页岩气高效开采的力学问题与挑战

页岩气是指赋存于富含有机质泥页岩中以吸附和游离状态为主要存在方式的天然气,中国资源量丰富,地域分布广泛.页岩气开采能缓解我国常规油气产量不足、煤化石燃料引起环境污染等问题,已成为中国绿色能源开发的重要领域.尽管北美页岩气"革命"取得了成功,目前也仅有预期产量5%～15%的采收率.与北美地区相比,中国页岩气埋藏深,赋存条件差,自然丰度低,因此,高效开采面临更多的困难和挑战.近年来,围绕国家重大能源战略需求,瞄准技术发展前沿,学术界和工业界联合对页岩气高效开采的关键科学和技术问题展开研究.本文结合近三年四川、重庆地区的页岩气试验区块遇到的新问题,针对中国未来3 500 m以下深部开采的新挑战,如地质沉积、裂缝发育构造不同、上覆压力增加、水平应力场变化等新问题,介绍和总结了目前中国页岩气高效开采面临的力学科学问题,主要包括多重耦合下的安全优质钻完井力学理论和方法、水力压裂体积改造和多尺度缝网形成机制、多尺度渗流力学特性与解吸附机理等."深部页岩气高效开采"的研究面向国家重大能源需求,科学意义重大,工程背景明确,需要工程力学、石油工程、地球物理、化学工程和环境工程等多学科专家合作,开展理论研究、物理模拟、数值模拟及现场试验等综合应用基础研究,取得高效开采页岩油气理论与技术的突破.学科交叉是研究页岩气高效开采问题、突破技术瓶颈的桥梁,只有力学与石油工程、地球科学等学科实现深度交叉融合,才能更加有效地推动页岩油气等非常规油气资源的开发.     

On IOM(q): The Incomplete Orthogonalization Method for Large Unsymmetric Linear Systems

The incomplete orthogonalization method (IOM(q)), a truncated version of the full orthogonalization method (FOM) proposed by Saad, has been used for solving large unsymmetric linear systems. However, no convergence analysis has been given. In this paper, IOM(q) is analysed in detail from a theoretical point of view. A number of important results are derived showing how the departure of the matrix A from symmetric affects the basis vectors generated by IOM(q), and some relationships between the residuals for IOM(q) and FOM are established. The results show that IOM(q) behaves much like FOM once the basis vectors generated by it are well conditioned. However, it is proved that IOM(q) may generate an ill-conditioned basis for a general unsymmetric matrix such that IOM(q) may fail to converge or at least cannot behave like FOM. Owing to the mathematical equivalence between IOM(q) and the truncated ORTHORES(q) developed by Young and Jea, insights are given into the convergence of the latter. A possible strategy is proposed for choosing the parameter q involved in IOM(q). Numerical experiments are reported to show convergence behaviour of IOM(q) and of its restarted version.     

Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

Based on the nonlocal theory and Mindlin plate theory, the governing equations (i.e., a system of partial differential equations (PDEs) for bending problem) of magnetoelectroelastic (MEE) nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle. The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions (MPS) to solve the governing equations numerically. It is confirmed that for the present bending model, the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points. The effects of different boundary conditions, applied loads, and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method. Some important conclusions are drawn, which should be helpful for the design and applications of electromagnetic nanoplate structures.     

计算奇异摄动法在燃烧反应系统简化中的应用

采用计算奇异摄动法构造典型燃烧反应系统的简化化学动力模型,基于燃烧反应控制方程寻找理想基向量,借助所得理想基向量实现快慢反应模态间的解耦,并给出参与性指数、原子团指针和重要性指数等关键参数,进而构造快模态状态方程和简化化学动力模型.典型CO-CH₄-Air混合燃烧反应系统的计算结果表明,由计算奇异摄动法得到的简化燃烧反应系统是原燃烧反应系统很好的近似.     

Extension of Whittaker equations to non-holonomic mechanical systems

In 1904, using the energy integral Whittaker studied the reduction of a dynamical problem to a problem with fewer degrees of freedom for the holonomic conservative systems and obtained the Whittaker equation^[1].In this article, Whittaker equations are extended to non-holonomic systems and the generalized Whittaker equations are obtained. And then these equations are transformed into Kiel-sen’s form.Finally an example is given.     

完全分配格序群的基和阿基米德核

本文对Redfield R.(Bases in completely distributive laffice-orderedgroups)定义的B-根作了推广,定义了B_n-根。在此基础上讨论了基和完全分配性及阿基米德核之间的关系,使该文中的主要结果只是本文的推论。     

箱式封闭油藏中水平井压力分析

本文研究了箱式封闭油藏水平井之三维不定常渗流问题。用积分变换、汇源叠加等方法求得其数学模型的Laplace变换解式并建立了快速、实用的应用方法,其中包括:水平井压力分布公式、井壁压力典型曲线计算方法、控制参数(团)调参分析。因而本文的结果可方便地用于水平井不稳定试井资料的分析与解释。     

孪函数N电子基向Slater多电子反对称基的展开

发展了一套孪函数多电子基向Slater行列式的展开方法,并得到展开系数的解析表达式,使得孪函数多电子基直接与Hartree-Fock从头计算相关联.     

Hybrid changeable basis galerkin technique for nonlinear analysis of structures

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TWO－PHASE FLOW FOR A HORIZONTAL WELL PENETRATING A NATURALLY FRACTURED RESERVOIR WITH EDGE WATER INJECTION

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