天然气水合物降压开采沉积物压缩效应数值模拟研究

深海天然气水合物降压开采过程中,沉积物的压缩会改变储层的物理力学特性,进而对天然气的开采效果产生显著影响.为揭示沉积物压缩效应下井周围储层物理力学特性演化规律,本文建立了考虑沉积物压缩效应的理论模型,通过COMSOL模拟研究了不同初始固有渗透率、初始水合物饱和度和井底压力条件下的降压开采中生产井周围储层的物理力学特性演化规律以及开采效果.结果表明:受沉积物压缩的影响,水合物分解区的渗透率随着与井筒距离的增加先增加后减少;产气与产水速率由零立即上升至峰值,然后迅速下降,并且考虑沉积物压缩时的产气与产水速率比不考虑时低;在水合物完全分解区,渗透率的大小与有效应力成负相关关系,未分解区渗透率的大小与水合物饱和度成负相关关系;井底压力越小,有效应力越大,生产井周围储层的渗透率下降越明显;初始水合物饱和度对产气与产水的影响存在拐点,饱和度拐点位于0.25与0.35之间,高水合物饱和度并不代表储层开采效果好,产气速率的高低还与储层的渗透率有关,高水合物饱和度储层的渗透率较低,产气速率较低;储层初始固有渗透率较高时显著促进了开采效果,但储层变形量较大增加了储层的不稳定性.     

Features of failure waves in highly-homogeneous brittle materials

To describe the deformation and evolution of damage of glassy brittle materials, a kinetic model, which takes into account the transformation of elastic energy into surface energy, is proposed. The failure kinetics are characterized by a power dependence on the dynamic overload, which is equal to the difference between the rates of change of elastic and surface energies relative to the increase in damage of the medium. The model is applied to the problem of a plane failure wave in a half-space arising from the application of a normal load to the boundary. An approximate asymptotic solution is constructed by combining the two power series for the regions of slow and rapid change of the solution. As found in previous experiments, at moderate loads the values of the velocity and longitudinal stress in the regions of elasticity and the failed state of the material are the same. As the load increases, the distribution of these quantities become two-wave, the amplitude of the forerunner being greater than the elastic limit under uniaxial compression. In that case the structure of the failure wave largely depends on the power index of the kinetic function in the neighbourhood of the static state. If the index is less than one, the kinetics exerts an influence only in a finite neighbourhood of the failure front.     

A new fractional derivative for solving time fractional diffusion wave equation

The time fractional diffusion wave equation, which can be used to describe wave diffusion process in this article, was studied. First of all, the diffusion wave equation can be extended to a generalized form in the sense of the regularized version of the $k$-Hilfer–Prabhakar ( $k$-H-P) fractional operator involving the $k$-Mittag- function. Then, the analytical solution can be obtained for this considered equation by using the Laplace transform method and the Fourier transform method. As a result, a novel and general solution have been found. The unconventional solution may show new result and phenomenon to wave diffusion process. Thereby, this research provides a window for discovering new diffusion mechanisms.