Nuclear Magnetic Resonance Echo Data Research Articles

Variational Mode Decomposition for NMR Echo Data Denoising

Nuclear magnetic resonance (NMR) relaxometry, a noninvasive and nondestructive method, is a key technique for unconventional reservoir evaluation. Echo data detected from NMR instrument, a kind of weak signal, however, is characterized by a low signal-to-noise ratio (SNR). The achievement of NMR relaxation spectra inversion of a high precision, for echo data with a low SNR, is a challenge, which will also affect the unconventional reservoir evaluation of NMR logging. In this article, a variational mode decomposition (VMD) method was proposed for NMR echo data denoising. NMR echo data were decomposed into an ensemble of intrinsic mode functions (IMFs) by the VMD method. The IMF number is an important parameter for VMD, and VMD results are different with various IMF numbers. An optimal selection method for the IMF number was proposed. The decomposed IMFs compose of signals with different frequencies. Noise is from high-frequency signal, but valuable data are from low-frequency signal. The effective IMFs in VMD were selected and summed as the denoised echo data. Numerical simulations and field NMR logging data processing were undertaken to evaluate the NMR echo data denoising effectiveness and practicality of the proposed VMD-based method. The results showed that the inverted NMR spectra exhibit a higher quality after the VMD-based denoise, compared with those for raw echo data and after the empirical mode decomposition (EMD) denoise. This indicates that a higher denoising quality is achieved by the VMD-based method than by the EMD-based method for NMR echo data.

A new method for capillary pressure curve prediction based on NMR echo data using integral transform, the quantum genetic algorithm, and the artificial neural network in tight sandstone

The capillary pressure curve (CPC) is an important tool with which to investigate the petrophysical properties and pore structure of oil and gas reservoir rocks. However, the method of obtaining the CPC directly via laboratory measurements is usually time-consuming and costly, prone to the contamination or destruction of core samples, and can only be applied to limited cores. A new method adopting integral transform, the quantum genetic algorithm, and the artificial neural network (IT-QGA-ANN) based on nuclear magnetic resonance (NMR) echo data is proposed to improve CPC prediction accuracy in tight sandstone. First, 7 parameters that characterize rock properties are directly extracted from echo data using integral transform. This process does not require to obtain the transverse relaxation time (T2) distribution by inversion of echo data, thereby avoiding the influence of inversion uncertainty. These characteristic parameters are then used as the input of the ANN, and the QGA method is utilized to optimize the weights and thresholds of ANN. Numerical simulation results prove the validity of integral transform to extract characteristic parameters. A total of 18 tight sandstones are used for mercury injection and NMR tests. The results indicate that, compared with the traditional nonlinear regression and ANN methods, the proposed IT-QGA-ANN method can more accurately predict the CPC. The proposed method achieves the direct and accurate transformation from echo data to the CPC, and provides important guidance for solving complex nonlinear problems in oil and gas reservoir evaluation based on NMR.

Compression Method of NMR Echo Data Obtained From Complex Pore Structure Formation

To reduce the redundancy of nuclear magnetic resonance (NMR) echo data, kernel principal component analysis (KPCA) is used in the compression. The algorithm of data compression using KPCA is introduced in detail, and the specific calculation process is given. Four commonly used kernel functions are selected: Gaussian kernel, linear kernel, polynomial kernel, and exponential kernel. The compression effect of KPCA based on these four kernel functions on the NMR echo data obtained from complex pore structure formation is compared and analyzed. The study found that: Principal component analysis (PCA) is not suitable for the compression of NMR echo data obtained from the formation with complex pore structure. Compared with PCA, KPCA based on all the four kernels has obvious advantages in computational efficiency. The compression capabilities of KPCA based on Gaussian kernel and exponential kernel are all lower than PCA. The compression capability (CA) of KPCA based on linear kernel is equivalent to PCA. KPCA based on polynomial kernel, when the kernel parameter <inline-formula> <tex-math notation="LaTeX">$\sigma \ge 2$ </tex-math></inline-formula>, its CA is higher than PCA. The compression accuracy of KPCA based on Gaussian kernel, linear kernel, and exponential kernel is stable in the formations with complex pore structure. KPCA based on polynomial kernel is sensitive to the kernel parameter, only when the kernel parameter <inline-formula> <tex-math notation="LaTeX">$\sigma =5$ </tex-math></inline-formula>, the optimal compression accuracy can be obtained. At this time, the optimal compression effect is obtained in the complex pore formation.

A novel method for NMR data denoising based on discrete cosine transform and variable length windows

Raw nuclear magnetic resonance (NMR) data detected exhibits a low signal-to-noise ratio (SNR). The inversion results suffer from the low SNR of echo data. It is therefore essential to denoise the data before NMR data inversion, to improve the accuracy of inverted NMR spectrum. In this paper, a denoising method was firstly proposed based on discrete cosine transform (DCT), whereby four window schemes were designed into one window, multiple non-overlapping windows of equal length, multiple overlapping windows of equal length, and variable length windows. The effectiveness of four schemes was verified and compared by numerical simulations, and it indicates that Denoising Fig. 5 with variable length windows is the optimum. Core experimental data and NMR logging data were used to verify the practicality of Denoising Fig. 5. The results indicated that Denoising Fig. 5 can be effectively used to reduce the noise of actual NMR data, and the processed NMR spectrum with Denoising Fig. 5 is more reliable. • Discrete Cosine Transform was first applied to the noise reduction of NMR echo data. • Variable Length Windows scheme can achieve the best denoising effect. • The proposed method can effectively improve the application effect of NMR logging.

A new method for predicting capillary pressure curves based on NMR echo data: Sandstone as an example

The mercury injection capillary pressure (MICP) curves have been widely used for the evaluation of the pore structure. In practical application, the MICP curves are usually obtained by the mercury injection experiment, but the experimental measurement can not obtain the MICP curves of the reservoir continuously. Since the pore size distribution obtained from the nuclear magnetic resonance (NMR) transverse relaxation time (T2) distribution is related to the pore-throat size distribution obtained from the MICP curve, so in previous studies, the MICP curves were predicted based on the NMR T2 distribution. However, the NMR T2 distribution obtained by the inversion of the NMR echo data has uncertainty, which affects the prediction accuracy of the MICP curves. In this paper, a new method for predicting the MICP curves of sandstone based on NMR echo data is proposed for the first time. Multiple characteristic parameters of the NMR echo data are calculated. The relationship between the parameters and the mercury saturation (Shg) is established at each capillary pressure point to predict the MICP curves. And the parameters of the MICP curves and the physical parameters are selected to create a reservoir classification index. The results show that the method for predicting the MICP curves of sandstone based on NMR echo data has high prediction accuracy and strong stability, and the reservoir classification index provides an accurate classification of sandstone reservoirs.

A nuclear magnetic resonance echo data filter method based on gray-scale morphology

Nuclear magnetic resonance (NMR) echo data measured in the oil field usually have a very low signal-to-noise ratio (S/N). The low S/N of echo data may affect the accuracy of the inversion results, which further leads to the inaccuracy of derived petrophysical parameter estimates. It is therefore important to filter the echo data to enhance the S/N before inversion. Existing filter methods focus on removing noise by compressing the echo data matrix or processing the echo data in time or frequency domain, which are not very efficient and can be affected by artificial interventions. We have developed a gray-scale morphology filter method based on the morphological difference between the echo data and noise. Either elliptical or triangular structure elements can be used for the morphology filter of NMR echo data. The size of the structure elements should be in the range of 1–5 echo spacings to prevent the echo data from being distorted. Comparing the inversion results of the unfiltered, morphology-filtered, singular value decomposition (SVD)-filtered, and wavelet-filtered echo data at different S/Ns, the morphology filter method yields the best results at low S/Ns and the morphology filter method and the wavelet filter method yield similarly good results at high S/Ns. The morphology filter method has the shortest run time compared to the SVD method and the wavelet filter method. Moreover, this morphology filter method is stable to handle random noise and different [Formula: see text] distribution models, and it also performs well on NMR well-logging data.

Characterization of pore structure of tight sandstone reservoirs based on fractal analysis of NMR echo data

The evaluation of the pore structure of tight oil and gas reservoirs has great significance for the characterization of the reservoir properties and the prediction of reservoir productivity. Fractal analysis is an effective method commonly used to evaluate reservoir pore structure. In previous studies, the fractal dimension of nuclear magnetic resonance (NMR) transverse relaxation time (T2) distribution was calculated to evaluate reservoir pore structure. However, due to the low signal-to-noise ratio (SNR) of the NMR echo data in tight sandstone reservoirs, the T2 distribution obtained by inversion of the echo data with low SNR has great uncertainty, which affects the evaluation accuracy of reservoir pore structure. In this paper, the fractal dimension of the NMR echo data (D_ECHO) is calculated to evaluate the pore structure of tight sandstone reservoirs for the first time. Fast Fourier transform is performed with the NMR echo data and then the D_ECHO is calculated. We analyze the correlation between the fractal dimension and the physical parameters and pore structure parameters, the results showed that 1) compared with the calculation of the fractal dimension of the T2 distribution, the calculation of the D_ECHO has higher stability, which can avoid the influence of the inversion uncertainty of echo data with a low SNR on the evaluation of the reservoir pore structure; 2) the fractal dimension is closely related to pore structure parameters, D_ECHO are well suited for characterizing the pore structure of tight sandstone reservoirs. As the heterogeneity of reservoirs increases, the D_ECHO increases. Numerical simulations, core experiments and NMR logging data processing results verify the effectiveness of the proposed method.

Nuclear Magnetic Resonance Characterization of Petrophysical Properties in Tight Sandstone Reservoirs

AbstractPermeability and bound water saturation (Swb) are key parameters reflecting the petrophysical properties of porous rocks. Nuclear magnetic resonance (NMR) has proved to be effective in investigating the properties of porous media. However, estimating Swb and the permeability in tight sandstone reservoirs based on conventional NMR methods, which requires the inversion of NMR echo data to obtain the transverse relaxation time (T2) distribution, proves to be a challenging task. In this study, a method is proposed to estimate Swb and the permeability in tight sandstone reservoirs based on the direct analysis of NMR echo data, thus avoiding the inversion process. A total of 20 tight sandstone samples from the Ordos Basin in China was taken for laboratory NMR measurements. The kernel function of the echo data was used to characterize the ratio distribution of bound water volume to pore volume for different pore sizes. Following this, an echo data calibration method was applied to estimate Swb without the inversion of the T2 distribution, and the window method was used to reduce the impact of noise in the echo data. Furthermore, models for estimating permeability were proposed based on the determined windows of the NMR echo data in the Swb estimation. The reliability of the proposed method for estimating Swb and permeability was verified by comparing the estimated and experimental results. Our study provides an efficient method for the estimation of petrophysical parameters in porous rocks based on the direct analysis of NMR echo data.

A Novel Inversion Combining NMR Log and Conventional Logs

Nuclear magnetic resonance (NMR) log is a powerful tool to obtain porosity and oil saturation in reservoir evaluation. NMR echo inversion, however, may give poor information in the two parameters if the ratio of signal-to-noise is not so good. Combining NMR log and some conventional logs, such as GR log, sonic log, and density log, a novel inversion algorithm is developed in this research. First, normalize the logging response, then, insert both the logging response equations and the definition equations of volume model into the NMR echo equations. By conducting the data inversion for both NMR echo and conventional logging data, the porosity and oil saturation can be calculated. The condition number of the inversion matrix is decreased, so, the inversion parameters own better stability and the random weak noise is stifled. Furthermore, the T2 spectral distribution derived from the new inversion seems to be sensitive to the small pores in tight reservoir. Due to the weak noise removal and sensitiveness of small pore, the novel inversion may be utilized in reservoir evaluation in shale oil and gas, such as the identification of “sweet spot”.

Petrophysical Parameter Calculation Based on NMR Echo Data in Tight Sandstone

Bound water saturation (Swb) and permeability are the important petrophysical parameters. However, the traditional methods for the calculation of Swb and permeability based on the nuclear magnetic resonance (NMR) transverse relaxation time (T2) distributions are not applicable for tight sandstone because the NMR data have a low signal-to-noise ratio and the calculation models have certain disadvantages. In this paper, we present a new method for the calculation of Swb and permeability using integral transforms (ITs) of the NMR echo data in tight sandstone. First, the tapered cutoff function was established using the Laplace transform function of the exponential hyperbolic sine function based on the film model; Swb was directly calculated from the echo data using the exponential hyperbolic sine transform without an inversion of the T2 distribution. The position and slope of the median point, both of which control the shape of the tapered cutoff function, were determined by core experiments. Subsequently, the tapered cutoff function representing the proportion coefficients of the free fluids in the pore space was added to the arithmetic mean of the T2 (T2am) as a weight to construct the weighted T2am (T2wam). T2wam was highly suitable for reflecting the seepage ability of the pores and was directly calculated from the NMR echo data using an IT without an inversion. A new permeability calculation model was developed based on T2wam. The numerical simulation and core experimental results verified the effectiveness of the new method.

An Inversion of NMR Echo Data Based on a Normalized Iterative Hard Thresholding Algorithm

The inversion of nuclear magnetic resonance (NMR) echo data requires solving the discrete Fredholm integral equation of the first kind, which is an ill-posed problem. In this letter, a surrogate objective function of an NMR inversion without an explicit regularization term based on least-squares fitting is introduced to avoid the process of choosing a regularization parameter, and a normalized iterative hard thresholding algorithm is proposed to solve the surrogate objective function. Furthermore, the inverted $T_{2}$ spectra of the proposed method, the truncated singular value decomposition method, the Butler–Reeds–Dawson method, and the least-squares QR decomposition method are compared using numerical simulation examples. The results show that the proposed method is superior to the other methods because the peaks of the inverted $T_{2}$ spectra with a shorter relaxation time are the most similar to the model at a low signal-to-noise ratio and the root-mean-square errors of the inverted $T_{2}$ spectra are the lowest. Finally, we process the NMR experimental data of tight sandstone using the four methods and verify the effectiveness of the proposed method for solving the NMR echo data inversion problem.

NMR Data Compression Method Based on Principal Component Analysis

Hundreds of thousands of echo data are collected in nuclear magnetic resonance (NMR) logging. In order to get the formation information, such as porosity, permeability, fluid type, fluid saturation, pore size distribution, etc., those NMR data need to be inversed. Generally, compression is implemented to the gathered significant amounts of NMR echo data before they are inversed to reduce the inversion computation. This paper puts forward a new kind of NMR echo data compression method based on the principle of principal component analysis (PCA). Aiming at losing the minimum information, original echo data were compressed by retaining those who contribute the largest amounts of information for reflecting the formation characteristics, and eliminating those who contribute little or even are redundant. One-dimensional and two-dimensional NMR echo data were simulated, and then compressed, respectively, using the PCA method. The NMR echo data before and after PCA compression were inversed respectively, and the inversion results of compressed and uncompressed were compared. The result showed that the PCA method could be used to compress the NMR echo data without losing much information even under a high compression ratio.

Inversion of nuclear magnetic resonance echo data based on maximum entropy

Nuclear magnetic resonance (NMR) [Formula: see text] inversion is an ill-posed problem in which regularization techniques are usually adopted to suppress the oscillations caused by noise in the solutions. The maximum entropy concept provides an unbiased way to obtain information from incomplete data, and it implicitly imposes a positive constraint on probability distribution, so we used the maximum entropy method to invert NMR echo data. We have developed a simple and effective method for solving the objective function of the maximum entropy method. First, the solution was replaced by a positive function to achieve the positive constraint of the solution, the objective function was converted to an unconstrained one, and then the Levenberg-Marquardt method was used to solve the newly obtained unconstrained objective function. To suppress the highly tilted tail at the short relaxation time of the [Formula: see text] distribution, a modified or normalized Shannon entropy function was used to replace the standard Shannon entropy function as the penalty term. Furthermore, the S-curve method was used to select the regularization parameter and the formula of the slope of the S-curve was developed. We have determined that the maximum entropy method was better able to separate the peaks of short and long relaxation times in the [Formula: see text] distribution in comparison with the truncated singular value decomposition method. This was true for low signal-to-noise ratio data derived from numerical simulation and the NMR log. In addition, the short relaxation peak caused by the norm smoothing method can also be reduced.

NMR Log Data De-noising Method Based on a Variable Order Wavelet Packet Domain Adaptive Filtering

To improve the de-noising effects of low signal to noise ratio (SNR) nuclear magnetic resonance (NMR) log data, improve the calculating precision of the porosity parameters of the reservoirs, this paper attempts to apply the wavelet packet domain adaptive filtering algorithm to de-noise the NMR log data. First of all, the algorithm is interpreted in detail. And then, the de-noise off phenomenon is analyzed in the de-noising process of simulant and NMR echo data using the wavelet (packet) domain adaptive filtering algorithm. The factors affecting the occasion of the phenomenon are studied systematically, and a variable order processing scheme is proposed to eliminate the influence of the existence of the de-noise off phenomenon on the inversed T2 spectra. As a result, the effectiveness of the algorithm is verified by the application in the numerical simulation and NMR log data, respectively. The results indicated that, comparing with wavelet domain adaptive filtering algorithm, wavelet packet domain adaptive filtering algorithm is more suitable for low SNR-NMR echo data de-noising.