Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The signif...Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.展开更多
Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Anal...Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.展开更多
A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with...A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.展开更多
Assuming seismic data in a suitable domain is low rank while missing traces or noises increase the rank of the data matrix,the rank⁃reduced methods have been applied successfully for seismic interpolation and denoisin...Assuming seismic data in a suitable domain is low rank while missing traces or noises increase the rank of the data matrix,the rank⁃reduced methods have been applied successfully for seismic interpolation and denoising.These rank⁃reduced methods mainly include Cadzow reconstruction that uses eigen decomposition of the Hankel matrix in the f⁃x(frequency⁃spatial)domain,and nuclear⁃norm minimization(NNM)based on rigorous optimization theory on matrix completion(MC).In this paper,a low patch⁃rank MC is proposed with a random⁃overlapped texture⁃patch mapping for interpolation of regularly missing traces in a three⁃dimensional(3D)seismic volume.The random overlap plays a simple but important role to make the low⁃rank method effective for aliased data.It shifts the regular column missing of data matrix to random point missing in the mapped matrix,where the missing data increase the rank thus the classic low⁃rank MC theory works.Unlike the Hankel matrix based rank⁃reduced method,the proposed method does not assume a superposition of linear events,but assumes the data have repeated texture patterns.Such data lead to a low⁃rank matrix after the proposed texture⁃patch mapping.Thus the methods can interpolate the waveforms with varying dips in space.A fast low⁃rank factorization method and an orthogonal rank⁃one matrix pursuit method are applied to solve the presented interpolation model.The former avoids the singular value decomposition(SVD)computation and the latter only needs to compute the large singular values during iterations.The two fast algorithms are suitable for large⁃scale data.Simple averaging realizations of several results from different random⁃overlapped texture⁃patch mappings can further increase the reconstructed signal⁃to⁃noise ratio(SNR).Examples on synthetic data and field data are provided to show successful performance of the presented method.展开更多
The high-value utilization of low-rank coal would allow for expanding energy sources,improving energy efficiencies,and alleviating environmental issues.In order to use low-rank coal effectively,the hypercoals(HPCs)wer...The high-value utilization of low-rank coal would allow for expanding energy sources,improving energy efficiencies,and alleviating environmental issues.In order to use low-rank coal effectively,the hypercoals(HPCs)were co-extracted from two types of low-rank coal and biomass via N-methyl-2-purrolidinone(NMP)under mild conditions.The structures of the HPCs and residues were characterized by proximate and ultimate analysis,Raman spectra,and Fourier transform infrared(FT-IR)spectra.The carbon structure changes within the raw coals and HPCs were discussed.The individual thermal dissolution of Xibu(XB)coal,Guandi(GD)coal,and the biomass demonstrated that the biomass provided the lowest thermal dissolution yield Y1 and the highest thermal soluble yield Y2 at 280℃,and the ash content of three HPCs decreased as the extraction temperature rose.Co-thermal extractions in NMP at various coal/biomass mass ratios were performed,demonstrating a positive synergic effect for Y2 in the whole coal/biomass mass ratios.The maximum value of Y2 was 52.25wt% for XB coal obtained with a XB coal/biomass of 50wt% biomass.The maximum value of Y2 was 50.77wt% for GD coal obtained with a GD coal/biomass of 1:4.The difference for the optimal coal/biomass mass ratios between XB and GD coals could be attributed to the different co-extraction mechanisms for this two type coals.展开更多
To reasonably utilize the coal direct liquefaction residue(DLR), contrasting research on the co-pyrolysis between different low-rank coals and DLR was investigated using a TGA coupled with an FT-IR spectrophotometer a...To reasonably utilize the coal direct liquefaction residue(DLR), contrasting research on the co-pyrolysis between different low-rank coals and DLR was investigated using a TGA coupled with an FT-IR spectrophotometer and a fixed-bed reactor. GC–MS, FTIR, and XRD were used to explore the reaction mechanisms of the various co-pyrolysis processes. Based on the TGA results, it was confirmed that the tetrahydrofuran insoluble fraction of DLR helped to catalyze the conversion reaction of lignite. Also, the addition of DLR improved the yield of tar in the fixed-bed, with altering the composition of the tar. Moreover, a kinetic analysis during the co-pyrolysis was conducted using a distributed activation energy model. The co-pyrolysis reactions showed an approximate double-Gaussian distribution.展开更多
Low-rank coal contains more inherent moisture, high alkali metals (Na, K, Ca), high oxygen content, and low sulfur than high-rank coal. Low-rank coal gasification usually has lower efficiency than high-rank coal, sinc...Low-rank coal contains more inherent moisture, high alkali metals (Na, K, Ca), high oxygen content, and low sulfur than high-rank coal. Low-rank coal gasification usually has lower efficiency than high-rank coal, since more energy has been used to drive out the moisture and volatile matters and vaporize them. Nevertheless, Low-rank coal comprises about half of both the current utilization and the reserves in the United States and is the largest energy resource in the United States, so it is worthwhile and important to investigate the low-rank coal gasification process. In this study, the two-stage fuel feeding scheme is investigated in a downdraft, entrained-flow, and refractory-lined reactor. Both a high-rank coal (Illinois No.6 bituminous) and a low-rank coal (South Hallsville Texas Lignite) are used for comparison under the following operating conditions: 1) low-rank coal vs. high-rank coal, 2) one-stage injection vs. two-stage injection, 3) low-rank coal with pre-drying vs. without pre-drying, and 4) dry coal feeding without steam injection vs. with steam injection at the second stage. The results show that 1) With predrying to 12% moisture, syngas produced from lignite has 538 K lower exit temperature and 18% greater Higher Heating Value (HHV) than syngas produced from Illinois #6. 2) The two-stage fuel feeding scheme results in a lower wall temperature (around 100 K) in the lower half of the gasifier than the single-stage injection scheme. 3) Without pre-drying, the high inherent moisture content in the lignite causes the syngas HHV to decrease by 27% and the mole fractions of both H2 and CO to decrease by 33%, while the water vapor content increases by 121% (by volume). The low-rank coal, without pre-drying, will take longer to finish the demoisturization and devolatilization processes, resulting in delayed combustion and gasification processes.展开更多
This paper studies the problem of recovering low-rank tensors, and the tensors are corrupted by both impulse and Gaussian noise. The problem is well accomplished by integrating the tensor nuclear norm and the l1-norm ...This paper studies the problem of recovering low-rank tensors, and the tensors are corrupted by both impulse and Gaussian noise. The problem is well accomplished by integrating the tensor nuclear norm and the l1-norm in a unified convex relaxation framework. The nuclear norm is adopted to explore the low-rank components and the l1-norm is used to exploit the impulse noise. Then, this optimization problem is solved by some augmented-Lagrangian-based algorithms. Some preliminary numerical experiments verify that the proposed method can well recover the corrupted low-rank tensors.展开更多
The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can b...The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.展开更多
At present, although the human speech separation has achieved fruitful results, it is not ideal for the separation of singing and accompaniment. Based on low-rank and sparse optimization theory, in this paper, we prop...At present, although the human speech separation has achieved fruitful results, it is not ideal for the separation of singing and accompaniment. Based on low-rank and sparse optimization theory, in this paper, we propose a new singing voice separation algorithm called Low-rank, Sparse Representation with pre-learned dictionaries and side Information (LSRi). The algorithm incorporates both the vocal and instrumental spectrograms as sparse matrix and low-rank matrix, meanwhile combines pre-learning dictionary and the reconstructed voice spectrogram form the annotation. Evaluations on the iKala dataset show that the proposed methods are effective and efficient for singing voice separation.展开更多
The low rank coalbed methane (CBM) has great potential for exploration and development in China, but its exploitation level is low at present stage. The pores are the storage space of CBM, so recognizing its structura...The low rank coalbed methane (CBM) has great potential for exploration and development in China, but its exploitation level is low at present stage. The pores are the storage space of CBM, so recognizing its structural characteristics has very important practical significance for the development of CBM. The samples of No. 4 and upper No. 4 coalbed in Dafosi were selected to carry out the analysis of mercury injection test, nitrogen adsorption test and scanning electron microscopy to study the different lithotypes of the pore structure, pore throat distribution and fracture character of low rank coal reservoir. The results showed that micropore of low rank coal in Dafosi relatively developed and the pore volume of vitrain was equivalent to durain. The pore throat of durain was larger than vitrain, the connectivity was better and the fissures were more developed. The percolation capacity and reservoir performance of upper No. 4 coal was better than No. 4 coal. Generally, the potential of exploration and development of upper No. 4 coal in the study area was better than that of No. 4, and the developed area of durain was more beneficial for the development of CBM.展开更多
Coal swelling in the presence of water as well as CO2 is a well-known phenomenon, and these may affect the permeability of coal. Quantifying swelling effects is becoming an important issue to verify the suitability of...Coal swelling in the presence of water as well as CO2 is a well-known phenomenon, and these may affect the permeability of coal. Quantifying swelling effects is becoming an important issue to verify the suitability of particular coal seams for CO2-enhanced coal bed methane recovery projects. In this report, coal swelling experiments using a visualization method in the CO2 supercritical conditions were conducted on crushed coal samples. The measurement apparatus was designed specifically for the present swelling experiment using a visualization method. Crushed coal samples were used instead of block coal samples to shorten equilibrium time and to solve the problem of limited availability of core coal samples. Dry and wet coal samples were used in the experiments because there is relatively limited information about how the swelling of coal by CO2 is affected by water saturation. Moreover, some coal seams are saturated with water in initial reservoir conditions. The maximum volumetric swelling was around 3% at 10 MPa for dry samples and almost half that at the same pressure for wet samples. The wet samples showed lower volumetric swelling than dry ones because the wet coal samples were already swollen by water. Experimental results obtained for swelling were comparable with other reports. Our visualization method using crushed samples has advantages in terms of sample preparation and experimental execution compared with the other methods used to measure coal swelling using block samples.展开更多
Given a symmetric matrix X, we consider the problem of finding a low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given positive integer, , which i...Given a symmetric matrix X, we consider the problem of finding a low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given positive integer, , which is nearest to X in a certain matrix norm. The problem is first solved with regard to four common norms: The Frobenius norm, the Schatten p-norm, the trace norm, and the spectral norm. Then the solution is extended to any unitarily invariant matrix norm. The proof is based on a subtle combination of Ky Fan dominance theorem, a modified pinching principle, and Mirsky minimum-norm theorem.展开更多
文摘Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.
文摘Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.
文摘A number of previous papers have studied the problem of recovering low-rank matrices with noise, further combining the noisy and perturbed cases, we propose a nonconvex Schatten p-norm minimization method to deal with the recovery of fully perturbed low-rank matrices. By utilizing the p-null space property (p-NSP) and the p-restricted isometry property (p-RIP) of the matrix, sufficient conditions to ensure that the stable and accurate reconstruction for low-rank matrix in the case of full perturbation are derived, and two upper bound recovery error estimation ns are given. These estimations are characterized by two vital aspects, one involving the best r-approximation error and the other concerning the overall noise. Specifically, this paper obtains two new error upper bounds based on the fact that p-RIP and p-NSP are able to recover accurately and stably low-rank matrix, and to some extent improve the conditions corresponding to RIP.
文摘Assuming seismic data in a suitable domain is low rank while missing traces or noises increase the rank of the data matrix,the rank⁃reduced methods have been applied successfully for seismic interpolation and denoising.These rank⁃reduced methods mainly include Cadzow reconstruction that uses eigen decomposition of the Hankel matrix in the f⁃x(frequency⁃spatial)domain,and nuclear⁃norm minimization(NNM)based on rigorous optimization theory on matrix completion(MC).In this paper,a low patch⁃rank MC is proposed with a random⁃overlapped texture⁃patch mapping for interpolation of regularly missing traces in a three⁃dimensional(3D)seismic volume.The random overlap plays a simple but important role to make the low⁃rank method effective for aliased data.It shifts the regular column missing of data matrix to random point missing in the mapped matrix,where the missing data increase the rank thus the classic low⁃rank MC theory works.Unlike the Hankel matrix based rank⁃reduced method,the proposed method does not assume a superposition of linear events,but assumes the data have repeated texture patterns.Such data lead to a low⁃rank matrix after the proposed texture⁃patch mapping.Thus the methods can interpolate the waveforms with varying dips in space.A fast low⁃rank factorization method and an orthogonal rank⁃one matrix pursuit method are applied to solve the presented interpolation model.The former avoids the singular value decomposition(SVD)computation and the latter only needs to compute the large singular values during iterations.The two fast algorithms are suitable for large⁃scale data.Simple averaging realizations of several results from different random⁃overlapped texture⁃patch mappings can further increase the reconstructed signal⁃to⁃noise ratio(SNR).Examples on synthetic data and field data are provided to show successful performance of the presented method.
基金financially supported by the National Natural Science Foundation of China (No. 51574023)
文摘The high-value utilization of low-rank coal would allow for expanding energy sources,improving energy efficiencies,and alleviating environmental issues.In order to use low-rank coal effectively,the hypercoals(HPCs)were co-extracted from two types of low-rank coal and biomass via N-methyl-2-purrolidinone(NMP)under mild conditions.The structures of the HPCs and residues were characterized by proximate and ultimate analysis,Raman spectra,and Fourier transform infrared(FT-IR)spectra.The carbon structure changes within the raw coals and HPCs were discussed.The individual thermal dissolution of Xibu(XB)coal,Guandi(GD)coal,and the biomass demonstrated that the biomass provided the lowest thermal dissolution yield Y1 and the highest thermal soluble yield Y2 at 280℃,and the ash content of three HPCs decreased as the extraction temperature rose.Co-thermal extractions in NMP at various coal/biomass mass ratios were performed,demonstrating a positive synergic effect for Y2 in the whole coal/biomass mass ratios.The maximum value of Y2 was 52.25wt% for XB coal obtained with a XB coal/biomass of 50wt% biomass.The maximum value of Y2 was 50.77wt% for GD coal obtained with a GD coal/biomass of 1:4.The difference for the optimal coal/biomass mass ratios between XB and GD coals could be attributed to the different co-extraction mechanisms for this two type coals.
基金Supported by National High-tech Research and Development Program of China(2011AA05A2021)the National Natural Science Foundation of China(21536009)Science and Technology Plan Projects of Shaanxi Province(2017ZDCXL-GY-10-03).
文摘To reasonably utilize the coal direct liquefaction residue(DLR), contrasting research on the co-pyrolysis between different low-rank coals and DLR was investigated using a TGA coupled with an FT-IR spectrophotometer and a fixed-bed reactor. GC–MS, FTIR, and XRD were used to explore the reaction mechanisms of the various co-pyrolysis processes. Based on the TGA results, it was confirmed that the tetrahydrofuran insoluble fraction of DLR helped to catalyze the conversion reaction of lignite. Also, the addition of DLR improved the yield of tar in the fixed-bed, with altering the composition of the tar. Moreover, a kinetic analysis during the co-pyrolysis was conducted using a distributed activation energy model. The co-pyrolysis reactions showed an approximate double-Gaussian distribution.
基金supported by the National Natural Science Foundation of China (No. 91320201 and No. 61471262)the International (Regional) Collaborative Key Research Projects (No. 61520106002)
文摘Low-rank coal contains more inherent moisture, high alkali metals (Na, K, Ca), high oxygen content, and low sulfur than high-rank coal. Low-rank coal gasification usually has lower efficiency than high-rank coal, since more energy has been used to drive out the moisture and volatile matters and vaporize them. Nevertheless, Low-rank coal comprises about half of both the current utilization and the reserves in the United States and is the largest energy resource in the United States, so it is worthwhile and important to investigate the low-rank coal gasification process. In this study, the two-stage fuel feeding scheme is investigated in a downdraft, entrained-flow, and refractory-lined reactor. Both a high-rank coal (Illinois No.6 bituminous) and a low-rank coal (South Hallsville Texas Lignite) are used for comparison under the following operating conditions: 1) low-rank coal vs. high-rank coal, 2) one-stage injection vs. two-stage injection, 3) low-rank coal with pre-drying vs. without pre-drying, and 4) dry coal feeding without steam injection vs. with steam injection at the second stage. The results show that 1) With predrying to 12% moisture, syngas produced from lignite has 538 K lower exit temperature and 18% greater Higher Heating Value (HHV) than syngas produced from Illinois #6. 2) The two-stage fuel feeding scheme results in a lower wall temperature (around 100 K) in the lower half of the gasifier than the single-stage injection scheme. 3) Without pre-drying, the high inherent moisture content in the lignite causes the syngas HHV to decrease by 27% and the mole fractions of both H2 and CO to decrease by 33%, while the water vapor content increases by 121% (by volume). The low-rank coal, without pre-drying, will take longer to finish the demoisturization and devolatilization processes, resulting in delayed combustion and gasification processes.
文摘This paper studies the problem of recovering low-rank tensors, and the tensors are corrupted by both impulse and Gaussian noise. The problem is well accomplished by integrating the tensor nuclear norm and the l1-norm in a unified convex relaxation framework. The nuclear norm is adopted to explore the low-rank components and the l1-norm is used to exploit the impulse noise. Then, this optimization problem is solved by some augmented-Lagrangian-based algorithms. Some preliminary numerical experiments verify that the proposed method can well recover the corrupted low-rank tensors.
基金supported by the National Natural Science Foundation of China(No.61271014)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20124301110003)the Graduated Students Innovation Fund of Hunan Province(No.CX2012B238)
文摘The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.
文摘At present, although the human speech separation has achieved fruitful results, it is not ideal for the separation of singing and accompaniment. Based on low-rank and sparse optimization theory, in this paper, we propose a new singing voice separation algorithm called Low-rank, Sparse Representation with pre-learned dictionaries and side Information (LSRi). The algorithm incorporates both the vocal and instrumental spectrograms as sparse matrix and low-rank matrix, meanwhile combines pre-learning dictionary and the reconstructed voice spectrogram form the annotation. Evaluations on the iKala dataset show that the proposed methods are effective and efficient for singing voice separation.
文摘The low rank coalbed methane (CBM) has great potential for exploration and development in China, but its exploitation level is low at present stage. The pores are the storage space of CBM, so recognizing its structural characteristics has very important practical significance for the development of CBM. The samples of No. 4 and upper No. 4 coalbed in Dafosi were selected to carry out the analysis of mercury injection test, nitrogen adsorption test and scanning electron microscopy to study the different lithotypes of the pore structure, pore throat distribution and fracture character of low rank coal reservoir. The results showed that micropore of low rank coal in Dafosi relatively developed and the pore volume of vitrain was equivalent to durain. The pore throat of durain was larger than vitrain, the connectivity was better and the fissures were more developed. The percolation capacity and reservoir performance of upper No. 4 coal was better than No. 4 coal. Generally, the potential of exploration and development of upper No. 4 coal in the study area was better than that of No. 4, and the developed area of durain was more beneficial for the development of CBM.
文摘Coal swelling in the presence of water as well as CO2 is a well-known phenomenon, and these may affect the permeability of coal. Quantifying swelling effects is becoming an important issue to verify the suitability of particular coal seams for CO2-enhanced coal bed methane recovery projects. In this report, coal swelling experiments using a visualization method in the CO2 supercritical conditions were conducted on crushed coal samples. The measurement apparatus was designed specifically for the present swelling experiment using a visualization method. Crushed coal samples were used instead of block coal samples to shorten equilibrium time and to solve the problem of limited availability of core coal samples. Dry and wet coal samples were used in the experiments because there is relatively limited information about how the swelling of coal by CO2 is affected by water saturation. Moreover, some coal seams are saturated with water in initial reservoir conditions. The maximum volumetric swelling was around 3% at 10 MPa for dry samples and almost half that at the same pressure for wet samples. The wet samples showed lower volumetric swelling than dry ones because the wet coal samples were already swollen by water. Experimental results obtained for swelling were comparable with other reports. Our visualization method using crushed samples has advantages in terms of sample preparation and experimental execution compared with the other methods used to measure coal swelling using block samples.
文摘Given a symmetric matrix X, we consider the problem of finding a low-rank positive approximant of X. That is, a symmetric positive semidefinite matrix, S, whose rank is smaller than a given positive integer, , which is nearest to X in a certain matrix norm. The problem is first solved with regard to four common norms: The Frobenius norm, the Schatten p-norm, the trace norm, and the spectral norm. Then the solution is extended to any unitarily invariant matrix norm. The proof is based on a subtle combination of Ky Fan dominance theorem, a modified pinching principle, and Mirsky minimum-norm theorem.
