GB2396018A

GB2396018A - Directional electromagnetic measurements insensitive to dip and anisotropy

Info

Publication number: GB2396018A
Application number: GB0404047A
Authority: GB
Inventors: Richard A Rosthal; Gerald N Minerbo; Dzevat Omeragic
Original assignee: Schlumberger Holdings Ltd
Current assignee: Schlumberger Holdings Ltd
Priority date: 2001-09-26
Filing date: 2002-08-23
Publication date: 2004-06-09
Anticipated expiration: 2022-08-23
Also published as: GB0404047D0; GB2396018B

Abstract

Methods for directional logging measurements provide estimates of the distance of a logging tool to a bed boundary using up-down measurements with tilted antenna configurations. The methods comprise determining a parameter of a formation traversed by a borehole, disposing a logging tool within the borehole, the tool comprising; a first antenna system including two receiver antennas (R21, R22) and a transmitter antenna (T1); a second antenna system including two receiver antennas (R11,R12 )and a transmitter antenna (T2); transmitting energy from the first transmitter antenna and measuring a signal at the receiver antennas of the second antenna system; transmitting energy from the second transmitter antenna and measuring a signal at the receiver antennas of the first antenna system; calculating signal attenuation in dB and phase shift of received signals, and using the calculated values to determine the formation parameter.

Description

GB 2396018 A continuation (74) Agent and/or Address for Service: Sensa

Gamma House, Enterprise Road, Chilworth Science Park, SOUTHAMPTON, Hampshire, SO16 7NS, United Kingdom

DIRECTIONAL ELECTROMAGNETIC MEASUREMENTS INSENSITIVE TO

DIP AND ANISOTROPY

Background of the Invention

Field of the Invention

The invention relates generally to the field of well logging. More particularly, the

invention relates to improved techniques in which instruments equipped with antenna systems having transverse or tilted magnetic dipoles are used for improved electromagnetic measurements of subsurface formations.

Background Art

Various well logging techniques are known in the field of hydrocarbon exploration and

production. These techniques typically use instruments or tools equipped with sources adapted to emit energy into a subsurface formation that has been penetrated by a borehole. In this description, "instrument" and "tool" will be used interchangeably to indicate, for example, an

electromagnetic instrument (or tool), a wire-line tool (or instrument), or a logging-while-drilling tool (or instrument). The emitted energy interacts with the surrounding formation to produce signals that are then detected and measured by one or more sensors. By processing the detected signal data, a profile of the formation properties is obtained.

Electromagnetic (EM) induction and propagation logging are well-known techniques.

The logging instruments are disposed within a borehole to measure the electrical conductivity (or its inverse, resistivity) of earth formations surrounding the borehole. In the present description,

any reference to conductivity is intended to encompass its inverse, resistivity, or vice versa. A typical electromagnetic resistivity tool comprises a transmitter antenna and one or more (typically a pair) receiver antennas disposed at a distance from the transmitter antenna along the axis of the tool (see FIG. 1).

Induction tools measure the resistivity (or conductivity) of the formation by measuring the current induced in the receiver antenna as a result of magnetic flux induced by currents flowing through the emitting (or transmitter) antenna. An EM propagation tool operates in a similar fashion but typically at higher frequencies than do induction tools for comparable

antenna spacings (about 106 Hz for propagation tools as compared with about 104 Hz for the induction tools). A typical propagation tool may operate at a frequency range of I kHz - 2 MHz.

Conventional transmitters and receivers are antennas formed from coils comprised of one or more turns of insulated conductor wire wound around a support. These antennas are typically operable as sources and/or receivers. Those skilled in the art will appreciate that the same antenna may be use as a transmitter at one time and as a receiver at another. It will also be appreciated that the transmitter-receiver configurations disclosed herein are interchangeable due to the principle of reciprocity, i.e., the "transmitter" may be used as a "receiver", and vice-versa.

A coil carrying a current (e.g., a transmitter coil) generates a magnetic field. The

electromagnetic energy from the transmitter antenna is transmitted into the surrounding formation, which induces a current (eddy current) flowing in the formation around the transmitter (see FIG. 2A). The eddy current in the formation in turn generates a magnetic field

that induces an electrical voltage in the receiver antennas. If a pair of spaced-apart receivers are used, the induced voltages in the two receiver antennas would have different phases and amplitudes due to geometric spreading and absorption by the surrounding formation. The phase difference (phase shift, 07) and amplitude ratio (attenuation, A) from the two receivers can be used to derive resistivity of the formation. The detected phase shift (I) and attenuation (A) depend on not only the spacing between the two receivers and the distances between the transmitter and the receivers, but also the frequency of EM waves generated by the transmitter.

In conventional induction and propagation logging instruments, the transmitter and receiver antennas are mounted with their axes along the longitudinal axis of the instrument.

Thus, these tools are implemented with antennas having longitudinal magnetic dipoles (LMD).

An emerging technique in the field of well logging is the use of instruments including antennas

having tilted or transverse coils, i.e., where the coil's axis is not parallel to the longitudinal axis of the support or borehole. These instruments are thus implemented with a transverse or tilted magnetic dipole (TMD) antenna. Those skilled in the art will appreciate that various ways are available to tilt or skew an antenna. Logging instruments equipped with TMD antennas are described in U.S. Pat. Nos. 6, 163,155, 6,147,496, 5,115,198, 4,319,191, 5,508,616, 5,757,191, 5,781,436, 6,044,325, and 6,147,496.

Figure 2A presents a simple picture, which is applicable if the borehole penetrates the formation in a direction perpendicular to the sedimentation layers. However, this is often not the situation. Often the borehole penetrates the formation layers at an angle other than 90 degrees (FIG. 2B). When this happens, the formation plane is said to have a relative dip. A relative dip angle, 0, is defined as the angle between the borehole axis (tool axis) and the normal to the plane of the formation (not shown).

Drilling techniques known in the art include drilling wellbores from a selected geographic position at the earth's surface, along a selected trajectory. The trajectory may extend to other selected geographic positions at particular depths within the wellbore. These techniques are known collectively as "directional drilling" techniques. One application of directional drilling is the drilling of highly deviated (with respect to vertical), or even horizontal, wellbores within and along relatively thin hydrocarbon-bearing earth formations (called "pay zones") over extended distances. These highly deviated wellbores are intended to greatly increase the hydrocarbon drainage from the pay zone as compared to "conventional" wellbores which "vertically" (substantially perpendicularly to the layering of the formation) penetrate the pay zone. In highly deviated or horizontal wellbore drilling within a pay zone, it is important to maintain the trajectory of the wellbore so that it remains within a particular position in the pay zone. Directional drilling systems are well known in the art which use "mud motors" and "bent subs" as means for controlling the trajectory of a wellbore with respect to geographic references, such as magnetic north and earth's gravity (vertical). Layering of the formations, however, may be such that the pay zone does not lie along a predictable trajectory at geographic positions distant from the surface location of the wellbore. Typically the wellbore operator uses information (such as LWD logs) obtained during wellbore drilling to maintain the trajectory of the wellbore within the pay zone, and to further verify that the wellbore is, in fact, being drilled within the pay zone.

Techniques known in the art for maintaining trajectory are described for example in ribe et al., Precise Well Placement using Rotary Steerable Systems and LWD Measurement, SOCIETY OF PETROLEUM ENGINEERS, Paper 71396, September 30, 2001. The technique described in this reference is based upon LWD conductivity sensor responses. If, as an example, the conductivity

of the pay zone is known prior to penetration by the wellbore, and if the conductivities of overlying and underlying zones provide a significant contrast with respect to the pay zone, a measure of formation conductivity made while drilling can be used as a criterion for "steering" the wellbore to remain within the pay zone. More specifically, if the measured conductivity deviates significantly from the conductivity of the pay zone, this is an indication that the wellbore is approaching, or has even penetrated, the interface of the overlying or underlying earth formation. As an example, the conductivity of an oil-saturated sand may be significantly lower than that of a typical overlying and underlying shale. An indication that the conductivity adjacent the wellbore is increasing can be interpreted to mean that the wellbore is approaching the overlying or the underlying formation layer (shale in this example). The technique of directional drilling using a formation property measurement as a guide to trajectory adjustment is generally referred to as "geosteering."

In addition to EM measurements, acoustic and radioactive measurements are also used as means for geosteering. Again using the example of an oil producing zone with overlying and underlying shale, natural gamma radioactivity in the pay zone is generally considerably less than the natural gamma ray activity of the shale formations above and below the pay zone. As a result, an increase in the measured natural gamma ray activity from a LWD gamma ray sensor will indicate that the wellbore is deviating from the center of the pay zone and is approaching or even penetrating either the upper or lower shale interface.

If, as in the prior examples, the conductivity and natural radioactivity of the overlying and underlying shale formations are similar to each other, the previously described geosteering techniques indicate only that the wellbore is leaving the pay zone, but do not indicate whether the wellbore is diverting out of the pay zone through the top of the zone or through the bottom of the zone. This presents a problem to the wellbore operator, who must correct the wellbore trajectory to maintain the selected position in the pay zone.

EM induction logging instruments are well suited for geosteering applications because their lateral (radial) depth of investigation into the formations surrounding the wellbore is relatively large, especially when compared to nuclear instruments. The deeper radial investigation enables induction instruments to "see" a significant lateral (or radial) distance from axis of the wellbore. In geosteering applications, this larger depth of investigation would make

possible detection of approaching formation layer boundaries at greater lateral distances from the wellbore, which would provide the wellbore operator additional time to make any necessary trajectory corrections. However, conventional propagation-type instruments are capable of resolving axial and lateral (radial) variations in conductivity of the formations surrounding the instrument, but the response of these instruments generally cannot resolve azimuthal variations in the conductivity of the formations surrounding the instrument.

U.S. Pat. Nos. 6,181,138 and 5,892,460 describe the use of TMD antennas to provide directional sensitivity related to bed boundaries. U.S. Pat. No. 5,892,460 proposes using propagation measurements and off-centered antennas from the tool axis for directional measurements. U.S. Pat. Nos. 5,781,436, 5,999,883, and 6,044,325 describe methods for producing estimates of various formation parameters from tri-axial measurements.

Disadvantages of these techniques include the coupled effects of dip and formation anisotropy on the resulting measurements.

It is desirable to have measurement techniques that eliminate adverse characteristics of measurements with TMD antennas in geosteering, well placement, directional drilling, or horizontal well drilling applications. It is also desirable to have systems and processes that are insensitive to dip and anisotropy for the estimation of bed boundary parameters.

Summary of the Invention

According to a first aspect of the invention, a method for determining a parameter of a subsurface formation traversed by a borehole comprises: a) disposing a logging instrument having a longitudinal axis within the borehole, said instrument equipped with: i. a first antenna system including a receiver antenna having its axis oriented in a first direction at angle at with respect to the instrument axis, a second receiver antenna having its axis oriented in a second direction at angle H2 with respect to the instrument axis, and a first transmitter antenna located at the mid-point between said first and second receiver antennas and having its magnetic moment oriented in a third direction at angle O3 with respect to the instrument axis; and s

ii. a second antenna system forming the mirror image of said first antenna system with respect to the central plane perpendicular to the instrument axis such that a third receiver antenna has its axis oriented in said first direction at said angle 0 with respect to the instrument axis, a fourth receiver antenna has its axis oriented in said second direction at said angle 02 with respect to the instrument axis and is separated from the third receiver antenna by the same distance as the first receiver antenna is separated from the second receiver antenna, and a second transmitter antenna is located at the mid-point between said third and fourth receiver antennas with its magnetic moment oriented in said third direction at said angle as with respect to the instrument axis; b) transmitting electromagnetic energy from the first transmitter antenna; c) measuring a signal associated with the transmitted energy at the third and fourth receiver antennas; d) calculating signal attenuation in dB and relative phase shift using the measured signal of step A; e) transmitting electromagnetic energy from the second transmitter antenna; f) measuring a signal associated with the transmitted energy at the first and second receiver antennas; g) calculating signal attenuation in dB and relative phase shift using the measured signal of step (f); and h) calculating a difference using values obtained from steps (d) and (g) to determine the formation parameter.

According to a second aspect of the invention, a method for determining a parameter of a subsurface formation traversed by a borehole comprises: a) disposing a logging instrument having a longitudinal axis within the borehole, said instrument equipped with: i. a first antenna system including a receiver antenna having its axis oriented in a first direction at angle D with respect to the instrument axis, a second receiver antenna having its axis oriented in a second direction at angle 02

with respect to the instrument axis, and a first transmitter antenna located at the mid-point between said first and second receiver antennas and having its magnetic moment oriented in a third direction at angle 03 with respect to the instrument axis; and ii. a second antenna system including a third receiver antenna having its axis oriented in said first direction at angle -a/ with respect to the instrument axis, a fourth receiver antenna having its axis oriented in said second direction at angle -H2 with respect to the instrument axis and separated from the third receiver antenna by the same distance as the first receiver antenna is separated from the second receiver antenna, and a second transmitter antenna located at the mid-point between said third and fourth receiver antennas with its magnetic moment oriented in a third direction at angle 03 with respect to the instrument axis; b) transmitting electromagnetic energy from the first transmitter antenna; c) measuring a signal associated with the transmitted energy at the third and fourth receiver antennas; d) calculating signal attenuation in dB and relative phase shift using the measured signal of step (c); e) transmitting electromagnetic energy from the second transmitter antenna; f) measuring a signal associated with the transmitted energy at the first and second receiver antennas; g) calculating signal attenuation in dB and relative phase shift using the measured signal of step (I); and h) calculating a sum using values obtained from steps (d) and (g) to determine the formation parameter.

According to a third aspect of the invention, a method for determining a parameter of a subsurface formation traversed by a borehole comprises: a) disposing a logging instrument having a longitudinal axis within the borehole, said instrument equipped with: i. a first antenna system including a receiver antenna having its axis oriented in a first direction at angle D/ with respect to the instrument axis, a

second receiver antenna with its axis oriented in a second direction at angle 02 with respect to the instrument axis, and a first transmitter antenna having its magnetic moment oriented in a third direction at angle 03 with respect to the instrument axis; and ii. a second antenna system forming the mirror image of said first antenna system with respect to the central plane perpendicular to the instrument axis such that a third receiver antenna has its axis oriented in said first direction at said angle 0/ with respect to the instrument axis, a fourth receiver antenna has its axis oriented in said second direction at said angle 02 with respect to the instrument axis, and a second transmitter antenna has its magnetic moment oriented in said third direction at said angle 03 with respect to the instrument axis wherein the mid-point between said first and second transmitter antennas coincides with the mid-point between said first and third receiver antennas and the mid-point between said second and fourth receiver antennas; b) transmitting electromagnetic energy from the first transmitter antenna; c) measuring a signal associated with the transmitted energy at the third and fourth receiver antennas; d) calculating signal attenuation in dB and relative phase shift using the signal measured in step c); e) transmitting electromagnetic energy from the second transmitter antenna; f) measuring a signal associated with the transmitted energy at the first and second receiver antennas; g) calculating signal attenuation in dB and relative phase shift using the signal measured in step (f); and h) calculating a difference using values obtained from steps (d) and (g) to determine the formation parameter.

Other aspects and advantages of the invention will be apparent from the following description and the appended claims.

Brief Description of Drawings

FIG.lis a schematic diagram of prior art induction or propagation tools.

FIGs. 2A and 2B are diagrams showing eddy currents induced by a logging tool in a formation with and without a dip, respectively..

FIG. 3 is a schematic diagram of a symmetrized cross-dipole directional induction measurement according to the invention.

FIG. 4 is a schematic diagram of an alternative symmetrized directional induction measurement according to the invention.

FIG. 5 is a schematic diagram of an alternative symmetrized directional induction measurement using a single transmitter-receiver pair according to the invention.

FIG. 6 is a schematic diagram of a basic antenna configuration for a propagation-type measurement according to the invention.

FIGs.7A-7I are schematic diagrams of variations of antenna configurations according to the invention.

FIGs. 8A and 8B are schematic diagrams of antenna configurations according to the invention. FIG. 9 is a graph of responses of directional measurements according to the configurations in FIG.8 as a function of dip angles in a formation with two boundaries and three regions, one of which is anisotropic.

FIG.lOis a graph of "up-down" responses of directional measurements according to the configurations in FIG.8 as a function of dip angles in a formation with two boundaries and three regions, one of which is anisotropic.

FIGs.llA-llD are schematic diagrams of variations of the antenna configurations shown in FIGs.8A and 8B.

FIG.12 is a schematic diagram of another variant of a directional antenna configuration according to the invention.

FIGs. 13A and 13B are schematic diagrams of two borehole compensated variants of directional antenna configurations according to the invention.

Detailed Description

Figure 3 illustrates a measurement technique according to the invention. The transmitters and receivers are approximated as point magnetic dipoles. The antennas labeled Z have a dipole moment along the tool axis; the antennas labeled X have a dipole moment perpendicular to the tool axis. The instrument does not move during this idealized measurement, but is displaced sideways in the Figure 3 for clarity. In the interest of clarity, the instrument axis is generally represented as a dashed line. The Z transmitter is activated, and the voltage measured on the X receiver is denoted Vzx. The X transmitter is then activated, and the voltage measured on the Z receiver is denoted Vxz. The cross-dipole measurement based on the difference Vzx - Vxz is used to obtain information about adjacent bed boundaries. The mathematical theory underlying the invention is now presented.

Basic properties of the cross-dipole measurement. For a transmitter carrying a current I, the voltage V measured at the receiver can be expressed in terms of a tensor transfer = impedance ZRT: V = IUR ZRT UT (1)

The transmitter antenna has a magnetic dipole moment oriented along the unit vector UT; the receiver antenna is oriented along UR The transfer impedanceZRT has the following symmetry property = =T ZRT = Z7R, (2)

where the superscript T denotes the transpose tensor.

Two sets of orthogonal unit vectors are introduced, US, uy, us, for the formation, and ux, us, uz, for the tool coordinates, with uz along the axis of symmetry of the tool. The z axis is perpendicular to the layers, oriented upward. The tool axis is in the x-z plane. The dip angle is denoted by cr. so that

UX=UXCOSa+U sing, Uy = Uy 7 uz=-uxsina+u cosa. (3) The symmetrized crossdipole measurement in the tool coordinates can be transformed to formation coordinates as follows: VZX VXZ I UZ Z*T UX I UX ZR7 UZ

=I(-uxsina+u cosa) ZRT (UX cosa+u sing) -I(uxcosa +u sina).ZRT (-losing + u cosa) (4) = I(cos a + sin a)(uz ZRT UX -UX ZRT U) (5) I(U ZRT UX UX ZRT U)

= V - V (6)

We get the same result in the tool coordinates as in the formation coordinates.

The voltage difference Vzx - Vx in the formation coordinates can be computed from: VZX VX = It ZRT U -UX Z RT UZ) = ikZoARATI H I) + h 4 |c (qP)}Z cZ BY (ZRZT)qdq- (7) Here AR and AT represent the area of receiver and transmitter respectively. Here ZO==376.70hmsis the impedance of free space, his the free-space propagation coefficient, and Hi" is a Hankel function of the first kind of order one. The distance between the receiver and transmitter antennas, projected horizontally, is P = 4(XR - XT) + (YR IT) (8)

The path of integration C must lie above the origin and below the singularities of ah,

The transfer impedance ZRT is expressed in terms of two scalar Green's functions y e and y h, These scalar Green's functions are solutions of the following ordinary differential equations (ODEs): d 1 d ye(z,z')+ :k2pl-q jre(z,z')=(Z-Z), (9) r (z, z) + | k l-q r h (Z. Z.) = (z-z i) ( 10) dz pl dz J The and,u in these equations denote the relative permitivity and permeability 1 id: Ho No 1 =;-±At, =(-± (ll) So to) So to) The subscripts h and v indicate horizontal and vertical components. Variability of the magnetic permeability is not interesting for this application; we will assume that the magnetic permeability is isotropic, =,ul, and constant. Because yh iS independent off, and - Via couples only to y h, it follows that - Vxz is independent of the vertical components of conductivity and perrnitivityEz.

The Green's function yhcan be constructed from solutions of a homogeneous one-

dimensional ODE: d __ Ash +:k21 _ q: = 0. (12) dz pl dz id Let or h- be a solution that is regular at z = -= and or h+ a solution that is regular at z = +. From these solutions, one can construct Green's functions by Lagrange's method. The Green's function yh can be expressed as yh(z z,) (Z<) (Z.) (13) where z< = min (z, z'), and z, = max (z, z). The Wronskian Ah, defined by

wh I [h-(z) d h+(Z) h+(Z) d h-(z)] (14) is independent of z. Equation (10) shows that the Green's functions yh is symmetric Y (ZR'Z7) = Y (ZT'ZR) (15)

Born Approximation. An approximate method of solving Equation (10) can be obtained by first constructing yh for a uniform background medium (subscript B)

YB(ZR,ZT) = 2ph exp( FB|ZR ZT|), (16) where /3B = If -(11)B k, real(,BB) 2 O. (17) Equation (10) is replaced by d 2 [Y (Zen) YB(ZZ)]+ (k 11 -q)[Y (Z,Z)-YB(Z'Z)]= [k 1,U1 (k S11)B]YB(Z,Z), (18) which can be solved iteratively. The first iteration is called the Born approximation h ( i) y h (z Z i)-k 2 | y B (Z. Z) [e l ( Z)-(Al) B.]Y B () ( 1 9) The Born approximation is accurate for low frequency, low conductivity, or low conductivity contrast. This iterative solution method cannot be applied to y e because Equation (9) does not have the required smoothness properties. The Born approximation is not valid for y e, nor for general tri-axial measurements.

By substituting Equation (19) in Equation (7), we obtain V -V u R k pa |Kgom(p' 2ZF-ZR ZT) 1(Z,4)dZF (20) The homogeneous medium terms cancel out. For the case where z T< ZR,, the Born kernel KBom is given by K exp(ik(l,ul) 2 5) Bom [3 S ' for ZR < Z F.

=o for ZT<ZF<ZR, cP exp(ik(l,ul) S) for ZF<ZT, (21) Lip S with 5 = + (2Zr -ZR -ZT)] ' (22) To simplify the contour integral, we used exp(ik(lpl) (P +z))=i H<(qp)e 2pd4. (23) Response in a uniform layer. In a uniform layer, Vzx - Vat can be evaluated analytically.

Suppose that the electrical parameters al, Al are independent of z in an interval z < z T< Z R < Z H. The solutions Or -, Or +, from Equation ( 12) , have the form Y/ A- (elm + R- -lo -2) (24) ye + = A+ (el' + R+ en (Z2ZH) (25) withy= ph. where l ph = |Y1 q2 _lplk, (26) \1 Yz choosing the branch of the square root that makes real (I > 0. Equation ( 13) gives h R e r R e '(2ZH ZR--T) Ire + J Y (zR zr) 1 1 R R+e2(ZH-Z) (27) This expression depends only on the sum of the vertical positions of the receiver and transmitter coils ZR + ZT - Generally, the magnitude of reflection coefficients is smaller than unity. The exponential factor in the denominator provides further attenuation since real (I > 0.

Thus one can expect that, in a thick layer, |R-R+e-2atzH-z:'l << 1 (28)

The expression in Equation (27) is then the sum of two contributions proportional to the reflection coefficients from the lower and upper boundaries. This gives a simple formula for interpreting the measurement in a thick uniform layer: At -Ye 0i R T I qH(4p)[Re-Pt-R±7-2 t' _R+e 2,, zA,']qdq (29) The measurement depends weakly on the antenna separation and dip angle through the distance p. Response at large distance from boundary. As seen in Equation (29), the effect of the upper and lower boundaries can be studied separately. Here we study the effect of the lower boundary. We assume that R+ = 0 or ZH X, Vat - Air olARATI I H<'(qp) R-e--R -T-2z' q2 d A simple approximation can be obtained if k 1 81Pl1 (P + (ZR + ZT-2zl;)) >> 1. (3 1) The Hankel function is replaced by its asymptotic expansion: H,t''(u):exp(iu - - 7r), 1 u 1 - x. (32) The stationary phase method is applied to the integral in Equation (30). The main contribution to the integral comes from the point qs where d (q) = 0, using the phase function )(q) = iQp- (4)(ZR +ZT -2z) (33) The position of the saddle point is qs = kJ:P [P + (ZR + AT -2z)] (34) The reflection coefficient, evaluated at qs, is pulled out of the integration V V ikZ lARAT]R-(q)| Ht''(qp)e-Z+Z7 Iraq dq (35) 47r c The integral is proportional to the field produced by an image transmitter at

Zl = 2ZL-Zr (36) Again we use the integral representation exp(ik(elPl) D) =1 H)(qp)e-Pt', q dq' (37) with D=2+(ZR-Z)2]/2 (38)

to get the approximate formula V - V ikZo 01 AR AT I R - () '3 exp(ik(ú1, u1) " 2 D) Reflection from a uniform half-space. A simple formula for the reflection coefficient it-is obtained if the medium is uniform below z=z. We use the subscript,for the electromagnetic parameters of the region z < z,. For the solution y', we must have A-(e +R-e-(z-2z)), for z>z,, y/ =ea'Z for z < z,. (40) At the boundary z = z,, yr and-y/ must be continuous, giving pldz A(eZ/ +Re(Z[2ZI))=e tZl' A- (earl _R- -A /-2:l)) 1 Aft (41) By solving these equations, we find /](q) + p (q) (42) where B(q)= Jq -Slink, Bl(q)=4q -(úlpl),k À (43) In Equation (39), R- must be evaluated at q = qs where qs arks/: peon +(ZR _Z,)2]-/2, (44)

Equation (42) may be rewritten as R- (I) (q) FL (q) = k2 p (C1)L S1 2 (45) (q) + FL (q)] (q) + FL (q)] The leading term is proportional to (C1)L ú1, as expected from the Born approximation, Equation (20).

Alternative implementation. Other antenna orientations may be used to obtain the same information. In Figure 4, the antennas labeled 1 have a dipole moment tilted at an angle 0, from the tool axis; the antennas labeled 2 have a dipole moment tilted at an angle 02.

Transmitter Tl is activated, and the voltage measured on receiver R2 is denoted Vat. Transmitter T2 is then activated, and the voltage measured on receiver RI is denoted V2. The difference Vl2 - V21 gives the same information as the difference Vzx - Vxz in Figure 3.

The directions of the dipole moments of the coils, represented by unit vectors u,, u2, can be expressed, in the tool coordinates, as us = UX sinBl + uz costs, U2 = UX Sin B2 + UZ COSB2 (46) Therefore = = V12 V21 IUl ZRT U2 -I U2 ZRT Ul = = I(ux sinks + uz costs) ZRT (UX sin02 + UZ COSB2) = I(UX Sin B2 + UZ COSB2) ZRT (UX Sin Bl + UZ COS0I) (47) = I (sin O2 cos O1 -sin BI cos 02)(U Z Z RT U X U X Z RT Z) (48) = sin(02 - 01) (Vzx - Vxz) Other variations are readily apparent. In Figure 4, the positions of transmitter To and receiver Ri may be interchanged. The positions of transmitter T2 and receiverR2 may also be interchanged.

A simple extension of alternative measurement is for the antenna pair with 02 = 180 -0,, as illustrated in Figure 5. It is a two-step measurement: data are acquired in a "primary" tool position, when the magnetic dipoles of the transmitter and receiver are directed towards the upper boundary, and in the position when the tool is rotated 180 about its axis from the primary position, when the dipoles are oriented towards the lower boundary. Basically, the measurement is taken when the field, i. e., the dipoles, are in the bedding plane. The dipole

moment of transmitter 7 is tilted at an angle 0, from the tool axis; and receiver R is tilted at angle 02. First, transmitter 7 is turned on, and the voltage, Sup, on receiver R. is recorded.

Second, tool is rotated for 180 , transmitters is turned on, and the voltage, VdOwn on receiver R. is recorded. The difference voltage, Vup VdOwn, is used to obtain information about adjacent bed boundaries. Propagation-type measurements. Cross-dipole coupling (XZ) is the principal measurement providing the directional up/down sensitivity. In the LWD environment, propagation style measurements are typically used, since they are relatively easy to build. With a propagation tool, XZ propagation measurements do not have directionality. Directional information is obtained with tilted antennas (at least one transmitter and/or receiver antenna tilted) and uses the difference between the tool response when it is looking up and the tool response when it is looking down. These "up-down" differential responses produce simple responses to bed boundaries. Both induction and propagation style directional measurements are sensitive to anisotropy at certain dip angles (e.g., a=90 and a=O ). This sensitivity can easily be confused with the response of the tool to a nearby bed.

The present invention relates to directional measurements that are insensitive to anisotropy of the formation at a wide range of dip angles and over a wide frequency range.

Some embodiments of the invention are based on anti-symmetrized antenna configurations or systems. "Anti-symmetry" or "anti-symmetric" as used herein refers to a configuration in which sets of transmitter-receiver arrangements are provided in opposite orientations along the tool axis, and these sets can be correlated with a standard symmetry operation (e.g., translation, mirror plane, inversion, and rotation) with respect to a point on the tool axis or a symmetry plane perpendicular to the tool axis.

According to embodiments of the invention, the logging tools may be adapted to measure the ratio or difference between the tool response when it is "looking" up and the tool response when it is "looking" down. These "up-down" differential responses produce simple responses to bed boundaries similar to the crossed-dipole measurements obtained with induction-type measurements. Implementing a directional measurement with up/down sensitivity using a propagation type tool relies on the use of tilted antennas, because in phase shift or attenuation, directionality information is lost if the transmitter and receiver antenna axes are mutually perpendicular and the transmitter or receiver axis is aligned with the tool axis. Figure 6 shows an antenna configuration providing an essential building block for directional propagation-style measurements of the invention. In this configuration, a transmitter antenna T1 is spaced apart from two receivers, R1 and R2, along the tool axis. The receivers R1, R2 are tilted with respect to the tool axis. "Direction" of an antenna as used herein refers to the orientation of the magnetic dipole of an antenna when energized (i.e., when it functions as a transmitter), whether the antenna is actually used as a transmitter or a receiver.

The equivalent configuration to that shown in Figure 6 is one with only one receiver, R1 for example (not shown). The equivalency is derived in the measurement. An "up-down" measurement is made. That is, a measurement is made when the tool is looking "up" and another is made when the tool is looking "down." The measurement is the ratio of the readings when the tool is looking up and when the tool is looking down. The "up-down" measurement is borehole compensated, i.e., the electronic noise is removed.

Figure 7 shows several antenna configuration embodiments of the invention. Though all the configurations are useful for directional measurements, configuration c is particularly useful because, in the limit, if the tool spacing is much longer than the receiver spacing, this configuration approaches the basic building block of Figure 6. In these directional measurements, responses are dependent on the tilt angles of the antennas. Such dependence may create unnecessary errors in the measurements. Therefore, an "up-down" measurement is made as described above. The "up" measurement is then subtracted from the "down" measurement, or vice versa, to remove the effects of the axial components. Such "up-down" measurements allow better manageability of the sensitivities with respect to tilt angles. The antennas may be tilted at

various angles or transverse as shown in (Fig. 7F-I). In the transverse case the effective area of the transverse antenna should be greater compared to the effective area of an axial antenna. It should be noted that for some antenna configurations, such as the one shown in Fig. 7F, the up-

down measurement is not directional since resulting attenuation is 0, and phase shift is 0 or 180 .

Embodiments of the invention use an anti-symmetric transmitter-receiver arrangement to remove the dip dependence. Two tool configurations insensitive to anisotropy at any dip are shown in Figure 8. These configurations correspond to Figure 7B and 7C. Similar layouts can be derived for all the other configurations of Figure 7. In each case, transmitter T1 is energized and the phase shift and attenuation from the receivers near T2 is measured. Then transmitter T2 is energized and the phase shift and attenuation from the receivers near T1 is measured. The tool reading is the difference between these two measurements. Since the individual measurements are identical in a homogeneous medium at any angle and with any anisotropy, the tool readings is zero in a homogenous medium at any dip. The measurement responses in a three-layer formation are shown in Figure 9. The tool reading is zero far from the boundary, and there is little sensitivity to anisotropy close to the boundary. Separation in responses comes from the fact that propagation responses are not symmetric if the transmitter and receiver location are interchanged. Making an up-down measurement contains only the directional information, even close to the boundary, as shown in Figure 10. It should be observed that attenuation responses are practically overlapping for different dip if all antennas are in the same medium, similarly to ideal XZ-ZX induction measurement (described above). The phase shift measurements are also overlapping, although responses are double-valued in the conductive bed ( 1 Slm).

Knowing the process to derive these measurements, the equivalent configurations producing similar results are shown in Figure 11. losing the configuration of Figure 8A as an example, the receivers closer to the corresponding transmitter in the transmitter-receiver pair (e.g., Rl I is closer to Tl than R12 is, and R21 is closer to T2 than R22 is) would be referred to as the "near" receivers (i.e., Rll and R21), whereas the others (i.e., R12 and R22) as the "far" receivers. There are two options: (1) using the depth shifting (11A and 1 IB); and (2) using tool layouts (for example, 11C and 11D) that require addition, instead of subtraction of two basic propagation measurements. It should be noted that configurations from Figure 11C-D do not read zero in homogenous medium, as configurations from Figure 8 do.

If we look at the phase shift and attenuation from the configuration in Figure 8, we can show that the behavior of this propagation tool to a bed boundary is very similar to the behavior of the cross-term XZ. We start with the observation that In f it = 8.68 À Attn - i À PhaseShift, (50) where Attenuation is measured in dB and Phase Shift is measured in degrees.

For a tool at an angle of 90 to the bedding (horizontal tool), the voltage ratio measured when T1 is energized is: Vzzuear + V near Vzz f Vxz f.

while the voltage ratio measured when T2 is energized is: Vzz near + V near Vzz f -Vzx f (52) Taking the difference ofthe log ratios gives: near near near near near near far _ f ar In: Vzz + VXZ _ In: Vzz + VZX = In: VZZ + Vxz + Ink Vzz Vxz \ vZzfar _ vxzfar) ( vZzfar _ vZxfar) lo vZznear + V near) vZzfar _ vZxfar) Now the directionality of the measurement is in the cross terms and Vxz = -Vzx. If we are not too close to the boundaries then the cross terms will be much less than the direct coupling and we can approximate: V near + V near V far _ V far 2V 2V Lear +V near) (Uzzf VXzfar) Vzz Vzz Thus the measurements of this propagation tool will approximate the measurements made by an ideal directional induction tool.

The general rule for directional propagation measurement is: Let M(0T, DRI, HR2) be a propagation measurement with tilted antenna, where OT iS the transmitter tilt and HR} and OR2 are tilts of two receiver antennas. If M (0T, ORI, HR2) is the measurement with

transmitter and receivers switched, (i.e., M is the mirror image of M with respect to the central plane perpendicular to the tool axis, with all antenna orientations preserved) then (M(0T, DRI, DR2)- M (0T, DRI, DR2))UP - (M(0T, DRI, DR2)- M (fir, DRI, DR2))DOWN (54) is not sensitive to anisotropy at any dip and is only sensitive to boundaries (subscripts UP and DOWN denote measurements when the tool is oriented up or down, with all dipoles in the plane perpendicular to the bedding.

This concept is useful when the base measurement M(OT, DRI, DR2) performs well in horizontal wells. The concept also includes tools with all antennas tilted, including transverse antennas. Figure 12 shows another embodiment of the invention. This configuration also provides a basic building block for directional propagation measurements insensitive to anisotropy at any dip.

An alternative to the two-receiver embodiment of the invention relies on depth shifting, which complicates its use for geosteering. Figure 13 shows two embodiments of the invention presenting possible options. These two-antenna systems do not read zero in the homogenous anisotropic medium at any dip, similarly to tools from Figure 11. One advantage of these configurations is that they are borehole compensated, while other measurements rely on "up-

down" to remove the electronic drift.

While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments

can be devised which do not depart from the scope of the invention as disclosed herein.

Accordingly, the scope of the invention should be limited only by the attached claims.

Claims

1. A method for determining a parameter of a subsurface formation traversed by a borehole, the method comprising: i) disposing a logging instrument having a longitudinal axis within the borehole, said instrument equipped with: i. a first antenna system including a receiver antenna having its axis oriented in a first direction at angle 0/ with respect to the instrument axis, a second receiver antenna having its axis oriented in a second direction at angle 02 with respect to the instrument axis, and a first transmitter antenna located at the mid-point between said first and second receiver antennas and having its magnetic moment oriented in a third direction at angle 03 with respect to the instrument axis; and ii. a second antenna system forming the mirror image of said first antenna system with respect to the central plane perpendicular to the instrument axis such that a third receiver antenna has its axis oriented in said first direction at said angle 0/ with respect to the instrument axis, a fourth receiver antenna has its axis oriented in said second direction at said angle 82 with respect to the instrument axis and is separated from the third receiver antenna by the same distance as the first receiver antenna is separated from the second receiver antenna, and a second transmitter antenna is located at the mid-point between said third and fourth receiver antennas with its magnetic moment oriented in said third direction at said angle 03 with respect to the instrument axis; b) transmitting electromagnetic energy from the first transmitter antenna; j) measuring a signal associated with the transmitted energy at the third and fourth receiver antennas; k) calculating signal attenuation in dB and relative phase shift using the measured signal of step A; 1) transmitting electromagnetic energy from the second transmitter antenna;

m) measuring a signal associated with the transmitted energy at the first and second receiver antennas; n) calculating signal attenuation in dB and relative phase shift using the measured signal of step (I); and o) calculating a difference using values obtained from steps (d) and (g) to determine the formation parameter.

2. The method of claim 1, wherein angles (3;, O2 and O3 are between 0 and 90 degrees with respect to the instrument axis.

3. The method of claim 1, wherein angle H3 is 0 and angles OJ and 02 are between 0 and 90 degrees with respect to the instrument axis.

4. The method of claim 1, further comprising: i) rotating the instrument by 180 degrees about its longitudinal axis; j) repeating steps (b) thru (h); and k) calculating a difference between signals obtained from steps (h) and (I).

5. A method for determining a parameter of a subsurface formation traversed by a borehole, the method comprising: a) disposing a logging instrument having a longitudinal axis within the borehole, said instrument equipped with: i. a first antenna system including a receiver antenna having its axis oriented in a first direction at angle HI with respect to the instrument axis, a second receiver antenna having its axis oriented in a second direction at angle O2 with respect to the instrument axis, and a first transmitter antenna located at the mid-point between said first and second receiver antennas and having its magnetic moment oriented in a third direction at angle O3 with respect to the instrument axis; and ii. a second antenna system including a third receiver antenna having its axis oriented in said first direction at angle -0 with respect to the instrument axis, a fourth receiver antenna having its axis oriented in said second direction at angle -02 with respect to the instrument axis and separated

from the third receiver antenna by the same distance as the first receiver antenna is separated from the second receiver antenna, and a second transmitter antenna located at the mid-point between said third and fourth receiver antennas with its magnetic moment oriented in a third direction at angle -03 with respect to the instrument axis; b) transmitting electromagnetic energy from the first transmitter antenna; c) measuring a signal associated with the transmitted energy at the third and fourth receiver antennas; d) calculating signal attenuation in dB and relative phase shift using the measured signal of step (c); e) transmitting electromagnetic energy from the second transmitter antenna; f) measuring a signal associated with the transmitted energy at the first and second receiver antennas; g) calculating signal attenuation in dB and relative phase shift using the measured signal of step (f); and h) calculating a sum using values obtained from steps (d) and (g) to determine the formation parameter.

6. The method of claim 5, wherein angles 0;, O2 and O3 are between 0 and 90 degrees with respect to the instrument axis.

7. The method of claim 5, wherein angle O3 is O and angles 0 and H2 are between 0 and 90 degrees with respect to the instrument axis.

8. The method of claim 5, further comprising: d) rotating the instrument by 180 degrees about its longitudinal axis; e) repeating steps (b) thru (h); and f) calculating a difference between signals obtained from steps (h) and (j).

9. A method for determining a parameter of a subsurface formation traversed by a borehole, the method comprising: a) disposing a logging instrument having a longitudinal axis within the borehole, said instrument equipped with:

i. a first antenna system including a receiver antenna having its axis oriented in a first direction at angle 0/ with respect to the instrument axis, a second receiver antenna with its axis oriented in a second direction at angle H2 with respect to the instrument axis, and a first transmitter antenna having its magnetic moment oriented in a third direction at angle 03 with respect to the instrument axis; and ii. a second antenna system forming the mirror image of said first antenna system with respect to the central plane perpendicular to the instrument axis such that a third receiver antenna has its axis oriented in said first direction at said angle 8/ with respect to the instrument axis, a fourth receiver antenna has its axis oriented in said second direction at said angle 02 with respect to the instrument axis, and a second transmitter antenna has its magnetic moment oriented in said third direction at said angle O3 with respect to the instrument axis wherein the mid-point between said first and second transmitter antennas coincides with the mid-point between said first and third receiver antennas and the mid-point between said second and fourth receiver antennas; b) transmitting electromagnetic energy from the first transmitter antenna; c) measuring a signal associated with the transmitted energy at the third and fourth receiver antennas; d) calculating signal attenuation in dB and relative phase shift using the signal measured in step c); e) transmitting electromagnetic energy from the second transmitter antenna; f) measuring a signal associated with the transmitted energy at the first and second receiver antennas; g) calculating signal attenuation in dB and relative phase shift using the signal measured in step (I); and h) calculating a difference using values obtained from steps (d) and (g) to determine the formation parameter.

10. The method of claim 9, wherein angles 0, 02 and H3 are between O and 90 degrees with respect to the instrument axis.

11. The method of claim 9, wherein angle O3 iS O and angles 0 and O2 are between 0 and 90 degrees with respect to the instrument axis.

12. l he method of claim 9, further comprising: i) rotating the instrument by 180 degrees about its longitudinal axis; j) repeating steps (b) thru (h); and k) calculating a difference between signals obtained from steps (h) and (1)