,U r = 1; and the relative complex dielectric constant is
~r = [r + i~(l I ct)~O )]
26
Note that k is defined such that when the conductivity ~ goes to zero, the
complex relative dielectric constant goes to the relative dielectric constant
equals the real relative dielectric constant ~r~
We now as~ume a model of the earth fommation wherein there
are two layers of diflerent p~upau,dliol~ constants k and differing complex
74
WO 95/24663 2 1 8 5 0 2 7 P~,ll. `O
relative dielectric constants Ec with the first region spanning (1 - 0) units of
length and the second region spanning 0 units of length. A plane wave
incident on the layers and passing through the layers without reflection will
have the fomm
(42) eik'eik~ )=ei~k,o+k,~l-o)]
where the subscripts 1 and 2 denote paldlllt:l~lb ~so~i~tPd with layers 1
and 2"~b,ue~ .!y. The effective pl~r ~ constant for this model, keff~ is
1 0 therefore
(43) keff= k2~ + kl(1- ~)
or on temms of the complex dielectric constant defined above
(44) kC~ = ko ~ = ko [~;~ ~ + ~ (1 - ~)]
Equation (44) is solved for the equivalent relative dielectric constant to obtain
(45) E~ = EC2~ +C~ ) +2(1
The model is now further related to actual earth ~ ;oll6~ The first region is
equated to connate water filling the pore space of the rock matrix with the
water fractional volume being 0 of the total formation volume. The second
region is equated to the rock matrix with the rock matrix fractional volume
25 being (1 - 0) of the total formation volume. Expanding equation (45) to
illustrate real and imaginary cu,"~o"~"ts and debiy"c~ ,g terms with respect
to the above formation model yields
WO 9~i/24663 2 1 8 5 02 9 P~
(46) ~f~ + i~rCJ ~ w + 2 q)(~ (Ew + i~w I m ) +
(1--~t) 2)E
where the subscripts w and m identify pdld~ with the water
5 and rock matrix cvl"~,u"~"Ls, respectively. Note that ~m is equal to zero.
The effective real dielectric constant is therefore corrupted by
the imaginary part of the dielectric constants of the two regions, and likewise
the effective conductivity is corrupted by the real parts of the relative dielectric
constants. That is
1û
(47) rc~ = Re(c,~ff); and (~ = COEo Im(E,~ Im)
In order to calculate the dielectric constants that we would expect to observe
in clean water saturat~d rocks, it will be assumed that the rocks are
15 co""vosed of two parts which comprise the rock matrix and the connate
water. The resistivity of the water and the porosity of the rock matrix are
varied within ,.:as~l)d~le limits and the dielectric constant of the cvlllbilldlivl1
of the two partsl which is the quantity actually sensed by the borehole
instrument, is calculated utilizing the two c~,"",one"L mixing l~ldl;VIlsiliy
20 derived above. The subscripts w and m designate pa,d",~ o~i~t~d
with the water and rock parts, respectively.
The It:ldliOI1:,11iv of equation (46) can be used to yldpll 'y
illustrate the functional It:ldlioll:~llips between the measured quantities and
the parameters which are of interest and which are to be citt~""i"ed. Figs.
25 27a and 27b are preserlted as typical illustrations of these l~ldliO~ ,Js.
The real part 890 of the effective dielectric constant as defined by equation
(46) is plotted in Fig. 27a as a function of the formation water resistivity,
denoted on the abscissa as 892, for various porosities 894. The abscissa is
IOydli: lllliC and the ordinate is linear. These plots are for a frequency ~)~= 2
30 MHz. The real part 91 of the formation effective conductivity is plotted in Fig.
76
WO 95/24663 2 ~ 8 5 û 2 9 1 ~
27b as a function of fonmation water resistivity 892, again at 6)l= 2 MHz and
again for varying porosities 894. Both the ordinate and the abscissa are
logarithmic. Similar plots can be generated for the real and imaginary
c.l",~,u"~"t~ of and ~cff at ~I= 2 MHz and likewise plots for both the real
and imaginary parts of(rcff and at a second frequencya)2=400 KHz. These
are graphical depictions of a set of four i"dt" ellde"t equations used to
d~ lll ,e the 'unknown" formation pa,dr"l:l6,b of interest, namely the
effective conductivity (or resistivity), the effective dielectric constant and the
water filled porosity of the formation.
5.4 D~ of Dielectric Con~t~t. ResistivUy and Porosity
Attention is again directed to Figs. 23 and 24 which show
resistivity and dielectric data"~b~,e.;li/cly. Fig. 23 depicts data from four
downhole systems, with the 2 MHz data being measured with a MWD system
and the remaining being measured with wireline systems. Fig. 24 depicts
dielectric data measured with the same systems. Dispersion of the
measurements as a function of frequency is clearly exhibited in both logs.
Based upon the previously discussed principles, the dispersion in the
resistivity measurements would be expected to be small at 2 MHz and lower
frequencies. Attention is drawn in particular to zone 846 which is known from
core data to be i",pe""edLle carbonate. Dispersion in this zone can only be
attributed to dielectric effects. Zone 842 is a sandstone which is known to be
permeable and therefore invaded with drilling fluids prior to running the
wireline logs. The observed dispersion in this zone must be attributed to, at
least in part, to invasion effects as well as dielectric effects. Data from zone846 will, therefore, be used to illustrate the d~ llli,ldlioll of dielectric
dispersion of resistivity measurements. Attention is further drawn to Fig. 26
which illustrates observed dielectric data superimposed upon laboratory
measurements of dielectric constant as a function of frequency published in
- 30 the previously cited Taherain reference. The curve as illustrated was fitted
using the model of Cole and Cole as previously referenced. At a depth of
77
WO95/24663 2 1 85029 .~, ~
1660 feet, dielectric constants measured at 2 MHz and 25 MHz are denoted
by the numerals 841 and 8211, respectively and the corresponding
resistivities are denoted by the numerals 838 and 827"~ e~,th/cly. These
values of eff and C~ff = 1/Reff are inserted into equation (46) at the
5 respective frequencies, real and imaginary parts of equation (46) are
equated yielding a set of four equations, and a non-linear regression scheme
such as a ridge regression is employed to solve for the resistivity of the waterRw= 1/5w= 0.16, the dielectric constant of the rock matrix m = 9.0, and
the fommation porosity 0 = 0.05 or 5 %. These are r~asc,l-able values for
10 i"",e""eal,ld carbonate and agree well with core data taken in zone 846.
5.5 Borehole C~ n~
The ability to accurately calculate amplitude attenuation and
phase shift, which are uninfluenced by mutual coupling and drift errors,
15 allows for meaningful wellbore calipering operations. An accurate
d~ llllillaliOI~ of the amplitude attenuation caused by the formation alone or
the wave propagating between receiving antennas 211, 213, and an
accurate measure of the phase difference between receiving antennas 211,
213, can be utilized with a library of graphs or data which are recorded in
20 computer memory. Fig. 28 depicts a graph of phase difference in degrees
versus attenuation in dB. With respect to these X- and Y-axes, a plurality of
curves are provided. A plurality of curves are provided which co,,~:,,uol,d to
borehole diameter, in inches. In Fig. 28, borehole diameters of 7", 8", 9", and
10" are graphed. A plurality of curves are provided which represent
25 fommation resistivity in ohm meters. Fig. 28 depicts formation resistivity
measurements of 0.2 ohm meters, 0.5 ohm meters, 1.0 ohm meters, 2.0 ohm
meters, and 200 ohm meters. This graph is accurate when the drilling mud
has a resistivity of 0.05 ohms meters (Rm). The graph of Fig. 28 is merely an
exemplary graph. In practice, a plurality of graphs or data sets are provided
30 for a plurality of mud l~ m
78
WO 95124663 2 t 8 5 0 2 9 r~l,~ 9! 14
Provided that the formation resistivity and the mud resistivity Rm
are known, the amplitude attenuation and phase shift of the el~.:t,u",ay"ttli~
i,.~r,._ ,9 field can be utilized to determine the diameter of the borehole in
the region of the logging prp~rQt"c For example, with reference to Fig. 28,
5 assuming that the formation resistivity is û.5 ohm meters and the mud
resistivity Rm is 0.05 ohm meters, a calculated amplitude attenuation of -66
dB and a phase difference of 55- indicates that the borehole has a diameter
of ap~lu,~i",dlely 9". In accoldd"ce with the present invention, central
processor 215 and digital signal processor 221 can be p~uyldrllllled to
1û pe,i~k,~lly or il,L~ ly calculate borehole diameter, and transmit it to
the surface utilizing mud pulse telemetry techniques. If the borehole
diameter is enlarged to 1û", this should be reflected by changes in the
amplitude attenuation and phase shiff. In contrast, if the borehole narrows in
diameter to 8", this would also be reflected in the amplitude attenuation and
15 phase shift measurements. Borehole calipering operations can only be
conducted if uncorrupted measurements of amplitude attenuation and phase
shift can be obtained. Since the present invention allows for the correction of
any corrupting influence of magnetic mutual coupling, or themmal and other
types of drift, such measurements can be utilized to accurately determine
2û borehole diameter. In the preferred ~",Lo.li",e"l of the present invention, aplurality of data sets are provided, each cor,~,.,u"di"9 to a different mud
resistivity Rm and a particular formation resistivity. These data sets are
contained within the tool model matrix rT~ which was discussed in a previous
section. The measurements of amplitude attenuation and phase shift are
25 then utilized to detemmine borehole diameter.
The above description may make other alternative
~",I,odi",t:"l~ of the invention apparent to those skilled in the art. It is
therefore the aim of the appended claims to cover all such changes and
3û ll~odiriudliol~:, as fall within the true spirit and scope of the invention.
79
WO 95124663 2 1 8 5 0 2 9
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C C,~, ~ ~ ,, " Y U U
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W ~
~ S C O = .= ,~ L
`Z~
O -- -- O
O
U 31 U
W0 95/24663 2 1 8 5 0 2 q r~
-
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81
W095124663 2 1 85029 r~~
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82
