2018 Vol. 39, No. 10

Display Method:
A Dynamic Evolution Model for the Stimulated Reservoir Volume of the Staged Fractured Horizontal Well in Shale Gas Reservoir
REN Lan, ZHAO Jinzhou, LIN Ran, ZHOU Changlin
2018, 39(10): 1099-1114. doi: 10.21656/1000-0887.380268
Abstract(748) HTML (53) PDF(939)
For shale gas reservoir, hydraulic fracturing in horizontal well is the key technology to guarantee its commercial exploitation, and the stimulated reservoir volume (SRV) is a critical parameter deciding the post-fracturing performance. The SRV estimation plays an important role in shale gas fracturing design as well as post-fracturing evaluation, so it has become a hot topic in shale fracturing research. Based on the limitations of existing SRV estimation methods, a dynamic evolution model was built to simulate the forming process of the SRV, which coupled several vital processes during shale fracturing, including the formation stress changing, the reservoir pressure rising and the natural fracture failure mechanism. The real physical process of the SRV formation was fully considered in this model, e.g., the non-planar propagation of multiple hydraulic fractures and the SRV extending with the reservoir permeability, etc., so the model can yield more reliable results for field application. The model was firstly validated with calculated results compared with on-site micro-seismic monitored data for a fractured horizontal well in the Weiyuan shale gas field in southwest China, then it was applied to analyze the forming process and extending behavior of the SRV. The research can not only improve the SRV estimation reliability of multi-stage and multi-cluster fracturing in horizontal shale gas wells, but also provide theoretical guidelines and potential applications for fracturing design and post-fracturing evaluation.
A Semi-Analytical Model for Moving Boundary of Radial Non-Darcy Flow in Low Permeability Reservoir
HOU Shaoji, ZHU Weiping, LIU Yuewu, ZHEN Huaibin, GAO Dapeng, LI Qi
2018, 39(10): 1115-1127. doi: 10.21656/1000-0887.380330
Abstract(860) HTML (88) PDF(629)
The threshold pressure gradient (TPG) generally exists in the seepage process of low permeability reservoir. In view of characteristics of low permeability seepage, the mathematical model for the moving boundary of non-Darcy flow was established, and the formula for calculating the moving speed of the boundary was given. The Laplace transform and the infinite series method were used to obtain the model’s general solution, and the Stehfest numerical inversion was conducted. The characteristics of moving boundary problems, the boundary change and propagation were discussed and explained in detail, and the phenomenon of TPG extending outward was explicated. The TPG effects on the bottom pressure and the pressure derivative were calculated, and the Gringarten-Bourdet charts under different conditions were given. The results show that, the low pressure percolation model is significantly different from the Darcy seepage model. For low permeability cases, the pressure drop expands with time and the pressure distribution curve is of compact support. The study on the low permeability problem with moving boundary, considering the influence of the TPG and the moving boundary, provides a theoretical basis for the seepage mechanism and production performance, interpretation and numerical simulation of low permeability oil reservoirs.
Bifurcation Analysis of the ENSO Recharge Oscillator With Time-Delayed Feedback
LIU Yudan, DU Zhiyuan, ZHAO Qiang
2018, 39(10): 1128-1136. doi: 10.21656/1000-0887.380332
Abstract(591) HTML (74) PDF(625)
The time-delayed impact on a class of nonlinear ENSO recharge oscillator models was investigated through transformation of the model equations into the Van der Pol-Duffing oscillator with time-delayed feedback. The Hopf bifurcation and stable limit cycles were obtained with the averaging method. Qualitative analysis shows that equilibrium stability of the ENSO system and its oscillation are closely related to the delayed feedback amplitude and time. Finally, numerical simulations were carried out to illustrate the analytical results.
Kinematic Analysis on Drag Anchor Installation in Clay Considering Shallow Failure Effects
WU Xiaoni, HU Cun, LI Ye
2018, 39(10): 1137-1148. doi: 10.21656/1000-0887.380226
Abstract(739) HTML (101) PDF(614)
The drag anchor is widely used in offshore engineering as a foundation for the mooring system due to high capacity and low cost. The prediction of kinematic behavior and trajectory is still challenging due to the complex interaction of the anchor fluke with soil. The existing plastic yield envelope method is generally used for the kinematic analysis, where the deep anchor failure is assumed to occur during the whole dragging process. In reality, the penetration is a process of anchor fluke being dragged into seabed soil continuously from shallow to deep depths. Obviously, the existing yield envelope method could not capture the effect of shallow anchor failure, which may lead to inaccurate prediction of the anchor trajectory. Finite element analyses were conducted firstly to obtain the influences of the anchor embedment depth and angle of the fluke on the drag anchor behaviors under unidirectional and combined loadings. The yield envelope for the shallow anchor failure was determined accordingly, with which the shallow failure effect can be taken into account for the yield envelop method. The effects of the fluke angle, the bearing capacity factor and the shallow zone size were investigated. The predicted trajectories with and without the shallow failure effect were compared. It is shown that the fluke angle and the shallow failure zone size influence significantly the kinematic behaviors and the trajectory of the drag anchor. The consideration of shallow failure results in a shallower predicted anchor embedment depth and a smaller anchor line force before the anchor penetration depth stabilizes, but hardly changes the ultimate embedment depth.
An Intermittent Chaos Control Method for a Class of Symmetric Impact Systems
DU Weixia, ZHANG Sijin, YIN Shan
2018, 39(10): 1149-1158. doi: 10.21656/1000-0887.380292
Abstract(762) HTML (58) PDF(660)
An intermittent chaos control method for symmetric impact systems was studied. The Hopf bifurcation control was applied to make a new control method for chaos control of such systems. The 2DOF elastic doubleimpact system was considered. Firstly, the mechanical model for the 2DOF system was built and its motion was divided into 4 stages according to the dynamic characteristics. Then, an appropriate Poincaré mapping was established; a suitable fixed phase plane was chosen, a linear controller was applied to the section to get the mapping with control, and the chaotic control explicit condition was obtained according to the stability criterion. Finally, numerical analyses of the original system and the controlled system were carried out respectively. The numerical results show that, the proposed method controls the chaos movement of the original system well, to achieve the desired goal and verify the correctness of the method. The method, with practical significance, is helpful to improve the stability, working efficiency and service life of the system.
A Symplectic Approach for Free Vibration of Functionally Graded Double-Nanobeam Systems Embedded in Viscoelastic Medium
ZHOU Zhenhuan, LI Yuejie, FAN Junhai, SUI Guohao, ZHANG Junlin, XU Xinsheng
2018, 39(10): 1159-1171. doi: 10.21656/1000-0887.390130
Abstract(737) HTML (75) PDF(653)
A new analytical approach was proposed for free vibration of functionally graded (FG) double-nanobeam systems (DNBSs) embedded in viscoelastic medium under the framework of symplectic mechanics and the nonlocal Timoshenko beam theory. In the Hamiltonian system, the dual variables of the displacement and the rotation angle are the generalized shear force and bending moment, respectively. The high-order governing partial differential equations in the classical Lagrangian system were simplified into a set of ordinary differential equations through introduction of an unknown vector composed of the fundamental variables and their dual variables. The free vibration of DNBSs was finally reduced to an eigenproblem in the symplectic space. Analytical frequency equations and vibration mode functions were directly obtained with the symplectic eigensolutions and boundary conditions. Numerical results verify the accuracy and efficiency of the presented method. A systematic parametric study on the small size effect, the interaction between the double nanobeams and the viscoelastic foundation influence, was also provided.
Analysis on the Energy Release Rate Considering the Difference Between J-Integrals With and Without a Crack
CHEN Changrong
2018, 39(10): 1172-1179. doi: 10.21656/1000-0887.380191
Abstract(783) HTML (67) PDF(542)
The difference between the J-integrals with and without a crack along a far-field contour was considered to analyze the energy release rate of the crack extension in an infinite plane. Two material cases were studied: a homogeneous material and a layered material. The constant displacement load was applied far from the crack, the crack was assumed to be perpendicular to the load, and the interfaces of the layered material were parallel to the load. The difference between the J-integrals with and without a crack represents the change of the far-field J-integral when a crack is introduced into the loaded material. For the central crack in a homogeneous infinite plane with a unit thickness, the energy release rate is the integral of the released strain energy density along the symmetry axis, and equals the product of the strain energy density without a crack and the perimeter of a circle, where the diameter of the circle is the crack length. For the central crack in an infinite plane of the layered material with a unit thickness, the energy release rate of crack extension equals the integral of the released strain energy density along the symmetry axis minus the change of the interface J-integral.
Dynamic Problems of Mode Ⅱ Cracks in 2D Octagonal Quasicrystals
MA Qing, WANG Guixia, LI Lianhe
2018, 39(10): 1180-1188. doi: 10.21656/1000-0887.380272
Abstract(684) HTML (81) PDF(612)
Based on the elasto-hydrodynamic model, the dynamic problems of mode Ⅱ cracks in octagonal 2D quasicrystals were investigated with the finite difference scheme. The dynamic responses of stress intensity factors to different loading periods and different specimen sizes were analyzed, respectively. Then the influence of different phonon-phason coupling elastic constants on the displacement component of the phason field was demonstrated. The results indicate that, the stress intensity factor increases with the loading period, while the curve approaches the curve under the step load. The wider the specimen size is, the longer the time will be for the stress wave to reach the crack tip, and the smaller the stress intensity factor will be. The crack loading is different from the board loading, for the change of the stress intensity factor under the former is greater than that under the latter. With the increasing phonon-phason coupling constant, the displacement component of the phason field rises. Because of the influence of the phonon and phonon-phason coupling effect, the displacement component of the phason field equals zero when the phonon-phason coupling constant is zero.
Optimality Conditions for Set-Valued Vector Equilibrium Problems With Constraints Involving Improvement Sets
CHEN Wang, ZHOU Zhiang
2018, 39(10): 1189-1197. doi: 10.21656/1000-0887.390104
Abstract(767) HTML (49) PDF(442)
The optimality conditions for setvalued vector equilibrium problems with constraints were investigated in locally convex spaces. Firstly, the concepts of the E-Henig properly efficient solution and the E-super efficient solution to the setvalued vector equilibrium problems with constraints involving improvement sets were introduced. Secondly, under the assumption of the nearly E-subconvexlikeness, the sufficient and necessary conditions for the setvalued vector equilibrium problem with constraints were established in the sense of the E-Henig proper efficiency. Finally, based on the nearly E-subconvexlikeness, the necessary conditions for the setvalued vector equilibrium problem with constraints were obtained in the sense of the E-super efficiency.
Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative
YANG Na, CHEN Longwei, XIONG Mei
2018, 39(10): 1198-1205. doi: 10.21656/1000-0887.380302
Abstract(791) HTML (47) PDF(498)
With the dynamic system method, the qualitative performance and the exact solution of the general nonlinear Schr?dinger equation with derivative were studied. Through the traveling wave transformation, the corresponding ordinary differential equation was deduced and the first integral was calculated. Under different parameter space conditions, the bifurcations of the general nonlinear Schrödinger equation with derivative were investigated, and the exact traveling wave solutions were obtained, such as solitary solutions, periodic solutions as well as kink and anti-kink solutions. The solitary wave solutions were considered through numerical simulation. The results show that the present findings improve the related previous conclusions.
Connectedness of Approximate Solution Sets to Parametric Generalized Vector Equilibrium Problems
JU Xingxing, CHEN Jiawei, ZHANG Junrong, LI Gaoxi
2018, 39(10): 1206-1212. doi: 10.21656/1000-0887.380279
Abstract(885) HTML (103) PDF(549)
Several approximate solution sets to generalized vector equilibrium problems were studied. The scalarization characterization of ε-approximate solutions to parametric generalized vector equilibrium problems was established by means of the C-subconvexlike property of the involved mappings. Further, the connectedness of the 2 types of approximate solution sets was derived with the scalarization methods. Finally, the relationships among these approximate solution sets were obtained under some typical conditions.