Holographic techniques for corrosion evaluation of wellbore pipes

A method includes obtaining a first small defect response at a given frequency of a first small defect on a first wellbore pipe positioned within a wellbore. A Fourier transform of the first small defect response is then calculated, and a first measured response at the given frequency of a first arbitrary metal loss defect in the first wellbore pipe is obtained with a sensor of a pipe inspection tool. A Fourier transform of the first measured response is then calculated, and a magnitude of the first arbitrary metal loss based on the Fourier transform of the first small defect response and the Fourier transform of the first measured response is then estimated.

BACKGROUND

After drilling a wellbore in the oil and gas industry, the drilled wellbore can be subsequently completed by cementing a string of metal pipes connected end-to-end within the wellbore. Commonly called “casing,” such pipes increase the integrity of the wellbore and provide a flow path between the earth's surface and selected subterranean formations. Some wellbores are lined with multiple concentrically-positioned pipes (i.e., concentric strings of casing). Moreover, in some wellbores, one or more production pipes are extended into a cased wellbore to provide a conduit for hydrocarbons to be conveyed to the earth's surface. Accordingly, as used herein, the term “pipe” or “wellbore pipe” will refer to metal pipes or pipelines that line the walls of a wellbore, such as casing, and may also refer to production pipes extended into a wellbore to facilitate hydrocarbon production operations.

During the lifetime of a well, wellbore pipes are exposed to high volumes of materials and fluids required to pass through them, including chemically aggressive fluids. In harsh environments, the pipes may be subject to corrosion that may affect their functionality. Consequently, the structural integrity of wellbore pipes may change over time due to chemical and mechanical interactions. Moreover, due to the length, volume, accessibility difficulties, and long time periods associated with the process, it is a costly task to monitor wellbore pipes and pipelines and intervene when required.

Electromagnetic (EM) sensing technologies and techniques have been developed for such monitoring applications and can generally be categorized into two groups: frequency-domain techniques and time-domain techniques. In frequency-domain techniques, measurements of the wellbore pipes are typically performed at a high frequency to characterize the innermost pipes and at a low frequency to characterize the outermost wellbore pipes. Time-domain techniques are based on the pulse eddy current and employ the transient response (decay response versus time) of the pipes to a pulse excitation. Proper analysis of the signal responses can determine metal losses in the pipes with better resolutions, and also improve the robustness of the characterization process to noise.

While EM sensing provides continuous, in situ measurements of the integrity of wellbore pipes, the available EM inspection tools do not effectively facilitate evaluation of multiple concentrically-positioned wellbore pipes.

DETAILED DESCRIPTION

The present disclosure is related to maintenance of wellbores in the oil and gas industry and, more particularly, to monitoring and evaluating corrosion in wellbore pipes, such as strings of casing or production tubing.

The embodiments disclosed herein describe holographic one-dimensional imaging techniques that improve the resolution of defect evaluation when using longer coil antennas for inspecting multiple concentrically-positioned wellbore pipes, such as casing or production tubing. The presently disclosed measurement tools and methods provide better resolution for monitoring the condition of wellbore pipes since small dimensional features of flaws, defects, and metal losses can be resolved with better accuracy. Moreover, while maintaining a good resolution, larger illuminating sources or sensors can be employed in accordance with the present embodiments, thereby allowing for monitoring multiple wellbore pipes with larger outer diameters.

The presently described methods acquire responses at multiple frequencies when employing frequency-domain eddy current technique. Alternatively, they acquire time-domain responses when employing pulse eddy current technique and convert time-domain data to frequency-domain data. Subsequently, presently described methods apply a multiple frequency holographic inversion algorithm. As a result, the robustness-to-noise may be improved significantly. Lastly, characterization of the wellbore pipes with better one-dimensional image resolution may provide an operator with a more precise evaluation of these components, and may ultimately lead to a significant positive impact on hydrocarbon production process.

FIG. 1is a schematic diagram of an exemplary wireline system100that may employ the principles of the present disclosure, according to one or more embodiments. As illustrated, the wireline system100may include a surface platform102positioned at the earth's surface and a wellbore104that extends from the surface platform102into one or more subterranean formations106. In other embodiments, such as in offshore operations, a volume of water may separate the surface platform102and the wellbore104. The wellbore104may be lined with one or more pipes108, also referred to as strings of casing. In some embodiments, portions of the wellbore104may have only one pipe108positioned therein, but other portions of the wellbore104may be lined with two or more concentrically-disposed pipes108. The pipes108may be made of plain carbon steel, stainless steel, or another material capable of withstanding a variety of forces, such as collapse, burst, and tensile failure.

The wireline system100may include a derrick110supported by the surface platform102and a wellhead installation112positioned at the top of the wellbore104. A pipe inspection tool114may be suspended into the wellbore104on a cable116. In some embodiments, the pipe inspection tool114may alternatively be suspended within a production pipe (not shown) positioned within the pipes108that line the wellbore104(i.e., casing). In such embodiments, the production pipe may extend by itself into the pipes108or alternatively be positioned adjacent to one or more eccentrically-located production pipes (not shown) that are also positioned within the pipes108. Accordingly, the pipes108may refer to strings of casing that line the wellbore104or at least one production pipe.

The pipe inspection tool114may comprise an electromagnetic, non-destructive inspection tool. Its operation may be based on either the flux-leakage principle or the eddy-current principle, or a combination thereof, and may be insensitive to non-conductive deposits and is operable irrespective of the nature of the fluid mixture flowing into/out of the wellbore104. The pipe inspection tool114can be used for the detection of localized damage or defects in the pipes108. In operation, the pipes108are subjected to a strong static magnetic field and, due to their ferromagnetic nature, the magnetic return flux is mainly confined to the inside of the pipes108. In the presence of discontinuities or defects in the metal, such as pits and holes caused by corrosion, the changes in the magnetic field can be detected with the pipe inspection tool114.

To accomplish this, the pipe inspection tool114may include one or more electromagnetic sensors118, which may be communicably coupled to the cable116. The cable116may include conductors for conveying power to the pipe inspection tool114and also for facilitating communication between the surface platform102and the pipe inspection tool114. A logging facility120, shown inFIG. 1as a truck, may collect measurements from the electromagnetic sensors118, and may include computing facilities122for controlling, processing, storing, and/or visualizing the measurements gathered by the electromagnetic sensors118. The computing facilities122may be communicably coupled to the pipe inspection tool114by way of the cable116.

The electromagnetic sensors118may include one or more electromagnetic coil antennas that may be used as transmitters, receivers, or a combination of both (i.e., transceivers) for obtaining in situ measurements of the pipe(s)108and thereby determine the structural integrity or condition of each pipe108. In some embodiments, the electromagnetic sensors118may be designed to operate in a centralized position within the innermost pipe108, such as through the use of one or more centralizers (not shown) attached to the body of the pipe inspection tool114. In other embodiments, however, the electromagnetic sensors118may be designed to be adjacent or in intimate contact with the inner wall of the innermost pipe108. In such embodiments, the electromagnetic sensors118may be mounted on one or more deployable sensor pads (not shown) positioned on actuatable arms (not shown) that move the electromagnetic sensors118radially outward toward the inner wall of the innermost pipe108.

FIG. 2Ais a schematic cross-sectional side view of a portion of the wellbore104, according to one or more embodiments. For simplicity, only one cross-sectional side of the wellbore104is shown inFIG. 2A. As illustrated, the wellbore104may include multiple pipes positioned therein and referenced as a first pipe1081, a second or m-th pipe108m, and a third or M-th pipe108M(collectively referred to herein as “pipes108”). As will be appreciated, usage of m and M is intended to show that any number of pipes108may be used, without departing from the scope of the disclosure. In some embodiments, the pipes1081,108m,108Mmay each line the wellbore104as concentrically-positioned strings of casing. In other embodiments, however, at least the first pipe1081may comprise a production pipe or tubing positioned within the m-th pipe108meither concentric or eccentric to the remaining pipes108m,108M.

In the illustrated embodiment, each pipe1081,108m,108Mmay include at least one defect, such as a spot or location of corrosion, shown inFIG. 2Aas a first defect2021, a second or m-th defect202m, and a third or M-th defect202M. As will be appreciated, the defects2021,202m,202Mmay be present on the inner or outer surfaces of the pipes1081,108m,108M, or both.

A pipe inspection tool204may be extended into the wellbore104and used to monitor the integrity of the pipes1081,108m,108M. The pipe inspection tool204may be similar to or the same as the pipe inspection tool114ofFIG. 1. As illustrated, the pipe inspection tool204may include an excitation source206, such as a transmitter coil or antenna. The pipe inspection tool204may also include one or more sensors2081and208Lsuch as a receiver coil (alternatively referred to as a receiver antenna). The sensors2081and208Lare shown inFIG. 2Aas a first sensor2081and an L-th sensor208, indicating that the pipe inspection tool204may include any number (“L”) of sensors2081and208Lwithout departing from the scope of the disclosure. The excitation source206may be configured to produce a magnetic field210(i.e., an excitation signal), and the sensors2081-208Lmay be configured to detect a return magnetic field212(i.e., a response signal) after having interacted with the pipes1081,108m,108M.

The first pipe1081may have an outer diameter D1, the m-th pipe108mmay have an outer diameter Dm, and the M-th pipe108Mmay have an outer diameter DM. Moreover, μ1, μm, and μMrefer to the relative magnetic permeability of the of the pipes1081,108m,108M, respectively, while T1, Tm, and TMrefer to the thickness of the pipes1081,108m,108M, respectively.

According to the present disclosure, measurement data from the pipes1081,108m,108Mmay be obtained by the sensors2081-208Lat multiple frequencies along the axial direction z within the wellbore104and may be utilized to reconstruct one-dimensional holographic images of the pipes1081,108m,108M. Obtained measurement data may be transmitted to the logging facility120(FIG. 1) via the cable116for processing and qualitative imaging of the pipes1081,108m,108M. The calculations and algorithms described herein may prove advantageous in enhancing the imaging resolution of any defects on the individual pipes1081,108m,108M, which may help facilitate proper remedial actions for the pipes1081,108m,108M, if needed.

In applying a holographic algorithm used to generate one-dimensional holographic images of the pipes1081,108m,108M, it is assumed that the measurement system of the pipe inspection tool204is linear, an assumption that is based on the well-known Born approximation. According to the Born approximation, an incident field is taken in place of a total field as the driving field at each point in a scattering plot, and a linear superposition method is applied to scattering by an extended body. Born approximation can be accurate if the scattered field is small in the scatterer, as compared to the incident field. Normally one would solve Maxwell's equations in three-dimensions to obtain accurate measurement data, but the Born approximation can be sufficiently accurate by approximating Maxwell's equations for scatters that are small (i.e., low scattering).

FIG. 2Bis another schematic cross-sectional side view of the wellbore104, according to one or more embodiments. For a linear measurement system, for example, a measured response for a small (but measurable) defect214in the m-th pipe108mmay first be obtained. The small defect214, also referred to herein as a “delta-like defect,” may comprise the smallest measureable metal loss region in the m-th pipe108m. The small defect214may exhibit various shapes, but should be as small as possible in the order of the resolution of the pipe inspection tool204or smaller (in particular along the z direction). Accordingly, the small defect214may be small, but sufficiently large to be measured by the pipe inspection tool204.

Once a measured response to the small defect214is obtained, measured responses for any other investigated defect or metal loss region (i.e., the defects2021,202m,202MofFIG. 2A) can be computed. In some embodiments, a response for the small defect214may be obtained by running a surface experiment under laboratory conditions to simulate the small defect214. In other embodiments, however, the small defect214can be physically measured using the pipe inspection tool204or another sensor device. The small defect214can be approximated with a Dirac delta function at a radial distance of Dm/2, i.e., δ(z, Dm/2), where z is the axial position along the m-th pipe and Dm/2 is the radial (r) position away from the pipe inspection tool204assuming that the small defect214is at z=0. In mathematics, the Dirac delta function is a distribution on the real number line that is zero everywhere except at zero, with an integral of one over the entire real line.

The response measured by a generic sensor over the z-axis at a single frequency ω is denoted by h(z, Dm/2, co). The measured response h(z, Dm/2, ω) may be calibrated such that it includes the response due to the small defect214only and not due to the pipes1081,108m,108m. This may be accomplished by recording the response over the z-axis twice; once with the presence of the small defect214and once without the presence of the small defect214, and then the difference of these two responses may be calculated to obtain a calibrated response “r”. Accordingly, the calibrated response r due to any arbitrary metal loss or defect function x(z, Dm/2) in the m-th pipe108m, such as the m-th defect202m(FIG. 2A), may be written in terms of the delta-like defect response h(z, Dm/2, co) as follows:
r(z,ω)≈x(z,Dm/2)*h(z,Dm/2,ω)  Equation (1).

The “*” in Equation (1) denotes a convolution operation along the z direction and ω denotes the operation frequency. The defect function x(z, Dm/2) includes the effect of equivalent metal loss at that particular z position. By taking the Fourier transform of both sides of Equation (1) with respect to the z variable, Equation (2) is derived as follows:
R(kz,ω)≈X(kz,Dm/2)H(kz,Dm/2,ω)  Equation(2).

The R, X, and H of Equation (2) are Fourier transforms of the calibrated response function r, the defect function x, and the measured response function h, respectively, and kzis the Fourier variable corresponding to the z direction. From Equation (2), it is observed that if the measured response h is obtained due to a delta-like defect in the m-th pipe108mbeforehand, and if the response due to an arbitrary metal loss function x in the same m-th pipe108mis measured, one can then estimate this metal loss function. This can be performed for any arbitrary metal loss, such as the m-th defect202m(FIG. 2A).

If calibrated responses R have been collected at N frequencies (for both delta-like and tested defects), writing Equation (2) leads to the following system of equations:

The system of equations provided in Equation (3) can be solved for X(kz, Dm/2) in the least squares sense. Such separate systems of equations have to be solved for all kzvalues, and once they are solved, the reconstruction image of the tested defect x(z, Dm/2) may be obtained by taking the inverse Fourier transform of X(kz, Dm/2) with respect to the kzvariable.

If time-domain data acquisition has been adapted (like in pulse eddy current) for a particular application, the Fourier transform of the collected data can be implemented to obtain frequency-domain data. Then, by proper sampling of the data in the frequency domain, one can construct the system of equations provided in Equation (3). As will be appreciated, using multiple frequency data may prove advantageous in improving the robustness-to-noise for the pipe inspection tool204.

The foregoing discussion is related to evaluating defects (i.e., corrosion) on a single pipe, such as the m-th pipe108m. It will be appreciated, however, that the imaging techniques of the present disclosure may be extended to applications where it may be necessary to inspect defects on multiple pipes, such as any of the pipes1081,108m,108M. In such applications, the calibrated response R described above may be approximated using the superposition principle. Briefly, the superposition principle states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. A linear function is one that satisfies the properties of superposition.

In other words, the calibrated response R may be obtained from the sum of the individual responses due to the corrosion on each pipe1081,108m,108M. Thus, assuming imaging of the metal loss variation for each pipe1081,108m,108Mis desired, Equation (2) may be rewritten as:
R(kz,ω)≈X(kz,D1/2)H(kz,D1/2,ω)+ . . . +X(kz,DM/2)H(kz,DM/2,ω)  Equation (4).

Writing Equation (4) at N frequencies leads to:

This system of equations can be solved for X(kz, Dm/2), m=1, 2, . . . , M in the least squares sense. Such separate systems of equations have to be solved for all kzvalues, and once they are solved, the reconstruction of the image of the pipes x(z, Dm/2), m=1, 2, . . . , M may be obtained by taking the inverse Fourier transform of X(kz, Dm/2), m=1, . . . , M with respect to the kzvariable.

Furthermore, it may be possible to acquire data with multiple sensors, such as any of the sensors2081-208L. When employing multiple sensors2081-208L, Equation (4) above may be written for each sensor2081-208Las follows:

In Equation (6), HL(kz, Dm/2, ω) is the Fourier transform of the calibrated delta-like defect response measured by the L-th sensor208Land for the small (delta-like) metal loss on the m-th pipe108m. Since the unknowns X(kz, Dm/2), m=1, . . . , M are common for all the equations above, a single system of equations can be derived as:

The system of equations in Equation (7) can be solved for X(kz, Dm/2), m=1, . . . , M in the least squares sense. Such separate systems of equations have to be solved for all kzvalues, and once they are solved, the reconstruction of the images of the pipes x(z, Dm/2), m=1, . . . , M may be obtained by taking the inverse Fourier transform of X(kz, Dm/2), m=1, . . . , M with respect to the kzvariable.

As will be appreciated, the dimensions and/or configuration of the sensors2081-208Lmay be altered to measure from the innermost pipe up to any particular number of pipes1081,108m,108M. More particularly, some of the sensors2081-208Lmay be smaller or shorter than other sensors2081-208Land, therefore, may be configured to measure the responses derived from a particular number of innermost pipes, for example only the first pipe1081. As a result, this may simplify the imaging process for the first pipe1081and provide a more precise estimate for the first pipe1081and others that are radially adjacent. These estimations can then be used to image the outer pipes, such as the m-th pipe108mto the M-th pipe108M, with better accuracy when acquiring the data from those pipes with proper choice of sensors and frequencies.

In the disclosed holographic imaging approaches describe above, it is assumed that the calibrated delta-like response is known a priori. This data can be recorded beforehand by measuring delta-like (small) metal loss regions or small holes for various numbers of pipes1081,108m,108Mwith variable magnetic permeability, thickness, and outer diameters. Such data can be stored in a library or database that may be accessed with the processing modules used to undertake the presently described methods. Alternatively, this information can be obtained from a proper forward model through simulations.

In order to image any of the defects2021,202m,202MofFIG. 2A(i.e., metal loss regions), a pre-requisite step is to estimate the relative magnetic permeability μ1, μm, μMof the pipes1081,108m,108M. This allows for using the previously recorded delta-like responses stored in the library (database) corresponding to the relative magnetic permeability μ1, μm, μMvalues. When acquiring data at multiple frequencies, the data at higher and lower frequencies can be employed to estimate the magnetic permeability μ values for innermost and outermost pipes1081,108m,108M, respectively. When acquiring data in the time-domain, the decay responses can be processed. Magnetic permeability μ values for the outer pipes, such as the pipes108mand108M, affect the response at longer decay times.

It is possible to first estimate the magnetic permeability μ of the inner most pipes from smaller or shorter sensors2081-208Land then, by having these values, estimate the magnetic permeability μ of the outermost pipes from the data acquired by larger or longer sensors2081-208L. It is also possible to estimate the magnetic permeability μ of all the pipes from the data acquired from the larger or longer sensors2081-208L. In the frequency-domain eddy current, this can be performed by processing the high frequency data to estimate the magnetic permeability of the innermost pipes and use them and the data acquired at lower frequencies to estimate the magnetic permeability of the outermost pipes. Alternatively, magnetic permeability of all pipes can be estimated from the data acquired at low frequencies. In the time-domain eddy current, this can be performed by dividing the decay response of the sensor into M regions, as shown in the plot300ofFIG. 3, such that at the beginning of the m-th sub-region the response due to the m-th pipe108mmay be observed. Then, by properly processing the values of the decay response at these sub-regions, the magnetic permeability of the pipes1081,108m,108Mcan be estimated.

In a traditional well logging process, it may not be practical to apply the foregoing methods for the entire well log in one shot because of the numerical cost and the stability issues. However, at selected depths within the wellbore104, a monitoring window may be defined and centered at the selected depths and the above-described holographic inversion algorithm may be solved at each depth. A separate depth range may be defined for the solution to the holographic algorithm. After the results at each depth are computed (e.g., at the logging facility120orFIG. 1or elsewhere), the results may be combined to obtain a single and complete one-dimensional log along the selected depths.

Since the presently-described approach is based on the Born approximation, it is valid when the defects in the pipes1081,108m,108Mare small. Due to the same reasoning, the results derived from the present embodiments are qualitative and can be employed only for imaging purposes without precisely estimating the thickness T1, Tm, and TMof the pipes1081,108m,108M. The metal loss function x provides an approximate evaluation of the extent of the defects2021,202m,202M(FIG. 2A).

In addition, the accuracy and resolution of the presently disclosed techniques may depend on the measurement of the delta-like defect response h. The defect for which the delta-like defect response h is measured, represents the smallest defect that can be imaged by the system. In other words, it determines the size of each pixel in the resulting image. Any larger defects can then be imaged with similar pixel size. In the present embodiments, the variation of the delta-like defect response h with the radial distance over the thickness T1, Tm, and TMof the pipes1081,108m,108Mis not discussed. Alternatively, the delta-like defect response h can be measured over the radial distance within the pipes1081,108m,108Mand this variation can be included in the image reconstruction process.

To show the performance of the presently disclosed methods, the following two simulation examples are provided. The following simulations are provided for illustrative purposes in describing the present subject matter and should in no way be considered limiting to the present disclosure.

Table 1 below provides the dimensions of transmitter and receiver coil antennas used in the first and second simulation examples, and Table 2 provides the dimensions of the core of each transmitter and receiver coil antenna.

FIGS. 4A and 4Bare schematic diagrams of wellbore zones400aand400b, respectively, where the first simulation example is undertaken. InFIGS. 4A and 4B, a pipe inspection tool402is lowered into the wellbore104that includes a single pipe404. InFIG. 4A, the pipe404includes a first metal loss region406, which comprises a 25.4 mm (1 inch) hole through the pipe404. InFIG. 4B, the pipe404includes a second metal loss region408aand a third metal loss region408b, where each metal loss region408a,408bcomprises a 25.4 mm (1 inch) hole through the pipe404at corresponding locations.

In the first simulation example, the acquired responses are processed to improve the imaging resolution for the pipe404, which exhibits a conductivity of σ=3.4×106and a relative magnetic permeability of μr=116. To obtain the delta-like defect response, the received responses were simulated over the z-axis for the first metal loss region406, as shown inFIG. 4A. The simulations were performed at a frequency of 200 Hz. As a tested case, the configuration shown inFIG. 4Bwas considered where the first and second metal loss regions408a,408bare to be imaged. The responses for the first and second metal loss regions408a,408bwere acquired at the same frequency (i.e., 200 Hz) over the z-axis.

FIG. 5is a plot500showing holographic imaging of the pipe404ofFIG. 4Bas compared to raw responses. After applying the holographic image reconstruction algorithm discussed herein, the two metal loss regions408a,408bare depicted in contrast with the raw response. More particularly, as compared to the raw response, the peaks of the metal loss regions408a,408bare prominently displayed at about −90 mm and about +90 mm, respectively. Accordingly, by applying the processing techniques described herein, improved resolution for one-dimensional pipe defect images may be obtained.

FIGS. 6A-6Care schematic diagrams of wellbore zones600a,600b, and600c, respectively, where the second simulation example is undertaken. InFIGS. 6A and 6B, a pipe inspection tool602is lowered into the wellbore104that includes a first pipe604aand a second pipe604b. InFIG. 6A, the first pipe604aincludes a first metal loss region606a, and inFIG. 6B, the second pipe604bincludes a second metal loss region606b, where each metal loss region606a,606bcomprises a 25.4 mm (1 inch) hole through the first and second pipes604a,604b, respectively. InFIG. 6C, the first pipe604aincludes a third metal loss region606cand the second pipe604bincludes fourth and fifth metal loss regions606dand606e, respectively, where each metal loss region606c,606d,606ecomprises a 25.4 mm (1 inch) hole through the corresponding pipes604a,604bat corresponding locations.

In the second simulation example, the acquired responses were processed to improve the resolution of the imaging for applications that include double pipes604a,604b, each of which exhibit a conductivity of σ=3.4×106and a relative magnetic permeability of μr=20. To obtain the delta-like defect responses, the received responses were simulated over the z-axis once for the first metal loss region606aon the first pipe604aand then once for the second metal loss region606bon the second pipe604b, and thereby obtaining two delta-like defect responses required for the holographic imaging. The simulations for the second example were performed at eight frequencies of 2 Hz, 5 Hz, 15 Hz, 30 Hz, 50 Hz, 80 Hz, 100 Hz, and 200 Hz.

As the tested case, the wellbore zone600cofFIG. 6Cwas considered, where the third, fourth, and fifth metal loss regions606c,606d,606eare to be imaged. The responses for the third, fourth, and fifth metal loss regions606c,606d,606ewere acquired at the same frequencies as those for the delta-like responses over the z-axis.FIG. 7is a plot700that shows the normalized raw responses obtained at the various frequencies for the wellbore zone600cofFIG. 6C.

FIGS. 8A and 8Bare plots800aand800bthat show reconstructed images of the third, fourth, and fifth metal loss regions606c,606d,606eof the wellbore zone600cofFIG. 6Cafter applying the presently disclosed holographic image reconstruction algorithm. More particularly,FIG. 8Adepicts a reconstructed one-dimensional image of the third metal loss region606con the first pipe604a, andFIG. 8Bdepicts a reconstructed one-dimensional image of the fourth and fifth metal loss regions606d,606eon the second pipe604b. As will be appreciated, the accuracy of the imaging process can be improved further by acquiring the responses at a wider range and larger number of frequencies and over larger scanned depths.

In order to demonstrate the efficiency of the presently described methods in improving image resolution, the processed images may be compared with raw responses. It is well-known that the response at higher frequencies can be employed to investigate the innermost pipes (i.e. the first pipe604a) and the responses at lower frequencies can be employed to investigate conditions of external or outermost pipes (i.e., the second pipe604b).

FIG. 9is a plot900that compares the processed image of the first pipe604awith the raw response at 200 Hz. InFIG. 9, it is observed that although the raw response at 200 Hz still shows the existence of one defect, the resolution has been improved significantly for the processed image.

FIG. 10is a schematic flowchart of an example method1000, according to one or more embodiments of the disclosure. In the method, a first small defect response is obtained at a given frequency of a first small defect on a first wellbore pipe positioned within a wellbore, as at1002. A Fourier transform of the first small defect response may then be calculated, as at1004. A first measured response is then obtained at the given frequency of a first arbitrary metal loss defect in the first wellbore pipe with a sensor of a pipe inspection tool, as at1006, and a Fourier transform of the first measured response is then calculated, as at1008. The magnitude of the first arbitrary metal loss may then be estimated based on the Fourier transform of the first small defect response and the Fourier transform of the first measured response, as at1010.

FIG. 11is a schematic flowchart of another example method1100, according to one or more embodiments of the disclosure. In the method1100, a pipe inspection tool is introduced into a wellbore having one or more wellbore pipes positioned therein, as at1102. A magnetic field is then generated at a given frequency with an excitation source included in the pipe inspection tool, as at1104, and a return magnetic field is received with one or more sensors of the pipe inspection tool, as at1106. Small defect responses are then determined at the given frequency by placing a small defect on each pipe of the one or more wellbore pipes, one at a time, as at1108, and a Fourier transform of the small defect responses is calculated, as at1110. A defect response is then obtained at the given frequency of one or more arbitrary metal losses on any of the wellbore pipes with the one or more sensors, as at1112, and a Fourier transform of the defect response is then calculated, as at1114. A magnitude of the arbitrary metal losses may then be estimated based on the Fourier transform of the defect response and the Fourier transform of the small defect responses, as at1116.

Those skilled in the art will readily appreciate that the methods described herein may be undertaken using a computerized system, such as the computing facilities122of the logging facility120ofFIG. 1. Computer hardware used to implement the various methods and algorithms described herein can include a processor configured to execute one or more sequences of instructions, programming stances, or code stored on a non-transitory, computer-readable medium. The processor can be, for example, a general purpose microprocessor, a microcontroller, a digital signal processor, an application specific integrated circuit, a field programmable gate array, a programmable logic device, a controller, a state machine, a gated logic, discrete hardware components, an artificial neural network, or any like suitable entity that can perform calculations or other manipulations of data. In some embodiments, computer hardware can further include elements such as, for example, a memory (e.g., random access memory (RAM), flash memory, read only memory (ROM), programmable read only memory (PROM), electrically erasable programmable read only memory (EEPROM)), registers, hard disks, removable disks, CD-ROMS, DVDs, or any other like suitable storage device or medium.

Executable sequences described herein can be implemented with one or more sequences of code contained in a memory. In some embodiments, such code can be read into the memory from another machine-readable medium. Execution of the sequences of instructions contained in the memory can cause a processor to perform the process steps described herein. One or more processors in a multi-processing arrangement can also be employed to execute instruction sequences in the memory. In addition, hard-wired circuitry can be used in place of or in combination with software instructions to implement various embodiments described herein. Thus, the present embodiments are not limited to any specific combination of hardware and/or software.

As used herein, a machine-readable medium will refer to any medium that directly or indirectly provides instructions to a processor for execution. A machine-readable medium can take on many forms including, for example, non-volatile media, volatile media, and transmission media. Non-volatile media can include, for example, optical and magnetic disks. Volatile media can include, for example, dynamic memory. Transmission media can include, for example, coaxial cables, wire, fiber optics, and wires that form a bus. Common forms of machine-readable media can include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, other like magnetic media, CD-ROMs, DVDs, other like optical media, punch cards, paper tapes and like physical media with patterned holes, RAM, ROM, PROM, EPROM and flash EPROM.

A. A method that includes obtaining a first small defect response at a given frequency of a first small defect on a first wellbore pipe positioned within a wellbore, calculating a Fourier transform of the first small defect response, obtaining a first measured response at the given frequency of a first arbitrary metal loss defect in the first wellbore pipe with a sensor of a pipe inspection tool, calculating a Fourier transform of the first measured response; and estimating a magnitude of the first arbitrary metal loss based on the Fourier transform of the first small defect response and the Fourier transform of the first measured response.

B. A method that includes introducing a pipe inspection tool into a wellbore having one or more wellbore pipes positioned therein, generating a magnetic field at a given frequency with an excitation source included in the pipe inspection tool, receiving a return magnetic field with one or more sensors of the pipe inspection tool, determining small defect responses at the given frequency by placing a small defect on each pipe of the one or more wellbore pipes, one at a time, calculating a Fourier transform of the small defect responses, obtaining a defect response at the given frequency of one or more arbitrary metal losses on any of the wellbore pipes with the one or more sensors, calculating a Fourier transform of the defect response, and estimating a magnitude of the arbitrary metal losses based on the Fourier transform of the defect response and the Fourier transform of the small defect responses.

Each of embodiments A and B may have one or more of the following additional elements in any combination: Element 1: further comprising obtaining a second small defect response at the given frequency of a second small defect on a second wellbore pipe positioned within the wellbore, obtaining a second measured response at the given frequency of a second arbitrary metal loss defect in the second wellbore pipe with the sensor of the pipe inspection tool, calculating a second Fourier transform of the second measured response, and estimating a magnitude of the second arbitrary metal loss based on the Fourier transform of the first and second small defect responses and the Fourier transform of the first and second measured responses. Element 2: wherein obtaining the second small defect response comprises running a computer model with pipe parameter inputs. Element 3: wherein the pipe parameter inputs are calculated from a given well plan. Element 4: wherein the pipe parameter inputs are calculated from previous measurements. Element 5: wherein obtaining the second small defect response comprises running a surface experiment with a small defect. Element 6: further comprising calibrating the first small defect response to obtain a calibrated small defect response of the first small defect, calculating a Fourier transform of the calibrated small defect response, calibrating the first measured response to obtain a calibrated defect response of the first arbitrary metal loss defect, calculating a Fourier transform of the calibrated defect response, and estimating a magnitude of the first arbitrary metal loss based on the Fourier transform of the calibrated defect response and the Fourier transform of the calibrated small defect response. Element 7: further comprising obtaining a solution of an equation that involves the Fourier transform of the calibrated defect response and the Fourier transform of the calibrated small defect response, calculating the inverse Fourier transform of the solution, and imaging the first arbitrary metal loss in the first wellbore pipe based on the inverse Fourier transform of the solution. Element 8: wherein the given frequency comprises a plurality of frequencies, the method further comprising obtaining a solution of a system of equations that involves the Fourier transform of the calibrated defect response and the Fourier transform of the calibrated small defect response, calculating the inverse Fourier transform of the solution, and imaging the first arbitrary metal loss in the first wellbore pipe based on the inverse Fourier transform of the solution. Element 9: wherein calibrating the first small defect response comprises obtaining a first response at the given frequency with the sensor over a first portion of the first wellbore pipe without the first arbitrary metal loss defect, obtaining a second response at the given frequency with the sensor over a second portion of the first wellbore pipe with the first arbitrary metal loss defect, and subtracting the first and second responses to obtain the calibrated defect response. Element 10: wherein obtaining the first small defect response comprises modelling the first small defect based on wellbore pipe data stored in a library or a database. Element 11: wherein obtaining the first small defect response comprises obtaining the first measured response with the sensor of the pipe inspection tool. Element 12: wherein obtaining the first small defect response of the first small defect comprises approximating the first small defect with a Dirac delta function ?(z, Dm/2) at a radial distance of Dm/2, where z is an axial position of the first small defect within the wellbore and Dm/2 is a radial position away from a center of the wellbore.

Element 13: further comprising calibrating the small defect responses to obtain corresponding calibrated small defect responses of the small defects, calculating a Fourier transform of the calibrated small defect responses, calibrating the defect response to obtain a calibrated defect response of the arbitrary metal losses on any of the wellbore pipes, calculating a Fourier transform of the calibrated defect response, and estimating a magnitude of the arbitrary metal losses based on the Fourier transform of the calibrated defect response and the Fourier transform of the calibrated small defect responses. Element 14: further comprising obtaining a solution of an equation that involves the Fourier transform of the calibrated defect response and the Fourier transform of the calibrated small defect response, calculating the inverse Fourier transform of the solution, and imaging the arbitrary metal loss in the wellbore pipe based on the inverse Fourier transform of the solution. Element 15: wherein the given frequency comprises a plurality of frequencies, the method further comprising obtaining a solution of a system of equations that involves the Fourier transform of the calibrated defect response and the Fourier transform of the calibrated small defect responses acquired from all the pipes, calculating the inverse Fourier transform of the solution, and imaging the arbitrary metal loss at each wellbore pipe based on the inverse Fourier transform of the solution. Element 16: further comprising monitoring the one or more wellbore pipes within the wellbore at a plurality of selected depths within the wellbore, estimating magnitudes of the arbitrary metal losses in the one or more wellbore pipes at each of the plurality of selected depths, and combining the magnitudes to obtain a one-dimensional log of the wellbore at the selected depths.

By way of non-limiting example, exemplary combinations applicable to A and B include: Element 2 with Element 3; Element 2 with Element 4; Element 6 with Element 7; Element 6 with Element 8; Element 6 with Element 9; Element 13 with Element 14; and Element 13 with Element 15.