可压缩流体饱和孔隙介质中孔隙压力波传播数值分析

首次将高精度时空守恒元/解元方法推广到可压缩流体饱和孔隙介质中孔隙压力波传播的数值计算中。将孔隙度梯度从源（汇）项中分离,直接引入流通量,改进了理论模型。通过对孔隙介质激波问题的数值模拟,验证了方法的精度和有效性。在此基础上,提出了孔隙介质中二维黎曼问题,并揭示了孔隙压力波存在接触间断、激波、膨胀波、压缩波等复杂的结构特征。该成果对二氧化碳地质封存、二氧化碳提高石油采收率、页岩气压裂开采以及地震破裂过程的研究具有重要的理论与应用意义。     

Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media

We describe a new approach for simulation of multiphase flows through heterogeneous porous media, such as oil reservoirs. The method, which is based on the wavelet transformation of the spatial distribution of the single-phase permeabilities, incorporates in the upscaled computational grid all the relevant data on the permeability, porosity, and other important properties of a porous medium at all the length scales. The upscaling method generates a nonuniform computational grid which preserves the resolved structure of the geological model in the near-well zones as well as in the high-permeability sectors and upscales the rest of the geological model. As such, the method is a multiscale one that preserves all the important information across all the relevant length scales. Using a robust front-detection method which eliminates the numerical dispersion by a high-order total variation diminishing method (suitable for the type of nonuniform upscaled grid that we generate), we obtain highly accurate results with a greatly reduced computational cost. The speed-up in the computations is up to over three orders of magnitude, depending on the degree of heterogeneity of the model. To demonstrate the accuracy and efficiency of our methods, five distinct models (including one with fractures) of heterogeneous porous media are considered, and two-phase flows in the models are studied, with and without the capillary pressure.     

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

In this paper, a numerical model is developed for the fully coupled hydro‐mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non‐wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two‐phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three‐phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro‐mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non‐wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiphase SPH modeling of free surface flow in porous media with variable porosity

This paper presents a numerical model for simulating free surface flow in porous media with spatially varying porosity. The governing equations are based on the mixture theory. The resistance forces between solid and fluid is assumed to be nonlinear. A multiphase SPH approach is presented to solve the governing equations. In the multiphase SPH, water is modeled as a weakly compressible fluid, and solid phase is discretized by fixed solid particles carrying information of porosity. The model is validated by several numerical examples including seepage through specimen, fast flow through rockfill dam and wave interaction with porous structure. Good agreements between numerical results and experimental data are obtained in terms of flow rate and evolution of free surface. Parameter study shows that (1) the nonlinear resistance law provides more accurate results; (2) particle size and porosity have significant influence on the porous flow.     

广义平面应力条件下径向渗流的液固耦合

考虑了多孔介质渗透率随孔隙变化的特点,建立了基本方程;对于广义平面应力条件下的径向渗流问题,提出了解耦方法,并求出了耦合条件下的孔隙压力及介质应力、应变、位移的解析解。实例计算表明,耦合效应不容忽略。      

A new computational strategy for solving two‐phase flow in strongly heterogeneous poroelastic media of evolving scales

We develop a new computational methodology for solving two‐phase flow in highly heterogeneous porous media incorporating geomechanical coupling subject to uncertainty in the poromechanical parameters. Within the framework of a staggered‐in‐time coupling algorithm, the numerical method proposed herein relies on a Petrov–Galerkin postprocessing approach projected on the Raviart–Thomas space to compute the Darcy velocity of the mixture in conjunction with a locally conservative higher order finite volume discretization of the nonlinear transport equation for the saturation and an operator splitting procedure based on the difference in the time‐scales of transport and geomechanics to compute the effects of transient porosity upon saturation. Notable features of the numerical modeling proposed herein are the local conservation properties inherited by the discrete fluxes that are crucial to correctly capture the fingering patterns arising from the interaction between heterogeneity and nonlinear viscous coupling. Water flooding in a poroelastic formation subject to an overburden is simulated with the geology characterized by multiscale self‐similar permeability and Young modulus random fields with power‐law covariance structure. Statistical moments of the poromechanical unknowns are computed within the framework of a high‐resolution Monte Carlo method. Numerical results illustrate the necessity of adopting locally conservative schemes to obtain reliable predictions of secondary recovery and finger growth in strongly heterogeneous deformable reservoirs. Copyright © 2011 John Wiley & Sons, Ltd.     

多尺度有限单元法求解非均质多孔介质中的三维地下水流问题

应用多尺度有限单元法模拟非均质多孔介质中的三维地下水流问题。与传统有限单元法相比，多尺度有限单元法的基函数具有能反映单元内参数变化的优点，所以这种方法能在大尺度上抓住解的小尺度特征获得较精确的解。在介绍多尺度有限单元法求解非均质多孔介质中三维地下水流问题的基本原理之后，对参数水平方向渐变垂直方向突变的非均质多孔介质中的三维地下水流和Borden实验场的三维地下水流分别用多尺度有限单元法和传统等参有限单元法进行了计算，结果表明在模拟高度非均质多孔介质中的三维地下水流问题时，多尺度有限单元法比传统有限单元法有效，既节省计算量又有较高的精度；在模拟非均质性弱的多孔介质中的三维地下水流问题时，多尺度有限单元法虽然也能在大尺度上获得较为精确的解，但效果不明显。     

Numerical modeling of porosity waves in the Nankai accretionary wedge décollement,Japan: implications for aseismic slip

Seismic and hydrologic observations of the Nankai accretionary wedge décollement, Japan, show that overpressures at depths greater than ～2 km beneath the seafloor could have increased to near lithostatic values due to sediment compaction and diagenesis, clay dehydration, and shearing. The resultant high overpressures are hypothesized then to have migrated in rapid surges or pulses called ‘porosity waves’ up the dip of the décollement. Such high velocities—much higher than expected Darcy fluxes—are possible for porosity waves if the porous media through which the waves travel are deformable enough for porosity and permeability to increase strongly with increasing fluid pressure. The present study aimed to test the hypothesis that porosity waves can travel at rates (kilometers per day) fast enough to cause aseismic slip in the Nankai décollement. The hypothesis was tested using a one-dimensional numerical solution to the fluid mass conservation equation for elastic porous media. Results show that porosity waves generated at depths of ～2 km from overpressures in excess of lithostatic pressure can propagate at rates sufficient to account for aseismic slip along the décollement over a wide range of hydrogeological conditions. Sensitivity analysis showed porosity wave velocity to be strongly dependent on specific storage, fluid viscosity, and the permeability–depth gradient. Overpressure slightly less than lithostatic pressure could also produce porosity waves capable of traveling at velocities sufficient to cause aseismic slip, provided that hydrogeologic properties of the décollement are near the limits of their geologically reasonable ranges.     

Simulating flows in multi-layered and spatially-variable permeability media via a new Gray Lattice Boltzmann model

The simulation of flow in porous and fibrous permeable media is of high importance in many scientific and industrial applications. Although the finite element models at the representative elementary volume scales are used to solve a huge amount of scientific and engineering problems, they are hardly used to efficiently simulate pore-fluid flow problems at the particle scales. This encourages the development of numerical models to match the needs of such studies. In this paper, we propose a new Gray Lattice Boltzmann numerical model for simulating fluid flow in permeable media. Unlike most previous models, our proposed model has the ability to simulate multi-layers and space-variable permeability while preserving the continuity of the macroscopic velocity field. The model is verified with the available analytical solutions and a derived analytical expression for the case of variable porosity. In addition, we examine the importance of introducing a transition layer with a defined porosity function near the boundaries and interfaces. If this layer exists in practice, then the numerical results reveal that it cannot be neglected, and its impact is significant on the obtained velocity distribution. Finally, in the light of the obtained results, we can state that the proposed model has great potential to simulate complex and heterogeneous media with smoothness and accuracy, so that it may enrich the research content of the emerging computational geosciences.     

Coupled theory of mixtures for clayey soils

In this work, elasto-plastic coupled equations are formulated in order to describe the time-dependent deformation of saturated cohesive soils (two-phase state). Formulation of these equations is based on the principle of virtual work and the theory of mixtures for inelastic porous media. The theory of mixtures for a linear elastic porous skeleton was first developed by Biot (Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics, 1955, 26, 188–185). An extension of Biot's theory into a nonlinear inelastic media was performed by Prevost (Mechanics of continuous porous media, International Journal of Engineering Science, 1980, 18, 787–800). The saturated soil is considered as a mixture of two deformable media, the solid grains and the water. Each medium is regarded as a continuum and follows its own motion. The flow of pore-water through the voids is assumed to follow Darcy's law. The coupled equations are developed for large deformations with finite strains in an updated Lagrangian reference frame. The coupled behavior of the two-phase materials (soil-water state) is implemented in a finite element program. A modified Cam-clay model is adopted and implemented in the finite element program in order to describe the plastic behavior of clayey soils. Penetration of a piezocone penetrometer in soil is numerically simulated and implemented into a finite element program. The piezocone penetrometer is assumed to be infinitely stiff. The continuous penetration of the cone is simulated by applying an incremental vertical movement of the cone tip boundary. Results of the finite element numerical simulation are compared with experimental measurements conducted at Louisiana State University using the calibration chamber. The numerical simulation is carried out for two cases. In the first case, the interface friction between the soil and the piezocone penetrometer is neglected. In the second case, interface friction is assumed between the soil and the piezocone. The results of the numerical simulations are compared with experimental laboratory measurements.     

裂隙岩体中污染物运移过程的数值模拟

基于双重介质理论模型建立了污染物在地下环境中运移的耦合数学模型,给出了有限元离散的数值格式。并以核废料储存过程中核素90Sr为例,采用所建立的数值模型模拟其在裂隙岩体中运移过程,预测了污染物的浓度分布范围和发展趋势。模拟结果表明:核素90Sr在处置库中运行40年后,下游地区的抽水井的浓度可达到3 100 Bq/m3,超出了国家规定的标准,为固体废物场址的选择以及污染的控制提供了决策依据。     

A comparison of multiscale methods for elliptic problems in porous media flow

We review and perform comparison studies for three recent multiscale methods for solving elliptic problems in porous media flow; the multiscale mixed finite-element method, the numerical subgrid upscaling method, and the multiscale finite-volume method. These methods are based on a hierarchical strategy, where the global flow equations are solved on a coarsened mesh only. However, for each method, the discrete formulation of the partial differential equations on the coarse mesh is designed in a particular fashion to account for the impact of heterogeneous subgrid structures of the porous medium. The three multiscale methods produce solutions that are mass conservative on the underlying fine mesh. The methods may therefore be viewed as efficient, approximate fine-scale solvers, i.e., as an inexpensive alternative to solving the elliptic problem on the fine mesh. In addition, the methods may be utilized as an alternative to upscaling, as they generate mass-conservative solutions on the coarse mesh. We therefore choose to also compare the multiscale methods with a state-of-the-art upscaling method – the adaptive local–global upscaling method, which may be viewed as a multiscale method when coupled with a mass-conservative downscaling procedure. We investigate the properties of all four methods through a series of numerical experiments designed to reveal differences with regard to accuracy and robustness. The numerical experiments reveal particular problems with some of the methods, and these will be discussed in detail along with possible solutions. Next, we comment on implementational aspects and perform a simple analysis and comparison of the computational costs associated with each of the methods. Finally, we apply the three multiscale methods to a dynamic two-phase flow case and demonstrate that high efficiency and accurate results can be obtained when the subgrid computations are made part of a preprocessing step and not updated, or updated infrequently, throughout the simulation. The research is funded by the Research Council of Norway under grant nos. 152732 and 158908.     

A porosity-gradient replacement approach for computational simulation of chemical-dissolution front propagation in fluid-saturated porous media including pore-fluid compressibility

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.     

Application of MODFLOW for simulating groundwater flow in the Trifilia karst aquifer, Greece

Karst aquifers can have a complex flow as a result of the formation of large conduits from dissolution features. As a result, a three-dimensional finite-difference groundwater flow model (equivalent porous media) may not apply as the dual porosity nature of karst features and the effects of turbulent flow cannot be directly simulated. Statistical analysis of karst hydrographs of the Trifilia aquifer in Greece showed the existence of a slightly karstified mass with high primary porosity that regulates the flow. An equivalent porous media model was developed to simulate the Trifilia karst aquifer using MODFLOW. Steady state and transient state calibration gave encouraging results for the equivalent porous media approach, which does not consider pipe flow or turbulence. Detailed hydrogeological research conducted in the area helped define the aquifer hydraulic conductivity zones and extent; and flux to/from the aquifer. Only hydraulic conductivity and specific yield were adjusted during calibration, as the flux to/from the system was considered known and applied as boundary conditions. Small mean absolute and RMS piezometric head error of the model under both steady and transient state conditions were achieved.     

考虑扩散路径的宾汉姆流体渗透注浆机制

浆液在多孔介质中的扩散路径对渗透扩散范围和注浆效果具有非常重要的影响。采用理论分析,以分形特征与宾汉姆流体在多孔介质中的渗流运动方程为基础,揭示了考虑扩散路径的宾汉姆流体渗透注浆机制,并利用团队前期开展的渗透注浆试验对其进行了验证。分析了多孔介质孔隙率、宾汉姆水泥浆液水灰比、多孔介质渗透系数、注浆压力、地下水压力等对扩散半径的影响变化规律。同时,基于Comsol Multiphysics平台,采用计算机编程技术二次开发得到了考虑扩散路径的宾汉姆流体渗透注浆机制的渗透注浆三维数值模拟程序,并以此开展了宾汉姆水泥浆液在多孔介质中渗透扩散形态效果的数值模拟。研究结果表明：与不考虑扩散路径的宾汉姆流体渗透注浆球形扩散公式获得的扩散半径理论计算值相比,采用考虑扩散路径的宾汉姆流体渗透注浆机制得到的扩散半径理论计算值更接近试验值。该研究成果可为实践注浆工程提供一定的理论支撑。     

Comparison of three models of dispersion in dual porosity media

The work presented in this paper shows that the probabilistic approach as well as the fractional Brownian motion model are reliable to simulate the dispersion of contaminant in the dual porosity media. Three models were tested on experimental data obtained by tracer tests in chalk characterized by a primary and a secondary porosity: a numerical model (MT3DMS), a probabilistic model based on the Bayesian approach and a fractional Brownian model. By using Einstein’s rule, it is demonstrated that the dispersion coefficient is time dependent and that the dispersion is ballistic which is a particular case of superdiffusion. A test of sensitivity was carried out and shows that the numerical model is slightly suitable to simulate the concentration in time and space for a given discharge starting from the physical parameters obtained by calibration for an other discharge because of the great sensitivity of its parameters according to the hydrodynamic conditions. On the other hand, the variability of the parameters of the two other models does not generate important errors on the values of simulated concentrations when other hydrodynamic conditions are considered.     

岩溶区地下水数值模拟研究进展

岩溶含水介质的不均一性导致岩溶地下水流动、溶质运移和热量迁移的数学模拟研究成为地下水模拟的难点。本文综述了岩溶区地下水流模拟的几种方法,重点阐述了等效多孔介质法、双重连续介质法和三重介质法的定义、发展过程和适用范围,并回顾了这几种方法的研究成果。从等效多孔介质法到三重介质法,模拟精度不断提高,适用范围也逐渐由大区域实际问题向小区域理论研究过渡。介绍了溶质运移模拟和热迁移模拟的研究方法及实例。溶质运移模拟以对流弥散方程为基础,其中尺度效应是溶质运移模拟的重点研究问题;热量迁移模拟应考虑地下热水密度变化对地下热水运动的影响。溶质运移模拟和热量迁移模拟往往是将迁移模型和已经调试成功的地下水流动模型相耦合,从而达到模拟溶质及热量迁移的目的。由于溶质运移和热量迁移的复杂性,现阶段水流模型多数处于等效多孔介质模型阶段。综合理论及实际应用,指出精确刻画裂隙及管道和注重基础数学算法是岩溶水数值模拟进步的关键。      

多尺度多孔介质有效气体输运参数的分形特征

非常规油气资源的孔隙结构及其连通性非常复杂,其孔隙尺度从毫米到纳米跨越多个量级.多孔介质中气体的输运过程不仅依赖于介质的多尺度微观结构特征,还依赖于气体的相关属性.气体在多尺度多孔介质中的输运过程包括无滑流、滑脱流和过渡流,涉及分子扩散和努森扩散等多种机制,因此很难用唯一的连续介质理论来描述气体的输运特征.大量的数据表明真实多孔介质中的内部孔隙具有分形标度特征,因此采用分形几何表征多尺度多孔介质的孔隙结构,引入孔隙分形维数和迂曲度分形维数定量表征多孔介质的微结构和弯曲流道,建立多尺度多孔介质气体输运过程的细观模型;推导了多尺度多孔介质中气体的有效渗透率和有效扩散系数,并讨论了多尺度多孔介质微结构参数和气体属性对于气体等效输运特性的定量影响.该研究不仅可以丰富渗流理论,且有利于深入理解非常规油气藏的产出机制.      

One‐dimensional dynamics of saturated incompressible porous media: analytical solutions and influence of inertia terms

The complexity of formulations for the hydromechanical coupled mechanics of porous media is typically minimised by simplifying assumptions such as neglecting the effect of inertia terms. For example, three formulations commonly employed to model practical problems are classified as fully dynamic, simplified dynamic and quasi‐static. Thus, depending on the porous media conditions, each formulation will have advantages and limitations. This paper presents a comprehensive analysis of these limitations when solving one‐dimensional fully saturated porous media problems in addition to a new solution that considers a more general loading situation. A phase diagram is developed to assist on the selection of which formulation is more appropriate and convenient regarding particular cases of porosity and hydraulic conductivity values. Non‐dimensional formulations are proposed to achieve this goal. Results using the analytical solutions are compared against numerical values obtained with the finite element method, and the effect of porosity is investigated. Copyright © 2016 John Wiley & Sons, Ltd.     

Constraint energy minimizing generalized multiscale finite element method in the mixed formulation

This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves the flow equation in a mixed formulation on a coarse grid by constructing multiscale basis functions. The resulting velocity field is mass-conservative on the fine grid. Our main goal is to obtain first-order convergence in terms of the mesh size which is independent of local contrast. This is achieved, first, by constructing some auxiliary spaces, which contain global information that cannot be localized, in general. This is built on our previous work on the generalized multiscale finite element method (GMsFEM). In the auxiliary space, multiscale basis functions corresponding to small (contrast-dependent) eigenvalues are selected. These basis functions represent the high-conductivity channels (which connect the boundaries of a coarse block). Next, we solve local problems to construct multiscale basis functions for the velocity field. These local problems are formulated in the oversampled domain, taking into account some constraints with respect to auxiliary spaces. The latter allows fast spatial decay of local solutions and, thus, allows taking smaller oversampled regions. The number of basis functions depends on small eigenvalues of the local spectral problems. Moreover, multiscale pressure basis functions are needed in constructing the velocity space. Our multiscale spaces have a minimal dimension, which is needed to avoid contrast dependence in the convergence. The method’s convergence requires an oversampling of several layers. We present an analysis of our approach. Our numerical results confirm that the convergence rate is first order with respect to the mesh size and independent of the contrast.