一类热传导方程多点源反演的唯一性和稳定性

在第一类Dirichlet边界条件下,研究了由表面热流密度来反演热传导方程多点源的唯一性和稳定性。即反演点源个数n、热源强度组合系数αi、点源位置si的唯一性和反演点源位置si的稳定性。利用热变换方法将热传导方程反问题转化为等价的双曲型方程反问题,然后通过分析等价的双曲型方程反问题得到原反问题的唯一性和条件稳定性结论。     

三维油藏中应力与渗流的摄动-有限元分析

提出了一个较为实际的石油油藏的三维力学模型。以已有的三维介质中应力与渗流耦合问题的变分原理为基础,用摄动法证明了光油藏厚度变化为小量时,三维问题或简化为平面应变问题,并可采用不同厚度的平面应变单元进行有限元分析,所得到的解即是该三维问题的零阶摄动解。给出了摄动法的推导和有限元格式,计算了一个水驱法进行油田二次开发的算例并给出了计算结果。     

A dual-porosity model considering the displacement effect for incompressible two-phase flow

The dual-porosity model is usually employed to simulate the flow in fractured reservoirs. However, its original form for the multiphase flow does not consider the displacement effect under macropressure gradient. Especially for the incompressible multiphase flow, it predicts zero transfer term between fracture and matrix, which is unreasonable. To improve this, a modified double-porosity model is proposed for incompressible two-phase flow, in which the displacement effect is considered and the corresponding shape factor is derived. For the anisotropic case, the shape factor of displacement depends upon the velocity direction. The accuracy and the efficiency of the proposed dual-porosity model are indicated through numerical tests.     

Poroelastic model for pile–soil interaction in a half‐space porous medium due to seismic waves

In this paper, frequency domain dynamic response of a pile embedded in a half‐space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half‐space and a fictitious pile. The extended porous half‐space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1‐D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half‐space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half‐space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile–half‐space system. Significant differences between conventional single‐phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright © 2007 John Wiley & Sons, Ltd.     

JHomogenizer: a computational tool for upscaling permeability for flow in heterogeneous porous media

This paper presents an object-oriented programming approach for the design of numerical homogenization programs, called JHomogenizer. It currently includes five functional modules to compute effective permeability and simple codes for computing solutions for flow in porous media. Examples with graphical output are shown to illustrate some functionalities of the program. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs. The software is freely available, and the open architecture of the program facilitates further development and can adapt to suit specific needs easily and quickly.     

近饱和条件下非饱和多孔介质渗流过程的数值分析

在非饱和多孔介质渗流分析中,近饱和条件下物理模型与数值模型之间的差异会导致数值不稳定问题。为解决这一问题,并保证模拟结果的可靠性,提出了3种方法,并在有限元分析程序U-DYSAC2中分别进行了程序代码的实施。通过数值试验与试验数据的比较,证实了在近饱和条件下土-水特征曲线和水力传导函数的高非线性可引起数值收敛性、稳定性和精度问题,而且在不同条件下含水率和基质吸力的预测结果差异明显。在3种方法中,修正的Van Genuchten模型（MVGM）方法对含水率的预测较为准确,而Line方法对基质吸力的预测较为合理。因此,解决在分析近饱和条件下非饱和多孔介质渗流问题时,为获得接近真实的模拟结果,采用合适的数值方法进行预测是非常关键的。     

Thermal effects in partially saturated soils: a constitutive model

The present paper is centred on the assessment of an elastic–plastic model for partially saturated soils, earlier proposed by the authors, for its predictive capability with respect to temperature changes, on the light of available experimental results. The model is cast within a constitutive framework that uses Bishop's stress and suction as main variables governing the volumetric response of the material. Some enhancement to the original temperature‐independent formulation is proposed. In particular, functions describing the yield surface and the compressibility modulus are modified to account for the shrinking of the elastic domain and for the increase of irreversible volumetric strain with heating. Some examples illustrate the main features of the present proposal. Comparison with some experimental results is also included. Copyright © 2005 John Wiley & Sons, Ltd.     

A pore-scale numerical model for flow through porous media

A pore-scale numerical model based on Smoothed Particle Hydrodynamics (SPH) is described for modelling fluid flow phenomena in porous media. Originally developed for astrophysics applications, SPH is extended to model incompressible flows of low Reynolds number as encountered in groundwater flow systems. In this paper, an overview of SPH is provided and the required modifications for modelling flow through porous media are described, including treatment of viscosity, equation of state, and no-slip boundary conditions. The performance of the model is demonstrated for two-dimensional flow through idealized porous media composed of spatially periodic square and hexagonal arrays of cylinders. The results are in close agreement with solutions obtained using the finite element method and published solutions in the literature. Copyright © 1999 John Wiley & Sons, Ltd.     

模拟裂隙多孔介质中变饱和渗流的广义等效连续体方法

描述了一种计算裂隙多孔介质中变饱和渗流的广义等效连续体方法。这种方法忽略裂隙的毛细作用,设定一个与某孔隙饱和度相对应的综合饱和度极限值,并假定：（1）如果裂隙多孔介质的综合饱和度小于该极限值,水只在孔隙中存在并流动,而裂隙中则没有水的流动;（2）如果综合饱和度等于或大于该极限值,水将进入裂隙,并在裂隙内运动。分析比较了等效连续体模型的不同计算方法,并给出了一个模拟裂隙岩体中变饱和渗流与传热耦合问题的应用算例。结果表明,所述方法具有一般性,可以有效地模拟裂隙多孔介质中变饱和渗流的基本特征。     

Part II. Discontinuous Galerkin method applied to a single phase flow in porous media

Discontinuous Galerkin numerical simulations of single phase flow problem are described in this paper. The simulations show the advantages of using discontinuous approximation spaces. hp convergence results are obtained for smooth solutions. Unstructured meshes and unsmooth solutions are also considered.     

The effect of stress boundary conditions on fluid-driven fracture propagation in porous media using a phase-field modeling approach

A phase-field approach for fluid-driven fracture propagation in porous media with varying constant compatible stress boundary conditions is discussed and implemented. Since crack opening displacement, fracture path, and stress values near the fracture are highly dependent on the given boundary conditions, it is crucial to take into account the impact of in situ stresses on fracturing propagation for realistic applications. We illustrate several numerical examples that include the effects of different boundary conditions on the fracture propagation. In addition, an example using realistic boundary conditions from a reservoir simulator is included to show the capabilities of our computational framework.     

Generalized Coarse Graining Procedures for Flow in Porous Media

This paper focuses on heterogeneous soil conductivities and on the impact their resolution has on a solution of the piezometric head equation: owing to spatial variations of the conductivity, the flow properties at larger scales differ from those found for experiments performed at smaller scales. The method of coarse graining is proposed in order to upscale the piezometric head equation on arbitrary intermediate scales. At intermediate scales large scale fluctuations of the conductivities are resolved, whereas small scale fluctuations are smoothed by a partialy spatial filtering procedure. The filtering procedure is performed in Fourier space with the aid of a low-frequency cut-off function. We derive the partially upscaled head equations. In these equations, the impact of the small scale variability is modeled by scale dependent effective conductivities which are determined by additional differential equations. Explicit results for the scale dependent conductivity values are presented in lowest order perturbation theory. The perturbation theory contributions are summed up with using a renormalisation group analysis yielding explicit results for the effective conductivity in isotropic media. Therefore, the results are also valid for highly heterogeneous media. The results are compared with numerical simulations performed by Dykaar and Kitanidis (1992). The method of coarse graining combined by a renormalisation group analysis offers a tool to derive exact and explicit expressions for resolution dependent conductivity values. It is, e.g., relevant for the interpretation of measurement data on different scales and for reduction of grid-block resolution in numerical modeling. This revised version was published online in July 2006 with corrections to the Cover Date.     

Traveling waves in a finite condensation rate model for steam injection

Steam drive recovery of oil is an economical way of producing oil even in times of low oil prices and is used worldwide. This paper focuses on the one-dimensional setting, where steam is injected into a core initially containing oil and connate water while oil and water are produced at the other end. A three-phase (oil, water, steam) hot zone develops, which is abruptly separated from the two-phase (oil + water) cold zone by the steam condensation front. The oil, water and energy balance equations (Rankine–Hugoniot conditions) cannot uniquely solve the system of equations at the steam condensation front. In a previous study, we showed that two additional constraints follow from an analysis of the traveling wave equation representing the shock; however, within the shock, we assumed local thermodynamic equilibrium. Here we extend the previous study and include finite condensation rates; using that appropriate scaling requires that the Peclet number and the Damkohler number are of the same order of magnitude. We give a numerical proof, using a color-coding technique, that, given the capillary diffusion behavior and the rate equation, a unique solution can be obtained. It is proven analytically that the solution for large condensation rates tends to the solution obtained assuming local thermodynamic equilibrium. Computations with realistic values to describe the viscous and capillary effects show that the condensation rate can have a significant effect on the global saturation profile, e.g. the oil saturation just upstream of the steam condensation front.     

热质输运-反应体系的石英溶解与沉淀的模拟研究

介质中热质输运-反应体系对于热质成矿、污物迁移等十分重要。这里利用热质流体输运动力学模型与石英溶解与沉淀的化学动力学模型,以及多孔介质的本构关系,建立了一个热质输运、反应动力学藕合模型。并使用此模型研究了局部的温度变化和颗粒半径不均一分布对研究区域内温度场和浓度场的变化情况,其结论是它们之间的耦合可能打破系统的平衡,驱使系统长时间持续进行流体输运-反应动力学过程。     

A new matrix for multiphase couplings in a membrane porous medium

The empirical Darcy's law of water transport in porous media, Fick's law of chemical diffusion, and Fourier's law of thermal transport have been widely used in geophysics/geochemistry for over 150 years. However, the strong couplings between water, temperature, and chemicals in a membrane porous medium have made these laws inapplicable and present a significant hurdle to the understanding of multiphase flow in such a material. Extensive experiments over the past century have observed chemical osmosis and thermal osmosis, but a model for understanding their underlying physicochemical basis has remained unavailable, because of the highly cross‐disciplinary and multiscale‐multiphase nature of the coupling. Based on the fundamental principles of nonequilibrium thermodynamics and mixture coupling theory, a rigorously theoretical and mathematical framework is proposed and a general model accounting for all of the coupled influences is developed. This leads to a simple and robust mathematical matrix for studying multiphase couplings in a membrane porous medium when all chemical components are electrically neutral.     

A model for moisture and heat flow in fractured unsaturated porous media

The present study investigates propagation of a cohesive crack in non‐isothermal unsaturated porous medium under mode I conditions. Basic points of skeleton deformation, moisture, and heat transfer for unsaturated porous medium are presented. Boundary conditions on the crack surface that consist of mechanical interaction of the crack and the porous medium, water, and heat flows through the crack are taken into consideration. For spatial discretization, the extended finite element method is used. This method uses enriched shape functions in addition to ordinary shape functions for approximation of displacement, pressure, and temperature fields. The Heaviside step function and the distance function are exploited as enrichment functions for representing the crack surfaces displacement and the discontinuous vertical gradients of the pressure and temperature fields along the crack, respectively. For temporal discretization, backward finite difference scheme is applied. Problems solved from the literature show the validity of the model as well as the dependency of structural response on the material properties and loading. Copyright © 2016 John Wiley & Sons, Ltd.     

Calculating the internodal transmissibilities using finite analytic method and its application for multi‐phase flow in heterogeneous porous media

In the traditional numerical reservoir simulations, the internodal transmissibility is usually defined as the harmonic mean of the permeabilities of the adjacent grids. This definition underestimates the phase flux and the speed of the saturation front, especially for the strong heterogeneous case. In this article, the internodal transmissibility is recalculated according to the nodal analytic solution. The redefined internodal transmissibility can be used directly to calculate the multiphase flow in the numerical reservoir simulations. Numerical examples show that, compared to the traditional numerical methods, the proposed scheme makes the convergences much faster as the refinement parameter increases, and the accuracy is independent of the heterogeneity. Copyright © 2016 John Wiley & Sons, Ltd.     

On the velocity covariance for steady flows in heterogeneous porous formations and its application to contaminants transport

We consider groundwater steady flow in a heterogeneous porous formation of random and stationary log-conductivity Y = ln K, characterized by the mean 〈Y〉, and the two point correlation function C _Y which in turn has finite, and different horizontal and vertical integral scales I and I _v , respectively. The fluid velocity V, driven by a given head drop applied at the boundary, has constant mean value U ≡ (U, 0, 0). Approximate explicit analytical expressions for transverse velocity covariances are derived. The adopted methodology follows the approach developed by Dagan and Cvetkovic (Spatial moments of kinetically sorbing plume in a heterogeneous aquifers, Water Resour. Res. 29 (1993) 4053) to obtain a similar result for the longitudinal velocity covariance. Indeed, the approximate covariances of transverse velocities are determined by requiring that they have the exact first order variances as well as zero integral scale (G. Dagan, Flow and Transport in Porous Formations (Springer, 1989)) , and provide the exact asymptotic limits of the displacement covariance of the fluid particles obtained by Russo (On the velocity covariance and transport modeling in heterogeneous anisotropic porous formations 1. Saturated flow, Water Resour. Res., 31 (1995) 129). Comparisons with numerical results show that the proposed expressions compare quite well in the early time regime, and for Ut/I >100. Since most of the applications, like assessing the effective mobility of contaminants or quantifying the potential hazards of nuclear repositories, require predictions over higher times the proposed approximate expressions provide acceptable results. The main advantage related to such expressions is that they allow obtaining closed analytical forms of spatial moments pertaining to kinetically sorbing contaminant plumes avoiding the very heavy computational effort which is generally demanded. For illustration purposes, we consider the movement of one contaminant species, and show how our approximate spatial moments compare with the numerical simulations.     

Two formulations for dynamic response of a cylindrical cavity in cross‐anisotropic porous media

Two formulations for calculating dynamic response of a cylindrical cavity in cross‐anisotropic porous media based on complex functions theory are presented. The basis of the method is the solution of Biot's consolidation equations in the complex plane. Employing two groups of potential functions for solid skeleton and pore fluid (each group includes three functions), the u–w formulation of Biot's equations are solved. Difference of these two solutions refers to use of two various potential functions. Equations for calculating stress, displacement and pore pressure fields of the medium are mentioned based on each two formulations. Copyright © 2009 John Wiley & Sons, Ltd.