A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ...A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.展开更多
A fracture propagation model of radial well fracturing is established based on the finite element-meshless method.The model considers the coupling effect of fracturing fluid flow and rock matrix deformation.The fractu...A fracture propagation model of radial well fracturing is established based on the finite element-meshless method.The model considers the coupling effect of fracturing fluid flow and rock matrix deformation.The fracture geometries of radial well fracturing are simulated,the induction effect of radial well on the fracture is quantitatively characterized,and the influences of azimuth,horizontal principle stress difference,and reservoir matrix permeability on the fracture geometries are revealed.The radial wells can induce the fractures to extend parallel to their axes when two radial wells in the same layer are fractured.When the radial wells are symmetrically distributed along the direction of the minimum horizontal principle stress with the azimuth greater than 15,the extrusion effect reduces the fracture length of radial wells.When the radial wells are symmetrically distributed along the direction of the maximum horizontal principal stress,the extrusion increases the fracture length of the radial wells.The fracture geometries are controlled by the rectification of radial borehole,the extrusion between radial wells in the same layer,and the deflection of the maximum horizontal principal stress.When the radial wells are distributed along the minimum horizontal principal stress symmetrically,the fracture length induced by the radial well decreases with the increase of azimuth;in contrast,when the radial wells are distributed along the maximum horizontal principal stress symmetrically,the fracture length induced by the radial well first decreases and then increases with the increase of azimuth.The fracture length induced by the radial well decreases with the increase of horizontal principal stress difference.The increase of rock matrix permeability and pore pressure of the matrix around radial wells makes the inducing effect of the radial well on fractures increase.展开更多
文摘A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.
基金Supported by the National Natural Science Foundation of China(51827804)CNPC Strategic Cooperation Science and Technology Major Project(ZLZX2020-01-05)Open Fund of State Key Laboratory of Rock Mechanics and Engineering(SKLGME021024).
文摘A fracture propagation model of radial well fracturing is established based on the finite element-meshless method.The model considers the coupling effect of fracturing fluid flow and rock matrix deformation.The fracture geometries of radial well fracturing are simulated,the induction effect of radial well on the fracture is quantitatively characterized,and the influences of azimuth,horizontal principle stress difference,and reservoir matrix permeability on the fracture geometries are revealed.The radial wells can induce the fractures to extend parallel to their axes when two radial wells in the same layer are fractured.When the radial wells are symmetrically distributed along the direction of the minimum horizontal principle stress with the azimuth greater than 15,the extrusion effect reduces the fracture length of radial wells.When the radial wells are symmetrically distributed along the direction of the maximum horizontal principal stress,the extrusion increases the fracture length of the radial wells.The fracture geometries are controlled by the rectification of radial borehole,the extrusion between radial wells in the same layer,and the deflection of the maximum horizontal principal stress.When the radial wells are distributed along the minimum horizontal principal stress symmetrically,the fracture length induced by the radial well decreases with the increase of azimuth;in contrast,when the radial wells are distributed along the maximum horizontal principal stress symmetrically,the fracture length induced by the radial well first decreases and then increases with the increase of azimuth.The fracture length induced by the radial well decreases with the increase of horizontal principal stress difference.The increase of rock matrix permeability and pore pressure of the matrix around radial wells makes the inducing effect of the radial well on fractures increase.
