Patent Application
20230068555
The present invention relates generally to hydrocarbon exploration using nuclear magnetic resonance (NMR) logging and, more specifically, to methods and systems to correct gradient distributions in downhole NMR.
In the field of logging (e.g. wireline logging, logging while drilling (LWD) and measurement while drilling (MWD)), NMR tools have been used to explore the subsurface based on the magnetic interactions with subsurface material. Some downhole NMR tools include a magnet assembly that produces a static magnetic field, and a coil assembly that generates radio frequency (RF) control signals and detects magnetic resonance phenomena in the subsurface material. Properties of the subsurface material can be identified from the detected phenomena.
NMR has two main experiments in oil field downhole usage. The first experiment is to assess T1 buildup of magnetization. The second experiment is to observe the decay of magnetization once it has been excited, in which the decay has a time constant of T2. In a gradient field, the measured apparent T2 is accelerated by the diffusion induced additional decay, which masks the intrinsic T2, i.e., the T2 value corresponding to measurement in a zero-gradient field.
Measurement of T1 is indirect and is done by varying the polarization times after magnetization has, through some means, been nullified or inverted. For downhole observation, a NMR measurement technique, designed by Carr, Purcell, Meiboom, and Gill and, hence, referred to as CPMG, is used. It is considered a T2 measurement. CPMG has an excitation pulse followed by several refocusing pulses to counter the magnetic gradients in downhole NMR systems.
A T1 sequence is typically done as: Saturation pulse—WaitTime—Excitation Pulse—Recover pulses. Typically, the sequence has several different wait times. The number of recovery pulses may be as few as 1 and as many as the electronics can handle. Typically, the number of recovery pulses is less than 5000 for downhole operation. Further, while an NMR logging tool moves during wireline logging or while drilling, tripping, the proton spins in the formation inside and in the vicinity of the tool's sensitive volume align themselves parallel or antiparallel to the static magnetic field generated by the NMR logging instrument, and the net magnetization by these spins obey Boltzmann statistics. The magnitude at which the magnetization does this is proportional to the magnetic field. However, as in any system that gets perturbed, it takes time to get to an equilibrium state. The rate at which the equilibrium is achieved is described by the time constant T1, mentioned above.
Today, high-gradient, side-looking NMR logging instruments are used and the field gradients generated by these tools inside a sensitive volume are non-uniform. On the other hand, conventional NMR interpretation algorithms approximate a uniform gradient within the sensitive volume. Such an approximation is tolerable when the gradient value is small, but causes distortion in relaxation time distribution for 1D inversion, and may result in inaccurate fluid typing and pore typing with 1D, 2D, and/or 3D inversion, if the gradient value is high. This problem is also dependent upon the underlying T2 distribution of the fluid, the diffusivity, and acquisition parameter settings, and is most significant for slow-relaxing formations and high diffusivity fluids at high inter-echo time settings.
The following detailed description illustrates embodiments of the present disclosure. These embodiments are described in sufficient detail to enable a person of ordinary skill in the art to practice these embodiments without undue experimentation. It should be understood, however, that the embodiments and examples described herein are given by way of illustration only, and not by way of limitation. Various substitutions, modifications, additions, and rearrangements may be made that remain potential applications of the disclosed techniques. Therefore, the description that follows is not to be taken as limiting on the scope of the appended claims. In particular, an element associated with a particular embodiment should not be limited to association with that particular embodiment but should be assumed to be capable of association with any embodiment discussed herein.
Embodiments and methods of the present disclosure provide embodiments and methods for correcting a gradient distribution in downhole NMR logging. In a generalized method, an NMR tool positioned in a borehole is used to acquire data. The data is inverted using an effective gradient to obtain an apparent T2 distribution having a first main peak and a distortion caused by a second spurious peak. The first main peak corresponds to the effective gradient. The distortion in the apparent T2 distribution is then corrected by integrating the signal corresponding to the spurious peak into the signal corresponding to the main peak. The corrected apparent T2 distribution and the effective gradient are then used to interpret the NMR data. Thereafter, the interpreted data is used to determine one or more characteristics of the surrounding hydrocarbon bearing formation or water reservoir (subsurface rock formation media).
A nuclear magnetic resonance (NMR) logging tool 26 is integrated into the bottom-hole assembly near the bit 14. The NMR logging tool 26 may take the form of a drill collar, i.e., a thick-walled tubular that provides weight and rigidity to aid the drilling process. As the bit extends the borehole through the formations, the NMR logging tool collects measurements relating to spin relaxation time (T1, T2, Tp, and/or T2*) distributions as a function of depth or position in the borehole. The NMR tool has a magnet, antenna, and supporting electronics. The permanent magnet in the tool causes the nuclear spins to build up into a cohesive magnetization, also sometimes referred to as polarization. The T2 is measured through the decay of excited magnetization while T1 is measured by the buildup of magnetization. Other tools and sensors can also be included in the bottomhole assembly to gather measurements of various drilling parameters such as position, orientation, weight-on-bit, borehole diameter, etc. Control/telemetry module 28 collects data from the various bottomhole assembly instruments (including position and orientation information) and stores them in internal memory, which may be able to store hundreds of hours of data. Selected portions of the data (raw or processed) can be communicated to surface receivers 30 by, e.g., mud pulse telemetry. Other logging-while drilling telemetry methods also exist and could be employed. For example, electromagnetic telemetry or through-wall acoustic telemetry can be employed with an optional repeater 32 to extend the telemetry range. Most telemetry systems also enable commands to be communicated from the surface to the control and telemetry module to configure the operation of the tools.
An alternative logging technique is tubing-conveyed logging.
Surface computer system 66 is configured to communicate with supervisory sub 64 to set logging parameters and collect logging information from the one or more logging tools 65 such as an NMR logging tool. Surface computer system 66 is preferably configured by software (shown in
In each of the foregoing logging environments, the logging tool assemblies preferably include a navigational sensor package that includes direction sensors for determining the inclination angle, the horizontal angle, and the rotational angle (a.k.a. “tool face angle”) of the bottom hole assembly. As is commonly defined in the art, the inclination angle is the deviation from vertically downward, the horizontal angle is the angle in a horizontal plane from true North, and the tool face angle is the orientation (rotational about the tool axis) or angle from the high side of the wellbore. In accordance with known techniques, wellbore directional measurements can be made as follows: a three-axis accelerometer measures the earth's gravitational field vector relative to the tool axis and a point on the circumference of the tool called the “tool face scribe line”. (The tool face scribe line is typically drawn on the tool surface as a line parallel to the tool axis.) From this measurement, the inclination and tool face angle of the bottom hole assembly can be determined. Additionally, a three-axis magnetometer measures the earth's magnetic field vector in a similar manner. Or gyro sensors can be used to measure angular velocity. From the combined gyro, magnetometer and accelerometer data, the horizontal angle of the bottom hole assembly may be determined. A motion sensing unit can also be included to track the position of the tool. In many cases, the motion sensing unit can derive the position information from the direction sensors.
The system 400 can include a control unit 425, a memory 430, an electronic apparatus 465, and a communications unit 435. The memory 430 can be structured to include a database. The control unit 425, the memory 430, and the communications unit 435 can be arranged to operate as a processing unit to control operation of the transmitter electronics 412 and the receiver electronics 414 and to perform operations on the signals collected by the receiver electronics 414 to process nuclear magnetic resonance data generated by the NMR logging tool 405. A processing unit 420, structured to process nuclear magnetic resonance data of the NMR logging tool 405, can be implemented as a single unit or distributed among the components of the system 400 including electronic apparatus 465. The control unit 425 and the memory 430 can operate to control activation of the transmitter electronics 412 to generate echo train sequences and recovery pulses. The control unit 425 and the memory 430 can operate to control selection of the receiver electronics 414 in the tool 405 and to manage processing schemes. The control unit 425, the memory 430, and other components of the system 400 can be structured, for example, to operate similar to or identical to the components discussed herein or similar to or identical to any of methods discussed herein.
The system 400 can also include a bus 457, where the bus 457 provides electrical conductivity among the components of the system 400. The bus 457 can include an address bus, a data bus, and a control bus, each independently configured or in an integrated format. The bus 457 can be realized using a number of different communication mediums that allows for the distribution of components of the system 400. Use of the bus 457 can be regulated by the control unit 425. Bus 457 can include a communications network.
In various embodiments, the peripheral devices 445 can include additional storage memory and other control devices that may operate in conjunction with the control unit 425 and the memory 430. In an embodiment, the control unit 425 can be realized as a processor or a group of processors that may operate independently depending on an assigned function. The system 400 can include display unit(s) 455, which can be used with instructions stored in the memory 430 to implement a user interface to monitor the operation of the tool 405 or components distributed within the system 400.
The components shown in
In view of the foregoing, multifrequency NMR logging instruments acquire data in several sensitive volumes. The location of the sensitive volume is determined by the magnetic field, the antenna design, and the operation frequency. For multifrequency operation, each frequency corresponds to a sensitive volume. Multifrequency NMR logging tools generally are configured such that the magnetic field strength, B0, is a function of r, (r is the distance between the front of the NMR logging tool surface to the center of the sensitive volume) and decrease monotonically as the distance from the tool surface increases. Since NMR resonance occurs when the operation frequency, f0 is at the Larmor precession frequency, fL, and the relationship between Larmor frequency and the magnetic field strength is:
f
L(r)=γB0(r) (1),
where, γ is the gyromagnetic ratio of proton.
So by selecting different operating frequencies, f0i, protons in the volume at the location r0i where the magnetic field is substantially close to B0 (roi) reaches resonance condition. As B0 (r) is a continuous function of r, and each sensitive volume has a finite width and shape, the magnetic field strength is not uniform within the sensitive volume, therefore the magnetic field gradient, which is defined as:
is also a continuous varying function of r, meaning that for a finite thickness of a sensitive volume, within the sensitive volume, the gradient is also not a constant. Here, d is a differential operator.
The above description is a simplified version which assumes the sensitive volume is azimuthally symmetric, and B0 and G is uniform along the tool's longitudinal direction. This azimuthal symmetry is only a valid approximation for a mandrel tool design, and the longitudinal uniformity requires the length of the antenna substantially large than it lateral dimension, which often is not used practically.
A side-looking NMR logging instrument, which gained popularity as a wireline NMR logging sensor configuration choice due to its multifrequency operation capability and its flexibility to operate in a wide range of wellbore diameters, has a more complicated magnetic field and gradient distribution. So Eqs. (1) and (2) need to be generalized to:
respectively. Here, x and y are the Cartesian coordinates on the lateral plane particularly to the antenna in a sensitive volume, and z is the longitudinal coordinate of the same location in the sensitive volume.
The thickness of a sensitive volume is defined by frequency selection, which is controlled by the field gradient, RF pulse width, shape, amplitude, and transmitter and antenna response functions, among others. When all other factors are the same, a crescent shape sensitive volume implies the magnetic field gradient is larger at the side tips than that at the center. Thus, it is quite clear the magnetic field gradient inside a sensitive volume is non-uniform.
The transfer functions of the RF circuit and transmitter may distort RF pulses in the sensitive volume regions, and subsequently modify the sensitive volume shape defined by the sensor configuration and ideal RF pulse realization. This may further complicate accuracy in spin dynamics modeling of the NMR response.
As mentioned previously, typical conventional approaches approximate the gradient distribution with an “effective” or “averaged” gradient value per sensitive volume. The effective gradient can be experimentally derived from a calibration tank filled with a fluid.
for a tank fluid, plotting the apparent relaxation time rate,
vs TE2 yields the gradient value G from the slope. Here, D is fluid diffusivity], T2,app is apparent transverse relaxation time without gradient distortion, and T2intrinsic is intrinsic transverse relaxation time.
The effective gradient or averaged gradient values are then used to interpret NMR logging data. For instance, in the inversion process, which transforms the time-domain echo decay data to be the parameter domain T1, T2, and/or diffusivity distribution, uses such approximation in the inversion matrix coefficients. Such approximation is tolerable when the gradient and TE values are small, but may cause distortion in relaxation time distribution for 1D inversion, and may result in inaccurate fluid typing and pore typing with 1D, 2D, and/or 3D inversion, if the gradient value is high, such as that with XMR tool.
From top to bottom in each of these figures, the data are derived from echo trains of seven sensitive volumes corresponding to lowest (top) to highest (bottom) frequencies. The highest frequency corresponds to the highest gradient value and vice versa. For the tank fluid, the distortion appears in T2 spectra as departing from a mono-modality pattern. When TE value is small, the distortion is relatively insignificant, as the mono-modality is largely preserved
In
Compare the T2 distributions corresponding to data acquired at different gradients (different sensitive volumes) in
Further, this problem of the spurious signal is also dependent upon underlying T2intrinsic distribution of the fluid, the diffusivity, and acquisition parameter settings (e.g., frequency), and is most significant for slow-relaxing formation and high diffusivity fluid at high interecho time setting. Thus, the effect becomes more significant for vuggy carbonate formation where the relaxation time is long.
The effective gradient values explain the shift of the main peak of the apparent T2 distributions in
Therefore, in view of the foregoing, the present disclosure is focused on addressing this need of correcting the apparent T2 distortion by effectively moving the spurious peak to the main peak such that the effective gradient can be used to interpret all signals. To say it another way, using the methods herein, the distortion of the apparent T2 distribution is corrected by integrating the spurious signal peak into the main peak signal.
In a first illustrative method, by reexamining Eq. (5), one can see that each spurious T2 peak corresponds to a different gradient value, departing from effective gradient, Geff, by ΔG (i.e., the amount that causes the spurious signal peak deviating from the main signal peak) and the spurious signal position depends on measurement parameters: frequency (thus Geff) and TE, the underlying fluid properties, D and T2intrinsic, both may not be single values but a distribution, in porous rock media and for multiple fluid phases within its pore space. Note that ΔG is frequency dependent. So, Eq. (5) can be rewritten as:
The distributions of the intrinsic T2 and diffusivity may fully or partially overlap with the main peak and the spurious peak of the apparent T2 distribution, thus directly correcting from apparent T2 spectra is not practically possible, without prior knowledge of T2intrinsic (abbreviated by T2int, and D distributions, which are the unknowns to be determined).
Accordingly, the first illustrative method of the present disclosure is a method that estimates ΔG from the spurious signal on a gradient distribution distorted T2apparent distribution. The fraction of porosity (Δϕs) of the spurious signal is obtained by integrating the area beneath the spurious signal distribution. Because ΔG is derived from specific measurement, and the exact position of the spurious T2apparent peak may be affected by data acquisition quality and inversion artifact, it is best estimated from the measurement that employed a long TE value. Alternatively, ΔG may also be derived from multiple data acquisitions with the same or different TE values to obtain an average of the ΔG value. In other words, we approximate the gradient distribution within a sensitive volume with dual gradient values Geff and GS=Geff+ΔG, with the corresponding porosity being Δϕeff=1−Δϕs and Δϕs, respectively. Under this dual gradient value approximation, each has a fixed fraction of porosity. If the dual gradient approximation is a good approximation, it shall remain unchanged by fluid properties and by data acquisition parameter TE. Therefore, in the inversion processing of the echo trains in this method, the part of the inversion matrix governing the diffusion decay should include two terms, as follows:
E(i,j,k)=Σm=1MΣn=1NΣp=1P[1−exp(−tW
where E is the echo amplitude, i is the ith echo idex, j is jth TE index, M is the number of T1 bins, m is the T1 bin index, N is the number of T2 bins, n is the T2 bin index, P is the number of D bins, p is the D bin index, tW is wait time, k is the index for kth wait time, and Gl,eff is lth sensitive volume effective gradient.
The amplitude of the porosity component A0,mnp corresponding to (T1,m, T2int,n, Dp) can be obtained by [from Eq. (7)]. Once A0,mnp is obtained, T2int distribution can be readily constructed, and the apparent T2 distribution (T2app) corresponding to Gl,eff can be obtained by modeling the echo train using:
E′(i,j,k)=Σm=1MΣn=1NΣp=1P[1−exp(−tW
followed by an inversion of echo train E′ with the kernel coefficient described by:
E″(i,j,k)=Σmm=1MΣn=1NA0,mn[1−exp(−tW
where T2app,n is the nth apparent T2 bin.
The above general description is for the most general case of three-dimensional inversion. However, those ordinarily skilled in the art having the benefit of this disclosure may adapt it into lower dimension inversions. Also, for those same skilled artisans, the foregoing description may also extend the binary gradient approach to more than 2 gradient values, such as one effective gradient plus two gradient values with Geffective+ΔG1 and Geffective+ΔG2 with corresponding fractional porosities of Δϕs1 and Δϕs2, and Δϕs1+Δϕs2+Δϕeff=1.
At block 912, subsequent NMR data has been obtained, the matrix is generated and the matrix data are inverted. At block 914, inversion processing of the matrix is performed to obtain a reconstructed apparent T2 distribution using the amplitude data in which the spurious signal peak has been integrated into the main peak, thus correcting the distortion. Optionally, at block 916, forward modeling may be performed in order to reconstruct the uniform-gradient-equivalent echo train.
Now a second illustrative method will be described. The first illustrative method described above includes an approximation which represents the gradient distribution in discrete few values with associated, fixed fractions of the signal intensities. While this method is computationally efficient, because the T2 distribution spectral resolution is subject to inversion artifact and spectral resolvability, the resolution of the spurious T2 peak from the main peak may not always be non-overlapping for some sensor configurations, and for some gradient distributions. For short TE, and for fast relaxation and slow diffusion fluids in a rock, the spurious peak has a much smaller amplitude.
Like the first method, this second alternative method also uses two gradients. However, one of the gradients is an effective gradient, while the other gradient is floating with a constraint of:
G
c
≤G
S
≤G
eff, (10),
where Gc is a predetermined cutoff value which is estimated by a sensor simulation of gradient distribution. Thus, there is an upper and lower bound. The Δϕs (signal amplitude associated with spurious peak) and Δϕeff (signal amplitude associated with the main peak) can be either fixed, or floating, but always constrained by:
Δϕs+Δϕeff=1 (11)
Equations (10) and (11) can be incorporated into the echo data inversion process to obtain a reconstructed T2 distribution. In certain illustrative embodiments, the inversion can include a single echo train or multiple echo trains for any given frequency.
At block 1012, subsequent NMR data has been obtained and data inversion is performed using the porosity constraint of Equation 11 and the amplitude (A0,mnp) is then obtained (at block 1214) for each component set (T1,m, T2int,n, Dp), to thereby generate a reconstructed apparent T2 distribution which removes the distortion.
A third illustrative alternative method makes a minimal approximation on GS and Δϕs, although Eqns. (10) and (11) are still implied. The difference between this third method and the previous methods is this method allows the GS and Δϕs to vary for different TE, D, and T2intrinsic variables.
In this third method, experimental data and data at a known TE, D, and T2intrinsic are acquired and the GS and Δϕs are determined from experimentally derived T2app distributions as G, TE, D, and T2intrinsic varies.
In certain illustrative methods, the experiments may include, but are not limited to, conducting repeated experiments in a calibration tank filled with a fluid with known D and T2intrinsic variables, then changing the fluid with a different set of D and T2intrinsic variables one at a time. The experiments may cycle through all frequencies, and for each frequency multiple TE data acquisition parameters are used. One way of varying different fluid T2intrinsic variables is by doping tap water with variable amounts of CuSO4 or a relaxation rate enhancing agent such as MnCl2. Another way of varying T2intrinsic and D of fluids is by heating the fluids in a calibration tank to different temperatures. Yet another way of varying T2intrinsic and D is to use oil of different viscosities, one at a time, to fill a calibration tank.
Ideally, more variation of fluids of T2intrinsic and D provides a sufficient wide range of fluid property ranges that are encountered in diverse reservoirs. Practically, it is difficult, if not possible, to exhaust every possible combination to build a correction lookup table. Therefore, a machine learning based interpretation method is employed in this illustrative method to predict the correction matrix coefficients that can be incorporated in inversion process. One such as interpolation problem can be formulated with a multivariable problem involving (Geff, Δϕs, GS, TE, D, and T2intrinsic). The training data may use the available experimental data, using artificial neural network and deep neural network techniques to predict (Δϕs, GS) for any missing data with a given (Geff, TE, D, and T2intrinsic) On the other hand, an alternative method is to train the interpolation model using the experimentally measured apparent T2 distribution that is subject to the distribution of gradient inside a sensitive volume, P(T2apparent), with all the fluid and data acquisition parameters. Here, the training data sets may consist of P(T2apparent), the T2 distribution corresponding to the effective gradient Q(T2,eff) as target, and TE, D, and T2intrinsic, and frequency f as inputs. The trained interpretation model is then used to predict P(T2apparent) and Q(T2,eff), for the missing data corresponding to the TE, D, and T2intrinsic, and frequency f where no experiment data are available.
With the P(T2apparent) and Q(T2,eff) predicted for any given f, TE, D, and T2intrinsic, one shall be able to construct a correction coefficient vector as follows:
Λ=Q(T2,eff)/∥Q(T2,eff)∥/P(T2apparent)/∥P(T2,apparent)∥ (12),
where Λ is a one dimensional vector, which can be integrated in the inversion kernel:
E″(i,j,k)=Σm=1MΣn=1NA0,mn·Λn·[1−exp(−tW
for 1D inversion, and for 3D inversion, the corresponding equation is:
E(i,j,k)=Σm=1M Σn=1NΣp=1PA0,mnp·Λn·[1−exp(−tW
The above description involves only the correction for a T2 dimension. In certain embodiments, there should be no correction required for T1 dimension because T1 is independent of gradient. On the other hand, diffusivity can also be affected by the distribution of gradient inside a sensitive volume, therefore, the same model training and prediction method, and the formulation of the correction matrix coefficient, can be extended to include diffusivity dimension, as well as for both T2 and D dimensions. In the latter case, the correction coefficient matrix becomes two dimensional:
Λ=Q′(Deff,T2,eff)/∥Q′(Deff,T2,eff)∥2/P′(Dapparent,T2apparent)/∥P′(Dapparent,T2apparent)∥2 (15)
In view of the foregoing,
At block 1108, the gradient associated with the spurious peak signal (GS) is calculated. At block 1110, a database is constructed which consists of all experimentally obtained variations of the signal amplitude associated with the spurious peak (Δϕs), field gradient associated with the spurious signal (GS), the effective gradient, spacing (TE), fluid diffusivity (D), and intrinsic T2relaxation time (T2intrinsic). At block 1112, a correction matrix model is trained using the database of block 1110 using a machine learning technique such as, but not limited to, artificial neural networks or deep neural networks. The trained correction matrix is the model used to correct the distortion of NMR data.
At block 1114, subsequent NMR data is obtained and the trained correction matrix model is used to determine correction coefficients, for example, for a given f, TE, D, and T2intrinsic Thereafter, inversion processing is performed on the trained correction matrix model to obtain a reconstructed apparent T2 distribution using the correction coefficients in which the spurious signal peak will be integrated into the main peak. As a result, the distortion is corrected.
Also in view of the foregoing,
At block 1206, a database is constructed that consists of all experimentally obtained variations of Geff, TE, D, and T2intrinsic. At block 1208, a correction matrix model is trained using the database of block 1406 using machine learning techniques such as, for example, artificial neural networks or deep neural networks to predict P(T2app) and Q(T2,eff). At block 1210, a correction coefficient vector is constructed. At block 1212, the inversion kernel is modified by including the correction coefficient vector. Thereafter, inversion processing of the trained correction matrix model is performed to obtain a reconstructed apparent T2 distribution using the modified inversion kernel in which the spurious signal peak has been integrated main peak, thereby correcting the distortion.
Accordingly, the illustrative methods described herein include two general approaches. The first approach approximates a gradient distribution by binary gradient values and uses experiment data to determine the binary gradient values and the corresponding signal strength for each sensitive volume in controlled fluid and experimental conditions. This model will then be integrated in the inversion kernel to eliminate the spurious signal caused by gradient distribution. The second approach combines laboratory experimental data on a fixed, limited number of fluids, together with forward modeling data, and machine learning techniques to predict the correction matrix coefficients for the entire application envelop, without making the binary gradient approximation. The correction matrix is integrated to the inversion kernel function. The resulting inversion kernel function replaces the original kernel function. These methods overcome the gradient distribution caused distortion and bias from NMR logging data, thereby yielding correct answers for bulk volume irreducible (BVI), pore typing, and fluid typing interpretation.
Embodiments and methods described herein further relate to any one or more of the following paragraphs:
1. A method to generate a model of an unknown magnetic field gradient distribution in a sensitive volume of a downhole nuclear magnetic resonance (“NMR”) logging tool, the method comprising acquiring data measurements from operation of an NMR logging tool, the data being obtained in a media in which fluid properties are known; conducting inversion processing of the data to obtain an apparent T2 distribution for each data measurement; computing an effect of a gradient distribution in a sensitive volume on the apparent T2 distribution, an effective porosity fraction and a spurious porosity fraction; forming a gradient distribution having a spurious gradient and an effective gradient associated with the effective and spurious porosity fractions; and generating the model by modifying an inversion matrix to include the effective gradient, spurious gradient, effective porosity fraction and spurious porosity fraction.
2. The method as defined in paragraph 1, wherein the inversion processing conducted to obtain the apparent T2 distributed is conducted with an effective gradient; and the spurious gradient is estimated.
3. The method as defined in paragraphs 1 or 2, wherein the spurious gradient is obtained by conducting a sensor response simulation of the gradient distribution.
4. The method as defined in any of paragraphs 1-3, wherein the spurious gradient included in the modified inversion matrix is constrained by an effective gradient and an upper bound gradient.
5. The method as defined in any of paragraphs 1-4, wherein the model is applied to process NMR logging data acquired in a subsurface rock formation media.
6. The method as defined in any of paragraphs 1-5, wherein fluid properties of the subsurface rock formation media are unknown.
7. A system comprising a nuclear magnetic resonance (NMR) logging tool; a control unit coupled to the NMR logging tool to control the NMR logging tool; and a downhole processor coupled to the NMR tool and the control unit to perform operations to: acquiring data measurements from operation of an NMR logging, the data being obtained in a media in which fluid properties are known; conducting inversion processing of the data to obtain an apparent T2 distribution for each data measurement; computing an effect of a gradient distribution in a sensitive volume on the apparent T2 distribution, an effective porosity fraction and a spurious porosity fraction; forming a gradient distribution having a spurious gradient and an effective gradient associated with the effective and spurious porosity fractions; and generating the model by modifying an inversion matrix to include the effective gradient, spurious gradient, effective porosity fraction and spurious porosity fraction.
8. The system as defined in paragraph 7, wherein: the inversion processing conducted to obtain the apparent T2 distributed is conducted with an effective gradient; and the spurious gradient is estimated.
9. The system as defined in paragraphs 7 or 8, wherein the spurious gradient is obtained by conducting a sensor response simulation of the gradient distribution.
10. The system as defined in any of paragraphs 7-9, wherein the spurious gradient included in the modified inversion matrix is constrained by an effective gradient and an upper bound gradient.
11. The system as defined in any of paragraphs 7-10, wherein the model is applied to process NMR logging data acquired in a subsurface rock formation media.
12. The system as defined in any of paragraphs 7-11, wherein fluid properties of the subsurface rock formation media are unknown.
13. A non-transitory computer program product including instructions which, when executed by at least one processor, causes the processor to a method comprising: acquiring data measurements from operation of an NMR logging tool, the data being obtained in a media in which fluid properties are known; conducting inversion processing of the data to obtain an apparent T2 distribution for each data measurement; computing an effect of a gradient distribution in a sensitive volume on the apparent T2 distribution, an effective porosity fraction and a spurious porosity fraction; forming a gradient distribution having a spurious gradient and an effective gradient associated with the effective and spurious porosity fractions; and generating the model by modifying an inversion matrix to include the effective gradient, spurious gradient, effective porosity fraction and spurious porosity fraction.
14. The computer program product as defined in paragraph 13, wherein the inversion processing conducted to obtain the apparent T2 distributed is conducted with an effective gradient; and the spurious gradient is estimated.
15. The computer program product as defined in paragraphs 13 or 14, wherein the spurious gradient is obtained by conducting a sensor response simulation of the gradient distribution.
16. The computer program product as defined in any of paragraphs 13-15, wherein the spurious gradient included in the modified inversion matrix is constrained by an effective gradient and an upper bound gradient.
17. The computer program product as defined in any of paragraphs 13-16, wherein the model is applied to process NMR logging data acquired in a subsurface rock formation media.
18. The computer program product as defined in any of paragraphs 13-17, wherein fluid properties of the subsurface rock formation media are unknown.
19. A method to generate a model of an unknown magnetic field gradient distribution in a sensitive volume of a downhole nuclear magnetic resonance (“NMR”) logging tool, the method comprising acquiring data measurements from operation of an NMR logging tool, the data being obtained in a media in which fluid properties are known; conducting inversion processing of the data measurements to obtain an apparent T2 distribution for each data measurement; identify a spurious porosity fraction and effective porosity fraction of the apparent T2 distribution; compute a spurious gradient associated with the spurious porosity fraction; constructing a database including experimentally obtained variations of NMR data including at least one of the spurious gradient or an effective gradient; and generating the model by training, via machine learning, a correction matrix model using the database.
20. The method as defined in paragraph 19, wherein the experimentally obtained variations of NMR data comprise a signal amplitude associated with the spurious peak (Δϕ_s) obtained using acquisition parameters including echo spacing (TE), frequency, fluid diffusivity (D), or intrinsic T2 relaxation time (T2intrinsic) of the known fluid properties.
21. The method as defined in paragraphs 19 or 20, wherein the model is applied to process NMR logging data acquired in a subsurface rock formation media.
22. The method as defined in any of paragraphs 19-21, wherein fluid properties of the subsurface rock formation media are unknown.
23. A system comprising a nuclear magnetic resonance (NMR) logging tool; a control unit coupled to the NMR logging tool to control the NMR logging tool; and a downhole processor coupled to the NMR tool and the control unit to perform operations to: acquiring data measurements from operation of an NMR logging tool, the data being obtained in a media in which fluid properties are known; conducting inversion processing of the data measurements to obtain an apparent T2 distribution for each data measurement; identify a spurious porosity fraction and effective porosity fraction of the apparent T2 distribution; compute a spurious gradient associated with the spurious porosity fraction; constructing a database including experimentally obtained variations of NMR data including at least one of the spurious gradient or an effective gradient; and generating the model by training, via machine learning, a correction matrix model using the database.
24. The system as defined in paragraph 23, wherein the experimentally obtained variations of NMR data comprise a signal amplitude associated with the spurious peak (Δϕs) obtained using acquisition parameters including echo spacing (TE), frequency, fluid diffusivity (D) of the known fluid properties, or intrinsic T2 relaxation time (T2intrinsic) of the known fluid properties.
25. The system as defined in paragraphs 23-24, wherein the model is applied to process NMR logging data acquired in a subsurface rock formation media.
26. The system as defined in any of paragraphs 23-25, wherein fluid properties of the subsurface rock formation media are unknown.
27. A non-transitory computer program product including instructions which, when executed by at least one processor, causes the processor to a method comprising: acquiring data measurements from operation of an NMR logging tool, the data being obtained in a media in which fluid properties are known; conducting inversion processing of the data measurements to obtain an apparent T2 distribution for each data measurement; identify a spurious porosity fraction and effective porosity fraction of the apparent T2 distribution; compute a spurious gradient associated with the spurious porosity fraction; constructing a database including experimentally obtained variations of NMR data including at least one of the spurious gradient or an effective gradient; and generating the model by training, via machine learning, a correction matrix model using the database.
28. The computer program product as defined in paragraph 27, wherein the experimentally obtained variations of NMR data comprise a signal amplitude associated with the spurious peak (Δϕs) obtained using acquisition parameters including echo spacing (TE), frequency, fluid diffusivity (D) of the known fluid properties, or intrinsic T2 relaxation time (T2intrinsic) of the known fluid properties.
29. The computer program product as defined in paragraphs 27 or 28, wherein the model is applied to process NMR logging data acquired in a subsurface rock formation media.
30. The computer program product as defined in any of paragraphs 27-29, wherein fluid properties of the subsurface rock formation media are unknown.
31. A method to generate a model of an unknown magnetic field gradient distribution in a sensitive volume of a downhole nuclear magnetic resonance (“NMR”) logging tool, the method comprising acquiring data measurements from operation of an NMR logging tool, the data being obtained in a media in which fluid properties are known; conducting inversion processing of the data measurements to obtain an apparent T2 distribution for each data measurement; conducting inversion processing of the data measurements to obtain t2 distribution corresponding to an effective gradient; constructing a database including experimentally obtained variations of NMR data; training, via machine learning, a correction matrix model using the database; using the trained correction matrix model to determine a correction coefficient vector; modifying an inversion kernel using the vector; and generating the model by training, via machine learning, a correction matrix model using the database.
32. The method as defined in paragraph 31, wherein the model is applied to process NMR logging data acquired in a subsurface rock formation media.
33. The method as defined in paragraphs 31 or 32, wherein fluid properties of the subsurface rock formation media are unknown.
34. A system comprising: a nuclear magnetic resonance (NMR) logging tool; a control unit coupled to the NMR logging tool to control the NMR logging tool; and a downhole processor coupled to the NMR tool and the control unit to perform operations to: acquiring data measurements from operation of an NMR logging tool, the data being obtained in a media in which fluid properties are known; conducting inversion processing of the data measurements to obtain an apparent T2 distribution for each data measurement; conducting inversion processing of the data measurements to obtain T2 distribution corresponding to an effective gradient; constructing a database including experimentally obtained variations of NMR data; training, via machine learning, a correction matrix model using the database; using the trained correction matrix model to determine a correction coefficient vector; modifying an inversion kernel using the vector; and generating the model by training, via machine learning, a correction matrix model using the database.
35. The system as defined in paragraph 34, wherein the model is applied to process NMR logging data acquired in a subsurface rock formation media.
36. The system as defined in paragraphs 34 or 35, wherein fluid properties of the subsurface rock formation media are unknown.
37. A non-transitory computer program product including instructions which, when executed by at least one processor, causes the processor to a method comprising: acquiring data measurements from operation of an NMR logging tool, the data being obtained in a media in which fluid properties are known; conducting inversion processing of the data measurements to obtain an apparent T2 distribution for each data measurement; conducting inversion processing of the data measurements to obtain T2 distribution corresponding to an effective gradient; constructing a database including experimentally obtained variations of NMR data; training, via machine learning, a correction matrix model using the database; using the trained correction matrix model to determine a correction coefficient vector; modifying an inversion kernel using the vector; and generating the model by training, via machine learning, a correction matrix model using the database.
38. The computer program product as defined in paragraph 37, wherein the model is applied to process NMR logging data acquired in a subsurface rock formation media.
39. The computer program product as defined in paragraphs 37 or 38, wherein fluid properties of the subsurface rock formation media are unknown.
Furthermore, any of the illustrative methods described herein may be implemented by a system comprising processing circuitry or a non-transitory computer readable medium comprising instructions which, when executed by at least one processor, causes the processor to perform any of the methods described herein.
Although various embodiments and methods have been shown and described, the disclosure is not limited to such embodiments and methods and will be understood to include all modifications and variations as would be apparent to one skilled in the art. Therefore, it should be understood that the disclosure is not intended to be limited to the particular forms disclosed. Rather, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the disclosure as defined by the appended claims.
