Fast Gaussian picking Method for NMR T₂ characteristic distributions of viscous crude oil containing impurities in free fluid state

Abstract

The nuclear magnetic resonance (NMR) T₂ distributions of free fluid are widely used to characterize the bulk relaxation properties of fluids. However, in the heavy crude oil of reservoirs in the western South China Sea, solid-phase impurities such as waxes, asphaltenes, and colloids result in multi-peak, broad-spectrum T₂ distributions. This complexity hinders accurate peak identification and fluid property analysis. To address this, typical crude oils from the study area were selected, and their free-fluid T₂ distributions were measured under reservoir-temperature conditions. The observed multi-peak patterns were analyzed to determine their physical and chemical origins. Based on the Gaussian distribution function, a fast Gaussian picking method is proposed to search for representative distribution peaks in crude oil in conjunction with extreme points. The non-negative least squares (NNLS) method is utilized to fit the data, and the complex T₂ distribution was decomposed into components representing different phases and viscosities. After mathematical-physical tests and demonstrations, the rapid classification of the T₂ distribution of the free-fluid state of impurity-containing viscous crude oil is realized. Applied to downhole NMR data, the method accurately captured the T₂ characteristics of such crude oils, offering a fast and reliable tool for analyzing complex bulk relaxation behaviors and fluid identification. Finally, the method’s performance, influencing factors, and applicability were discussed.

Introduction

Accurate understanding of the physicochemical properties of subsurface crude oil is the key to the success of petroleum exploration and development, in which the bulk relaxation characteristics of crude oil in the free-fluid state are also a central focus of research^1,2. The lateral relaxation characteristics of the free fluid of many types of crude oils, such as thick oils and crude oils with multiple impurities, which are distributed in large quantities around the globe, are often difficult to obtain accurately³. Certain reservoirs in the western South China Sea are shallowly buried and loosely cemented. The crude oil produced is characterized by high viscosity, easy to condense, and contains solid-phase impurities such as paraffin, asphalt, and colloid⁴. This leads to the nuclear magnetic resonance transverse relaxation time distributions (NMR T₂ distributions) of solid-liquid mixed-phase crude oil in the free-fluid state to have multi-peak broad characteristics⁵. The relaxation time distributions of complex compositions as well as highly viscous crude oils will overlap with those of bound water and gases, making it difficult to pick up the distribution peaks’ positions and characteristics of crude oil and other compositions. These challenges are further exacerbated by the fact that T₂ distributions are typically obtained via Inverse Laplace Transform (ILT) of Carr-Purcell-Meiboom-Gill (CPMG) echo trains—a classic ill-posed mathematical problem. As a result, the inversion process is highly sensitive to noise and regularization choices, often yielding non-unique or unstable solutions⁶. For crude oils with multiple relaxation components, this ill-posed nature leads to broadened and overlapping peaks in the resulting T₂ distributions, making accurate peak identification and decomposition extremely difficult. Many scholars have carried out a lot of related researches to address these difficulties.

NMR logging technology measures the resonance signals of hydrogen nuclei in subsurface samples under an external magnetic field, providing insights into reservoir composition, porosity, fluid volumes (both bound and movable), permeability, and crude oil viscosity⁷. The transverse relaxation characteristic (T₂ relaxation time) of crude oil in the free fluid state reflects nuclear spin distribution across different T₂ times. This parameter is widely applied to identify and quantify free and bound fluids in formations⁸. In the free-fluid state, the T₂ relaxation time can reflect the motion behavior and viscous properties of fluid molecules in the pores. Bloembergen et al. derived the relaxation equations (BPP theory) due to molecular rotational diffusion in free-state liquids, caused by spin reorientation of molecular cores⁹. Kleinberg argued that the free-fluid relaxation time is approximately linear with respect to the ratio of viscosity and temperature at low fluid viscosities, while the thick oil relaxation time has a power-law relationship with the viscosity-temperature ratio¹⁰. Freedman et al. established a linear relationship between the logarithmic mean of T₂ and viscosity in logarithmic coordinates by measuring the transverse relaxation time (T₂) of crude oil at several different viscosities¹¹. Coates et al. proposed a method for analyzing the pore structure of rocks based on T₂ relaxation time distributions, which provides a fundamental theory for understanding the behavior of crude oil in pore media¹². Xie et al. investigated the effect of temperature on the NMR relaxation properties of crude oil by using a 2 MHz NMR spectrometer, and gave the relational equations for the variation of the relaxation time with the temperature and the viscosity of crude oil at 2MHz¹³. In the same year, Xie et al. measured the relaxation time of selected degassed crude oil samples using two NMR spectrometry instruments operating at different frequencies. They established the relationship between the relaxation time and the crude oil viscosity, the viscosity-to-temperature ratio and the Larmor frequency. Additionally, they investigated the effect of the instrumental measurement echo interval (TE) on the distribution of apparent transverse relaxation time (T₂) in heavy oil. Likewise, there are other NMR T₂ analysis techniques that can be used to resolve reservoir fluid composition information¹⁴. However, it is known from previous studies that these methods have a weak ability to identify fluids in low porosity reservoirs and do not identify fluids well when there is an oil, gas and water overlap in the T₂ distribution¹⁵. In response to these problems, many researchers have proposed a variety of improved methods to enhance the resolution of NMR T₂ distributions. Appel et al. reported that by measuring the transverse relaxation time spectra of cores at different temperatures and comparing them with the NMR properties of bulk oil, they found that they were able to differentiate between different pore fluids and identify the response of the oil phase in the NMR signal¹⁶. Freedman et al. provided a field example of the MRF2 magnetic resonance fluid characterization method, which illustrates the application of two-dimensional NMR maps of relaxation times and molecular diffusion rates to identify fluids and characterize them in a complex and multi-fluid environment¹⁷. Nielsen et al. found that impurities cause further overlap and distortion of the NMR T₂ spectral peaks¹⁸. Hu et al. proposed a constructive water spectroscopy method to identify fluid properties in reservoirs¹⁹. Zhang et al. proposed to use continuous wavelet transform and asymmetric Gaussian function to split the NMR T₂ spectrum into a number of component spectra for intra-pore fluid component identification in shale oil reservoirs²⁰. Huang et al. proposed to reversely decompose the NMR logging spectra to obtain multiple sub-spectra, and used laboratory NMR experiments to determine the fluid properties and pore information of the sub-spectra²¹.

Many constructive results have been achieved by previous researchers in the characterization of transverse bulk relaxation in the free fluid state. However, there is still insufficient research on viscous crude oil with impurities, wax, and colloids in the free fluid state in sandstone reservoirs in the western South China Sea, limiting the understanding of their bulk relaxation and fluid characteristics. Current methods struggle to accurately separate the relaxation distributions of thick and light oils and bound water in highly viscous and complex crude oils. To solve the above problems, a fast Gaussian picking method is proposed in this study, with a view to effectively separating and recognizing the T₂ distributions peaks of the free-fluid state in viscous crude oil. The process is as follows: (i) Measure the NMR T₂ distributions of typical crude oil free fluid state under the geothermal conditions in the study area. (ii) Propose a fast Gaussian picking method based on the Gaussian distribution function to decompose the NMR T₂ distribution into multiple T₂ component distributions. (iii) Conduct mathematical and physical tests to verify the effectiveness of the decomposition. (iv) Achieve rapid classification of the free-fluid state T₂ distributions of impurity-containing viscous crude oil and extract its characteristic parameters. (v) Validate the reliability and accuracy of the proposed method.

Data

Study area

The South China Sea is one of the largest marginal seas in the western Pacific Ocean and plays a crucial role in regional geological and geophysical studies. The exploration scope of the western part of the South China Sea crude oil field mainly includes the Chinese sea area south of the two Guangdong landmasses and west of 113°10′ East Longitude, including mainly the Beibuwan Basin and the western part of the Pearl River Mouth Basin (Fig. 1). The Beibuwan oil field is situated in the Weixi’nan sag, characterized by a complex fault-block stratigraphic structure with well-developed faults. The oil reservoir primarily comprises tectonic and lithological traps, abundant in oil and gas, and represents the principal crude oil production area of the western South China Sea oil fields to date²². The main oil-bearing system in the Weixi’nan sag is the Weizhou Formation. For a long time, the accuracy of fluid identification in the Weizhou Formation is only about 25%, and the low accuracy of fluid identification has restricted the effectiveness of rolling exploration in the oilfield^23,24. Crude oil from this region is characterized by high wax content and high viscosity and is a thick oil. Crude oils produced in the Beibuwan waters tend to contain a high percentage of solid-phase impurities such as paraffins, asphaltenes and gums, resulting in their tendency to solidify at low temperatures and poor fluidity. These characteristics provide a unique opportunity to study the fluid properties of crude oil.

Fig. 1.

Overview of geological structural characteristics in the study area. The complete map was created by the authors using ArcGIS 10.8 (https://desktop.arcgis.com/).

Samples and experiments

To verify and demonstrate the application of the fast Gaussian picking method in processing the free fluid state NMR T₂ characteristic distributions of viscous crude oil containing impurities. In this study, three sandstone cores of the target layer in the study area and two sets of stratigraphic crude oils are selected as experimental samples for NMR experiments. The indoor NMR analyzer (MesoMR12-060 H-I) used in the experiment is a high-precision low-field NMR analyzer that integrates spectroscopy and imaging analysis (Fig. 2). Its main frequency is 12 MHz, the magnet type is a permanent magnet, the magnetic field strength is: 0.5 ± 0.03T, and the probe coil diameter is 60 mm. The method is field-strength independent in principle, since the T₂ relaxation time of crude oils is governed by molecular motion and surface relaxation mechanisms rather than by the external magnetic field B₀²⁰. Only the signal-to-noise ratio and resolution may vary with instrument field strength, which can be mitigated by proper data smoothing. The technical parameters related to the experiment are as follows: minimum echo interval 0.06 ms, number of echoes 2000, and number of scans 64. The CPMG pulse sequence was used for echo string inversion of the T₂ distribution.

Fig. 2.

Schematic diagram of indoor NMR analyzer.

(modified from Wei et al.²⁵).

The NMR and corresponding experiments can be conducted. Representative samples of formation crude oil are selected from the study area and its physical and chemical properties (e.g., density, viscosity, wax content, asphaltenes content, colloidal content, etc.) are recorded. To ensure that the crude oil samples remained in the free-fluid state under reservoir-temperature conditions, each sample was gently heated to the in-situ formation temperature (about 90–115 °C) using a thermostatic chamber. The heating process is performed only to restore the natural temperature conditions and to homogenize the solid-phase impurities such as waxes and asphaltenes. No chemical alteration or phase transformation occurred during heating, and the process is reversible upon cooling. In this study, the “free-fluid state” refers to the physical condition in which the crude oil sample exists as a homogeneous liquid phase without confinement by pore structures or rock surfaces. Under this state, the measured NMR T₂ relaxation behavior reflects only the intrinsic molecular mobility of the viscous crude oil, free from surface relaxation or pore-size effects. Prior to measurement, all crude oil samples were degassed under vacuum to remove dissolved and free gases, thereby preventing bubble formation in the NMR tube. The measurements were carried out in a fully sealed environment to ensure that no gas phase was present in the system. Preliminary tests confirmed that the T₂ distributions of the samples before and after heating showed negligible differences, confirming the reversibility and stability of the sample state during measurement. Afterwards, the samples are placed in the NMR analyzer and the relevant technical parameters described above are set. Multiple measurements are taken for each sample to ensure the reliability and reproducibility of the data. Afterwards, the acquired raw T₂ relaxation curves need to be processed to remove noise and interference signals. The relaxation curves were converted to T₂ distributions using an echo string inversion algorithm, and the initial distribution of the T₂ distributions was recorded.

Experimental data

Three sandstone cores from the target layer in the study area were selected as experimental samples for NMR experiments. The related parameters of the samples are shown in Table 1. The porosity ranges from 14.19% to 20.8%, with an average of 18.58%, and the permeability ranges from 14.55 mD to 29.5 mD, with an average of 20.483 mD. The samples are all 1 inch in size and are in standard plunger shape. The three core samples are grouped and numbered. The three cores are taken from two different coring wells at a depth of 1543.95–3045.6 m, and the selected core samples are taken from the water layer or the oil-water layer. All sandstone samples are characterized by moderate porosity and predominantly water-wet conditions, minimizing the influence of rock wettability on T₂ distributions.

Table 1.

Petrophysical parameters of core samples.

Well name	Coring depth(m)	Rock sample number		Porosity(%)	Permeability (mD)	Group segment	Remark
A1	1543.95	1		20.8%	29.5	Weizhou Formation	Water layer
	1606.91	2		20.75%	14.55		Water layer
A2	3045.6	3		14.19%	17.4		Oil-bearing water layer

In addition, several crude oil samples in this study were collected from the Weizhou Formation, and relevant experimental data were collected to more fully understand the NMR T₂ characteristic distributions of the free-fluid state. The area is known for its hydrocarbon-rich reserves, and the specific information on the crude oil samples is presented in Table 2 below, and these parameters provide a basic overview of the physical and chemical properties of the crude oil under study.

Table 2.

Data sheet on physical and chemical properties of crude oil in the Eastern slope zone of the weixi’nan sag.

Well name	Stratum	Burried depth(m)	Stratigraphic pressure (Mpa)	stratigraphical temperature (℃)	Crude oil density 20℃ (g/cm3)	Dynamic viscosity 60℃ (mPa.s)	Wax content (%)	Silicone (%)	Asphaltene (%)
A1	Weizhou Formation 1	2129.26	21.111	90.10	0.782	29.59	21.10	17.14	2.75
A1	Weizhou Formation 1	2428.30	24.450	105.96	0.8915	79.65	19.72	19.07	7.90
A2	Weizhou Formation 2	2821.67	28.386	115.16	0.8937	109.69	20.21	20.56	5.83

Method

Signal characteristics of NMR T₂ distributions

Impurity-containing viscous crude oils are a class of oils with complex components and multiphase systems. In this multiphase environment, the NMR measured relaxation signal of crude oil consists of the overall superposition of multiple relaxation components. Using the CPMG pulse sequence, an echo string signal containing information about the crude oil is measured (e.g., Fig. 3)²⁶. The transverse relaxation signal of crude oil measured by the CMPG method can be expressed by the multi-exponential decay formula:

1

Fig. 3.

CPMG sequence acquisition echo string.

where M (t) is the amplitude of the transverse relaxation signal at time t; i is the middle wave number of the echo string; M_i (0) denotes the magnitude of the echo signal of the ith fluid component when the moment of t = 0; t is the acquisition time, which is usually an integer multiple of the dialing back interval; and T_2i denotes the T₂ relaxation time of the ith fluid component, ms.

According to Eq. (1), the measured crude oil hydrogen atomic nuclear spin echo train signal is subjected to multi-exponential inversion fitting to obtain the NMR T₂ distribution (e.g., Fig. 4). From the inversion process of the NMR T₂ distribution, it is known that it is consistent with the normal Gaussian distribution. From the basic theory of NMR, the original NMR T₂ distribution Y can usually be regarded as a distribution consisting of a linear superposition of n independent Gaussian distribution curves²⁷. Assuming that the T₂ distribution of the ith independent component is represented by the analytic peak function f_i (T₂), the original T₂ distribution Y (T₂) can be expressed as:

2

Fig. 4.

NMR T₂ distribution of crude oil Sample A1 (Weizhou Formation, western South China Sea) obtained under reservoir-temperature conditions (12 MHz, 90 °C). The T₂ distribution is obtained by ILT inversion of the CPMG echo train.

Therefore, it is also possible to decompose the original NMR T₂ distribution into a T₂ decomposition spectrogram converged from multiple component distributions, further refine and analyze the T₂ component distributions features, and use these features to identify the crude oil fluid properties, which has a better application effect.

The signal characteristics of the NMR T₂ distribution include the following main aspects. Firstly, the peak positions in the NMR T₂ distribution reflect the relaxation times of different components in the magnetic field. The relaxation time of different components depends on its molecular structure and environment and other factors. By observing the positions of the peaks, it is possible to determine the types of different components present in the crude oil. Solid-phase impurities alter the T₂ relaxation behavior of crude oils mainly through physical restriction of molecular motion and enhancement of surface relaxation. These solid components can form semi-solid networks or adsorbed layers within the liquid phase, increasing the surface-to-volume ratio of hydrogen-bearing domains and thereby accelerating spin-lattice and spin-spin relaxation²⁸. As a result, the overall T₂ spectrum shifts toward shorter relaxation times and exhibits broader peak shapes. Secondly, the sum of the longitudinal amplitudes of all points in the NMR T₂ distribution is related to the content of the component in the crude oil. By measuring the cumulative size of the longitudinal amplitude of all points in the T₂ distribution, the relative content of each component in the crude oil can be quantitatively analyzed. This quantitative relationship assumes that the hydrogen index (HI) of each component is approximately similar, such that the NMR signal amplitude is directly proportional to the volume fraction of hydrogen-bearing fluids. For systems containing fluids with significantly different hydrogen indices, a correction factor or normalization using the known HI of each component can be applied to improve quantitative accuracy. Thirdly, the relative position and intensity of different peaks in the NMR T₂ distribution can reveal the interaction between components. For example, the degree of overlap between peaks can indicate the interaction or aggregation phenomenon between components²⁹.

Fast Gaussian picking method

Based on the signal characteristics of NMR T₂ distribution, a fast Gaussian picking method is proposed to process and analyze the NMR T₂ distribution. This method is the basis of the adaptive decomposition method of NMR T₂ distribution components. It uses the mathematical properties of Gaussian functions to decompose the signal, which can more accurately describe the characteristics of complex signals and extract parameters of Gaussian peaks in the T₂ distribution, such as peak position and peak shape³⁰. Its features include strong suppression of noise, accurate signal peak localization, and high computational efficiency. This makes the Gaussian picking method a viable option when dealing with NMR T₂ feature distributions of crude oil in free-fluid state. In this study, the investigated viscous crude oils are measured under free-fluid conditions at laboratory temperature to eliminate the influence of pore confinement and surface relaxation. This experimental setup ensures that the observed T₂ distributions primarily reflect intrinsic molecular mobility rather than rock-fluid interactions. The proposed fast Gaussian picking method itself, however, does not require the free-fluid assumption. Because it is based purely on mathematical decomposition of the T₂ spectrum, the same algorithm can be applied to confined fluids or core samples, where the T₂ components correspond to different relaxation domains. The “free fluid state” in this work refers only to the laboratory condition for validation, not a theoretical limitation of the method. Using this method, the quantitative analysis of the components in impurity-containing viscous crude oil can be realized, which can provide basic data for further research on the properties and components of crude oil. As mentioned before, an NMR T₂ distribution can be regarded as a linear superposition of multiple normal distribution curves (Fig. 5). The multi-Gaussian distribution function is chosen for the constructor:

3

Fig. 5.

NMR T₂ distribution Gaussian component signals.

where n denotes that there are n components within the crude oil; A_i denotes the maximum amplitude of the ith component; α_i denotes the relaxation time of the ith component, ms; σ_i denotes the width of the Gaussian peak of the ith component; T_2,k denotes the relaxation time variable and A(T_2,k) denotes the intensity of the T₂ signal at the time T_2,k.

Adaptive decomposition of NMR T₂ distribution components

The adaptive decomposition method of NMR T₂ distribution component is based on the relationship between the signal intensity of NMR T₂ distribution data and the relaxation properties of the different components on a time scale. By fitting the T₂ distributions into multiple independent normal distribution curves, the molecular motion and environmental information of the samples can be revealed. The detailed flow of the decomposition method is shown in Fig. 6.

Fig. 6.

Flow chart of the decomposition method of T₂ distribution.

In general, the T₂ distribution data needs to be pre-processed first. On the one hand, since the data are sourced in different ways, to ensure the universality of the method, the number of points of the T₂ distribution needs to be unified and the data need to be normalized. On the other hand, the raw T₂ distributions obtained by using NMR analyzers are usually affected by noise, artifacts, and other interferences from the instrument, the environment, or other sources. In order to improve the quality and interpretability of the data and conduct subsequent data analysis and interpretation, necessary measures, such as de-noising, outliers, or smoothing, need to be taken. These processing measures help retain and enhance the physically meaningful features of the T₂ distribution. Specifically, noise suppression and smoothing improve the stability of the baseline and reveal weak short-T₂ components that are often obscured in raw data. Outlier removal eliminates spurious spikes generated by the instrument, allowing the true peak shapes to be preserved. Normalization and point-number unification ensure that the amplitudes and peak areas of different samples are comparable, which is essential for subsequent peak decomposition and quantitative interpretation. In addition to the above factors, the original T₂ distribution is also affected by the ILT method itself. All T₂ distributions in this study were obtained from a Niumag low-field NMR analyzer combined with the ILT algorithm inversion. The algorithm introduces the singular value decomposition (SVD) technology to trim and reduce noise on the echo matrix to alleviate the impact of ill-conditioned problems on the inversion results. Although SVD improves numerical stability, ILT is still inherently ill-conditioned and sensitive to input parameters (such as T₂ grid settings, smoothing factors, and noise levels), which can easily lead to problems such as peak shift, over-smoothing of the distribution, or false signals³¹. To this end, based on regional expertise and the characteristic T₂ relaxation behavior of free and bound fluids in crude oil. The following strategies were implemented to ensure accurate and physically meaningful inversion results: (1) the T₂ grid was set from 0.01 to 10,000 ms on a logarithmic scale; (2) all samples were processed with a consistent smoothing parameter and regularization level to maintain comparability; (3) the original echo signal was subjected to exponential windowing and baseline correction to enhance the signal-to-noise ratio; (4) The final inversion results were supplemented by manual review to ensure that all distributions were physically reasonable and fully covered the fluid state.

After that, peak detection is required to locate the peaks in the NMR T₂ distribution. The peak finding is the process of locating and extracting the peaks in the T₂ distribution data, i.e., the peaks of signal intensity corresponds to different T₂ values. In the T₂ distribution, the peaks reflect the decay rates of different spin components, while the positions and intensities of the peaks provide information about the interior of the sample, and peak finding is very crucial for understanding the molecular motions and the environment of crude oil samples³². For the NMR T₂ distributions of impurity-containing viscous crude oil in free-fluid state, this paper adopts the peak finding method at the extreme point. The extreme point peak finding method is usually based on the extreme values (local maxima) in the T₂ distributions data. The location of the peaks is located by finding the points with zero derivatives, and the second-order derivatives are used to determine whether these points are local maxima or not. Assuming that y(t) is the signal intensity in the T₂ distribution data and t is the corresponding T₂ time, the formula is as follows:

4

5

where Eq. (4) indicates that the points in the T₂ distribution data where the derivatives are found to be zero are the extreme points. Equation (5) indicates that in these extreme points. The negative second-order derivatives indicate local maxima.

This is followed by a Gaussian fit of the T₂ component distribution. The Gaussian distribution function is used as the objective function. The initial parameters of the Gaussian peaks (e.g., mean and standard deviation) are estimated by distribution analysis or a priori knowledge. Since the decomposition process inevitably introduces errors, constraints are introduced to ensure more reasonable results. To ensure physical consistency, the total longitudinal amplitude of all Gaussian components should approximately match the amplitude of the original T₂ distribution. This approach more accurately reflects the presence of different porosities in reservoirs while optimizing the shape of component distributions. It facilitates more precise identification of various porosities and fluid types in the subsurface reservoir in a physical sense, allowing the algorithm to adapt to different data scenarios. The constraint equation is expressed as follows:

6

where S_0i is the cumulative sum of the longitudinal signal amplitudes of the ith component distribution and S₀ is the cumulative sum of the longitudinal signal amplitudes of the total distribution.

Finally, the T₂ decomposition distributions are fitted and optimized using a non-negative least squares (NNLS) method to decompose the crude oil T₂ distributions into the contributions of individual components. The specific objective is to minimize the sum of error squares and find the parameters such that the difference between the fitted T₂ signal and the actual measured T₂ signal is minimized. Equation (3) in the previous section has defined the NMR logging crude oil relaxation signal. The objective function of the least squares method for fitting the Gaussian peak is:

7

where Q is the number of data points; T_2,k is the kth time point; A_processed (T_2,k) is the actual measurement at the kth time point; n is the number of Gaussian peaks; A_i is the amplitude of the ith Gaussian peak; T_2,k denotes the relaxation time variable, ms.

In the study, the adaptivity demonstrated by the decomposition method of NMR T₂ distributions is mainly reflected in two key aspects. Firstly, the peaks in the T₂ distribution are located by using the peak-finding method with extreme points, which indicates that this method can accurately reflect the different components present in the crude oil. It can also effectively capture the information of the porosity of the crude oil reservoir, providing a more detailed analysis of the characteristics of the geological reservoir. Secondly, a constraint is introduced, i.e., the sum of the longitudinal amplitudes of all points in the control distribution is approximately equal to the sum of the longitudinal amplitudes of all points in the total distribution. This principle corresponds to the importance of equal porosity in oil reservoirs. This is because the sum of the longitudinal amplitudes of all points of the NMR T₂ distribution reflects information about the pore structure in a rock or other sample³³. Specifically, the sum of the longitudinal amplitudes of all points can be interpreted as the total bulk of pores at various scales in the sample. The method effectively delineates the relative contributions between components so that the sum matches the sum of the longitudinal amplitudes of all points of the original distribution.

NMR T₂ distribution decomposition and fitting

In the decomposed T₂ spectra obtained by the proposed fast Gaussian picking method, each fitted Gaussian component corresponds to a relaxation population with distinct mobility characteristics. Impurity-related components are characterized by short relaxation times and relatively small amplitudes, reflecting restricted molecular motion and enhanced surface relaxation caused by the presence of solid phases. Based on previous NMR studies^34,35 and our laboratory observations, peaks with T₂ values below approximately 50 ms can be attributed to solid-associated or semi-solid phases, whereas peaks between 50 and 500 ms mainly represent colloidal or partially confined fluid. The long-T₂ components (> 500 ms) correspond to the free-fluid phase of crude oil. Although these boundaries may vary slightly with temperature and oil composition, they provide a reproducible criterion for identifying impurity-related relaxation components in viscous crude oils. The three distributions of T₂ in Fig. 7 conform to the above-described characteristics respectively.

Fig. 7.

T₂ distribution component decomposition effect and comparison.

A T₂ distribution of a crude oil sample, plotted using 200 data points is shown in Fig. 7. Three peaks are identified using the extreme value peak-finding method. Table 3 presents the peak detection information of the NMR T₂ distribution of the crude oil sample, compared with the transverse relaxation time of the peaks after fitting and optimization. The positions and widths of the three peaks were input into a normal distribution function as initial parameters. These are then fitted and optimized using the NNLS algorithm, resulting in the three component distributions (corresponding to component distributions 1 to 3 in Fig. 7). Comparing the original T₂ distribution with the fitted T₂ distribution shows that the two distribution lines overlap well. This indicates that the fitting optimization algorithm can accurately approximate the actual T₂ distribution data. Furthermore, the fitting parameters effectively describe the contributions of various T₂ components in the sample.

Table 3.

Comparison of lateral relaxation times of the original and fitted peaks of the NMR T₂ distribution of a crude oil sample.

Peak number	Raw measured transverse relaxation time (ms)	Fitting optimization transverse relaxation time (ms)	Relative error	Evolution
1	1.503	1.498	0.333%	Slightly reduced
2	29.387	29.380	0.024%	Slightly reduced
3	383.411	384.837	0.372%	Slightly increased

From the previous section, combined with the theory of NMR logging, it can be known that the sum of the longitudinal amplitudes of all points in the NMR T₂ distribution can be interpreted as the total bulk of pores of various scales in the sample. By numerical calculation, the cumulative sum of the longitudinal amplitudes of all points of the original and the fitted T₂ distributions of this crude oil sample is almost equal (shown in Table 4). The cumulative sum of the longitudinal amplitudes at all points of the component distributions of components 1–3 and their ratio to the cumulative sum of the longitudinal amplitudes at all points of the original NMR T₂ distribution are calculated. As can be seen from Table 3, the sum of the longitudinal amplitudes of all points of the three component distributions is almost equal to the sum of the longitudinal amplitudes of all points of the fitted T₂ distribution. The ratio of the sum of the longitudinal amplitudes of all points of the three component distributions to the sum of the longitudinal amplitudes of all points of the original T₂ distribution reaches 99.12%, which is a very good fit as well. Therefore, the T₂ component distributions reasonably decompose the total pore information of the crude oil samples, and also completely tabulate the original T₂ distributions information.

Table 4.

The cumulative comparison of the longitudinal amplitude of the data points of the original and fitted NMR T₂ distributions.

Distribution name	The sum of the longitudinal amplitudes of all points	Component distribution name	The sum of the longitudinal amplitudes of all points in the component distribution	Serving size (%)	The sum of the longitudinal amplitudes of all points in the component distribution	Degree of fit
		Component distribution 1	8058.458	69.16
Original NMR T2 distribution	11652.667	Component distribution 2	1971.435	16.92	11550.139	99.12%
		Component distribution 3	1520.246	13.05
NMR T2 fitting distribution	11550.138					99.99%

Application and results

Experimental data test

Many studies have confirmed the strong positive correlation between transverse relaxation time and rock porosity^36,37. When analyzing rock porosity and pore structure, the fast Gaussian picking method can be used as a means of analysis. In order to verify the practical application of the method in this paper, several rock samples from the Weizhou Formation section in the thick oil region in the western part of the South China Sea are selected for the white oil-driven formation water experiments. This experiment used this method to analyze the saturated white oil T₂ distributions of formation water displaced by white oil in different rock samples. The corresponding characteristic of T₂ distributions can be obtained by using the fast Gaussian picking method. In this study, to distinguish the pore information depicted by different component distributions, the pores represented by the component distributions from short relaxation time to long relaxation time are referred to as small, medium and large pores, respectively²¹.

Before the experiment, the rock samples were first pretreated, including the removal of impurities, drying and other operations. Then, the samples were placed in the NMR analyzers and scanned and acquired by setting the corresponding parameters. Using the adaptive decomposition method of NMR T₂ distribution components. The T₂ distribution decomposition diagrams of the three rock samples in the white oil-excavated formation water to the saturated white oil state can be obtained (Fig. 8). These diagrams illustrated rock samples dominated by different pore structures.

Fig. 8.

T₂ distribution decomposition results (a. Saturated white oil T₂ distribution of rock sample No. 1; b. Saturated white oil T₂ distribution of rock sample No. 2; c. Saturated white oil T₂ distribution of rock sample No. 3).

Figure 8a shows the predominance of small pores in the rock samples. The T₂ distribution decomposition plots show a clear predominance of short T₂ components, suggesting that the flow of white oil in the small pores is restricted and that water is more effective in draining the smaller pores relative to the white oil. The T₂ distributions are mainly concentrated in shorter time ranges, indicating a higher number of small pores in the samples. This may imply that the rocks have high porosity but relatively small pore sizes, leading to challenges in crude oil recovery and requiring more refined reservoir development strategies.

Figure 8b illustrates the predominance of large pores. Compared to Fig. 8a, the large pore-dominated rock samples show a significant increase in the long T₂ component of the T₂ distribution. This suggests that white oil flows more freely in the larger pores and that water drainage is relatively weak in these large pores. The samples contain more large pores and relatively fewer small pores, indicating that the rock is less porous but has larger pores. This scenario may provide better conditions for oil recovery, but the distribution and flow characteristics of the crude oil in the larger pores also need to be considered.

Figure 8c depicts a situation where both large and small pores are present, with a slight predominance of large pores. The T₂ distribution decomposition plot shows a wider range of peaks, including signal intensities from both medium and large pores. Compared to the previous two plots, this plot has a relatively large number of long T₂ components corresponding to large pores and short T₂ components corresponding to small and medium pores, indicating a relatively large number of large pores in the sample. This suggests that white oil exhibits distributional differences in different pore sizes. The effect of multi-scale pore structure on reservoir recovery needs to be comprehensively considered.

Field application

To verify the feasibility of the proposed method, it is applied to an oil well A in an oil field in the western study area of the South China Sea. Well A is located in the eastern part of the field and the reservoir is mainly composed of alternating layers of water-wet sandstone and shale interbedded with good reservoir properties. The logging instrument was lowered into the well after calibration. At each measurement depth, the T₂ relaxation time can be obtained.

The following figure illustrates the results of the integrated interpretation processing of depth logging for well A (Fig. 9). Data were obtained using Baker Hughes’ Drill-Following Logging Series tool. In the first track of Fig. 9, the curves shown are CAL (caliper), DCAV (Dual Caliper and Voltage) and GR (Gamma Ray), which are all very helpful in displaying stratigraphic properties. The second track is depth, and its unit is meter. The third track displays various resistivity measurements (P40H, A40H, P34H, P28H, P22H, P16H) of propagation resistivity instrument, which help to identify fluid types and stratigraphic boundaries. The fourth track displays TNPH (Total Neutron Porosity) and ROBB (Resistivity Oil-Based Mud Borehole Corrected), which are primarily used to help assess the pore structure and electrical properties of a rock or sediment. The fifth track shows a number of gas profiles, such as CO2, NC4, etc., which indicate the type of gas present in the formation and its relative content, as well as the changes of porosity, permeability, and fluid saturation of the formation. The sixth track shows the interpreted lithology, including oil zones, sand layers, shale layers and porosities. The NMR T₂ distribution obtained using the Baker Hughes MagTrak LWD tool is shown in the seventh track. The eighth track displays the interpretation conclusions, showing the overall conclusions drawn from the well log data. It can be seen that the strata at different depths in Well A exhibit different lithology and fluid properties. The dark green blocks represent the oil layer, the brown blocks represent the dry layer, and the blue slightly embedded green blocks represent the oil-water-bearing layer. In order to analyze the fluid properties of these strata in more detail, we selected three depth points for T₂ distribution feature analysis.

Fig. 9.

Comprehensive logging interpretation of well A and the decomposition distributions at depth of 3318.6 m (a), 3363.4 m (b) and 3365.3 m (c).

At depth of 3318.6 m, the NMR T₂ decomposition distribution is shown in Fig. 9a. The T₂ distribution at this depth point is calculated by the fast Gaussian picking method, which results in the presence of three peaks located at about 1100 ms, 2100 ms, and 2600 ms, respectively. The distribution of the overall T₂ distribution shows that the distribution of the T₂ peaks at this depth point is relatively broad and the spacing between the decomposition distributions is large. This indicates that the crude oil in this layer section contains more impurities and the fluid properties are more complicated. The Component distribution 1 is between 0.3-1700ms, and the peak is broad and relatively flat, indicating that this component corresponds to a fluid with high viscosity, probably heavy crude oil or asphaltene with a lot of impurities. Due to its shorter relaxation time and broader peak, it indicates that the molecular motion is more restricted. This may be due to the presence of impurities that increase the viscosity of the fluid, causing the intermolecular interactions to increase and the relaxation process to slow down. Such peaks are usually found in crude oils that contain more suspended solids or high viscosity components. And the Component distribution 2 is in the range of 1700-2300ms, and the peak is relatively narrow and symmetric, which indicates that this component corresponds to a moderate fluid viscosity and may be a clean light crude oil. The long relaxation time and narrow peak indicate relatively free molecular motion and low impurity content. This situation usually occurs when the fluid is relatively pure and the intermolecular interactions are weak. Component distribution 3 between 2200-2700ms, and the peak has a long relaxation time, indicating that this component corresponds to a fluid with very low viscosity, probably a gas or a light oil with low viscosity. The longest relaxation time indicates that the molecules are moving very freely and are essentially unbound. This may be due to the large amount of gas or low-viscosity fluid in this component, which makes the relaxation process fast and free.

At the depth of 3363.4 m, the NMR T₂ decomposition distribution is shown in Fig. 9b. The distribution of T₂ peaks at this depth point is concentrated and to the right, indicating that the T₂ relaxation time of the free fluid is longer, representing higher oil content and cleaner oil. From the decomposition distribution, the main peaks are concentrated between 1500-2600ms, indicating that the free oil phase dominates. This situation usually indicates that the pore structure of the rock at this depth is large and well-connected, which is favorable for the existence and flow of light oil. In addition, there exists a smaller and narrower decomposition distribution between 2300 and 2700 ms with a short and sharply increasing relaxation time. This component distribution indicates that this peak corresponds mainly to light oil or free fluid. Light oils are more mobile, resulting in longer T₂ relaxation times and higher signal amplitudes. Overall, the crude oil at this depth has a low impurity content and a good free-fluid condition. In addition, there is almost no short T₂ component in the decomposition distribution, which further indicates that the water content in this layer is extremely low. This may be because the rock pore structure in this layer is not conducive to water retention, or the formation temperature at this depth is high, causing water to evaporate or lose.

At depth of 3365.3 m, the NMR T₂ decomposition distribution is shown in Fig. 9c. The T₂ distribution at this depth point is calculated by the fast Gaussian picking method to yield the presence of three distribution peaks located at about 1500 ms, 2000 ms, and 2400 ms, respectively. One of the component distributions 1 is in the range of 900–2300 ms, which indicates that the molecular motion is more restricted due to its shorter relaxation time and broader peaks. This may be due to the presence of impurities that increase the viscosity of the fluid, making the intermolecular interactions enhanced and the relaxation process slower. Component distribution 2 between 1500-2700ms, and the peak relaxation time is moderate and the peak is broader, indicating that the molecular motion is relatively free, but there are still certain impurities. This situation usually occurs when the fluid viscosity is moderate and contains a small amount of impurities. It indicates that this component corresponds to a medium fluid viscosity, probably a medium viscosity crude oil. Component 3 between 2300 and 2700 ms, and the peak rises sharply and has a long relaxation time, indicating that the molecules are moving very freely and are essentially unbound. This may be due to the large amount of gas or low-viscosity liquid in this component, which makes the relaxation process fast and free. It suggests that the fluid corresponding to this component has a very low viscosity, which may be a gas or a low-viscosity light oil.

Discussions

This study measures and analyzes the NMR T₂ distributions of viscous oil samples from a reservoir in the western South China Sea, revealing a multi-peak broad-spectrum distribution. Detailed analysis of the physical and chemical properties of crude oil samples confirms that solid impurities (e.g., wax, asphaltenes, colloid) play a crucial role in distribution broadening and multi-peak phenomena. These impurities not only alters the rheological properties of the crude oil, but also introduces additional relaxation components in the NMR signal. The solid-liquid mixed phases result in significantly larger differences in relaxation times, which in turn led to the complication of the T₂ distributions.

The fast Gaussian picking method based on Gaussian distribution function proposed in this paper can effectively decompose complex NMR T₂ distribution lines and obtain the T₂ distribution response feature information in a shorter time through the extreme point search and NNLS method fitting. To ensure the physical significance and reliability of Gaussian peak decomposition in the NMR T₂ distribution, constraints are introduced during the process. Specifically, to ensure physical consistency, the total longitudinal amplitude of all gaussian components should approximately match the amplitude of the original T₂ distribution. This approach effectively prevents overfitting during the decomposition process, ensures the stability and reliability of the results, and enhances the analysis of fluid properties in impurity-laden viscous crude oil. The resolution of the fluid properties of each component in impurity-containing viscous crude oil is improved. In the specific decomposition process, the NNLS method was used to optimize the parameters of the Gaussian peak. The constraints on the Gaussian peak decomposition results are further strengthened to ensure that the T₂ distributions of each component have clear physical meaning and negative values are avoided. The experimental results show that the method can quickly and accurately identify multiple T₂ component distributions representing different phase compositions and different viscosity fluids. In particular, the method demonstrates superior adaptability and stability when treating thick oil samples with high solid-phase impurities such as waxes, asphaltenes and gums.

All NMR T₂ distributions in this study were obtained by the ILT method based on SVD clipping implemented within the low-field NMR analyzer. ILT is a classical but ill-posed inverse problem. It is highly sensitive to parameter settings such as the T₂ grid, smoothing level, and regularization method. These parameters directly affect the reconstructed peak shape, number, and shoulder structure in the T₂ distribution, thereby indirectly influencing the accuracy of the subsequent peak recognition algorithm. Although SVD clipping enhances the numerical stability and suppresses noise, excessive smoothing or peak fusion may still occur in samples with low signal-to-noise ratios or closely spaced relaxation components, particularly in cases where the boundary between free and bound fluids is indistinct. Additionally, due to the exponential nature of CPMG decay, short-T₂ components decay rapidly and are more susceptible to noise amplification during inversion. When a uniform regularization strength is applied across the T₂ domain, this can lead to disproportionate smoothing in the low-T₂ region, causing sharp peaks to appear broadened or merged, while long-T₂ peaks remain relatively intact. This introduces a positional bias in peak width interpretation, especially for fast-relaxing fluid components. To mitigate these situations, we combined regional information to ensure consistent inversion settings and conducted manual inspection of distribution features to detect signs of over-smoothing.

Compared with conventional decomposition approaches such as the continuous wavelet transform (CWT) and asymmetric Gaussian fitting, the proposed fast Gaussian picking method introduces a combination of physical and mathematical constraints. It integrates extremum-point detection to automatically identify potential peak positions with NNLS optimization under amplitude-conservation constraints. Although the relative content of crude oil components can in principle be estimated by manually selecting the peaks in overlapping T₂ distributions, such manual processing is highly subjective and sensitive to operator experience, especially when the spectra contain overlapping peaks or significant noise. The proposed method adds value by introducing an automated and physically constrained fitting framework. This method minimizes human bias, improves reproducibility, and achieves more stable fitting performance for multi-peak spectra. This design differs fundamentally from wavelet- or LM-based methods that rely on subjective parameter selection and iterative fitting from user-defined initial values. The proposed approach achieves a high level of automation by eliminating manual peak identification, while also offering faster computation that makes it suitable for processing large datasets or for real-time logging interpretation. Moreover, the amplitude-conservation constraint ensures stable and reproducible decomposition results, reducing dependence on empirical parameter tuning. These characteristics make the method particularly effective for analyzing viscous crude oils whose T₂ spectra exhibit smooth and symmetric distributions representing free-fluid relaxation components. It is important to note that while the proposed method performs well on T₂ distributions with distinct or moderately overlapping symmetric peaks. Its performance becomes less robust when applied to distributions with strong asymmetry or shoulder features. For instance, as shown in Fig. 9a, the T₂ distribution of a viscous crude oil sample exhibits a broad main peak accompanied by a left shoulder, which may correspond to a mixture of large molecular components such as asphaltenes and colloids. This kind of distribution shape, commonly observed in heavy oils, is not optimally captured by the current method due to the inherent symmetry of Gaussian basis functions. In such cases, other alternative distributions such as log-normal or Chi-squared functions may offer better fitting accuracy and physical interpretability. While this study focuses on establishing a rapid and generalizable peak-picking framework, we acknowledge that future work could expand the method to incorporate asymmetric basis functions or adaptively adjust model selection based on distribution morphology. Moreover, complementary measurements such as T₁-T₂ correlation or 2D NMR logging may offer more comprehensive insight into fluid characterization under these challenging conditions. Such improvements would enhance the method’s applicability to a broader range of complex fluid systems.

The pore-size distribution (PSD) and rock wettability can significantly affect the NMR T₂ responses by altering the surface relaxation behavior of fluids within the pore space. In general, smaller pores provide larger surface-to-volume ratios, resulting in enhanced surface relaxation and a shift of the T₂ spectrum toward shorter relaxation times. Similarly, rock wettability determines which phase dominates the surface relaxation process: in water-wet rocks, oil primarily resides in the pore centers and exhibits longer T₂ values, whereas in oil-wet systems, part of the oil phase is adsorbed on the rock surface, producing shorter T₂ components that overlap with impurity-related T₂ components. In this study, the tested sandstone samples from the Weizhou and Liushagang Formation are characterized by moderate porosity (average 18.58%) and a predominantly water-wet surface, as reported in previous core analyses from the same field. Therefore, the effect of wettability on the measured T₂ distributions is relatively minor compared with the influence of viscosity and free-fluid behavior. The observed variations in the T₂ spectra are thus primarily attributed to the intrinsic properties of the viscous crude oils rather than differences in pore structure or surface affinity. It is also worth noting that the proposed fast Gaussian picking method is a mathematical decomposition approach that does not rely on prior knowledge of rock wettability. The algorithm can be applied to any NMR T₂ distribution to identify distinct relaxation components, even when the wettability of the rock is unknown. In such cases, the method remains effective for separating overlapping peaks; however, the physical interpretation of short-T₂ components should be made with caution, as they may originate either from solid-phase impurities within the crude oil or from enhanced surface relaxation associated with oil-rock interactions. This ambiguity can be reduced by integrating the decomposed spectra with auxiliary data such as saturation information, core-flooding experiments, or temperature-dependent measurements, which help differentiate impurity-induced effects from wettability-related ones. Therefore, while the algorithm itself is generally applicable, its interpretive accuracy can be further improved when wettability information becomes available.

To ensure the reliability and comparability of the data, it is recommended that the samples be standardized prior to the experiment to ensure relatively consistent measurement conditions for each sample. At the same time, the properties of viscous crude oil containing impurities are greatly affected by temperature. The temperature and pressure of the sample should be strictly controlled to maintain the characteristics of the crude oil in its natural state, thereby avoiding errors caused by changes in environmental conditions. Besides, experimental results may be affected by the noise level of the NMR signal. For samples with low signal-to-noise ratios, further signal processing or consideration of other noise suppression techniques may be required to improve data quality.

In crude oils containing solid-phase impurities such as waxes, asphaltenes, and gums, the effect of the presence of solid-liquid mixed phases on the T₂ distributions is mainly physical in nature, with the solid-phase impurities acting as molecular-motion restrictors in liquid crude oils, leading to a shortening of the T₂ relaxation time. The measurement and processing of NMR T₂ distributions in this study primarily involve physical processes, such as molecular motion and spin interactions, without involving chemical reactions. The experiments are conducted at ground temperature conditions to ensure that the samples are in a free-fluid state. This control only affects the physical state and ignores chemical changes. The fast Gaussian picking method is also based on physical signal processing techniques, which also primarily relying on physical processes.

Conclusions

In this study, we address the challenge of analyzing the NMR T₂ distribution of impurity-containing viscous crude oil in the free-fluid state from a reservoir in the western South China Sea by proposing a fast Gaussian picking method based on the Gaussian distribution function, combined with the NNLS method to decompose the T₂ distribution. The following key conclusions were drawn through experimental verification and practical application: (1) The fast Gaussian picking method can effectively identify and pick up representative peaks in the NMR T₂ distribution of thick oil-like crude oil. Compared to traditional methods, it offers significant advantages in processing time and accuracy, significantly simplifying the analysis of complex multi-peak T₂ distributions. After mathematical-physical tests and field applications, the method is verified to have high robustness and applicability, as it can distinguish between different phase compositions and fluid characteristics of varying viscosities in crude oil. (2) Analysis of T₂ component distributions from three different solid-liquid mixed-phase crude oil groups in the Weizhou Formation of the thick oil region in the western South China Sea, under saturated white oil conditions, shows that this method quickly and accurately characterizes different fluid components within pores and provides information on different pore scales in stratigraphic rocks. Through the application of actual well data from the western part of the South China Sea, multiple broader NMR T₂ distribution peaks are observed, which correspond to oil phases of different viscosities or mixed oil phases. This method decomposes complex T₂ distribution signals into simple Gaussian peaks, facilitating a better understanding of fluid properties in the formation. The analysis indicates that the peaks of the T₂ distributions of the free-fluid state are primarily concentrated in the high relaxation time region. This aligns with the more active molecular motion and longer relaxation time of the free fluid. In viscous crude oils, the relaxation characteristics of NMRT₂ distributions are significantly influenced by impurities and high viscosity. The distribution and amplitude of component distributions reflect the physical properties of fluids with varying phase compositions and viscosities. (3) Due to regional variations in rock samples and crude oil compositions, it is necessary to calibrate the upper and lower limits of the oil-bearing characteristic distributions of impurity-containing viscous crude oil reservoirs through petrophysical experiments, and to determine the specific basis for division, so as to facilitate the smooth evaluation of reservoir free fluids. (4) While the proposed method shows reliable performance for typical NMR T₂ distributions, its recognition accuracy is still influenced by the quality and stability of the ILT inversion. Moreover, in cases where the T₂ distribution exhibits significant asymmetry or shoulder structures—such as those associated with asphaltene-rich heavy oils—the use of symmetric Gaussian basis functions may limit the fitting performance. Future work may consider the other incorporation of asymmetric basis functions to improve robustness across a wider range of fluid systems.

Author contributions

Xinyi Zhang: Conceptualization, Methodology, Data curation, Visualization, Writing-original draft. Zhen Qin: Validation, Project administration, Writing—review & editing. Xue Zhang: Data collection and interpretation, Investigation. Shaocheng Luo: Investigation. Ke Huang: Investigation. Xu Dong: Investigation. Yicong Huang: Data curation. Kangjian Wei: Investigation.

Funding

This research was funded by the National Natural Science Foundation of China (Nos. 42364009 and 41804097), the Open Fund (SMIL-2020-05) of Hubei Subsurface Multi-scale Imaging Key Laboratory (China University of Geosciences), the Jiangxi University Student Innovation Training Program (S202410405021), the Cooperative Education Project of the Ministry of Education (230804213220658), the Supply-demand Docking Employment and Education Project of the Ministry of Education (2023122674433), the Jiangxi Natural Science Foundation of Province (20224BAB203044), the Research Topic of Teaching Reform of the East China University of Technology (DHJG-24-14), the Graduate Workstation Construction Project of the East China University of Technology (2022-02), the Practical Teaching Construction Project of the East China University of Technology (DHSY-202503) and the Doctoral Research Initiation Fund Project (DHBK2017109) of the East China University of Technology.

Data availability

The data used to support the findings of this study have not been made available because the data also forms part of an ongoing study. However, the corresponding authors may provide access upon justified request.

Declarations

Competing interests

The authors declare no competing interests.