Note: Descriptions are shown in the official language in which they were submitted.
F-6071(72)-L(PAC~ Z ~ 5
Methcd for Determi~inq Electrical AnisotroPy_of
a Core Sam~ from a Subterrare~n Formation
This invention relates to a method for determdndng electrical
anisDtrcpy of a core sample from a subterranean formation. The
inv~ntion also relates t~ apparatus for determinlng resistivity
of a core sa~ple o~ a swbterranein formation.
Hydrocarbon saturation SO is generall~ deeermined frcm water
saturation Sw as follows:
So = 1 - SW (1)
Water ~aturation present in a subkerranean formation is typically
dekermdned from interpretation of conventional electrical (i.e.,
resistivity) logs recQrded in a borehole drilled thr~gh the
formation. Water saturation of the available pore space of the
; ; formation is determinsd fro~ the resistivity log neasurements
us m g the Archie equation set forth in l'The Electrical
Resistivity LLg As ~n Aid In Determu mng Some Reservoir
Charac~eristics", Trans. AIME, Vol. 46, pp. 54-62, 1942, by G. E.
Archie. Ihis equation is expressed as follows:
,
Sw = RW/~mRt (2)
Where Sw is the fractional water saturation (i.e. free and bound
wa~er of the formation expressed as a per oe nt of the available
pore spa oe of the formation), ~ is the formation wa~er
resistivity, ~ is the formation porosity, ~ is the formation
electrical resisti~ity, n is ~he saturation exponent and m is ~he
porosity or oementation e~ponent. Tlh~ Archie equation may be
expressed in other ways and ~here are numerous methods in the art
for determining, m~asuring or otherwi æ o~tainLng the various
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,
. :
F-6071~72)-L(PAC) 2 ~ ~ 9
co~ponents needed to predict fractional water saturation Sw from
the formation resistivity, ~ , using tha equation in any of its
forms.
Archie defined two quantities that providel ~he basis or his
water saturation equation (1). m e first quantity i5 the
formation factor F which defines the Pffect of the rock matrix on
the resistivity of water as follcws:
F Ro/ ~ ( )
where RQ - resistivity of water saturated rock and
= water resistivity.
'
Archie reasoned that for a given value of ~, the ~ormation
factar F w~uld decrease wi~h increasing poro6ity, ~, to some
exponent m:
F= 1/~ (4)
is porosity exponent m has also bea~me knawn as the Archie
ce~tation exponent. mus A;r~ie provided~ a useful
c~harac~rization of a roc~k ~ully saturated with a con~ucting
ls~ine in t~ms of the wat~r resistivi~ Rw~ poro~;ity ~ and a rock
paramet~ m. It i5 important to note ~hat Ar~hie ass~ned all
cor~tance to be in the brine.
q~e second quantity is the resistivity ~ndex I defined as the
ratio of t:he resistivity o~ a roc3c partially sat~Yrated wit~h water
and hydrocarbon, E~, to the s~u[e roc~k saturated ~ully with water,
Rol as follaws:
I = Rt/Ro (5)
. ~ '` :
.
2~
F-6071(72)-L(PAC)
Archie reasoned tha~ as the water saturation decreased (i.e.
hydro OE ~on saturation increased~ the resistivity Rt and hence I
would increase to some exponen~ n:
I = 1/Swn (6)
where Sw = volume of water in pores/total pore volume.
This exponent n has become known as the Archie saturation
~ t. It is again impor~ant to ncte that Archie assNm3d all
oonductance to be in the krine and fur~her that all pores within
the rock have the same water satNration Sw.
. .
It is these two eq~ations (4) and ~6~ for ~he forma~ion factor F
and r sistivity index I respectively that Archie csmbined to
provide the water saturation expression Sw of equation ~2).
Certain log5 have provided formation resistivity ~ and porosity
. Water samples provide ~he best ~alues for ~. Standard
practioe is to measure rock sample resistivlties Ro and ~ for a
number of water saturations and to plok the logarithm of I versus
the logarithm of Sw. Archie's equations assume such a logarithmic
plo~ can be fit by a strai~ht line with slo~e of -n.
~a~y oore samples are, h~wever, not ho~gencus and electrically
isotropic. Fo~r such core samples, the Archi~ saturation exponent
n will be strongly dependent on the direction the resistivity
measurement is made. For example, a saturation exponent measured
across permeability karriers within a core sample may ke one and
a half times as large as if it were measured paral~el to ~he
permeability barriers. qhls dl~ference can have a large
detrimental e~fect on the det~xmination of hydrocarbon reserves
derived from the calculated water saturation of equation (2j. It
is, therefore, an object of thQ present invention to determine
,
.
:; ~.- , .. . . .
F-6071(72)-L(PAC) ~ 5~ 9
resistivity of a core sample that is electrically anisotrqpic and
to identify the degree of anisotropy changes as the ~rine
saturation of the core sample changes so that an accurate water
saturation can be calc~lated frcm equation (2).
According to one ~ of the present invention there is
prcvided a method for determinln~ electrical aniso~ropy of a core
sample from a subterranean formation, cc~prising the ~teps of:
a) shaping s~id oore sample Lnto the form of a
cylinder;
b~ applying a conLmng pressure to said care sample;
c) satuYating said core sample with a fir~t fluid;
d) passing a current through said fluid-saturated
core sample;
e) measur m g volta~es i~ a plurali.ty of radial
directions thrcl3h said core sample which are
normal to the cylindrical axis of said oore sample
; at each of a plurality of spaced-apart positions
alon~ said axis;
f) determinin~ electrical resistivities in aid
plurality of radial directions thrcu3h said core
sample frcm said plurality of measured voltages;
and
g) comparing each of said determined electrical
resistivities to identify the radial direction of
any electrical anisokropy in said core sample.
F-6071(72)-L(PAC)
Preferably the step of measuring voltages co~prises:
h) establishing an initial fluid saturation within
said core sample;
i) m~asNring voltages in a plurality of radial
directions thrcugh said core sample, which are
~ normal t3 the cylindrical axis of said oor~ at
: each of a plurality of spaced-apart positions
along said axis at said initial fluid ~ on;
j) altering said fl~id saturation within said core
sample a plurality of tim~s and repea~ing the
electrical resistivity determinations for each
~ differing fluid satlration~
~: : Desirably ~he step of altering flu1d saturation co~prises ~he
step of mcvi~g the fluid ~n said core sample in a direction
parallel to said axis.
.
~ It is pre ~ that step (i) comprises:
.
k) oontacti~g the cuter surfa oe of said core sample
with ~n array of electrodes at each o~ a p~urality
of spaced-apart positions along ~he length of said
core sample, each of said arrays being in a plane
normal to said axls and the electrodes in each of
said arrays being equally spaced at an even number
Oæ positions abcut the outer surfa oe of said core
san~ples;
. , :, . ~
:~: , ~ , - ~-
:
F-6071(72)-L~P~C) ~ ~ g
1) m~asuring the voltage across each paLr of
electrodes that are spaced 180 apart about said
core sample; and
m) utilizing the voltage measurements aGross each
pair of electrades to de~ermine the electrical
resistivity of the core sample in a radial
direction tbrough said core sample normal to said
axis between said pairs of electrodes.
m e step of shaping said core sample may be ~arried cut by
CNtting the core such that the cylindrical axis of said core
sa~ple is at an angle to the kedding plane of said sub~erranean
formation.
After step (g) at least a portion of said first fluid may be
displaced wi~h a secon~ fluid of differlng el~ctrical
conductivity, and steps (d) to (g~ are repeated.
The first ~luid ma~ be el ~ ically oonduotive with said seoond
fluid bein~ electrically non-oonduotive; or the first fluid may
be electrically non-oonductive with said second fluid being
electrically condu tive.
AYxx~liing to anokher a ~ of the invention there is provided
apparatus for determinin~ resistivity of a ~ore sample of a
subterranean forma~ion, ocmprising:
~) a sleeva oontainLng a cylindrical oore sample of a
subterranRan formation which can be satNrated with
a fluid;
F-6071(72)-L(PAC)
b) means for apply ~ a current through said oore
sample;
c~ means for measuring voltages in a plurality of
radial directions thLo~gh said core sample normal
to tha cylindri ~ axis of said oore sample in
response to the flow of said curren~ thLw gh said
: core ~ le; and
d~ means for determininI electrical resisti~ities in
said plurality of radial directions through said
core samples from sai~ measured voltages.
Preferably said ~ for masuring voltages ccmprises:
e) at least ~ne electrode array e~tending throu~h
said sleeve and naXing contact with ~he cuter
surface of said oore sample, said array being in a
plane normal to the cylindrical axis of said core
sa~ple and having an even number of elec*rodes
equally spaced arcund said sleeve; and
f) mRans connec*ed to said electrcdes for melsNrir~
: the voltage acrcss each pair of electrodes ~hat
are spaoed lB0 apart around said sleeve in
response to the flow of said current through said
: core sample.
Each of said electrodes may pass thrGugh said sleeve and extend
outwarl frcm the inner surface of said sleeve, and be provided
with a rounded end for m~king contact with the outer surface of
said core sample. The rounded end is preferably spherical or
semi-spherical
~ .
F--6071(72~ -L(PAC)
8 Z~5~?~J9
Desirably each of said electrodes is n~ulded irrto said sleeve.
In a preferred constru~ion ea~h of said elec~odes ca~rises:
g) a c~Tlin~ical ma~n body ~; and
h) a s~erical-like end m~ f~ m3kir~ oontac~
with the ~ surface of said 003~ mple.
me er;~l men~er may be recess0d a~ace~t said main body m~r~.
Ihe erld ~er may be semi~herical with diameter greate~ ~
fflat of said main bo ~ ~ ~ Ihe flat portion of said
semi~spherical end me~ber ~ay ke adjacent said ~sin body memker
and n~rmal to the cylindrical axis of said main body member.
.
Preferabl~ the apparatus according to the invention inclu~es:
i~ a flui~ inlet po6itione1 in a first end of said
sleeve tbrough which a se~ond fluid can be
injected under pressNre in~o the f ~ end of said
core sample for displacLng said:first fluid fr~n a
second end of said core sample, said second fluid
being immiscible with said first fluid and of
opposite electrical conductance;
: j) a porous mRmker p~sitioned adjacent a seaond en~
of said sleeve tbrough which said first fluid can
be discharged from the s~cond end of said core
sample through said porous m~mber;
k) a fluld inlet positioned in the second end of said
sleeve throu~h which said first fluid is
dischar~ed frcm said sleeve after having been
F-6071(72)-L(PA~) Z ~?5 ~.~5~9
displaoe d from the second end of said core sample
through said porcus ~ r;
l~ a plurality of said electrode arrays dispos~d at
spaoe d-a ~ positions alo~g the length of said
sleeve, and m2king co~tact with the au~er surfa oe
of said core sample at said spaced-apart
positions, each of said arrays beLng in a plane
normal to said cylindrical axis; and
; m) n~ans for applyLng a confin~ng pressure thro~gh
said sleeve to said oore sa~ple. :~
~ans for may be provlded for ~ ing said determined
resistivities to identify the radial direction of any electrical
: . anisotropy within said core sample in the plane of each of said
elec*rcde arrays anl along ~he length o~ said oore s~ple between
said~electrode arrays.
Rrf o is now made to the acoompanying drawin~s, in which :
FIG. 1 illustrates prior art apparatus for carrying out
resistivity determinations on core samples of aui*~ an
formations;
FIG. 2 illustrates apparat~s enplo~ing electrode array~ for
carrying out resistivity ~ rements on electric~lly anisokro~ic
core samples of subkerranean formations in accordanoe with the
present .mvention;
FIG. 3 is a cross-sectional view thra~h the apparabus of FIG. 2
showin~ in detail one of the electrode ærays of Fl.G. 2; and
F-6071(72)-L(PAC) ~5~9
FIG. 4 illustrates one configuration for the electrodes of each
of the electrode æ rays of FIGS. 2 and 3.
A system that has been successfully used in carrying out linear
resistivity determina~ions along a ccre sample from a
~ anean formation is shown in FIG. 1 (prior art). A pressure
sleeve 10, pre~erably natural or synthetic rubber, surrounds a
cylindrical core sample 11 of a porous rock to ~e ~ red f~r
resistivity at a plurality of fluid saturations. Positio~ed
between the core sample 11 and end 12 of the pressure slee~e 10
is a porous nember 13, whi~h is p1rmearl~ to a first fluid
satura~ing the core sample, kut is imperneab1e t~ a secand f~Llid
used to displace the first flLud frcm the core sample. qhe
sec~nd, or displacing fluid, is immiscible wi~h the first flLIid
saturating the core sa~ple ~nd is of different electrical
conductivity. This first saturation fluid is the wetting fluid
for the porous member 13, which by way of example, may be a
ceramic plate or a ~ . Sleeve 10 is placad inside a
suitable pressure vessel (not ~hown) that ~an be pressurized l~p
to several thousand pc~nds per square inch (several million Pa).
Typical of SLtCh pr ~ e vessels are those described in
US-A-3,839,899; US-A-4,688,238; and US-A-4,379,407. m rcugh sLlch
a pressure vessel a ]pressure is applied to the sleeve lO and
henoe to the porous roc~ 11. m e pressure should be sufficient to
ellminate any fluid annulus between the sleeve 10 and the surfaoe
of the core sample. A`fluid inlet 14 and a ~luid outlet 15 fa3d
into the ends 16 and 12 respectively o~ the sleeve 10. Eoth inlet
14 and outlet 15 also serve as current oonducting electrodes for
pas~ing current from a source 20 tbrough the porous rock 11. A
pair of voltage electrodes 17a and 17b penekrate sleeve lO and
m~ke contact wit'h the porous ro~k at spaced locations along the
lengtlh of the porous rock. The voltage across ~he porous rock 11
between ~he electrodes 17a and 17b is measured by the unit 21.
`: ~
F-6071(72)-l,(PAC) 11
The core sample of porous ro~k 11 is initially fully saturated,
by way of example, with an electrically conducting fluid, such as
salt water, and placed under confining pr~ssure. A current is
passed ~hrcugh the porGus rock and a voltage along the len3th of
the porous roc~ is measured between el ~ s 17a and 17b. Such
voltage measurements may be carried cut in acoordance with the
di~closure of US-A-4,467,642; US-A-4,546,318; and US-A-4,686,477.
Frcm ~his v~ltage the resistance of the porous rock along its
length bet~e~n electrodes 17a and 17b is determin3d using Qhm's
Law~ m e resistivity, or its reciprocal conducti~ity of the
porous rock is determined using ~he determined resi~tance, the
length and ~he cross-sectional area of the oore. A displacing
fluid suc'h as a nonconducking oil or gas, m~y then be foroel
inlet 14 into end 18 of porous rock 11 t4 change the
fluid saturation condition prior to the making of the ne~t
resistivity m~asNreNent.
Typical of such a resistivity determin inq system of FIG. 1 are
those described in US-A-4,907, 448; US-~-4 ,926,128 and
US-A-4, 924 ,187 .
Havir~ naw described a typical resistivity det~mi~tion ca~ried
aIt in a single direction along the axial direction of a
cylin~rical core sal[ple as ~hawn in ~[G. l, the pres~nt invention
of providing te~;or o~npo~ents of resistivity, or oonductivity,
needed for interpretin~ elect;ric lo~s of a m~rrar~n formation
with anisotrapic E~rties }: y measuring and cc~aring
resistivity in a plurality of radial directions ~a~h a
c~ lirx~ical core sample of the formation and normal to its
c~ylir~rical axis will naw be des ~ ibed. A transversely isatrcpic
cylindrical core sample of the formation is cut so ~hat the
formation bedding plane is at an angle to the cylindrical axis of
the cDre sa~ple. The core sample is initially saturated with an
.
F-6071(72)-L(PAC) 12
electrically conducting fluid such as salt water, and placed
within sleeve 10 under confining pressure representative of
in-situ pressure. m e core sample is oQntacted with an array o
electrodes contained by sleeve 10 at each ~f a plurality of
spaoed-apart po6itions along the length of the coxe sample, such
as electrode arrays A, B and C of FIG. 2 for example. Each such
array ~-C lies in a plane normal to the axis O:e the care sample
and the electrcdes in eaclh array are equally spaoed at an even
number of positions about the sleeve 10.
FIG. 2 shows a palr of su~h electrodes Ai and Ai+N which are
spaoed-apart 180 about sleeve 10 (wi~h i = 1 to N). FIG~ 3 is a
cross-sectional view taken ~ h the sleeve 10 and core samp:Le
11 a~ the axial position of array A with 24 electrodes ~ -~24
being shcwn (cross-sectioning of sleeve 10 being cmitted for
clarit~). As can be seen in FIG. 3 there are 12 elec*rode pairs
at 180 spao0d-apart positions about sleeve 10 such as electrode
~ ~ 3 ~ ~ 4 ~ 2 and A24. A current is passed
through oore sample 11 and a voltage is measured acro6s each of
the Ai a~d Ai~N, ~ and Bi~N, and Ci and C ~N electrode pairs
spaoed-apart 180 about the arrays A, B and C such as shown by
voltage unit 22 acrc6s electrode pair ~ -~ 3 for example. These
voltages as well as a voltage n~asured along the axial length of
the core sample by unit 21, such as shcwn in FIG. 1, are used to
determine the electrical resistivities of the oore sample bo~h
along the oore sample and in t,he plurality of radial directions
thro~h the e sample n~rmal to core sample axis between ~he
electrodes of eac1h oorresponding electrode pair. Following these
measurements, the fluid saturation in the oore sample may be
altered any number of times w.it'h suc~h n~asNrements being repeated
for ea~h differing fluid saturation.
':
F-6071(72)-L(PAC) 13 ~ 3
From these resistivities normal to the axis of the core sample at
a plurality of positions along the axis of the core sample the
desired tensor ccmponents of resistivity, or conductivity, needed
for interpreting electric logs of suiberraDean formations with
anisokropi~ properties are det ~ . Small core samples cut
parallel and n~rmal to small but closely spaced layerings of
different formation sediments show any electrical anis~rcpy that
~ght exist. Iwo oore samples cut normal and parallel to a
bedding plane may not be identical in all respects ex oept for the
direction of the planes relative to the cylindrical axis of the
core samples and it would be dlfficult to obtain the same partial
water saturations in each core sample for cc~parison
n~w#~nn~ents. A single cylindrical core sample cut with the
bedding plane at an angle to the axis of ~he oore sample as
described above is utilizsd in accordance with the present
invention to overoome such limitations.
Referring now to FIG. 4, there is shown a preferred configuration
for the elec*rodes of each of the electrode arrays A-C. For
purpose of example, electrcdes ~ -~3 are shown molded into a
rubker sleeve 10 with cylindrical main boqy mEmbers 30-32 and
spherical-l~ke end members 33-35 for making oontact wit]h the
outer sur~a oe of a core sample by e~benlina outward from the
inner surfaoe of sleeve 10 by a dis~ance P. AS sho~n in FIG. 4,
end m~mkers 33-35 are semispherical with recessed portions, or
lips, 36-38, being normal to the outer surfaoe of the cylindrical
main body memkers 30-32. Su~h a semls~herical end member provides
for enhanced adhesion to the rubb~r sleeve 10.
Whlle the foregoing has described a preferred embodiment of the
present inven~ion, it is to be understood that vario~s
mcdifications or ~hanges may be made within ~he scope of the
append~d claims.
