T2 Distribution Research Articles

An improved model assessing variation characteristics of pore structure of sandy soil thawing from extremely low temperature using NMR technique

During the construction of subway connecting passages in major cities in China, in last decades the artificial freezing method has gradually been becoming one of the most safe and effective methods in excavating saturated sandy soils. This work aims at exploring the changes of pore size and relaxation time induced by temperature change using NMR technology. Sandy soil samples were retrieved from a subway construction site in Beijing. In the laboratory experiments, these samples were loaded by different extremely low temperatures and natural convection thawing. The T2 (i.e., relaxation time) distribution curves and real-time temperature throughout the thawing process were recorded. It was observed that the variation of T2 distribution curves and pore structure changes with temperature may be divided into four stages, i.e., Stage I: spherical and cylindrical pores with radius r = 0.3 nm are formed at temperature lower than −28.0 °C; Stage II: the water adsorbed in pores melts and pore radius increases to the range of 0.3 nm < r < 32.0 nm as temperature increases in the range of −28.0 °C ∼ -0.2 °C; Stage III: capillary water in the pores with radius >32.0 nm melts rapidly as temperature increases in the range of −0.2 °C ∼ 0.7 °C; Stage IV: small amount of pores transform from small-sized absorptive pores and large-sized capillary pores to medium-sized absorptive pores as temperature increases to above 0.7 °C°. The specific threshold temperature and the threshold relaxation time are found as −0.2 °C and 5.17 ms respectively. By quantitatively analyzing the incremental change of T2 distribution curves and the rising temperature, an improved Gibbs-Thomson equation and a Two-Staged model of T2LM-Tmel (the geometric mean of relaxation time - the absolute value of temperature) and T2-Tmel (relaxation time - the absolute value of temperature), which are applicable to NMR technology, were proposed. Based on these results, a new pore structure evolution model of frozen sandy soil thawing from extremely-low temperature was proposed.

Study on fine characterization and reconstruction modeling of porous media based on spatially-resolved nuclear magnetic resonance technology

Abstract At present, image analysis and digital core are the main approaches for porous media reconstruction modeling, and they are both based on the real pore skeleton physical structure of porous media. However, it is difficult to reconstruct the reservoir and seepage characteristics of the real samples because of the limitations of accuracy in characterization techniques (imaging). In order to solve this problem and break through the barriers caused by the lack of accuracy, Spin-echo serial peripheral interface sequence of low field nuclear magnetic resonance is used to test the saturated water rock core with spatially resolved T2 distributions. Based on the experimental results of 1D T2 distributions, a novel method for fine reconstruction modeling of porous media is proposed, and the porous media model reconstructed by this new method better reproduces the reservoir and seepage characteristics of the original samples. Taking some of the tested porous media cores (P58 and Y75) as examples, representative elementary volume (REV)-lattice Boltzmann method (LBM) is used to simulate the flow field. Ensuring that the error of standard case is only 0.36% when multi-relaxation time REV-LBM is used, the distribution of porosity and permeability have been calculated and compared with the experimental data. The overall permeability error of the reconstructed porous media model is only 6.15 and 7.60%, respectively. Furthermore, the porosity and permeability error of almost all measuring points can be maintained within 3 and 8%. In addition, this method improves the efficiency of the existing reconstruction modeling methods, reduces the test cost, and makes the reconstruction modeling of porous media easier to operate, which has promising development prospects.

Quantitative Investigation on Natural Gas Flooding Characteristics in Tight Oil Cores after Fracturing Based on Nuclear Magnetic Resonance Technique

SummaryTight reservoirs are mainly developed by injecting various gases after fracturing. However, the formed fractures are complex, and different fracture conditions have an important impact on the gas injection effect. In addition, natural gas is considered to be suitable for the development of tight reservoirs in China because of the abundant gas source and no corrosion. For this paper, the natural gas injection experiments were studied by combining mercury intrusion porosimetry (MIP) measurements and nuclear magnetic resonance (NMR) measurements. The method can be used to study the distribution characteristics of core pore structure and the recovery characteristics of oil in different pore spaces.In this work, the tight cores of the Changqing Oil Field were selected for fracturing for the natural gas flooding experiments. At first, the distribution characteristics of the core pore structure were studied based on the MIP and NMR measurements. The conversion relationship between the core pore throat radius and the relaxation time (T2) was decided. The NMR T2 distribution was transformed into the distribution of oil in pore space with different throat radii. Then, the gasflooding experiments were conducted to study the oil recovery law of tight cores with different fracture conditions. Finally, the recovery characteristics of oil in different pore spaces were analyzed based on the NMR results of cores.The results show that the pore throat radius of the core is mainly distributed in the range of 0.001 to 10 μm. The oil is mainly stored in the pore space whose pore throat radius ranges from 0.01 to 1 μm. The natural gas also mainly drives the saturated oil in the pore space with a pore throat radius of 0.01 to 1 μm. The increase in fracture area improves the distribution of oil in the larger pore space. In the process of natural gasflooding, with the increase of gas injection, the oil began to be recovered, and then gas was observed at the end of the core. With the continuous injection of natural gas, the rate of recovering oil gradually slowed down, and finally gas breakthrough occurred. The displacement oil process of the nonfractured core was uniform and slow. However, the oil and gas rapidly flowed along the fracture when the natural gas displaced the oil in the fractured core. The oil in the matrix was poorly recovered. Gasflooding mainly recovered the saturated oil in the matrix of nonfractured cores and the saturated oil in the fracture of fractured cores. As the fracture length increased, the oil recovery became lower and the gas breakthrough occurred earlier. The higher fracture density increased the fracture area, which also increased the oil recovery and caused a more intense gas breakthrough.In this paper, the displacement law of tight oil cores by injecting natural gas and the recovery characteristics of oil in different space pores were illuminated. The results can provide theoretical guidance for the formulation of the natural gas injection development plan in tight reservoirs.

Sorption Characteristic of Thermally Modified Wood at Varying Relative Humidity

Thermal modification (TM) is commonly used for improving the performance of wood under varying environmental conditions. The effect of TM on the hygroscopic properties of wood has been studied extensively; however, the sorption mechanism and the states of water of thermally modified wood (TMW) at varying relative humidity (RH) is limited. In this work, Douglas fir was modified at 180 °C, 200 °C and 220 °C for a duration of 2 h and the Hailwood–Horrobin model and NMR relaxometry were used after specimens were conditioned at eight different RHs. The results showed that TM inhibited monolayer and polylayer moisture sorption with increasing modification temperatures in all RHs. The lower slope of the sorption isotherms in TMW decreased compared with the control, indicating that the TM increased the hygroscopical stability of wood. The T2 distribution indicated that no free water was observed in the hygroscopic moisture range. The mobility of water molecules in the cell walls was decreased by TM intensity and increased by increasing RH.

Experimental Study on the Impact of Clay Distribution and Mineralogy on NMR T2 and Internal Gradient: Insights From Well-Controlled Physical Samples

Summary Nuclear magnetic resonance (NMR) is a reliable tool for petrophysical evaluation and the characterization of pore structures. Compared to conventional carbonate reservoirs, sandstone reservoirs contain higher amounts of ferromagnetic and paramagnetic ions (such as iron, nickel, or manganese) usually found in microporous clay aggregates. The interpretation of petrophysical data in sandstone formations can be complicated by variations in clay mineralogy and distribution patterns (laminated, structural, and dispersed). Nevertheless, the impact of clay distribution patterns on NMR signals is not well understood. This study aims to investigate the impact of clay mineralogy and distribution patterns on the T2 relaxation times and internal gradient (i.e., inhomogeneity in the magnetic field). Glass beads were mixed with three different clay minerals characterized by no iron content (kaolinite) to higher iron content (illite and nontronite). The bead-clay mixtures were prepared at a fixed clay content but with variable clay distribution patterns to examine the impact of clay distribution alone. NMR T2 measurements at several echo times were performed on the pure glass beads and the mixtures to evaluate how clay mineralogy and distribution patterns affect the T2 and the internal gradient of the host glass beads. At a given clay distribution pattern, a more significant decrease in T2 relaxation times and a larger increase in the internal gradient of glass beads were observed when adding clays with higher iron content. This is explained by the higher surface relaxivity, and magnetic susceptibility caused when introducing clay with higher iron content. Such an impact can complicate the characterization of NMR-derived pore sizes as similar pore size distribution (PSD) can have very different T2 distribution and the logarithmic mean of T2 relaxation time distribution (T2LM) values. Micro-computed tomography (µCT) images were acquired to compute the PSD to compare it with ones obtained from the NMR measurements. The PSD for the three clay minerals showed almost the same distribution using µCT; however, they showed totally different T2 relaxation times distributions. That is due to the significant impact of the internal gradient causing a distortion in the magnetic field. Thus, careful consideration must be taken before converting the NMR data into PSD. The introduction of iron-free kaolinite resulted in a negligible impact on the internal gradient of glass beads regardless of the clay distribution pattern. On the other hand, the addition of dispersed iron-rich clays (illite and nontronite) results in up to two orders of magnitude increase in internal gradients, compared to mixtures with laminated and structural clays (at the same clay mineralogy and content). Moreover, dispersed clay mixtures display larger changes in T2LM and porosity as a function of increasing echo time. The results from this study suggest that changes in T2LM and the logarithmic mean of the effective internal gradient distribution geff,LM, compared to the clean host sand, can provide insight into iron-rich clay distribution. Larger changes in any given clay content and mineralogy would suggest a more dominant dispersed clay distribution while negligible changes would suggest a laminated distribution.

Classification of Tight Sandstone Reservoirs Based on the Nuclear Magnetic Resonance T2 Distribution: A Case Study on the Shaximiao Formation in Central Sichuan, China

The classification of tight sandstone reservoirs is of significance for hydrocarbon exploration and production. Different from conventional reservoirs, tight sandstone reservoirs are characterized by a complex pore structure and strong heterogeneity. Tight sandstone reservoir classification may not be reliable with conventional reservoir classification methods. In this paper, a classification method of tight sandstone reservoirs was proposed on the basis of the nuclear magnetic resonance (NMR) transverse relaxation (T2) distribution, and it was employed for reservoir classification on the Shaximiao Formation in central Sichuan, China. As a result of the complex pore structure of a tight sandstone reservoir, the NMR T2 distribution is characterized by the presence of multiple peaks. Therefore, the three-peak Gaussian function was used to fit the T2 distribution and obtain the characteristic parameters. On the basis of high-pressure mercury intrusion (HPMI) experiments, the correlation between the characteristic parameters of the NMR T2 distribution and pore structure parameters and petrophysical properties was analyzed, and then the optimal characteristic parameters of the NMR T2 distribution were selected according to the results of correlation analysis and used to establish the pore structure index. In combination of petrophysical properties with the pore structure index, the model for classification of tight sandstone reservoirs was established by the naive Bayesian method based on hierarchical clustering, and the accuracy of the model was verified by k-fold cross-validation. Finally, the effectiveness of the proposed method was verified using the actual NMR logging data in conjunction with the oil test data. The results showed that the method for classification of tight sandstone reservoirs based on the NMR T2 distribution can provide effective guidance for production capacity evaluation.

Fractal-based NMR permeability estimation in tight sandstone: A case study of the Jurassic rocks in the Sichuan Basin, China

Permeability is a crucial parameter evaluating tight sandstone reservoir. Previous permeability estimation methods based on nuclear magnetic resonance (NMR) are commonly suitable for well-sorted, highly porous and unconsolidated sandstone, but incurring large errors when applied to tight sandstone. This study introduces the fractal dimension based NMR permeability estimation for tight sandstone. Core permeability and NMR measurements were performed on thirty tight sandstone samples selected from the Jurassic rocks in the Sichuan Basin, China. We proposed two fractal-based NMR permeability models for tight sandstone in the studying area, which are considered as the modifications of the SDR and T-C models, examining the applications on core plug samples and comparing the results with other permeability models. Results show that tight sandstones have wider T2 distribution and weaker correlation between throat size and pore size than unconsolidated/clean sandstones. The proposed coefficient-based optimal fitting method can obtain more accurate fractal dimensions of micropores and macropores than these achieved by subjective and empirical methods and commonly used T2cutoff method. The proposed models introduced in this research have two advantages: (1) the models have high accuracy since the effective pore structure parameters (porosity, FFI/BVI and T2LM) are adopted. The complex pore structure of tight sandstones is considered by using fractal dimensions. (2) the models are easy to implement by following the concise formats of the Timur-Coates model and SDR model. In practice, the models can be applied to predict permeability of tight sandstone in the lab, or in the field requiring NMR T2 distributions as basic data, integrating core permeability to determine fitting parameters in the models.

Application of XGBoost model for in-situ water saturation determination in Canadian oil-sands by LF-NMR and density data

Water saturation determination is among the most challenging tasks in petrophysical well-logging, which directly impacts the decision-making process in hydrocarbon exploration and production. Low-field nuclear magnetic resonance (LF-NMR) measurements can provide reliable evaluation. However, quantification of oil and water volumes is problematic when their NMR signals are not distinct. To overcome this, we developed two machine learning frameworks for predicting relative water content in oil-sand samples using LF-NMR spin–spin (T2) relaxation and bulk density data to derive a model based on Extreme Gradient Boosting. The first one facilitates feature engineering based on empirical knowledge from the T2 relaxation distribution analysis domain and mutual information feature extraction technique, while the second model considers whole samples’ NMR T2-relaxation distribution. The NMR T2 distributions were obtained for 82 Canadian oil-sands samples at ambient and reservoir temperatures (164 data points). The true water content was determined by Dean-Stark extraction. The statistical scores confirm the strong generalization ability of the feature engineering LF-NMR model in predicting relative water content by Dean-Stark—root-mean-square error of 0.67% and mean-absolute error of 0.53% (R2 = 0.90). Results indicate that this approach can be extended for the improved in-situ water saturation evaluation by LF-NMR and bulk density measurements.

Effects of Lithium Slag on the Frost Resistance of Cement-Soil.

In this study, the effect of lithium slag (LS) on the frost resistance of cement-soil was evaluated. The results of freeze–thaw damage on the surface of the cement-soil, freeze–thaw mass loss, unconfined compression strength, triaxial shear strength, cohesion, and internal friction angle were tested at various freeze–thaw cycles after 90 days of curing when LS was incorporated into the cement-soil at different proportions (0%, 6%, 12%, and 18%). Combining nuclear magnetic resonance (NMR) T2 distribution and scanning electron microscopy (SEM) microscopic images, the mechanism of the effect of LS on the cement-soil was also analyzed. The experiment confirmed that the surface freeze–thaw damage degree and mass loss value of the cement-soil decreased after incorporating different LS contents, and that the unconfined compression strength, triaxial shear strength, cohesion, and internal friction angle also improved significantly compared with the specimens without LS. In this experiment, the optimization level of the cement-soil performance with different LS content was ranked as 12% > 18% > 6% > 0%. According to the NMR and SEM analysis results, the LS content of 12% can optimize the internal pore structure of the cement-soil and strengthen the bond between aggregate particles, hence inhibiting the extension of freeze-swelling cracks induced by freeze–thaw cycles. In conclusion, LS can effectively enhance the frost resistance of cement-soil, and the optimum content in this experiment is 12%.

An adsorption model for cylindrical pore and its method to calculate pore size distribution of coal by combining NMR

Coalbed methane (CBM) adsorption is closely related to pore size distribution in coal, the study of its adsorption state and pore characteristics of coal are of great significance to its exploitation and storage. In this paper, an extended simplified local density adsorption (SLD) model is proposed, which can be applied to cylindrical pores. Combining with the nuclear magnetic resonance (NMR) tests, the extended SLD model can predict the adsorption amount and pore size distribution of the whole sample without destroying its original pore structure. Three coal samples collected from different areas are selected for NMR test to measure T2 distribution and Magnetic Resonance Imaging (MRI) image. Then, the adsorption amount of the samples are obtained under constant temperature and different pressures. The fitting coefficients of the extend SLD model and experimental data of the three samples are all greater than 0.99, indicating that the proposed model matches the experimental results well. The two parameters obtained by fitting, transverse surface relaxivity (K) and the total number of pore (N), combined with T2, can get the radius and number of each pore in the sample. The inversion results show that the number summation of micropores and mesopores of the three samples are all exceeds 99%. However, due to the small pore size of micropores and mesopores, the pore volume summation of the three coal samples occupied by fractures and macropores are all over 27%. Further observation of cylindrical pore size and fluid molecular position shows that the distance between fluid-solid molecules is the main factor affecting the adsorption. The results of this paper are beneficial to predict and calculate the adsorption amount and pore size distribution of coal.

Simultaneous Assessment of Wettability and Water Saturation Through Integration of 2D NMR and Electrical Resistivity Measurements

Summary Nuclear magnetic resonance (NMR) transverse relaxation (T2) measurements are sensitive to fluid saturations and wettability of the rocks. However, quantifying wettability index solely from NMR T2 models relies on accurate estimates of water saturation. It has been shown that integrating resistivity measurements and NMR T2 distributions enables simultaneous assessment of wettability and water saturation. Nevertheless, there still exist significant uncertainties in this approach in the presence of multiple types of fluids with overlapping transverse relaxation times or multimodal pore-size distribution. Thus, the objectives of this paper are (a) to introduce a new multiphysics workflow integrating 2D NMR with resistivity measurements to simultaneously quantify wettability index and water/hydrocarbon saturation and (b) to verify the reliability of the introduced workflow with core measurements in different rock types. The workflow starts by using 2D diffusivity-transverse relaxation (D-T2) or longitudinal-transverse relaxation (T1-T2) measurements to estimate fluid saturations. We use a nonlinear inversion algorithm to fit a multimodal Gaussian distribution to the 2D NMR measurements. We then calculate water and hydrocarbon saturations using the fluid volumes estimated from the multimodal Gaussian distribution. This estimate of water/hydrocarbon saturation is an input to our new physics-based resistivity model that explicitly incorporates the influence of wettability. The inputs to the resistivity model include water saturation, resistivity index, and pore-geometry-related parameters. In the core-scale verification step, we compare the results of wettability and fluid saturations obtained from the new workflow with gravimetrically assessed water saturation and Amott index measurements on core sample. We successfully verified the reliability of the new workflow with experimental measurements. Estimated water saturation using the introduced workflow resulted in an average relative error of less than 7% compared to the gravimetrically assessed water saturations. Wettability indices obtained from the workflow were in agreement with those estimated using Amott indices. The average absolute error between the estimated wettability indices and the Amott indices was 0.27. In conclusion, results demonstrated that integration of 2D NMR and electrical resistivity measurements enables reliable and simultaneous assessment of wettability and water saturation in different rock types. The method introduced in this paper is promising for reliable and real-time wettability assessment, both in the laboratory and in-situ condition. It provides a physics-based and robust method to accurately and simultaneously estimate water/hydrocarbon saturation and wettability in hydrocarbon-bearing rocks.

A Review of Historical Studies for Water Saturation Determination Techniques

Water saturation is the most significant characteristic for reservoir characterization in order to assess oil reserves; this paper reviewed the concepts and applications of both classic and new approaches to determine water saturation. so, this work guides the reader to realize and distinguish between various strategies to obtain an appropriate water saturation value from electrical logging in both resistivity and dielectric has been studied, and the most well-known models in clean and shaly formation have been demonstrated. The Nuclear Magnetic Resonance in conventional and nonconventional reservoirs has been reviewed and understood as the major feature of this approach to estimate Water Saturation based on T2 distribution. Artificial intelligence has recently been used to predict water saturation and other parameters in the reservoir characterization process using seismic data, so the main idea of this technique and a list of the author's researchers have been reviewed. In this review article, the reference approach using core analysis by distillation-extraction and retorting techniques have been explained, as well as the saturation-height method, which is based on the capillary pressure concept and wettability. Finally, alternative experimental approaches based on scanning are expressed in this manner.

Research on the Effect of Freeze-Thaw Cycles at Different Temperatures on the Pore Structure of Water-Saturated Coal Samples.

To study the pore structure transformation of coal at different temperatures, freeze–thaw cycle experiments at different temperature intervals (20 to −20 °C, 20 to −40 °C, 20 to −196 °C) were carried out. The low-field nuclear magnetic resonance equipment was used to characterize the peak area, pore size distribution, and pore number of each group of coal samples. The pore transformation effect of coal samples at different temperature intervals was compared, and the change characteristics of the pore structure of coal samples under the freeze–thaw action were explored. The research shows that the freeze–thaw cycles at different freezing temperature intervals have obvious differences in the effect of coal pore transformation. The area of each peak spectrum in the T2 distribution curve of coal samples increased significantly under the action of freeze–thaw cycles in different freezing temperature intervals. The increased value of the number of mesopores and macropores shows the phenomenon of “first increase and then decrease” with the increase of the temperature difference. There is a quadratic function relationship between the temperature difference in the freezing temperature interval and the proportion change rate of the adsorption pore or seepage pore. The continuous increase of the temperature difference has a certain marginal effect on the proportion change rate of seepage pores and adsorption pores in coal.

Study on the Plugging Limit and Combination of CO2 Displacement Flow Control System Based on Nuclear Magnetic Resonance (NMR)

CO2 displacement is an important technology to reduce emissions and improve crude oil recovery, as well as prevent CO2 escape. Effective storage is key to the successful implementation of this technology, especially for medium and high permeability reservoirs. The current flow control systems that are applied to seal gas escape are mainly gas/water alternation, CO2 foam, and CO2 foam gel, but there is no clear understanding of the plugging limits of various flow control systems and the mechanism of their combined use of residual oil. Therefore, in this paper, a series of core replacement experiments are conducted for different flow control systems and their combinations. The quantitative characterization of the core pore size distribution before and after the replacement is carried out using the NMR technique to try and determine the plugging limits of different plugging systems, and to investigate the residual oil utilization patterns of self-designed flow control system combinations and common flow control system combinations under two reservoir conditions with and without large pores. The results show that the plugging limits of water/gas alternation, CO2 foam, and CO2 foam gel systems are 0.86–21.35 μm, 0.07–28.23 μm, and 7–100 μm, respectively, as inferred from the T2 (lateral relaxation time) distribution and pore size distribution. When different combinations of flow control systems are used for repelling, for reservoirs without large pore channels, the combination of flow control systems using higher strength CO2 foam first can effectively improve the degree of crude oil mobilization in small pore throats, compared to using gas/water alternation directly. For reservoirs containing large pore channels, using high-strength CO2 foam gel first to seal the large pore channels increases the degree of utilization of the large pore channels; using water/gas alternation first causes damage to the middle pore channels; High-strength CO2 foam gel seals the large pore channels when the plugging strength is not enough; and using water/gas alternation can effectively improve the degree of utilization of small and medium pore channels. The results of this paper can provide theoretical guidance for the multi-stage flow control of CO2 displacement in the field.

A Bayesian Optimization Approach to the Simultaneous Extraction of Intrinsic Physical Parameters fromT1 andT2 Relaxation Responses

SummaryNuclear magnetic resonance (NMR) relaxation responses in porous media provide a sensitive probe of the microstructure and yet are influenced by a number of factors which are not easily detangled. Low-field T2 transverse relaxation measurements can be carried out quickly and are frequently used as pore size distributions, while adding T1 longitudinal relaxation measurements provides additional insights into surface properties and fluid content. Here we present an inverse solution workflow extracting related intrinsic physical parameters of the system by fitting experiment and numerical simulation(s). An efficient NMR forward solver for the simultaneous calculation of T1 and T2 responses is introduced, which honors existing inequality relationships between T1 and T2 parameters. We propose a Bayesian optimization approach that jointly identifies T1- and T2-related properties satisfying physical constraints by simultaneously fitting T1 and T2 experiments to simulations. This dual-task inverse solution workflow (DT-ISW) identifies the solution by minimizing the sum of the L2 norm of the fitting residuals of both T1 and T2 distributions into a single objective and jointly models the two highly correlated objectives with high efficiency using the vector-valued Gaussian process (GP) kernel for transfer learning. A multimodal search strategy is used to identify nonunique solution sets of the problem. The workflow is demonstrated on Bentheimer sandstone, identifying five intrinsic physical parameters. The performance of the joint DT-ISW (DT-ISW-J) is compared to a sequential DT-ISW (DT-ISW-S) approach as well as an independent single-task ISW (ST-ISW) of the T1 and T2 responses. Both dual-task versions converge more than two times faster than the single-task version. DT-ISW-J equally minimizes the L2 norm of T1 and T2 fitting residuals whereas DT-ISW-S only preferentially minimizes the objective assigned higher importance. A Pareto optimal solution (POS) is provided to allow operators to subjectively balance the preference of T1 and T2 data fits for the slightly conflicting objectives. The ability to extract five intrinsic physical parameters simultaneously provides new techniques for tracking wettability alteration and assessing the influence of clay amount and distribution on petrophysical property estimates.

On the Multivariate Analysis of Students' Academic Performance in Wassce in Public Senior Secondary Schools in Rivers State (2018-2020)

The paper examined students' performance in six subjects from WAEC examination from 2018 to 2020 using multivariate analysis through Hotelling T2 distribution and paired t-test statistics. Four objectives where formulated and used for this study. Based on the factors in the objectives, relevant related literatures were reviewed. A secondary data extracted from the WAEC results from the public senior secondary schools under study were used for this study and the analyses of the data were done using Hotelling T2 distribution, Quadratic form, and paired t-test statistics. All computations were done via Microsoft Excel 2010, SPSS (version 23.0) and MINITAB (version 16.0). The Hotelling T2 statistics results between the students' academic performance for (2018 &amp; 2019), (2019 &amp; 2020) and (2018 &amp; 2020) were all significant. Paired t-test statistics results showed a decrease in the Students' average performance for four subjects (Mathematics, English Language, Marketing and Biology), while an increase in the Students' average performance for Economics and Civic Education subjects. It was discovered that students' average performances in Economics and Civic Education subjects were better than other subjects. This research recommend the effective implementation of the Nigeria education policies that emphasizes on teachers qualification, years of teaching experience and the UNESCO policy on Teacher-Students ratio (this policy stipulates that the maximum number of students that should be in a secondary class is 25), since there is significant difference between students' average performance for four subjects.

Study on Freezing-Thawing damage mechanism and evolution model of concrete

Freezing-thawing (F-T) cycle is one of the main reason of concrete damage in cold regions. F-T cycle mainly lead to degradation of macroscopic mechanical properties of concrete by changing the number of micropores, mesopores and macropores, and causing severely damage to its internal texture. The variations of the physical and mechanical properties of concrete sample with different inclination angle of internal flaw exposed to different F-T cycles (0, 10, 30 and 50 cycles) under unconfined compression condition was deeply investigated based on the acoustic emission (AE) and nuclear magnetic resonance (NMR) technology. The evolution of the internal cracks are tracked in real-time by AE monitoring systems during the entire test process. Meanwhile, the micro-structure of the concrete sample after F-T cycle treatment is microscopically observed with T2 distribution by low-field nuclear magnetic resonance. The results show that the peak strength of concrete decreases with the increasing F-T cycles and increases as the increasing inclination angle of prefabricated flaw. The elastic modulus decreased gradually with the increase of F-T cycles. The elastic modulus of the sample without F-T cycles treatment increases with the increase of inclination angle of prefabricated flaw. As the flaw inclination angle increases from 0° to 90°, the F-T cycles increases from 0 to 50, the peak strain shows an obvious discreteness without monotone change. When the number of F-T cycle reaches 50, concrete blocks fall off from the sample surface. A continuum damage model considering F-T damage from different pore size is finally introduced to describe the damage evolution of concrete during compression test. The research results can be used to quantitatively evaluate the strength of concrete samples treated by F-T cycle without mechanical tests.

NMR transverse relaxation of the clay-rich shale in inhomogeneous magnetic field: A numerical study

We conducted comprehensive numerical simulations to probe the low field nuclear magnetic resonance (NMR) relaxation of the clay-rich shale in inhomogeneous magnetic field. Under the guidance of the Bloch equation, the relaxation property of a unimodal distributed clay-rich shale is simulated using the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. Both the magnetization and the transverse relaxation time (T2) spectrum are obtained to investigate influential factors such as the excitation pulse angle, the refocusing pulse angle, the pulse duration, the echo spacing, as well as the off-resonance frequency. The simulation result showed that the field inhomogeneity contributes great influence on the NMR relaxation, particular in high magnetic field strength and high off-resonance frequency. We observed that in standard CMPG pulse sequence, the amplitude of the T2 distribution is negatively correlated with the off-resonance frequency and can be compensated by the empirical regression. Moreover, the excitation pulse angle poses great impact on the amplitude of the T2 distribution, but has less influence on the T2 distribution and its peak value. On the contrary, both the amplitude and the peak value of the T2 spectrums are also impacted by the refocusing pulse angle, especially in higher magnetic field inhomogeneity. The refocusing pulse angle is preferable higher than 150° for the clay-rich shale since it helps the spins to rephrase quickly. In additional, the echo spacing is ideally reduced to as low as its minimal value for the measurement of samples with short relaxation component. The result provides comprehensive knowledge on influential factors of the NMR relaxation of the clay-rich shale, which is useful for the optimization of the pulse sequence, the acquisition conditions, as well as the manipulation of the magnetization data.

Fluid space reformation law of liquid nitrogen fracturing coal based on NMR T1–T2 spectra and inspiration for coalbed methane production

The low porosity and permeability characteristics of coal seams have become the main bottleneck restricting high-efficiency extraction of coalbed methane. At present, enhanced fracturing and permeability enhancement technologies are often used to transform the pore structure of coal reservoirs, aiming to improve the permeability of coal bodies. In order to study the evolution law of coal pore and pore fluid occurrence space under the action of liquid nitrogen (LN2) cold shock, this paper takes lignite in saturated and centrifugal state as the research object. After freezing and thawing of LN2, the coal samples were tested by nuclear magnetic resonance. Through the T1-T2 spectrum and 3D peak map, the change process of coal pore fluid occurrence space was quantitatively characterized, and the change of T2 distribution and T2 spectrum area was used to reflect the coal pore evolution process. The results shows that after the same coal sample is frozen for 5, 50, and 150 min, the free water storage space expands by 86.7%, 101.4%, and 120.1%, respectively, the effective porosity ratios are 62.5%, 66.7%, and 80.4%, respectively, 5, 15, and 25 cycles after freeze–thaw cycles, the free water storage space was expanded by 146.9%, 170.6%, and 220.1%, respectively, the effective porosity ratios were 71.5%, 75.4%, and 83.3%, respectively. Further analysis shows that with the increase of LN2 freezing time and the number of freeze–thaw cycles, the occurrence space of free water in the pores increases significantly, and the occurrence space of irreducible water gradually decreases. This study can provide some basic support for the quantitative evaluation of the pore structure of LN2 fracturing coal in field applications.

A statistical learning perspective on the inversion of NMR relaxation data

T 2 distribution is a powerful tool in the low-field nuclear magnetic resonance technique. The T2 distribution obtained from time-domain data involves an ill-posed inverse Laplace transformation. Tikhonov regularization with an L2 penalty term is most commonly used in this kind of problem, and the discrepancy principle, generalized cross-validation, L-curve, and S-curve methods are widely used in the selection of the regularization parameter. However, these selection approaches require prior knowledge, such as an accurate estimation of the threshold level of noise or setting a default value. In this paper, we propose a new method—the stability-enhanced k-fold cross-validation (SECV) approach—to perform a robust automatic search for the regularization parameter from a statistical learning perspective. In addition to considering test set residuals, additional terms—the Pearson’s correlation coefficients of the solutions of the disjoint subsets—are put forward to enhance the stability of the solution and make a trade-off between its imitative effect and interpretability. A bimodal T2 distribution model was constructed, and abundant echo trains with different noise levels were generated for the validation of the proposed method. The relative error of the estimates is used as a measure to evaluate the performance. The inversion results from the SECV method were compared with the solutions from the conventional methods, and the results showed that the proposed method is robust without manual intervention and suitable for both low- and high-signal-to-noise ratio data. Finally, mercury injection and nuclear magnetic resonance experiments were carried out on rock core samples to verify the correctness of our method.