共查询到20条相似文献，搜索用时 382 毫秒
1.
Chongbin Zhao Lynn B. Reid Klaus Regenauer-Lieb Thomas Poulet 《Computational Geosciences》2012,16(3):735-755
In dealing with chemical-dissolution-front propagation problems in fluid-saturated porous media, the chemical dissolution front represented by the porosity of the medium may have a very steep slope (i.e., a very large porosity gradient) at the dissolution front, depending on the mineral dissolution ratio that is defined as the equilibrium concentration of the dissolved minerals in the pore-fluid to the solid molar density of the dissolvable minerals in the solid matrix. When the mineral dissolution ratio approaches zero, the theoretical value of the porosity gradient tends to infinity at the chemical dissolution front. Even for a very small value of the mineral dissolution ratio, which is very common in geochemical systems, the porosity gradient can be large enough to cause the solution hard to converge when the conventional finite element method is used to solve a chemical dissolution problem in a fluid-saturated porous medium where the pore-fluid is compressible. To improve the convergent speed of solution, a porosity-gradient replacement approach, in which the term involving porosity-gradient computation is replaced by a new term consisting of pore-fluid density-gradient and pressure-gradient computation, is first proposed and then incorporated into the finite element method in this study. Through comparing the numerical results obtained from the proposed approach with the theoretical solutions for a benchmark problem, it has been demonstrated that not only can the solution divergence be avoid, but also the accurate simulation results can be obtained when the proposed porosity-gradient replacement approach is used to solve chemical-dissolution-front propagation problems in fluid-saturated porous media including pore-fluid compressibility. 相似文献
2.
The basic equations for fluid-saturated porous media proposed by Biot are modified by replacing the classical linear elastic model of the solid skeleton with the Kelvin–Voigt model. Thus, the new theory can take into account the viscoelastic effect of the solid skeleton. After the establishment of appropriate boundary and initial conditions, a time-domain series solution for the transient response of a fluid-saturated single-layer poroviscoelastic medium is obtained by using the finite Fourier transform and the corresponding analytical inverse transform. Several numerical examples are provided to illustrate the validity of the exact solution and to investigate the influence of the viscosity coefficient, permeability coefficient, and load frequency on the transient response of a fluid-saturated single-layer poroviscoelastic medium. 相似文献
3.
Practical civil engineering problems are usually formulated in an infinite half-space domain, and a selected finite domain is required to analyze the dynamic responses of a fluid-saturated porous medium by the finite element method (FEM). Devising a method to deal with the boundaries of the finite domain is the key issue for this open system. In this paper, a two-dimensional spring–dashpot artificial boundary (SDAB) for transient analysis in a fluid-saturated porous media is developed. Based on Biot’s dynamic theory of fluid-saturated porous media, the normal and tangential boundary stress formulae are deduced for out-going cylindrical body waves. The boundary stress is proportional to displacement and velocity, thus continuously distributed dashpots and springs can be placed on the artificial boundaries in the normal and tangential directions to simulate the energy absorption of the infinite media outside of the finite domain for the interior distributed source problems. In this paper, the input seismic motion can be realized by applying an equivalent load on the SDAB for the seismic scattering problems of exterior distributed sources. Numerical examples are given and the analyzed results show that the SDAB and the method of wave motion input have good stability and acceptable accuracy. 相似文献
4.
Mathematical modelling of the ascent of free fluid through relatively strong rock, deep in the Earth's mantle, presents a challenge in geomechanics. Here the medium is considered as fluid-saturated, porous, elastic and bounded, and the fluid enters at a point source. An explicit finite difference method is developed for the numerical solution to the problem of the dilatation of a fluid-saturated porous elastic sphere due to a point fluid source of constant strength at the centre of the sphere. A cubic spline interpolant is used to evaluate a definite integral which occurs in the boundary condition for the pore fluid pressure at the surface of the sphere. The numerical solutions for the dilatation and pore fluid pressure are compared with analytical solutions and the absolute and relative errors of the numerical solutions are calculated. When the fluid source is switched on, the pore fluid pressure starts to decrease, reaches a minimum value and then steadily increases. The initial time rate of decrease of the pore fluid pressure is independent of the radial distance from the source. It decreases as the radius of the sphere increases and vanishes for a point fluid source in an infinite porous elastic medium. 相似文献
5.
Biot's equations of wave propagation through fluid-saturated porous elastic media are discretized spatially using the finite element method in conjunction with Galerkin's procedure. Laplace transformation of the discretized equations is used to suppress the time variable. Introducing Laplace transforms of constituent velocities at nodal points as additional variables, the quadratic set of equations in the Laplace transform parameter is reduced to a linear form. The solution in the Laplace transform space is inverted, term by term, to get the complete time history of the solid and fluid displacements and velocities. Since the solution is exact in the time domain, the error in the calculated response is entirely due to the spatial approximation. The procedure is applied to one-dimensional wave propagation in a linear elastic material and in a fluid-saturated elastic soil layer with ‘weak’, ‘strong’ as well as ‘moderate’ coupling. With refinement of the spatial mesh, convergence to the exact solution is established. The procedure can provide a useful benchmark for validation of approximate temporal discretization schemes and estimation of errors due to spatial discretization. 相似文献
6.
This study examines the time-dependent poromechanics behavior of a fluid-saturated spherical inclusion embedded inside a fluid-saturated
porous medium with different poroelastic properties. Both media comprise compressible constituents with distinctively defined
poroelastic parameters. It is assumed that the inclusion is subjected to a fluid source at the center. The problem is formulated
and solved using Biot theory of poromechanics. The contrasts in inclusion and the medium matrix stiffnesses and their respective
hydraulic conductivities can be recognized as two competing factors, which affect the inclusion’s rate of expansion during
fluid injection. Findings show a certain type of behavior that the inclusion exhibits at the onset of fluid injection when
having greater stiffness than the medium matrix, where the inclusion experiences some decrease in the pore pressure. Compared
to what announced as the stress redistribution due the Mandel–Cryer effect in earlier researches on dilation of free spheres,
this study shows that the associated phenomenon would be likewise attributed to the coupled nature of pressures and deformations
in the theory of poroelasticity. However, it is a consequence of the inclusion-matrix stiffness contrast where a dilating
free sphere can be regarded as a special case of this new problem. The asymptotic expansions of pressure terms verify the
existence of such an effect. The results of this study would put forward very good insight in some engineering applications. 相似文献
7.
流体饱和两相多孔介质动力反应计算分析 总被引：2，自引：1，他引：1
基于流体饱和两相多孔介质的弹性波动方程组,运用显式逐步积分格式与局部透射人工边界相结合的时域显式有限元方法对该波动方程组进行求解,对两相介质在输入地震波作用下的弹性动力反应进行计算和分析;对在是否考虑孔隙流体渗流的两种情况下计算得到的两相介质弹性动力反应结果的差异进行对比研究,从而揭示孔隙流体渗流对两相介质动力反应性质的影响。计算结果表明：两相介质弹性动力反应时程的波形与入射地震波的波形相同,且弹性动力反应的峰值出现的时刻对应于入射地震波的峰值出现的时刻;孔隙流体的渗流将对两相介质的弹性动力反应性质产生显著的影响。数值计算同时表明,时域显式有限元方法是进行流体饱和两相多孔介质弹性动力反应计算分析的一种有效的方法。 相似文献
8.
This paper deals with the computational aspects of nonaqueous phase liquid (NAPL) dissolution front instability in two-dimensional
fluid-saturated porous media of finite domains. After the governing equations of an NAPL dissolution system are briefly described,
a combination of the finite element and finite difference methods is proposed to solve these equations. In the proposed numerical
procedure, the finite difference method is used to discretize time, while the finite element method is used to discretize
space. Two benchmark problems, for which either analytical results or previous solutions are available, are used to verify
the proposed numerical procedure. The related simulation results from these two benchmark problems have demonstrated that
the proposed numerical procedure is useful and applicable for simulating the morphological evolution of NAPL dissolution fronts
in two-dimensional fluid-saturated porous media of finite domains. As an application, the proposed numerical procedure has
been used to simulate morphological evolution processes for three kinds of NAPL dissolution fronts in supercritical NAPL dissolution
systems. It has been recognized that: (1) if the Zhao number of an NAPL dissolution system is in the lower range of the supercritical
Zhao numbers, the fundamental mode is predominant; (2) if the Zhao number is in the middle range of the supercritical Zhao
numbers, the (normal) fingering mode is the predominant pattern of the NAPL dissolution front; and (3) if the Zhao number
is in the higher range of the supercritical Zhao numbers, the fractal mode is predominant for the NAPL dissolution front. 相似文献
9.
《Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy》2000,25(2):175-181
In the paper the one-equation model of humidity transfer in unsaturated macroscopically heterogeneous porous media is presented. The homogenization method by two-scale asymptotic expansions is used to derive the upscaled form of the Richard equation, which is commonly used when the medium is considered as macroscopically homogeneous. This equation is highly non-linear due to the pressure-dependence of the hydrodynamic characteristics of the porous medium. The domain of validity of the model is explicitly given, namely: the length-scales separation, the characteristic time scale condition and the ratio of the hydrodynamic characteristics being of the same orders of magnitude. The effective capillary capacity and the effective hydraulic conductivity for an equivalent continuum are defined in terms of geometry and local hydrodynamic characteristics of the porous medium. A procedure of determination of the effective suction curve and the effective hydraulic conductivity curve as functions of the average water content for any type of the macroscopic heteregeneity for which the method can be applied, is provided. Since the problem is non-linear this procedure involves the resolution of a local boundary value problem formulated over a period for each value of suction. In two or three-dimensional cases, this problem can be solved using the numerical methods for any geometry of the medium. In a one-dimensional case it was shown that the analytical solution gives the well-known results of harmonic and arithmetic mean. 相似文献
10.
A mixed finite element–boundary element solution for the analysis of two-dimensional flow in porous media composed of rock blocks and discrete fractures is described. The rock blocks are modelled implicitly by using boundary elements whereas finite elements are adopted to model the discrete fractures. The computational procedure has been implemented in a hybrid code which has been validated first by comparing the numerical results with the closed-form solution for flow in a porous aquifer intercepted by a vertical fracture only. Then, a more complex problem has been solved where a pervious, homogeneous and isotropic matrix containing a net of fractures is considered. The results obtained are shown to describe satisfactorily the main features of the flow problem under study. © 1997 by John Wiley & Sons, Ltd. 相似文献
11.
The problem of multiphase phase flow in heterogeneous subsurface porous media is one involving many uncertainties. In particular, the permeability of the medium is an important aspect of the model that is inherently uncertain. Properly quantifying these uncertainties is essential in order to make reliable probabilistic-based predictions and future decisions. In this work, a measure-theoretic framework is employed to quantify uncertainties in a two-phase subsurface flow model in high-contrast media. Given uncertain saturation data from observation wells, the stochastic inverse problem is solved numerically in order to obtain a probability measure on the space of unknown permeability parameters characterizing the two-phase flow. As solving the stochastic inverse problem requires a number of forward model solves, we also incorporate the use of a conservative version of the generalized multiscale finite element method for added efficiency. The parameter-space probability measure is used in order to make predictions of saturation values where measurements are not available, and to validate the effectiveness of the proposed approach in the context of fine and coarse model solves. A number of numerical examples are offered to illustrate the measure-theoretic methodology for solving the stochastic inverse problem using both fine and coarse solution schemes. 相似文献
12.
An analytical solution is proposed for transient flow and deformation coupling of a fluid‐saturated poroelastic medium within a finite two‐dimensional (2‐D) rectangular domain. In this study, the porous medium is assumed to be isotropic, homogeneous, and compressible. In addition, the point sink can be located at an arbitrary position in the porous medium. The fluid–solid interaction in porous media is governed by the general Biot's consolidation theory. The method of integral transforms is applied in the analytical formulation of closed‐form solutions. The proposed analytical solution is then verified against both exact and numerical results. The analytical solution is first simplified and validated by comparison with an existing exact solution for the uncoupled problem. Then, a case study for pumping from a confined aquifer is performed. The consistency between the numerical solution and the analytical solution confirms the accuracy and reliability of the analytical solution presented in this paper. The proposed analytical solution can help us to obtain in‐depth insights into time‐dependent mechanical behavior due to fluid withdrawal within finite 2‐D porous media. Moreover, it can also be of great significance to calibrate numerical solutions in plane strain poroelasticity and to formulate relevant industry norms and standards. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
13.
针对河堤、水坝、高速公路档水墙等存在多孔单元介质中的定常渗流问题,将渗流Laplace方程,通过数学变换转化为边界积分方程,进而离散为线性代数方程组。采用边界元编写FORTRAN程序。计算结果表明:该法与有限元法相比,占用CPU时间短,不需要网格化分,使繁杂问题简单化,同时很好地切近实际。 相似文献
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15.
二维饱和多孔介质因点汇诱发比奥固结的解析解 总被引：1，自引：0，他引：1
给出了有限二维饱和多孔介质因点汇诱发的Biot固结的一个解析解。其中假设多孔介质为均匀各向同性和线弹性,假设孔隙压力场符合第1类边界条件,数学模型采用可压缩多孔介质模型。利用傅里叶和拉普拉斯变换及相应反演获得了双重无穷项级数和形式的精确解。然后特别探讨了定流量点汇诱发的稳态解析解,并用文献现有解析解进行了验证。所提出的解析解适合于验证数值解,并可用于深入分析有限二维多孔介质的流-固耦合行为。 相似文献
16.
This paper presents a semianalytical approach for solving first-order perturbation (FOP) equations, which are used to describe dissolution-timescale reactive infiltration instability (RII) problems in fluid-saturated rocks. The proposed approach contains two parts because the chemical dissolution reaction divides the whole problem domain into two subdomains. In the first part, the interface-condition substitution strategy is used to derive the analytical expressions of purely mathematical solutions for the FOP equations in the upstream subdomain, where the dissolution chemical reaction is ceased and the FOP equations are weakly coupled. In the second part, the finite element method (FEM) is used to derive the analytical expressions of numerical solutions for the FOP equations in the downstream subdomain, where the dissolution chemical reaction needs to be considered and the FOP equations are strongly coupled so that it is impossible to derive purely mathematical solutions for them. Particular attention is paid to the development of the element-by-element forward marching strategy, which is associated with the use of the FEM for solving this new kind of scientific problem. The related analytical results demonstrated that (1) both the dynamic characteristic of a reactive infiltration system and the dimensionless wavenumber can have pronounced influences on the distribution of the FOP dimensionless acid concentration within the entire domain of the dissolution-timescale RII problems in fluid-saturated rocks and (2) the FOP dimensionless acid concentration distribution exhibits two significantly different patterns in the upstream and downstream subdomains of the dissolution-timescale RII system. 相似文献
17.
The problem of finite element simulation of incompressible fluid flow in porous medium is considered. The porous medium is characterized by the X‐ray microtomography technique in three dimensions. The finite calculus‐based stabilization technique is reviewed to implement the equal order finite element interpolation functions for both velocity and pressure. A noble preconditioner, the nodal block diagonal preconditioner, is considered whose performance is thoroughly investigated. Combining this preconditioner with a standard iterative solver during the computational homogenization procedure, it is possible to carry out the large‐scale fluid flow simulation for estimating permeability of the porous medium with reasonable accuracy and reliability. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Thermal oil recovery processes involve high pressures and temperatures, leading to large volume changes and induced stresses. These cannot be handled by traditional reservoir simulation because it does not consider coupled geomechanics effects. In this paper we present a fully coupled, thermal half‐space model using a hybrid DDFEM method. A finite element method (FEM) solution is adopted for the reservoir and the surrounding thermally affected zone, and a displacement discontinuity method is used for the surrounding elastic, non‐thermal zone. This approach analyzes stress, pressure, temperature and volume change in the reservoir; it also provides stresses and displacements around the reservoir (including transient ground surface movements) in a natural manner without introducing extra spatial discretization outside the FEM zone. To overcome spurious spatial temperature oscillations in the convection‐dominated thermal advection–diffusion problem, we place the transient problem into an advection–diffusion–reaction problem framework, which is then efficiently addressed by a stabilized finite element approach, the subgrid‐scale/gradient subgrid‐scale method. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献