This disclosure relates to identifying properties of a geological formation using a downhole electromagnetic measurement. More specifically, this disclosure relates to techniques for determining a formation conductivity from propagation measurements.
This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present techniques, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as an admission of any kind.
Producing hydrocarbons from a wellbore drilled into a geological formation is a remarkably complex endeavor. In many cases, decisions involved in hydrocarbon exploration and production may be informed by measurements from well logging tools (e.g., downhole well logging tools) that are conveyed deep into the wellbore. The measurements may be used to infer properties or characteristics of the geological formation surrounding the wellbore. One example of such downhole well logging tools are propagation well logging tools. However, conventional processing methods for handling the measurements may lead to relatively high processing times as well as memory requirements for storing the processed measurements.
A summary of certain embodiments disclosed herein is set forth below. It should be understood that these aspects are presented merely to provide the reader with a brief summary of these certain embodiments and that these aspects are not intended to limit the scope of this disclosure. Indeed, this disclosure may encompass a variety of aspects that may not be set forth below.
One embodiment of the present disclosure relates to a method. The method includes acquiring, via a processor, propagation measurements in a wellbore through a geological formation using one or more propagation downhole well logging tools having at least two receivers. The method also includes converting, via the processor, the propagation measurements to two apparent conductivities based at least in part on a frequency associated with the propagation measurements, a relative longitudinal position of the at least two receivers, and a phase shift measurement and an attenuation measurement.
Various refinements of the features noted above may be undertaken in relation to various aspects of the present disclosure. Further features may also be incorporated in these various aspects as well. These refinements and additional features may exist individually or in any combination. For instance, various features discussed below in relation to one or more of the illustrated embodiments may be incorporated into any of the above-described aspects of the present disclosure alone or in any combination. The brief summary presented above is intended to familiarize the reader with certain aspects and contexts of embodiments of the present disclosure without limitation to the claimed subject matter.
Various aspects of this disclosure may be better understood upon reading the following detailed description and upon reference to the drawings in which:
One or more specific embodiments of the present disclosure will be described below. These described embodiments are examples of the presently disclosed techniques. Additionally, in an effort to provide a concise description of these embodiments, certain features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions may be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would still be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.
When introducing elements of various embodiments of the present disclosure, the articles “a,” “an,” and “the” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Additionally, it should be understood that references to “one embodiment” or “an embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features.
In the present context, the term “about” or “approximately” is intended to mean that the values indicated are not exact and the actual value may vary from those indicated in a manner that does not materially alter the operation concerned. For example, the term “about” or “approximately” as used herein is intended to convey a suitable value that is within a particular tolerance (e.g., ±10%, ±5%, ±1%, ±0.5%), as would be understood by one skilled in the art.
As mentioned above, oil and gas exploration organizations may make certain oil and gas production decisions, such as determining where to drill, based at least in part on well log data. More specifically, a well logging tool acquires well logging measurements, which may be processed (e.g., normalized, de-noised, provided as inputs to a model, etc.) by a suitable computing device to generate the well log data. As referred to herein, “well log data” is a measurement or a property derived from measurements versus depth or time, or both, of one or more properties (e.g., resistivity, conductivity, dip and azimuth, and the like) in or around a wellbore, and thus, may be used to identify a location within the wellbore that corresponds to an area of interest (e.g., hydrocarbons, an organic deposit, a “bed” or layer of sedimentary rock, or stratum, and the like). At least in some instances, the well log data may be transformed into one or more visual representations (e.g., a well log) that are presented as hard copies or on an electronic display, where each visual representation of the one or more visual representations may depict the well log data resulting from the well logging measurements.
One type of well logging measurement that may be used to inform the oil and gas production decisions are propagation well logging measurements. In general, propagation well logging measurements may be acquired using one or more propagation well logging tools that each include a number of transmitter coils and receiver coils. As should be understood by one of ordinary skill in the art, a propagation well logging tool may operate at a frequency (e.g., approximately 100 kHz, 200 kHz, 300 kHz, 400 kHz, 1000 kHz, 2000 kHz, and the like), which may facilitate the determination of certain properties of a geological formation, such as the resistivity and dielectric properties. It should be noted that measuring the resistivity and dielectric properties may enable differentiation between certain components that are present within the geological formation such as water, oil, and gas. However, while the ability to measure at these frequencies may be advantageous for differentiating between these components (e.g., water and oil) based at least in part on the resistivity and dielectric properties, propagation well logging measurements at these frequencies (e.g., measured by a receiver of the propagation well logging tool) may be adversely affected due to the skin effect.
Conventional propagation well logging tools may process the phase shift and attenuated propagation measurements using an inversion in order to generate conductivity and/or resistivity well logs. Existing processes for inverting the measurements (e.g., the phase shift and attenuate measurements) may be computationally expensive (e.g., having high memory usage), and thus take a relatively large amount of time to process the measurements to generate the well logs, which are used for informing oil and gas productive decisions.
Accordingly, the present disclosure relates to techniques for processing propagation well logging measurements to generate an apparent conductivity and/or apparent resistivity based at least in part on the propagation well logging measurements without using an inversion or a resistivity transform. In particular, the disclosed techniques for processing the propagation well logging measurements may utilize a tool constant that is based on a relative longitudinal position of at least two of the receivers of the propagation well logging tool. The disclosed tool constant and the apparent conductivity and/or the apparent resistivity may be used to generate apparent conductivity and/or apparent resistivity well logs. In some embodiments, the apparent conductivity may be a phase shift apparent conductivity and/or an attenuation apparent conductivity. As discussed in further detail with regard to
With this in mind,
Moreover, although the propagation well logging tool 12 is described as being a wireline downhole tool, it should be appreciated that any suitable conveyance may be used. For example, the propagation well logging tool 12 may instead be conveyed as a logging-while-drilling (LWD) downhole tool as part of a bottom hole assembly (BHA) of a drill string, conveyed on a slickline or via coiled tubing, and so forth. For the purposes of this disclosure, the propagation well logging tool 12 may be any suitable measurement downhole tool that acquires propagation logging measurements through depths of the wellbore 16.
Many types of propagation well logging tools 12 may acquire propagation well logging measurements in the wellbore 16. These include, for example, a compensated dual resistivity (CDR) downhole tool, an array resistivity compensated (ARC) downhole tool, PERISCOPE, and the like. The propagation well logging tool 12 may provide propagation logging measurements 26 to a data processing system 28 via any suitable telemetry (e.g., via electrical signals pulsed through the geological formation 14 or via mud pulse telemetry). The data processing system 28 may process the propagation logging measurements 26 to identify a horizontal conductivity and/or horizontal resistivity, a vertical conductivity and/or vertical resistivity, a dip and an azimuth at various depths of the geological formation 14 in the wellbore 16.
To this end, the data processing system 28 thus may be any electronic data processing system that can be used to carry out the systems and methods of this disclosure. For example, the data processing system 28 may include a processor 30, which may execute instructions stored in memory 32 and/or storage 34. As such, the memory 32 and/or the storage 34 of the data processing system 28 may be any suitable article of manufacture that can store the instructions. The memory 32 and/or the storage 34 may be ROM memory, random-access memory (RAM), flash memory, an optical storage medium, or a hard disk drive, to name a few examples. A display 36, which may be any suitable electronic display, may provide a visualization, a well log, or other indication of properties in the geological formation 14 or the wellbore 16 using the propagation logging measurements 26.
Based on the identified locations and properties of the hydrocarbon deposits, certain downhole operations on positions or parts of the geological formation 14 may be performed (process block 44). That is, hydrocarbon exploration organizations may use the locations of the hydrocarbon deposits to determine locations in the wellbore to isolate for extracting liquid, frack, and/or drill into the Earth. As such, the hydrocarbon exploration organizations may use the locations and properties of the hydrocarbon deposits and the associated overburdens to determine a path along which to drill into the Earth, how to drill into the Earth, and the like.
After exploration equipment has been placed within the geological formation 14, the hydrocarbons that are stored in the hydrocarbon deposits may be produced (block 46) via natural flowing wells, artificial lift wells, and the like. Further, the produced hydrocarbons may be transported (block 48) to refineries and the like via transport vehicles, pipelines, and the like. Further still, the produced hydrocarbons may be processed (block 50) according to various refining procedures to develop different products using the hydrocarbons.
It should be noted that the processes discussed with regard to the method 40 may include other suitable processes that may be based at least in part on the locations and properties of hydrocarbon deposits as indicated in the seismic data acquired via one or more seismic survey. As such, it should be understood that the processes described above are not intended to depict an exhaustive list of processes that may be performed after determining the locations and properties of hydrocarbon deposits within the geological formation.
With the foregoing in mind,
As shown in the illustrated embodiment, the first receivers 54 are disposed at a longitudinal distance 64 from the transmitters 52, and the second receivers 56 are disposed at a longitudinal distance 66 from the transmitters 52. As discussed in more detail below regarding the discussion of
The illustrated example of the propagation well logging tool 12 is shown communicatively coupled to the data processing system 28. As discussed herein, the propagation well logging tool 12 (e.g., multi-axial well logging tool) may acquire measurements within a wellbore 16 of the geological formation 14. The processor 30 of the data processing system 28 may receive these measurements. The memory 32 may store information such as control software, frequency, configuration data, etc. The memory 32 may include a volatile memory, such as random access memory (RAM), and/or a nonvolatile memory, such as read-only memory (ROM). The memory 32 may store a variety of information and may be used for various purposes. For example, the memory 32 may store processor-executable instructions including firmware or software for the processor 30 to execute. In some embodiments, the memory 32 is a tangible, non-transitory, machine-readable-medium that may store machine-readable instructions for the processor 30 to execute. The memory 32 may include ROM, flash memory, a hard drive, or any other suitable optical, magnetic, or solid-state storage medium, or a combination thereof. The memory 32 may store data, instructions, and any other suitable data.
As shown in the illustrated embodiment, the propagation well logging tool 12 is within a geological formation 14 having conductivity and permittivity with a traverse isotropy. In the illustrated embodiment, the downhole tool axis (e.g., Z-axis 62) of the triaxial propagation well logging tool 12 is aligned to the normal of the lamination planes 68 (e.g., the interfaces of geological layers). Each lamination (e.g., geological layer), a few of which are shown (e.g., 68a, 68b, 68c, and 68d), of the geological formation 14 has a conductivity and/or a permittivity that is approximately homogeneous along X-axis 58 and the Y-axis 60, while the conductivity and/or permittivity may vary along the Z-axis 62. In the current embodiment, all the light-colored laminations (e.g. 68a and 68c) share the same conductivity, and all the dark-colored laminations (e.g. 68b and 68d) share the same conductivity. Therefore, the conductivity, σ, and the permittivity, ∈, of all laminations as a whole may be represented by the equations:
where σh and σv are the horizontal conductivities (e.g., along the X-axis 58 and the Y-axis 60) and the vertical conductivities (e.g., along the Z-axis 62), respectively, and εh and εv are the horizontal permittivity and the vertical permittivity, respectively. The general directions of the horizontal conductivities and vertical conductivities are shown in the axis 70. The unit vectors {circumflex over (x)}, ŷ, and {circumflex over (z)} correspond to X-axis 58, Y-axis 60, and Z-axis 62. As referred to herein, the transmitters 52 and the receivers (e.g., first receivers 54 and second receivers 56) that are generally aligned with the X-axis 58 and the Y-axis 60 are referred to as being coplanar (e.g., coplanar transmitters and/or coplanar receivers) and the transmitters 52 and the receivers (e.g., first receivers 54 and second receivers 56) that are generally aligned with the Z-axis 62 are referred to as being coaxial or coaxial receivers (e.g., coaxial transmitters and/or coaxial receivers).
With the foregoing in mind,
Generally, the process 80 includes acquiring (process block 82) propagation measurements associated with a geological formation using one or more propagation well logging tools having at least two receivers (e.g., a first receiver 54 and a second receiver 56). The process 80 also includes converting (process block 84) the propagation measurements to apparent conductivity measurements based at least in part on a frequency associated with the propagation measurement, a relatively longitudinal position of the receivers (e.g., a first receiver 54 and a second receiver 56), and a phase shift measurement and/or an attenuation measurement. Further, the process 80 includes generating (process block 86) one or more apparent conductivity well logs based at least in part on the apparent conductivity measurements. While process 80 is discussed above with respect to apparent conductivity measurements, it should be noted that the apparent conductivity may also be represented as an apparent resistivity measurement.
In process block 82, the data processing system 28 (e.g., processor 30) may receive and/or acquire propagation measurements from a propagation well logging tool 12. In some embodiments, acquiring the propagation measurements from the propagation well logging tool 12 may include the processor 30 sending suitable control signals to the propagation well logging tool 12 to begin acquiring the propagation measurements. As discussed herein, the propagation measurements may include phase shift measurements and/or attenuation measurements.
In process block 84, the processor 30 may convert the propagation measurements to apparent conductivity measurements based on a frequency (e.g., an operating frequency of the propagation well logging tool 12 such as approximately 100 kHz, 200 kHz, 400 kHz, 1000 kHz, 2000 kHz, 2 MHz, and the like). It should be noted that converting the propagation measurements may depend on the orientation of the receivers (e.g., a first receiver 54 and a second receiver 56) and the transmitter(s) 52 of the propagation well logging tool 12. That is, in some embodiments, the propagation measurements may be acquired by a coaxial propagation well logging tool, a coplanar propagation well logging tool, a triaxial propagation well logging tool, and the like, as discussed in further detail below. In any case, the processor 30 may convert the propagation measurements based on a relative longitudinal position of the receivers (e.g., a first receiver 54 and a second receiver 56) as discussed in further detail below (e.g., with regards to equation 31). Then, in process block 86, the processor 30 may generating apparent conductivity well logs based on the apparent conductivity measurements.
The discussion below provides an example for converting the propagation measurements to apparent conductivity, as described above with regards to process block 84. For a coaxial propagation downhole tool (e.g., having transmitter coil and receiver coils that are oriented along the Z-axis 62, the voltages induced in the two receiver coils (e.g., the first receiver 54 and the second receiver 56) are:
And for a coplanar propagation downhole tool (e.g., having transmitter coil and receiver coils oriented along the X-axis 58 or Y-axis 60), the voltages induced in the two receiver coils are:
For both Eqns. (3) and (4), I is the current in the transmitter coil, ω is the angular frequency, ω=2πf where f is the frequency of current I. NT and NR
k
h=√{square root over (iωμ(σh−iωεh))} (5)
k
v=√{square root over (iωμ(σv−iωεv))} (6)
In some embodiments, kh and kv may be expressed in terms of a complex number:
In the above, αh and αv are phase shifts corresponding to σh and εh, and σv and εv, respectively; βh and βv are attenuations corresponding to σh and εh, and σv and εv, respectively.
In certain conventional propagation processing techniques, the ratio of voltages at the two receivers (e.g., first receiver 54 and second receiver 56) is acquired and converted to phase shift and attenuation. The voltage ratio measurement can compensate for transmitter gains. A composite downhole tool using two or more transmitter coils may provide compensation for receiver gains and borehole rugosity. In the following, low-frequency asymptotic expressions of phase shift and attenuation are derived for an elemental downhole tool. Low-frequency asymptotic expressions of a fully compensated downhole well logging tool consisting of multiple transmitters and receivers are then given by means of the superposition of those of elemental downhole tools.
As discussed above, certain technique for using propagation measurements utilize the ratio of the voltages measured by the receivers. For the co-axial propagation well logging tool, the logarithm of the ratio of the voltages at the receivers are, in accordance with equation 3:
Denoting the moment of the receivers by MR
Without loss of generality, assuming that MR
Eqn. 11 may be expanded in powers of khL using Taylor's expansion for the ln z function:
Using Eqn. 12, the third term on the right-hand side of Eqn. 10 may be written as:
ΔL≡L2−L1 (14)
And noting that:
Using Eqns. (14) and (15), Eqn. (13) becomes:
Noting that:
Therefore, when |ikhL2|<1:
Substituting Eqns. (18)-(20) into Eqn. (16) produces:
The first term on the right-hand side of Eqn. (21) is attributed to the geometrical decay of EM wave in the air and can be removed from the two sides. Then:
It is noted that the first order term −ikhΔL in Eqn. (16) is cancelled out due to the first term of Eqn. (16). When the frequency is low
Recall that:
k
h
2=ωμ(ωεh+iσh), (24)
The above asymptotic form suggests that the attenuation and phase shift measurements can be converted to apparent conductivity as is normally done for induction measurements. To this end, let:
Using the polar form of the two complex voltages, i.e.:
V
zz,j
=|V
zz,j
|e
iϕ
, j=1,2. (27)
the attenuation and phase shift in Eqn. (26) can be written as:
A downhole tool constant may be defined for the coaxial propagation well logging tool:
then the apparent conductivity of the coaxial propagation downhole tool is:
The asymptotic forms in the above are opposite to those of apparent conductivity for the coaxial induction downhole tool. Alternatively, the apparent conductivity can be defined as:
Then:
The asymptotic forms of the second definition for the apparent conductivity are the same as those of the coaxial induction downhole tool. Both forms of the definition indicate that the phase shift apparent conductivity σa,zzPS is a measure of conductivity and the attenuation apparent conductivity σa,zzAT a measure of permittivity or dielectric constant when the frequency is low.
The logarithm of the ratio of voltages at the two coplanar receivers is:
As with the ratio for the coaxial propagation downhole tool, assuming that NR
In some embodiments, an error calibration may be performed to account for the shield and tool geometry that may improve the measurements, in at least some instances. The error calibration may include determining the attenuation and/or phase shift measurements for the tool in air (e.g., by acquiring an additional propagation measurement at the surface above the geological formation, in a lab, and the like) and/or under ambient conditions and then modifying the propagation measurements obtained downhole accordingly, such as via a background subtraction.
According to Eqn. (9), the third part of Eqn. (37) can be expanded as:
Note that:
Where:
Recall the expansion given in Eqn. (17), when
Substituting Eqns. (43)-(45) into Eqn. (39), and rearranging the results, it can be shown that:
It is noted that the first order term −ikhΔL in Eqn. (39) is cancelled out due to the first term of Eqn. (43). Moreover, the second order term of kh in Eqn. (43) is also cancelled out due to the first term of Eqn. (44). Therefore, the only second term is that of kv. As with Eqn. (22), the first term on the right-hand side of Eqn. (46) is the geometrical decay of EM wave in the air and can be removed from the two sides. Then:
When the frequency is low:
Recall that:
k
v
2=ωμ(ωεv+iσv), (49)
Therefore:
As with Eqn. (25), the asymptotic form in the above suggests that the attenuation and phase shift measurements can be converted to apparent conductivity measurements. In a similar manner, let:
Using the polar form of the two complex voltages, i.e.:
V
xx,j
=|V
xx,j
|e
iϕ
, j=1,2. (52)
The attenuation and phase shift in Eqn. (51) can be written as:
Define the following downhole tool constant for the coplanar propagation downhole tool:
Accordingly, the apparent conductivity of the coplanar propagation downhole tool is:
The asymptotic forms in the above are opposite to those of apparent conductivity for the coplanar induction downhole tool. As with the coaxial voltage ratio, an alternative to the apparent conductivity of Eqn. (57) may be given by:
Accordingly:
The asymptotic forms of the second definition for the apparent conductivity are the same as those of the coplanar induction downhole tool. Both forms of the definition indicate that the phase shift apparent conductivity σa,xxPS is a measure of conductivity and the attenuation apparent conductivity σa,xxAT a measure of permittivity or dielectric constant when the frequency is low.
A fully compensated propagation downhole tool may compensate for both the transmitter and receiver gains. In one example, the z-axis of the downhole tool coordinates coincides with the downhole tool axis (e.g., Z-axis 62), and there are in total NT transmitters, some of which are below R1 and R2, and the rest of which are above R1 and R2. The positive direction of the Z-axis is pointed from R1 to R2. If Tl, the l-the transmitter is on the lower side of the two receivers, the logarithmic voltage ratio of R1 and R2 is:
If Tl is on the upper side of the receivers, the voltage ratio is:
Eqns. (63) and (64) can be combined into one equation such that:
where γl=sgn(LT
The terms related to receiver gains can be separated out, yielding:
For a fully compensated downhole tool:
The above compensation condition must be satisfied so that the receiver gains are eliminated from the combined logarithmic voltage ratio given in Eqn. (67). With this in mind, Eqn. (67) becomes:
For the l-th transmitter, the voltage ratio can be written as:
In the above equation, ATT
It has been shown in the above that the air-signal-corrected voltage ratio can be converted to the apparent conductivity as follows:
In the above, KT
For an elemental coplanar downhole tool:
Substituting Eqns. (73) and (74) in Eqn. (69) yields the following equation:
Recall that when the frequency is low, the apparent conductivity of an elemental voltage ratio approaches the true conductivity of the formation, i.e.:
σa,T
Here, for a coaxial measurement, σ=σh, ε=εh; for a coplanar measurement, σ=σv, ε=εv, assuming the downhole tool axis is perpendicular to the lamination plane. Using the above asymptotic form in Eqn. (75), then:
AT
C
+iPS
C≈Σl=1N
Eqn. (77) suggests that the apparent conductivity for the combined phase shift and attenuation measurements can be defined as:
where:
As with the apparent conductivity of an elemental voltage ratio, σa,C of the compensated downhole tool approaches the true conductivity of the formation,
σa,C≈σ−iωε, (81)
when the frequency is relatively low.
Generally, the process 90 includes acquiring (process block 92) propagation measurements associated with a geological formation using one or more propagation well logging tools having at least two receivers (e.g., a first receiver 54 and a second receiver 56). The process 80 also includes converting (process block 94) the propagation measurements to apparent conductivity measurements based at least in part on a frequency associated with the propagation measurement, a relatively longitudinal position of the receivers, and a phase shift measurement and/or an attenuation apparent measurement, and the apparent conductivity includes a phase shift apparent conductivity and an attenuation apparent conductivity. Further, the process 90 includes determining (process block 96) the skin effect corrected apparent conductivity based the apparent conductivity. Further still, the process 90 includes determining (process block 98) the dielectric constant based on the apparent conductivity. While process 90 is discussed above with respect to apparent conductivity measurements, it should be noted that the apparent conductivity may also be represented as an apparent resistivity measurement.
In process block 92, the data processing system 28 (e.g., processor 30) may receive and/or acquire propagation measurements from a propagation well logging tool 12. In some embodiments, acquiring the propagation measurements from the propagation well logging tool 12 may include the processor 30 sending suitable control signals to the propagation well logging tool 12 to begin acquiring the propagation measurements. As discussed herein, the propagation measurements may include phase shift measurements and/or attenuation measurements.
In process block 94, the processor 30 may covert the propagation measurements to apparent conductivity measurements based on a frequency (e.g., an operating frequency such as approximately 100 kHz, 200 kHz, 400 kHz, 1000 kHz, 2000 kHz, 2 MHz, and the like). It should be noted that converting the propagation measurements may depend on the orientation of the receivers (e.g., first receiver 54 and second receiver 56) and the transmitter(s) 52 of the propagation well logging tool 12. That is, in some embodiments, the propagation measurements may be acquired by a coaxial propagation well logging tool, a coplanar propagation well logging tool, a triaxial propagation well logging tool, and the like, as discussed in further detail below. In any case, the processor 30 may convert the propagation measurements based on a relative longitudinal position of the receivers (e.g., first receiver 54 and second receiver 56) as discussed in further detail below (e.g., with regards to equation 31). Then, in process block 96, the processor 30 may determine the skin effect corrected apparent conductivity based on the apparent conductivity, as discussed in more detail below.
Substituting Eqn. (22) in Eqn. (35), the following equation ensues
When the displacement current is negligible, namely, when ωεh<<σh, Eqn. (80) reduces to
In component form:
It should be noted that the leading term of σa,zzAT is identical to the second term of σa,zzPS in terms of magnitude but the sign is opposite. This relationship can be used to correct the skin effect on σa,zzPS by simply adding σa,zzAT to σa,zzPS, namely:
σa,zzPS,C≈σa,zzPS+σa,zzAT. (86)
The above may be true for a coaxial elemental propagation downhole tool.
In a generally similar manner, for a coplanar elemental propagation downhole tool, it can be shown that when the displacement current is negligible, the following equation may hold true:
In component form:
As with σa,zz, the leading term of σa,zzAT is identical to the second term of σa,zzPS in terms of magnitude but the sign is opposite. Likewise, this relationship can be used to correct the skin effect on σa,xxPS by simply adding σa,xxAT to σa,xxPS, namely:
σa,xxPS,C≈σa,xxPS+σa,xxAT. (90)
The apparent conductivity of a fully compensated downhole tool is a linear superposition of those of the underlying elemental downhole tools. Therefore, the skin effect correction schemes given in Eqns. (86) and (90) may hold true for a fully compensated downhole tool.
Additionally or alternatively, in process block 98, the processor 30 may determine the apparent dielectric constant based on the apparent conductivity as discussed in more detail below.
For example, the apparent dielectric constants may be defined as follows:
The above two expressions are for a coaxial and coplanar elemental downhole tool, respectively, and are obtained using the second form of apparent conductivity for both tools. In a highly resistive formation (e.g., above a resistivity threshold, such as where ωεh>>σh and/or ωεv>>σv) apparent dielectric constants given in Eqns. (91) and (92) may provide an estimate of horizontal and vertical dielectric constants, respectively.
A Multi-Array Propagation Tool with a Uniform Tool Constant
The tool constants given in Eqns. (31) and (56) for are a function of spacing and frequency. Therefore, the tool constants may be used for optimizing tool design. In one application, the tool constants for all arrays of a multi-array propagation tool consisting of multiple elemental arrays may be selected such that:
where j is the index for the arrays, M is the total number of arrays, and C is a constant number. The subscript α of Kααj is the orientation of the transmitter and receiver coils, α=x,z. Such a selection ensures that the measurements from all arrays have the same skin effect. It should be noted that this property may be important when using the spread of logs from multiple arrays for a quick invasion evaluation.
As shown in the graphs depicted in
As shown in the graphs depicted in
In particular,
In particular,
More specifically,
As mentioned above, the techniques of the present disclosure may be used for designing a multi-array propagation well-logging tool having a uniform tool constant.
Accordingly, the present disclosure relates to techniques for processing propagation well logging measurements to generate an apparent conductivity and/or apparent resistivity based at least in part on the propagation well logging measurements without using an inversion or a resistivity transform. In particular, the disclosed techniques for processing the propagation well logging measurements may utilize a tool constant that is based on a relative longitudinal position of at least two of the receivers of the propagation well logging tool. Using the disclosed tool constant, apparent conductivity and/or apparent resistivity may be computed, which may be used to generate apparent conductivity and/or apparent resistivity well logs. In some embodiments, the apparent conductivity may be a phase shift apparent conductivity and/or an attenuation apparent conductivity. As discussed herein, the phase shift apparent conductivity may provide a measure of formation conductivity and the attenuation apparent conductivity may provide a measure of the skin effect. In some embodiments, the phase shift apparent conductivity may be corrected for the skin effect using the attenuation apparent conductivity to generate an improved apparent conductivity that may be representative of the true formation conductivity.
The specific embodiments described above have been shown by way of example, and it should be understood that these embodiments may be susceptible to various modifications and alternative forms. It should be further understood that the claims are not intended to be limited to the particular forms disclosed, but rather to cover modifications, equivalents, and alternatives falling within the spirit and scope of this disclosure.
The present document is based on and claims priority to U.S. Provisional Application Ser. No. 63/002,945, filed Mar. 31, 2020, which is incorporated herein by reference in its entirety.
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/US2021/024949 | 3/30/2021 | WO |
Number | Date | Country | |
---|---|---|---|
63002945 | Mar 2020 | US |