Nuclear magnetic resonance T2 spectral form decomposition method based on asymmetric singular Gaussian mixture model

Abstract

The invention discloses a nuclear magnetic resonance T2 spectral shape decomposition method based on an asymmetric singular Gaussian mixture model, and the method comprises the following steps: S1, obtaining nuclear magnetic resonance T2 data of a target rock, and building a rock nuclear magnetic resonance T2 relaxation time spectrum fitting model of the asymmetric singular Gaussian mixture model; s2, preprocessing the nuclear magnetic resonance T2 data, and initializing parameters of a fitting model; s3, establishing a likelihood function as an evaluation index of the fitting model; s4, calculating a prior probability and a posterior probability of the likelihood function, and updating parameters of the fitting model; s5, repeating the step S4 until the cycle stop standard is reached and the maximum likelihood value is reached, and obtaining a corresponding parameter at the moment; and S6, substituting the parameters obtained in the step S5 into the fitting model to obtain the disassembled nuclear magnetic resonance T2 spectral form. According to the method, the rock nuclear magnetic resonance T2 relaxation time spectrum fitting model of the asymmetric singular Gaussian mixture model is adopted, so that the rock nuclear magnetic resonance T2 spectrum shape with higher precision can be obtained through decomposition.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas exploration and development, and particularly to a method for decomposing nuclear magnetic resonance T2 spectral shapes based on an asymmetric singular Gaussian mixture model. Background Art

[0002] Oil and gas reservoirs generally have developed fractures and cavities, and the pore structure is complex. The analysis of pore structure characteristics has always been the focus of oil and gas exploration and development. Among them, the morphology of the nuclear magnetic resonance T2 spectrum can directly reflect the pore size distribution and connectivity of rocks, providing an irreplaceable quantitative tool for rock reservoir evaluation. Its necessity is not only reflected in improving the accuracy of parameters such as porosity and permeability, but more importantly, in supporting key links such as reservoir classification, fluid identification, and engineering optimization. It is the technical cornerstone for the efficient development of complex oil and gas reservoirs. However, components with shorter T2 relaxation times in rocks (such as micropores) will produce wider peaks, while components with longer T2 relaxation times (such as pores and cavities) produce narrower peaks. If the pore sizes of the two peaks are similar or the fluid types are similar, the peak widths will partially overlap, resulting in signal mixing in the trough region. Therefore, effectively decomposing the nuclear magnetic resonance spectral shape is an important step in analyzing the pore characteristics of rocks.

[0003] There are generally two methods for dividing rock pore characteristics by nuclear magnetic resonance. The first is the nuclear magnetic resonance T2 cut-off value method. The T2 cut-off value time is the critical relaxation time for distinguishing movable fluid from bound fluid. After dividing the spectral shape into two parts by the relaxation time, it is necessary to reconstruct the distributions of movable fluid and bound fluid by means of a symmetric Gaussian function model. The second is the least squares method. This method establishes a symmetric Gaussian function model as the objective function based on characteristic parameters, and gradually reduces the fitting error by setting constraint conditions and optimization algorithms (least squares method) to achieve the decomposition of the nuclear magnetic resonance T2 spectral shape. The above technical methods for decomposing the spectral shape can all achieve the division of rock pore structure and the identification of internal pore fluids to a certain extent. However, the premise assumptions of both methods are that the true nuclear magnetic resonance T2 spectral shape conforms to the symmetric Gaussian model morphology, ignoring the differences between the true spectral shape and the symmetric Gaussian curve, including the concavity and convexity of the left and right half curves and the shape of the spectral peak (pulse-like or platform-like). Therefore, the symmetric Gaussian model cannot fully represent the true nuclear magnetic resonance T2 spectral shape morphology, and the conclusions drawn based on this model are biased. Summary of the Invention

[0004] In view of the above problems, the present invention aims to provide a method for decomposing nuclear magnetic resonance T2 spectral shapes based on an asymmetric singular Gaussian mixture model.

[0005] The technical solution of the present invention is as follows:

[0006] A method for decomposing nuclear magnetic resonance T2 spectral shapes based on an asymmetric singular Gaussian mixture model, comprising the following steps:

[0007] S1: Obtain the nuclear magnetic resonance T2 data of the target rock and establish a fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock. The fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock is an asymmetric singular Gaussian mixture model;

[0008] S2: Preprocess the nuclear magnetic resonance T2 data and initialize the parameters of the fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock;

[0009] S3: Establish a likelihood function as the evaluation index of the fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock;

[0010] S4: Calculate the prior probability and posterior probability of the likelihood function and update the parameters of the fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock;

[0011] S5: Repeat step S4 until the loop stop criterion is reached, the likelihood function reaches the maximum likelihood value, and obtain the corresponding parameters at this time;

[0012] S6: Substitute the parameters obtained in step S5 into the fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock to obtain the disassembled nuclear magnetic resonance T2 spectrum shape.

[0013] Preferably, in step S1, the asymmetric singular Gaussian mixture model is:

[0014]

[0015] In the formula: T 2,pt is the nuclear magnetic resonance T 2,pt spectrum shape function of a certain type of pore; the subscript pt represents the pore type, pt ∈ (MP, P, H), and MP, P, and H represent micropores, pores, and holes respectively; N is the discrete data point number, N ∈ (1, N max ); N max is the last point number; t represents the number of cycles, and t + 1 represents the next cycle; β pt is the singular factor of a certain type of pore; α L,pt is the left scale parameter; α R,pt is the right scale parameter; Γ() is the gamma distribution of nuclear magnetic resonance of the rock; μ pt is the expected value of a certain type of pore on the nuclear magnetic intensity spectrum.

[0016] Preferably, in step S2, the following formula is used to preprocess the nuclear magnetic resonance T2 data:

[0017]

[0018] Where: h(N) is the contribution degree of the nuclear magnetic resonance intensity at point N to the entire nuclear magnetic resonance T2 spectrum; H(N) is the nuclear magnetic resonance intensity value at the Nth point;

[0019] The parameters for initialization include the expected value μ pt , the left scale parameter α L,pt and the right scale parameter α R,pt ;

[0020] The initial value of the said expected value μ pt is determined by the first-order difference and the second-order difference of the contribution degree h(N):

[0021] h (1) (N) = H(N) - H(N - 1) = 0 (3)

[0022] h (2) (N) = h (1) (N) - h (1) (N - 1) < 0 (4)

[0023] Where: h (1) (N) is the first-order difference of the contribution degree at the Nth point; H(N - 1) is the nuclear magnetic resonance intensity value at the (N - 1)th point; h (2) (N) is the second-order difference of the contribution degree at the Nth point; h (1) (N - 1) is the first-order difference of the contribution degree at the (N - 1)th point;

[0024] The initial value of the said left scale parameter α L,pt and the said right scale parameter α R,pt are respectively determined by the following formulas:

[0025]

[0026]

[0027] Where: σ L,pt is the conversion coefficient of the left half-branch scale parameter of the expected value of the nuclear magnetic resonance T2 spectrum of the rock; σ R,pt is the conversion coefficient of the right half-branch scale parameter of the expected value of the nuclear magnetic resonance T2 spectrum of the rock; h(i) is the contribution degree of the nuclear magnetic resonance intensity at point i to the entire nuclear magnetic resonance T2 spectrum; h(μ pt ) is the expected contribution degree of a certain pore type.

[0028] Preferably, in step S3, the likelihood function is:

[0029]

[0030] Where: L pt (N, θ pt ) is the likelihood function of a certain pore type; θpt The parameter set, θ, of the likelihood function for a certain pore type pt ∈(π pt , μ pt , α L,pt , α R,pt , β pt );z pt (N) is the posterior probability of a certain pore type; π pt is the prior probability of a certain pore type, π pt ∈(π MP , π P , π H );

[0031] In step S4, the prior probability is calculated by the following formula:

[0032]

[0033] The posterior probability is calculated by the following formula:

[0034]

[0035] In the formula: z all (N, t), z MP (N, t), z P (N, t), z H (N, t) are the posterior probabilities of all pores, micropores, pores, and cavities in the rock, respectively; C all (N, t), C MP (N, t), C P (N, t), C H (N, t) are the prior values of all pores, micropores, pores, and cavities in the rock, respectively.

[0036] Preferably, in step S4, the parameter update specifically includes the following sub-steps:

[0037] S41: Update the prior probability according to the posterior probability, and the formula is as follows:

[0038]

[0039] S42: Update the expected value of the next iteration according to the posterior probability and the expected value at the current iteration number, and the formula is as follows:

[0040]

[0041] Q L,pt (μ pt (t + 1)) - Q R,pt (μpt (t + 1)) = 0 (14)

[0042] Where: Q L (μ(t + 1)), Q R (μ(t + 1)) are respectively the left - hand sub - function and the right - hand sub - function of the rock pore type;

[0043] S43: Update the left - hand scale parameter through the following formula:

[0044]

[0045] Where: K L (t) is the conversion coefficient of the left - hand scale parameter of the rock micropore;

[0046] S44: Update the right - hand scale parameter through the following formula:

[0047]

[0048] Where: K R (t) is the conversion coefficient of the right - hand scale parameter of the rock micropore;

[0049] S45: Update the singular factor through the following formula:

[0050]

[0051] Where: B pt (t + 1) is the singular factor function of the rock pore; B L,pt (t + 1) is the left - hand singular sub - function; B L,pt (t + 1) is the right - hand singular sub - function; Ψ() is the first - order derivative of the gamma distribution Γ().

[0052] Preferably, when updating the expected value and the singular factor, the Newton iteration method is used to calculate the approximate solution of the iteration function.

[0053] Preferably, in step S5, the loop stop criterion is to reach the set number of loops or the increment of the parameter values of the upper and lower two generations is less than the set accuracy.

[0054] Preferably, the set accuracy is 10 -8 .

[0055] The beneficial effects of the present invention are as follows:

[0056] By establishing a fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of rocks with an asymmetric singular Gaussian mixture model, the present invention can be more in line with the true nuclear magnetic resonance T2 spectrum shape, so that a rock nuclear magnetic resonance T2 spectrum with higher accuracy can be decomposed and obtained. Description of the Drawings

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0058] Figure 1 It is a schematic flow chart of the nuclear magnetic resonance T2 spectrum decomposition method based on the asymmetric singular Gaussian mixture model of the present invention;

[0059] Figure 2 It is a schematic diagram of the disassembly effects of a target spectrum one using different methods in a specific embodiment;

[0060] Figure 3 It is a schematic diagram of the disassembly effects of a target spectrum two using different methods in a specific embodiment;

[0061] Figure 4 It is a schematic diagram of the disassembly effects of a target spectrum three using different methods in a specific embodiment. Detailed implementation manners

[0062] The following further describes the present invention in conjunction with the accompanying drawings and embodiments. It should be noted that, without conflict, the embodiments in the present application and the technical features in the embodiments can be combined with each other. It should be pointed out that unless otherwise specified, all technical and scientific terms used in the present application have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs. The term "including" or "comprising" and the like used in the present invention disclosure means that the elements or items appearing before this word cover the elements or items listed after this word and their equivalents, without excluding other elements or items.

[0063] As Figure 1 shown, the present invention provides a nuclear magnetic resonance T2 spectrum decomposition method based on an asymmetric singular Gaussian mixture model, including the following steps:

[0064] S1: Obtain the nuclear magnetic resonance T2 data of the target rock and establish a fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock, and the fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock is an asymmetric singular Gaussian mixture model.

[0065] In a specific embodiment, the asymmetric singular Gaussian mixture model is:

[0066]

[0067] In the formula: T 2,pt is the nuclear magnetic resonance T of a certain type of pore 2,ptSpectral shape function; the subscript pt represents the pore type, where pt ∈ (MP, P, H), and MP, P, and H represent micropores, pores, and holes, respectively; N is the discrete data point number, where N ∈ (1, N max ); N max is the last point number; t represents the number of cycles, and t + 1 represents the next cycle; β pt is the singular factor of a certain type of pore; α L,pt is the left scale parameter; α R,pt is the right scale parameter; Γ() is the gamma distribution of nuclear magnetic resonance of rocks; μ pt is the expected value of a certain type of pore on the nuclear magnetic resonance intensity spectrum.

[0068] In the above embodiment, when the singular factor approaches 0, the peak appears as a pulse shape; when the singular factor approaches ∞, it appears as a plateau shape; when the singular factor is equal to 2, the model degenerates into a Gaussian model. The initial value of the singular factor is defaulted to 2.

[0069] The true nuclear magnetic resonance T2 spectral shape of rocks does not conform to the symmetric Gaussian model assumed in the prior art. In the above embodiment, the present invention uses the gamma distribution to describe the nuclear magnetic resonance data. Compared with other distribution functions (such as normal distribution, Poisson distribution, etc.), it has the advantages of natural adaptability to positive data, multi-parameter modeling, and its physical background corresponding to the nuclear magnetic resonance theory. Moreover, the present invention improves the gamma distribution by introducing the singular factor, so that it can better conform to the true nuclear magnetic resonance T2 spectral shape, thereby enabling the present invention to decompose and obtain a higher-precision nuclear magnetic resonance T2 spectral shape of rocks.

[0070] S2: Preprocess the nuclear magnetic resonance T2 data and initialize the parameters of the nuclear magnetic resonance T2 relaxation time spectrum fitting model of the rock.

[0071] In a specific embodiment, the following formula is used to preprocess the nuclear magnetic resonance T2 data:

[0072]

[0073] In the formula: h(N) is the contribution degree of the nuclear magnetic resonance intensity at point N to the entire nuclear magnetic resonance T2 spectrum; H(N) is the nuclear magnetic resonance intensity value at the Nth point;

[0074] The parameters for initialization include the expected value μ pt , the left scale parameter α L,pt and the right scale parameter α R,pt ;

[0075] The expected value μ pt is determined by the first-order difference and the second-order difference of the contribution degree h(N):

[0076] h(1) (N) = H(N) - H(N - 1) = 0 (3)

[0077] h (2) (N) = h (1) (N) - h (1) (N - 1) < 0 (4)

[0078] Where: h (1) (N) is the first-order difference of the contribution degree at the Nth point; H(N - 1) is the nuclear magnetic resonance intensity value at the (N - 1)th point; h (2) (N) is the second-order difference of the contribution degree at the Nth point; h (1) (N - 1) is the first-order difference of the contribution degree at the (N - 1)th point;

[0079] The left scale parameter α L,pt and the right scale parameter α R,pt The initial values of are determined by the following formula respectively:

[0080]

[0081] Where: σ L,pt is the conversion coefficient of the left half-branch scale parameter of the expected value of the rock nuclear magnetic resonance T2 spectrum; σ R,pt is the conversion coefficient of the right half-branch scale parameter of the expected value of the rock nuclear magnetic resonance T2 spectrum; h(i) is the contribution degree of the nuclear magnetic resonance intensity at point i to the entire nuclear magnetic resonance T2 spectrum; h(μ pt ) is the expected contribution degree of a certain pore type.

[0082] In the above embodiment, the contribution degree of each test point can be considered that the data set is the superposition of the nuclear magnetic intensities of various pores in the rock, including three parts: micropores, pores, and holes. Due to the different spatial sizes of the pores, the effects of diffusion relaxation, surface relaxation, and volume relaxation are different. The smaller the pore, the shorter the T2 relaxation time, and vice versa, the longer the relaxation time. Therefore, the nuclear magnetic intensities of pores of different sizes have their own intensity expectations, which are the relaxation times corresponding to the maximum peaks on the rock nuclear magnetic resonance T2 spectrum. In the discrete data, the point number N represents time, and the initial value of the intensity expectation is the peak position, that is, the point number determined by the first-order difference and the second-order difference of the contribution degree h(N).

[0083] S3: Establish a likelihood function as the evaluation index of the fitting model of the rock nuclear magnetic resonance T2 relaxation time spectrum.

[0084]

[0085] Where: L pt (N, θ pt ) is the likelihood function of a certain pore type; θ ptThe set of parameters, θ, for the likelihood function of a certain pore type pt ∈(π pt , μ pt , α L,pt , α R,pt , β pt ); z pt (N) is the posterior probability of a certain pore type; π pt is the prior probability of a certain pore type, π pt ∈(π MP , π P , π H );

[0086] In the above embodiments, the prior probability represents the probability that can be obtained before the experiment or sampling based on past experience and analysis; after introducing nuclear magnetic resonance of rocks, it represents the ratio of the sum of the nuclear magnetic intensity contribution rates of a certain pore type to the sum of the nuclear magnetic intensity contribution rates of all pore types. π MP is the prior probability of micropores, representing the ratio of the sum of the nuclear magnetic intensity contribution rates of micropores to the sum of the nuclear magnetic intensity contribution rates of all pore types; π P is the prior probability of pores, representing the ratio of the sum of the nuclear magnetic intensity contribution rates of pores to the sum of the nuclear magnetic intensity contribution rates of all pore types; π H is the prior probability of holes, representing the ratio of the sum of the nuclear magnetic intensity contribution rates of holes to the sum of the nuclear magnetic intensity contribution rates of all pore types. The posterior probability refers to the updated probability distribution of an event or parameter after observing the data, characterizing the contribution weight of each data point to the entire nuclear magnetic resonance. When decomposing the nuclear magnetic resonance T2 spectrum, since it contains multiple types (micropores, pores, and holes), the initial value of the posterior probability can enable the model to quickly converge to a reasonable parameter space.

[0087] S4: Calculate the prior probability and the posterior probability of the likelihood function, and update the parameters of the nuclear magnetic resonance T2 relaxation time spectrum fitting model of the rock.

[0088] In a specific embodiment, the prior probability is calculated by the following formula:

[0089] In step S4, the prior probability is calculated by the following formula:

[0090]

[0091] The posterior probability is calculated by the following formula:

[0092]

[0093]

[0094] Where: z all (N, t), zMP (N, t), z P (N, t), z H (N, t) are the posterior probabilities of all pores, micro-pores, pores, and cavities in the rock, respectively; C all (N, t), C MP (N, t), C P (N, t), C H (N, t) are the prior values of all pores, micro-pores, pores, and cavities in the rock, respectively.

[0095] In a specific embodiment, the update parameters specifically include the following sub-steps:

[0096] S41: Update the prior probability according to the posterior probability, and the formula is as follows:

[0097]

[0098] S42: Update the expected value of the next iteration according to the posterior probability and the expected value at the current iteration number, and the formula is as follows:

[0099]

[0100] Q L,pt (μ pt (t + 1)) - Q R,pt (μ pt (t + 1)) = 0 (14)

[0101] In the formula: Q L (μ(t + 1)), Q R (μ(t + 1)) are the left and right sub-functions of the pore type of the rock, respectively;

[0102] S43: Update the left scale parameter through the following formula:

[0103]

[0104] In the formula: K L (t) is the conversion coefficient of the left scale parameter of the micro-pores in the rock;

[0105] S44: Update the right scale parameter through the following formula:

[0106]

[0107] In the formula: K R (t) is the conversion coefficient of the right scale parameter of the micro-pores in the rock;

[0108] S45: Update the singular factor through the following formula:

[0109]

[0110] Where: B pt (t + 1) is the rock pore singularity factor function; B L,pt (t + 1) is the left singular sub - function; B L,pt (t + 1) is the right singular sub - function; Ψ() is the first - order derivative of the gamma distribution Γ().

[0111] In the above - mentioned embodiment, when calculating formula (19), it is necessary to substitute the three partial pore types in B pt (t + 1) and the three partial pore types in B L,pt (t + 1), B L,pt (t + 1) into the calculation one - by - one after corresponding them respectively.

[0112] In a specific embodiment, when updating the expected value and the singularity factor, since the introduced singularity factor makes the formulas (formula (14) and formula (19)) have no analytical solution, the Newton - Raphson iteration method is used to calculate the approximate solution of the iteration function. The calculation formula is:

[0113]

[0114] After deformation:

[0115]

[0116] Where: x represents μ and β; f x (t) represents the iteration equation corresponding to x (i.e., formula (14) and formula (19)); f x '(t) represents the first - order derivative of f x (t).

[0117] Substitute the approximate solution obtained by the Newton - Raphson iteration method into the corresponding formula for calculation. If the result is less than the set accuracy, the approximate solution is correct; otherwise, it is wrong.

[0118] S5: Repeat step S4 until the loop stop criterion is reached, the likelihood function reaches the maximum likelihood value, and obtain the corresponding parameters at this time.

[0119] In a specific embodiment, the loop stop criterion is to reach the set number of loops or the increment of the parameter values of the upper and lower two generations is less than the set accuracy. Optionally, the set accuracy is 10 -8 .

[0120] S6: Substitute the parameters obtained in step S5 into the rock nuclear magnetic resonance T2 relaxation time spectrum fitting model to obtain the disassembled nuclear magnetic resonance T2 spectrum shape.

[0121] In this embodiment, the fitting curve generated by using the parameter set corresponding to the maximum likelihood value through the rock nuclear magnetic resonance T2 relaxation time spectrum fitting model is the one that is closest to the true rock nuclear magnetic resonance T2 spectrum shape.

[0122] In a specific embodiment, it further includes the step of performing error analysis on the obtained results. Specifically, it includes the following sub-steps: Construct an image of the objective function by using the obtained maximum likelihood parameters through the rock nuclear magnetic resonance T2 relaxation time spectrum fitting model, and record the parameter values corresponding to each data point. Compare the function spectrum generated by the objective function with the true rock nuclear magnetic resonance spectrum in terms of the area difference, and calculate the error size by calculating the difference between the fitting value and the true spectrum value of each data point. The calculation formula is as follows:

[0123]

[0124] In the formula: D value is the area difference; M is the number of data points; y i is the value of the asymmetric singular Gaussian mixture model corresponding to each point; is the original data. The smaller the D value value is, the better the fitting data.

[0125] In a specific embodiment, taking a certain rock reservoir as an example, the nuclear magnetic resonance T2 cut-off value method, the existing symmetric Gaussian model (GMM) and the asymmetric singular Gaussian model (AGGMM) of the present invention are respectively used to disassemble three target nuclear magnetic resonance T2 spectra of the rock reservoir. The results are as Figures 2 - 4 shown. The area difference is used to compare the errors of the three methods. The results are shown in Table 1:

[0126] Table 1 Comparison of fitting effects of different algorithms

[0127] Figure Name <![CDATA[T2-D value (%)]]> <![CDATA[GMM-D value (%)]]> <![CDATA[AGGMM-D value (%)]]> Spectrum 1 12.84 15.05 3.44 Spectrum 2 17.31 17.05 1.67 Spectrum 3 21.67 7.11 1.39

[0128] From Figures 2 - 4 and Table 1, it can be seen that as the spectral decomposition difficulty increases, the errors of the T2 cut-off method and the GMM algorithm for decomposing the spectral shape become larger and larger, and the decomposition effect becomes worse and worse. The area error of the algorithm of the present invention based on the asymmetric singular Gaussian mixture model is relatively stable, and the decomposition effect is better than the first two algorithms. The spectral shape disassembled by the present invention is more consistent with the true nuclear magnetic resonance T2 spectral shape. Under the same precision constraint, even if the setting of the asymmetric singular Gaussian mixture model for spectral decomposition is too different from the true spectral shape, a better convergence result can still be obtained.

[0129] In summary, the present invention can disassemble and obtain a rock nuclear magnetic resonance T2 spectral shape that is more in line with the true spectral shape. Compared with the prior art, the present invention has made significant progress.

[0130] The above are only the preferred embodiments of the present invention and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above in the preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments by using the above-disclosed technical content without departing from the technical solution of the present invention. However, as long as it does not depart from the technical solution of the present invention, any simple modification, equivalent change, and modification made to the above embodiments based on the technical essence of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A method for decomposing the nuclear magnetic resonance T2 spectral shape based on an asymmetric singular Gaussian mixture model, characterized in that, It includes the following steps: S1: Obtain the nuclear magnetic resonance T2 data of the target rock, and establish a fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock. The fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock is an asymmetric singular Gaussian mixture model; S2: Preprocess the nuclear magnetic resonance T2 data, and initialize the parameters of the fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock; S3: Establish a likelihood function as an evaluation index for the fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock; S4: Calculate the prior probability and posterior probability of the likelihood function, and update the parameters of the fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock; S5: Repeat step S4 until the loop stop criterion is met, the likelihood function reaches the maximum likelihood value, and obtain the corresponding parameters at this time; S6: Substitute the parameters obtained in step S5 into the fitting model for the nuclear magnetic resonance T2 relaxation time spectrum of the rock to obtain the disassembled nuclear magnetic resonance T2 spectrum shape.

2. The nuclear magnetic resonance T2 spectral shape decomposition method based on an asymmetric singular Gaussian mixture model according to claim 1, wherein In step S1, the asymmetric singular Gaussian mixture model is: where: T 2,pt is the nuclear magnetic resonance T 2,pt spectral shape function of a certain type of pore; the subscript pt represents the pore type, pt ∈ (MP, P, H), and MP, P, and H represent micropores, pores, and holes, respectively; N is the discrete data point number, N ∈ (1, N max ); N max is the last point number; t represents the number of cycles, and t + 1 represents the next cycle; β pt is the singular factor for a certain type of pore; α L,pt is the left scale parameter; α R,pt is the right scale parameter; Γ() is the gamma distribution of nuclear magnetic resonance of rocks; μ pt is the expected value of a certain type of pore on the nuclear magnetic intensity spectrum.

3. The method for decomposing the nuclear magnetic resonance T2 spectral shape based on the asymmetric singular Gaussian mixture model according to claim 2, wherein In step S2, the following formula is used to preprocess the nuclear magnetic resonance T2 data: where: h(N) is the contribution degree of the nuclear magnetic resonance intensity at point N to the entire nuclear magnetic resonance T2 spectrum; H(N) is the nuclear magnetic resonance intensity value at the Nth point; The parameters for initialization include the expected value μ pt , the left scale parameter α L,pt and the right scale parameter α R,pt ; The expected value μ pt The initial value is determined by the first-order difference and the second-order difference of the contribution degree h(N): h (1) (N) = H(N) - H(N - 1) = 0 (3) h (2) (N) = h (1) (N) - h (1) (N - 1) < 0 (4) Where: h (1) (N) is the first-order difference of the contribution degree at the Nth point; H(N - 1) is the nuclear magnetic resonance intensity value at the (N - 1)th point; h (2) (N) is the second-order difference of the contribution degree at the Nth point; h (1) (N - 1) is the first-order difference of the contribution degree at the (N - 1)th point; The left scale parameter α L,pt and the right scale parameter α R,pt are initially determined by the following equations: where: σ L,pt is the conversion coefficient of the scale parameter of the left half branch of the expected value of the rock nuclear magnetic resonance T2 spectrum; σ R,pt is the conversion coefficient of the scale parameter of the right half branch of the expected value of the rock nuclear magnetic resonance T2 spectrum; h(i) is the contribution degree of the nuclear magnetic resonance intensity at point i to the entire nuclear magnetic resonance T2 spectrum; h(μ pt ) is the expected contribution degree of a certain pore type.

4. The method for decomposing the nuclear magnetic resonance T2 spectrum based on the asymmetric singular Gaussian mixture model according to claim 3, characterized in that In step S3, the likelihood function is: where: L pt (N, θ pt ) is the likelihood function of a certain pore type; θ pt is the parameter set of the likelihood function of a certain pore type, θ pt ∈(π pt , μ pt , α L,pt , α R,pt , β pt ); z pt (N) is the posterior probability of a certain pore type; π pt is the prior probability of a certain pore type, π pt ∈(π MP , π P , π H ); In step S4, the prior probability is calculated by the following formula: The posterior probability is calculated by the following formula: where: z all (N, t), z MP (N, t), z P (N, t), z H (N, t) are the posterior probabilities of all pores, micropores, pores, and cavities of the rock, respectively; C all (N, t), C MP (N, t), C P (N, t), C H (N, t) are the prior values of all pores, micropores, pores, and cavities of the rock, respectively.

5. The method for decomposing nuclear magnetic resonance T2 spectral shape based on an asymmetric singular Gaussian mixture model according to claim 4, wherein, In step S4, updating the parameters specifically includes the following sub-steps: S41: Update the prior probability according to the posterior probability, and the formula is as follows: S42: Update the expected value of the next iteration according to the posterior probability and the expected value at the current iteration number, and the formula is as follows: Q L,pt (μ pt (t + 1)) - Q R,pt (μ pt (t + 1)) = 0 (14) Where: Q L (μ(t + 1)), Q R (μ(t + 1)) are the left and right half-branch sub-functions of the rock pore type, respectively; S43: Update the left scale parameter by the following formula: Where: K L (t) is the conversion coefficient of the left scale parameter of the rock micropores; S44: Update the right scale parameter by the following formula: Where: K R (t) is the conversion coefficient of the right-scale parameter of the rock micropores; S45: Update the singular factor by the following formula: Where: B pt (t + 1) is the rock pore singularity factor function; B L,pt (t + 1) is the left singularity sub-function; B L,pt (t + 1) is the right singularity sub-function; Ψ() is the first derivative of the gamma distribution Γ().

6. The method for decomposing the nuclear magnetic resonance T2 spectral shape based on the asymmetric singular Gaussian mixture model according to claim 5, wherein When updating the expected value and the singular factor, the Newton iteration method is used to calculate the approximate solution of the iteration function.

7. The method for decomposing the nuclear magnetic resonance T2 spectral shape based on the asymmetric singular Gaussian mixture model according to any one of claims 1-6, characterized in that, In step S5, the loop stop criterion is to reach the set number of loops or the increment of the parameter values of the upper and lower generations is less than the set accuracy.

8. The method for decomposing the nuclear magnetic resonance T2 spectral shape based on the asymmetric singular Gaussian mixture model according to claim 7, wherein The set precision is 10 -8 .

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