In neutron and photon transport problems,anisotropic scattering is of great importance for the particle flux,especially when the angular flux has a strong forward peak in shielding analyses.The conventional Legendre e...In neutron and photon transport problems,anisotropic scattering is of great importance for the particle flux,especially when the angular flux has a strong forward peak in shielding analyses.The conventional Legendre expansion is widely used in discrete ordinates transport codes because of algebraic simplifications with spherical harmonics for the scattering source.However,negative cross sections caused by the finitely truncated expansion may give rise to a negative source and flux.A simple method is adopted,based on integrating functions of scattering moments,to evaluate anisotropy and convergence of expanded functions.A series of problems were designed with angular fluxes of different anisotropy,and numerical simulations were performed using the ARES transport code to study different treatments and algorithms for scattering.Results show that the diagonal transport approximation is more stable and obtains a similar accuracy with the extended approximation.A conservative fixup for the negative source could ensure particle balance and improve computational accuracy significantly for photon transport.The effect of anisotropic scattering is problem-dependent,and no distinct differences among various methods are observed for volume source problems with a continuous energy source.For beam source problems,flux results are sensitive to negative scattering functions,and strictly nonnegative cross sections need to be implemented.展开更多
Producing complex fracture networks in a safe way plays a critical role in the hot dry rock (HDR) geothermal energy exploitation. However, conventional hydraulic fracturing (HF) generally produces high breakdown press...Producing complex fracture networks in a safe way plays a critical role in the hot dry rock (HDR) geothermal energy exploitation. However, conventional hydraulic fracturing (HF) generally produces high breakdown pressure and results only in single main fracture morphology. Furthermore, HF has also other problems such as the increased risk of seismic events and consuption of large amount of water. In this work, a new stimulation method based on cyclic soft stimulation (CSS) and liquid nitrogen (LN2) fracturing, known as cyclic LN2 fracturing is explored, which we believe has the potential to solve the above issues related to HF. The fracturing performances including breakdown pressure and fracture morphology on granites under true-triaxial stresses are investigated and compared with cyclic water fracturing. Cryo-scanning electron microscopy (Cryo-SEM) tests and X-ray computed tomography (CT) scanning tests were used for quantitative characterization of fracture parameters and to evaluate the cyclic LN2 fracturing performances. The results demonstrate that the cyclic LN2 fracturing results in reduced breakdown pressure, with between 21% and 67% lower pressure compared with using cyclic water fracturing. Cyclic LN2 fracturing tends to produce more complex and branched fractures, whereas cyclic water fracturing usually produces a single main fracture under a low number of cycles and pressure levels. Thermally-induced fractures mostly occur around the interfaces of different particles. This study shows the potential benefits of cyclic LN2 fracturing on HDR. It is expected to provide theoretical guidance for the cyclic LN2 fracturing application in HDR reservoirs.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11505059,11575061)the Fundamental Research Funds for Central Universities(No.2017XS087)
文摘In neutron and photon transport problems,anisotropic scattering is of great importance for the particle flux,especially when the angular flux has a strong forward peak in shielding analyses.The conventional Legendre expansion is widely used in discrete ordinates transport codes because of algebraic simplifications with spherical harmonics for the scattering source.However,negative cross sections caused by the finitely truncated expansion may give rise to a negative source and flux.A simple method is adopted,based on integrating functions of scattering moments,to evaluate anisotropy and convergence of expanded functions.A series of problems were designed with angular fluxes of different anisotropy,and numerical simulations were performed using the ARES transport code to study different treatments and algorithms for scattering.Results show that the diagonal transport approximation is more stable and obtains a similar accuracy with the extended approximation.A conservative fixup for the negative source could ensure particle balance and improve computational accuracy significantly for photon transport.The effect of anisotropic scattering is problem-dependent,and no distinct differences among various methods are observed for volume source problems with a continuous energy source.For beam source problems,flux results are sensitive to negative scattering functions,and strictly nonnegative cross sections need to be implemented.
基金supported by the Youth Program of the National Natural Science Foundation of China(52004299)Major Project of the National Natural Science Foundation of China(52192621)+2 种基金the National Science Foundation for National R&D Program for Major Research Instruments of China(51827804)Beijing Outstanding Young Scientist Program(BJJWZYJH01201911414038)the National Science Foundation for Distinguished Young Scholars of China(51725404).
文摘Producing complex fracture networks in a safe way plays a critical role in the hot dry rock (HDR) geothermal energy exploitation. However, conventional hydraulic fracturing (HF) generally produces high breakdown pressure and results only in single main fracture morphology. Furthermore, HF has also other problems such as the increased risk of seismic events and consuption of large amount of water. In this work, a new stimulation method based on cyclic soft stimulation (CSS) and liquid nitrogen (LN2) fracturing, known as cyclic LN2 fracturing is explored, which we believe has the potential to solve the above issues related to HF. The fracturing performances including breakdown pressure and fracture morphology on granites under true-triaxial stresses are investigated and compared with cyclic water fracturing. Cryo-scanning electron microscopy (Cryo-SEM) tests and X-ray computed tomography (CT) scanning tests were used for quantitative characterization of fracture parameters and to evaluate the cyclic LN2 fracturing performances. The results demonstrate that the cyclic LN2 fracturing results in reduced breakdown pressure, with between 21% and 67% lower pressure compared with using cyclic water fracturing. Cyclic LN2 fracturing tends to produce more complex and branched fractures, whereas cyclic water fracturing usually produces a single main fracture under a low number of cycles and pressure levels. Thermally-induced fractures mostly occur around the interfaces of different particles. This study shows the potential benefits of cyclic LN2 fracturing on HDR. It is expected to provide theoretical guidance for the cyclic LN2 fracturing application in HDR reservoirs.
