In order to investigate propagation regularity of hydraulic fractures in the mode of multi-well pads, numerical modeling of simultaneous hydraulic fracturing of multiple wells was conducted. The mathematical model was...In order to investigate propagation regularity of hydraulic fractures in the mode of multi-well pads, numerical modeling of simultaneous hydraulic fracturing of multiple wells was conducted. The mathematical model was established coupling rock deformation with fluid flow in the fractures and wellbores. And then the model was solved by displacement discontinuity method coupling with implicit level set method. The implicit method was based on fracture tip asymptotical solution and used to determine fracture growth length. Simulation results showed that when multiple wells were fractured simultaneously, adjacent fractures might propagate towards each other, showing an effect of attraction other than repulsion. Fracture spacing and well spacing had significant influence on the propagation path and geometry of multiple fractures. Furthermore, when multiple wells were fractured simultaneously, stress reversal regions had a large area, and stress reversal regions were distributed not only in the area between fractures but also on the outside of them. The area of stress reversal regions was related to fracture spacing and well spacing. Results indicated that multi-well fracturing induced larger area of stress reversal regions than one-well fracturing, which was beneficial to generating complex fracture network in unconventional reservoirs.展开更多
Currently there are two approaches for a multi-class support vector classifier(SVC). One is to construct and combine several binary classifiers while the other is to directly consider all classes of data in one optimi...Currently there are two approaches for a multi-class support vector classifier(SVC). One is to construct and combine several binary classifiers while the other is to directly consider all classes of data in one optimization formulation. For a K-class problem(K>2),the first approach has to construct at least K classifiers,and the second approach has to solve a much larger op-timization problem proportional to K by the algorithms developed so far. In this paper,following the second approach,we present a novel multi-class large margin classifier(MLMC). This new machine can solve K-class problems in one optimization formula-tion without increasing the size of the quadratic programming(QP) problem proportional to K. This property allows us to construct just one classifier with as few variables in the QP problem as possible to classify multi-class data,and we can gain the advantage of speed from it especially when K is large. Our experiments indicate that MLMC almost works as well as(sometimes better than) many other multi-class SVCs for some benchmark data classification problems,and obtains a reasonable performance in face recognition application on the AR face database.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.51234007&51490654)the National Science Foundation for Young Scientists of China(Grant No.51404291)+1 种基金Fundamental Research Funds for Central Universities(Grant Nos.14CX05024A&14CX02045A)Shandong Provincial Natural Science Foundation(Grant No.ZR2014EEQ010)
文摘In order to investigate propagation regularity of hydraulic fractures in the mode of multi-well pads, numerical modeling of simultaneous hydraulic fracturing of multiple wells was conducted. The mathematical model was established coupling rock deformation with fluid flow in the fractures and wellbores. And then the model was solved by displacement discontinuity method coupling with implicit level set method. The implicit method was based on fracture tip asymptotical solution and used to determine fracture growth length. Simulation results showed that when multiple wells were fractured simultaneously, adjacent fractures might propagate towards each other, showing an effect of attraction other than repulsion. Fracture spacing and well spacing had significant influence on the propagation path and geometry of multiple fractures. Furthermore, when multiple wells were fractured simultaneously, stress reversal regions had a large area, and stress reversal regions were distributed not only in the area between fractures but also on the outside of them. The area of stress reversal regions was related to fracture spacing and well spacing. Results indicated that multi-well fracturing induced larger area of stress reversal regions than one-well fracturing, which was beneficial to generating complex fracture network in unconventional reservoirs.
基金supported by the National Natural Science Foundation of China (No. 60675049)the National Creative Research Groups Science Foundation of China (No. 60721062)the Natural Science Foundation of Zhejiang Province, China (No. Y106414)
文摘Currently there are two approaches for a multi-class support vector classifier(SVC). One is to construct and combine several binary classifiers while the other is to directly consider all classes of data in one optimization formulation. For a K-class problem(K>2),the first approach has to construct at least K classifiers,and the second approach has to solve a much larger op-timization problem proportional to K by the algorithms developed so far. In this paper,following the second approach,we present a novel multi-class large margin classifier(MLMC). This new machine can solve K-class problems in one optimization formula-tion without increasing the size of the quadratic programming(QP) problem proportional to K. This property allows us to construct just one classifier with as few variables in the QP problem as possible to classify multi-class data,and we can gain the advantage of speed from it especially when K is large. Our experiments indicate that MLMC almost works as well as(sometimes better than) many other multi-class SVCs for some benchmark data classification problems,and obtains a reasonable performance in face recognition application on the AR face database.
