1. Field of the Invention
The invention relates generally to well logging using resistivity logging tools. More particularly, the invention relates to methods and systems for reliable determination of formation conductivities.
2. Background Art
Electromagnetic (EM) induction logging instruments are well known in the art. These instruments are used to determine the electrical properties (conductivity, or its converse, resistivity) of earth formations penetrated by a wellbore. Measurements of formation conductivities may be used to estimate the fluid contents of the earth formations because hydrocarbon-bearing earth formations are associated with lower conductivity (higher resistivity).
Physical principles of EM induction logging are described in, H. G. Doll, “Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud,” Journal of Petroleum Technology, vol. 1, p. 148, Society of Petroleum Engineers, Richardson Tex. (1949). Since then, many improvements and modifications to EM induction logging instruments have since been devised. For example, U.S. Pat. No. 3,510,757 issued to Huston and assigned to the assignee of the present invention discloses an EM logging instrument equipped with transverse antennas for measuring formation relative dips. U.S. Pat. No. 6,304,086 B1 issued to Minerbo et al. and assigned to the assignee of the present invention discloses EM logging instruments for evaluating formation resistivities in high-contrast thin layers or formations with high dip angles.
In a conventional EM logging instrument, the transmitter and receiver coils (antennas) have their magnetic dipoles substantially aligned with the longitudinal axis of the instrument. The antennas on these tools are referred to as longitudinal magnetic dipoles (LMD) antennas. With an LMD tool, eddy currents are induced in the earth formations to flow in ground loops that are substantially perpendicular to the axis of the tool. The eddy currents then induces secondary magnetic fields that in turn generate voltages in the receiver antennas. The magnitudes of the detected signals relate to the magnitudes of the eddy currents, which in turn relate to the formation conductivities. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. In these situations, the responses (signals) received by a receiver of an LMD induction instrument will be dominated by the eddy currents flowing in the conductive layers. In contrast, less-conductive layers will have less or little contribution to the overall responses. Consequently, non-conductive layers are often missed using the conventional LMD logging tools despite the fact that they are hydrocarbon-bearing.
To overcome this problem, new EM induction instruments typically include transmitter and/or receiver antennas that have their magnetic dipoles substantially perpendicular to the axis of the instrument. These antennas are referred to as transverse magnetic dipole (TMD) antennas. The TMD antennas induce eddy currents to flow in loops parallel to the tool axis. Thus, the eddy currents flow through various layers in a vertical well. In this manner, the sedimentation layers act like resistors in series in the eddy current loops. Therefore, the signals (voltages) received by a TMD tool is more affected by the more resistive layers—i.e., the hydrocarbon-bearing layers.
Examples of TMD instruments include tri-axial induction instruments that have three transmitter antennas arranged in orthogonal orientations and three receiver antennas oriented in the corresponding orthogonal orientations. In a tri-axial induction tool energized in three orthogonal directions, individual receiver coils aligned in the same three orthogonal directions measure the voltages induced by eddy currents flowing in the surrounding formations. The implementation of tri-axial antennas, for example, may be found in U.S. Pat. No. 3,510,757 issued to Huston and U.S. Pat. No. 5,781,436 issued to Forgang et al.
Tri-axial induction logging instruments can provide improved evaluation of heterogeneous rock formations. In addition to being able to locate thin hydrocarbon-bearing layers, these tools can also provide improved estimation of hydrocarbon reserves in anisotropic reservoirs. Examples of anisotropic reservoirs (or formations) include highly-laminated formations. These formations can be characterized by two electrical parameters: the resistivity parallel to the bedding designated as Rh and the resistivity perpendicular to the bedding designated as Rv. When wells are drilled in reservoirs that may include anisotropic sedimentation layers, it is important for the operators to be able to quickly estimate (preferably in real time while the data is being acquired) the degree of anisotropy of a particular zone in order to make sure that the well is following the planned path or stay within the pay zone.
Although tri-axial or TMD instruments can provide improved measurements for the evaluation of formation resistivity, the raw measurements provided by these instruments, like those obtained with LMD tools, are affected by skin effects, environmental effects, shoulder-bed effects, and formation relative dips.
Skin effects are characterized by non-linear responses of the received signals in relation to the formation conductivities. Skin effects result primarily from interactions between eddy currents flowing in adjacent loops in the formation. The magnitudes of skin effects depend on a complicated function of the coil system operating frequency, the effective length of the antenna system, and the conductivity value of the adjacent formation, among other things.
Shoulder-bed effects result from eddy currents that flow in sedimentation layers lying above and/or below the layer being investigated. The shoulder-bed effects are particularly problematic if the layer under investigation is less conductive than the adjacent beds. In this case, the conductive adjacent beds will have significant (or dominant) contribution in the received signals.
To some extent, the skin effects and the shoulder-bed effects can be mitigated by tool designs and logging parameters. For example, U.S. Pat. No. 2,582,314 issued to Doll and U.S. Pat. No. 3,067,383 issued to Tanguy disclose induction tools having multiple transmitter and receiver coils arranged in specific relationships to “focus” the sonde response function by narrowing the width of the main lobe and attenuating the side-lobes. In an alternative approach, U.S. Pat. No. 2,790,138 issued to Poupon discloses an induction logging tool having two separate induction coil arrangements, which have the same geometrical center so that responses from the two coil arrangements may be used to cancel the contributions from the side-lobes.
In addition to tool design, signal processing methods have been developed to improve measurement accuracy by reducing skin effects and shoulder-bed effects. Examples of signal processing approaches include phasor processing disclosed in U.S. Pat. No. 4,513,376 issued to Barber and U.S. Pat. No. 4,471,436, issued to Schaefer et al. In addition, U.S. Pat. Nos. 4,818,946 and 4,513,376 issued to Barber disclose methods of processing the induction log measurements to reduce the unwanted contributions in the log measurements by minimizing the side-lobes in the sonde response function used to correlate the voltage measurements with true formation conductivity. The sonde response function is known as a vertical sensitivity curve of the induction tool. Furthermore, U.S. Pat. No. 6,304,086 B1 issued to Minerbo et al. also discloses a tool and a new processing method (the Grimaldi processing) that can provide measurements with minimal skin effects and shoulder-bed effects. In addition, this tool can output in real time an estimate of Rv. and Rh in an anisotropic formation.
Although prior art tools and methods can produce good resistivity estimates, there is still a need for new methods for formation resistivity evaluation that are insensitive to insensitive to skin effects, shoulder-bed effects, and formation relative dips.
One aspect of the invention relates to methods for determining an electrical property of a formation using at least two sets of orthogonal resistivity measurements. A method for determining an electrical property of a formation in accordance with the invention includes acquiring a first resistivity measurement by energizing a first transmitter and receiving a first signal in a first receiver, wherein the first transmitter and the first receiver are disposed on the logging tool in a first orientation substantially parallel to a longitudinal axis of the logging tool; acquiring a second resistivity measurement by energizing a second transmitter and receiving a second signal in a second receiver, wherein the second transmitter and the second receiver are disposed on the logging tool in a second orientation that is substantially orthogonal to the first orientation; and deriving the electrical property of the formation from a difference measurement that is derived from the first resistivity measurement and the second resistivity measurement
One aspect of the invention relates to methods for estimating an anisotropic resistivity ratio of an anisotropic formation. A method for estimating an anisotropic resistivity ratio of an anisotropic formation in accordance with the invention includes acquiring a first resistivity measurement by energizing a first transmitter and receiving a first signal in a first receiver, wherein the first transmitter and the first receiver are disposed on the logging tool in a first orientation substantially parallel to a longitudinal axis of the logging tool; acquiring a second resistivity measurement by energizing a second transmitter and receiving a second signal in a second receiver, wherein the second transmitter and the second receiver are disposed on the logging tool in a second orientation that is substantially orthogonal to the first orientation; and deriving the anisotropic resistivity ratio from a ratio of the first resistivity measurement and the second resistivity measurement.
One aspect of the invention relates to methods for estimating an anisotropic resistivity ratio of an anisotropic formation. A method for estimating an anisotropic resistivity ratio of an anisotropic formation in accordance with the invention includes acquiring a first resistivity measurement by energizing a first transmitter and receiving a first signal in a first receiver, wherein the first transmitter and the first receiver are disposed on the logging tool in a first orientation substantially parallel to a longitudinal axis of the logging tool; acquiring a second resistivity measurement by energizing a second transmitter and receiving a second signal in a second receiver, wherein the second transmitter and the second receiver are disposed on the logging tool in a second orientation that is substantially orthogonal to the first orientation; and deriving the anisotropic resistivity ratio from a ratio of the first resistivity measurement and the second resistivity measurement.
One aspect of the invention relates to systems for determining an electrical property of a formation. A system for determining an electrical property of a formation in accordance with the invention includes a computer having a memory storing a program having instructions for: acquiring a first resistivity measurement by energizing a first transmitter and receiving a first signal in a first receiver, wherein the first transmitter and the first receiver are disposed on the logging tool in a first orientation substantially parallel to a longitudinal axis of the logging tool; acquiring a second resistivity measurement by energizing a second transmitter and receiving a second signal in a second receiver, wherein the second transmitter and the second receiver are disposed on the logging tool in a second orientation that is substantially orthogonal to the first orientation; and deriving the electrical property of the formation from a difference measurement that is derived from the first resistivity measurement and the second resistivity measurement.
Other aspects and advantages of the invention will be apparent from the following description and the appended claims.
Embodiments of the present invention relate to methods and systems for estimating conductivity of rock formations. Specifically, the present invention is directed to methods and systems that can provide consistent and accurate conductivity measurements that are less sensitive to skin and shoulder-bed effects, regardless of the relative dips of the formation bedding. The conductivities obtained using embodiments of the present invention may include an apparent conductivity, and a conductivity parallel or perpendicular to the formation bedding. In addition, the present invention provides a method for estimating the anisotropic resistivity ratio in anisotropic formations.
In the following description, the term “conductivity” is used interchangeably with “resistivity” because one is the reciprocal of the other and either can be used to characterize the electrical properties of a material. In addition, the description uses induction logging as an example. However, one of ordinary skill in the art would appreciate that embodiments of the invention may also be applied to orthogonal sets of measurements obtained from propagation logging. Therefore, both induction and propagation measurements are expressly within the scope of the invention. Furthermore, methods of the invention may also be used to process previously acquired measurements that include two sets of orthogonal measurements, i.e., reprocessing of existing data. Thus, any reference to logging or data-acquisition steps in this description is only for illustration and is not intended to limit every embodiment of the invention.
Embodiments of the present invention relate to methods for probing a rock formation using at least two orthogonal sets of induction measurements. The at least two orthogonal sets of induction measurements are obtained by energizing two transmitters having their magnetic dipoles in orthogonal directions (e.g., one parallel to and the other perpendicular to the tool axis) and receiving the induced signals (voltages) in two receivers having their magnetic dipoles oriented in the same directions as the transmitter magnetic dipoles. For example, the first transmitter and receiver pair have their magnetic dipoles aligned with the tool axis (i.e., longitudinal magnetic dipole (LMD) antennas), and the second transmitter and receiver pair have their magnetic dipoles perpendicular to the tool axis (i.e., transverse magnetic dipole (TMD) antennas). One of ordinary skill in the art would appreciate that the orthogonal sets of induction measurements may be acquired using any induction logging tool equipped with at least one transmitter and at lest one receiver, each including an LMD and a TMD antennas. Examples of the antenna arrangements may include a tri-axial array, which includes a tri-axial transmitter and a tri-axial receiver. In this description, a transmitter or a receiver may include a single coil (antenna) or a group of coils arranged in a set. For example, a tri-axial transmitter or a tri-axial receiver includes three coils arranged in orthogonal directions. While preferred embodiments of the invention use orthogonal antennas that are either parallel or perpendicular to the tool axis, orthogonal antennas that deviate from these orientations (i.e., tilted antennas) may also be used.
The logging tool 205 may be any conventional induction tool capable of providing two orthogonal measurements, e.g., a tri-axial array logging tool that includes a tri-axial transmitter and a tri-axial receiver.
For clarity, the following description assumes that the tool has a single transmitter and a single receiver, as shown in
In accordance with embodiments of the invention, the first set of measurements may be made using the transmitter and receiver antennas (coils) having their magnetic dipoles aligned with the tool axis (z-axis). These antennas, which are traditionally referred to as longitudinal magnetic dipole (LMD) antennas, are referred to as “Tzz” for the transmitter and “Rzz” for the receiver in
A second set of measurements may be made using transmitter and receiver antennas having their magnetic dipoles perpendicular to the tool axis—i.e., along the x-axis or y-axis. These transmitter and receiver antennas are traditionally referred to as transverse magnetic dipole (TMD) antennas. They are referred to as “Txx” or “Tyy” for the transmitter and “Rxx” or “Ryy” for the receiver in
The induced voltages (signals) Vzz and Vxx are proportional to quantities shown in equation (1) and (2).
Vxx=iKeikL(−1+ikL+k2L2) ( 2)
where
is the transmitter-receiver spacing, and k is the wave number. In the low frequency limit with negligible dielectric effect, the wave number k may be defined as:
where δ is the skin effect, which is a function of the operation frequency (ω=2πf), magnetic permeability of the medium (μ), and the conductivity of the medium (σ):
As can be seen from equation (3a), the skin effect (δ) is a function of the tool operation frequency (ω). If the operating frequency (ω) is not too high, then the skin effect may not be significant. If the skin effect (δ) is not significant relative to the transmitter-receiver spacing (L) (i.e., L/δ<1), then the skin effect is only a perturbation to the measurements. Under these conditions, taking the difference between the induced voltages Vzz (equation (1)) and Vxx (equation (2)), yields equation (4) or (5):
or,
The real part of equation (4) is proportional to the formation conductivity, σ.
Equation (6) shows that the real part of (Vzz−Vxx) is proportional to a with an error term proportional to
Therefore, the real part of (Vzz−Vxx) shown in equation (6) provides a measurement of formation conductivity that is much less affected by the skin effect (δ). In comparison, Vzz, which is conventionally used to derive the classical σzz, has an error term proportional to
and, therefore, is more affected by the skin effect (δ). Thus, the real part of (Vzz−Vxx) should be able to provide more reliable determinations of the formation conductivities. This is illustrated in
Curve 33, which is based on Re(Vzz)−Im(Vxx), has less skin effects than either curve 31 (Vxx) or curve 32 (Vzz). This is because some skin effects are cancelled out in the difference measurements. It is known that the imaginary part of a signal correlates with the skin effect and that Vxx suffers more from skin effects. Therefore, the Im(Vxx) term provides a good skin effect correction and, thus, the difference measurement Re(Vzz)−Im(Vxx) is expected to have less skin effects. What is surprising is that the difference measurement Vzz−Vxx is the least affected by the skin effects (see curve 34), even less than the Re(Vzz)−Im(Vxx) measurement (curve 33).
In addition to being less affected by skin effects, the difference measurement (Vzz−Vxx) is also less affected by the shoulder-bed effects.
The above description shows that the difference measurement Vzz−Vxx has less skin effects, less shoulder-bed effects, and a better vertical resolution, when compared with either the Vxx measurement or the Vzz measurement. These properties of the Vzz−Vxx measurement predict that the Vzz−Vxx difference measurement should be able to provide better estimates of true formation resistivities and more precise bed boundaries.
The better definition of bed boundaries and better estimates of the resistivity in each layer makes it possible to provide better weight for each detected boundary, i.e., more accurate weight that is proportional to the contrast between the adjacent beds. The better resistivity estimates and boundary definition obtained from Vzz−Vxx may serve as inputs for the inversion of more complex data sets, such as those obtained with tri-axial arrays. More importantly, the difference measurements Vzz−Vxx can produce reliable estimates regardless of the formation dips. These advantages of the Vzz−Vxx measurements have also been observed in real formations, e.g., the Oklahoma 2 test formation (
As noted above, in addition to providing more accurate estimates of the conductivity, the Vzz−Vxx measurement also provides better defined bed boundaries.
The above description shows that a simple difference measurement, Vzz−Vxx, can provide an improved estimate of formation resistivity with less skin effects and shoulder-bed effects. However,
Some embodiments of the invention provide more reliable estimates of the horizontal and vertical resistivities in anisotropic formations. In a formation with a low relative dip, if the logging operation is performed with low frequencies (i.e., negligible skin effects), the real part of the Vzz measurements is proportional to the formation conductivity in the horizontal planes, σh, while the real part of the Vxx measurements is proportional to the formation conductivity in the vertical direction, σv. Various methods have been reported for deriving the σh and σv values from the Vzz and Vxx measurements. However, the σh and σv values thus derived are not always accurate because the Vzz and Vxx measurements are sensitive to the skin effects and the shoulder-bed effects. In addition, the Vzz and Vxx measurements are sensitive to the relative dips.
It is found that the ratio of the real parts of these two measurements, Vzz/2Vxx, is approximately proportional to the square of the anisotropy coefficient (λ2), i.e.,
Therefore, if the horizontal conductivity (σh) can be estimated, then the vertical conductivity (σv) can be derived from the Vzz/2Vxx ratio and the estimated σh.
According to embodiments of the present invention, the Vzz−Vxx measurements can be used to derive accurate estimates of σh. The σh thus obtained can then be used to derive the σv from the estimated σh and the Vzz/2Vxx ratio. As noted above, the resistivities derived from the Vzz−Vxx measurements are less sensitive to skin effects and shoulder-bed effects. Therefore, the estimates of σh and σv thus derived are more reliable.
Thus, the new measurements Vzz−Vxx and Vzz/2Vxx according to embodiments of the invention can provide extremely useful information in the inversion of full tri-axial induction measurements. These measurements provide three important parameters: the precise bed boundary location, an approximate initial guess to the inversion algorithm and an initial guess for the anisotropy ratio Rv/Rh. The more accurate estimates can speed up the inversion process.
The above approach to estimating Rv/Rh from the Vzz and Vxx measurements is feasible only when there is no or minimal dip. Some embodiments of the invention relate to method for providing reliable resistivity estimates in anisotropic formations even when the formations have significant relative dips.
Effects of formation anisotropy on resistivity measurements in a homogeneous anisotropic formation were first described by Moran and Gianzero. See Moran and Ginzero, “Effect of Formation Aniostropy on Resistivity Anisotropy measurements,” Geophysics, Vol. 44, pp. 1266-1286, (1979). The equations for anisotropic formation resistivity calculations derived by Moran and Ginzero are referenced to a coordinate system tied to the formation layers. Because resistivity measurements may be acquired with tools not perpendicular to the formation layers (e.g., a formation with relative dips), these equations are often difficult to apply. In U.S. Pat. No. 6,584,408 issued to Omeragic (“the Omeragic patent”) and assigned to the assignee of the present invention, these equations were simplified to a reference frame relative to the logging tool. This patent is incorporated by reference in its entirely. The Omeragic patent discloses a procedure for determining anisotropic formation parameters from tri-axial measurements in formations with relative dips. According to one procedure, the horizontal conductivity (πh) of the formation is first determined from the tri-axial measurements by using cross coupling terms. Then, the dip angle (α) is derived from the measurements and the estimated σh. Finally, the vertical conductivity (σv) of the formation is derived from the horizontal resistivity (σh) and the dip (α).
The method disclosed in the Omeragic patent first derives the horizontal conductivity (σh) from coupling terms in tri-axial measurements by solving the following equation: (T′zz−Lh)(T′xx−Th)=(Txz)2. As noted above, the horizontal conductivity (σh) of a formation may be more reliably obtained from the Vzz−Vxx measurements regardless of the relative dips. Therefore, the horizontal conductivity (σh) may be more conveniently obtained from the difference measurement (Vzz−Vxx).
Once the horizontal conductivity (σh) is available, the dip angle (α) can be determined according to the following equation that is disclosed in the Omeragic patent:
where T′xx and T′zz are the strike-rotated xx (Vxx′) and xz couplings (Vxz′), and Th is the xx coupling (Vxx) in an isotropic formation having a conductivity σh. The term “strike-rotated” means that the reference coordinate system has been rotated to remove the strike (azimuthal angle) of the dipping plane. The process of removing strike from the measurements is disclosed in the Omeragic patent. An alternative to obtaining the relative angle (α) is to use:
where T′zz is the strike-rotated zz coupling (Vzz′), and Lh is the zz coupling (Vzz) in an isotropic formation having a conductivity σh.
Equations (8) and (9) may be combined using the formula for the sum of tan−1 to give:
or,
Either of these two equations may be used to calculate the formation dip angles (α). However, equation (11) is more robust in extreme cases (0 or 90°), and it is undetermined (0/0) only if there is no anisotropy.
As noted above, the horizontal conductivity (σh) may be derived from the xz coupling (Vxz) or the Vzz−Vxx measurement. Note that the horizontal conductivity (σh) derived from the Vzz−Vxx measurement corresponds to the no anisotropy situation (i.e., an isotropic formation where Lh=Th). Therefore, equation (11) cannot be used if σh is derived from the Vzz−Vxx measurement. In this case, the alternative approach is to use following expression for the first guess of the relative dip,
Once the horizontal conductivity (σh) and the relative (α) are available, these parameters can be used to obtain an estimate of the vertical conductivity σv according to the following equation:
Equation (13) is simpler than the equation for deriving the σv disclosed in the Omeragic patent. However, it should be noted that σ is a function of σv. Therefore, the above expression should be run recursively. Furthermore, (2Th+Lh) is proportional to σ in an isotropic formation. Therefore, equation (13) in essence derives anisotropy from the difference between the actual tool reading and what the tool would read if there is no anisotropy. The vertical conductivity (σv) estimate obtained from equation (13) may then be used in an iterative solver to determine refined horizontal conductivity (σh) and vertical conductivity (σv) from a full set of tri-axial resistivity measurements.
The two orthogonal measurements at each depth are then manipulated to obtain the desired difference measurement (Vzz−Vxx or 1/2(3/2Vzz−Vxx)) and/or the ratio of the measurements (Vzz/2Vxx). (Step 152). The resulting difference measurement (Vzz−Vxx or 1/2(3/2Vzz−Vxx)) may be used to estimate the formation conductivity (σ) and to define the bed boundaries (Step 153). The estimated formation conductivity (σ) and the bed boundaries may be used as initial inputs for the inversion of full tri-axial measurements (step 154). As noted above, because the Vzz−Vxx or 1/2(3/2Vzz−Vxx) measurements provide better estimates of the formation conductivity and bed boundaries, the inversion of the full tri-axial measurements may be performed more efficiently. Particularly, the estimates derived from the difference measurements are not sensitive to formation dips. Therefore, embodiments of the invention can provide reliable formation resistivity parameters regardless of the formation relative dips.
If the formation is anisotropic, the derived formation conductivity (σ) corresponds to an initial estimate of a formation conductivity parallel to the bedding plane (σh). If the formation dips are not significant, the ratio (Vzz/2Vxx) may be used to provide Rv/Rh or the anisotropy coefficient (λ) (step 155). The anisotropy coefficient (λ) together with the estimated σh may then be used to derived formation relative dips (δ) and/or the formation conductivity perpendicular to the bedding planes (σv) (step 156). Embodiments of the invention can provide better estimates of the horizontal conductivity (σh) and anisotropy coefficient (λ). Therefore, the derived parameters for the anisotropic formation are more reliable.
If the formation dips are not negligible, an alternative approach to deriving formation resistivity parameters is to estimate the horizontal conductivity (σh) using the Vzz−Vxx measurements. Once the horizontal conductivity (σh) is known, the dip angle (α) can then be determined from a full set of tri-axial measurements according to methods described above, i.e., equations (8)-(12) (step 155). Once the horizontal conductivity (σh) and the dip angle (α) are available, the vertical conductivity (σv) can then be determined (step 156).
Note that the above steps for deriving horizontal conductivity (σh) may further include using the initial estimate derived from the difference measurement in an iterative process to solve for more accurate horizontal conductivity (σh) using the full set of resistivity measurements (e.g., tri-axial measurements). This iterative process, if included, may be performed before the horizontal conductivity (σh) is used together with the Rv/Rh ratio or the dip angle (α) to solve for the vertical conductivity (σv).
Some embodiments of the invention relate to systems for performing the methods described above. A system in accordance with embodiments of the invention may be a stand-alone unit for performing methods of the invention or may be incorporated into a drilling tool. A system in accordance with the invention typically includes a processor and a memory. In some embodiments, a system may be implemented on a general-purpose computer having a processor, a memory, and may optionally include other hardware. For example, as shown in
In a system in accordance with the invention, the memory stores a program readable by the processor. The program, for example, may include instructions for performing the above described methods: obtaining resistivity measurements that include at least two orthogonal measurements (for example using a tri-axial tool), deriving difference measurements and/or a ratio of the two orthogonal measurements, estimating the formation conductivity and bed boundaries, estimating the anisotropy coefficient, deriving the horizontal and vertical conductivity of an anisotropic formation, and deriving dip angles in formations with dipping planes.
A system in accordance with the present invention provides new and improved techniques to evaluate formation electrical properties, e.g., resistivity (or conductivity), bed boundaries, anisotropy coefficient, and relative dips. 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 herein. The program storage device may take the form of, for example, 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. The program of instructions may be in “object code,” i.e., in binary form that is executable 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.
Advantages of the invention may include one or more of the following. The methods can provide more accurate estimates of formation conductivities, which are less affected by skin effects and shoulder-bed effects. In addition, the estimates are not affected by the formation dips. Therefore, reliable results may be obtained regardless of the formation dips. Furthermore, the methods of the invention also can provide more precise definition of bed boundaries. Thus, embodiments of the invention can provide more accurate initial estimates of the conductivity and bed boundaries for the inversion of full tri-axial measurements.
Some embodiments of the invention provide convenient methods for calculating the formation anisotropy coefficient. This coupled with the more reliable estimate of the horizontal conductivity of the formation makes it possible to derive more accurate vertical conductivity of the formation. In addition, some embodiments of the invention provide convenient ways to calculate formation relative dips. Thus, even in a formation with relative dips reliable estimates of anisotropic formation resistivity parameters may be derived.
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.