Patent Description:
Corrosion of metal pipes is an ongoing issue. Efforts to mitigate corrosion include use of corrosion-resistant alloys, coatings, treatments, and corrosion transfer, among others. Also, efforts to improve corrosion monitoring are ongoing. For downhole casing strings, various types of corrosion monitoring tools are available. One type of corrosion monitoring tool uses electromagnetic (EM) fields to estimate pipe thickness or other corrosion indicators. As an example, a multi-channel induction tool may collect data on pipe thickness to produce an EM log. The EM log data may be interpreted to determine the condition of production and inter mediate casing strings, tubing, collars, filters, packers, and perforations through different channels transmitted by the multi-channel induction tool. Log data may be utilized for estimating material properties and individual thicknesses of nested pipes using multi-frequency multi-spacing induction measurements. By analyzing the signal levels at these different channels through inversion, it may be possible to relate a certain received signal to a certain metal loss or gain at each pipe. In order to get accurate estimate of the metal loss and/or gain, other pipe properties such as the magnetic permeability and the electrical conductivity may also be estimated. Accurately estimating the magnetic permeability µ and the electrical conductivity σ may be beneficial in determining metal loss and/or gain in pipes. <CIT> discloses a method of determining casing thicknesses in a pipe string. <CIT> discloses a method of determining tubing permeability in a pipe string.

According to a first aspect, there is provided a method according to claim <NUM>. A system according to claim <NUM> is also provided. Various preferred features are recited in the dependent claims.

These drawings illustrate certain aspects of some examples of the present disclosure, and should not be used to limit or define the disclosure.

This disclosure may generally relate to methods for estimating the magnetic permeability µ and the electrical conductivity σ through searching for the optimum combination of µ and σ that minimizes the mismatch between a measured signature of a feature of known metal thickness and a corresponding synthetic signature obtained from running a forward model. After the material properties of the pipes have been estimated, individual thicknesses are estimated through model-based inversion. Other processing steps in the workflow may ensure high-quality inversion with minimal processing time.

During operations, electromagnetic (EM) sensing may provide continuous in situ measurements of parameters related to the integrity of pipes in cased boreholes. As a result, EM sensing may be used in cased borehole monitoring applications. Multi-channel induction tools (which may also be referred to as an EM logging tool) may be configured for multiple concentric pipes (e.g., for one or more) with the first pipe diameter varying (e.g., from about two inches to about seven inches or more). Multi-channel induction tools may measure eddy currents to determine metal loss and use magnetic cores at the transmitters. The multi-channel induction tools may use pulse eddy current (time-domain) and may employ multiple (long, short, and transversal) coils to evaluate multiple types of defects in double pipes. It should be noted that the techniques utilized in time-domain may be utilized in frequency-domain measurements. The multi-channel induction tools may operate on a conveyance. Multi-channel induction tools may include an independent power supply and may store the acquired data on memory. A magnetic core may be used in defect detection in multiple concentric pipes.

Monitoring the condition of the production and intermediate casing strings is crucial in oil and gas field operations. EM eddy current (EC) techniques have been successfully used in inspection of these components. EM EC techniques consist of two broad categories: frequency-domain EC techniques and time-domain EC techniques. In both techniques, one or more transmitters are excited with an excitation signal, and the signals from the pipes are received and recorded for interpretation. The received signal is typically proportional to the amount of metal that is around the transmitter and the receiver. For example, less signal magnitude is typically an indication of more metal, and more signal magnitude is an indication of less metal. This relationship may allow for measurements of metal loss, which typically is due to an anomaly related to the pipe such as corrosion or buckling.

In case of multiple nested pipe strings, the received signal may be a non-linear combination of signals from all pipes. As a result, it is not possible, in general, to use a simple linear relationship to relate the signal received to metal loss or gain for pipe strings composed of three or more nested pipes. In order to address this problem, a method called "inversion" is used. Inversion makes use of a forward model and compares it to the signal to determine the thickness of each pipe. The forward model is executed repeatedly until a satisfactory match between the modeled signal and measured signal is obtained. The forward model typically needs to be run hundreds of times or more for each logging point. As a result, it needs to be a computationally efficient model. In order to achieve the computational efficiency, certain simplifications of the real problem need to be considered for the forward model. One of the most significant simplifications is the centralization assumption, where each pipe is assumed to be perfectly centered with respect to other pipes as well as the measurement instrument. Making such an assumption significantly improves the forward modeling computational efficiency and allows a feasible EM multi-pipe inspection solution. However, it also results in artifacts at depths where such assumption is invalidated, i.e. where eccentricity effects exist. The ideas that are disclosed below facilitate identification and removal of such artifacts.

<FIG> illustrates an operating environment for a multi-channel induction tool <NUM> as disclosed herein. Multi-channel induction tool <NUM> may comprise a transmitter <NUM> and/or a receiver <NUM>. In examples, multi-channel induction tool <NUM> may be an induction tool that may operate with continuous wave execution of at least one frequency. This may be performed with any number of transmitters <NUM> and/or any number of receivers <NUM>, which may be disposed on multi-channel induction tool <NUM>. In additional examples, transmitter <NUM> may function and/or operate as a receiver <NUM>. Multi-channel induction tool <NUM> may be operatively coupled to a conveyance <NUM> (e.g., wireline, slickline, coiled tubing, pipe, downhole tractor, and/or the like) which may provide mechanical suspension, as well as electrical connectivity, for multi-channel induction tool <NUM>. Conveyance <NUM> and multi-channel induction tool <NUM> may extend within casing string <NUM> to a desired depth within the wellbore <NUM>. Conveyance <NUM>, which may include one or more electrical conductors, may exit wellhead <NUM>, may pass around pulley <NUM>, may engage odometer <NUM>, and may be reeled onto winch <NUM>, which may be employed to raise and lower the tool assembly in the wellbore <NUM>. Signals recorded by multi-channel induction tool <NUM> may be stored on memory and then processed by display and storage unit <NUM> after recovery of multi-channel induction tool <NUM> from wellbore <NUM>. Alternatively, signals recorded by multi-channel induction tool <NUM> may be conducted to display and storage unit <NUM> by way of conveyance <NUM>. Display and storage unit <NUM> may process the signals, and the information contained therein may be displayed for an operator to observe and stored for future processing and reference. In examples, an operator may be defined as an individual, group of individuals, or an organization. Alternatively, signals may be processed downhole prior to receipt by display and storage unit <NUM> or both downhole and at surface <NUM>, for example, by display and storage unit <NUM>. Display and storage unit <NUM> may also contain an apparatus for supplying control signals and power to multi-channel induction tool <NUM>. Typical casing string <NUM> may extend from wellhead <NUM> at or above ground level to a selected depth within a wellbore <NUM>. Casing string <NUM> may comprise a plurality of joints <NUM> or segments of casing string <NUM>, each joint <NUM> being connected to the adjacent segments by a collar <NUM>. There may be any number of layers in casing string <NUM>. For example, a first casing <NUM> and a second casing <NUM>. It should be noted that there may be any number of casing layers.

<FIG> also illustrates a typical pipe string <NUM>, which may be positioned inside of casing string <NUM> extending part of the distance down wellbore <NUM>. Pipe string <NUM> may be production tubing, tubing string, casing string, or other pipe disposed within casing string <NUM>. Pipe string <NUM> may comprise concentric pipes. It should be noted that concentric pipes may be connected by collars <NUM>. Multi-channel induction tool <NUM> may be dimensioned so that it may be lowered into the wellbore <NUM> through pipe string <NUM>, thus avoiding the difficulty and expense associated with pulling pipe string <NUM> out of wellbore <NUM>.

In logging systems, such as, for example, logging systems utilizing the multi-channel induction tool <NUM>, a digital telemetry system may be employed, wherein an electrical circuit may be used to both supply power to multi-channel induction tool <NUM> and to transfer data between display and storage unit <NUM> and multi-channel induction tool <NUM>. A DC voltage may be provided to multi-channel induction tool <NUM> by a power supply located above ground level, and data may be coupled to the DC power conductor by a baseband current pulse system. Alternatively, multi-channel induction tool <NUM> may be powered by batteries located within the downhole tool assembly, and/or the data provided by multi-channel induction tool <NUM> may be stored within the downhole tool assembly, rather than transmitted to the surface during logging (corrosion detection).

Multi-channel induction tool <NUM> may be used for excitation of transmitter <NUM>. Transmitter <NUM> may transmit electromagnetic fields into subterranean formation <NUM>. It should be noted that transmitter <NUM> may transmit across any number of channels and at any number of frequencies, which may produce any number of electromagnetic fields. The electromagnetic fields from transmitter <NUM> may be referred to as a primary electromagnetic field. The primary electromagnetic fields may produce Eddy currents in casing string <NUM> and pipe string <NUM>. These Eddy currents, in turn, produce secondary electromagnetic fields that may be sensed along with the primary electromagnetic fields by receivers <NUM>. Characterization of casing string <NUM> and pipe string <NUM>, including determination of pipe attributes, may be performed by measuring and processing these electromagnetic fields. Pipe attributes may include, but are not limited to, pipe thickness, pipe conductivity, and/or pipe permeability.

As illustrated, receivers <NUM> may be positioned on the multi-channel induction tool <NUM> at selected distances (e.g., axial spacing) away from transmitters <NUM>. The axial spacing of receivers <NUM> from transmitters <NUM> may vary, for example, from about <NUM> inches (<NUM>) to about <NUM> inches (<NUM>) or more. Without limitation, receivers <NUM> may record measurements across any number of channels and at any number of frequencies. It should be understood that the configuration of multi-channel induction tool <NUM> shown on <FIG> is merely illustrative and other configurations of multi-channel induction tool <NUM> may be used with the present techniques. A spacing of <NUM> inches (<NUM>) may be achieved by collocating coils with different diameters. While <FIG> shows only a single array of receivers <NUM>, there may be multiple sensor arrays where the distance between transmitter <NUM> and receivers <NUM> in each of the sensor arrays may vary. In addition, multi-channel induction tool <NUM> may include more than one transmitter <NUM> and more or less than six of the receivers <NUM>. In addition, transmitter <NUM> may be a coil implemented for transmission of magnetic field while also measuring EM fields, in some instances. Where multiple transmitters <NUM> are used, their operation may be multiplexed or time multiplexed. For example, a single transmitter <NUM> may transmit, for example, a multi-frequency signal or a broadband signal. While not shown, multi-channel induction tool <NUM> may include a transmitter <NUM> and receiver <NUM> that are in the form of coils or solenoids coaxially positioned within a downhole tubular (e.g., casing string <NUM>) and separated along the tool axis. Alternatively, multi-channel induction tool <NUM> may include a transmitter <NUM> and receiver <NUM> that are in the form of coils or solenoids coaxially positioned within a downhole tubular (e.g., casing string <NUM>) and collocated along the tool axis.

Transmission of EM fields by the transmitter <NUM> and the recordation of signals by receivers <NUM> may be controlled by display and storage unit <NUM>, which may include an information handling system <NUM>. As illustrated, the information handling system <NUM> may be a component of the display and storage unit <NUM>. Alternatively, the information handling system <NUM> may be a component of multi-channel induction tool <NUM>. An information handling system <NUM> may include any instrumentality or aggregate of instrumentalities operable to compute, estimate, classify, process, transmit, receive, retrieve, originate, switch, store, display, manifest, detect, record, reproduce, handle, or utilize any form of information, intelligence, or data for business, scientific, control, or other purposes. For example, an information handling system <NUM> may be a personal computer, a network storage device, or any other suitable device and may vary in size, shape, performance, functionality, and price. Information handling system <NUM> may include a processing unit <NUM> (e.g., microprocessor, central processing unit, etc.) that may process EM log data by executing software or instructions obtained from a local non-transitory computer readable media <NUM> (e.g., optical disks, magnetic disks). The non-transitory computer readable media <NUM> may store software or instructions of the methods described herein. Non-transitory computer readable media <NUM> may include any instrumentality or aggregation of instrumentalities that may retain data and/or instructions for a period of time. Non-transitory computer readable media <NUM> may include, for example, storage media such as a direct access storage device (e.g., a hard disk drive or floppy disk drive), a sequential access storage device (e.g., a tape disk drive), compact disk, CD-ROM, DVD, RAM, ROM, electrically erasable programmable read-only memory (EEPROM), and/or flash memory; as well as communications media such wires, optical fibers, microwaves, radio waves, and other electromagnetic and/or optical carriers; and/or any combination of the foregoing. Information handling system <NUM> may also include input device(s) <NUM> (e.g., keyboard, mouse, touchpad, etc.) and output device(s) <NUM> (e.g., monitor, printer, etc.). The input device(s) <NUM> and output device(s) <NUM> provide a user interface that enables an operator to interact with multi-channel induction tool <NUM> and/or software executed by processing unit <NUM>. For example, information handling system <NUM> may enable an operator to select analysis options, view collected log data, view analysis results, and/or perform other tasks.

Multi-channel induction tool <NUM> may use any suitable EM technique based on Eddy current ("EC") for inspection of concentric pipes (e.g., casing string <NUM> and pipe string <NUM>). EC techniques may be particularly suited for characterization of a multi-string arrangement in which concentric pipes are used. EC techniques may include, but are not limited to, frequency-domain EC techniques and time-domain EC techniques.

In frequency domain EC techniques, transmitter <NUM> of multi-channel induction tool <NUM> may be fed by a continuous sinusoidal signal, producing primary magnetic fields that illuminate the concentric pipes (e.g., casing string <NUM> and pipe string <NUM>). The primary electromagnetic fields produce Eddy currents in the concentric pipes. These Eddy currents, in turn, produce secondary electromagnetic fields that may be sensed along with the primary electromagnetic fields by the receivers <NUM>. Characterization of the concentric pipes may be performed by measuring and processing these electromagnetic fields.

In time domain EC techniques, which may also be referred to as pulsed EC ("PEC"), transmitter <NUM> may be fed by a pulse. Transient primary electromagnetic fields may be produced due the transition of the pulse from "off" to "on" state or from "on" to "off" state (more common). These transient electromagnetic fields produce EC in the concentric pipes (e.g., casing string <NUM> and pipe string <NUM>). The EC, in turn, produce secondary electromagnetic fields that may be measured by receivers <NUM> placed at some distance on the multi-channel induction tool <NUM> from transmitter <NUM>, as shown on <FIG>. Alternatively, the secondary electromagnetic fields may be measured by a co-located receiver (not shown) or with transmitter <NUM> itself.

It should be understood that while casing string <NUM> is illustrated as a single casing string, there may be multiple layers of concentric pipes disposed in the section of wellbore <NUM> with casing string <NUM>. EM log data may be obtained in two or more sections of wellbore <NUM> with multiple layers of concentric pipes. For example, multi-channel induction tool <NUM> may make a first measurement of pipe string <NUM> comprising any suitable number of joints <NUM> connected by collars <NUM>. Measurements may be taken in the time-domain and/or frequency range. Multi-channel induction tool <NUM> may make a second measurement in a casing string <NUM> of first casing <NUM>, wherein first casing <NUM> comprises any suitable number of pipes connected by collars <NUM>. Measurements may be taken in the time-domain and/or frequency domain. These measurements may be repeated any number of times and for second casing <NUM> and/or any additional layers of casing string <NUM>. In this disclosure, as discussed further below, methods may be utilized to determine the location of any number of collars <NUM> in casing string <NUM> and/or pipe string <NUM>. Determining the location of collars <NUM> in the frequency domain and/or time domain may allow for accurate processing of recorded data in determining properties of casing string <NUM> and/or pipe string <NUM> such as corrosion. As mentioned above, measurements may be taken in the frequency domain and/or the time domain.

In frequency domain EC, the frequency of the excitation may be adjusted so that multiple reflections in the wall of the pipe (e.g., casing string <NUM> or pipe string <NUM>) are insignificant, and the spacing between transmitters <NUM> and/or receiver <NUM> is large enough that the contribution to the mutual impedance from the dominant (but evanescent) waveguide mode is small compared to the contribution to the mutual impedance from the branch cut component. The remote-field eddy current (RFEC) effect may be observed. In a RFEC regime, the mutual impedance between the coil of transmitter <NUM> and coil of one of the receivers <NUM> may be sensitive to the thickness of the pipe wall. To be more specific, the phase of the impedance varies as: <MAT> and the magnitude of the impedance shows the dependence: <MAT> where ω is the angular frequency of the excitation source, µ is the magnetic permeability of the pipe, σ is the electrical conductivity of the pipe, and t is the thickness of the pipe. By using the common definition of skin depth for the metals as: <MAT> The phase of the impedance varies as: <MAT> and the magnitude of the impedance shows the dependence: <MAT>.

In RFEC, the estimated quantity may be the overall thickness of the metal. Thus, for multiple concentric pipes, the estimated parameter may be the overall or sum of the thicknesses of the pipes. The quasi-linear variation of the phase of mutual impedance with the overall metal thickness may be employed to perform fast estimation to estimate the overall thickness of multiple concentric pipes. For this purpose, for any given set of pipes dimensions, material properties, and tool configuration, such linear variation may be constructed quickly and may be used to estimate the overall thickness of concentric pipes. Information handling system <NUM> may enable an operator to select analysis options, view collected log data, view analysis results, and/or perform other tasks.

Monitoring the condition of pipe string <NUM> and casing string <NUM> may be performed on information handling system <NUM> in oil and gas field operations. Information handling system <NUM> may be utilized with Electromagnetic (EM) Eddy Current (EC) techniques to inspect pipe string <NUM> and casing string <NUM>. EM EC techniques may include frequency-domain EC techniques and do include a time-domain EC technique. In time-domain and frequency-domain techniques, one or more transmitters <NUM> may be excited with an excitation signal and receiver <NUM> may record the reflected excitation signal for interpretation. The received signal is proportional to the amount of metal that is around transmitter <NUM> and receiver <NUM>. For example, less signal magnitude is typically an indication of more metal, and more signal magnitude is an indication of less metal. This relationship may be utilized to determine metal loss, which may be due to an abnormality related to the pipe such as corrosion or buckling.

<FIG> shows multi-channel induction tool <NUM> disposed in pipe string <NUM> which may be surrounded by a plurality of nested pipes (i.e. first casing <NUM> and second casing <NUM>) and an illustration of anomalies <NUM> disposed within the plurality of nested pipes. As multi-channel induction tool <NUM> moves across pipe string <NUM> and casing string <NUM>, one or more transmitters <NUM> may be excited, and a signal (mutual impedance between <NUM> transmitter and receiver <NUM>) at one or more receivers <NUM>, may be recorded.

Due to Eddy current physics and electromagnetic attenuation, pipe string <NUM> and/or casing string <NUM> may generate an electrical signal that is in the opposite polarity to the incident signal and results in a reduction in the received signal. Typically, more metal volume translates to more lost signal. As a result, by inspecting the signal gains, it is possible to identify zones with metal loss (such as corrosion). In order to distinguish signals that originate from anomalies at different pipes of a multiple nested pipe configuration, multiple transmitter-receiver spacing and frequencies may be utilized. For example, short spaced transmitters <NUM> and receivers <NUM> may be sensitive to first casing <NUM>, while longer spaced transmitters <NUM> and receivers <NUM> may be sensitive to second casing <NUM> and/or deeper (3rd, 4th, etc.) pipes. By analyzing the signal levels at these different channels with inversion methods, it is possible to relate a certain received signal to a certain metal loss or gain at each pipe. In addition to loss of metal, other pipe properties such as magnetic permeability and conductivity may also be estimated by inversion methods. However, there may be factors that complicate interpretation of losses. For example, deep pipe signals may be significantly lower than other signals. Double dip indications appear for long spaced transmitters <NUM> and receivers <NUM>. Spatial spread of long spaced transmitter-receiver signals for a collar <NUM> may be long (up to <NUM> feet (. <NUM> meter)). Due to these complications, methods may need to be used to accurately inspect pipe features.

<FIG> illustrates workflow <NUM> for estimating material properties and individual thicknesses of pipe string <NUM>, first casing <NUM>, second casing <NUM>, and/or a plurality of casings outside second casing <NUM> (e.g., referring to <FIG>). Workflow <NUM> may be performed on an information handling system <NUM> (e.g., referring to <FIG>). The method may begin with step <NUM> taking a multi-frequency, multi-receiver, multi-transmitter log, however, pre-recorded data from a previously taken log data may be utilized. In examples, multi-channel induction tool <NUM> may take measurements with at least one frequency, on at least one receiver <NUM>, and with at least one transmitter <NUM> (e.g., referring to <FIG>). In examples, there may be multiple frequencies and receivers <NUM> to be able to differentiate between corrosion on multiple casing strings <NUM>. Multiple measurements may also be taken with different transmitters <NUM> at a given time.

In step <NUM> an operator may define at least on inversion zone based on a pipe plan, wherein each inversion zone contains a fixed number of concentric pipes, and the inner/outer diameters of pipes may be invariant in the zone. At least one inversion zone may be defined in log data, each zone corresponding to a range in log data. In each of these ranges, the pipe configuration may be invariant (i.e., no change in the number of pipes, individual pipe weights, or individual inner diameters of the pipes). Determination of inversion zones may be based on the well plan. If the well plan is not be available, the inversion zones may be determined by visual inspection (i.e. based on visible shifts in the baseline of log data). <FIG> illustrates an example of a well plan <NUM>. In this example, four inversion zones may cover the entire well plan <NUM>. As illustrated in <FIG>, well plan <NUM> may comprise pipe string <NUM>, first casing <NUM>, second casing <NUM>, a conductor casing <NUM>, and wherein cement may be disposed in annulus <NUM> between each casing. Referring back to <FIG>, step <NUM> may include locating at least one collar <NUM> (e.g., referring to <FIG>) on at least one pipe string <NUM>. Locating collars <NUM> on each one of pipe strings <NUM> may be performed manually by inspecting raw measurements. For example, short spaced transmitters <NUM> and receivers <NUM> may be sensitive to pipe string <NUM>, while long spaced spaced transmitters <NUM> and receivers <NUM> may be progressively sensitive to deeper pipes, such as first casing <NUM>, second casing <NUM>, and/or conductor casing <NUM> (e.g., referring to <FIG>). Without limitation, locating collars <NUM> may be automated. Alternatively, locating collars <NUM> may also be done through independent measurements such as caliper or ultrasonic logs of individual pipes, if available.

Step <NUM> includes extracting at least one abnormality <NUM> (e.g., referring to <FIG>) in log data that corresponds to a known or assumed metal thickness. Abnormality <NUM> is a collar <NUM> disposed on at least one pipe in pipe string <NUM>. In examples, thicknesses of collar <NUM> may be pre-known from available information on the type of collars <NUM> used on each pipe string <NUM>, or assumed as some reasonable value (e.g., <NUM>" (. <NUM>) for collars <NUM> on pipe string <NUM>, and <NUM>" (. <NUM>) for collars <NUM> on outer pipes, such as first casing <NUM>, second casing <NUM>, and/or conductor casing <NUM>).

In step <NUM> the operator may extract representative signatures of a zone transition. A zone transition may be a recording in log data where multi-channel induction tool <NUM> (e.g., referring to <FIG>) may be passing through the end of a pipe in pipe string <NUM>, the top of a pipe, from a heavier pipe to a lighter pipe, and/or vice versa. Zone transitions may occur when a casing string starts, ends, gets heavier, or lighter. These may be typically reflected as changes in nominal signal levels as illustrated in <FIG>. A transition feature, which may indicate a zone transition, may be defined as the ratio, or difference, between the nominal signal levels of two distinct zones. Although the features may be classified as a 'transition' feature, the two zones may be adjacent.

From this information, in step <NUM>, referring back to <FIG>, the method may search for pipe material properties that may minimize the difference between responses extracted from log data and simulated responses. It should be noted that simulated responses may be a simulated feature, such as corrosion, reduction in material, increase in material, and/or the like that may be known to the operator. The material properties found may be looped into step <NUM> through step <NUM> to refine collar picks from pipe string <NUM>. Additionally, in step <NUM> material properties may be utilized to estimate µ and σ. The features extracted from log data in the previous step may be used as input to an algorithm that estimates overall pipe material properties such as relative magnetic permeability (µ, or mu) and electric conductivity (σ, or sigma) of the pipes. The workflow of such a workflow <NUM> is shown in <FIG>.

<FIG> illustrates a workflow <NUM>, which may be a linear search over a given range of µ and/or σ values (also called a search vector), and chooses the optimum combination that minimizes the mismatch between the measured and synthetic features. Workflow <NUM> may begin with step <NUM>, which may produce a forward model. Forward model may be formed from known pipe nominals (OD, thickness) & pipe types in step <NUM>, search vectors for µ and σ in step <NUM>, and/or known or assumed collar thickness in step <NUM>. The forward model in step <NUM> may be processed by information handling system <NUM> (e.g., referring to <FIG>) to compute synthetic collar signatures and/or zone transition in step <NUM>. From the computations, information handling system <NUM> may filter and normalize signatures in step <NUM>. To compute a mismatch in step <NUM>, multi-frequency, multi-spacing measurements in step <NUM> are taken. From measurements in step <NUM>, information handling system <NUM> may compute measured collar signatures and/or zone transition in step <NUM>. The measurements in step <NUM> may filter and normalize signatures in step <NUM>. Thus, the forward model and actual measurements may be compared to compute a mismatch in step <NUM>. A µ and σ may be found to minimize the mismatch in step <NUM>, which may lead to a final estimated product of µ and σ in step <NUM>.

The primary advantage of performing a linear search may be inherent parallelism. Each individual µ and σ combination may be tested on a different information handling system <NUM> (e.g., referring to <FIG>), using well known parallelization frameworks such as MPI, OpenMP, Spark, Hadoop, and the like. The independence of each µ and/or σ test offers great flexibility in choosing the parallelization scheme. Certain schemes (such as Spark) do not work when communication across nodes is required, which may not be the case in the current workflow. For example, computing the mismatch in step <NUM> may be evaluated for each element in the µ, σ search vectors based on collar and zone transition responses as follows: <MAT> where η is defined as the index of the pipe number from <NUM> to N. N is the total number of pipes. Where µn is the permeability of pipe n and σn is the conductivity of pipe n. Additionally, m is the index of measurements at different frequencies and receivers <NUM> from <NUM> to NRx X NTX × Nf X NRx is the number of receivers <NUM>, NTx is the number of transmitters <NUM>, and Nf is the number of frequencies. Additionally, variable listed below may be defined as:.

It should be noted that amplitudes may be in linear or log scale. Additionally, collar features may be defined in terms of their relative deviation from the nominal (or baseline) signal level. (e.g. <MAT>). Workflow <NUM> may also be used to refine the assignment of collars <NUM> (e.g., referring to <FIG>) in step <NUM> for locating at least one collar <NUM>, as illustrated in workflow <NUM>. This may be needed in cases with multiple pipes (<NUM> or more), where it may be difficult to make the right assignment of collar picks in outer pipes by manual inspection. Refining collars assignment may be done by running workflow <NUM> on different permutations of collar assignments, and picking the solution that minimizes the mismatch function for step <NUM>.

Referring back to workflow <NUM> and <FIG>, after implementing workflow <NUM>, an inversion may be utilized to estimate the thickness of individual pipes on pipe string <NUM>. Before inversion, pre-inversion techniques may be performed. For example in step <NUM>, workflow <NUM> may select valid channels based on a well plan, signal quality, and conformity with a forward model (per zone). Each inversion zone may have bad and/or undesirable channels based on signal quality, well plan, or conformation with the forward model. For example, signal quality may review channels with low signal quality (e.g., low signal-to-noise ratio), which may be identified and marked as invalid. Additionally, selecting channels based on the signal quality may be done before running the estimation of the pipe material parameters. Comparing against a well plan, the number of receivers <NUM> or frequencies may be adjusted based on the number of pipes and the out diameter of the outermost pipe. When determining conformity with the forward model, some channels may not conform to the forward model that is used in the inversion. This may be due to some non-physical behavior of the channel, or could be due to an overly-simplified forward model that may not capture the physics of some channels. An operator may mark these channels as invalid.

In step <NUM>, selected channels may be calibrated to minimize the difference between measured and simulated responses using known pipe nominals and pipe material properties. The measured log may be calibrated prior to running inversion to account for the deviations between measurement and simulation (forward model). The deviations may arise from several factors, including the nonlinear behavior of the magnetic core, magnetization of pipes, mandrel effect, and inaccurate well plans. Multiplicative coefficients and constant factors may be applied, either together or individually, to the measured log for this calibration. The calibrated measured logs may then be inserted into an inversion algorithm that may solve for a set of pipe parameters, including but not limited to, the individual thickness of each pipe, percentage of metal loss or gain, the individual µ and/or σ of each pipe, the total thickness of each pipe, the eccentricity of each pipe, and/or the inner diameter of each pipe. This inversion algorithm may determine a set of pipe parameters by adjusting them until a cost function is minimized. The underlying optimization algorithm may be any one of the commonly-used algorithms, including but not limited to, the steepest descent, conjugate gradient, Gauss-Newton, Levenberg-Marquardt, and Nelder-Mead. Although the preceding examples may be conventional iterative algorithms, global approaches such as evolutionary and particle-swarm based algorithms may also be used. In examples, the cost function may be minimized using a linear search over a search vector rather than a sophisticated iterative or global optimization. The linear search, as mentioned earlier, has the advantage of being readily parallelizable, which may reduce computational loads on information handling system <NUM>. An example of the inversion cost function that may use the calibrated measurements is given below: <MAT> where m̂ is a vector of M complex-valued calibrated measurements such that m̂nom = snom.

The cost function above contains three terms: the magnitude misfit, the phase misfit, and the regularization that is used to eliminate spurious non-physical solutions of the inversion problem. Alternatively, real and imaginary parts of the measurement and phase may also be used in the cost function. Many other norms (other than the <NUM>-norm and <NUM>-norm above) may also be used. In examples, calibration becomes unnecessary by using a self-calibrated inversion cost function given below: <MAT> where x is the vector of N unknowns (model parameters), x = [t<NUM>,. , tp, µ<NUM>,. , µp, σ<NUM>,. ], Np is the number of pipes, and m = vector of M complex-valued measurements at different frequencies and receivers <NUM> (e.g., referring to <FIG>). Additionally, mnom is the vector of M complex-valued nominal measurements. These may be computed as the signal levels of highest provability of occurrence within a given zone. Further, s(x) is the vector of M forward model responses, snom is the vector of M complex-valued forward model responses corresponding to the nominal properties of the pipes, Wm,abs, Wm,angle are the measurement magnitude and phase weight matrices. M × M is a diagonal matrices used to assign different weights to different measurements based on the relative quality or importance of each measurement. Additionally, Wx is N × N diagonal matrix of regularization weights and xnom is the vector of nominal model parameters. For N-dimensional vector y, ∥y∥<NUM> = Σi=<NUM>|yi| and |y|<NUM> = Σi=<NUM>|yi|. It should also be noted that the division s(x)/s is element-wise division. The type of cost function in Equation (<NUM>) is independent of the calibration as long as it is multiplicative. Therefore, the calibration step may become unnecessary if Equation (<NUM>) is used as the cost function in inversion.

From the calibrations, the calibrations may be utilized for solving for optimum regularization parameters for use in inversion in step <NUM>, referring to workflow <NUM> in <FIG>. As mentioned above, the last term in Equation (<NUM>) or Equation (<NUM>) is called the regularization term, and the weights Wx are called regularization parameters. Regularization is a common optimization technique for dealing with ill-posedness (or extreme sensitivity to errors in measurement) which are often encountered in practical applications. The choice of the optimum regularization weights (parameters), which determines the weight of the regularization term in the cost function with respect to the misfit term, may be automated. In essence, the optimum regularization weights are chosen by the minimization of the negative correlation (or mirroring) between curves of various pipe thicknesses. Mirroring usually points to ill-posedness in the problem, which is remediated by regularization. The optimum regularization parameter is the one that minimizes the mirroring between thickness curves.

To finalize pre-inversion techniques in step <NUM> calibrated measurements are inverted for a set of pipe properties at each depth point. After inversion in step <NUM>, in step <NUM> post-processing may be utilized to invert log data to remove artifacts due to inversion model limitation. Output logs (i.e. those for the set of pipe parameters estimated by the inversion algorithm) may be post-processed to remove artifacts such as ghost collars (shadow copies of a collar on pipes at the same depth), double peaks (due to finite spacing between transmitter - receiver), and/or eccentricity effects (false metal gain on one or more pipes associated with eccentricity over a multi-joint range). It should be noted that logs may be a digital or hard copy that may present thickness, defects, and/or any other pipe properties as a function of depth from the surface.

The removal of ghosts and double peaks may be readily automated since locations of collars <NUM> (Referring to <FIG>) may be known. The eccentricity effect removal may be automated by searching for false metal gains on multiple pipes over a multi-joint range. The artifacts may be removed using various interpolation techniques (e.g. linear, polynomial, spline), or by subtraction of a certain polynomial. In another embodiment, the above operations may be applied before calibration and inversion as pre-processing steps. Resolution enhancement techniques such as deconvolution could also be applied either in per- or post-processing to mitigate ghosting and double peak issues. In step <NUM> the final product may be a thickness estimation of individual pipes. As discussed above, improvements to current technology are that an inversion based on the forward model disclosed in this invention will ensure accurate estimation of features with large swings from nominals such as collars and deep defects. Additionally, the forward model disclosed above may ensure that all non-noisy channels are incorporated in the inversion without having the channels exhibiting high non-linearity which breaks a linearized model assumption. Additionally, the method for building the pre-computed table disclosed above provides an error control by increasing the number of sampling points in steps and checking for the error between the full-model and the interpolation-based (fast) model after each step. Thus, the fast forward model disclosed is more accurate than the linearized model and faster to compute than a full model. It will improve performance by removing the need to investigate channels to discard those that break the linearized model.

Claim 1:
A method for determining properties of a pipe string (<NUM>) using multi-channel induction measurements, comprising:
disposing a multi-channel induction tool (<NUM>) in a cased hole;
obtaining a multi-channel measurement;
forming (<NUM>) a log from the multi-channel measurement;
extracting (<NUM>), from data in the log, at least one abnormality, which has a pre-known or assumed metal thickness, the abnormality being a collar (<NUM>) disposed on a pipe in the pipe string (<NUM>);
performing (<NUM>) a search of pipe material properties to find a set of pipe material properties that minimize a mismatch between the measured response of the pre-known or assumed abnormality and a corresponding synthetic signature obtained by running a forward model; and
inverting (<NUM>) the log for the set of pipe material properties at one or more depth points; the method characterized in that
the multi-channel measurement comprises multi-frequencies and multi-spacing measurements recorded using a frequency-domain eddy current technique, wherein the multi-channel measurement comprises measurements, with different sizes and at different time delays, at a receiver (<NUM>), using a time-domain eddy current technique.