Optimization of fracturing perforation is of great importance to the commingling gas production in coal measure strata.In this paper,a 3 D lattice algorithm hydraulic fracturing simulator was employed to study the eff...Optimization of fracturing perforation is of great importance to the commingling gas production in coal measure strata.In this paper,a 3 D lattice algorithm hydraulic fracturing simulator was employed to study the effects of perforation position and length on hydraulic fracture propagation in coal measures of the Lin-Xing block,China.Based on field data,three lithologic combinations are simulated:1)a thick section of coal seam sandwiched by sandstones;2)a thin coal seam layer overlay by gas-bearing tight sandstone;3)two coal seams separated by a thin layer of sandstone.Our simulation shows that perforation position and length in multi-layer reservoirs play a major role in hydraulic fracture propagation.Achieving maximum stimulated volume requires consideration of lithologic sequence,coal seam thickness,stress states,and rock properties.To improve the combined gas production in coal measure strata,it is possible to simultaneously stimulate multiple coal seams or adjacent gas-bearing sandstones.In these cases,perforation location and length also significantly impact fracture propagation,and therefore should be carefully designed.Our simulation results using 3 D lattice algorithm are qualitatively consistent with laboratory physical simulation.3 D lattice models can be used to effectively simulate the fracture propagation through layers in coal measure strata.The numerical results provide guidance for perforation optimization in the hydraulic fracturing of coal measure strata.展开更多
Random sampling algorithm was proposed firstly by Schnorr in 2003 to find short lattice vectors,as an alternative to enumeration.The follow-up developments in random sampling were mainly proposed by Fukase and Kashiwa...Random sampling algorithm was proposed firstly by Schnorr in 2003 to find short lattice vectors,as an alternative to enumeration.The follow-up developments in random sampling were mainly proposed by Fukase and Kashiwabara in 2015 and Aono and Nguyen in 2017.Although they extended the sampling space compared to Schnorr's work through the natural number representation,they did not show how to sample specifically in practice and what vectors should be sampled,in order to find short enough lattice vectors.In this paper,the authors firstly introduce a practical random sampling algorithm under some reasonable assumptions which can find short enough lattice vectors efficiently.Then,as an application of this new random sampling algorithm,the authors show that it can improve the performance of progressive BKZ algorithm in practice.Finally,the authors solve the Darmstadt's Lattice Challenge and get a series of new records in the dimension from 500 to 825,using the improved progressive BKZ algorithm.展开更多
基金the financial support by the National Key Research and Development Program of China(Grant No.2020YFC1808102)the Natural Science Foundation of China(No.51874328 and No.52074311)。
文摘Optimization of fracturing perforation is of great importance to the commingling gas production in coal measure strata.In this paper,a 3 D lattice algorithm hydraulic fracturing simulator was employed to study the effects of perforation position and length on hydraulic fracture propagation in coal measures of the Lin-Xing block,China.Based on field data,three lithologic combinations are simulated:1)a thick section of coal seam sandwiched by sandstones;2)a thin coal seam layer overlay by gas-bearing tight sandstone;3)two coal seams separated by a thin layer of sandstone.Our simulation shows that perforation position and length in multi-layer reservoirs play a major role in hydraulic fracture propagation.Achieving maximum stimulated volume requires consideration of lithologic sequence,coal seam thickness,stress states,and rock properties.To improve the combined gas production in coal measure strata,it is possible to simultaneously stimulate multiple coal seams or adjacent gas-bearing sandstones.In these cases,perforation location and length also significantly impact fracture propagation,and therefore should be carefully designed.Our simulation results using 3 D lattice algorithm are qualitatively consistent with laboratory physical simulation.3 D lattice models can be used to effectively simulate the fracture propagation through layers in coal measure strata.The numerical results provide guidance for perforation optimization in the hydraulic fracturing of coal measure strata.
基金supported by the National Natural Science Foundation of China under Grant Nos.62032009 and 62102440。
文摘Random sampling algorithm was proposed firstly by Schnorr in 2003 to find short lattice vectors,as an alternative to enumeration.The follow-up developments in random sampling were mainly proposed by Fukase and Kashiwabara in 2015 and Aono and Nguyen in 2017.Although they extended the sampling space compared to Schnorr's work through the natural number representation,they did not show how to sample specifically in practice and what vectors should be sampled,in order to find short enough lattice vectors.In this paper,the authors firstly introduce a practical random sampling algorithm under some reasonable assumptions which can find short enough lattice vectors efficiently.Then,as an application of this new random sampling algorithm,the authors show that it can improve the performance of progressive BKZ algorithm in practice.Finally,the authors solve the Darmstadt's Lattice Challenge and get a series of new records in the dimension from 500 to 825,using the improved progressive BKZ algorithm.
