Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

The nonlinear effects of unsteady multi-scale shale gas percolation,such as desorption,slippage,diffusion,pressure-dependent viscosity,and compressibility,are investigated by numerical simulation.A new general mathematical model of the problem is built,in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability.Based on the Boltzmann transformation,an efficient semi-analytical method is proposed.The problem is then converted into a nonlinear equation in an integral form for the pressure field,and a related explicit iteration scheme is constructed by numerical discretization.The validation examples show that the proposed method has good convergence,and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature.Desorption,slippage,and diffusion have significant influence on shale gas flows.The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.     

指数二分性与高阶Melnikov函数

本文利用指数二分性理论和Liapunov－Schmidt方法，研究了当Melnikov函数具有高阶零点时的横截同宿轨道的存在性，得到了一个所谓的高阶Melnikov函数     

BIFURCATION OF DEGENERATE HOMOCLINIC ORBITS

ＢＩＦＵＲＣＡＴＩＯＮＯＦＤＥＧＥＮＥＲＡＴＥＨＯＭＯＣＬＩＮＩＣＯＲＢＩＴＳ￥ＺｅｎｇＷｅｉｙａｏ（ＨｕｎａｎＬｉｇｈｔｉｎｄｕｓｔｒｙＣｏｌｌｅｇｅ，４１０００７）Ａｂｓｔｒａｃｔ：Ｔｈｅｍａｉｎｐｕｒｐｏｓｅｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｉｎｖ...     

关于и.г.малкин的一个问题

本文证明了若系统有一致连续的偏导数,则系统的零解在经常扰动下稳定可推出零解一致指数型渐近稳定。     

Investigation on nonlinear multi-scale effects of unsteady flow in hydraulic fractured horizontal shale gas wells

A unified mathematical model is established to simulate the nonlinear unsteady percolation of shale gas with the consideration of the nonlinear multi-scale effects such as slippage, diffusion, and desorption. The continuous inhomogeneous models of equivalent porosity and permeability are proposed for the whole shale gas reservoir including the hydraulic fracture, the micro-fracture, and the matrix regions. The corresponding semi-analytical method is developed by transforming the nonlinear partial differential governing equation into the integral equation and the numerical discretization. The non-linear multi-scale effects of slippage and diffusion and the pressure dependent effect of desorption on the shale gas production are investigated.     

Encapsulation of tricopper cluster in a synthetic cryptand enables facile redox processes from CuICuICuI to CuIICuIICuII states

One-pot reaction of tris(2-aminoethyl)amine (TREN), [Cu^I(MeCN)₄]PF₆, and paraformaldehyde affords a mixed-valent [TREN₄Cu^IICu^ICu^I(μ₃-OH)](PF₆)₃ complex. The macrocyclic azacryptand TREN₄ contains four TREN motifs, three of which provide a bowl-shape binding pocket for the [Cu₃(μ₃-OH)]³⁺ core. The fourth TREN caps on top of the tricopper cluster to form a cryptand, imposing conformational constraints and preventing solvent interaction. Contrasting the limited redox capability of synthetic tricopper complexes reported so far, [TREN₄Cu^IICu^ICu^I(μ₃-OH)](PF₆)₃ exhibits several reversible single-electron redox events. The distinct electrochemical behaviors of [TREN₄Cu^IICu^ICu^I(μ₃-OH)](PF₆)₃ and its solvent-exposed analog [TREN₃Cu^IICu^IICu^II(μ₃-O)](PF₆)₄ suggest that isolation of tricopper core in a cryptand enables facile electron transfer, allowing potential application of synthetic tricopper complexes as redox catalysts. Indeed, the fully reduced [TREN₄Cu^ICu^ICu^I(μ₃-OH)](PF₆)₂ can reduce O₂ under acidic conditions. The geometric constraints provided by the cryptand are reminiscent of Nature''s multicopper oxidases (MCOs). For the first time, a synthetic tricopper cluster was isolated and fully characterized at Cu^ICu^ICu^I (4a), Cu^IICu^ICu^I (4b), and Cu^IICu^IICu^I (4c) states, providing structural and spectroscopic models for many intermediates in MCOs. Fast electron transfer rates (10⁵ to 10⁶ M⁻¹ s⁻¹) were observed for both Cu^ICu^ICu^I/Cu^IICu^ICu^I and Cu^IICu^ICu^I/Cu^IICu^IICu^I redox couples, approaching the rapid electron transfer rates of copper sites in MCO.

Geometric constraints and site isolation provided by the cryptand enable reversible redox of tricopper μ-oxo cluster.     

Liquid Transport Through Nanoscale Porous Media with Strong Wettability

Transport in Porous Media - It is important to investigate interfacial effects on liquid transport characteristics through nanopores with strong wettability due to potential applications in several...     

低渗油层压裂水平井两相流研究

依据压裂水平井不同流动区域的流动规律, 将压裂水平井的渗流分为裂缝中的高速非达西流 动区、裂缝控制影响的椭圆渗流区、远离裂缝的基质非达西渗流区, 考虑启动压力梯度的影 响, 对压裂水平井两相渗流进行了分析, 得到了低渗透油层压裂水平井的产量公式. 研究结 果表明, 裂缝的导流能力越大, 压裂水平井的产量越高. 但随着开采时间的增加, 其产量递减幅度越 大; 压裂裂缝长度越小, 压裂水平井的初始产量越高. 但随着生产时间的推移, 压裂裂缝的 长度越大, 产量的递减幅度越小; 中间裂缝长, 两翼裂缝短的情况下, 压裂水平井的产量最 高.     

页岩气致密储层渗流模型及压裂直井产能分析

页岩气储层中存在大量的纳微米孔隙,其中气体的流动规律不同于常规气藏. 文章考虑克努森扩散及解吸作用的影响,建立页岩气稳态条件下产能公式,利用渗流阻力法得到了页岩气储层压裂直井产能方程.结合生产实例,进行了数值模拟计算. 结果表明：当裂缝导流能力达到0.12μm²·cm 后,产气量增幅减小,由此对裂缝导流能力进行优化. 游离气产量占总产气量的85%～90%,游离气对总产气量贡献较大. 该模型为页岩气产能预测及开发指标优化提供了理论依据.     

Emerging weak antilocalization effect in Ta0.7Nb0.3Sb2 semimetal single crystals

Weak antilocalization (WAL) effect is commonly observed in low-dimensional systems, three-dimensional (3D) topological insulators and semimetals. Here, we report the growth of high-quality Ta_0.7Nb_0.3Sb₂ single crystals via the chemical vapor transport (CVT). Clear sign of the WAL effect is observed below 50 K, probably due to the strong spin−orbital coupling in 3D bulk. In addition, it is worth noting that a relatively large MR of 120% appears under 1 T magnetic field at T = 2 K. Hall measurements and two-band model fitting results reveal high carrier mobility (>1000 cm²·V⁻¹·s⁻¹ in 2–300 K region), and off-compensation electron/hole ratio of ~8:1. Due to the angular dependence of the WAL effect and the fermiology of the Ta_0.7Nb_0.3Sb₂ crystals, interesting magnetic-field-induced changes of the symmetry of the anisotropic magnetoresistance (MR) from two-fold (≤ 0.6 T) to four-fold (0.8–1.5 T) and finally to two-fold (≥ 2 T) are observed. This phenomenon is attributed to the mechanism shift from the low-field WAL dominated MR to WAL and fermiology co-dominated MR and finally to high-field fermiology dominated MR. All these signs indicate that Ta_0.7Nb_0.3Sb₂ may be a topological semimetal candidate, and these magnetotransport properties may attract more theoretical and experimental exploration of the (Ta,Nb)Sb₂ family.