Abstract:
A logging tool is disclosed having transmitting and receiving antennas to measure formation anisotropy. The antennas may preferably be combinations of toroidal, horizontal electric dipole, and horizontal magnetic dipole antennas. In one embodiment, the tool: (a) induces a current flow in the tubing or drill string traversing the formation in a borehole; (b) measures a signal difference between two receiver antennas on the drill string; (c) determines an apparent conductivity of the formation from the resistive component of the signal difference; and (d) uses the apparent conductivity to calculate an anisotropy coefficient with a knowledge of the horizontal conductivity. The tool may further determine a second apparent conductivity of the formation from the reactive component of the signal difference, and use both apparent conductivities to calculate the anisotropy coefficient and the horizontal conductivity. The vertical conductivity can also be determined from these two calculated values in the usual manner.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application claims priority to U.S. Provisional Patent Application No. 60/302,823 filed on Jul. 3, 2001, and entitled “Method And Apparatus Using Toroidal Antenna for Measuring Electrical Anisotropy.” This application is also related to commonly owned U.S. Pat. No. 6,181,138, issued Jan. 30, 2001, and entitled “Directional Resistivity Measurements for Azimuthal Proximity Detection of Bed Boundaries.” These references are incorporated herein by reference. 

   STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
   Not applicable. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention generally relates to the measurement of electrical characteristics of formations surrounding a wellbore. More particularly, the present invention relates to a method for determining horizontal and vertical resistivities in anisotropic formations. 
   2. Description of Related Art 
   The basic principles and techniques for electromagnetic logging for earth formations are well known. Induction logging to determine the resistivity (or its inverse, conductivity) of earth formations adjacent a borehole, for example, has long been a standard and important technique in the search for and recovery of subterranean petroleum deposits. In brief, the measurements are made by inducing electrical current flows in the formations in response to an AC transmitter signal, and then measuring the appropriate characteristics of a receiver signal generated by the formation current flows. The formation properties identified by these signals are then recorded in a log at the surface as a function of the depth of the tool in the borehole. 
   It is well known that subterranean formations surrounding an earth borehole may be anisotropic with regard to the conduction of electrical currents. The phenomenon of electrical anisotropy is generally a consequence of either microscopic or macroscopic geometry, or a combination thereof, as follows. 
   In many sedimentary strata, electrical current flows more easily in a direction parallel to the bedding planes, as opposed to a direction perpendicular to the bedding planes. One reason is that a great number of mineral crystals possess a flat or elongated shape (e.g., mica or kaolin). At the time they were laid down, they naturally took on an orientation parallel to the plane of sedimentation. The interstices in the formations are, therefore, generally parallel to the bedding plane, and the current is able to easily travel along these interstices which often contain electrically conductive mineralized water. Such electrical anisotropy, sometimes called microscopic anisotropy, is observed mostly in shales. 
   Subterranean formations are often made up of a series of relatively thin beds having different lithological characteristics and, therefore different resistivities. In well logging systems, the distances between the electrodes or antennas are great enough that the volume involved in a measurement may include several such thin beds. When individual layers are neither delineated nor resolved by a logging tool, the tool responds to the formation as if it were a macroscopically anisotropic formation. A thinly laminated sand/shale sequence is a particularly important example of a macroscopically anisotropic formation. 
   If a sample is cut from a subterranean formation, the resistivity of the sample measured with current flowing parallel to the bedding planes is called the transverse or horizontal resistivity ρ H . The inverse of ρ H  is the horizontal conductivity σ H . The resistivity of the sample measured with a current flowing perpendicular to the bedding plane is called the longitudinal or vertical resistivity, ρ v , and its inverse the vertical conductivity σ v . The anisotropy coefficient λ is defined as:
 
λ=√{square root over (σ h /σ v .)}  (1)
 
   In situations where the borehole intersects the formation substantially perpendicular to the bedding planes, conventional induction and propagation well logging tools are sensitive almost exclusively to the horizontal component of the formation resistivity. This is a consequence of the induced currents flowing in horizontal planes in the absence of formation dip or well deviation. Indeed, regarding Galvanic devices, the lack of sensitivity to anisotropy is even more stringent due to the “paradox of anisotropy,” which states that any array of electrodes or sensors deployed along the axis of a wellbore in a vertical well is insensitive to the vertical component of resistivity, despite the intuitive expectation to the contrary. 
   At present, there exists only one commercial instrument that measures the vertical resistivity. B. Kriegshauser, et al., describe this instrument in “A new multicomponent induction logging tool to resolve anisotropic formations,” 41 st  Annual Logging Symposium, Society of Professional Well Log Analysts, paper D, pps. 1-14, 2000. This instrument employs multiple multi-component coils (i.e., transmitter and receiver coils having axial and transverse orientations). This instrument may be unduly complex and provide measurements that are difficult to interpret. Further, the design of this wireline instrument may not be adaptable to a measurement while drilling (MWD) implementation. A simpler method and apparatus for measuring vertical resistivity would be desirable. 
   SUMMARY OF THE INVENTION 
   The above-described problems are in large part addressed by using a logging tool with antennas configured to measure formation anisotropy. In one embodiment, the method comprises (a) inducing a current flow in the tubing or drill string traversing the formation in a borehole; (b) measuring a signal difference between two toroidal receiver antennas on the drill string; (c) determining an apparent conductivity of the formation from the resistive component of the signal difference; and (d) using the apparent conductivity with an additional measurement of horizontal conductivity to calculate an anisotropy coefficient. The method may further include determining a second apparent conductivity of the formation from the reactive component of the signal difference, and using both apparent conductivities to calculate directly both the horizontal conductivity and the anisotropy coefficient. The horizontal and vertical conductivities can also be determined from the two apparent conductivities. It should be noted that determining the apparent conductivity and/or calculating the anisotropy coefficient as described above may be done by surface processing equipment. 
   In an alternative embodiment, a horizontal electric dipole may be used as a transmitter, where imposing an alternating voltage on it produces electric fields in the formation, which in turn generate alternating currents. The generated alternating currents are preferably measured to register the amount of resistance and reactance present in the formation. This measurement yields anisotropy data, and horizontal and vertical conductivities. Preferably, at least one horizontal magnetic dipole receiver is used to measure the generated current by measuring the amount of magnetic field it induces. In addition, multiple horizontal magnetic receivers may be used to create a differential signal measurement. 
   In yet another embodiment, a horizontal magnetic dipole may be used as the transmitter, where imposing an alternating voltage on it produces magnetic fields in the formation, which in turn generate alternating currents. The generated alternating currents are preferably measured to register the amount of resistance and reactance present in the formation. This measurement yields anisotropy data, and horizontal and vertical conductivities. Preferably, at least one horizontal electric dipole receiver is used to measure the generated current by measuring the amount of electric field it induces. In addition, multiple horizontal electric receivers may be used to create a differential signal measurement. 
   The disclosed methods may provide advantages in determining the parameters of anisotropic earth formations in both wireline applications and/or MWD applications. For example, the tool is expected to work particularly well in high-conductivity formations where the existing induction tools are deficient due to skin effect. Additionally, because the sensitivity to anisotropy is a volumetric effect as opposed to a boundary effect for Galvanic devices, there is a greater sensitivity to anisotropy. In addition due to the fact that the tool operates on straightforward principles, the ease of log interpretation is enhanced. Also, in the case of MWD, the tool design advantageously reduces the borehole and invasion effects on the measurement and enhances the depth of investigation. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A better understanding of the present invention can be obtained when the following detailed description of the preferred embodiment is considered in conjunction with the following drawings, wherein like parts have been given like numbers: 
       FIG. 1  shows a preferred embodiment of the antenna configuration using toroidal receivers and transmitters; 
       FIG. 2  shows a theoretical formation current flow induced in an isotropic formation by a toroid tool of  FIG. 1 ; 
       FIG. 3  shows another embodiment of the antenna configuration using alternate combinations of receivers and transmitters; 
       FIG. 4  is a graph relating apparent conductivity to horizontal conductivity for different formation anisotropies; 
       FIG. 5  is a graph relating apparent resistivity to apparent reactivity for different formation anisotropies; 
       FIG. 6  is a graph relating horizontal resistivity to apparent resistivity for different formation anisotropies; and 
       FIG. 7  shows the information of  FIG. 6  in a different form. 
     While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the drawings and detailed description thereto are not intended to limit the invention to the particular form disclosed, but on the contrary, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims. 
   

   DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
   Terminology 
   It is noted that the terms horizontal and vertical as used herein are defined to be those directions parallel to and perpendicular to the bedding plane, respectively. 
   Tool Configuration 
     FIG. 1  shows a logging tool  100  that is part of drillstring located in a wellbore  102  that passes through a formation  104 . The tool includes at least one transmitter antenna  106  and at least two receiver antennas  108 ,  110 . The transmitter antenna  106  and receiver antennas  108  and  110  are toroidal antennas, although as explained below the antennas  106 ,  108 , and  110  may include other antenna types. A toroidal antenna has a spirally-wound high-permeability core that forms a closed loop around an electrical conductor. In the logging tool  100 , the electrical conductor is preferably a portion of a drill string, but it is not so limited, in fact the logging tool  100  also renders itself to wireline applications. In the preferred embodiment, the core is circular with a generally-rectangular cross section, but other geometries (e.g., a circular cross-section) would also suffice. 
   The toroidal transmitter antenna  106  operates when an alternating current is supplied to the spiral wire winding around the antenna core. A changing current flow in the winding induces a changing magnetic field in the core, which in turn induces a current I Total  in the logging tool  100 . The current I Total flows along the logging tool  100  where part of the current I Total -I 1  radiates into the formation and returns to the drillstring on the opposite side of the transmitter antenna  106 , and the rest of the current I, continues to flow in the logging tool  100  through the toroidal receiver  108 . The toroidal receivers  108  and  110  operate when a changing current flows along the enclosed electrical conductor, in this case logging tool  100 . Current I 1  flows along the logging tool  100  and induces a changing magnetic field in the core of receiver  108 , which in turn induces a changing voltage that is measured in the winding of the receiver  108 . At this point, part of the current I 1 -I 2  radiates into the formation just after the receiver  108  and returns to the drillstring on the opposite side of the antenna  106 , and the rest of the current  12  continues along the drillstring to the toroidal receiver  110 . The voltage in the winding of toroidal receiver  110  generated as a result of I 2  is measured similarly to the voltage measurement of the receiver  108 . The logging tool  100  is thereby able to determine the amount of current radiated into the formation in each of two regions. The current I 2  that passes through receiver  110  is radiated from the drillstring in the region below receiver  110  (the “bit region”). The current that passes through receiver  108  minus the current that passes through receiver  110  (I 1 -I 2 ) is radiated from the drillstring in the region between the receivers (the “lateral region”). It should be noted that receiver  108  and receiver  110  are intended to be used in a differential manner such that the voltage difference between the receivers results from the difference in their respective current flows or the difference in their magnetic fields. Thus, the amount of current dissipated into the lateral region can be easily calculated and the width of the lateral region is varied as the distance between the toroidal receivers  108  and  110 . Also, note that the toroidal receivers used in a differential arrangement may be sized differently depending upon their relative proximity to the transmitter so as to achieve zero offset. For example, receiver  108  as shown in  FIG. 1  is sized smaller than receiver  110  because the magnetic field induced by transmitter  106  is stronger in receiver  108  than in receiver  110  due to their relative distance from the transmitter  106 . It should be noted that the although the system described in  FIG. 1  has been addressed in the context of a MWD application, it is not so limited and may be applied to wireline applications. 
     FIG. 2  shows current flow lines (and equipotential lines) indicated by numerical simulation for an isotropic formation. The lateral current I 1 -I 2  is shown as well as the bit current I 2 . Of course, these current lines will be different for anisotropic formations, but the general principle remains the same. 
   An alternate antenna configuration is shown in  FIG. 3 , where alternate antenna combinations of horizontal electric dipoles (HED) and horizontal magnetic dipoles (HMD) are used. A BED antenna includes two wires oriented opposite each other. Each wire in the BED represents a pole (e.g., a positive pole and a negative pole), such that as an electromotive force is applied to the BED, an electric field is generated. A HMD antenna includes a coil of wire having two ends where an electromotive force is applied that in turn generates a magnetic field. The magnetic field orients itself to the dipoles of the HMD in a similar manner that the electric field orients itself to the dipoles of the HED. Akin to  FIG. 1 ,  FIG. 3  shows a logging tool  100  that is part of a drillstring located in a wellbore  102  that passes through a formation  104 . The tool includes at least one transmitter antenna  202 , which preferably is a HED. Also there are at least two receiver antennas  204  and  206  both configured as HMD. As one ordinary of skill in the art having the benefit of this disclosure will appreciate, the system described in  FIG. 3  is generally applicable to wireline applications, however it may also be applicable to MWD applications. 
   The transmitter  202  operates when an alternating voltage is applied to it and electric fields are generated in the formation  104 . The electric fields induced in the formation  104  by the transmitter  202  bring about currents. Since the formation  104  is both reactive and resistive, there are resistive currents induced that are in phase, and reactive currents that are in quadrature (i.e., 90° out of phase). These currents further induce magnetic fields in the formation  104  that are proportional to the amount of resistance and/or reactance present. The induced magnetic fields are measured at various positions along the logging tool  100  by the receiver  204  and the receiver  206 . 
   The receivers  204  and  206  preferably are fashioned such that the coil is formed around the periphery the cylindrical sections a and b as indicated by the directional arrows. In general, receivers  204  and  206  provide a measurable voltage in coils a and b that is proportional to the magnetic field passing through them. Receivers  204  and  206  preferably operate in a differential manner such that the voltage appearing in coils a and b of receiver  204  minus the voltage appearing in coils a and b of receiver  206  is the desired measurement. 
   It should be noted that although  FIG. 3  shows a specific combination using a HED for the transmitter and two HMDs for the receivers, a converse arrangement would be evident to one of ordinary skill in this art in having the benefit of this disclosure. For example, a HMD may be used as the transmitter while HEDs may be used as the differential receivers. Furthermore, additional receivers may be fashioned along the logging tool to provide measurements at different effective depths in the formation. Also, the receivers and/or transmitters may be azimuthally tunable resistivity measurement tools as described in commonly owned U.S. Pat. No. 6,181,138. In this manner, specific coil configurations can be synthesized to provide the optimum transmit and receive structures in accordance with the preferred embodiments disclosed herein. 
   The apparent conductivity of the formation, is a function of the voltages measured by the two receiver antennas. The voltages measured from each receiver has an in-phase component up resulting from resistive formations and a quadrature component resulting from reactive components. The apparent conductivity may preferably be calculated from the difference between the in-phase voltages measured by the receiver antennas:
 
σ a   =K ( V   2   −V   1 ),  (2)
 
where V 1  and V 2  are the voltages received in-phase with the transmitter signal (“resistive component”), and K is a constant for the logging tool. It should be noted that determining the apparent conductivity and/or calculating the anisotropy coefficient as described above may be done by either the logging tool or the processing equipment located at the surface (not shown in the drawings.)
 
   As shown in  FIG. 4 , the apparent conductivity is a function of both the horizontal conductivity and the anisotropy coefficient of Equation (1). In the preferred embodiment of the tool  100 , an unrelated method is used to determine the horizontal conductivity. For example, a standard induction tool may be used to measure the σ h . With the horizontal conductivity measurement from the unrelated source and the apparent conductivity measurement from the present logging tool, the anisotropy coefficient can be determined from the function shown in FIG.  4 . The vertical conductivity can then be determined from the horizontal conductivity measurement and the anisotropy coefficient. 
   If a separate determination of horizontal conductivity is unavailable or infeasible, then the present logging tool can be configured to determine the apparent conductivity from the reactive components of the receiver signals in addition to the apparent conductivity from the resistive components of the receiver signals. From the resistive and reactive apparent conductivities, both the horizontal conductivity and the anisotropy coefficient can be determined as shown in FIG.  5 . From these values, the vertical conductivity may be calculated. 
     FIG. 6  shows the function of  FIG. 4  on a logarithmic scale with different axes. The apparent resistivity (the inverse of conductivity) measured by the tool is shown as a function of the horizontal resistivity of the formation. Here it may be observed that a ten-fold increase in anisotropy yields a 75% change in the apparent resistivity. Accordingly if the method of  FIG. 5  is used, there may be some loss of sensitivity in high-resistivity formations. This sensitivity problem might be aggravated by a loss of amplitude in the reactive voltage caused by a reduced skin-effect in highly resistive formations. 
   A different presentation of the same data set as in  FIG. 6  can be made in the form of a skin effect correction chart as in FIG.  7 . It is clear that at normal operating frequencies the toroidal tool has only a modest amount of skin effect which is easily corrected. In fact, if the appropriate skin effect correction is applied, the apparent resistivity Ra of the tool is approximated within a few percent error: 
    R a =λ 1/4 R h .  (3) 
   Note that in  FIG. 2 , the current flow lines (initially) run perpendicular to the drillstring. This advantageously reduces the borehole and invasion effects on the measurement and enhances the depth of investigation. The proposed tool is expected to work particularly well in salty muds where the existing tools are deficient. The tool operates on straightforward principles, and accordingly is expected have advantages over existing tools in terms of cost and ease of interpretation. 
   Theory of Operation 
   In accompaniment with the preferred embodiments, the following analysis serves as a theoretical guide. Referring first to a vertical toroid (VTR) transmitter and a VTR receiver system where the VTRs are assumed to behave as point toroids, magnetic coupling (for a wireline application) can be expressed in units of apparent conductivity: 
                   σ   a     +     i   ⁢           ⁢     σ   x         =       ⁢         σ   v       λ   2       ⁢     (     1   -     i   ⁢           ⁢     k   h     ⁢   L       )     ⁢     ⅇ     ⅈ   ⁢           ⁢     k   h     ⁢   l           ,           ⁢     (   4   )                   -&gt;       ⁢       σ   v       λ   2         ,           ⁢     (   5   )               
 
where the limiting form of Equation (5) represents the response in the absence of skin effect.
 
   Focusing now on the case of RMD transmitters and HED receivers, the electric coupling can be shown to be: 
                   σ   a     +     i   ⁢           ⁢     σ   x         =       ⁢         σ   h         k   h   2     ⁢     L   2         ⁢     (     1       λ   2     +   1       )     ⁢     (     1   -       ik   h     ⁢   L       )     ⁢     ⅇ     ⅈ   ⁢           ⁢     k   h     ⁢   L           ,           ⁢     (   6   )                   -&gt;       ⁢       σ   v       λ   2         ,           ⁢     (   7   )               
 
where the limiting form of Equation (7) represents the response in the absence of skin effect. Also, in the case of HED transmitters and HMD receivers, the magnetic coupling can be shown to be identical to Equations (6) and (7). It should be noted from the above analysis, that electric coupling measured by an electric dipole receiver can be replaced with a measurement of the magnetic field by a coil whose receiver plane is orthogonal to the electric dipole antenna, thus different combinations of horizontal versus vertical and magnetic versus electric dipole configurations are supported by this analysis. In addition, Equations (4)-(7) illustrate the perceived benefits of using the embodiments of FIG.  1  and  FIG. 3  in measuring σ v  as well as measuring overall anisotropy.
 
   Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such variations and modifications.