The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving ...The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.展开更多
A plane strain mode 1 crack tip field with strain gradient effects is investigated.A new strain gradient theory is used.An elastic-power law hardening strain gradient material is considered and two hardening laws,i.e....A plane strain mode 1 crack tip field with strain gradient effects is investigated.A new strain gradient theory is used.An elastic-power law hardening strain gradient material is considered and two hardening laws,i.e.a separation law and an integration law are used respectively.As for the material with the separation law hardening,the angular distributions of stresses are consistent with the HRR field,which differs from the stress results;the angular distributions of couple stresses are the same as the couple stress results.For the material with the integration law hardening,the stress field and the couple stress field can not exist simultaneously,which is the same as the conclusion,but for the stress dominated field,the an- gular distributions of stresses are consistent with the HRR field;for the couple stress dominated field,the an- gular distributions of couple stresses are consistent with those in Ref.However,the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only,while the crack tip field of mode 1 is dominated by the tension gradient,which will be shown in another paper.展开更多
The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain grad...The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dom- inant strain field is irrotational. For mode Ⅰ plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist si- multaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode Ⅱ plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode Ⅱ plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode Ⅰ and mode Ⅱ, because the present theory is based only on the rotational gradi- ent of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.展开更多
Investigated in this paper are the effects of strain gradients onthe stress distribution near an interface. The quasi-axis-symmetryinterface problem is solved by using the couple stress theory and theper- turbation me...Investigated in this paper are the effects of strain gradients onthe stress distribution near an interface. The quasi-axis-symmetryinterface problem is solved by using the couple stress theory and theper- turbation method. The results show that a boundary layer existsnear an interface or a fixed boundary, where the shear stressperpendicular to the interface is significantly different from thatobtained from the classical elasticity theory.展开更多
The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void...The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void shape effect and the Fleck-Hutchinson phenomenological strain gradient plasticity theory is employed to capture the size effects. It is found that the combined effects of void size and void shape are mainly controlled by the remote stress triaxiality. Based on this, a new size-dependent void growth model similar to the Rice-Tracey model is proposed and an important conclusion about the size-dependent void growth is drawn： the growth rate of the void with radius smaller than a critical radius rc may be ignored. It is interesting that rc. is a material constant independent of the initial void shape and the remote stress triaxiality.展开更多
In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calcula...In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calculate these terms and the modelled equations. Discrepancies between model calculations and measurements are quite often attributed to incorrect modelling, while the suitability and accuracy of the numerical methods used are seldom scrutinized. Instead, alternate near-wall and Reynolds-stress models are proposed to remedy the incorrect turbulent flow calculations. On the other hand, if care is not taken in the numerical treatment of the Reynolds-stress gradient terms, physically unrealistic results and solution instability could occur. Previous studies by the author and his collaborators on the effects of numerical methods have shown that some of the more commonly used numerical methods could enhance numerical stability in the solution procedure but would introduce considerable inaccuracy to the results. The flow cases chosen to demonstrate these inaccuracies are a backstep flow and flow in a square duct, where flow complexities are present. The current investigation attempts to show that the above-mentioned effects of numerical methods could also occur in the calculation of a developing plane channel flow, where flow complexities are absent. In addition, this study shows that the results thus obtained lead to a predicted skin friction coefficient that is influenced more by the numerical method used than by the turbulence model invoked. Together, these results show that numerical treatment of the Reynolds-stress gradients in the equations play an important role, even for a developing plane channel flow.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.51404232)the China Postdoctoral Science Foundation(Grant No.2014M561074)the National Science and Technology Major Project,China(Grant No.2011ZX05038003)
文摘The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.
基金the National Natural Science Foundation of China (No.19704100)Science Foundation of Chinese Academy of Sciences (Project KJ951-1-20)CASK.C.Wong Post-doctoral Research Award Fund and the Post Doctoral Science Fund of China.
文摘A plane strain mode 1 crack tip field with strain gradient effects is investigated.A new strain gradient theory is used.An elastic-power law hardening strain gradient material is considered and two hardening laws,i.e.a separation law and an integration law are used respectively.As for the material with the separation law hardening,the angular distributions of stresses are consistent with the HRR field,which differs from the stress results;the angular distributions of couple stresses are the same as the couple stress results.For the material with the integration law hardening,the stress field and the couple stress field can not exist simultaneously,which is the same as the conclusion,but for the stress dominated field,the an- gular distributions of stresses are consistent with the HRR field;for the couple stress dominated field,the an- gular distributions of couple stresses are consistent with those in Ref.However,the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only,while the crack tip field of mode 1 is dominated by the tension gradient,which will be shown in another paper.
文摘The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dom- inant strain field is irrotational. For mode Ⅰ plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist si- multaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode Ⅱ plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode Ⅱ plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode Ⅰ and mode Ⅱ, because the present theory is based only on the rotational gradi- ent of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.
基金the National Natural Science Foundation of China (No.19891180).
文摘Investigated in this paper are the effects of strain gradients onthe stress distribution near an interface. The quasi-axis-symmetryinterface problem is solved by using the couple stress theory and theper- turbation method. The results show that a boundary layer existsnear an interface or a fixed boundary, where the shear stressperpendicular to the interface is significantly different from thatobtained from the classical elasticity theory.
基金The project supported by the National Natural Science Foundation of China(A10102006)the New Century Excellent Talents in Universities of China.
文摘The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void shape effect and the Fleck-Hutchinson phenomenological strain gradient plasticity theory is employed to capture the size effects. It is found that the combined effects of void size and void shape are mainly controlled by the remote stress triaxiality. Based on this, a new size-dependent void growth model similar to the Rice-Tracey model is proposed and an important conclusion about the size-dependent void growth is drawn： the growth rate of the void with radius smaller than a critical radius rc may be ignored. It is interesting that rc. is a material constant independent of the initial void shape and the remote stress triaxiality.
文摘In wall-bounded turbulent flow calculations, the past focus has been directed to the modelling of the Reynolds-stress gradients. Not much attention has been paid to the effects of the numerical methods used to calculate these terms and the modelled equations. Discrepancies between model calculations and measurements are quite often attributed to incorrect modelling, while the suitability and accuracy of the numerical methods used are seldom scrutinized. Instead, alternate near-wall and Reynolds-stress models are proposed to remedy the incorrect turbulent flow calculations. On the other hand, if care is not taken in the numerical treatment of the Reynolds-stress gradient terms, physically unrealistic results and solution instability could occur. Previous studies by the author and his collaborators on the effects of numerical methods have shown that some of the more commonly used numerical methods could enhance numerical stability in the solution procedure but would introduce considerable inaccuracy to the results. The flow cases chosen to demonstrate these inaccuracies are a backstep flow and flow in a square duct, where flow complexities are present. The current investigation attempts to show that the above-mentioned effects of numerical methods could also occur in the calculation of a developing plane channel flow, where flow complexities are absent. In addition, this study shows that the results thus obtained lead to a predicted skin friction coefficient that is influenced more by the numerical method used than by the turbulence model invoked. Together, these results show that numerical treatment of the Reynolds-stress gradients in the equations play an important role, even for a developing plane channel flow.
