WO2009058126A1

WO2009058126A1 - Time to depth conversion for logging systems and methods

Info

Publication number: WO2009058126A1
Application number: PCT/US2007/082922
Authority: WO
Inventors: Jim R. Wilson
Original assignee: Halliburton Energy Services, Inc.
Priority date: 2007-10-30
Filing date: 2007-10-30
Publication date: 2009-05-07

Abstract

Logging systems and methods often collect logging data as a function of time and rely on independently generated tool position measurements that may be inadequate. If the logging tool assembly includes at least two highly correlated logging sensors with a fixed measurement spacing, the techniques disclosed herein can be used to determine tool velocity and sensor-specific depth functions for each measurement signal. The depth functions, when combined with time- dependent logging signals, enable the conversion of time-dependent signals into spatial position- dependent signals. At least some of the disclosed techniques are tailored for azimuthally-sensitive instruments and will account for tool tilt relative to the borehole axis.

Description

Time to Depth Conversion for Logging Systems and Methods

BACKGROUND

Oil field operators demand a great quantity of information relating to the parameters and conditions encountered downhole. Such information typically includes characteristics of the earth formations traversed by the borehole, and data relating to the size and configuration of the borehole itself. The collection of information relating to conditions downhole, which commonly is referred to as "logging," can be performed by several methods including wireline logging and "logging while drilling" (LWD).

In wireline logging, a probe or "sonde" is lowered into the borehole after some or the entire well has been drilled. The sonde hangs at the end of a long cable or "wireline" that provides mechanical support to the sonde and also provides an electrical connection between the sonde and electrical equipment located at the surface of the well. In accordance with existing logging techniques, various parameters of the earth's formations are measured and as the sonde is pulled uphole. As measurements are taken, an index wheel at the surface measures the remaining length of cable to estimate the sonde's position at any given time. At the surface, the cable length readings (with corrections for stretch due to tension) are combined with the sensor readings to form various sensor logs as a function of depth.

In LWD, the drilling assembly includes sensing instruments that measure various parameters as the formation is being penetrated. While LWD techniques allow more contemporaneous, and often more accurate, formation measurements, it is difficult to establish and maintain a direct electrical connection in an LWD environment. Consequently, alternative (limited bandwidth) communication channels are typically employed for obtaining LWD logging information, and typically the bulk of the logging data is stored in tool memory until the drilling assembly returns to the surface. At the surface, the logging data (which has been recorded as a function of time) is combined with measurements from an index wheel or other mechanism that measures the length of the drill string in the hole as a function of time. In both the above described logging methods, the surface measurements of length/position as a function of time serve as a map for time-to-depth conversion, i.e., translating the time-based sensor measurements into position-based sensor measurements. However, being performed at the surface, such measurements are subject to inaccuracies due to expansion of the drillstring or wireline. Such inaccuracies can cause difficulties and additional expense in evaluating completion intervals and achieving effective well completion.

BRIEF DESCRIPTION OF THE DRAWINGS

A better understanding of the disclosed invention embodiments can be obtained when the following detailed description is considered in conjunction with the following drawings, in which: Fig. 1 is an environmental view of an illustrative logging while drilling (LWD) environment; Fig. 2 is a side view of a drillstring in a borehole; Fig. 3 shows graphs of time-based sensor measurements; Fig. 4 shows a graph of a depth-based sensor measurement; Fig. 5 shows a tilted tool in a borehole;

Fig. 6 is a flowchart of an illustrative logging method having time-to-depth conversion; and Fig. 7 is an illustrative processing system for log data.

While the invention is susceptible to various modifications and alternative forms, specific embodiments thereof are given by way of example in the drawings and the following description. 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.

NOMENCLATURE

Certain terms are used throughout the following description and claims to refer to particular system components. This document does not intend to distinguish between components that differ in name but not function. The terms "including" and "comprising" are used in an open- ended fashion, and thus should be interpreted to mean "including, but not limited to...". The term "couple" or "couples" is intended to mean either an indirect or direct electrical, mechanical, or thermal connection. Thus, if a first device couples to a second device, that connection may be through a direct connection, or through an indirect connection via other devices and connections. The term "depth" is used to indicate position along the borehole axis. The term "vertical depth" is used to indicate position along a vertical line.

DETAILED DESCRIPTION

Logging systems and methods often collect logging data as a function of time and rely on independently generated tool position measurements that may be inadequate. If the logging tool assembly includes at least two highly correlated logging sensors with a fixed measurement spacing, the techniques disclosed herein can be used to determine tool velocity and sensor-specific depth functions for each measurement signal. The depth functions, when combined with time- dependent logging signals, enable the conversion of time-dependent signals into spatial position- dependent signals. At least some of the disclosed techniques are tailored for azimuthally-sensitive instruments and will account for tool tilt relative to the borehole axis. The disclosed techniques enable accurate spatial mapping of data gathered as a function of time, thereby reducing well completion costs and improving formation evaluation accuracy.

Fig. 1 shows a drilling platform 2 equipped with a derrick 4 that supports a hoist 6. Drilling of a well bore, for example, the borehole 20, may be carried out by a string of drill pipes 8 connected together by "tool" joints 7 so as to form a drill string. The hoist 6 suspends a kelly 10 that is used to lower the drill string through rotary table 12. Connected to a lower end of the drill string is a drill bit 14. The borehole 20 is drilled by rotating the drill string and/or by using a downhole motor to rotate the drill bit 14. Drilling fluid is pumped by recirculation equipment 16 through supply pipe 18, through drilling kelly 10, and down through an interior passageway of the drill string 8. The drilling fluid exits the drill string through apertures in the drill bit 14. The fluid then travels back up to the surface through the borehole 20 via an annulus 30 between an exterior surface of the drill string and the borehole wall. At the surface, the fluid flows into a "mud" pit 24, from which it may be drawn by recirculation equipment 16 to be cleaned and reused. The drilling mud may serve to cool the drill bit 14, to carry cuttings from the base of the borehole 20 to the surface, and to balance the hydrostatic pressure from the surrounding formation.

The drill bit 14 is part of a bottom-hole assembly that includes one or more logging while drilling (LWD) tools 26 and a telemetry transceiver 28. Other LWD tool assemblies 32 may be located along the length of the drillstring. The various LWD tools 26, 32 acquire information regarding the surrounding formations, and the telemetry transmitter 28 may be used to communicate selected telemetry information to a surface transceiver 30, perhaps via one or more telemetry repeaters. In some embodiments, control signals may be communicated from the surface transceiver 30 to the telemetry transceiver 28 to control the operating parameters of the bottom- hole assembly. For example, the bottom-hole assembly may be steerable, enabling the borehole 20 to be steered into and along formations of interest.

Fig. 2 shows a side view of a drill string 8 in order to define a convenient coordinate system. In this example, the drill string includes four logging instruments S1-S4, each spaced at a corresponding distance AZ_n from an arbitrary reference point on the drill string. This arbitrary reference point may be, e.g., the top or bottom of the bottom-hole assembly, the measure-point of a selected sensor, the center of the sensor array, the position of the drill bit, etc. At least two of the spaced instruments (e.g., Sl and S3) are chosen to have a high measurement correlation. For example, Sl and S3 may be of the same or similar types, or may in fact be identical. Of course, identical tools are expected to yield nearly identical measurements that by definition are highly correlated. (Where correlation values of signals having zero mean are normalized so that a correlation of 1 indicates identity and a correlation of -1 indicates additive inverses, correlation values with magnitudes in excess of 0.5 are considered to indicate high correlation.) Tools of different types that may be expected to have high correlations include the following pairs: TOOL 1 TOOL2 medium-depth resistivity deep resistivity galvanic resistivity induction resistivity neutron porosity shear wave velocity neutron porosity density

When different types are employed, it will be beneficial to perform depth-resolution matching as described in U.S. Patent 5,581,024. Such matching improves the correlation delay measurement accuracy.

Assuming the arbitrary reference point is positioned in the borehole at depth z(t), the depth of sensor n is: z_n(t) = z(t) -AZ_n . (1)

Thus, given the sensor measurements as a function of time for sensor n, s_n(t), and the reference point depth z(t), the sensor measurements as a function of depth s_n(z) can be readily determined and plotted. It is in this sense that the reference point depth serves as a map for time-to-depth conversion.

Fig. 3 shows illustrative sensor measurements as a function of time Si(t) and S3(t). The sensor measurements are highly correlated, but due to changes in velocity, the correlation delay τ varies with time. The correlation delay can be determined in a number of ways. In some embodiments, a window function (such as a rectangular function r(t) that is only nonzero between -T/2 and T/2) is used to determine the value of correlation delay that maximizes:

The correlation delay τ will be a function of the initial window position to. (Note that if sensor Sj is chosen to be the leading sensor, the correlation delay will be uniformly negative. In some embodiments, the sensor signals may be normalized and shifted to zero mean before processing to determine correlation delay.)

Different window functions (and lengths) may be employed, and in some embodiments, the time scale of one sensor signal may be scaled relative to that of the other sensor signal based on the tested value of correlation delay. Various tradeoffs between correlation delay estimation accuracy, robustness, and search complexity can be chosen. For example, Bartlett (triangular) windows, Harm windows, Hamming windows, Blackman windows, and Kaiser windows are suitable for different tradeoffs in computational complexity, while longer window lengths may increase estimate robustness at the cost of resolution. It is expected that the correlation delays will be determined numerically, and hence computational complexity may be a significant factor where prompt results are needed.

In the example of Fig. 3, it can be seen that the correlation delay τ is initially xj, but it decreases to τ₂ before increasing to τ₃. The key observation here is that the tool moves a fixed distance between the correlated sensor readings, and hence this fixed distance can be used as a scale when converting from time-domain to depth. Assuming the inter-sensor distance L (= ΔZi - ΔZ₃) is fixed, one can readily determine that the tool velocity increases (L/τ₂ is larger than L/τi) and decreases (L/τ₃ is smaller than L/τi) in this example. The fixed inter-sensor distance gives rise to the following observation:

L = j;^»+τ('->v(θdf = j;;;£^+τ('°^+Λ/)v(o<# . (3)

Assuming that the inter-sample spacing of each sensor signal is Δt, the overlap of the integrals can be eliminated, yielding: ι;_: ^+Atvit)dt = ι;:₊ ⁺?jf°^+At)At)dt . w

If the velocities are assumed to be constant for the duration of each integral, this equation reduces to: v(0 = v(t + r(ϊ))[Δ/ + τ{t) - τ(t - Δ/)]/Δ/ . (5)

(Recall that the calculation of correlation delays τ may be structured to provide uniformly negative values.) Thus, if the velocity is carefully recorded through the first distance L, it becomes possible to determine the velocity at all later times from the correlation delays using equation (5). Over such a limited distance, and particularly if performed near the surface, the initial velocity measurements may be expected to be highly accurate.

Other approximations for the integrals in equation (4) are possible. For example, a straight-line approximation can be used to replace the integrals, so that: i [v(/_{o +} Δ/)+ v(/_o)]Δ/ =

(6) \ [v(t_o + At + τ(t_o + At))+ v(t_o + T(O)][At + <t_o + At) - τ(t_o)]

Solving for the latest velocity gives:

v(t) = [v(/ + τ(t))+ v(t -At + τ(t - At))\ 1 + ^{T(t) T(t At)} -v(t - At) . (7)

To further refine the velocity estimates, other integral approximations may be attempted. As a subsequent step, equation (3) may be evaluated and the interval velocities adjusted to minimize error accumulation from the integral approximations. In some embodiments, additional accuracy is obtained by combining correlation delays (or the resulting velocity estimates) from multiple sensor pairs. Much greater accuracies are expected if different inter-sensor spacings are used, e.g., Ix and 1Ox, or Ix, 2x, 4x, and 8x. These additional sensors may be particularly useful when used with flexible drilling assemblies. The flexure of such assemblies may introduce distance and velocity estimation errors between the short-spaced detectors that can be compensated for with the measurements between the long-spaced detectors.

Once the velocity values have been determined for each sampling time, the depth function z(t) can be found: z(0= JX0<# . (8) or in discrete form: z(t_k+l) = z(t_k) + v(t_k)At . (9)

At this point, equation (1) may be used with the known sensor offsets to generate depth- based logs such as that shown in Fig. 4. Many modern sensors have azimuthal sensitivity with high spatial resolution (producing signals s_n(θ,t), where θ is the borehole azimuth). The tool assemblies for such sensors include a tool orientation sensor to track the tool orientation as the drill string rotates and changes direction. The orientation sensor package often includes both magnetic field sensing and gravitational field sensing mechanisms such as magnetometers and accelerometers. However, other existing orientation sensors are known and can be used.

The depth function for azimuthally-sensitive sensors is affected by tool tilt and azimuthal orientation. Fig. 5 shows an illustrative azimuthally sensitive tool 8 tilted at an angle α from the borehole axis as represented by vector 51. The tilt direction β is measured as the angle between the x-axis of the borehole coordinate system and the projection of vector 51 on the x-y plane. The borehole coordinate system can be arbitrarily defined by the driller, but convention has the z-axis parallel to the borehole axis, and the x-axis oriented north (for vertical boreholes) or up toward the "high side" of the borehole (for horizontal or slanted boreholes).

Assuming that sensors Sl and S3 are azimuthally sensitive, they measure formation properties in tilted planes 54 and 56. Along the tool axis, the planes are separated by distance L. However, when the distance measurement is made parallel to the borehole axis, the planes are separated by distance D=L/cos(α). In other words, when the distance measurement is made along a particular azimuth, the correlation distance varies with tilt angle. If the velocity measurement is made parallel to the borehole axis, equation (3) can be re-stated:

If the tilt is assumed to vary slowly with respect to the sample rate (so that CL(J₀) ∞ <x{t_o + At), the same iterative velocity equations (5), (7) result. However, it can be seen from Fig. 5 that when the sensor plane intersect the borehole walls at an angle, an azimuthal dependence exists for the depth function. Using the calculated depth function from equation (8) or (9) as a base, the azimuthally-corrected depth function becomes: z(θ,t) = z{t) + Rtan(α(0)cos(/?(0 - Θ) , (12) where the tilt angle α(t) and tilt direction β(t) are measured by orientation instruments in the tool. (The borehole axis direction may be determined from a moving average of the tilt angle and tilt direction measurements. The short-term deviations from the moving averages indicate the tilt angle and direction relative to the borehole axis.) It should be noted that in equation (12) the azimuthal angle θ is specified with respect to the borehole axis, not the tool axis. When the tool sensors are offset from the borehole axis, a corresponding correction should be applied to the tool's measurements of azimuthal orientation. Some embodiments employ caliper tools to monitor tool offsets and tilt.

The inter-sensor distances should also be corrected for tilt, so that equation (1) becomes:

A ^r7 z_n(θ,t) = z{θ,t) -a— . (13) cos(α(/))

Fig. 6 is a flowchart of an illustrative logging method employing time-to-depth conversion. The illustrated steps may be performed by software in a surface processing facility such as a desktop computer. However, other suitable implementations exist and will be readily recognized by those skilled in the art, including portable computers, embedded systems, or remote processing facilities. As one example of the latter implementation, a real-time operating center (RTOC) may receive data from on-site sensors, process the data, and distribute the results in real-time to all affected sites including other drilling operations in the region. RTOC personnel may monitor the data collection and processing results, and may attach expert analysis for use as the on-site personnel deem beneficial. hi block 602, the processor retrieves the sensor data and tool orientation data, which has been collected as a function of time. The processor also retrieves setup data such as the sensor types, inter-sensor distances and any initial velocity measurements over the first span of tool movement. (If the tool includes gyroscopes or accelerometers, the initial velocity measurements may be estimated from their measurements.) The processor determines which sensors are identical and/or are of highly correlated types, and in block 604 the processor determines the correlation delays for the signals from those sensors. In block 606, the processor determines the tool velocity v(t) as a function of time. Equations (5) or (7) above provide iterative methods for performing this velocity determination from the correlation delays. These iterative calculations may be used alone or in combination with other velocity measurements or calculations, e.g., accelerometer measurements, index wheel measurements, electromagnetic tracking of bit position, etc.

In block 608, the velocity function v(t) is used to determine a depth function z(t), e.g., in accordance with equation (8) or (9). For azimuthally sensitive tools, the processor determines a tilt- corrected depth function z(θ,t) such as that given by equation (12). With the appropriate depth function, the processor converts each of the sensor measurements s_n(t) or S_n(O ,t) from time domain to spatial domain, e.g., s_n(z) or S_n(θ,z). In block 608, the processor displays the sensor measurements as a function of position and/or stores the measurements in memory for additional processing. Though many logs are displayed as traces as a function of depth (see, e.g., Fig. 4), the azimuthally sensitive logs may be displayed as two-dimensional images. One image axis represents azimuthal angle, another axis represents depth, and the intensity of the image pixel represents the measured property value at that depth and azimuth.

Fig. 7 shows a desktop computer that collects logging data from a logging tool, either via telemetry or bulk data download, and processes it in accordance with one or more methods disclosed herein to generate and display depth-based logs. The computer includes a chassis 116, a display 122, and one or more input devices 124. A processor within chassis 116 is coupled to the display 122 and the input devices 124 to interact with a user. The display 122 and the input devices 124 together operate as a user interface. The display 122 often takes the form of a video monitor, but may take many alternative forms such as a printer, a speaker, or other means for communicating information to a user. The input device 124 is shown as a keyboard, but may similarly take many alternative forms such as a button, a mouse, a keypad, a dial, a motion sensor, a camera, a microphone or other means for receiving information from a user. In some embodiments, the display 122 and the input devices 124 are integrated into the chassis 116 (e.g., a laptop or handheld computer).

In addition to a processor, the chassis 116 includes a memory, a persistent information storage device, and usually a network interface. The processor gathers information from the various system elements, including input data from the input devices and program instructions and other data from the memory, the information storage device, or from a remote location via the network interface. The processor carries out the program instructions and processes the data accordingly. The program instructions may further configure the processor to send data to other system elements, including information for the user which may be communicated via the display 122.

The processor, and hence the computer as a whole, generally operates in accordance with one or more programs stored on the information storage device. One or more of the information storage devices may store programs and data on removable storage media such as a floppy disk or an optical disc 120. Whether or not the information storage media is removable, the processor generally copies portions of the programs into the memory for faster access, and may switch between programs or carry out additional programs in response to user actuation of the input device. The additional programs may be retrieved from the information storage device or may be retrieved from remote locations via the network interface. One or more of these programs configures the computer to carry out at least one of the time-to-depth conversion methods disclosed herein.

Stated in another fashion, the methods described above can be implemented in the form of software that can be communicated to a computer or another processing system on an information storage medium such as an optical disk, a magnetic disk, a flash memory, or other persistent storage device. Alternatively, such software may be communicated to the computer or processing system via a network or other information transport medium. The software may be provided in various forms, including interpretable "source code" form and executable "compiled" form. The various operations carried out by the software may be written as individual functional modules within the source code.

Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. For example, rather than displaying the logs, the processor may store the logs as a function of depth and azimuth. Each log value may have an explicit depth value associated with it, or an evenly-spaced grid may be assumed and the position of the log values may be indicative of the appropriate grid point. Interpolation may be used to determine appropriate log values when such predetermined grids are employed. It is intended that the following claims be interpreted to embrace all such variations and modifications.

Claims

CLAIMS WHAT IS CLAIMED IS:

1. A logging method that comprises: collecting logging measurements as a function of time with a tool assembly having at least two instruments that make correlated measurements; measuring correlation delay as a function of time between measurements of said instruments; determining a tool velocity as a function of time based at least in part on the correlation delay; and storing the logging measurements in a manner that associates the measurements with spatial position in the borehole.

2. The method of claim 1, wherein said storing comprises: determining a tool depth as a function of time based at least in part on the tool velocity; and storing the tool depth function with the logging measurements.

3. The method of claim 1, wherein said storing comprises: determining a tool depth as a function of time based at least in part on the tool velocity; and storing each logging measurement value with a corresponding depth value.

4. The method of claim 1, wherein said storing comprises: determining a tool depth as a function of time based at least in part on the tool velocity; and for each depth point in an evenly-spaced array of depth values, storing an appropriate log measurement value based at least in part on the tool depth function.

5. The method of claim 1, further comprising: collecting tool orientation measurements as a function of time; and establishing a tool tilt angle and tilt direction as a function of time based at least in part on the orientation measurements.

6. The method of claim 5, wherein said storing comprises: determining a tool depth as a function of time and azimuth based at least in part on the tool velocity and the tilt angle and tilt direction measurements; and storing each logging measurement value with a corresponding depth and azimuth value.

7. The method of claim 5, wherein said storing comprises: determining a tool depth as a function of time and azimuth based at least in part on the tool velocity and the tilt angle and tilt direction measurements; and for each point in an evenly-spaced depth-azimuth grid, storing an appropriate log measurement value based at least in part on the tool depth function.

8. The method of claim 1, wherein said at least two instruments are axially-spaced, azimuthally- sensitive acoustic tools.

9. A processing system that comprises: a memory that stores time-to-depth conversion software; and a processor coupled to the memory to execute the software, wherein the software causes the processor to: retrieve signal data collected by a logging tool, wherein the signal data includes time- dependent signals from at least two axially-spaced sensors that make correlated measurements; measure a time-dependent correlation delay between the signals; and determine a time-dependent tool velocity base at least in part on the correlation delay.

10. The system of claim 9, wherein the software further causes the processor to establish a time- dependent tool depth based at least in part on the tool velocity.

11. The system of claim 10, wherein the software further causes the processor to associate a tool depth with each sample of the signals.

12. The system of claim 11, wherein the software further causes the processor to determine a signal measurement for each of a series of evenly spaced tool depths.

13. The system of claim 10, wherein the signal data includes tool orientation information, and wherein the software further causes the processor to determine a time-dependent tool tilt angle.

14. The system of claim 13, wherein the software further causes the processor to determine a sensor-specific depth for each sensor based at least in part on the tool depth and the tool tilt angle.

15. The system of claim 14, wherein the software further causes the processor to: associate a borehole azimuth with each sample of the signals; and determine a dependence of the time-dependent tool depth on borehole azimuth based at least in part on the tool tilt angle.

16. A computer-readable medium that, when engaged in an operable relationship with a computer, communicates software comprising: a collection module that enables the computer to retrieve time-dependent logging signals gathered by a tool assembly having at least two similar logging instruments at a fixed axial spacing; a correlation module that enables the computer to process signals from said logging instruments to determine a time-dependent correlation delay; a velocity module that enables the computer to process the correlation delay to determine a time- dependent tool velocity; a depth module that enables the computer to process the tool velocity to determine a time- dependent tool depth; and a conversion module that enables the computer to combine the time-dependent logging signals with the tool depth to store the logging signals as a function of depth.

17. The medium of claim 16, wherein the depth module further enables the computer to process tool orientation signals to provide a tool depth that varies with time and borehole azimuth.

18. The medium of claim 17, wherein the depth module further enables the computer to account for tool tilt when providing the tool depth.

19. The medium of claim 18, wherein the depth module further enables the computer to provide azimuth- and time-dependent depths for each logging instrument.

20. The medium of claim 16, wherein the software further comprises a display module that enables the computer to display at least one instrument log as a function of depth.