Note: Descriptions are shown in the official language in which they were submitted.
BACKGROUN~: OF THE INVENTION
This invention relates to an apparatus and method for
investigating subsurface formations and, more particularly, to
an apparatus and method for determining a composite parameter of
the formation water in ~ormations surrounding a borehole, for
example the composite conductivity of the formatlon water.
Using the composite parameter, other useful information, for
example a determination of water saturation, can be accurately
made, even in shaly formations.
The amount of oil or gas contained in a unit volume o~ a
subsurface reservoir is a product of its porosity and lts hydro-
carbon saturation. The total porosity of a formation,
designated ~t~ is the fraction of the formatlon unit volume
occupied by pore spaces. Hydrocarbon saturation, designated
Sh, is the fraction of the pore volume filled with hydrocarbons.
In addit.ion to the poro~ity and hydrocarbon saturatlon~ two
other ~actoxs are necessary to determine whether a reYervoir has
commercial potential; viz., the area of the reservolr and its
producibility. In evaluaking producibility, it i9 important to
know how easily fluld can flow through the pore sys~em. This
depends upon the manner in which the pores ~re interconnected
and i~ a property known as permeability.
To determine the amount o~ producible hydrocarbons in a
formation, it i5 useful to obtain a measure of the bulk volume
~raction of hydrocarbons displaced ln invasion o~ the
~ ` J
~.~2(~3
drilling mud during the drilling operation. During dril~ing,
the mud in the b~rehole is usually conditioned so that the
hydrostatic pressure of the mud column is greater than the
pr.essure of the formations. The differential pressure
forces mud filtrate into the permeable formations. Very
close to the borehoLe, virtually all of the formation watèr
and some of the formation hydrocarbons, if present, are
flushed away by the mud filtrate. This region is known as
the "~lushed zone". The bulk volume fraction o.f hydro-
carbons 'displaced by invasion in the flushed zone is anindication of the amount of "movable" hydrocarbons in the
particular portion of.the formations. This bulk volume
fraction of the hydrocarbons displaced by invasion can be
t( h Shr), where Shr is the residual hydro-
carbon saturation in the flushed zone (i.e., the sakurationo~ hydrocarbons which wexe nok flushed away by the mud
~iltrate and yenerall~ considered as i.mmovabl~j. '.rhe
saturation of the mud ~ ra~e, designated as Sx ~ can be
represented as
5 ~ S ) (1)
xo hr
The saturation of hydrocarbons in the uninvaded formations,
designated Sh, can be expressed as
, S = (l - S ) (2)
, h w
where S is the water saturation of the formations; i.e.,
w
the'fraction of the pore spaces filled ~ith water. From
the equations (1) and (Z), it can be seen that the previously
set for~h expression for the ~ulk volume fraction of oil
displaced by invasion, ~ Sh - Shr), can be expressed as
~t ( ~ Shr)~ ~ (SXO ~ Sw) ~3)
GPnerallyj relatively accurate determinations of ~tcan
be obtained usi~g known logging techniques, so accurate
determinations of S and S are highly useful, inter alia,
xo w
for detenmining the bulk volume fraction of hydxocarbons
displaced by invasion and, therefore, the fraction of
producible hydrocarbons for particular formations surround
ing the boxehole.
Classical prLor art techniques exist for
detenmining water saturation a-nd/or related parameters.
It has been established that the resistivity of a clean
formation (i.e., one containing no appreciable amount of
clay), fully saturated with water, is proportional to the
resistivity o~ the water. The constant o proportionality,
designated F, is called the formation factor. Thus we
have R
F - (4)
where R is the resistivity of the formation 1~0% saturated
with water of resistivity R . Formation factor is a
functio~ of porosity, and can be expressed as
F ~ ~ m
where a and m are generally taken to be 1 and 2, respectiveiy.
Using these values,~the true xesistivity, designated R , of a
clean formation is expressed as
t Sn 2 (6)
w t
r ;,~
where n, the saturation~ exponent, is generally taken to
be 2. Using the classical equation set forth, one con-
ventional prior art technique computes a value, designated
Ro which is a computed "wet" resistiv.ity value and
assumes that the formation is fully saturated with water;
i.e., Sw = l. From relationship (6), it can be seen that
2 (7)
o ~. ... .
In this computation,~t may ~e obtained from logging
information, for example f~om neutron and/or density log
readings, and..Rw may.be.obtained from local knowledge o
connate water.resistivity or, for example, from a clean
water-bearing section of a resistivity log. The computed
value of R is compared.with a measured value of
resistivity, designated R:t,.obtained, for example, ~rom a
deep investigation resistivity or induction log. In zone~
having no hydrocarbons Ro will'tr~ck Rt, but when R is
less than R , there is an indication.of the presence of
t
hydxocarbons. Thus,.by overlaying the computed wet
- reslstivity (Ro) and the measured resistivity (Rt),
pstential hydrocarbon bearing zones can be identified.
From equations.(6) and t7), it is seen that another way of
using this information is ~o obtain a computed value of apparent
water saturation, designated S , from th~ relationship
S ~ ~ (8)
W, ~ ,, Rt -' -
5ubstantial deviations of Sw from unity also indicate
p~ential hydrocarbon.bearing zones.
,
--6--
The described types o techniques are ef~ective
in rela~ively clean fo~ma~ions, but in shaly formations
the shales contrib~te to the conductivity, and the usual
resistivity relationships, as set forth, do not apply.
Accordingly, and for example, the previously described
overlay or Ro and Rt can lead to incorrect conclusions in
a shale section of the formations, and the overlay in
these sections (as well as the -determination of water
saturation taken therefrom) is generally, of necessity,
ignored. In addition to the results being less useful than
they might be, this consequence can tend to diminish.the
credibility of tha entire computed log comparison and is
a disadvantage when at~empting to conmercially exploit the
. resultant.information. Accurate determination of Sw can also
15 - be difficult in shale sections. 0f course, these are juist
limited eixamples of how shaliness can interfere with measure-
ment interpretation, but similax problems with shaliness arise
in other situat.ions, such as when invaded zoae characteristics
~like SxO) are ~kO be dei~ermined or when interpreting readings
Erom thermal decay time logs in cased boreholes.
A number of te~hniques,'of varying complexity,
are in axistence.for alding in the interpretation of results
obtained in shaly formations. The manner in which shaliness
afects a log reading depends on the proportion of shale and
its physical proper~ies. It may al50 depend upon the way ~he
shale is distributed in khe formations. It is generally
believad that tha shaly material'is distributed in shaly
sands in thre~i possible ways;'i'.e., "laminar shale" where
the shale exists in ~he form of laminae be~ween which are
. . I . . -
. . .. .. . .
, . . . . i, . ;, .
layers of sand, "structu~al shale" where the shale exists
as grains or nodules ln the formation matrix, and "dispersed
shale" where the shaly material is dispersed throughout the
sand partially filling the i~tergranular interstices.
Shaly-sa~d e~aluations are typLcally made by assuming a
particular type of shale distribution model and incorporating
into the modeL information which indicates the volume of
shale or the like. ~or example, in a laminated sand-shale
simplified model, an equation of the form of equation (6)
is set forth, but includes a second term which is a function
of the bulk-volume fraction of shale in the laminae. The
same is true for another known model wherein a term is
developed which depends upon the volume ~raction of shale
as determined from a total clay indicatorO In a disperse~
shale simplified model, values are developed for an
"intermatrix porosity" which includes all the space
occupied by fluids and dispersed shale and another value is
developed representing ~he ~raation of ~ha~ porosity
occupied by the shale. Still another approach relates
the conductivity contribution of the shale to its cation
exchange capacity, this capacity being determined, inter
alia, from the volume of clay.
The described prior art techniques, which require
~ either a determination of the volume of shale or clay, or
similar inf~rmation, have been satisfactory in some
applications. However, in addition to the difficulty of
accurately obtaining Lnformation concerning the volume and
composition of shale or clay and its conductivity, a further
problem with prior art simplified models is that various
forms of shale may occur simultaneously in the same
~ormation. Reliable techniques, some of which use
extensive ~tatistical txeatment of data, do exist and
generally yieLd good re~ults, but tend to be relatively
complex and may re~uire either powerful computing equip-
ment and/or substantial processing time.
It is one object of the present invention to
provide a solution to the indicated prior art problems
and to se~ forth techni~ues which are effective even in
shaly formations, but which are not unduly complex or
dif~ficul~ to lmplement.
- .
,
r
... .. : '' ' .
- -- .
_9_.
.
~ ~213 ~i~3
SUMMARYJOF THE INVENTION
_
Applicant has discovered that determination of
a "composite" parameter of the formation water in forma-
ions surroundin~ a borehole, for example the composite
' conductivi~y of the foxmati.on water, allows a relatively
accurate determination o ~ormation characteristics, such as
water saturation, the.det~rmined values being meaningful
even in.shaly regLons of the formations.. In contrast to
past approaches which attempted to determine the volume of
shale or clay presen~ in the formations and then introduce
appropriate factors which often involve substantial guesswork,
applicants' teGhnique determines a composite water parameter, .
for example a compos1te water conducti~ity, which represents
the conductivity o~ the bulk water in the ormations, in-
cluding both free water and bound water. Bound water trapped
in shales is accounted for in this determination, so unlike
priox techniques, the shales can be consldered as having a
porosi~y. Havi.n~ de~ermined the composite water conductivity,
water saturation can be directly obtained usiny reL~tively
straigh~forward relationships which do not require estimates
of the volume of shale in the formations. Shale effects are
- accounted for in the present Lnvention by the dif~erent con-
duc~ivities (or o.ther parame~er such as capture crosssections)
of the formation water constituents (free and bound) which
make up the total water. . As used herein, "free water" is
generally lntended to mean water that is reasonably free to
be moved u~d~r normal reservoir dynamics, whereas "bound water"
is generally intended to mean water that is not reasonably free
to be moved under normal reservoir dynamics.
L3
In accordance with a broad aspect of the lnvention, there
is provided an apparatus for determining a composite parameter
(such as the composite conductivity or the composite capture
cross section) of the formation water in formations surrounding
a borehole. Means are provided for derivlng a first quantity
representative of the parameter attributable -to the free water
in the formations. Means are also provided for deriving a second
quantity representative of the fraction of bound water in the
formations. (As will become clear, the second quantity could
alternatively be obtained indirectly from the fraction of free
water.) Further means are provided for deriving a third
quantity representative of the parameter attributable to the
bound water in the formationsO The composite parameter is then
determined as a function of the first, second and third
quantities.
Ln one form of the invention, a -fourth quantity is
derived, as the diference between the third and flr~t
quantities. The aomposite parameter ls then dekermined as the
sum o~ the first quantity and the product o~ the second and
fourth quantities.
In an embodiment of the present inventlon the composite
water conductivity, designated aWC~ ~ expressed by the follo~ing
relationship:
' = ~ ~ wb (a - a ) (9)
wc wf S~ wb w~
where u is the conductivity of the free water in the forma-
wf
tions, G iS the conducti~ity of the bound water in the
wb
formations, Sw is the water saturation of the formations (which
equals ~w), and Swb is the saturatlon of the bound water in the
~ t
formations (which equals ~wb). The expresslon
~t
-- 11 --
(9) apportions the composite water conduc~ivity as between
the ~onductivity of the free water (the above-indicated
first quantity) and the conductivity of a difference term
which expresses the difference between the conductivities
of the bound water and the free water (the above-indicated
fourth quantity). Mathematical manipulation shows that
another form of expression (9) is.
- wc - ( 5 w S wb (10)
w w
In this form, the composite water conductivity can be
viewed as the sum of a first term,which represents the
fraction of free water times the conductivity of the ~ree
water, plus a second term which represénts the fraction of
bound water times the conductivity of the bound water.
As implied above, the ~raction of ~ree water, S /Sw, (which
is the unity complement of the bound water fraction -since
the total water volume consists of the ~ree water volume
plu~ the bound water volume) could alternately he used in
expressions (~) or (10)~ For example, the form of expres-
sion (la) would then be
= Swf ~ ~ (sw _ Sw~) ~ (lOa)
F Sw wf --~~~-S ~ -~ wb
which can be seen to be eguivalent to (lOj since Sw = SWf + Sw~.
Accordingly, when the term "fraction of bound water", or
the like, is used in this context, ik will be understood
that its complement (the fraction of free water) could aiter-
natively be employed in appropriate form.
. -12-
~I~Z~S4:3
In another embodiment of the invention, the composite
parameter of the formation water is the composite capture cross
section, designed 2WC. As is known in the art, capture cross
section is a measure of the fraction of thermal neutrons
absorbed per unit time, and is typically measured using a thermal
neùtron decay time ('INDT'l) logging device of the type described,
for example, in United States Patent No. RE 28,477 issued
July 8, 1975 to William B. ~elligan. The composite capture
cross section, ~wc~ is expressed herein as
~wc ~wf ~ wb (~wb ~wf) (11)
which is similar to expression (9), but where ~wf is the ~apture
cross section of the free water in the formations and ~wb is the
capture cross section of the bound water in the formations.
In àccordance with a further feature of the invention, a
value of water saturation is generated and provides meaningfwl
information even in shaly regions. This obviates the prior art
technique of estimating an appropriate "cementatlon" exponent
for shaly formations.
In accordance with still further features of the
invention, relationships similar to (9) or (10) can be set forth
in terms of a generalized parameter, "P"~ and utilized to obtain
a free, a bound, or a composite water parameter, depending on
what information is desired and what information i5 measurable
or deriveable. In particular, if it is desired to obtain a
parameter of the free water, one can set forth the following
generalized relationship which is similar in form to relation-
ship (9) above
Pwc = P~ ~ wb (P~b - Pwf) (9a)
where PWc is a composite water parameter, PWb ~s a bound water
paramater, and Pwf is the free water parameter to be determined.
In one embodiment of the invention, the free water parameter to
be determined is in the form of a ~ariable ~w awf' defined as
the signal attenuation attributable to formations when assuming
that substantially all of the water therein is free water.
Means are provided for deriving a functlon representative o~ the
parameter (attenuation in this case) in at least one region of
the formations (typically a clean sand region) in whlch
substantially all of the water present is free water. Means are
also provided for deriving a quantity representative of water
content in the formations surrounding a particular depth location
in the borehole. This quantlt~ may be tpl, the travel time o~
microw~e electromagnetic energy~ in the ~ormations, which is
dependent on water conten~. The free water parameter (in the
form of the variable ~w awf in this case) at the particular depth
level is then determined from the derived function and the water
content representative quantityt ~easurements o~ attenuation
and travel time are typically obtained uslng an J~E~' microwave
electromagnetic propagation logglng de~ice.
In the terms of attenuation, ~, the relationship (9a) can
be expressed as
Sw ~ (9b)
- 14 -
where awb is the bound water counter part of awf~ and ~ c is a "composite"
attenuation for the actual formation water.
As will be described further hereinbelow, the "apportionment"
of attenuation, as between the free and bound water which is indicated by
expression (9b) leads to a technique for determining the fraction of bound
water, S b/S once the values of a, a f and awb have been established. In
particular, Swb/Sw can be dete~nined from
Swb ~wc wf (9c)
S ~ a - a
w wb wf
which follows directly from relationship (9b).
According to another broad aspect of the invention there is
provided apparatus for determining the water saturation of formations
surrounding a borehole, comprising:
means for deriving a irst quantity representati~e of the
conductivity of the free water in said formations;
means for derivLng a second quantity representatlve of the
fraction of bound water in said formations;
means for deriving a third quantity representative of the
conductivity of the bound water in said formations;
means for deriving a quantity representative of the measured
conductivity of the formations; and
means for determining the water saturation of the formations as
a function of said first, second and third quantities and said measured
conductivity representative quantity.
In accordance with another aspect of the invention there is pro-
vided a method for determining a composite parameter of the formation water
in formations surrounding a borehole, comprising the steps of:
deriving a first quantity representative of said parameter
-15-
attributable to the free water in said formations;
deriving a second quantity representative of the fracti.on of
bound water in said formations;
deriving a third quantity representative of said parameter
attributable to the bound water in said format.ions; and
determining said composite parameter as a function of said irst,
second, and third quantities.
In accordance with another aspect of the invention there is
provided a method for determining the composite conductivity of the forma-
tion water in formations surrounding a borehole, comprising the steps of:
deriving a first quantity representative of the conductivity of
the free water in said formations;
deriving a second quantity representative of the fraction of
bound water in said formations;
deriving a third quantity representative of the conductivity of
the bound water in said formations; and
determining said composite water conductivity as a function o:E
sai.d :Ei.rst~ second and third quant:it:i.es.
~ccording to another aspsct of the i.nvention there is provided
a method for determining the water saturation of formations surrounding a
borehole, comprising the steps of:
deriving a first quantity represen~ative of the conductivity of
the free water in said formations;
deriving a second quantity representative of the fraction of
bound water in said formations;
deriving a third quantity representative of the conductivity of
the bound water in said formations;
derivi.ng a quantity representative o:E the measured conductivity
of the formations; and
determining the water saturation of the :Eormat:ions as a function
-15a-
of said first, second and third quantities and said measured conductivity
representative quantity.
Further features and advantages of the invention will become
more readily apparent from the following detailed description when taken
in conjunction with the accompanying drawings.
-15b-
BRIEF.~ESCRIPTIOW.OP THE DR~WINGS
FIG. 1 is a simpIi~ed block diagram of an
apparatus in accordance with an embodiment of the
in~ention.
'
FIG. 2 is a bLock diagram of the computing
module 60 of FIG. 1.
- FIG. 3 is a block diagram of the computing
module 70 of FIG. 1.
FIG. 4 is a block diagram of the computing
module 80 of FIG. 1.
FIG. 5 is a frequenGy cross-plot useful in
obtaining subsurface characteristic values that can be
utllized in the present invention.
FIG. 6 is a log of values, including computed
values, versus depth which illustrates how the invention
. can be utilized.
..
, FIG. 7 is a block diagxam of circuitry useful in
- obtaining a signal representative of apparent composi~e capture
cross section of subturface formations.
.
p
S~L3
FIG. ~ is a block diagram ~f a circuit useful
in obtaining values of apparent water capture cross section
of subsurface formations.
.. ,
FIG~ 9 is a block diagr~m of a circui~ useful
in obtaining signals representative o a "wet" capturP
cross section th~t can be compared to measured values of
capture cross section.
FIG.-lO is a block diagram-o a circuit useful
in obtaining values of the invaded zone water saturation.
.
lQ FIG. 11 is a block diagram of a circuit useful
in obtaining an alternate value of bound water saturation.
~ IG. 12 is a block diagram o a circuit useful
in obtaining a si~nal representati~e of the bound water
~xaction.
FIG. 13 is a frequency cross-plot useful in
obtaining su~surface characteristic values that can he
utilized in the present invention.
FIG. 14 is a block diagram of a circuit for
' obtaining signals re~resentative of free water attenuation,
bulk free water attenuation, and EMP-derived conductivity.
,
-17- ,
.
~ ~Z~JS~3
DESCRIPTION OF THE: PRE:FERRFD EMBODIMENT
Referring to Figure 1, there is shown a representative
embodiment of an apparatus in accordance with the present
invention for investigating subsurface formations 31 traversed
by a borehole 32. The borehole 32 is typically filled with a
drilling fluid or mud whlch contains finely divided solids in
suspension. The investigating apparatus or logging device 40 is
suspended in the borehole 32 on an armored ca,ble'33, the length
of which ~ubstantially determines the relative depth of the
device 40, The cable length is controlled by suitable means at
the surface such as a drum and winch mechanism (not shown).
Circuitry 51, shown at the sur~ace, although portions thereof
may typically be downhole, represents the overall processing
circuitry ~or the various logglng units of apparatu~ 40.
The investigating apparatus 40 includes a suitable
resistivity-determining device such as an induction logging
device 41. As is known in the art, ~ormation reslstivity or
conductivity is indicated by the lnduction log readinys, the
measured conducti~ity bei.ny deslynated as ~t~ The do~mhole
investigating apparatus also includes a sidewall epithermal
neutron exploring device 42 having a source and detector mounted
on a skid 42A. A device of this type i5 disclosed, ~or example,
in United States Patent No. 2,769,918 issued November 6, 1956 to
Charles W. Tittle~ Each count regiskered in the epithermal
neutron detectox is recelved by a processing circuit in the
overall circuitry 51 which includes a function former that
operates in well known manner to produce a signal ~N which
represents the ~ormation poroslty as determined by the neutron
logging device. The investigating apparatus 40 ~urther lncludes
- 18 -
)5~3
a formation density exploring device 43 for producing well
logging measurements which can be utilized to calculate the bulk
density o~ the adjoining formations, in known manner~ In this
regard, a skid 43A houses a source and two detectors (nok shown~
spaced dif~erent differences ~rom the source. This arrangement
o~ source and detectors produces signals that correspond to the
bulk density of the earth formations as is described, for
example, in the United States Patent No. 3,321,625 issued
May 23, 1967 ~o John S. ~ahl. The circuitry 51 includes
conventional circuits which convert the signals derived from the
short and long spacing detectors to a computed bulk density. If
desired, a caliper signal may also be applied in determining
bulk density, as is known in the art. The resulting bulk
density is applied to porosity computing circuitry within the
block 51 which computes the poroslty, as deri~ed from the bulk
densi~y, in well known fashion. The derived porosity ls
designated as ~D. The invest.igatiny appar~tus includes a still
further de~ice 44 which i9 a ga~na ray logglng device ~or
measuring the natural radioactivity of the ~ormations. The
2n device 44, as known in the art, may typically include a detector,
for example a scintillation counter, ~hic~ measures the gamma
radiation originating in the formations adjacent the detector~
An output of circuitry 51 is a signal designated l'G~" which
represents the gamma ray log reading. Further de~ices may be
provided, as required in accordance with variations of the
invention as described hereinbelow. For example, a device 45 is
available ~or obtaining measurement of the spontaneous potential
(''SPI') of the formations. This device may be o~ the type
disclosed in Unlted St.ates Patent No. 3,453,530 issued ~uly 1,
1969 to George Attali, thls patent als~ di.sclo~ing deep and
shallow reslstivity devices. Also, an electromagnetic propaga-
tion tool ("EMP") 46 ls a~ailable, and includes a pad member 46A
~I n _
~ ~Z~:)5~i~
that has transmitting and receiving antennas therein. Microwave
electromagnetic energy is transmitted -throuyh the formations
(typically the invaded zone) and formation characteristics are
determined by measuring the attenuation and/or phase (or
velocity) of received microwave energy. This type of logginy
tool is described in United States Patent No. 3,944,910 issued
March 16, 1976 to Rama Rau. Measurements indicatlve of attenu-
ation, designated ~, and of travel time (which depends on
velocity), designated tpl, a.re a~ailable from this tool. Also,
in United States Patent No. 4,158,165 issued June 12, 1979 to
George R. Coates and United States Patent No. 4,156,177 issued
May 22, 1979 to George R~ Coates, there are disclosed techniques
for obtaining an "EMP"-derived conducti~lty measurement,
designated EMP' and for obtaining a measurement o~ bound water
filled porosity, designated ~b. Signals representative of
these measurement values are illustrated as being available
outputs of circultry 51. An NDT (Neutron Detection Tool) device
47, for example of the type disclosed in United States Patent No.
RE 28,477, is also available and re~ults in an output capture
cross section value, ~, ~rom proce~sing circuitry 51.
To keep the investigatlng apparatus 40 centered in the
borehole, extendable wall-engaging men~ers 42B, 43B and 46B may
be provided opposite the ~embers 42A, 43~ and 46A. For centering
the upper portion of the investigating apparatus, centralizers 49
may also be provided. As noted, a borehole caliper can be
combined with the arms which extend the skids and supply a signal
representative o~ borehole diameter to the circuitry 51.
While all of the measurements to be used in practising
the invention are known, for ease of explanation in this illus-
tra~ive embodiment, as being derived ~xom a single exploring
~ - 20
S9~3
device, it will be understood that the~e measurements could
typically be derived from a plurallty o~ exploring devices which
are passed through the borehole at different times. In such
case, the data from each run can be stored,
- 20a -
~5~3
such as on magnekia tape, ~or subsequent proc~sing consi~ent
with the principles of the invention. Also, the data may be
darived from a remote location, such as by txansmission there~
. from.
One or more of the signal outputs of block 51 are
illustrated in FIG. 1 as being available to computing modules
60, 70, 80 and 510. In the embodiment of FIG. 1, the computi~g
module 60 generates a signal representative of an apparent
composite water conductivity, designated a' , consistent with
the relationship. (9). The computing module 70 is responsive
to the signal representative f wc~ and to the signals from
block 51 (in~pa~ticular a porosity-indica~ive signal), to gener-
ate a "wet" conductivity signal, ~'. The computing module 80
generates a computed value of water saturation, Sw, in accordance
with a relationship to be set orth. The computing module 510
is utilized in the generation of free and bound water attenua-
tion values~and a signal representative of the bouna water rac-
tion. These slgnals, along with some or all of the output4 o
cirauitry 51, are recorded as a funation o depth on recorder 90
Re~erring to FIG~. 2 and 3, there are shown embodl-
ments o the computing module~, 60 and 70 of F~G. 1. I~itially,
structural components of the modules will be described, The
source of variouc signals, along with further rationale of the
- configurations, will.then be set forth. A pair of difference
: . circuits. 601 and 602 are provided. The po~itive input terminal
of circuit 601 recei~es ~he signal GR, i.e., a signal representa-
tive of the output of the gamma ray logging device 44. The
positive input terminal of circuit 602 receives a signal desig-
nated GP~Wb, which is a signal leve} representative of a gamma
ray log level ~or the bound water of the formations being inves-
tigated. The negative input terminals of both difference circuits
601 and 602 receive a signal 1QVe1 designated GRW, which is a
gamma ray log level for the free water in the formations being
investigated. The outputs o~ circuit 601 and 602, which are
-21
respectively GR-GRW~ and GRWb-~Rw~, are coupled to a ~atio
circuit 603 which produ~es a signal proportional to the ratio
of the output ~f:,circuit 601 divided by the output Q~ circui~
. 692. The output of ratio cixcuit 603 is a signal represen-
tative of Swb, i.e., the saturation of the bound water of
the formations in accordance with the relationship
S GR-GRWf . ~12)
wb GRWb-GRwf .
The output of ratio circuit 603 is coupled via
limiter 604 to one input to a multiplier circuit 605. The
other input to multiplier circuit 605 is the output of a
difference circuit 606. The circuit 606 receives at its
posltive input terminal a signal level representative of
awb, i.e. the conductivity of the bound water in the forma-
tions being investigated. The negative input terminal of
lS difference circuit 606 receives a signal level représentative
- o of , i.e. the conductivity o~ the free water of the orma-
tions. This latter signal is also one. input to a summing
circuit 607 wh*se other input is the output o multiplier
circ~it 605. The output o~ summing.circuit 607 is a siynal
representative of the apparent composite water conducivity
of the formations being investigated, i..e.
. ~wco awf + SWb(~Wb ~ ~wf) (13)
".,,. ' ' .
This expression is seen to be the same as th~ expression
(9) above for composite water conducti~ity, a , except that
25. Sw is assumed to be 1, which means that the result is an
"apparent" composlte water conductivity.
.
-22
.
.
)5~
In FIG. 3 there is shown an implementa~ion of .
the computing mp~ule 70 of FIG. 1 which is utilized ko
generate a signai representative of aO ~ i.e. the computed
"wet" conductivity of the investigated formations. The cir
S cuitry 51 (FIG. 1) includes a porosi-ty computing circuit
511 which is responsive to the signals representative o~
~N and ~D. The circuit 511.uses this in.formation, in well
known manner, to produce a signal generally known as ~ND
that incorporates information from both the neutron and the
density log readings to obtain an indication of formation
total porosity, designated ~ Techniques for obtaining
~ND are well known in the.art, and a suitable neutron-density
porosity computing circuit is disclosed, for example, in
. the U. S. Patent No. 3,590,228 of Bur~eA. It will be under-
stood however, that any suitable alternate techni~ue for ob-
taining ~t can be employed, including, for example, techniques
that use other logging inorma~ion, such as from a sonic log.
The output of circui~ 511 is coupled to a squaring circuit 701
whose output is accordingly proportional to ~ . This signal
is, in turn, coupled to one input .terminal of a multiplier
circuit 702, the other input to which is ~wco ~ i.e. the
apparent composite water conductivity as determined by com-
puting module 60 (FIG. 1, PIG. 2). Accordingly, the output
of multiplLer circuit 702 (which is also the output of com-
25 , puting module 70 -- FIG. 1), is a signal proportional to ~wco
multiplied by ~ , and is thus indicative of the computed ~Iwet~
. conductivi~ty Qf the formations, ~O , in accordance with a
-relationship analagous to (7).above; viz.:
~ ' 2
a = a ~ . (14)
wco t
-23-
The manner in which the inputs to compuking
module 60 can be devel~ped will now be described. In
particular, one ~referred techni~ue for obtaining values
of S b~ ~ b and awf is as follow~: ~og values of at, GR
and ~t are.initially obtained over a depth ranye of interest7
Using the measured resistivity, a (which is preferably a
deep resistivity measurement), one can compute, at each
depth level over ~he range o~ interest, a value designated
a as . .
wa
- ' at (15)
. wa ~?
. ' ~
This is similar in form to relationship (7~ above, and it is
seen that awa is a simple computed apparent water conductivity
~not to be confused with the apparent composite water conduc-
. tivity, a ~ , developed in accordance with relationship ~13)];
that is, ik is the compu;ted value of water conductivity that
would be expecked in order ~ox the obtained resistivity
measurement (at) ~o result ~rom the ob~ained total porosity
measurement, assuming that the totaL porosity is water-filled
(viz. assuming that S - 1). Stated another way, a formation
of porosity ~t which is filled with water of conductivity
o would (according t~ the basic Archie relationship) result
in the measured formation conductivity at. If desired, a
- computi~g circuit of t~e type employed in FI~. 3 (which uses
an analagous relation~hip to develop aO from aWcO) could be
utilized to obtain a in accordance wikh relationship (15)
by substituting at as the conduckivity inpuk to multiplier
702. Having obtained ~wa at sach depth level over the
depth range of interest, the invexse of these values can now
be utilized, in conjunction with gamma ray (GR~ log readings
taken over ~he same depth range, to yenerate a frequency
~z~
cross-plot o the type illustrated in FIG. 5. Frequency
cross-plots ar~ ~ommonly~used in the well logging art ~see,
for example, Schlumberger "Log Interpretation-Volume II",
1974 Edition). At each depth level, the values of l/a
wa
and GR result in a point on the cross-plot. When all points
have been plotted, the number of points which fall within each
small elemental area ~of a selected size) on the plot are
summed and presented numerically. The resultant plot is as
shown in FIG. 5, with the numbers thereon representative of
the requency of occurrence of points at each particular
elemental area on the plo~. In the illustrated example, the
region designated by enclosure 501 contained the highest con-
centration of points (i.e. more than five points at each
elemental area), so the frequencies of occurrence within this
region are omitted for clarity of illustration. The positlon
on the GR axis designated as GRWE is indicated by the line
of lowest gamma ray readings on the plot, as shown in dashed
line. The position on the GR axis de~ignated as GRWb is
indica~ed by the GR value at which increasing GR no longer
results in increaslng values of 1/~ . This means tha~ at
GRwb essentially all the water in the formations is bound
(typically by whatever shali~ess in present). Any further
shaliness would mean an increase in G~, but would no~ increase
the bound water fraction since essentially all water present
25 . was indicated as bound at the GR b line. The fraction of
bound water is then determined by intPrpolation between the
reference~lines GR ~ and GR ~, tnat is, as
GR-GR
Swb GR GR~ (16)
-~5-
.
~ t~ 3
The line on the l/o axis at which l/awa no longer
varies substantially w~th GR ~beyond GRW~ ndicakive
of l/owb, since, as prevlously no~ed, at this poink on the
plot essentially all ofithe formàtion water is bound~ Accord-
ingly awb is derived from the dashed line labelled with this
designation. Applicant has found that awb is substantially
a constan~ and has a value of about 7mhos/m at 75C. It is
not, however, considered a universal constant and may vary
somewhat in different regions. In any event, it is deter-
mi~able f~om e.g. the cxoss-plot of FIG. 5. The value of the
free water conductivity ~ ~, can be obtained, for example,
from the free water dashed line on the FIG. 5 plot. Alter-
natively, as is known in the art, a f can be obtained from
a clean sand section of a resistivity log or from local
- knowledge. It will be understood that alternate techniques
can be utilized to obtain at least some of the values con-
sidered herein.
With values of GRw, GRW~, awf, and awb having
been established for the depth range of interest, correspond-
ing signal levels can be input to the computing module 60
~FIG. 2). Now, log values o~ GR (as a function of depth
can be input to module 60 and a can be output and recorded
wco
(if desixed) on a dynamic basis. At the same time, the com-
puting module 70 ~FIG. 3) ge~erates a as an output to recorder
90. This signal can now be overlayed with at, to great ad-
- vantage in identify~ng potential hydrocarbon bearin~ zones.
~IG. 6 illustrates the nature of the signals which
can be recorded by ~he recorder 90 in the embodiment of FIG. 1.
The ver~ical xis represents depth. The middle track shows
the inverses of a (dashed line) and at(dashed line); i.e. t
the computed "wet" resistivity and the measured deep resistivity,
~26
reslJ~ctively. q~hc r~gions of diverycnce oE thesa cur~s,
for example the regions aesignated 2 and 3, indicate that
the me~sur~d decp ~esistivity is substantially greater than
the compute~ "wet" resistivity (or, conversely, that the
S measurcd dc~ con~uctivity is substantiall~ lcss than thc
computed "wet" conduo~ivity), thexeby indicating tha~ they
are potenti~l hy~rocarbon bearing zones. The left hand txac~.
illustrates the output of a spontaneous poten~ial (SP) lo~
over the samc de~th range. The relatively hi~h value of
the SP, for example in the regions designated 4 and 5 are at
.. . . . _ .. _ . .. . . . . , .. .. . . . .. . . . . . . . .. . . .. . .. ... . .. .. . . . . . . _ .
the shale baseline_and_characteristic_of_shaly xegions._ It
is seen that the resistivity cur~es generally track each
other even in the snaly zones, as should he the case for
water-bearin~j shaL~ reyions~ This continuous trackin~ of
the measurc~ an~ d~rived resistivity signals is an important
advantage of the present invention since comparable prior
art t~chniques ar~ generally unreLiable in shaly regions,
as discusscd in ~hc ~ackground section hereof.
~ e~ermination of a computed val.ue oE wat~r
satura~ion, ~w / will now be considered. l~elation (9) above
indicat~d that the composite water con~uctivity, u , is
expressed ~s:
wc wf ~ Sw ~awb ~ awf) (9)
.
From equation (6) we can write
.
t ~ awS2~2 (17~
where aw is the (unknown) actual conductivity of the forma-
tion water. ~ubstituting the expression for composite water
con~uctivit~ ((TWc) for ~w in (17) yives:
- -27-
~ J
at~ ~WcsW~-t
Sw[awf ~ wb ~ wf)]
Sw
= ~tS2~Wf + ~tSwswb('Jwb wf t18)
The apparent wa~er conductiv1ty a (as described
wa
in conjunction with FIG. 5) is equal to at/~2t. Substituting
,
into ~18) gives
= S ~ ~ S S (~ - ~ ) (19)
wa w wf w wb wb w~
which can be rewrltten as:
wE] w [Swb(awb ~ awf)]Sw ~ awa = (Z0)
This quadradic equation cBn be solved or Sw to obtain:
~_~ .
~S bt b ~ aw~)] ~ 4awfCwa ~ Swb(~wb aw~? ~21)
w
Frorn relationship ~21) it is seen that a value of water sat-
uration, obtained usLng the composite (free and hound) water
technique of the present invention, can provide meaning~ul
lS information even in shaly regions, since the ef~ects of the
shales in binding a portion of the tormation waters is accountcd
for in the relationshipO Accordingly, the prior art technique
of estLmating an appropr1a~e "cementatlon" exponent for shaly
formations is obviated.
. FIG. 4 illustrates an implementation of the computing
module 80 90 utilized to æenerate a aigna~ rep~esenta-tive-of
computed water saturation, designated Sw, in accordance with
relationship (21). The signal representative of "true" or
measured re~istivity, a~ (FIG. 1~, is one input to a ratio cir-
2S cuit 811. l'he o~ller inpu~ to ratio circui~ is thc out~ut of
,
,
~--.
a squaring circuit ~12 ~rnose input is a signal representa-
tive sf ~t. A~rdinglx,~ the output of ratio circuit 811 is
proportional to ~t/~t f which equals the apparent formation
conductivity, ~wa This signal is, in turn, coupled as one
input to a multiplier circuit 805 whose other input is a
slgnal representative o ~wf The output of mul~iplier 805
is coupled, with a welghting factor of 4, to one input of a
summing circuit 804. The signal a f i$ al50 coupled to the
. nagative input terminal of a difference circuit 801, the pos-
itive input terminal of which receives a signal representative
f ~ b. The output of dif~erence circui~ 801 is one input
to a multiplier 802.. The other input to multiplier 802 is
a signal representative of Swb, which may be derived, for
example, from the output of the limiter 604.of FIG. 2.
Accordingly, the output of multiplier 802 is a signal repre- .
SWb(~wb aw~). This signal is coupled to a
squaring circult 803 and to the po~itive input terminal o
a d.ifference circuit 807. The output o~ squaring circuit
803 is coupled to the other input terminal of summing circui-t
804 whose output is, in turn, coupled to a square root circuit
806. The output of the square root circuit 806 is coupled
to the negative input termlnal of dif~erence circuit 807.
The output of difference circuit 807 is coupled to one input
of a ratio circuit 8~8~ the other input o~ which receives
25 , the signal represent~ive of ~ ~, this si~nal being afforded
a weighting factor of 2. The output oX ratio circuit 808 is
the desired signal representative of Sw, in accordance with
relationship (21). Thé right track of FIG. 6 illustrates the ,.
recorded values o~ the compute~ water saturation, S .
-29
)S~3
The determination o~ a composite conductivity and
determination o~ water saturatlon, in accordance with the
principles of the invention, applles equally well in the invaded
zone of the formations. In the relationships (9) and (18) for
example, the quantity aw~ would be replaced by am~ (i.e. the
conductivity of the invading mud ~lltrate) and the water satura-
tion Sw would be replaced by the ln~aded zone saturation SXO.
The EMP logging device referred to a~ove measures characteristics
of the invaded zone. In the abovereferenced United States Patent
Application Serial No. 788,393, a technique is disclosed for
measuring ~wb using an EMP logging device. This technique can be
utilized as an alternate herein for obtaining Swb from
Swb = ~wb~t' ~n above-mentioned United States Patent No.
4,158,165 it is disclosed that conductivity as measured using an
EMP device, and designated ~EMP~ i9 related to the conductivity :~
of the ~ormation w~ater~ aw, as a linear function of water~filled
porosity, ~, i.e.:
EMP a~ '~w ~22)
Since S~ w~'~t and '~w '~t 5w~ relation5hip (22) can be
expressed as: .
~EMP ~t Sw ~w ~23) :
Substituting the expression (9) composite water conducti~ity for
aw into (23) gives:
~EMP ~t Sw [~wf + 5~b (~wb ~ ~wf)~
w
~ ~t Sw Uwf + ~t 5wb ( wb wf) (24)
- 30 -
~.~Z~ 43
Substituting ~mf for awf and SXO ~or 5~ and solving for SXO
yields
S~ t Swb (~wb ~mf) (25)
xo ~mf
Referring to Figure 10, there is shown a block diagram
of a computing module 80' suitable for obtainlng a signal which
represents the computed invaded zone water saturation, SXO~ in
accordance with relationship (25). A ratio circuit 111 receives
as one input a signal representati~e of aEMp, and as its other
input a signal representative of ~t. ~he signal ~MP may be
derived from the EMP de~ice 46 (Figure 1) by using processing
circuitry 51 as disclosed, for example, ln the above-referenced
United States Patent No. 4,153,165. Another ratio circuit 112
receives as one input a slgnal representative of ~wb~ and as its
other input the signal representative of total porosity, ~t. As
noted just above, ~wb can be derived from the measurements taken
with an EMP loggin~ de~ice and, ln this example, is utillzed, in
conjunction with (~t~ to obkain Swb (the output o.~ xatlo circuit
112). It will be understood, however, that Swb can be obtained
using alternate techniques, such as those described herein. A
difference circuit 113 receives as its input the signals
representative of ~wb (which may be obtained as indicated abo~e
and is typically, although not necessarily, about 7mhos/m) and
~mf. The outputs of ratio circuit 112 and difference circuit
113 are coupled to a multiplier clrcuit ll4 whose output is
therefore Swb (~wb ~ ~mf) The output of ratio circuit 111 and
multiplier circuit 114 are coupled to still another difference
circuit 115~ The output of difference circuit 115 i5 therefore
seen to .represent the numerator in expression (25). This output,
and the signal representative of ~mf~ are the inputs to another
- 31 -
ratio circuit 116, whose output is seen to be representative of
SxO, in accordance with expression (25). Thls signal can be
recorded, in the manner of the illustration in Figure 5.
The spontaneous potentlal measurements from SP device 45
(Figure 1) CRn also be used, for example, as an alternate
technique for obtaining values of Swb. The SP measurement can
be expxessed as
S 6
SP K loglo sxO amf (26)
where K is a constant dependent upon absolute temperature and
~mf is a composite conductivity for the invaded zone mud
filtrate, similar in form to ~wc as expressed by relationship
(9)~ Using relationship (9) as a basis, we have:
w ~wc Sw aw~ ~ Swb (~b ~ ~wf) (27)
and SxO amf = SxO amE ~ Swb (awb m:E
ubstitutiny (27) and (28) into (26) and rearranging gives:
S 10SP/K _ w wf = Sb wb (1 - 10 / ) ~ 10 ~ a f (29)
In a water~bearing region of the formations where SxO = Sw
relationship (29) reduces to:
SWb = 1 + V
awb/amf (1 _ 10SP/K (30)
whexe v loSP/K
32 -
h; ~
? ~ '~t ' "i ~
~.~L2~5~3
There~ore, the relationship (30) can be utilized (taking
SP from a water-bearing reyion) as an alternate technique
~or obtaining S~b~ FIG. 11 illustrates circuitr~_t~at
can be utilized to obtain a signal r$presentative o 5 b
in accordance with relationship (30). The co~ination
of ratio circuit 121~ antilog circuit 122, difference
circuit 124 and multiplier 126 are used to obtain the
~umexator, while ratio circuit 123, antilos circuit 122,
and difference circuit 125 are used to obtain the
denominator of v~ The ratio circuit 127 then yields v
and summing circuit 128 and inverter 129 are used to
obtain a signal representative of Swb.
.
. -33- ,
In the prevLausly described embodiments, the
de~ermined composite parameter of the formations has been
thq composite conduc$ivity (or resistivity). Another
com~osite paramet~r which can be determined is the
composite captuxe cross section, as obtained using an NDT
log plus inputs correspon~ing to those indicated above.
As is well known, the ~DT is particulaxly useful in cased
holes where resistivity logs canno~ be used. In such
case, the relationship (~)as set forth ahove is:
wc wf Sw ~wb wf) (11)
An apparent composite capture cross section, designated ~ ,
can be obtained in the same manner that a was developed
wco
above, and ~y using the computing module 60' illustrated in
FIG. 7. In FIG. 7, the multiplier 705, di~ference circuit
706, and summing cixcuit 7~7 sperate in ~he same ~ashion as
the corre~ponding unit3 605, 606 and 607 of FIG. 2. Suitable
value~ of ~w~ ~wb and Swb can be obtai~ed by cross~plotting
against GR in the manner described in conjunction with FIG. 5.
The only difference is that instead of using relationship (15)
to obtain a computed apparent water conductivity, an apparent
water capture cross section, ~wa~ to be plotted against GR,
is obtained fram the known relationship
,
= ma ~ ~ - (31)
wa ~t ma
where ~ is the matrix capture cross section for the
ma ~
particular lithology encountered~ The circuitry of FIG. 8,
including difference circuit 881, ra~io circuit 882 and
summi~g circuit 883, can be employed to obtain ~ in accordance
.
-3~-
with xelatlonship (31). ~ter plottlng ~wa against GR, ~f and
~wb can be determined, ~or example, as indicated in conjunction
with Figure 5. Swb can be obtained uslng the arrangement of
circuits 601, 602r 603, 604 o~ Figure 2, as described in
con~unction therewith. Ha~ing determined ~wco~ one can now
compute a "wet" capture cross section (analagous to ~O obtained
using relationship (14) above) from:
~ o ~t ~ wco ~ t) ~ma (32)
The circuitry of Figure 9l including difference circuit 901,
multipliers 902 and 903, and summing circuit 904, can be utilized
to generate a signal representative of ~O. This signal can then
be overlayed with the measured log value, ~, in the manner
illustrated in the central track of Figure 5, to reveal potential
hydrocarbon bearing zones.
A ~urther composite parameter which can be expressed by
the generalized relationship (9a) is attenuation, a, i.e. the
relative attenuation (typically corrected Eor tempera-ture and
~preading loss) measured by the microwave electromaynetic
propagation tool ("EMP" - 46 of Figure 1). The relationship for
this parameter is set forth above (9b), and will be considered
momentarily. Firstl and as set forth in United States Patent No.
4,092,583 issued May 30, 1978 to George R. Coates~ consider that
the measured attenuation of the bulk ~ormation (designa-ted a) can
be expressed as
a ~ ~w aWC ~ w) am
where aWc is the attenuation attributable to the formation water
(i~eO, its composite water, in accordance with the principles
hereo~) and ~m is the attenuation attributable to the ~ormation
matrix. Since am is very small compared to a~, one can
- 35 -
L3
wxite
~ (34)
w ~c
This relationship expresses th t the bulk formation attenuation
is volumetrically "adjuste~" by a factor ~ to take account of
the fact that loss is essentially only occurring in that rac-
tion of the bulk formatlon o cupied by the waterO Returning,
now, to relation~hip (9b), we have
a = a + S (c~ - a ) ( 9b)
wc wf wb wb wf
w
where a f is the attenuation attributable to the free water
(i.e. the attenuation which one would measure with the "EMP"
logging device in a theoretical environment con~isting exclu-
sively of the formation free water), awb is the attenuation
attributable to the bound water (i.e. the attenuation which
one would measure with the. "EMP"' logging device in a theore~ical
environmen~ consi~king exclusively of the ormation bound water),
and a a is the attenuati.on at~ributable ~o the composite water
~i.e~ the a~tenua~ion which one would measure with a"EMP"
logging device in a theoretical environment consisting exclu-
sively of the ac~ual formation water).
Solving re~ationship (9b) for the bound water frac-
tion, S /S~, yields the relationship (9c) first sPt forth
wb w
above~ . :
. S ~ - a
wb = wc wf (9c~
S
wl wb w
, . , , ,~
~36- .
~1 ~219S4;3
In the form of the present invention, awf and ~wb
(or these parameters multiplied by water filled porosity,
~W, to obtain "bulk" variables ~a ~ and ~ b) are determined
using attenuation and travel time (or velocity) measurements ...
taken with an electromagnetic propagation logging device such
as "EMP" 46 of FIG. 1~ The conductivity ~generally of thè
formation invaded zone) obtained using the "EMP" device,
designated aEMp, can be expressed as
EMP ~ - ' ~35)
K
where K is a constant., t 1 is the measured travel time through
the formations, and a is the bulk attenuation determined from
the measured a~tenuation correc~ed for spreading loss and tem-
perature, where a ~ ~w ~wc (relationship (34) above). While
the relationship (35). for conductivity is expected ko hold
~ substantiall.y independenk of the sali~ity of the formation
water, i~ has been ob~erved ~hat fxequently aEMp exceeds the
conductivity measured from other tools~ An explana~ion for
the observed di~erence~ in conductivity is that not all of
the losses represented by the bulk attenuation measurement
~ are due to the conductivity or salinity of the formation
water. Extraordinary losses are believed to ~ccur in the
presence of bound water, these losses being more dielectric
than conduc.tive in nature., Applicant has dlsco~ered that
treating bound water losses separate from the ordinary expected
, free water losses resolves the problem and produces more realis-
tic values o~ ~ . In accordance with a feature of the inven-
E~P -
tion, and as will be described; an attenuation representa-tive
variable is de~ermined that is, inter alia, more appropriate
-37- .
for use in obtaining aE~1p~ In the example below, this attenu-
ation representative variable is the free water variable
~ a f. The determined variable is.also useful in conjunction
with other techniques where attenuation is utilized as an input
or a correction.~
Referring to FIG. 12-, th~re is shown implementation
of the computing module 510 of FIG. 1 which is utilized to
generate a signal representative of the bound water fraction,
S /S . A pair of difference circuits 501 and.502 are pro-
vided~ The positive input terminal o~ circuit 501 receives asignal representative of the quantity aWc and ths negative
input terminal o2 circuit 501 receives a signal representative
of the quantity awf The positive input terminal of circuit
502 receives a signal representative of the quantity awb, and
the negative input terminal of circuit 502 receives the signal
represenkakive of the quantity aw~ The outputs o di~erence
circuit~ 501 and 502 are respective.ly coupled to a ratio circuit
503 which produces a signal proportional to the ratio of the
output o~ circuit 501 divided by the output of circuit 502.
- 20 The output of ratio circuit 503 is accordingly a siynal repre-
sentative of the bound water fraction, S /S ,.in accordance
. wb w
with relationship (9c). In-actuality, and as will be clarified
shortly, the inputs to computing module 510 may each have a
common multiplier, ~ .
. The manner'in which the inpuks to computing module
51~ can be developed will now be described. In iarticular,
one preferred technique ~or deriving values of a ~ and a~b
(or, of related bulk attenuation variables ~ a ~ and ~wawb)
i~ as follows: Log values of a (attenuation) and t 1 (travel
time) are initially obtained over a range of depth levels of
-38-
43
interest(e~g.,using EMæ device 46 o~ FIG. 1 - these outputs
being indicated as bei~g a~ailable from processing circuitry
51). The obtained values of a and tpl are cross plotted, as
show~ in the frequency cross plot of FIG. 13. The values o~
~ may first be corrected for temperature and ~or spreading loss.
The cross plot of FIG. 13 can be initially understood by recog-
nizing that higher porosity generally results in higher values
of bo~h at~enuation and travel time (at least, when that porosity
contains water~. This i~ because the water is much lossier than
the rock matrix tthus: greater attenuation) and the velocity
of the electromagnetic energy through water is lower than through
the matrix (thus; greater travel tLme). Accordingly, increasing
value of tpl and ~ on the cross plot generally correspond to
increasing values of porosity. It can be noted that a could
alternatively be cross-plotted against other non-conductivity
related measuremen~ re~lectiny to~al poxosity, ~t~ such as ~ND~
previously described.
The polnt designated tpm on the tpl axi~ repxesents
the travel time through the for~ation matrixO Two trend lines,
designated as the "free water trend line" and the "bound water
trend line" are constructed by starting at the point t m and
drawing lines through the approximate bottom and top edges of-
the main cluster of points on the cross plot. These trend lines
ca~ be understood in the following terms: In those portions of
2S the formations containing substantially only free water, both
t 1 and a will i~crease with porosity, with the increase in
travel timè bei~g dependent upon the volume of water and the
increase in attenuation being dependent upon both the vol~me
of water and its conductivity. Accordingly, the slope of the
free water trend line will depend upon the conductivity or
39_
.
iL3
lossiness associated with the free water. The same will
generally be true of those portions of the formations in which
substantially all of the.water is bound water. However, in
this case, attenuation will be a function of not only the
volume of water and its conductivity, but also o~ the higher
losses, included dipolar losses, associated with the bound
water. Accordingly, the bound water trend line has substan-
tially greater slope than the free water trend line. It will
~e understood that these.trends representing the relationships
between attenuation and travel time in a substantially free
water region ( such as a clean sand ) and a bound water region
(such as a shale) could be determined initially from logs taken
in such formation regions. Also, it will be understood that
these relationships are determinable functions which need not
necessarily be linear, but are .illustrated as being linear in
the graph of FIG. 13.
Eaving established ~xee water and bound wat~r trend
line~ ~or ~unctions), one can now, at each depth level o~
interest, obtain a free water attenua~lon quantity represen~a-
tive of the attenuation attributabl~ to the formations (sur-
roundin~ the depth Ievel of interest) if substantially all of the
water in the formations was free water. Similarly, one can
derive a bound water attentuation quantity representative of
~he attenuation a~trlbutabls to said formations (surrounding
the depth level o.f interest) if substantially all of the water
in the formations was bound water. Using these.quantities/
in conjunction with the measured attenuation at the depth leveL
of interest, one can then determine the bound water frac.tion in
the forma~ions~surrounding the particular dep~h level. With
.
.
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r
5~3
reference to FIG. 13, consider the illustrated individual
point (a, tpl) and the vertical line drawn ~herethrough. At
the particular measured value of t 1' the intersection with
free water trend line indicates the attenuation value that
one would have measured if the water in the pore spaces of
this particular formation contained exclusively free water
(i.e., ~ wf~ whereas the intersection with the bound water
trend line indicates the attenuation that would have been
. measured if the pore spaces of this formation contained exclu-
10 sively bound water (i.e., ~ ~w~) In actuality, the measured
attenuation (~ = ~w aWc) is an attenuation which has a value
between these two extreme values, and the total water in the
pore spaces san be considered as a composite water having attenu-
ation aWc Accordingly, it is seen that relationship (9c) and
15 the output of computiny module 510 represents a linear apportion-
ment betwçen the.~wo extreme va~ues and yields the bound waker
fraction, S b/S . tNote that the multiplier ~ be~ore each
term will be can~elled in the output ~ computing mod~le 510
i~ ~wawc/ ~w~w and ~wwb ar~ used as the input quan~ities.)
20 In addition to the use of ~w~wf and ~wawb in obtaining
the bound water fraction, the bul~ formation attenuation if all
the water was free water (i.e., ~ a ~ is useful, as first noted
w wf
above, i~ determining a , since attenuation due to whate.~er
EMP
bound water is present will not tnen result in an unduly high
value of aEMp. In particular, o can be determined- from
EMP ~ ~w ~wf pl (36)
K
which is a modified ~orm of relationship ~35) wherein the bulk
free water attenuation(~W~ is substituted or the bulk com-
posite water attenuation (~ aw which is the equivalent of the
.-41
n7 ~9S~3
measured a in accordance with (3~) above).
An alternative technique or obtaining the bulk
fxee water attenuation, ~ a f, is to use the apparatus of
FIG. 14. A ratio circuit 431 receives at its inputs signals
repxesentative of a and ~w, bo~h as determined from measure~
ments taken with an EMP device 46 (FIG. 1) in a clean non-
hydrocarbon-bearing region of the formations in which sub-
stantially all of ~he water present is free water. (The
signal representative f ~w may be obtained, ~or example,
... . ..
using the technique of U. S. Patent_No. 4~09~ 3)~_.The --- ------
rat1o a/~w, in this region, will be representative of awf in
accordance with relationships ~34) and t9b), where S b= for
this case. In parti~ular
w wc ~w awf ~ ~w Swb (awb _ ~ f) (37
a = ~ a (when S - 0) (38)
w wf wb
. so that aw~ W when swb = o. Having obtained the parameter
a ~or the foxmations, the variable (~ a (i~e., the bulk ree
wf w w~
water attenuation) can now be determined at a particular depth
level of intere~t by multiplying the output of ratio circuit 431
by a signal representative f ~w a~ that depth level; this being
implemented by multiplier circuit 432. A further multiplier
circuit 433 can then be employed to obtain a signal representa-
tive o aEMp in accordance with relationship ~36). It will be
understood ~hat anaIagous circuitry could be used ~o obtain a
corresponding bound wa~er parameter, ~w~, from information in
a shaley region, and then the bulk bound water attenuation at
~5 specific depth levels of lnterest coul~ be obtained using a _ .
multipli~r circuit to p~oduce a signal representative of ~ a b.
The sig~als representative of ~ ~ f and aEMp can also be recorded,
if desired, by. recorder 90 o~ FIG. 1.
--42--
~1 ~?~OS43
It can be noted, in the context of obtaining either
the bound water or free water related values, that non-linear
interpolation can be employedj if desired (e.g., in FIG. 13J.
Further, since t may be affected by residual hydrocarbons
S left in the formation near the borehole, the indicated attenu-
ation corresponding to free or bound water conditions may be
slightly inaccurate. However, since both t 1 and ~ will decrease
due to hydrocarbon effects, there is some compensation in the
indicated bound or free water saturations. Whén awf or ~wawf
is determi~ed, the hydrocarbon effects will lower corxesponding
t 1 valuesand-will produce slightly lower ~ f values and hence,
when applied in conductivity measurements, lower aEMp values.
Use of a ~t measurement (relativel~-indçpendent of hydrocarbon
e~fects) in place of tpl, in the technique illustrated in
lS FIG. 13~ may be advisable in some instances.
- The invention has been descrihed with reerence to
particular embodiments, but variations within the spirit and
scope of the invention will occur to thos~ skilled :in the art.
For example, while circuitry ha~ been described ~or generating
analog signals representative of the desired quantities, i~
will be understood~that a general purpose digital computer
could readily be programmed to implement the techniques as set
forth herein. Also, while conductivity values have been utilized
for purposes of illustration, it will be recognized that the
inver~es o values u~ilized herein could be employed in conjunc
- tion with the i~verse of conductivity; i.e., resistivity.
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