CA1120543A - Apparatus and method for determining characteristics of subsurface formations - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
The determination of a "composite" parameter of the formation water in formations surrounding a borehole, for example the composite conductivity of the formation water, is used in the disclosure to obtain a relatively accurate determination of formation characteristics, such as water saturation. The determined values are meaninful even in shaly regions of the formations. The disclosed technique determines a composite water parameter, for example a composite water conductivity, which represents the conductivity of the bulk water in the formations, including both free water and bound water. Bound water trapped in shales is accounted for in this determination so the shales can be considered as having a porosity. Having determined the composite water conductivity, water saturation can be directly obtained using relatively straigthforward relationships which do not require estimates of the volume of shale in the formations. Shale effects are accounted for by the different conductivities (or other parameter such as caputre cross sections) of the formation water constituents (free and bound) which make up the total water.

Description

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.

, 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.

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 (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) 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 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 )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 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.

.

.
.

)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 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:

~ 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 .

)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) ~.~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 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 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

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 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 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 .
.

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.

~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.

Claims (42)

CLAIMS:

1. Apparatus for determining a composite parameter of the formation water in formation surrounding a borehole, comprising:
means for deriving a first quantity representa-tive of said parameter attributable to the free water in said formations;
means for deriving a second quantity representa-tive of the fraction of bound water in said formations;
means for deriving a third quantity representa-tive of said parameter attributable to the bound water in said formations; and means for determining said composite parameter as a function of said first, second, and third quantities.

2. Apparatus as defined by claim 1 further comprising means for deriving a fourth quantity representa-tive of the difference between said first and third quantities.

3. Apparatus as defined by claim 2 wherein said parameter is determined as the sum of said first quantity and the product of said second and fourth quantities.

4. Apparatus as defined by claim 1 wherein the parameter is the capture cross section.

5. Apparatus as defined by claim 2 wherein the parameter is the capture cross section.

6. Apparatus as defined by claim 3 wherein the parameter is the capture cross section.

7. Apparatus for determining the composite conductivity of the formation water in formations surround-ing a borehole, comprising:
means for deriving a first quantity representa-tive of the conductivity of the free water in said forma-tions;
means for deriving a second quantity representa-tive of the fraction of bound water in said formations;
means for deriving a third quantity representa-tive of the conductivity of the bound water in said formations; and means for determining said composite water conductivity as a function of said first, second and third quantities.

8. Apparatus as defined by claim 7 further comprising means for deriving a fourth quantity representa-tive of the difference between said first and third quantities.

9. Apparatus as defined by claim 8 wherein said composite water conductivity is determined as the sum of said first quantity and the product of said second and fourth quantities.

10. Apparatus as defined by claim 7 further comprising means for deriving a fifth quantity representa-tive of the fraction of free water in said formations, and wherein said composite water conductivity is determined as the sum of first and second products, the first product being said fifth quantity times said first quantity and the second product being said second quantity times said third quantity.

11. Apparatus as defined by claim 7 wherein said composite conductivity, , is determined as where ?wf is the conductivity of the free water in said formations, ?wb is the conductivity of the bound water in said formations, Swb is the bound water saturation in said formations, and Sw is the water saturation in said formations.

12. Apparatus as defined by claim 7 wherein said composite conductivity is an apparent composite water conductivity, , and is determined as where ?wf is the conductivity of the free water in said forma-tions, ?wh is the conductivity of the bound water in said formations, and Swb is the bound water saturation in said formations.

13. Apparatus as defined by claim 12 further comprising means for determining a computed "wet"
conductivity of said formations, , as where ?t is the total porosity of said formations.

14. Apparatus for determining the water saturation of formations surrounding a borehole, comprising:
means for deriving a first quantity representative of the conductivity of the free water in said formations;
means for deriving a second quantity representative 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.

15. Apparatus as defined by claim 14 further comprising means for deriving a quantity representative of the porosity of said formations, and wherein said water saturation determination is also a function of said porosity representative quantity.

16. Apparatus as defined by claim 15 wherein said means for determining water saturation comprises means responsive to said measured conductivity representative quantity and said porosity representative quantity for deriving a quantity representative of the apparent water conductivity of said formations, the water saturation determination then being a function of said first, second, and third quantities and said apparent water conductivity representative quantity.

17. Apparatus as defined by claim 16 wherein said water saturation is determined as where ?wf is the conductivity of the free water in said forma-tions, ?wb is the conductivity of the bound water in said formations, Swb is the bound water saturation in said formations, and is the apparent water conductivity of said formations.

18. Apparatus as defined by claim 14 wherein the determined water saturation is the water saturation of the invaded zone of said formations.

19. Apparatus as defined by claim 18 wherein said first quantity is representative of the conductivity of the mud filtrate in the invaded zone of said formations.

20. Apparatus as defined by claim 19 wherein said quantity representative of measured conductivity is a conductivity as derived from an EPT logging device.

21. Apparatus as defined by claim 20 wherein said saturation of the invaded zone of said formation, , is determined as where ?mf is the conductivity of the mud filtrate invading said formations, ?wb is the conductivity of the bound water in said formations, Swb is the bound water saturation in said formations, ?t is the total porosity of said formations, and ?EMP is the conductivity of the invaded formation as determined by an EPT
logging device.

22. 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 attributable to the free water in said formations;
deriving a second quantity representative of the fraction of bound water in said formations;
deriving a which quantity representative of said parameter attributable to the hound water in said formations; and determining said composite parameter as a function of said first, second, and third quantities.

23. The method as defined by claim 22 further comprising the step of deriving a fourth quantity representative of the differ-ence between said first and third quantities.

24. The method as defined by claim 23 wherein said parameter is determined as the sum of said first quantity and the product of said second and fourth quantities.

25. The method as defined by claim 22 wherein the parameter is the capture cross section.

26. The method as defined by claim 23 wherein the parameter is the capture cross section.

27. Apparatus as defined by claim 24 wherein the parameter is the capture cross section.

28. A method for determining the composite conductivity of the formation water in formations surrounding a borehole, comprising the steps of:
deriving a first quantity representative of the conduct-ivity 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 conduct-ivity of the bound water in said formations; and determining said composite water conductivity as a function of said first, second and third quantities.

29. The method as defined by claim 28 further comprising the step of deriving a fourth quantity representative of the difference between said first and third quantities.

30. The method as defined by claim 29 wherein said composite water conductivity is determined as the sum of said first quantity and the product of said second and fourth quantities.

31. The method as defined by claim 28 further comprising means for deriving a fifth quantity representative of the fraction of free water in said formations, and wherein said composite water conductivity is determined as the sum of first and second products, the first product being said fifth quantity times said first quantity and the second product being said second quantity times said third quantity.

32. The method as defined by claim 28 wherein said composite conductivity, , is determined as where is the conductivity of the free water in said formations, is the conductivity of the bound water in said formations, Swb is the bound water saturation in said formations, and Sw is the water saturation in said formations.

33. The method as defined by claim 28 wherein said composite conductivity is an apparent composite water conductivity, , and is determined as where is conductivity of the free water in said formations, is the conductivity of the bound water in said formations, and Swb is the bound water saturation in said formations.

34. The method as defined by claim 33 further comprising the step of determining a computed "wet"
conductivity of said formations, , as where ?t is the total porosity of said formations.

35. A method for determining the water saturation of 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;
deriving a quantity representative of the measured conductivity of the formations; and determining the water saturation of the formations as a function of said first, second and third quantities and said measured conductivity representative quantity.

36. The method as defined by claim 35 further comprising the step of deriving A quantity representative of the porosity of said formations, and wherein said water saturation determination is also a function of said porosity representative quantity.

37. The method as defined by claim 36 wherein said step of determining water saturation comprises deriving a quantity representative of the apparent water conductivity of said formations in response to said measured conductivity representative quantity and said porosity representative quantity, the water saturation determination then being a function of said first, second, and third quantities and said apparent water conductivity representative quantity.

38. The method as defined by claim 37 wherein said water saturation is determined as where ?wf is the conductivity of the free water in said formations, ?wb is the conductivity of the bound water in said formations, Swb is the bound water saturation in said formations, and ?wa is the apparent water conductivity of said formations.

39. The method as defined by claim 35 wherein the determined water saturation is the water saturation of the in-vaded zone of said formations.

40. The method as defined by claim 39 wherein said first quantity is representative of the conductivity of the mud filtrate in the invaded zone of said formations.

41. The method as defined by claim 40 wherein said quantity representative of measured conductivity is a conductivity as derived from an EPT logging device.

42. The method as defined by claim 41 wherein said saturation of the invaded zone of said formation, Sxo, is determined as where ?mf is the conductivity of the mud filtrate invading said formations, ?ab is the conductivity of the bound water in said formations, Swb is the bound water saturation in said formations, ?t is the total porosity of said formations, and ?EMP is the conductivity of the invaded formation as determined by an EPT logging device.