On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through ...On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.展开更多
Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu,according to the form of the generalized convection-diffusion equations which model...Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu,according to the form of the generalized convection-diffusion equations which model the radial porous flow with dispersion and adsorption,a local discontinuous Galerkin method for radial porous flow with dispersion and adsorption was developed,a high order accurary new scheme for radial porous flow is obtained.The presented method was applied to the numerical tests of two cases of radial porous,i.e., the convection-dispersion flow and the convection-dispersion-adsorption flow,the corresponding parts of the numerical results are in good agreement with the published solutions,so the presented method is reliable.Reckoning of the computational cost also shows that the method is practicable.展开更多
Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on ...Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.展开更多
Estimation of the transpiration rate for a tree is generally based on sap flow measurements within the hydro-active stem xylem. In this study, radial variation of sap flow velocity（Js） was investigated at five depth...Estimation of the transpiration rate for a tree is generally based on sap flow measurements within the hydro-active stem xylem. In this study, radial variation of sap flow velocity（Js） was investigated at five depths of the xylem（1, 2, 3, 5 and 8 cm under the cambium） in three mature Xinjiang poplar（Populus alba L. var. pyramidalis） trees grown at the Gansu Minqin National Studies Station for Desert Steppe Ecosystem from May to October 2011. Thermal dissipation probes of various lengths manufactured according to the Granier＇s design were installed into each tree for simultaneous observation of the radial patterns of Js through the xylem. The radial patterns were found to fit the four-parameter GaussAmp equation. The peak Js was about 27.02±0.95 kg/（dm2？d） at approximately 3 to 5 cm deep from the cambium of the three trees,and the lowest Js appeared at 1 cm deep in most of the time. Approximately 50% of the total sap flow in Xinjiang poplar occurred within one-third of the xylem from its outer radius, whereas 90% of the total sap flow occurred within two-fifth of the xylem. In addition, the innermost point of the xylem（at 8-cm depth）, which appeared as the penultimate sap flow in most cases during the study period, was hydro-active with Js,8 of 7.55±3.83 kg/（dm2？d）. The radial pattern of Js was found to be steeper in midday than in other time of the day, and steeper diurnal fluctuations were recorded in June, July and August（the mid-growing season）. Maximum differences between the lowest Js（Js,1 or Js,8） and the highest Js（Js,3 or Js,5） from May through October were 12.41, 17.35, 16.30, 18.52, 12.60 and 16.04 g/（cm2？h）, respectively. The time-dependent changes of Js along the radial profile（except at 1-cm depth） were strongly related to the reference evapotranspiration（ET0）. Due to significant radial variability of Js, the mean daily sap flow at the whole-tree level could be over-estimated by up to 29.69% when only a single probe at depth of 2 cm was used. However, the accuracy of the estimation of sap flow in Xinjiang poplar could be significantly improved using a correction coefficient of 0.885.展开更多
文摘On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.
文摘Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu,according to the form of the generalized convection-diffusion equations which model the radial porous flow with dispersion and adsorption,a local discontinuous Galerkin method for radial porous flow with dispersion and adsorption was developed,a high order accurary new scheme for radial porous flow is obtained.The presented method was applied to the numerical tests of two cases of radial porous,i.e., the convection-dispersion flow and the convection-dispersion-adsorption flow,the corresponding parts of the numerical results are in good agreement with the published solutions,so the presented method is reliable.Reckoning of the computational cost also shows that the method is practicable.
文摘Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.
基金supported by the National Natural Science Foundation of China (31070628)Field support for this research was provided by Gansu Minqin National Studies Station for Desert Steppe Ecosystem
文摘Estimation of the transpiration rate for a tree is generally based on sap flow measurements within the hydro-active stem xylem. In this study, radial variation of sap flow velocity（Js） was investigated at five depths of the xylem（1, 2, 3, 5 and 8 cm under the cambium） in three mature Xinjiang poplar（Populus alba L. var. pyramidalis） trees grown at the Gansu Minqin National Studies Station for Desert Steppe Ecosystem from May to October 2011. Thermal dissipation probes of various lengths manufactured according to the Granier＇s design were installed into each tree for simultaneous observation of the radial patterns of Js through the xylem. The radial patterns were found to fit the four-parameter GaussAmp equation. The peak Js was about 27.02±0.95 kg/（dm2？d） at approximately 3 to 5 cm deep from the cambium of the three trees,and the lowest Js appeared at 1 cm deep in most of the time. Approximately 50% of the total sap flow in Xinjiang poplar occurred within one-third of the xylem from its outer radius, whereas 90% of the total sap flow occurred within two-fifth of the xylem. In addition, the innermost point of the xylem（at 8-cm depth）, which appeared as the penultimate sap flow in most cases during the study period, was hydro-active with Js,8 of 7.55±3.83 kg/（dm2？d）. The radial pattern of Js was found to be steeper in midday than in other time of the day, and steeper diurnal fluctuations were recorded in June, July and August（the mid-growing season）. Maximum differences between the lowest Js（Js,1 or Js,8） and the highest Js（Js,3 or Js,5） from May through October were 12.41, 17.35, 16.30, 18.52, 12.60 and 16.04 g/（cm2？h）, respectively. The time-dependent changes of Js along the radial profile（except at 1-cm depth） were strongly related to the reference evapotranspiration（ET0）. Due to significant radial variability of Js, the mean daily sap flow at the whole-tree level could be over-estimated by up to 29.69% when only a single probe at depth of 2 cm was used. However, the accuracy of the estimation of sap flow in Xinjiang poplar could be significantly improved using a correction coefficient of 0.885.
