Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent...Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameteri- zation in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in trans- versely homogeneous elliptically anisotropic media. Seis- mic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in ellipti- cally anisotropic media with an irregular surface.展开更多
The injection of fuel-generated CO2 into oil reservoirs will lead to two benefits in both enhanced oil recovery （EOR） and the reduction in atmospheric emission of CO2. To get an insight into CO2 miscible flooding pe...The injection of fuel-generated CO2 into oil reservoirs will lead to two benefits in both enhanced oil recovery （EOR） and the reduction in atmospheric emission of CO2. To get an insight into CO2 miscible flooding performance in oil reservoirs, a multi-compositional non-isothermal CO2 miscible flooding mathematical model is developed. The convection and diffusion of CO2-hydrocarbon mixtures in multiphase fluids in reservoirs, mass transfer between CO2 and crude, and formation damages caused by asphaltene precipitation are fully considered in the model. The governing equations are discretized in space using the integral finite difference method. The Newton-Raphson iterative technique was used to solve the nonlinear equation systems of mass and energy conservation. A numerical simulator, in which regular grids and irregular grids are optional, was developed for predicting CO2 miscible flooding processes. Two examples of one-dimensional （1D） regular and three-dimensional （3D） rectangle and polygonal grids are designed to demonstrate the functions of the simulator. Experimental data validate the developed simulator by comparison with 1D simulation results. The applications of the simulator indicate that it is feasible for predicting CO2 flooding in oil reservoirs for EOR.展开更多
A finite-difference method with spatially non-uniform grids was developed to simulate elastic wave propagation in heterogeneous anisotropic media. The method is very simple and requires less compution time. Complicate...A finite-difference method with spatially non-uniform grids was developed to simulate elastic wave propagation in heterogeneous anisotropic media. The method is very simple and requires less compution time. Complicated geometric structures, such as low-velocity layers, cased boreholes and nonplanar interfaces, are treated with fine non-uniform grids. Unlike the multi-grid scheme, this method does not require interpolation between the fine and coarse grids and all grids are computed in the same spatial iteration. Planar or nonplanar surfaces including underground lens and cased boreholes are easily treated in a way similar to regular grid points. The Higdon抯 absorbing boundary condition was used to eliminate boundary reflections. Numerical simulations show that the method has satisfactory stability and accuracy. The proposed scheme more efficiently simulates wave propagation in heterogeneous anisotropic media than conventional methods using regular rectangular grids of equal accuracy.展开更多
In this paper, a mathematical model for the urban rainstorm water logging wasestablished on the basis of one- and two-dimensional unsteady flow theory and the technique ofnon-structural irregular grid division. The co...In this paper, a mathematical model for the urban rainstorm water logging wasestablished on the basis of one- and two-dimensional unsteady flow theory and the technique ofnon-structural irregular grid division. The continuity equation was discretized with the finitevolume method. And the momentum equations were differently simplified and discretized for differentcases. A method of ''special passage'' was proposed to deal with small-scale rivers and open channels.The urban drainage system was simplified and simulated in the model. The method of ''open slot'' wasapplied to coordinate the alternate calculation of open channel flow and pressure flow in drainagepipes. The model has been applied in Tianjin City and the verification is quite satisfactory.展开更多
The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) descr...The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.展开更多
High-resolution global non-hydrostatic gridded dynamic models have drawn significant attention in recent years in conjunction with the rising demand for improving weather forecasting and climate predictions.By far it ...High-resolution global non-hydrostatic gridded dynamic models have drawn significant attention in recent years in conjunction with the rising demand for improving weather forecasting and climate predictions.By far it is still challenging to build a high-resolution gridded global model,which is required to meet numerical accuracy,dispersion relation,conservation,and computation requirements.Among these requirements,this review focuses on one significant topic—the numerical accuracy over the entire non-uniform spherical grids.The paper discusses all the topic-related challenges by comparing the schemes adopted in well-known finite-volume-based operational or research dynamical cores.It provides an overview of how these challenges are met in a summary table.The analysis and validation in this review are based on the shallow-water equation system.The conclusions can be applied to more complicated models.These challenges should be critical research topics in the future development of finite-volume global models.展开更多
基金financial support for this work contributed by the National Key Research and Development Program of China(Grants Nos.2016YFC0600101,2016YFC0600201 and 2016YFC0600302)the National Natural Science Foundation of China(Grants Nos.41522401 and 41474068)
文摘Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameteri- zation in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in trans- versely homogeneous elliptically anisotropic media. Seis- mic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in ellipti- cally anisotropic media with an irregular surface.
基金Parts of this work were supported by the National Science and Technology Major Projects (2011ZX05009-002, 2011ZX05009–006)the Fundamental Research Funds for the Central Universities, the Project-sponsored by SRF for ROCS, SEM, and the joint research on "Investigation of Mathematical Models and Their Applications for Oil, Water and CO2 Flow in Reservoirs" between Colorado School of Mines, U.S.A and PetroChina Research Institute of Petroleum Exploration & Development (RIPED), CNPC, China
文摘The injection of fuel-generated CO2 into oil reservoirs will lead to two benefits in both enhanced oil recovery （EOR） and the reduction in atmospheric emission of CO2. To get an insight into CO2 miscible flooding performance in oil reservoirs, a multi-compositional non-isothermal CO2 miscible flooding mathematical model is developed. The convection and diffusion of CO2-hydrocarbon mixtures in multiphase fluids in reservoirs, mass transfer between CO2 and crude, and formation damages caused by asphaltene precipitation are fully considered in the model. The governing equations are discretized in space using the integral finite difference method. The Newton-Raphson iterative technique was used to solve the nonlinear equation systems of mass and energy conservation. A numerical simulator, in which regular grids and irregular grids are optional, was developed for predicting CO2 miscible flooding processes. Two examples of one-dimensional （1D） regular and three-dimensional （3D） rectangle and polygonal grids are designed to demonstrate the functions of the simulator. Experimental data validate the developed simulator by comparison with 1D simulation results. The applications of the simulator indicate that it is feasible for predicting CO2 flooding in oil reservoirs for EOR.
基金the Chinese National Petroleum Corporation Foundation (No. 2002CXKF-4)
文摘A finite-difference method with spatially non-uniform grids was developed to simulate elastic wave propagation in heterogeneous anisotropic media. The method is very simple and requires less compution time. Complicated geometric structures, such as low-velocity layers, cased boreholes and nonplanar interfaces, are treated with fine non-uniform grids. Unlike the multi-grid scheme, this method does not require interpolation between the fine and coarse grids and all grids are computed in the same spatial iteration. Planar or nonplanar surfaces including underground lens and cased boreholes are easily treated in a way similar to regular grid points. The Higdon抯 absorbing boundary condition was used to eliminate boundary reflections. Numerical simulations show that the method has satisfactory stability and accuracy. The proposed scheme more efficiently simulates wave propagation in heterogeneous anisotropic media than conventional methods using regular rectangular grids of equal accuracy.
文摘In this paper, a mathematical model for the urban rainstorm water logging wasestablished on the basis of one- and two-dimensional unsteady flow theory and the technique ofnon-structural irregular grid division. The continuity equation was discretized with the finitevolume method. And the momentum equations were differently simplified and discretized for differentcases. A method of ''special passage'' was proposed to deal with small-scale rivers and open channels.The urban drainage system was simplified and simulated in the model. The method of ''open slot'' wasapplied to coordinate the alternate calculation of open channel flow and pressure flow in drainagepipes. The model has been applied in Tianjin City and the verification is quite satisfactory.
基金supported by the National Natural Science Foundation of China (Grant No. 11002029)
文摘The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.
基金Supported by the National Key Research and Development Program of China(2017YFC1502201)Basic Scientific Research and Operation Fund of Chinese Academy of Meteorological Sciences(2017Z017)。
文摘High-resolution global non-hydrostatic gridded dynamic models have drawn significant attention in recent years in conjunction with the rising demand for improving weather forecasting and climate predictions.By far it is still challenging to build a high-resolution gridded global model,which is required to meet numerical accuracy,dispersion relation,conservation,and computation requirements.Among these requirements,this review focuses on one significant topic—the numerical accuracy over the entire non-uniform spherical grids.The paper discusses all the topic-related challenges by comparing the schemes adopted in well-known finite-volume-based operational or research dynamical cores.It provides an overview of how these challenges are met in a summary table.The analysis and validation in this review are based on the shallow-water equation system.The conclusions can be applied to more complicated models.These challenges should be critical research topics in the future development of finite-volume global models.
