三维非均匀不稳定渗流方程的自适应网格粗化算法

将渗透率自适应网格技术应用于三维非均匀不稳定渗流方程的网格粗化算法中,在渗透率或孔隙度变化异常区域自动采用精细网格,用直接解法求解渗透率或孔隙度变化异常区域的压强分布,在其它区域采用不均匀网格粗化的方法计算,即在流体流速大的区域采用精细网格.用该方法计算了三维非均匀不稳定渗流场的压降解,结果表明三维非均匀不稳定渗流方程的三维非均匀自适应网格粗化算法的解在渗透率或孔隙度异常区的压强分布规律与采用精细网格的解非常逼近,在其它区域压强分布规律与粗化算法的解非常逼近,计算速度比采用精细网格提高100多倍.     

Simulation of low-Reynolds-number flow via a time-independent lattice-Boltzmann method

We present a numerical method to solve the equations for low-Reynolds-number (Stokes) flow in porous media. The method is based on the lattice-Boltzmann approach, but utilizes a direct solution of time-independent equations, rather than the usual temporal evolution to steady state. Its computational efficiency is 1-2 orders of magnitude greater than the conventional lattice-Boltzmann method. The convergence of the permeability of random arrays of spheres has been analyzed as a function of mesh resolution at several different porosities. For sufficiently large spheres, we have found that the convergence is quadratic in the mesh resolution.     

致密多孔介质中气体渗流的格子Boltzmann模拟

为了能用格子Boltzmann方法来正确地刻画致密多孔介质中微尺度流动问题,对单通道模型进行推广,并将其应用于孔隙群里气体渗流的数值模拟.通过对部分具有代表性的多孔介质中的实际流动问题进行模拟,研究渗透率与平均压力和Knudsen数之间的相互关系.基于理论分析及相关文献中的试验结果,验证模拟结果,为用格子Boltzmann方法深入研究气体渗流问题奠定基础.     

利用多松弛格子Boltzmann方法预测多孔介质的渗透率

多孔介质内的流动问题在工程热物理领域有着重要的研究价值和应用背景。本文利用多松弛格子Boltzmann方法详细预测了两种二维多孔介质中的渗透率。研究结果表明:一方面,多松弛模型可以用来克服由单松弛模型带来的一些不足;另一方面,借助于达西定律,多松弛模型可以准确预测多孔介质的渗透率,并将计算结果与已有文献做了对比。     

含低渗透夹层的非均质双重介质垂向干扰的精确解

本文建立了单一介质、双重介质中由两个渗透层被一个致密低渗透层隔开的多层油藏渗流的数学模型,并求得了无穷大地层的精确解和长时渐近解。利用这个解可以在双重介质层状油藏的单井、多井试井中解释压力恢复曲线、垂向干扰试井和垂向脉冲试井。     

气孔分布特性对含水多孔介质气体扩散的影响

本文基于多孔介质的气孔分布特性,计算了多孔介质在含水状态下的扩散性能,并且比较了采用两种方式计算相对渗透率时的相对扩散性能。其结果表明,基于气孔分布的计算结果低于与气孔分布无关的计算结果。另外,疏水性含水多孔介质的扩散性能低于亲水性含水多孔介质的扩散性能,基于气孔分布计算含水多孔介质的气体扩散性能时,Wyllie公式并不适用。     

A fractional-order Darcy's law

By using spatial averaging methods, in this work we derive a Darcy's-type law from a fractional Newton's law of viscosity, which is intended to describe shear stress phenomena in non-homogeneous porous media. As a prerequisite towards this end, we derive an extension of the spatial averaging theorem for fractional-order gradients. The usage of this tool for averaging continuity and momentum equations yields a Darcy's law with three contributions: (i) similar to the classical Darcy's law, a term depending on macroscopic pressure gradients and gravitational forces; (ii) a fractional convective term induced by spatial porosity gradients; and (iii) a fractional Brinkman-type correction. In the three cases, the corresponding permeability tensors should be computed from a fractional boundary-value problem within a representative cell. Consistency of the resulting Darcy's-type law is demonstrated by showing that it is reduced to the classical one in the case of integer-order velocity gradients and homogeneous porous media.     

A stochastic multiscale framework for modeling flow through random heterogeneous porous media

Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to characterize the system. Any realistic modeling of these transport phenomena has to resolve two key issues: (i) the multi-length scale variations in permeability that these systems exhibit, and (ii) the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes.A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Recent developments in linear and non-linear model reduction techniques are used to convert the limited information available about the permeability variation into a viable stochastic input model. An adaptive sparse grid collocation strategy is used to efficiently solve the resulting stochastic partial differential equations (SPDEs). The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given.     

Direct measurement of porous media local hydrodynamical permeability using gas MRI.

The concept of hydraulic permeability is at the core of modeling single phase or multi-phase flow in heterogeneous porous media, as it is the spatial distribution of the permeability that primarily governs the behavior of fluid flow in the medium. To date, the modeling of fluid flow in porous media has been hampered by poor estimates of local permeability. Magnetic Resonance Imaging is well known for its ability to measure non-invasively the local density and flow rate of different fluids saturating porous media [1,2]. In this paper we demonstrate the first non-invasive method for the direct measurement of a single projection of the local permeability tensor of a porous medium using gas-phase MRI. The potential for three-dimensional imaging of the medium permeability is also discussed. The limitations of the method are listed and results are presented in a model porous medium as well as in a real oil reservoir rock.     

孔隙介质包裹的充液管道结构中导波传播特性

研究孔隙介质包裹的充液管道中纵向导波传播特性,分析孔隙介质参数对频散曲线的影响。建立了孔隙介质包裹充液管道的结构模型,利用孔隙介质弹性波动理论,建立对应的频散方程,数值模拟计算得到该模型的频散曲线和时域波形,并分析了孔隙介质参数以及管壁厚度对频散曲线的影响。结果表明孔隙介质的渗透率对于导波频散的影响较小,孔隙度的改变对时域波形的位移幅度影响较大。同时,导波存在衰减,且衰减随孔隙度增大而增大。所得结论为埋地管道无损检测方面提供一定理论参考。      

Macroscopic capillarity without a constitutive capillary pressure function

This paper challenges the foundations of the macroscopic capillary pressure concept. The capillary pressure function, as it is traditionally assumed in the constitutive theory of two-phase immiscible displacement in porous media, relates the pressure difference between nonwetting and wetting fluid to the saturation of the wetting fluid. The traditional capillary pressure function neglects the fundamental difference between percolating and nonpercolating fluid regions as first emphasized in R. Hilfer [Macroscopic equations of motion for two phase flow in porous media, Phys. Rev. E 58 (1998) 2090]. The theoretical approach proposed here starts from residual saturations as the volume fractions of nonpercolating phases. The resulting equations of motion open the possibility to describe flow processes where drainage and imbibition occur simultaneously. The theory predicts hysteresis and process dependence of capillary phenomena. The traditional theory is recovered as a special case in the residual decoupling approximation. Explicit calculations are presented for quasistatic equilibrium profiles near hydrostatic equilibrium. The results are found to agree with experiment.     

随机多孔介质的蒙特卡罗重构与渗流特性模拟

根据多孔介质微观结构的分形尺度标度特征,采用蒙特卡罗方法分别重构随机多孔介质的微观颗粒和孔隙结构,并基于分形毛管束模型研究多尺度多孔介质的气体渗流特性,建立多孔介质微观结构和宏观渗流特性的定量关系。结果表明：分形蒙特卡罗重构的多孔介质微细结构接近真实介质结构,气体渗流特性的计算结果与格子玻尔兹曼模拟数据较为吻合; 多孔介质气体渗透率随着克努森数的增加而增大,孔隙分形维数对于气体渗流的微尺度效应具有显著影响,而迂曲度分形维数对于表观渗透率和固有渗透率的比值影响可以忽略。提出的分形蒙特卡罗方法具有收敛速度快且计算误差与维数无关的优点,有利于深入理解多尺度多孔介质的渗流机理。     

气体动理学格式模拟多孔介质流动的可行性

将气体动理学格式（GKS）拓展到模拟多孔介质内的低速渗流,并检验在孔隙尺度上模拟不可压缩低速流动的可行性与有效性.结果表明：GKS具有二阶空间精度,能够较精确地计算多孔介质的渗透率;相比于单松弛格子玻尔兹曼方法,GKS能够精确实现壁面无滑移边界条件,从而正确反映渗透率与黏性无关的特性;对于Berea砂岩切片结构中的复杂流动,模拟结果与实验吻合较好,能较精确地计算渗透率.给出GKS模拟达西渗流的马赫数选取准则,为研究多孔介质流动提供新的工具.     

Propagation characteristics of guided waves in a liquid filled pipe embedded in a porous medium

A model of a liquid-filled pipe embedded in a porous medium is built to research its wave propagation characteristics,and to analyze the effect of the parameters of porous media on the dispersion.The dispersion equations are established on the basis of the elastic-dynamic theory of the liquid-saturated porous solid.The characteristic of dispersion and the time domain waveform in pipes of different thicknesses and with different porous-medium parameters are discussed theoretically and numerically.Results reveal that the porosity has little impact on dispersion,and the attenuation of guided wave increases with porosity,whilst the porosity influences the displacement amplitude of the time domain waveform.It is hard to detect the permeability variation of the media by the dispersion.The drawn conclusion can provide some theoretical instruction and guidance for the nondestructive testing of buried pipe.     

A new numerical method for the analysis of the permeability anisotropy ratio

By combining the lattice Boltzmann method with the three-dimensional computer-simulated images of porous media,a new numerical experimental methodology is used to determine the permeability anisotropy ratio of porous media.The results compare well with the laboratory experimental data.     

A dynamic deformation model of an elastoplastic porous medium

A closed system of equations is obtained for dynamic deformation of an elastoplastic Prandtl-Reiss porous medium. The heterogeneous approach makes it possible to describe the properties of such media in a wide range of loading rates within the theory of plastic flow with the kinematic simplification. The hydrodynamic deformation theory of porous media [1, 2] has been first correctly generalized to the case of including the deviator components of the stress tensor of the medium. The well-known functions of the model are determined from analyzing the fundamental deformations of the corresponding spherical cells.Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–53, July, 1992.     

On hydraulic permeability of random packs of monodisperse spheres: Direct flow simulations versus correlations

Hydraulic permeability is studied in porous media consisting of randomly distributed monodisperse spheres by means of computational fluid dynamics (CFD) simulations. The packing of spheres is generated by inserting a certain number of nonoverlapping spherical particles inside a cubic box at both low and high packing fractions using proper algorithms. Fluid flow simulations are performed within the interparticulate porous space by solving Navier-Stokes equations in a low-Reynolds laminar flow regime. The hydraulic permeability is calculated from the Darcy equation once the mean values of velocity and pressure gradient are calculated across the particle packing. The simulation results for the pressure drop across the packing are verified by the Ergun equation for the lower range of porosities (<0.75), and the Stokes equation for higher porosities (∼1). Using the results of simulations, the effects of porosity and particle diameters on the hydraulic permeability are investigated. Simulations precisely specified the range of applicability of empirical or semi-empirical correlations for hydraulic permeability, namely the Carman-Kozeny, Rumpf-Gupte, and Howells-Hinch formulas. The number of spheres in the model is gradually decreased from 2000 to 20 to discover the finite-size effect of pores on the hydraulic permeability of spherical packing, which has not been clearly addressed in the literature. In addition, the scale dependence of hydraulic permeability is studied via simulations of the packing of spheres shrunk to lower scales. The results of this work not only reveal the validity range of the aforementioned correlations, but also show the finite-size effect of pores and the scale-independence of direct CFD simulations for hydraulic permeability.