AU657518B2

AU657518B2 - Method for determining electrical anisotropy of a core sample from a subterranean formation

Info

Publication number: AU657518B2
Application number: AU12876/92A
Authority: AU
Inventors: Wyatt Wendell Givens; William David Kennedy
Original assignee: Mobil Oil AS
Current assignee: Mobil Oil AS
Priority date: 1991-03-19
Filing date: 1992-03-12
Publication date: 1995-03-16
Anticipated expiration: 2012-03-12
Also published as: NO921058D0; DE4208953A1; AU1287692A; NO921058L; CA2063289A1; GB2254703A; GB9203883D0; GB2254703B

Description

AUSTRALIA

Patents Act 57 5 18 COMPLETE SPECIFICATION

(ORIGINAL)

Class Int. Class Application Number: Lodged: Complete Specification Lodged: Accepted: Published: Priority Related Art: Name of Applicant: Mobil Oil Corporation .Actual Inventor(s): Wyatt Wendell Givens William David Kennedy Address for Service: I' PHILLIPS ORMONDE FITZPATRICK Patent and Trade Mark Attorneys 367 Collins Street Melbourne 3000 AUSTRALIA Invention Title: a METHOD FOR DETERMINING ELECTRICAL ANISOTROPY OF A CORE SAMPLE FROM A SUBTERRANEAN FORMATION 'Our Ref 282131 :POF Code: 1462/1462 0 The following statement is a full description of this invention, including the best method of performing it known to applicant(s): 6006 F-6071 (72) -L(PAC) 1A Method for DetermininQ Electrical Anisotropy of a Core Sample from a Subterranean Formation This invention relates to a method for determining electrical anisotropy of a core sample from a subterranean formation. The invention also relates to apparatus for determining resistivity of a core sa'iple of a subterranean formation.

Hydrocarbon saturation S o 0 is generally determined from water saturation S as follows: 0 s o 1 s w (1) S0 Water saturation present in a subterranean formation is typically determined from interpretation of conventional electrical Seg0o o 0 resistivity) logs recorded in a borehole drilled through the formation. Water saturation of the available pore space of the formation is determined from the resistivity log measurements using the Archie equation set forth in "The Electrical 00 Resistivity Log As An Aid In Determining Some Reservoir a Characteristics", Trans. AIME, Vol. 46, pp. 54-62, 1942, by G. E.

a 00 Archie. This equation is expressed as follows: 00 0 0" Where S w is the fractional water saturation free and bound 000ee: 9 water of the formation expressed as a percent of the available pore space of the formation), Rw is the formation water resistivity, is the formation porosity, Pt is the formation electrical resistivity, n is the saturation exponent and m is the porosity or cementation exponent. The Archie equation may be expressed in other ways and there are numerous methods in the art for determining, measuring or otherwise obtaining the various F-6071 (72) -L(PAC) 2 components needed to predict fractional water saturation S W from the formation resistivity, Rt, using the equation in any of its forms.

Archie defined two quantities that provided the basis for his water saturation equation The first quantity is the formation factor F which defines the effect of the rock matrix on the resistivity of water as follows: F =R 0IRw (3) where R 0 =resistivity of water saturated rock and *R water resistivity.

*fee*: Archie reasoned that for a given value of Pthe formation factor F would decreas(. with increasing porosity, 1, to some exponent m: 9*F =1Ile (4) This porosity exponent m has also become known as the Archie cementation exponent. Thus Archie provided a useful cbaracterizatiodn of a rock fully saturated with a conducting brine in terms of the -water resistivity Rw, porosity 4i and a rock parameter m. It is important to note that Archie assumed all conductance to be in the brine.

The second quantity is the resistivity index I defined as the ratio of the resistivity of a rock partially saturated with water and hydrocarbon, Rt, to the same rock saturated fully with water, Ras follows: I R/o F-6071 (72) -L (PAC) 3 Archie reasoned that as the water saturation decreased e hydrocarbon saturation increased) the resistivity Rt and hence I would increase to sane exponent n: I =l/Sw (6) where sw. volume of water in pores/total pore volume.

This exponent n has become known as the Archie saturation exponent. It is again hmrtant to note that Archie assumed all conductance to be in the brine and further that all pores within thle rock have the same water saturation sw It is these two equations and for the formation factor F and resistivity index I respectively that Archie combined to provide the water saturation expression Sw of equation certain logs have provided formation resistivity It and porosity Water samples provide the best values for Rw. standard practice is to measure rock sample resistivities ROand Rt for a number of water saturations and to plat the logarithm of I versus the loggrithm of sw. Archie' s equations assume such a logarithmic plot can be fit by a straight line with sl.ope of -n.

Many core samples ar e, however, not homogenous and electrically S.**isotropic. For such :ore samples, the Archie saturation exponent n will be strongly dependent on the direction the resistivity 5 measurement is made. For example, a saturation exponent measured across permeability barriers within a core sample may be one and a half times as large as if it were measured parallel to the permeability barriers. This difference can have a large detrimental effect on the determination of hydrocarbon reserves derived from the calculated water saturation of equation It is, therefore, an object of the present invention to determine F-6071(72) -L(PAC) 4 resistivity of a core samle that is electrically anisotropic and to identify the degree of anisotropy changes as the brine saturation of the core saxple changes so that an accuate water saturation can be calculated from equation According to one aspect o-f the present invention there is provided a method for determining electrical anisotrquy of a core sample from a subterranean formation, comprising the steps of: a) shaping said core sample into the form of a b) placing said core sample into a sleeve and applying a confining pressure to said core sample sufficient to eliminate any fluid annulus between the sleeve and said core sample; c) saturating said core sample with a first fluid; d) jassing a current through said fluid-saturated core sample; e) measuring voltages in a plurality of radial directions through said core sample which are normal to the cylindrical axis of said core sample at each of a plurality of spaced-apart positions along said axis; 9 9** *0 9. 9 9 *9 OS 0* 9 0 0 *905 bOOe 9.

0* *9 *0*909 9 *0 0 9 S 0* 9 f) determining electrical resistivities plurality of radial directions through sample from said plurality of measured and in said said core voltages; S

J

,0' ~Di~ g) comparing each of said determined electrical resistivities to identify the radial direction of any electrical anisotropy in said core sample.

F-6071(72)-L(PAC) Preferably: h) an initial fluid saturation is established within said core sample; i) voltages are measured in a plurality of radial directions through said core sample, which are normal to the cylindrical axis of said core at each of a plurality of spaced-a -t positions along said axis at said initial fluid saturation; and j) said fluid saturation is altered within said core sample a plurality of times and repeating the electrical resistivity determinations for each differing fluid saturation.

Desirably the step of altering fluid saturation comprises the e** step of moving the fluid in said core sample in a direction parallel to said axis.

e SIt is preferred that: k) the outer surface of said core sample is contacted with an array of electrodes at each of a plurality of spaced-apart positions along the length of said core sample, each of said arrays being in a plane normal to said axis and the electrodes in each of said arrays being equally spaced at an even number of positions about the outer surface of said core samples; 4'r F 1 II F-6071(72) -L(PAC) 6 1) the voltage is measured across each pair of electrodes that are spaced 1800 apart in each array about said core sample; and m) the voltage measurements across each pair of electrodes is utilised to determine the electrical resistivity of the core sample in a radial direction through said core sample normal to said axis between said pairs of electrodes.

The step of shaping said core sample may be carried out by cutting the core such that the cylindrical axis of said core sample is at an angle to the bedding plane of said subterranean formation.

After step at least a portion of said first fluid may be displaced with a second fluid of differing electrical conductivity, and steps to are repeated.

The first fluid may be electrically conductive with said second fluid being electrically non-conductive; or the first fluid may S: be electrically non-conductive with said second fluid being electrically conductive.

According to another aspect of the invention there is provided apparatus for determining resistivity of a core sample of a subterranean formation, comprising: Sa) a sleeve containing a cylindrical core sample of a subterranean formation which can be saturated with a fluid; F-6071(72) -L(PAC) 7 b) means for applying a current through said core sample; c) means for measuring voltages in a plurality of radial directions through said core sample normal to the cylindrical axis of said core sample in response to the flow of said current through said core sample; and d) means for determining electrical resistivities in said plurality of radial directions through said core smples from said measured voltages.

Preferably said means for measuring voltages comprises: e) at least one electrode array extending through said sleeve and making contact with the outer surface of said core sample, said array being in a plane normal to the cylindrical axis of said core sample and having an even number of electrodes equally spaced around said sleeve; and 4 04 S f) means connected to said electrodes for measuring the voltage across each pair of electrodes that are spaced 1800 apart in each array around said sleeve in response to the flow of said current through said core sample.

Each of said electrodes may pass through said sleeve and extend outward from the inner surface of said sleeve, and be provided with a rounded end for making contact with the outer surface of said core sample. The rounded end is preferably spherical or semi-spherical F-6071(72)-L(PAC) 8 Desirably each of said electrodes is moulded into said sleeve.

In a preferred construction each of said electrodes comprises: g) a cylindrical main body member; and h) a spherical-like end member for making contact with the outer surface of said core sample.

The end member may be recessed adjacent said main body member.

The end member may be semi-spherical with diameter greater than that of said main body member. The flat portion of said semi-spherical end member may be adjacent said main body member and normal to the cylindrical axis of said main body member.

Preferably the apparatus according to the invention includes: i) a fluid inlet positioned in a first end of said sleeve through which a second fluid can be injected under pressure into the first end of said core sample for displacing a first fluid from a second end of said core sample, said second fluid being immiscible with said first fluid, wherein either said first fluid is electrically conducting and said second fluid is electrically non-conducting, or said first fluid is electrically non-conducting and said second fluid is electrically conducting;

S

j) a porous member positioned adjacent the second end of said sleeve through which said first fluid can be discharged from the second end of said core sample through said porous member; i a fluid outlet positioned in the second end of 1 said sleev through which said first fluid is discharged from said sleeve after having boen F-6071(72) -L(PAC) 9 displaced frn' the second end of said core sample through said porous member; 1) a plurality of said electrode arrays disposed at spaced-apart positions along the length of said sleeve, and making contact with the outer surface of said core sample at said spaced-apart positions, each of said arrays being in a plane normal to said cylindrical axis; and m) means for applying a confining pressure through said sleeve to said core sample, which is sufficient to eliminate any fluid annulus between said sleeve and said core sample.

Means for may be provided for comparing said determined resistivities to identify the radial direction of any electrical anisotropy within said core sample in the plane of each of said electrode arrays and along the length of said core sample between said electrode arrays.

iii!!i Reference is now made to the accompanying drawings, in which: FIG. I illustrates prior art apparatus for carrying out resistivity determinations on core samples of subterranean SOO: formations; 4 OGO~ IG. 2 illustrates apparatus employing electrode arrays for carrying out resistivity measurements or, electically anisotropic core samples of subterranean formtions in accordance with the Q •e•present invention; em 0 FrIG. 3 is a cross--ional view through the apparatus of i.

showing in detail one of ne electrode arrays of stG. 2;ane F-6071 (72) -L(PAC) FIG. 4 illustrates one configuration for the electrodes of each of the electrode arrays of FIGS. 2 and 3.

A system that has been successfully used in carrying out linear resistivity determinations along a core sample fran a subterranean formation is shown in FIG. 1 (prior art). A pressure sleeve 10, preferably natural or synthetic rubber, surrounds a cylindrical core sample 11 of a porous rock to be measured for resistivity at a plurality of fluid saturations. Positioned between the core sample 11 and end 12 of the pressure sleeve is a porous member 13, which is permeable to a first fluid saturating the core sample, but is irly-rmeable to a second fluid used to displace the first fluid from the core sample. The second, or displacing fluid, is imiscible with the first fluid saturating the core sample and 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 membrane. Sleeve 10 is placed inside a suitable pressure vessel (not shown) that can be pressurized up to several thousand pounds per square inch (several million Pa).

Typical of such pressure vessels are those described in US-A-3,839,899; US-A-4,688,238; and US-A-4,379,407. Through such a pressure versel a pressure is applied to the sleeve 10 and hence to the porous rock 11. The pressure should be sufficient to eliminate any fluid annulus between the sleeve 10 and the surface *s of the core sample. A fluid inlet 14 and a fluid outlet 15 feed into the ends 16 and 12 respectively of the sleeve 10. Both inlet 14 and outlet 15 also serv as current conducting electrodes for passing current fran a source 20 tlr-gh the porous rock 11. A paifr of voltage electrodes 17a and 17b penetrate sleeve 10 and make contact with the porous rock at spaced locations along the length of the porous rc-k. '.me voltage across the porous rock 11 between the electrodes 17a and 17b i-s easured by the unit 21.

F-6071(72) -L(PAC) 11 The core sample of porous rock 11 is initially fully saturated, by way of example, with an electrically conducting fluid, such as salt water, and placed under confining pressure. A current is passed through the porous rock and a voltage along the length of the porous rock is measured between electrodes 17a and 17b. Such voltage measurements may be carried out in accordance with the disclosure of US-A-4,467,642; US-A-4,,546,318; and US-A-4,686,477.

From this voltage the resistance of the porous rock along its length between electrodes 17a and 17b is determined using Ohm's Law. The resistivity, or its reciprocal conductivity of the e 6 porous rock is determined using the determined resistance, the length and the cross-sectional area of the core. A displacing fluid such as a nonconducting oil or gas, may then be forced through inlet 14 into end 18 of porous rock 11 to change the S fluid saturation condition prior to the making of the next resistivity measurement Typical of such a resistivity determining system of FIG. 1 are those described in US-A-4,907,448; US-A-4,926,128 and US-A-4,924,187.

Having now described a typical resistivity determination carried out in a single direction along the axial direction of a cylindrical core sample as shown ir FIG. 1, the present invention of providing tensor components of resistivity, or conductivity, needed for interpreting electric logs of a subterranean formation with misotropic properties by measuring and comparing resistivity in a plurality of radial directions through a cylindrical core sample of the formation and normal to its cylindrical axis will 'la be described. A transversely isotropic cylindrical core sample of the formation is cut so that the formatio bedding plane is at an angle to the cylindrical axis of the core sample. 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. The core sample is contacted with an array of electrodes contained by sleeve 10 at each of a plurality of spaced-apart positions along the length of the core sample, such as electrode arrays A, B and C of FIG. 2 for example. Each such array A-C lies in a plane normal to the axis of the core sample and the electrodes in each array are equally spaced at an even number of positions about the sleeve FIG. 2 shows a pair of such electrodes A i and A. which are spaced-apart 1800 about sleeve 10 (with i 1 to FIG. 3 is a "p cross-sectional view taken through the sleeve 10 and core sample 11 at the axial position of array A with 24 electrodes -A4 being shown (cross-sectioning of sleeve 10 being omitted for 4 0 clarity). As can be seen in FIG. 3 there are 12 electrode pairs at 1800 spaced-apart positions about sleeve 10 such as electrode pairs Al and AlI A 2 and A14 A12 and A 24 A current is passed through core sample 11 and a voltage is measured across each of the A i and A iN, B i and Bi+N, and C i and Ci+ N electrode pairs spaced-apart 1800 about the arrays A, B and C such as shown by voltage unit 22 across electrode pair A 1

A

3 for example, These voltages as well as a voltage measured along the axial length of the core sample by unit 21, such as shown in FIG. 1, are used to determine the electrical resistivities of the core sample both 0 along the core sample and in the plurality of radial directionstrough the core sample normal to core sample axis between the electrodes of each corresponding electrode pair. Following these measurements, the fluid saturation in the core sample may be altered any number of times with such measure4mnts being repeated for each differing fluid saturation.

F-6071 (72) -L(PAC) 13 Frm these resistivities normal to the axis of the core sample at a plurality of positions along the axis of the core sa, ple the desired tensor components of resistivity, or conductivity, needed for interpreting electric logs of subterranean formations with anisotropic properties are determined. Small core samples cut parallel and normal to small but closely spaced layerings of different formation sediments show any elecrical anisotropy that might exist. Two core samples cut normal and parallel to a bedding plane may not be identical in all respects except for the direction of the planes relative to the; cylindrical axis of the core samples and it would be difficult to obtain the same partial Co water saturations in each core sample for comparison measurements. A single cylindrical core sample cut with the bedding plane at an angle to the axis of the core sample as described above is utilized in accordance with the present invention to overcome such limitations.

Referring now to FIG. 4, there is shown a preferred configuration for the electrodes of each of the electrode arrays A-C. For a.

purpose of example, electrodes A 1

-A

3 are shown molded into a rubber sleeve 10 with cylindrical main body members 30-32 and spherical-like end members 33-35 for making contact with the

S

outer surface of a core sample by extending outward from the inner surface of sleeve 10 by a distance P. As shown in FIG. 4, end members 33-35 are semispherical with recessed portions, or

S.

lips, 36-38, being normal to the outer surface of the cylindrical main body members 30-32. Such a semispherical end member provides for enhaned adhesion to the rubber sleeve While the foregoing has described a preferred embodiment of the present invention, it is to be understood that various modifications or changes may be made within the scope of the appended claims.

Claims

1. A method for determining electrical apisotropy of a core sample from a subterranean formation, including the steps of: a) shaping said core sample into the form of a cylinder; b) placing said core sample into a sleeve and applying a pressure to said core sample sufficient to eliminate any fluid annulus between the sleeve and said core sample; c) saturating said core sample with a first fluid; d) passing a current through said fluid-saturated core sample; e) measuring voltages in a plurality of radial directions through said core sample which are g.. normal to the cylindrical axis of said core sample at each of a plurality of spaced-apart positions along said axis; f) determining electrical resistivities in said too: plurality of radial directions through said core sample from said plurality of measured voltages; and S• g) comparing each of said determined electrical resistivities to identify the radial direction of any electrical anisotropy in said core sample. A method according to claim I wherein 0, (72) -L (PAC) h) an initial fluid saturation is established within said core sample; i) voltages are measured in a plurality of radial directions through said core sample, which are normal to the cylindrical axis of said core at each of a plurality of spaced-apart positions along said axis at said initial fluid saturation; and j) said fluid saturation is altered within sai d core sample a plurality of times and repeating the electrical resistivity determinations for each differing fluid saturation.

3. A method according ~to claim 2 wherein the iftep of altering fluid saturation includes the step of moving the fluid in said core sample in a direction parallel to said axis.

4.AmtoScorigt.li 2o hri $see 4 A meth d aring becim 2qal ora3ewherein evnumr *fes ~o poiton a)ou the outer surface of said coresapeicotte w th anlara of eectrds atrs each puaityo ofcroe ha r spaced100apart poiton aleateleg h saida nomlt said axiesupe andh elcrdsieaho ydg F-6071 (72) -L(PAC) 16 c) the voltage measurements across each pair of electrodes are utilised to determine the electrical resistivity of the core sample in a radial direction through said core sample normal to said axis between said pairs of electrodes. A method according to any preceding claim wherein the step of shaping said core sample is carried out by cutting the core such that the cylindrical axis of said core sample is at an angle to the bedding plane of said subterranean formation.

6. A method according to any preceding claim wherein after step at least a portion of said first fluid is displaced with a second fluid of differing electrical conductivity, and steps %o to are repeated. 7o A method according to claim 6 whrein said first fluid is electrically conductive and said second fluid is electrically non-conductive.

8. 1 method according to claim 6 wherein said first fluid is electrically non-conductive and said second fluid is electrically conductive.

9. Apparatus for determini.g resistivity of a core sample of a subterranean formation, including: a) a sleeve containing a cylindrical core sample of a subterranean formation which can be saturated with a fluid; b) means for applying a current throt, gh said core sample; Ile, F-607l (72) -L(PAC) 17 c) means for measuring voltages in a plurality of radial directions through said core sample normal to the cylindrical axis of said core sample in response to the flow of said current through said core sample; and d) means for determining electrical resistivities in said plurality of radial directions through said core samp~les from said measured voltages. Apparatus according. to claim '9 wherein said means for measuring~ Voltages includes: e) at least one electrode array extending through **said sleeve and making contact with the outer surface of said core sample, said array being in a plane normal to the cylindrical, axis of said core a sample and having an even number of electrodes equally spaced around said sleeve; and 6 means connected to said electrodes for measuring the voltage across each pair of electrodes that are spaced 1800 apart in each array around said sleeve in response to the flow of said current through said core sample. Apparatus according to claim 10 wherein each of said electrodes passes through said sleove and extends outward fro the inner surface of said sleeve with a rounded end for making contact with the outer surface of said core sample.

12. Apparatus according to claim, 11 wherein each of said electrodes is molded into said sleeve. F-6071(72) -L(PAC) 18

13. Apparatus according to claim 11 or 12 wherein said rounded end is spherical.

14. Apparatus according to claim 11 or 12 wherein said rounded end is semi-spherical. Apparatus according to any of claims 10 to 13 wherein each of said electrodes includes: g) a cylindrical main body member; and h) a spherical-like end member for making contact with the outer surface of said core sample.

16. Apparatus according to claim 15 wherein said end mem, is recessed adjacent said main body member.

17. Apparatus according to claim 15 or 16 wherein said end member is semi-spherical with diameter greater than that of said main body member.

18. Apparatus of claim 17 wherein the flat portion said semi-spherical end member is adjacent said main body meau r and normal to the cylindrical axis of said main -body member.

19. Apparatus according to any of claims 10 to 15 further including: i) a fluid inlet positioned in a first end of said sleeve through which a second fluid can be injected under pressure into the first end of said core sample for displacing a first fluid from a second end of said core sample, said second fluid .I c v Lc r I F F-6071 (72) -L(PAC) 19 being imniscible with said f irst fluid, wherein either said first fluid is electrically conducting and said second fluid is electrically non-conducting, or said first fluid is electrically non-conductin~g and said second fluid is electrically conducting. j) a porous menber positioned adjacent the second end of said sleeve through which said f irsi- fluid can be discharged from the second end of said core sample through said porous member; k) a fluid outlet positioned in the second end of see said sleeve through which said first fluid is di:"clarged from said sleeve after having been displaced from the second end of said core sample through said porous member; 1) a plurality of said electrode arrays disposed at to spaced-apart positions along the length of said sleeve, and making contact with the outer surface too:of said core sample at said spaced-apart positions, each of said arrays being in a plane normal to said cylindrical axis; and in) means for applying a confining pressure through said sleeve to said cor, sample, which is sufficient to elhiinate anyj fluid annulus between said sleeve and said core sample. Apparatus according to claimn 16 further including means for comparing said determined resistivities to identify the radial direction of any electrical anisotropy within said core sample in the plane of each of said electrode arrays and along the length "Ot of said core sample between said electrode arrays. T-) Nit1 20

21. Apparatus substantially as hereinbefore described with reference to any one of Figures 2 to 4. DATED: 16 NOVEMBER, 1994 PHILLIPS ORMONDE FITZPATRICK Attorneys for: MOBIL OIL CORPORATION *964 0 0 0 ,00*0 0 6* I?- 3 2 90981 F-6071(72)-L(PAC) Al 3Q Abstract of the Disclosure A method for determining electrical anisotropy of a core sample franom a subterranean formation. The method comprises the steps of: shaping said core sample into the form of a cylinder; app'ying a confining pressure to said core sample; saturating said core sample with a first fluid; passing a current through said fluid-saturated core sample; measuring voltages in a plurality of radial directions through said core sample which are normal to the cylindrical axis of said core sample at each of a plurality of spaced-apart positions along said axis; determining electrical resistivities in said plurality of radial directions through said core sample from said plurality of measured voltages; and comparing each of said determined electrical resistivities to identify the radial direction of any electrical anisotropy in said core sample. Apparatus for determining resistivity of a core sample of a subterranean formation is also disclosed. *w 4f V, 41 Z k* 0* 6 .m q qe "0 0 'I /T