Finite element analysis of wave propagation in fluid-saturated porous media

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含液多孔介质力学问题的边界元方法

提出了一种含液多孔介质力学问题的边界元求解方法.首先将问题分解为一系列含单孔流体夹杂的子问题,然后针对每个子问题建立了流体孔体积变化率与流体压力之问的函数关系,进一步采用边界元方法建立了以各流体孔压力为基本未知量的线性代数方程组,最后根据所求出的各流体孔的压力计算含液多孔介质内各点的位移、变形和应力.为了说明方法的有效...     

Characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media

According to generalized characteristic theory, a characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media was performed. The characteristic differential equations and compatibility relations along bicharacteristics were deduced and the analytical expressions for wave surfaces were obtained. The characteristic and shapes of the velocity surfaces and wave surfaces in the transversely isotropic fluid-saturated porous media were discussed in detail. The results also show that the characteristic equations for stress waves in pure solids are particular cases of the characteristic equations for fluid-saturated porous media.     

正交各向异性含液饱和多孔介质中应力波的传播

基于Biot的孔隙介质理论，研究了正交各向异性含液饱和多孔介质中应力波的传播特性．本文引入动态渗透率，导出了整个实频域内应力波传播的复特征方程及其解析解，给出了各种应力波成分的波速和衰减的解析表达武，计算了频散曲线和衰减曲线，并讨论了各类应力波之间的耦合关系及介质的各向异性对应力波传播的影响．     

Rayleigh waves in orthotropic fluid-saturated porous media

In this paper, we are interested in the propagation of Rayleigh waves in orthotropic fluid-saturated porous media. This problem was investigated by Liu and Liu (2004). The authors have derived the secular equation of the wave but that secular equation is still in implicit form. The main aim of this paper is to derive explicit secular equation of the wave. By employing the method of polarization vector, the secular equations of Rayleigh waves in explicit form is obtained. This equation recovers the dispersion equation of Rayleigh waves propagating in pure orthotropic elastic half-spaces. Remarkably, the secular equation obtained is not a complex equation as the one derived by Liu and Liu, it is a really real equation.     

Parameters inversion of fluid-saturated porous media based on neural networks

The multi-layers feedforward neural network is used for inversion of material constants of fluid-saturated porous media. The direct analysis of fluid-saturated porous media is carried out with the boundary element method. The dynamic displacement responses obtained from direct analysis for prescribed material parameters constitute the sample sets training neural network. By virtue of the effective L-M training algorithm and the Tikhonov regularization method as well as the GCV method for an appropriate selection of regularization parameter, the inverse mapping from dynamic displacement responses to material constants is performed. Numerical examples demonstrate the validity of the neural network method. Project supported by the National Natural Science Foundation of China (Nos. 19872002 and 10272003) and Climbing Foundation of Northern Jiaotong University.     

流体饱和两相多孔介质拟静态问题的混合有限元方法

针对基于混合物理论的两相多孔介质模型,采用Galerkin加权残值有限元法,导出求解所静态问题的基于us-uF-P变量的混合有限元方程,由于系统方程的系数矩阵非定,进而针对该方程组提出了一种失代求解方法,并由分片试验得出节点压力插值函数的阶须低于固体相节点的位移插值函数的阶的结论,算例结果表明,采用基于u2-uF-p变量的混合法计算所得的固体相和流体相速度以及固体相的有效应力与罚方法一致,而压力值的粗度高于罚方法。     

双相介质P波波动方程小波域多尺度模拟

相比于单相介质理论而言,双相介质理论更接近实际地层的真实情况,因此在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用。传统的波动方程数值解法由于本身固有的不足不利于求解诸如双相介质波动方程等复杂的非线性和不规则性问题;而小波方法则由于自身良好的特性可以用来构建解决此类问题的自适应性算法。本文详细推导了双相介质P波波动方程的有限差分矩阵表示形式,利用小波变换将其转移到小波域,设置阈值形成更为稀疏的迭代矩阵以构建自适应算法,从而达到减少计算量,增加地震波场数值模拟灵活性和准确性的目的。地球物理勘探的数值模拟实例验证了方法的有效性。     

基于显式有限元方法的两相介质弹塑性动力反应计算分析

针对增量形式的流体饱和两相多孔介质弹塑性波动方程组,运用基于显式逐步积分格式的时域显式有限元方法对该波动方程组进行求解,并应用基于SMP破坏准则的弹塑性动力本构模型描述两相介质的动力反应性质,对两相介质在输入地震波作用下的弹塑性动力反应进行计算和分析,将计算结果与相应的弹性动力反应的计算结果进行对比;对本文应用的弹塑性...     

Numerical simulation and homogenization of two-phase flow in heterogeneous porous media

A mathematically rigorous method of homogenization is presented and used to analyze the equivalent behavior of transient flow of two incompressible fluids through heterogeneous media. Asymptotic expansions and H-convergence lead to the definition of a global or effective model of an equivalent homogeneous reservoir. Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method. Numerical experiments involving the simulation of incompressible two-phase flow have been performed for each heterogeneous medium and for the homogenized medium as well as for other averaging methods. The results of the simulations are compared in terms of the transient saturation contours, production curves, and pressure distributions. Results obtained from the simulations with the homogenization method presented show good agreement with the heterogeneous simulations.     

Averaging methods for numerical simulations of flows through heterogeneous porous media

Many natural rock systems contain small patches of different permeability which affect the flow of fluids through them. As these heterogeneities become smaller and more numerous, they become harder to model numerically. We consider how to reduce the computational effort required in simulations by incorporating their effects in the boundary conditions at the edges of each grid block. This is in contrast with current methods which involve often arbitrary changes in the fluid properties. The method is restricted to the case of widely-spaced patches, which simplifies interaction effects. The system then reduces to an array of dipoles, and two averaging methods are proposed for finite grid blocks. Several infinite systems, including vertical and horizontal bands, are also considered as further approximations. There is a great wealth of existing results from different fields which lead to identical mathematical problems and which can be used in these cases. Finally, we consider how to use these techniques when the precise configuration of the grid block is not known, but only its statistical properties. This can lead to results which are very different from the deterministic case.     

Rayleigh waves in anisotropic porous media and the polarization vector method

In this paper, the propagation of Rayleigh waves in orthotropic non-viscous fluid-saturated porous half-spaces with sealed surface-pores and with impervious surface is investigated. The main aim of the investigation is to derive explicit secular equations and based on them to examine the effect of the material parameters and the boundary conditions on the propagation of Rayleigh waves. By employing the method of polarization vector the explicit secular equations have been derived. These equations recover the ones corresponding to Rayleigh waves propagating in purely elastic half-spaces. It is shown from numerical examples that the Rayleigh wave velocity depends strongly on the porosity, the elastic constants, the anisotropy, the boundary conditions and it differs considerably from the one corresponding to purely elastic half-spaces. Remarkably, in the fluid saturated porous half-spaces, Rayleigh waves may travel with a larger velocity than that of the shear wave, a fact that is impossible for the purely elastic half-spaces.     

Seismic propagation simulation in complex media with non-rectangular irregular-grid finite-difference

This paper presents a finite-difference (FD) method with spatially non-rectangular irregular grids to simulate the elastic wave propagation. Staggered irregular grid finite difference operators with a second-order time and spatial accuracy are used to approximate the velocity-stress elastic wave equations. This method is very simple and the cost of computing time is not much. Complicated geometries like curved thin layers, cased borehole and nonplanar interfaces may be treated with nonrectangular irregular grids in a more flexible way. Unlike the multi-grid scheme, this method requires no interpolation between the fine and coarse grids and all grids are computed at the same spatial iteration. Compared with the rectangular irregular grid FD, the spurious diffractions from “staircase” interfaces can easily be eliminated without using finer grids. Dispersion and stability conditions of the proposed method can be established in a similar form as for the rectangular irregular grid scheme. The Higdon‘s absorbing boundary condition is adopted to eliminate boundary reflections. Numerical simulations show that this method has satisfactory stability and accuracy in simulating wave propagation near rough solid-fluid interfaces. The computation costs are less than those using a regular grid and rectangular grid FD method.     

饱和两相介质动力固结问题时域求解的精细时程积分方法

针对u-p形式的饱和两相介质波动方程,采用精细时程积分方法计算固相位移u,采用向后差分算法求解流体压力p,建立了饱和两相介质动力固结问题时域求解的精细时程积分方法。针对标准算例,对该方法的计算精度进行了校核。开展了该方法相关算法特性的研究,对采用不同数值积分方法计算非齐次波动方程特解项计算精度的差异进行了对比研究,并对采用不同积分点数目的高斯积分法计算特解项条件下计算精度的差异进行了对比研究。研究结果表明,(1)该方法具有良好的计算精度。(2)计算非齐次波动方程特解项的数值积分方法中,梯形积分法的计算精度最差,高斯积分法、辛普生积分法和科茨积分法都具有较好的计算精度。(3)增加高斯积分点数目对于提高计算精度的作用并不显著。     

Multiresolution Symplectic Scheme for wave propagation in complex media

A fast adaptive symplectic algorithm named Multiresolution Symplectic Scheme (MSS) was first presented to solve the problem of the wave propagation (WP) in complex media, using the symplectic scheme and Daubechies‘ compactly supported orthogonal wavelet transform to respectively discretise the time and space dimension of wave equation. The problem was solved in multiresolution symplectic geometry space under the conservative Hamiltonian system rather than the traditional Lagrange system. Due to the fascinating properties of the wavelets and symplectic scheme, MSS is a promising method because of little computational burden, robustness and reality of long-time simulation.     

剧变截面圆管内渗流的数值计算方法

对于剧变截面圆管的渗流问题写出不可压缩渗流的基本方程组,对直接求解原始变量(速度和压力)的数值计算方法作出改进。先由非主流方向的运动方程计算压力,后由主流方向的运动方程计算主流方向的速度分量,再由连续性方程计算非主流方向的速度分量。这样可以避免在一般的求解原始变量方法中由连续性方程计算压力时出现的困难和麻烦。根据本方法和剧变截面圆管的特点,采用半交错不等距非正交贴体混合网格系。本文详细写出差分方程和迭代计算公式,对剧变截面圆管内的渗流算例进行数值计算。本方法的优点是简单和实用,在工程上具有较大的应用价值。     

A non-linear analysis of non-isothermal wave propagation in linear-elastic fluid-saturated porous media

The non-isothermal dynamic behaviour of saturated porous media is analysed numerically employing the finite element method and taking energy convection due to large pore fluid displacements into account. A different pore fluid reference temperature is introduced in order to allow properly for heat convection: this concept is usually neglected in the literature and is discussed and analysed herein. The numerical procedure is validated in a simple problem of hot fluid injection in a steady seepage flow and by comparing the numerical results, neglecting energy convection, with those obtained with a novel solution of the linearised equations, presented herein, which is based on the transfer functions and Fourier transforms method. Finally, the effects of energy convection in wave propagation are analysed: in a pervious porous medium the flux of energy due to energy convection is much greater than the one due to heat conduction; in any case, wave propagation can be considered completely adiabatic even when energy convection is taken into account. Thus the validity of the results presented in the literature and based on the linearised theory is demonstrated.     

Penalty finite element method for nonlinear dynamic response of viscous fluid-saturated biphase porous media

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饱和多孔介质大变形分析的一种有限元-有限体积混合方法

建立了饱和多孔介质大变形分析的一种有限元-有限体积混合计算方法.将饱和多孔介质视为由固体骨架和孔隙水组成的两相体,其基本方程包括动力平衡方程和渗流连续方程.基于u-p假定和更新的Lagrange方法,饱和多孔介质的动力平衡方程在空间域内采用有限元方法进行离散,而渗流连续方程在空阃域内则采用有限体积法进行离散.通过两个数值算例,一维有限弹性固结和动力荷载作用下堤坝动力响应的计算,验证了该方法的有效性.     

Weighted average flux method and flux limiters for the numerical simulation of shock waves in rigid porous media

The one‐dimensional flow field generated by the passage of a shock wave in a rigid, thermoelastic porous foam has been simulated using a two‐phase mathematical model. The work presented here makes use of the weighted average flux method to solve the system of six equations that govern the problem. Spurious oscillations are eliminated through the application of total variation diminishing limiting methods. Four different limiters were tested: van Leer, SuperA, MinA and van Albada. Numerical tests were carried out to verify the performance of each flux limiter in terms of accuracy. The results were compared to analytical and previously obtained data to assess the performance of the mathematical model. Excellent agreement was obtained. Copyright © 2002 John Wiley & Sons, Ltd.