GB2417783A - Method for characterising a subsurface formation - Google Patents

Abstract

A method for characterizing a subsurface formation with a logging instrument disposed in a borehole penetrating the formation, the logging instrument having a longitudinal axis and being equipped with at least a transmitter system and a receiver system that collectively comprise at least one set of upper antennas and one set of lower antennas, comprises the steps of: ```positioning the logging instrument within the borehole so that the transmitter system and receiver system are disposed in the vicinity of a formation boundary of interest; ```measuring the azimuthal orientation of the logging instrument; ```transmitting electromagnetic energy into the formation using the transmitter system; ```measuring signals associated with the electromagnetic energy transmitted by the transmitter system using the receiver system; ```composing a symmetrized directional measurement using the measured signals; and ```plotting the determined directional measurement as a function of depth for a plurality of different depths; and ```using a discontinuity in the rate of the change in the plotted directional measurement to identify the depth at which at least one of the upper and lower antennas crosses the formation boundary.

Description

METHODS AND APPARATUS FOR CHARACTERISING A SUBSURFACE

FORMATION

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 dipole-moment representations are used for electromagnetic measurements of subsurface formations and for defining the reservoir bedding structure and formation dip, as well as placing wells with respect to geological boundaries in a reservoir.

Background of the Related Art

Information that characterizes dips within a subsurface formation of interest is important for understanding the deposition environment of the sedimentary rocks, and for the development and execution of a well drilling plan for oil and gas exploration. The dip and strike of a formation bed can be extracted from seismic maps and from borehole images.

Seismic maps provide large-scale structural information, and borehole images provide information related to the local formation environment penetrated by the borehole. Both information types are useful information for hydrocarbon prospecting. Dip information extracted from borehole images, however, is usually of higher accuracy than that extracted from seismic maps.

Various well logging techniques are known in the field of hydrocarbon exploration and production for evaluating the subsurface formation penetrated by a borehole. These techniques typically use instruments or tools equipped with sources adapted to emit energy into the formation. In this description, "instrument" and "tool" will be used interchangeably to indicate, for example, an electromagnetic instrument (or tool), a wireline 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, an image or profile of the formation properties is obtained.

Commercial tools presently offered for producing electrical borehole images include the GeoVision Resistivity (GVR) tool and the Azimuthal Density Neutron (ADN) tool (both "while drilling" tools) and the Formation Microresistivity Imager (FMI) tool (a wireline tool), all owned and offered through logging services by Schlumberger, the assignee of the present invention. Dips are extracted from borehole images by identifying bed boundary interfaces on the image or by determining correlations between images measured at different sensors. The accuracy of the dip estimate from images is affected by many factors including the quality of the images, the vertical resolution of the tool, the skills of the geologist, and - in deviated wells - the accuracy of the borehole survey.

Among the above-mentioned imaging tools, the FMI tool provides the highest quality wellbore images due to its employment of measurement electrodes having small sizes (e.g., 0.2-inches). The accuracy of the apparent dip from the FMI tool's images is typically around 0.5 for typical high dip angles (or dip heights). For lower apparent dip, the accuracy degrades to several degrees. Furthermore, the FMI tool and other electrode tools work only in conductive mud.

The GVR tool provides real-time dip services, but only for apparent dips larger than 53 . Analysis of the obtained real-time image at the surface can remove this restriction, but since the image is acquired using one-inch electrode buttons, the quality of the image does not permit accurate determination of dip when relative dip is low. The fast rate of penetration can also affect the image quality and thus dip accuracy from the image. Like the FMI tool, the GVR tool works only in conductive mud.

For oil-based and synthetic muds, the Oil Base MicroImager (OBMI) tool, also by Schlumberger, may be used to provide image services. The quality of the image is poorer than that of the FMI tool, and the error on determined dips will be larger than that of the FMI tool. Currently, no electric image tools provide dip services in both conductive and insulating mud.

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

The logging instruments are disposed within a borehole on a wireline or via a drill string "while drilling" 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 Figure 1).

Induction tools measure the resistivity (or conductivity) of the formation by measuring the voltage induced in the receiver antenna(s) as a result of magnetic flux induced by AC currents flowing through the emitting (or transmitter) antenna. So-called propagation tools operate in a similar fashion, but typically at higher frequencies than do induction tools for comparable antenna spacings (about 1 o6 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 l 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 used 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.

The antennas operate on the principle that a coil carrying an AC current (e.g., a transmitter coil) generates a magnetic field. The electromagnetic energy from the transmitter antenna of a logging tool disposed in a borehole is transmitted into the surrounding regions of the formation, and this transmission induces an eddy current flowing in the formation around the transmitter (see Figure 2A). The eddy current induced in the formation, which is a function of the formation's resistivity, generates a magnetic field that in turn induces an electrical voltage in the receiver antennas. If a pair of spaced-apart receivers is 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, up) and amplitude ratio (attenuation, A) from the two receivers can be used to derive the resistivity of the formation. The detected phase shift (P) 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 dipole- moments (LMD). Figure 2A presents a simplified representation of electromagnetic (EM) energy flowing from such a logging instrument disposed in a borehole portion or segment that penetrates a subsurface formation in a direction perpendicular to a formation bed of interest. This is not, however, an accurate depiction of all the numerous segments that make up a borehole - particularly when the borehole has been directionally-drilled as described below. Thus, segments of a borehole often penetrate formation layers at an angle other than degrees, as shown in Figure 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) BA and the normal N to the plane P of a formation bed of interest.

It is well known that the response of a logging tool will be affected by the Connation bedding structures surrounding the segment of the borehole in which the tool is disposed. For electromagnetic logging tools, this is known as the shoulder bed effect. Accordingly, the responses of conventional induction and propagation tools having LMD antennas are affected by the formation bedding and its dips. However, such tools are inherently non-directional and, therefore, are incapable of providing azimuthal information about the bedding structure.

Thus, commercially available wireline induction and LWD propagation resistivity tools are presently unable to accurately determine dip.

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 tool or borehole. These instruments are thus implemented with a transverse or tilted magnetic dipole-moment (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, e.g., in: U.S. Patent 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. The response of such tools will depend on the azimuthal orientation of the tool in a dipping formation. Therefore, useful information about earth structure, in particular the dip and strike, can be obtained from a proper analysis of azimuthal or directional measurements.

U.S. Patent Application Publication No. 2003/0055565 to Omeragic, presently assigned to Schlumberger, derives closed-form expressions for the calculation of anisotropic formation parameters from tri-axial induction measurements. U.S. Patent No. 6,163,155 to Bittar, assigned to Dresser, discloses a method and apparatus for simultaneously determining the horizontal resistivity, vertical resistivity, and relative dip angle for anisotropic earth formations by software rotation of orthogonal coils to achieve decoupling between the horizontal and vertical resistivity. U. S. Patent No. 6,556,016 to Gao et al, assigned to Halliburton, discloses an induction method for determining approximate dip angle of anisotropic earth formation utilizing tri-axial measurements. These applications are limited to formations with anisotropy.

DEFINITIONS

Certain terms are defined throughout this description as they are first used, while certain other terms used in this description are defined below: "Apparent dip" means the angle that a (dipping) bed makes a horizontal plane, as measured in any direction other than perpendicular to the strike.

"Bed" or Bedding" means the stratification or layering of sediment or deposits that typically occurs in subsurface formations (which are typically rock).

"Binning" means the sorting of measured waveforms - particularly formation responses to transmitted electromagnetic energy - into groups based on values of parameters, and can be performed for one parameter determined from the waveform or for several parameters. An example of a binning criterion can be frequency or period of a component of the waveform. Another example is the association of the measured waveform with the azimuthal angle of the tool orientation "Dip" or "dip angle" means the angle that a (dipping) bed makes with a horizontal plane, as measured perpendicular to the strike.

"Inversion" or "invert" means deriving a model (a.k.a. "inversion model") from measured data (e.g., logging data) that produces responses most consistent with the measured data according to certain criteria As an example, a measured waveform can be used to construct the best subsurface formation model which produces responses that best fits the measurement through iteratively adjusting the model parameters.

"Relative dip" or "relative dip angle" means the angle between the borehole axis (or tool axis) and the normal direction to a plane defined by a formation bed of interest.

"Symmetry" or "symmetric," as used herein, refers to a configuration in which sets of transmitter-receiver arrangements are provided in opposite orientations along the longitudinal axis of a tool (e.g., 0, 180 -0), such that these transmitter-receiver 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.

Symmetrization refers to a procedure in which responses of symmetric partners are added or subtracted to generate a combined response.

"Toolface" refers to the angular orientation of an instrument about its longitudinal axis, and represents an angle subtended between a selected reference on the instrument's housing (e.g., a drill collar) and either the gravitationally uppermost wall of the wellbore or geographic north. s

SUMMARY OF THE INVENTION

According to one aspect of the present invention, there is provided a method for characterizing a subsurface formation with a logging instrument disposed in a borehole penetrating the formation, the logging instrument having a longitudinal axis and being equipped with at least a transmitter system and a receiver system that collectively comprise at least one set of upper antennas and one set of lower antennas, the method comprising the steps of: positioning the logging instrument within the borehole so that the transmitter system and receiver system are disposed in the vicinity of a formation boundary of interest; measuring the azimuthal orientation of the logging instrument; transmitting electromagnetic energy into the formation using the transmitter system; measuring signals associated with the electromagnetic energy transmitted by the transmitter system using the receiver system; composing a symmetrized directional measurement using the measured signals; and plotting the determined directional measurement as a function of depth for a plurality of different depths; and using a discontinuity in the rate of the change in the plotted directional measurement to identify the depth at which at least one of the upper and lower antennas crosses the formation boundary.

According to another aspect of the present invention, there is provided a logging apparatus for characterizing a subsurface formation penetrated by a borehole, including a body adapted for conveyance in the borehole and having a longitudinal axis. The body of the logging apparatus may be adapted for conveyance and rotation within a drill string, and for conveyance with a wireline. A transmitter system is carried by the body for transmitting electromagnetic energy into the formation. A receiver system is carried by the body for measuring signals associated with the electromagnetic energy transmitted by the transmitter system. Means are also provided for determining the relative azimuth of a formation boundary of interest in the vicinity of the borehole, for composing a symmetrized directional measurement using signals measured by the receiver system and the relative boundary azimuth determined by the azimuth-determining means, and for determining the relative dip of the formation boundary using the composed directional measurement.

In a particular embodiment of the inventive apparatus, the transmitter system includes at least one antenna having a magnetic dipole-moment that is tilted with respect to the axis of the logging instrument by an angle 0, and the receiver system includes at least one antenna having a magnetic dipole-moment that is tilted with respect to the axis of the logging instrument by an angle 180-0.

In a further embodiment of the inventive apparatus, the transmitter system includes at least first and second transmitter antennas, and the receiver system includes at least first and second receiver antennas. The antennas are oriented such that the first transmitter and first receiver antennas define a first symmetric antenna pair, and the second transmitter and second receiver antennas define a second symmetric antenna pair.

In a further embodiment of the inventive apparatus, the transmitter system includes two transmitter antennas, with each transmitter antenna having a magnetic dipole-moment aligned with the instrument axis. The receiver system includes two transverse, mutually orthogonal receiver antennas, with the two receiver antennas being positioned between the two transmitter antennas. Alternatively, the apparatus may be configures with reciprocal receivers and transmitters (two transmitter antennas being positioned between the two receiver antennas).

In a particular embodiment, the transmitter system includes tri-axial transmitter antennas, and the receiver system includes tri-axial receiver antennas.

The azimuth-determining means may include a tool face sensor, and/or a computer- readable medium having computer-executable instructions for determining the relative azimuth of the formation boundary of interest.

The composing means includes, in one embodiment, a computer-readable medium having computer-executable instructions for composing a symmetrized directional measurement using signals measured by the receiver system and the relative boundary azimuth determined by the azimuth-determining means.

The relative dip-determining means may include a computer-readable medium having computer-executable instructions for determining the relative dip of the formation boundary using the composed directional measurement.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the above recited features and advantages of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to the embodiments thereof that are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments.

Figure 1 shows schematic diagrams of prior art induction or propagation tools.

Figures 2A and 2B are elevational views showing eddy currents induced by a logging tool in a borehole penetrating a formation without and with a relative dip, respectively.

Figure 3 is an elevational representation of a conventional rotary drilling string in which the present invention may be employed to advantage.

Figure 4 is a schematic representation of a basic directional measurement logging tool having symmetrical transmitter and receiver antenna pairs.

Figure 5 is a schematic representation of a directional measurement logging tool disposed in a borehole segment that lies within a single formation bed, whereby symmetrized directional measurements are designed to be insensitive to dip a and anisotropy.

Figure 6 is a schematic representation of a directional measurement logging tool disposed in a borehole segment that traverses a bed boundary to penetrate two formation beds, whereby symmetrized directional measurements nearly constant and are proportional to dip for a given resistivity profile when the transmitter(s) and receiver(s) are positioned on opposite sides of the bed boundary.

Figure 7 is a resistivity plot depicting a single formation boundary that divides two adjacent formation beds.

Figures 8A-8C show plots representing the formation responses (conventional resistivity and symmetrized directional measurements) to electromagnetic energy transmitted by a logging tool oriented along a borehole/tool axis, with the logging tool having antennas positioned on either side of the boundary.

Figure 9 shows the response of symmetrized directional propagation signals plotted as a function of true vertical depth (TVD) for different dip angles when crossing a bed boundary, according to one aspect of the present invention.

Figure 10 shows a similar response to that of Figure 9, but the propagation signals are normalized by dip angle, on a logarithmic scale.

Figure 1 1 shows a similar normalized response to that of Figure 10, on a linear scale.

Figure 12 shows a similar response to that of Figure 9, but representing a single transmitter-receiver (TR) pair prior to symmetrization.

Figure 13 shows a similar response to that of Figure 10, but representing two co- located TR pairs.

Figure 14 shows the equivalent induction tool response for a symmetrized TR pair (XZ-ZX measurement), normalized by dip angle.

Figure 15 is a work flow diagram for dip determination in accordance with one aspect of the present invention.

DETAILED DESCRIPTION

Figure 3 illustrates a conventional drilling rig and drill string in which the present invention can be utilized to advantage. A land-based platform and derrick assembly 10 are positioned over a wellbore 11 penetrating a subsurface formation F. In the illustrated embodiment, the wellbore 11 is formed by rotary drilling in a manner that is well known.

Those of ordinary skill in the art given the benefit of this disclosure will appreciate, however, that the present invention also finds application in directional drilling applications as well as rotary drilling, and is not limited to land-based rigs. It will further be appreciated that the present invention is not limited to "while-drilling" applications, but also has utility in wireline applications (as described further below).

A drill string 12 is suspended within the wellbore 11 and includes a drill bit 15 at its lower end. The drill string 12 is rotated by a rotary table 16, energized by means not shown, which engages a kelly 17 at the upper end of the drill string. The drill string 12 is suspended from a hook 18, attached to a traveling block (also not shown), through the kelly 17 and a rotary swivel 19 which permits rotation of the drill string relative to the hook.

Drilling fluid or mud 26 is stored in a pit 27 formed at the well site. A pump 29 delivers the drilling fluid 26 to the interior of the drill string 12 via a port in the swivel 19, inducing the drilling fluid to flow downwardly through the drill string 12 as indicated by the directional arrow 9. The drilling fluid exits the drill string 12 via ports in the drill bit 15, and then circulates upwardly through the region between the outside of the drill string and the wall of the wellbore, called the annulus, as indicated by the direction arrows 32. In this manner, the drilling fluid lubricates the drill bit 15 and carries formation cuttings up to the surface as it is returned to the pit 27 for recirculation.

The drill string 12 further includes a bottomhole assembly, generally referred to as 34, near the drill bit 15 (in other words, within several drill collar lengths from the drill bit). The bottomhole assembly includes capabilities for measuring, processing, and storing information, as well as communicating with the surface. The bottomhole assembly 34 thus includes, among other things, a measuring and local communications apparatus 36 for determining and communicating the resistivity of the formation F surrounding the wellbore 11. The communications apparatus 36, also known as a resistivity tool, includes a first pair of transmitting / receiving antennas T. R. as well as a second pair of transmitting / receiving antennas T', R'. The second pair of antennas T', R' are symmetric with respect to the first pair of antennas T. R. as is described herein. The resistivity tool 36 further includes a controller to control the acquisition of data, as is known in the art.

The BHA 34 further includes instruments housed within drill collars 38, 39 for performing various other measurement functions, such as measurement of the natural radiation, density (gamma ray or neutron), and pore pressure of the formation F. At least some of the drill collars are equipped with stabilizers 37, as are well known in the art.

A surface/local communications subassembly 40 is also included in the BHA 34, just above the drill collar 39. The subassembly 40 includes a toroidal antenna 42 used for local communication with the resistivity tool 36 (although other known local-communication means may be employed to advantage), and a known type of acoustic telemetry system that communicates with a similar system (not shown) at the earth's surface via signals carried in the drilling fluid or mud. Thus, the telemetry system in the subassembly 40 includes an acoustic transmitter that generates an acoustic signal in the drilling fluid (a.k.a., "mud-pulse") that is representative of measured downhole parameters.

The generated acoustical signal is received at the surface by transducers represented by reference numeral 31. The transducers, for example, piezoelectric transducers, convert the received acoustical signals to electronic signals. The output of the transducers 31 is coupled to an uphole receiving subsystem 90, which demodulates the transmitted signals. The output of the receiving subsystem 90 is then coupled to a computer processor 85 and a recorder 45.

The processor 85 may be used to determine the formation resistivity profile (among other things) on a "real time" basis while logging or subsequently by accessing the recorded data from the recorder 45. The computer processor is coupled to a monitor 92 that employs a graphical user interface ("GUI") through which the measured downhole parameters and particular results derived therefrom (e.g., resistivity profiles) are graphically presented to a user.

An uphole transmitting system 95 is also provided for receiving input commands from the user (e.g., via the GUI in monitor 92), and is operative to selectively interrupt the operation of the pump 29 in a manner that is detectable by transducers 99 in the subassembly 40. In this manner, there is two-way communication between the subassembly 40 and the uphole equipment. A suitable subassembly 40 is described in greater detail in U.S. Patents Nos. 5,235,285 and 5,517,464, both of which are assigned to the assignee of the present invention. Those skilled in the art will appreciate that alternative acoustic techniques, as well as other telemetry means (e.g., electromechanical, electromagnetic), can be employed for communication with the surface.

Two types of coil antennas are used to compose measurements with directional sensitivity. One type achieves its directional sensitivity by having the antenna either offset, e.g., from the center of a logging tool's longitudinal axis, or partially covered. Directional measurements can also be made with at least one antenna configured so that its magnetic dipole-moment is not aligned with the longitudinal axis of the tool carrying the antenna. The present invention relates to the second type of directionally-sensitive antenna.

Figure 4 schematically illustrates a basic resistivity tool 36 for directional electromagnetic (EM) wave measurement. The tool 36 includes a transmitter antenna T that fires an EM wave of some frequency f and a receiver antenna R that is some distance L away.

Also shown is the symmetric pair (T', R') in accordance with the teachings of U.S. Patent Application Publication No. 20003/0085707 ("Minerbo et al") assigned to the assignee of the present invention. For clarity and simplification, the discussion that follows will be limited to the transmitter antenna T and the receiver antenna R. although it is generally applicable to the symmetric antenna pair, T' and R'. It should be noted that although the tiled dipole-moment of the two symmetrization pairs are on the same plane in Figure 4, this is not required in the current invention. As will be clear in the subsequent discussion, signals from two pairs that have their dipole-moment in different planes can still be added together to achieve equivalent results if the extracted coefficients or directional phase-shift or attenuation are used in the symmetrization operation. In operation, the receiver antenna R will register a voltage VRT induced

by the EM wave from the transmitter antenna T and its secondary currents produced in the formation penetrated by the borehole containing the logging tool 36. Both antennas T and R are fixed on the tool 36 and thus physically rotate with the tool. This is contrasted with the alternative wireline application of the present invention, wherein virtual antennas are "rotated" with software (i.e., the measured voltage signals are "rotated" about the axis of the logging instrument to a plane that is perpendicular to the boundary of interest using a rotation matrix corresponding to the determined boundary azimuth).

The tool 36 is equipped with a toolface sensor within one of the drill collars 38, 39 for continuously indicating the azimuthal orientation of the logging instrument, and a controller for controlling the first and second transmitter-receiver antenna pairs so as to selectively transmit electromagnetic energy into the formation and measure the voltage signals associated with the transmitted electromagnetic energy as a function of the azimuthal orientation of the logging instrument. The toolface sensor employs one of: magnetometers to indicate the azimuthal orientation of the logging instrument with respect to earth's magnetic north; gravitation sensors to indicate the azimuthal orientation of the logging instrument with respect to the earth's gravity vector; or other suitable means that are known in the art. The antenna orientations may be assumed to form angles f3T for the transmitter antenna T. and OR for the receiver antenna R. The azimuthal variation of the coupling voltage as the tool rotates can then be expressed in terms of the coupling of Cartesian components of the magnetic dipole-moments as: vRr ( ) [ it cos OT COS BR + 2 ( V,y + Vyy) si n AT sin9R] +[V sin OT COS0R + Vet COS0TSiNlBR]COS+[VY Sin6'T COSBR + VY CO T R] +[2 (Vie + VrY)sin6T sinBR]sin 2 + [2 (Via - Vyy)sin61T sin 6'R]cos2 = Co(07,oR)+CIc(eT,oR)Cos+Cls(0T'6R)sin+C2c(9T,oR)Cos2+C2s(oTtoR) (1.1) where a set of complex coefficients Co,Cc,Csc2cc2s has been defined to represent the amplitudes of the different components of the measured formation response. The complex coefficients are thus defined as: CO (f9T 69R) = [V= COS O7. COS fJR + 2 (Vie + Vyy) sin {1rsin0R] CIC (f97 OR) e [Vie sin f9T COS f9R + V, COS IT sin6R] CIS((9T,OR) = [Vat sin6,r cos BR + VY COS f9T sin BR] (all (OT, OR) = [ 2 ( Vie Vyy) si n 6'T s in OR] C2s(H7.,0R) = [2 (Vy0r + Vxy)SinOT sin OR] (1.2) According to one aspect of the present invention, it is recognized that these coefficients are functions of formation resistivity, borehole deviation, and azimuth angle at the tool location.

With a symmetrization operation, i.e., (LIT BR), Eq. (1. 1) is simplified to: V(O _ VR] ((/)' BT FIR) VRT ((/)' fJR BT) [ vzx] sin(0T BR) cos 46 + 2[V,,z -V<,, ] sin(oT -BR) sin CIC(RT,CR)COSI + C''(67,RR)sin) (1.3) All the second-order harmonics (C2c, C2s) disappear after the subtraction because they are symmetric with respect to the exchange of transmitter and receiver tilt angles. Thus symmetrization simplifies azimuthal variation of the anti-symmetrized signal.

At this stage, the reference point of the azimuthal angle is arbitrary. For planner geometry, if we choose angle reference point as the direction projected by the normal vector of the bedding plane to the tool plane, then Vie = Vy = 0 by symmetry and V(O would have a pure cosdependence. In actual application, the orientation of the bedding is unknown. However, given any reference, the bedding orientation can be calculated by: = tang [|Cls (AT BIER)|] = tans' [| Via - Vy | bed ICIC(0T,PR)| |V-Em | (1.4) With rotation //bed X will be normal to the bedding and thus V(O is exactly [Vie - V" ] aside from a multiplication constant 2 sing - OR) . Once the voltage at each of the receiver coils due to each of the transmitter coils is determined, the total measurement can be determined: by adding the voltages in the case of an induction tool; or by taking the complex ratio of the voltages in the case of a propagation tool. For example, for the propagation logging device of FIG. 4, the absolute value of the voltage at each receiver can be obtained as the square root of the sum of squares of the real and imaginary parts of the complex voltage (Eq. 1.1), and the ratio of the absolute values provides the attenuation, from which the attenuation-determined resistivity Red can be obtained (resistivity of formations at a relatively deep depth of investigation around the receivers). The phase for each receiver is obtained from the arc-tangent of the ratio of the imaginary and real parts of the complex voltage, and the phase shift is the difference in phase at the two receivers. The phase-shift-determined resistivity RpS can then be obtained (resistivity of formations at a relatively shallow depth of investigation around the receivers).

For propagation-style measurements, the difference of the logarithmic of the voltages (or the ratio) between two measurements is taken. Following the teachings of Minerbo et al, we take the amplitude of the azimuthal response, i.e., the difference in phase-shift and attenuation of measurement, at angle and that at (+ +180), evaluated at the maximum of the voltage response. This leads to approximately, from Eqs. (1.1-2): VRT() Co(oT'aR)+Clc(eT,oR) CoSI7+Cl&(6T'0R)Sin+C2c(eT'0R)CoS2+C2s(eT'0R)Sin2 VRT(180+47) CO(7',RR)C,c(6T'0R)cos) - c,3(r'0R)sin+c2c(07'0R)cos2+c2s(Br,ER)sin2 1+2 Co(8r,R)+CIc(6r'R)COS+CIs(6r'6R)sin} 0(67''9R) +C2c(0r'0R)cos2 +C2,(0T,R)sin 2' [Vxz sin0T coSBR + Vzx cos0TsinBR]cos+[Vyz sin0T coSBR + Vy coS0TsinBR] sin) =1+2 1 1 1 Vzz COS6T COS0R + 2 [VXX + Vyy]sin BTsin0R + 2 [[Vyx + Vxy]sin BTsinBR sin 2 + 2 [[VXX - Vyy]sin RTsinBR COS 2 (1.5) The maximum of I V I is achieved at ps = 0 if x is chosen to be the direction normal to the bedding. Evaluated at the angle = 0, Eq. (1.5) produces: VR T (O) CO (6JT 69R) +CI C ([9T R) - - 1+2 VRT(180) Co(0r,R)+C2c(0T,R) 1 [Vxz sin T cos BR + VZX cos OTsinBR] = +2 VZZ C S0T C S0R + V Sin0Tsin0R (1.6) This, however, is still not the pure xz-zx type of responses that are desired, i.e., which are insensitive to bedding anisotropy and dip angle.

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.

Now with a symmetrization procedure (6JT G}R), as prescribed by Minerbo et al, we have: VRT (0P OT (9R) VRT (1 80'R (}T) [V.r, V=, ] sill(OT -R) - 1 + 2 VRT (1 8O, {77 R) VR7 (0, 6]R {}T) ZZ T f9R + VXX sin {7T sinBR (1. 7) This again is similar to the response of the induction type, although the denominator still has some components that are not simply [xz-zx]. This proves that the symmetrization procedure for propagation style measurement can produce responses similar to that of the symmetrized induction type, but not a pure type. It is also true that propagation measurement can be done at two arbitrary orientations in the azimuthal response.

Thus, the orientation of the bedding is determined by examining the azimuthal dependence of the logging tool response. One technique for extracting the different components (i.e., coefficients) of the azimuthal response is disclosed in a U.S. patent application by Li et al. entitled "Directional Electromagnetic Wave Resistivity Apparatus and Method" filed on April 21, 2004 and assigned Serial No. 10/709,212, wherein the measured azimuthal variation of a signal is fitted to approximate functions. In particular, the azimuthal response is fitted according to extracts of the relevant sin and cos terms of the directional measurements, taken iteratively. Such a fitting algorithm is done in a digital signal processor through an integer algorithm so it is fast enough to be performed for all channels within 4-ms of sampling time. The precise use of azimuth angle information, and the randomization of the acquisition sequences, makes the algorithm robust to tolerate irregular tool rotation as well as stick-and-slip under rough drilling conditions. This way, all the data are used to obtain the up/down signal instead of only the data in the two bins, thus improving the signal-to-noise ratio in the measurement. The use of precise azimuth angles also makes the determined bedding orientation more precise.

The detail algorithm can be described as follows.

Floating point implementation: starting with an initial value of matrix Pa and vector UO, then proceeding to the algorithm described below with measurement y(,) and basis r = (I cost, sing, cos2I, sin246,)T, where P is a matrix of dimension M x M and U and r are vectors of dimension M. M is the dimension of the basis function. After iteration N. then U will converge to a value which represents the coefficients of the expression. This algorithm is stable and convergence is usually achieved within 10-15 iterations.

The detailed algorithm is shown below: initialize PO and UO; for m = 1 to Nsamples Pm l rm l rn-| Pn-] m 1 + rm-1 Pal_| rn, I Um Um l -Pm rn'-l (Ym-l -Um I rm I) next m; return (U); where: N samples is the total number of samples acquired in one cycle, M is the dimension of the approximate function vector (number of approximation functions), U is the vector of fitting coefficients of dimension M, r is the vector of approximate function values at each measure position of dimension M, and P is a matrix of dimension M x M. In many cases, floating point implementation will be too expensive to perform with presently available downhole cpu's because there may be hundreds of channels to be fitted and the data acquisition for each azimuth angle has to be quite short (ms) in order for the angle to be accurate at higher rotation speed. In these situations, an integer implementation can be applied, with some modification, to improve accuracy (e.g., use 32-bits for multiplication), perform resealing to avoid overflow, and to accelerate convergence. The values of the basis function can also be pre-generated and stored in memory so as to be interpolated later to obtain the value for the true angle , . Since only the relevant signals are extracted in the fitting technique, only the useful coefficients need to be saved. Thus, in this case, it's only necessary to save 5 coefficients, as compared to 32 if one were to bin all the data using the 32-bin example. Those skilled in the art will appreciate the advantages of the inventive technique which include the accuracy of the extracted signal and a particular improvement in the accuracy of the azimuthal angle.

From these fitting coefficients, the bedding boundary azimuthal (strike) angle may be determined.

Figure 5 is a schematic representation of a directional measurement logging tool 36' having an axis BA and being disposed in a borehole segment 11 that lies within a single formation bed B2. The bed B2 is separated from overlying bed Be by a boundary P', and is separated from an underlying bed B3 by a boundary P2. In this configuration, symmetrized directional measurements obtained from couplings TIMER' and T2-R2 (according to Minerbo at al) have proven to be insensitive to dip a and anisotropy.

Figure 6, however, illustrates a configuration wherein such directional measurements are extremely sensitive to dip. Thus, Figure 6 is a schematic representation of a directional measurement logging tool 36" having an axis BA and disposed in a borehole segment 11' that traverses a bed boundary P'. The borehole 11' penetrates two formation beds Be, B2, and the logging tool is configured (and positioned) so that transmitter To and receiver R2 are disposed on one side of the boundary Pi, while transmitter T2 and receiver Rat are disposed on the other side of the boundary P'. In such an arrangement, the symmetrized directional measurements obtained with tool 36" are nearly constant and are proportional to dip for given a resistivity profile.

Figure 7 is a resistivity plot depicting a borehole segment axis BA that traverses a single formation boundary PI that divides two adjacent formation beds Be, B2. In this example, the adjacent formation beds exhibit a 20/1 Am resistivity transition across the boundary P', and a dip a=5 .

Figures 8A-8C show plots representing the formation responses to electromagnetic energy transmitted by a logging tool as oriented in Figure 7, with the antennas of the logging tool being on opposite ides of the boundary P' (in similar fashion to Figure 6). Thus, Figure 8A depicts a conventionally-determined resistivity profile across beds Be, B2. Figures 8B, 8C depict attenuation and phase shift, respectively, resulting from symmetrized directional measurements with the antennas located across the formation boundary (as in Figure 7).

Accordingly, the portions of the plotted curves in Figures 8B and 8C that are nearly constant (i.e., the nearly "flat" lower segments) represent the measurements taken while the antennas were positioned on either side of the boundary Pi.

The symmetrized directional response was found to be insensitive to the dip angles and anisotropy for high relatively dip angle (e.g., >60 ) and when both transmitter and receivers are on the same side of the boundary (see Minerbo at al). For smaller relative dip (e.g., <40 ), it turns out that the response of the symmetric directional measurements (xz-zx type) is directly proportional to the relative dip angle, if transmitters and receivers are on opposite sides of the boundary, as will be described below.

Figure 9 shows the response of a directional propagation signal at lOOkHz, plotted as a function of the tool position in true vertical depth (TVD) when crossing from a bed of 1 ohm-m to a bed of 10 ohm-m. The signal gradually increases as the relative dip angle increases. At zero relative dip, there is no variation of signal coming out of the structure as tool rotates because of symmetry. Thus the signal is null. However, as soon as the relative dip becomes non-zero, a finite signal will be generated. In fact, as observed from the plot, even at 1 relative dip, the phase shift signal is slightly larger than 1 , which is quite sizeable considering the accuracy of the measurement that can be achieved with the present-day electronics.

Figure 10 shows the same response as Figure 9 for relative dip angles up to 30 , but with the phase-shift and attenuation signals normalized by the relative dip angle. The normalized curves stack on top of each other, independent of the dip angle. This is especially true in the middle when the transmitter and receiver are on opposite side of the bed boundary.

What this means is that the phase shift and attenuation signal from the symmetrized response is linearly proportional to the dip angle and this proportionality constant is almost independent of the tool position when T and R are on opposite side of the boundary. Of course the linear factor depends on TR spacing, measurement frequency and the resistivity of the two beds-mostly on the value of the more conductive part of the two beds.

Dip angle-normalized responses of the 100 kHz directional measurements are again presented in Figure 11 including angles up to 70 , on a linear scale. The scaling coefficient for a phase shift of 50 is shown to be 2% smaller, and for 70 is 6% smaller, than for smaller phase shift angles. Attenuations are more sensitive, showing changes of 15% and 40% at 50 and 70 , respectively.

It is important to note that such simplicity of response is a direct result of symmetrization. Figure 12 shows the response of the individual TRR pairs before symmetrization, under exactly the same configuration as in Figure 9. The responses are much more complex. The linear relationship between measured signals and the formation dip that we clearly see for symmetrized TR configurations no longer holds. Symmetrization simplifies the tool response to bed boundary in high angle wells and it again does the same thing for dip sensitivity. The underlying physics are related.

Figure 9-12 are for TR antenna pairs not located at the same physical spaces, even though the TR distance is fixed for the two pair as required for symmetrization. Figure 13 shows the normalized response for two colocated TR pairs. This is to be compared with Figure 10. The response of colocated and non-colocated TR pairs to dip is quite similar.

Figure 14 shows the equivalent induction tool response of (xz-zx) symmetric pairs at 10kHz, normalized to the apparent dip angle. Both the real and imaginary portions of the receiver voltage can be scaled as dip, to a very good approximation. The proportionality factor is almost a constant for the real part of the voltage and varies linearly with distance, when the transmitter and receiver pair are on two sides of the interface.

The simple relationship of symmetrized directional response to relative dip will allow for accurate determination of the relative dip and azimuth of the structure bedding. For example, at dip=1 , the phase-shift signal from Figure 9 is about 0.09 dB and 1.6 . Even with the electronics, the phase-shift and attenuation can be measured to 0.02 and 0.004 dB, respectively. This means that dip can be measured with an accuracy of 0. 01 -0.03 , if such accuracy is required - in which case very accurate sensors will be utilized. By comparison, this degree of accuracy is two orders of magnitude smaller than what known borehole imaging tools can provide. More realistically, taking into account the anticipated environmental effect, it is possible to measure relative dips with an accuracy of 10%, even at very low relative dip angles.

Once the relative dip is determined, the directional response can be used to derive the distance to boundary estimate when the sensors are away from the boundary.

It is also interesting to note the drastic difference between the tool response when the receivers and the transmitters are on opposite sides of the boundary and that when both transmitters and receivers are on the same side. The slope of the responses as a function of depth abruptly changes when the crossing occurs. This change can be used to identify the bed boundary position accurately.

The technique applies to both wireline induction and LWD propagation tools, independent of the method of conveyance. For "while drilling" applications, this information can be obtained in real-time by sending the measurements up-hole and analyzing them at the surface, or by analyzing the data downhole first and then sending the dip structure information up to the surface.

Those skilled in the relevant art will appreciate that while the response depends on bedding properties such as resistivities, it also depends the receiver-transmitter spacing and frequency.

A particular aspect of the present invention will now be described, with reference to Figure 15. Real-time directional measurements are acquired, the bed boundary azimuth is determined, and directional measurements are composed (all as described above), using a logging instrument disposed in a borehole in the vicinity of one or more beds of interest (box 110).

Resistivities of the formation on each side of the identified boundary are determined using standard resistivity measurements, induction or propagation (box 105). Selected directional channels from the acquired directional voltage signals are useful for precisely determining the dip angle and location of the boundary. The determined dip angle may be confirmed using different directional channels from the acquired directional voltage signals, using a look-up table, or by inversion techniques (box 120). The simple chart or look-up table procedure is originally thought for single boundary dip determination.

A symmetrized measurement response is generated, and this response is scaled based on known resistivities, to predict the dip angle of the formation bed (i.e., a boundary for the bed) of interest. The scaling step corresponds to a scaling coefficient. A boundary for the formation bed of interest is identified by moving the logging instrument within the borehole, generating new directional measurements and symmetrized response, scaling the symmetrized response, and observing changes in the response (box 120).

In one embodiment, the apparent dip-determining step comprises using a look-up table. In this instance, the method further includes the steps of determining a scaling factor for a selected pair of determined resistivities by calculating the boundary directional-response per unit dip, determining the relative dip by dividing the composed directional measurement by the scaling factor, and using a look-up table for the selected pair of resistivities and the determined relative dip and azimuth to determine the true dip. The look- up table can be pre- computed for numerous resistivity pairs. Then from apparent resistivities, we can easily find in the table how many units (de", dB or Volts) per deg dip we have. The alternative is to build a 3D look-up table with the dip included, and employ the simple look-up table procedure.

Alternatively, a scaling factor is determined from the determined resistivity profile by calculating the boundary directional response per unit dip, and determining the relative dip by dividing the composed directional measurement by the scaling factor.

In another embodiment, the relative dip-determining step comprises an inversion. The inversion preferably includes the steps of selecting one or more directional measurements to be used in the inversion, selecting an appropriate inversion model, verifying that the selected inversion model is consistent with other information, and determining the dip and selected inversion model parameters. The determined selected inversion model parameters preferably include the position of the formation boundary position, and resistivities of the formation beds on either side of the boundary.

The model building or selection step (box 125) preferably includes selecting the simplest model that fits the known information, and creating a visualization of the selected directional measurements. The model selection step preferably further includes the use of algorithms to penalize the model complexity, such as Akaike Information Criterion. The model-based inversion should be flexible, to allow selection of parameters, from 1 (dip only) to 6 (dip, boundary position and anisotropic resistivities of two beds). The process may be interactive or batch log processing. The model-based inversion can be used for one or more boundaries (arbitrary resistivity profile).

It will be apparent to those skilled in the art that this invention may be implemented using one or more suitable general-purpose computers having appropriate hardware and programmed to perform the processes of the invention. The programming may be accomplished through the use of one or more program storage devices readable by the computer processor and encoding one or more programs of instructions executable by the computer for performing the operations described above. The program storage device may take the form of, e.g., one or more floppy disks; a CD ROM or other optical disk; a magnetic tape; a read-only memory chip (ROM); and other forms of the kind well known in the art or subsequently developed. The program of instructions may be "object code," i.e., in binary form that is executable more-or-less directly by the computer; in "source code" that requires compilation or interpretation before execution; or in some intermediate form such as partially compiled code. The precise forms of the program storage device and of the encoding of instructions are immaterial here. Thus these processing means may be implemented in the surface equipment, in the tool, or shared by the two as known in the art. It will also be appreciated that the techniques of the invention may be used with any type of well logging system, e.g. wireline tools, LWD/MWD tools, or LWT tools.

It will be understood from the foregoing description that various modifications and changes may be made in the preferred and alternative embodiments of the present invention without departing from its true spirit.

This description is intended for purposes of illustration only and should not be construed in a limiting sense. The scope of this invention should be determined only by the language of the claims that follow. The term "comprising" within the claims is intended to mean "including at least" such that the recited listing of elements in a claim are an open group. "A," "an" and other singular terms are intended to include the plural forms thereof unless specifically excluded.

Claims (15)

1. A method for characterizing a subsurface formation with a logging instrument disposed in a borehole penetrating the formation, the logging instrument having a longitudinal axis and being equipped with at least a transmitter system and a receiver system that collectively comprise at least one set of upper antennas and one set of lower antennas, the method comprising the steps of: positioning the logging instrument within the borehole so that the transmitter system and receiver system are disposed in the vicinity of a formation boundary of interest; measuring the azimuthal orientation of the logging instrument; transmitting electromagnetic energy into the formation using the transmitter system; measuring signals associated with the electromagnetic energy transmitted by the transmitter system using the receiver system; composing a symmetrized directional measurement using the measured signals; and plotting the determined directional measurement as a function of depth for a plurality of different depths; and using a discontinuity in the rate of the change in the plotted directional measurement to identify the depth at which at least one of the upper and lower antennas crosses the formation boundary.

2. A logging apparatus for characterizing a subsurface formation penetrated by a borehole, the apparatus comprising: a body adapted for conveyance in the borehole and having a longitudinal axis; a transmitter system carried by the body for transmitting electromagnetic energy into the formation; a receiver system carried by the body for measuring signals associated with the electromagnetic energy transmitted by the transmitter system, and means for determining the relative azimuth of a formation boundary of interest in the vicinity of the borehole, for composing a symmetrized directional measurement using signals measured by the receiver system and the relative boundary azimuth determined by the azimuth-determining means, and for determining the relative dip of the formation boundary using the composed directional measurement.

3. The logging apparatus of claim 2, adapted for conveyance and rotation in a drill string.

4. The logging apparatus of claim 2, adapted for conveyance by a wireline.

5. The logging apparatus of claim 2, wherein the transmitter system includes at least one antenna having a magnetic dipole-moment that is tilted with respect to the axis of the logging instrument by an angle 0, and the receiver system includes at least one antenna having a magnetic dipole-moment that is tilted with respect to the axis of the logging instrument by an angle 180-0.

6. The logging apparatus of claim 2, wherein the transmitter system includes at least first and second transmitter antennas, and the receiver system includes at least first and second receiver antennas.

7. The logging system of claim 6, wherein the antennas are oriented such that the first transmitter and first receiver antennas define a first symmetric antenna pair, and the second transmitter and second receiver antennas define a second symmetric antenna pair.

8. The logging apparatus of claim 2, wherein the transmitter system includes two transmitter antennas, with each transmitter antenna having a magnetic dipole-moment aligned with the instrument axis.

9. The logging apparatus of claim 8, wherein the receiver system includes two transverse, mutually orthogonal receiver antennas, with the two receiver antennas being positioned between the two transmitter antennas.

10. The logging apparatus of claim 8, wherein the receiver system includes two transverse, mutually orthogonal receiver antennas, with the two transmitter antennas being positioned between the two receiver antennas.

11. The logging apparatus of claim 2, wherein the transmitter system includes tri-axial transmitter antennas, and the receiver system includes tri-axial receiver antennas.

12. The logging apparatus of claim 2, wherein the azimuth-determining means includes a tool face sensor.

l 3. The logging apparatus of claim 2, wherein the azimuth-determining means includes a computer-readable medium having computer-executable instructions for determining the relative azimuth of the formation boundary of interest.

14. The logging apparatus of claim 2, wherein the composing means includesa computer- readable medium having computer-executable instructions for composing a symmetrized directional measurement using signals measured by the receiver system and the relative boundary azimuth determined by the azimuth-determining means.

15. The logging apparatus of claim 2, wherein the relative dipdetermining means includes a computer-readable medium having computerexecutable instructions for determining the relative dip of the formation boundary using the composed directional measurement.