GB2254703A

GB2254703A - Determining resistivity anisotropy in core samples

Info

Publication number: GB2254703A
Application number: GB9203883A
Authority: GB
Inventors: Wyatt Wendell Givens; William David Kennedy
Original assignee: Mobil Oil Corp
Current assignee: ExxonMobil Oil Corp
Priority date: 1991-03-19
Filing date: 1992-02-24
Publication date: 1992-10-14
Anticipated expiration: 2012-02-24
Also published as: AU1287692A; NO921058D0; GB9203883D0; AU657518B2; NO921058L; CA2063289A1; GB2254703B; DE4208953A1

Description

112,5) 4 7 0 3 1 Method for PgterminiLig Electrical Anisotropy a Core

sa=le from a Subterranean Formation This invention relates to a method for determining electrical anisatrepy of a core sample from a subterranean formation. The invention also relates to apparatus for resistivity of a core smrple of a subterranean formation.

Hydrocarbon saturation So is generally determined from water saturation sw as follows:

so = 1 - Sw (1) water saturation present in a subte formation is typically determined from interpretation of conventional electrical (i.e., 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 Resistivity Log As An Aid In Detennining Some Reservoir Ciaracteristics", Trans. ADE, Vol. 46, pp. 54-62, 1942, by G. E. Archie. ghis equation is expressed as follows:

n = R/,X (2) %,ere $w is the fractional water saturation (i.e. free and bound water of the formation expressed as a percent of the available pore space of the formation), RW is the formation water resistivity, 4 is the formation porosity, Rt 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 1 2 cnerits needed to predict fractional water saturation S;w from the formation resistivity, Pt, using the equation in any of its form.

Archie def ined two quantities that provided the basis for his water saturation equation (1). The first quantity is the formation factor F which defines the effect of the rock matrix on the resistivity of water as follows:

F = %/RW (3) where % = resistivity of water saturated rock and P,w = water resistivity.

Archie reasoned that for a given value of RW, the formation factor F would decrease with increasing porosity, , to some exponent m:

F = 114P (4) This porosity exponent m has also become laxym as the Archie cementation exponent. 'Ibus Archie provided a useful cbaracterization of a rock fully saturated with a conducting brine in terns of the water resistivity RW, porosity ik and a rock parameter m. It is inportant 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, Pt, to the same rock saturated fully with water, RO, as follows:

I = Rt/Ro (5) 3 Archie reasoned that as the water saturation decreased (i. e. hydrocarbon saturation increased) the resistivity Pt and hence I would increase to some exponent n:

I= 1/ n (6) k e SW = volume of water in pores/total pore volume.

Miis exponent n has become krxxm as the Archie saturation exponent. It is again important to note that Archie assumed all conductance to be in the brine and further that all pores within the rock have the same water saturation Sw.

It is these two equations (4) and (6) for the formation factor F and resistivity index I respectively that Archie combined to provide the water saturation expression S of equation (2).

w, certain logs have provided formation resistivity IRt and porosity ib. Water samples provide the best values for RW. Standard practice is to measure rock sample resistivities RO and Rt for a number of water saturations and to plot the logarithm of I versus the logarithm of S w. Archie's equations assume such a logarithmic plat can be fit by a straight line with slope of -n.

Many core samples are, however, not homogenous and electrically isotropic. For such core samples, the Archie saturation exponent n will be strongly dependent on the direction the resistivity 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 (2). It is, therefore, an object of the present invention to determine 4 resistivity of a core le that is electrically anisatrepic and to identify the degree of anisat changes as the brine saturation of the core sainple es so that an accurate water saturation can be from equation (2).

According to one aspect of the present invention there is provided a method for determining electrical anisatrcpy of a core le, from a subterranean fcrmtiOnt cORPrISIng the steps Of:

a) shaping said core sanple into the form of a cylinder; b) applying a confining pressure to said core le; c) saturating said core sainple, with a first fluid; d) passing a current thr said fluid-saturated core sanple; e) measurirxj voltages in a plurality of radial directions through said core sample which are normal to the cylindrical axis of said core sanple, at each of a plurality of spaced-apart positions alonq said axis; f) determining electrical resistivities in said plurality of radial directions through said core sanple from said plurality of measured voltages; and g) caqmring each of said determined electrical resistivities to identify the radial direction of any electrical anisotropy in said core sauple.

Preferably the step of measuring voltages cmprises:

h) establishing an initial fluid saturation within said core sapple; i) measuring voltages 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) altering said fluid saturation within said core le a plurality of times and repeating the e.Lectrical resistivity determinations for each differing fluid saturation.

Desirably the step of altering fluid satuiration rises the step of moving the fluid in said core sample in a direction parallel to said axis.

It is preferred that step (i) c=prises:

contacting the outer surface of said core sample 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; 6 measuring the voltage across each pair of electrodes that are spaced 18011 apart about said core sample; and Ift) utilizing the voltage measurements across each pair of electrodes 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 care sample may be carried out by cutting the care such that the cylindrical axis of said core sample is at an angle to the bedding plane of said subterranean formation.

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

M-ke- first fluid may be electrically conductive with said second fluid being electrically non-canductive; or the first fluid may be electrically non-conductive with said secvnd 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:

a) a sleeve containing a cylindrical core sample of a subterranean formation which can be saturated with a fluid; 7 b) means for applying a current tin said core sample; c) means for measuring voltager. 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 samples from said measured voltages.

Preferably said means for measuring voltages comprises:

e) at least one electrode array extending thr said sleeve and making contact with the o 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 f) me= connected to said electrodes for measuring the voltage across each pair of electrodes that are spaced 18011 apart around said sleeve in response to the flow of said.current through said core sample.

Each of said electrodes may pass thr said sleeve and extend outward from. the inner surface of said sleeve, and be provided with a rounded end for baking contact with the outer surface of said core sauple. The rounded end is preferably spherical or semi-spherical 1 8 Desirably each of said electrodes is ded into said sleeve.

In a preferred construction each of said electrodes comprises:

g) a cylindrical main body me; and h) a spherical-like end member for making contact with the outer surface of said core sample.

!Ihe end mmbw may be recessed adjacent said main body re. The end member my be semi-spherical with diameter greater than that of said main body rmanber. The flat portion of said semi-spherical end ranber may be adjacent said main body rember 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 said first fluid ftcn a second end of said core sample, said second fluid being imiscible with said first fluid and of opposite electrical conductance; a porous member positioned adjacent a second end of said sleeve through which said first fluid can be discharged from the second end of said core sample through said porous:)er; a fluid inlet positioned in the second end of said sleeve through which said first fluid is discharged from said sleeve after having been 9 displaced frcm the second end of said core sainple through said porous er; 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 sauple 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 sapple.

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

Reference is now made to the accompanying drawings, in which FIG. 1 illustrates prior art apparatus for carrying out resistivity determinations m core sainples of subterranean formations;

FIG. 2 illustrates apparatus eMPlOYing electrode arraYs for carrying out resistivity reasurmmts on electrically anisatropic core sanples of subterranean formations; in accordance with the present invention; FIG. 3 is a cross-sectional view through the apparatus of FIG. 2 showing in detail one of the electrode arrays of FIG. 2; and FIG. 4 illustrates one configuration for the electrodes of each of the electrode arrays of FIGS. 2 and 3.

A system that bas been successfully used in carrying out linear resistivity determinations along a core sample from 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 10 is a porous member 13, which is penneable to a first fluid saturating the core sample, but is impermeable to a second fluid used to displace the first fluid from the core sample. The second, or displacing fluid, is immiscible with the first fluid saturating the core sample and is of different electrical conductivity. Ihis first saturation fluid is the wetting fluid for the porous manber 13, which by way of exwple, 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 vessel a pressure is applied to the sleeve 10 and hence to the porous rock 11. The pressure should be sufficient to eliminate any fluid amulus between the sleeve 10 and the surface 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 serve as current conducting electrodes for passing current from a source 20 through the porous rock 11. A pair 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 rock. The voltage across the porous rock 11 between the electrodes 17a and 17b is measured by the unit 21.

11 The core le of porous rock 11 is initially f ully saturated, by way of exanple, with an electrically conducting f luid, 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-4j,467,642; US-A-4,546,318; and US-A-4,686,477.

From this voltage tlip- resistance of the porous rock along its length between electrodes 17a and 17b is determined using Cbm's law. The resistivity, or its reciprocal conductivity of the porous rock is determined using tile 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 thr inlet 14 into end 18 of porous rock 11 to dbange the fluid saturation condition prior to the making of the next resistivity measurement.

l?pical of such a resistivity detennirdxxj 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 in FIG. 1, the present invention of providing tensor cnents of resistivity, or conductivity, needed for interpreting electric logs of a subterranean formation with anisatrapic properties by measuring and cring resistivity in a plurality of radial directions through a cylindrical core le of the formation and normal to its cylindrical axis will now be described. A transversely isotropic cylindrical core sample of the formation is cut so that the formation bedding plane is at an angle to the cylindrical axis of the core le. The core sample is initially saturated with an 12 electrically conducting fluid such as salt water, and placed within sleeve 10 under confining pressure representative of in-situ pressure. The care 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 care sample, such as electrode arrays A, B and C of FIG. 2 for exuple. Each such array A-C lies in a planie 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 10.

FIG. 2 shows a pair of such electrodes Ai and A14N which are spaced-apart 18011 about sleeve 10 (with i = I to N). FIG. 3 is a cross-sectional view taken through the sleeve 10 and core sample 11 at the axial position of array A with 24 electrodes A17A24 being shown (cross-sectioning of sleeve 10 being omitted for clarity) - As can be seen in FTG. 3 there are 12 electrode pairs at 180 spaced-apart positions about sleeve 10 such as electrode Pairs A. and A1V A2 and A14 - A12 and A24. A current is passed through core sample 11 and a voltage is measured across each of the Ai and Aj4N, 13i and.., and Ci and C1,, electrode pairs spaced-apart 180(1 about the arrays A, B and C such as shown by voltage unit 22 across electrode pa:Lr A,7A13 for example. r1hese voltages as well as a voltage measured along the axial length of the core sample by unit 21, such as shown in FTG. 1, are used to determine the electrical resistivities of the core sample both along the core sample and im the plurality of radial directions through 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 measurements being repeated for each differing fluid saturation.

13 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 ccwponents of resistivity, or conductivity,. needed for interpreting electric logs of subterranean formations with anisotrcpic properties are determined. Small core samples cut parallel and normal to small but closely spaced layerings of different formation sediments show arry electrical anisotropy that might exist. Two core saTrples 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 water saturations in eadi core sample for cmparison A single cylindrical core sample cat witli the bedding plane at an angle to the axis of the core swiple 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 purpose of exnple, electrodes A17A3 are shown molded into a rubber sleeve 10 with cylindrical main body members 30-32 and spberical-like end members 33-35 for making contact with the outer surface of a core sample by extending outward frau the inner surface of sleeve 10 by a distance P. As shown in FIG. 4, end mem)Ders 33-35 are semispherical with recessed portions, or lips, 36-38, being normal to the outer surface of the cylindrical main body members 30-32. Such a semispherical end medDer provides for enhanced adhesion to the rubber sleeve 10.

&ile the foregoing has described a preferred embodi of the present invention, it is to be understood that various redifications or changes my be made within the scope of the appended claims.

14 claims 1. A method for determining electrical anisotropy of a care sample frem a subterranean formation, cising the Of:

a) shaping said core sample into the form of a Cylinder; b) applying a confining pressure to said core sample; c) saturating said core sainple 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 sapple, which are 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 Plurality of radial directions through said core sample frcm said plurality of measured voltages; and g) ccaparing each of said determined electrical resistivities to identify the radial direction of any electrical anisotrcpy in said core sample.

2. A method according to claim 1 wherein the step of measuring voltages carrprises:

is h) establishing an initial fluid saturation within said core sample; measuring voltages 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 altering said fluid saturation within said 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 step of altering fluid saturation cmprisw the step of caving the fluid in said core sample in a direction parallel to said axis.

4. A method according to claim 2 or 3 wherein step (i) cises:

a) contacting the outer surface of said core sample with an array of electrodes at each of a plurality of spaced-apart positions along the length of said core saTLple, 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; b) measuring the voltage across each pair of electrodes that are spaced 1800 apart about said core sample; and 16 c) utilizing the voltage measurer across each pair of electrodes to determine the electrical resistivity of the core sarple in a radial direction thr said core sample normal to said axis between said pairs of electrodes.

5. A method according to arry preceding claim wherein the step of shaping said core le is carried out by cutting the core such that the cylindrical axis of said care sample is at an angle to the bedding plane of said subterranean formation.

6. A method according to ariy preceding claim wherein after step (g) at least a portion of said first fluid is displaced with a second fluid of differing electrical conductivity, and steps (d) to (g) are repeated.

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

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

9. Apparatus for determining resistivity of a core sample of a subterranean formation, cceprising:

a) a sleeve containing a cylindrical core sanple of a subterranean formation which can be saturated with a fluid; b) means for applying a current thr said core saTrple; 17 means for measuring voltages in a plurality of radial directions tbrough 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) mans for determining electrical resistivities in said plurality of radial directions through said core samples from. said measured voltages.

10. Apparatus according to claim 9 wherein said means for measuring voltages ocuprises:

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 f) means connected to said electrodes for measuring the voltage across each pair of electrodes that are spaced 18011 apart around said sleeve in response to the flow of said current through said core sample.

11. Apparatus according to claim 10 vfti--min each of said electrodes passes through said sleeve and extends outward from the inner surface of said sleeve with a rounded end for making contact with the outer surface of said care sample.

12. Apparatus according to claim 11 w1herein each of said electrodes is molded into said sleeve.

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-ical.

15. Apparatus according to arry of claims 10 to 14 wherein 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 sampile.

16. Apparatus according to claim 15 ein said end mmydj,-= is recessed adjacent said main body member.

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

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

19. Apparatus according to any of claims 10 to 15 further comprising:

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 said first fluid from a second end of said core smple, said second fluid 19 being 1=zcible with said first fluid and of cpposite electrical corductance; j) a porous member positioned adjacent a second end of said sleeve th which said first fluid can be discharged from the second end of said core le tbr said porous member; k) a fluid inlet positioned in the second end of said sleeve through which said first fluid is discharged from said sleeve after having been displaced frcan the second end of said core le thr said porous member; 1) a plurality of said electrode arrays disposed at spacgd-apart positions along the length of said sleeve, and making contact with the outer surface of said core sauple at said spaced-apart positions, each of said arrays being in a plane nonnal to said cylindrical axis; and m) means for applying a confining pressure through said sleeve to said core le.

20. Apparatus according to claim 16 further including means for ccaparing said determined resistivities to identify the radial direction of any electrical anisctrcpy within said core sanple in the plane of each of said electrode arrays and along the length of said core sanple between said electrode arrays.