A hierarchical fracture model for the iterative multiscale finite volume method

An iterative multiscale finite volume (i-MSFV) method is devised for the simulation of multiphase flow in fractured porous media in the context of a hierarchical fracture modeling framework. Motivated by the small pressure change inside highly conductive fractures, the fully coupled system is split into smaller systems, which are then sequentially solved. This splitting technique results in only one additional degree of freedom for each connected fracture network appearing in the matrix system. It can be interpreted as an agglomeration of highly connected cells; similar as in algebraic multigrid methods. For the solution of the resulting algebraic system, an i-MSFV method is introduced. In addition to the local basis and correction functions, which were previously developed in this framework, local fracture functions are introduced to accurately capture the fractures at the coarse scale. In this multiscale approach there exists one fracture function per network and local domain, and in the coarse scale problem there appears only one additional degree of freedom per connected fracture network. Numerical results are presented for validation and verification of this new iterative multiscale approach for fractured porous media, and to investigate its computational efficiency. Finally, it is demonstrated that the new method is an effective multiscale approach for simulations of realistic multiphase flows in fractured heterogeneous porous media.     

高速通道压裂裂缝的高导流能力分析及其影响因素研究

高速通道压裂是近年在非常规致密油气资源开采中出现的新工艺, 已在世界范围内推广实施, 并取得了良好的增产效果. 该技术可使支撑剂在人工压裂缝中形成簇团式分布, 从而形成油气高速流动通道, 提高裂缝的导流能力. 但目前对于高速通道压裂裂缝高导流能力的形成机理及其影响因素尚不清楚. 对此, 本文从流体力学理论出发, 首先将高速通道压裂裂缝内形成的支撑剂簇团视为渗流区域, 簇团间的大通道视为自由流动区域; 然后基于Darcy-Brinkman方程建立了裂缝内的流动数学模型, 采用均匀化理论对该流动数学模型进行了尺度升级, 推导得到了高速通道压裂裂缝的渗透率, 揭示了其高导流能力的形成机理; 并以此为基础, 分析了不同支撑剂簇团形状、大小以及分布方式等因素对其导流能力的影响, 可为高速通道压裂工艺参数设计与优化提供基础.     

非均一多孔介质中的水热迁移研究

孔隙裂隙非均一多孔介质中水热迁移的研究，国际上只是近年来才开始取得明显的进展。在发育裂隙的孔隙岩层中同时存在着两种渗流系统：孔隙总体积较大、渗透性相对弱的多孔岩块和总体积较小、渗透性却相对较强的分割多孔块体的裂隙。从而提出了“孔隙一裂隙二重性”假定，即地下水主要贮存在孔隙中，而水的运动主要在裂隙中进行，用一个一阶量描述孔隙裂隙间水流（热流）的传递耦合项。本文导出描述孔隙─裂隙岩层中的水流和热迁移的基本微分方程，建立起相应的数学模型，并成功地用于我国西藏羊八井热田分布参数模型的水热迁移研究。     

缝洞型介质流动模拟的多尺度分解法

缝洞型介质通常具有非均质性强、结构多尺度的特征.传统数值方法在解决此类多尺度流动问题时,难以兼顾计算精度与计算效率,无法实际应用.对此,本文提出了多孔介质流体流动的多尺度分解法,并应用于缝洞介质流动模拟,能够大幅减小计算的复杂度,同时,可以通过控制均化程度控制计算精度.该方法将求解空间分为若干个子空间的正交直和,从而获得一个近线性的计算复杂度;以分层计算的方式实现了快速计算,另外这种方法是一种无网格方法,具有较好的地层适应性.同时,采用离散缝洞模型简化缝洞结构,进一步提高了计算效率.详细阐述了基于多尺度分解法的多孔介质流体流动数值计算格式的建立,重点介绍了如何在不同的层次上计算基函数.数值结果表明,本文提出的计算方法不仅能够准确捕捉多孔介质中的精细流动特征,而且具有很高的计算效率,是一种有效的流动模拟方法.     

基于相场方法的孔隙尺度油水两相流体流动模拟

基于真实岩心颗粒粒径分布，利用过程法构建疏松砂岩油藏的三维孔隙结构模型，利用相场方法建立两相流体流动数学模型并利用有限元方法进行求解，研究驱替速度、流体性质、润湿性对剩余油分布以及采出程度的影响.结果表明：驱替速度的增大和油水粘度比的减小会导致较大的毛管数，进而有利于采出程度的提高；就润湿性而言，水湿条件下毛管力是水驱油的动力，而在油湿条件下是阻力，因此水湿岩心采出程度更高.同时，从孔隙尺度对油水渗流机理及剩余油分布机理进行揭示，结果表明：由于多孔介质的复杂孔隙结构，流体在流经不同孔隙时呈现不同的流动特征，进而对油水两相流整体的压力分布、流速分布造成重要影响.     

Lattice Boltzmann method on quadtree grids for simulating fluid flow through porous media: A new automatic algorithm

During the past two decades, the lattice Boltzmann (LB) method has been introduced as a class of computational fluid dynamic methods for fluid flow simulations. In this method, instead of solving the Navier Stocks equation, the Boltzmann equation is solved to simulate the flow of a fluid. This method was originally developed based on uniform grids. However, in order to model complex geometries such as porous media, it can be very slow in comparison with other techniques such as finite differences and finite elements. To eliminate this limitation, a number of studies have aimed to formulate the lattice Boltzmann on the unstructured grids. This paper deals with simulating fluid flow through a synthetic porous medium using the LB method and on the quadtree grid structure. To this end, the LB method was used on nonuniform grids coupled with a technique for image reconstruction which resulted in the quadtree grids for simulation of fluid flow through porous media. Accuracy and efficiency of this algorithm is compared against the conventional LB method based on uniform grids. While the decrease in computational time in the proposed LB method on nonuniform grids is found to be significant regarding the size of the initial and reconstructed images, the same level of accuracy is obtained when compared with the conventional LB method on uniform grids.     

基于离散裂缝模型的裂缝性油藏注水开发数值模拟

针对目前裂缝性油藏数值模拟方法存在的问题,基于单裂缝等效的概念,建立离散裂缝模型.对宏观大裂缝进行显式降维处理,在保证高计算效率的同时能够真实地反映裂缝对整个油藏流体流动的影响.详细阐述模型的基本原理,基于Galerkin加权残量法推导有限元数值计算格式,实现二维问题的数值模拟,通过算例验证模型和算法的正确性.以此为基础,分析裂缝对注水开发效果的影响.计算结果表明,对于裂缝发育程度不高尤其是当油藏中存在数条控制着流体流动方向的大裂缝时,离散裂缝模型具有很好的适用性.     

水平井体积压裂缝网表征及流动耦合模型

针对岩石脆性系数高且发育天然裂缝的储层,提出表征水平井体积压裂形成裂缝网络的三种基本模式,并将渗流过程划分为油藏流动和缝网内部流动.在此基础上,利用势叠加原理导出油藏流动控制方程,利用有限差分方法建立缝网内部有限导流等式;其次,采用星三角变换法处理人工缝与天然缝的交汇流动;最后,耦合两部分流动矩阵方程得到水平井体积压裂缝网渗流数学模型.该模型表明:当水平井改造段长度一定时,压裂段数与段内分簇数是决定产能的最主要因素,其次是人工裂缝半长和人工缝导流能力,而天然裂缝密度和导流能力对产量影响较小.实例应用表明,实际产油量与模型计算值一致,误差较小.     

用格子玻尔兹曼方法研究流动-反应耦合的非线性渗流问题

根据格子玻尔兹曼计算技术以及相应渗流理论，对多孔介质内流动-反应(矿物介质的溶解等)耦合这一非线性渗流问题进行了数值研究，计算结果与解析解基本符合.数字图像重构技术反映的结果表明流体流动和反应之间可以发生强烈的耦合和反耦合作用，同时可以形成条带结构这一自组织现象，与实验和其他理论分析结果符合也很好. 关键词： 非线性渗流 耦合反应 数值模型     

多孔介质两相流的局部守恒有限元分析

用局部守恒有限元法研究多孔介质两相渗流问题.详细阐述局部守恒有限元法的基本原理,推导两相渗流问题的局部守恒有限元计算格式并编制相应的计算程序.通过一维Buckley-Leverett两相渗流算例验证该方法的正确性.应用局部守恒有限元法和混合有限元法分别对2个模型进行分析对比.计算结果表明局部守恒有限元法具有良好的鲁棒性及适用性,相较于混合有限元法,处理过程简单,计算时间缩短,为标准有限元法应用于复杂渗流问题提供了一种途径.     

Coupling transfer matrix method to finite element method for analyzing the acoustics of complex hollow body networks

This paper exposes a procedure to couple multiport transfer matrices to finite elements for analyzing the acoustics of automotive hollow body networks with a minimum of memory requirements and computational time. Generally, hollow body networks are made up from a series of elongated fluid partitions similar to ducts or waveguides. These fluid partitions generally contain complex elements: junctions, noise control elements, and cavities. The location and type of these elements in the network, mainly the noise control elements (e.g., sealing parts), may impact the noise inside a car. In the proposed hybrid method, the elongated fluid partitions are modeled with fluid finite elements. All complexities are modeled with two-port or multiport transfer matrices. The coupling of these matrices to finite elements is naturally done at the weak integral formulation stage of the acoustical problem. The coupling does not add any degrees of freedom to, nor modify, the original finite element matrix system. Consequently, changing locations and types of noise control elements in the hollow body network is fast and does not require rebuilding the finite element system. This enables optimizing the acoustics of a complex network on a desktop computer. The hybrid method is compared to experimental results on a tee-shaped hollow body networks. Good correlations are obtained.     

裂缝性介质多尺度深度学习模型

结合人工神经网络建立裂缝介质多尺度深度学习流动模型.基于一套粗网格和一套细网格,通过在粗网格上训练数据,多尺度神经网络能够以较少的自由度训练出准确的神经网络.并在粗网格上通过求解局部流动问题获得多尺度基函数,结合神经网络进一步得到精细网格的解.基于离散裂缝的流动方程可视为多层网络,网络层数依赖于求解时间步数.阐述裂缝介质多尺度机器学习数值计算格式的建立,介绍如何使用多尺度算法构建离散裂缝模型的多尺度基函数,并采用超样本技术进一步提高计算准确性.数值结果表明,多尺度有限元算法与机器学习结合是一种有效的流体流动模拟算法.     

Experimental study and theoretical analysis of fluid resistance in porous media of glass spheres

Porous media have a wide range of applications in production and life, as well as in science and technology. The study of flow resistance in porous media has a great effect on industrial and agricultural production. The flow resistance of fluid flow through a 20-mm glass sphere bed is studied experimentally. It is found that there is a significant deviation between the Ergun equation and the experimental data. A staggered pore-throat model is established to investigate the flow resistance in randomly packed porous media. A hypothesis is made that the particles are staggered in a regular triangle arrangement. An analytical formulation of the flow resistance in random porous media is derived. There are no empirical constants in the formulation and every parameter has a specific physical meaning. The formulation predictions are in good agreement with the experimental data. The deviation is within the range of 25%. This shows that the staggered pore-throat model is reasonable and is expected to be verified by more experiments and extended to other porous media.     

Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method

We present a stable numerical scheme for modelling multiphase flow in porous media, where the characteristic size of the flow domain is of the order of microns to millimetres. The numerical method is developed for efficient modelling of multiphase flow in porous media with complex interface motion and irregular solid boundaries. The Navier–Stokes equations are discretised using a finite volume approach, while the volume-of-fluid method is used to capture the location of interfaces. Capillary forces are computed using a semi-sharp surface force model, in which the transition area for capillary pressure is effectively limited to one grid block. This new formulation along with two new filtering methods, developed for correcting capillary forces, permits simulations at very low capillary numbers and avoids non-physical velocities. Capillary forces are implemented using a semi-implicit formulation, which allows larger time step sizes at low capillary numbers. We verify the accuracy and stability of the numerical method on several test cases, which indicate the potential of the method to predict multiphase flow processes.     

A model for strong attenuation and dispersion of seismic P-waves in a partially saturated fractured reservoir

In this work we interpret the data showing unusually strong velocity dispersion of P-waves (up to 30%) and attenuation in a relatively narrow frequency range. The cross-hole and VSP data were measured in a reservoir, which is in the porous zone of the Silurian Kankakee Limestone Formation formed by vertical fractures within a porous matrix saturated by oil, and gas patches. Such a medium exhibits significant attenuation due to wave-induced fluid flow across the interfaces between different types of inclusions (fractures, fluid patches) and background. Other models of intrinsic attenuation (in particular squirt flow models) cannot explain the amount of observed dispersion when using realistic rock properties. In order to interpret data in a satisfactory way we develop a superposition model for fractured porous rocks accounting also for the patchy saturation effect.     

A Lattice Boltzmann Model for Fluid-Solid Coupling Heat Transfer in Fractal Porous Media

We report a lattice Boltzmann model that can be used to simulate fluid-solid coupling heat transfer in fractal porous media. A numerical simulation is conducted to investigate the temperature evolution under different ratios of thermal conductivity of solid matrix of porous media to that of fluid. The accordance of our simulation results with the solutions from the conventional CFD method indicates the feasibility and the reliability for the developed lattice Boltzmann model to reveal the phenomena and rules of fluid-solid coupling heat transfer in complex porous structures.     

Numerical simulation of deformation and fracture of a material with a polysilazane-based coating

The paper studies the localization of plastic deformation and fracture in a material with a porous coating. A dynamic boundary value problem in the plane strain formulation is solved. The numerical simulation is performed by the finite difference method. The composite structure corresponds to the experimentally observed one and is specified explicitly in the calculation. A generation procedure of the initial finite-difference grid is developed to describe the coating structure with adjustable porosity and geometry of the substrate-coating interface. Constitutive equations for the steel substrate include an elastic-plastic model of an isotropically hardening material. The ceramic coating is described by a brittle fracture model on the basis of the Huber criterion which accounts for crack nucleation in triaxial tension zones. It is shown that the specific character of deformation and fracture of the studied composite results from the presence of local tensile regions in the vicinity of pores and along the coating-substrate interface, in both tension and compression of the coated material. The interrelation between inhomogeneous plastic flow in the steel substrate and crack propagation in the coating is studied.     

Poroelastic modeling of seismic boundary conditions across a fracture

Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.     

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.     

表征体元尺度渗流的离散统一动理学格式

结合表征体元尺度的通用渗流模型,提出离散统一动理学格式（DUGKS）渗流方法,分别用均匀网格和非均匀网格计算二维Poiseuille、Couette、方腔流等经典渗流问题,检验DUGKS渗流方法的有效性和非均匀网格应用的优势,将DUGKS渗流方法应用到裂缝系统中.