A method for effectively deconstructing nuclear magnetic resonance relaxation time spectra

Abstract

The present invention discloses a method for effectively disassembling a nuclear magnetic resonance relaxation time spectrum, comprising the following steps: S1, constructing a probability density function of pores and caves according to the distribution characteristics of pores and caves in a core nuclear magnetic resonance T2 spectrum; S2, setting the sum of the nuclear magnetic spectrum areas to 1, randomly generating n data points within the interval of pore distribution, and dividing all the data points into multiple data sets by screening peak values; S3, calculating a likelihood function; S4, calculating a priori probability that each data point belongs to a pore or a cave; S5, updating various parameters in an iterative method using the priori probability; and S6, calculating a new logarithmic likelihood based on the updated parameters, and updating the expected E in the iterative method. p and E v , expected E p and E v Repeat steps S2 to S5 until the convergence condition is met and the iteration is terminated. The present invention combines nuclear magnetic resonance testing with an iterative method to decompose the nuclear magnetic resonance spectrum, thereby improving the accuracy of the spectral shape distribution.

Description

Technical Field

[0001] The invention relates to the technical field of carbonate reservoir mining, in particular to a method for effectively disassembling nuclear magnetic resonance relaxation time spectra. Background Art

[0002] Nuclear magnetic resonance (NMR) is a nondestructive method for determining pore structure and is widely used for core pore structure analysis. Effective decomposition of NMR spectra is a crucial step in analyzing the pore and vug characteristics of carbonate rocks. Currently, two methods are commonly used to decompose NMR relaxation time spectra: the local minimum method and the least squares method. The local minimum method considers the effective relaxation time distribution range as the domain and the porosity component as the function value. Within the domain, the minimum function value is the global minimum. The NMR relaxation spectrum is divided into pore and vug components at the relaxation time corresponding to the minimum porosity component; that is, the spectrum is cut at the trough of the NMR relaxation time spectrum, with the pore component on the left and the vug component on the right. The decomposition of spectral features using the local minimum method results in large errors, and the ranges of pores and vugs do not match the actual ranges. The second method is the least squares method, which seeks the optimal function match for the NMR data by minimizing the sum of squared errors, minimizing the sum of squared errors between the obtained data and the actual NMR data. The fitted spectrum represents the pore portion on the left and the cave portion on the right. The spectrum decomposed by the least squares method does not meet the actual pore distribution characteristics of the core, and the decomposition of the overlapping signal portions is unreasonable, with significant differences compared to the overlapping portions in the original data spectrum. This decomposition method results in the pore portion radius being larger than the actual radius and the cave portion radius being smaller than the actual radius. Therefore, the existing technology lacks an effective method for decomposing the spectrum. Summary of the Invention

[0003] In response to the problems of inaccuracy and high time cost in existing local minimum method and least squares method for decomposing spectral shape, the present invention provides a new method for effectively decomposing nuclear magnetic resonance relaxation time spectrum, which improves the accuracy of spectral shape distribution.

[0004] The present invention combines nuclear magnetic resonance testing with an iterative method to provide a method for effectively decomposing nuclear magnetic resonance relaxation time spectra. The steps are as follows:

[0005] S1. Based on the distribution characteristics of pores and caves in the core nuclear magnetic resonance T2 spectrum, the probability density functions of pores and caves are constructed; the formula is as follows:

[0006] y p =φ t2 (t 2i |E p ,∑ p )

[0007] y v =φ t2 (t 2i|E v ,∑ v )

[0008] Where: y p is the probability density function of the pore part; y v is the probability density function of the cave part; t 2i is the core NMR data point, t 2i represents the i-th data point, i=1, 2…n; E p 、E v are the expectations of the pore part and the cave part respectively; ∑ p ,∑ v is the variance of the pore part and the cave part; φ t2 is the probability density function.

[0009] S2, data initialization;

[0010] First, the initial log-likelihood is calculated to select the initial estimate, and the peak amplitude of each group is normalized to set the sum of the NMR spectrum area to 1. N data points are randomly generated within the interval of pore distribution, with the value of n ranging from 3000 to 8000. All data points are divided into multiple data sets by screening the peaks; the number of data sets is equal to the number of NMR spectrum peaks, and the distribution range of each data set is characterized by the frequency of occurrence of the porosity component.

[0011] S3, calculate the likelihood function;

[0012] The NMR relaxation time is considered as a finite number of independent data sets. The expectation and variance of the pore part and the expectation and variance of the cave part are introduced to solve the maximum likelihood estimation of the distribution function. When using the iterative method, it is assumed that the data points are independent, and the likelihood function is given by the probability density function. The likelihood function formula is as follows;

[0013]

[0014] Where: n is the number of data points; w p is the probability that the data point belongs to the pore part; w v is the probability that the data point belongs to the cave; t 2i is the i-th data point, i=1,…n; is the probability density function of the pore part, is the probability density function of the cave part; 0 represents the number of iterations.

[0015] S4. Determine the expected E p and E v , expected E p and E vare the probabilities of each data point coming from a pore or a cave, respectively, calculated based on the current parameters. The prior probability calculation formula for each data point belonging to a pore or a cave is as follows:

[0016]

[0017] Where: T ip is the prior probability that the i-th data point belongs to a pore; T iv is the prior probability that the i-th data point belongs to a cave; n p and n v are the expected matrices of pores and caves respectively; m is the number of iterations, l is the sequence number of the data point; K represents the number of Gaussian models; is the weight matrix of the lth data point.

[0018] S5. Use the prior probability to update the parameters in the iterative method. The update calculation formula is as follows:

[0019]

[0020]

[0021] Where m and m+1 are the number of iterations; n is the number of data points; and T is the transpose.

[0022] S6. Based on the updated parameters, calculate the new log-likelihood according to the following formula and update the probability w of pores and caves in the iterative method p and w v , expected E p and E v , variance Σ p and Σ v Repeat steps S2 to S5 until the convergence condition is met δ=0.001, the iteration ends; the expected E of pores and caves after iteration is finally obtained p and E v , variance Σ p and Σ v ;

[0023]

[0024] Where m and m+1 are the number of iterations.

[0025] Compared with the prior art, the present invention is beneficial in that:

[0026] (1) Compared with the local minimum method and the least squares method, the spectrum shape disassembled by the method of the present invention has a smaller error than the original spectrum after reconstruction, which improves the accuracy of the disassembled spectrum shape. Moreover, in nuclear magnetic resonance analysis, when the sample size is small, the least squares method is prone to overfitting, resulting in poor model generalization ability. The method of the present invention can complete the disassembly without requiring too many samples.

[0027] (2) Accurately decomposing the relaxation time spectrum is an important step in analyzing pore structure and evaluating water saturation. The spectrum decomposition analysis of the present invention is based on the results of nuclear magnetic resonance experiments and is easier to combine with nuclear magnetic resonance logging, thereby making it easier to apply the method in mines and evaluate water saturation, and having greater practicality.

[0028] Other advantages, objectives and features of the present invention will be reflected in part from the following description and will be understood by those skilled in the art through study and practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is the normalized processing result of the nuclear magnetic resonance data of core M1-1.

[0030] Figure 2 This is a comparison diagram of the effects of the method of the present invention and the least squares method on the nuclear magnetic resonance spectrum of the core M1-1.

[0031] Figure 3 The figure is a comparison diagram of the effects of the method of the present invention and the least squares method on the nuclear magnetic resonance spectrum of the core M1-2. DETAILED DESCRIPTION

[0032] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0033] The present invention combines nuclear magnetic resonance experimental data and establishes an effective method for disassembling nuclear magnetic resonance relaxation time spectrum based on an iterative method, which specifically includes the following steps:

[0034] (1) Constructing the probability density function of the pore space based on the NMR relaxation time spectrum;

[0035] Taking core M1-1 as an example, the core NMR data is input and the probability density functions of pores and caves are constructed based on the distribution characteristics of pores and caves in its NMR T2 spectrum. The formula is as follows:

[0036] y p =φ t2 (t 2i |E p ,∑ p )

[0037] y v =φ t2 (t 2i |E v ,∑ v )

[0038] Where: y p is the probability density function of the pore part; y v is the probability density function of the cave part; t 2i is the core nuclear magnetic resonance data; E p 、E v are the expectations of the pore part and the cave part, respectively, and their values ​​are the peak values ​​corresponding to the pore part and the cave part in the NMR data; Σ p ,Σ v is the variance of the pore part and the cave part, which is half of the total spectrum variance.

[0039] The overall probability density function is as follows

[0040]

[0041] Where: E is the expectation; Σ is the variance.

[0042] (2) Data initialization:

[0043] During the data initialization process, 5000 data points are randomly generated within the range of pore distribution according to the amplitude of the NMR relaxation time spectrum. Taking the core M1-1 as an example, Figure 1 As shown, assuming that each data point is independent, the initial log-likelihood is calculated to select the initial estimate, and the peak amplitude of each group is normalized so that the sum of the NMR spectrum area is 1. Data points are randomly generated according to the NMR relaxation time spectrum amplitude. All data points are divided into two data sets by screening the peak values. The distribution range of each data set is characterized by the frequency of occurrence of the porosity component.

[0044] (3) Calculate the likelihood function:

[0045] The method of the present invention regards the NMR relaxation time as a finite number of independent data sets, and introduces the expected E of the pore part to better describe the distribution characteristics of the data set. p and variance Σ p , and the expected E of the cave part v and variance Σ v, solve for the maximum likelihood estimate of the distribution function. The expectation is the sum of the possible outcomes in the NMR relaxation time spectrum multiplied by the probability of each outcome. The variance is a measure of the degree of dispersion from the mean value in the NMR relaxation time spectrum. When using the iterative method, it is assumed that the data points are independent, and the likelihood function is given by the probability density function. However, the probability of each point occurring is very small, and the product will become extremely small, which can easily cause floating point underflow, which is not conducive to calculation and observation. Therefore, the log function is used for calculation, and the formula is as follows:

[0046]

[0047] Where: n is the number of data points; w p is the probability that the data point belongs to the pore part; w v is the probability that the data point belongs to the cave; t 2i is the i-th data point, i=1,…n; is the probability density function of the pore part, is the probability density function of the cave part.

[0048] (4) Expected E p 、E v The probability of each data point coming from a pore or a cave is calculated based on the current parameters, that is, the sum of the possible results in the NMR relaxation time spectrum multiplied by the sum of their result probabilities. Let the expectation matrix n of pores and caves be p and n v is a random matrix, and the formula for the prior probability of each data point belonging to pores and caves (i.e., the frequency of each porosity component belonging to pores and caves) is as follows:

[0049]

[0050] Where: T ip is the prior probability that the i-th observation data belongs to the pore; T iv is the prior probability that the i-th observation data belongs to a cave; n p 、n v are the expectation matrices of pores and caves, respectively.

[0051] (5) Update iteration parameters;

[0052] The parameters in the iterative method are updated using the prior probability, and m+1 is the number of iterations. The probability that a data point belongs to a pore or a cave is w p 、w v , the expectation of pores and caves is E p 、E v , the variance of pores and caves is ∑ p ,∑ v They can be updated and obtained using the following formulas:

[0053]

[0054]

[0055] (6) Calculate the new NMR log-likelihood.

[0056] The new log-likelihood is calculated according to the following formula, and the probability w of pores and caves in the iterative method is updated: p 、w v , expected E p 、E v , variance∑ p ,∑ v Repeat steps (2) to (5) until the convergence condition is met. δ is 0.001 and the iteration is terminated.

[0057]

[0058] In order to more intuitively compare the effect of the invention method, in this embodiment, the expected E p 、E v , variance Σ p ,Σ v Regenerate the NMR spectrum. Taking the core M1-1 as an example, the generated NMR spectrum is compared with the original data and the least squares method. Figure 2 Taking the core M1-2 as an example, the comparison between the NMR spectrum generated by the present invention and the least squares method and the original data is shown in FIG. Figure 3 It can be seen that the relaxation time spectrum obtained by the method of the present invention has a smaller error, while the NMR relaxation time spectrum reconstructed by the least squares method has a larger difference. The method of the present invention improves the accuracy of the disassembled NMR relaxation time spectrum.

[0059] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with this profession can make some changes or modifications to equivalent embodiments of the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for effectively disassembling nuclear magnetic resonance relaxation time spectra, characterized in that: The following steps are involved: S1. Construct the probability density functions of pores and caves based on the distribution characteristics of pores and caves in the core nuclear magnetic resonance T2 spectrum; S2, data initialization; First, the initial log-likelihood is calculated to select the initial estimate, and the peak amplitude of each group is normalized to make the sum of the NMR spectrum area equal to 1. N data points are randomly generated within the interval of the hole distribution, and all data points are divided into multiple data sets by screening the peak values. The number of data sets is equal to the number of NMR spectrum peaks, and the distribution range of each data set is characterized by the frequency of occurrence of the porosity component; S3, calculate the likelihood function; The NMR relaxation time is considered as a finite number of independent data sets. The expectation and variance of the pore part and the expectation and variance of the cave part are introduced to solve the maximum likelihood estimation of the distribution function. When using the iterative method, it is assumed that the data points are independent, and the likelihood function is given by the probability density function. The likelihood function formula is as follows; Where: n is the number of data points; w p is the probability that the data point belongs to the pore part; w v is the probability that the data point belongs to the cave; t 2i is the i-th data point, i=1, 2…n; is the probability density function of the pore part, is the probability density function of the cave part; 0 represents the number of iterations; S4. Determine the expected E p and E v , expected E p and E v are the probabilities of each data point coming from a pore or a cave, respectively, calculated based on the current parameters. The prior probability calculation formula for each data point belonging to a pore or a cave is as follows: Where: T ip is the prior probability that the i-th data point belongs to a pore; T iv is the prior probability that the i-th data point belongs to a cave; n p and n v are the expected matrices of pores and caves respectively; m is the number of iterations; l is the sequence number of the data point; K represents the number of Gaussian models; is the weight matrix of the lth data point; S5. Using the prior probability to update the parameters in the iterative method; S6. Based on the updated parameters, calculate the new log-likelihood according to the following formula and update the probability w of pores and caves in the iterative method p and w v , expected E p and E v , variance∑ p and ∑ v Repeat steps S2 to S5 until the convergence condition is met δ=0.001, the iteration ends; the expected E of pores and caves after iteration is finally obtained p and E v , variance∑ p and ∑ v ; Where m and m+1 are the number of iterations.

2. The method for effectively disassembling nuclear magnetic resonance relaxation time spectrum according to claim 1, wherein: In step S5, the update calculation formula of each parameter is as follows: Where m and m+1 are the number of iterations; n is the number of data points; and T is the transpose.

3. The method for effectively disassembling nuclear magnetic resonance relaxation time spectrum according to claim 1, wherein: In step S1, the probability density functions of the pores and caves are constructed, and the formulas are as follows: y p =φ t2 (t 2i |E p ,∑ p ) y v =φ t2 (t 2i |E v ,∑ v ) Where: y p is the probability density function of the pore part; y v is the probability density function of the cave part; t 2i is the i-th data point, i=1, 2…n; E p 、E v are the expectations of the pore part and the cave part respectively; Σ p ,Σ v is the variance of the pore part and the cave part; φ t2 is the probability density function.

4. The method for effectively disassembling nuclear magnetic resonance relaxation time spectrum according to claim 1, wherein: In step S2, the value range of n is 3000-8000.

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