Are upwind techniques in multi-phase flow models necessary?

Two alternatives of primary variables are compared for two-phase flow in heterogeneous media by solving fully established benchmarks. The first combination utilizes pressure of the wetting fluid and saturation of the non-wetting fluid as primary variables, while the second employs capillary pressure of the wetting fluid and pressure of the non-wetting fluid. While the standard Galerkin finite element method (SGFEM) is known to fail in the physical reproduction of two-phase flow in heterogeneous media (unless employing a fully upwind correction), the second scheme with capillary pressure as a primary variable without applying an upwind technique produces correct physical fluid behaviour in heterogeneous media, as observed from experiments.     

XFEM modeling of hydraulic fracture in porous rocks with natural fractures

Hydraulic fracture (HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method (XFEM) coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures (NFs). In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex fracture network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk (KGD) model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.     

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     

多孔介质中卡森流体的分形分析

研究了非牛顿流体中的卡森流体在多孔介质中的流动特性.基于服从分形分布的弯曲毛细管束模型,运用分形几何理论推导出了该流体在多孔介质中流动的流量、流速、启动压力梯度和有效渗透率的分形解析解.模型中的每一个参数都有明确的物理意义,它将卡森流体在多孔介质中的流动特性与多孔介质的微结构参数有机联系起来.文中给出了卡森流体的流速、启动压力梯度和有效渗透率随着各影响因素的变化趋势,并进行了讨论.所得分形模型可以更深刻地理解卡森流体在多孔介质中流动的内在物理机理. 关键词： 多孔介质 卡森流体 分形     

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.     

Stochastic langevin model for flow and transport in porous media

We present a new model for fluid flow and solute transport in porous media, which employs smoothed particle hydrodynamics to solve a Langevin equation for flow and dispersion in porous media. This allows for effective separation of the advective and diffusive mixing mechanisms, which is absent in the classical dispersion theory that lumps both types of mixing into dispersion coefficient. The classical dispersion theory overestimates both mixing-induced effective reaction rates and the effective fractal dimension of the mixing fronts associated with miscible fluid Rayleigh-Taylor instabilities. We demonstrate that the stochastic (Langevin equation) model overcomes these deficiencies.     

Direct pore-level modeling of incompressible fluid flow in porous media

We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier–Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid–solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 μm resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.     

圆管内插入螺旋片状多孔介质的换热性能及场协同分析

采用数值计算的方法,以水为流动介质,研究了圆管内插入螺旋片状多孔介质在充分发展的层流区的换热及流动综合性能,并与环状和圆柱状多孔介质插入物进行了对比,此外,利用场物理量协同原理对计算结果进行了分析。结果表明,在圆管内插入螺旋片状多孔介质可以有效提高换热与流动的综合性能,其PEC达到3.60～3.95.     

Magnetic resonance imaging: applications of novel methods in studies of porous media.

NMR imaging is finding broad applications in nonbiological areas including the study of fluid flow and fluid ingress in porous media. The porous media include at the one end mineral rocks and various building materials through various solid plastic materials to foodstuffs at the other end of the spectrum. The fluids within these various media range from crude oil and water mixtures, and water itself, to a range of organic solvents in plastic materials. This paper is concerned with the flow and ingress of water through Bentheimer sandstone and Ninian reservoir specimens, and also in solid nylon blocks.     

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.     

Fluid flow control with transformation media

We introduce a new concept for the manipulation of fluid flow around three-dimensional bodies. Inspired by transformation optics, the concept is based on a mathematical idea of coordinate transformations and physically implemented with anisotropic porous media permeable to the flow of fluids. In two situations-for an impermeable object placed either in a free-flowing fluid or in a fluid-filled porous medium-we show that the object can be coated with an inhomogeneous, anisotropic permeable medium, such as to preserve the flow that would have existed in the absence of the object. The proposed fluid flow cloak eliminates downstream wake and compensates viscous drag, hinting at the possibility of novel propulsion techniques.     

微多孔介质非牛顿流体格子Boltzmann模拟

根据修正Blake-Kozeny方程对Herschel-Bulkley模型的非牛顿流体在微多孔介质中流动的定量描述,通过增加外力项建立了非牛顿流体在宏观多孔介质中的格子Boltzmann模型,并将该模型应用到平板多孔介质中非牛顿流体的电渗驱动流模拟。对多孔介质渗透性参数和非牛顿流体流变性参数的影响进行模拟和分析,获得了各种参数对多孔介质中非牛顿流体流动速度的影响规律。     

Shear zones and wall slip in the capillary flow of concentrated colloidal suspensions

We image the flow of a nearly random close packed, hard-sphere colloidal suspension (a "paste") in a square capillary using confocal microscopy. The flow consists of a "plug" in the center while shear occurs localized adjacent to the channel walls, reminiscent of yield-stress fluid behavior. However, the observed scaling of the velocity profiles with the flow rate strongly contrasts yield-stress fluid predictions. Instead, the velocity profiles can be captured by a theory of stress fluctuations originally developed for chute flow of dry granular media. We verified this both for smooth and rough walls.     

Pores resolving simulation of Darcy flows

A theoretical formulation and corresponding numerical solutions are presented for microscopic fluid flows in porous media with the domain sufficiently large to reproduce integral Darcy scale effects. Pore space geometry and topology influence flow through media, but the difficulty of observing the configurations of real pore spaces limits understanding of their effects. A rigorous direct numerical simulation (DNS) of percolating flows is a formidable task due to intricacies of internal boundaries of the pore space. Representing the grain size distribution by means of repelling body forces in the equations governing fluid motion greatly simplifies computational efforts. An accurate representation of pore-scale geometry requires that within the solid the repelling forces attenuate flow to stagnation in a short time compared to the characteristic time scale of the pore-scale flow. In the computational model this is achieved by adopting an implicit immersed-boundary method with the attenuation time scale smaller than the time step of an explicit fluid model. A series of numerical simulations of the flow through randomly generated media of different porosities show that computational experiments can be equivalent to physical experiments with the added advantage of nearly complete observability. Besides obtaining macroscopic measures of permeability and tortuosity, numerical experiments can shed light on the effect of the pore space structure on bulk properties of Darcy scale flows.     

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.     

Time-of-flight flow imaging using NMR remote detection

A time-of-flight imaging technique is introduced to visualize fluid flow and dispersion through porous media using NMR. As the fluid flows through a sample, the nuclear spin magnetization is modulated by rf pulses and magnetic field gradients to encode the spatial coordinates of the fluid. When the fluid leaves the sample, its magnetization is recorded by a second rf coil. This scheme not only facilitates a time-dependent imaging of fluid flow, it also allows a separate optimization of encoding and detection subsystems to enhance overall sensitivity. The technique is demonstrated by imaging gas flow through a porous rock.     

A Particle Resistance Model for Flow through Porous Media

A particle model for resistance of flow in isotropic porous media is developed based on the fractal geometry theory and on the drag force flowing around sphere. The proposed model is expressed as a function of porosity, fluid property, particle size, fluid velocity （or Reynolds number） and fractal characters D f of particles in porous media. The model predictions are in good agreement with the experimental data. The validity of the proposed model is thus verified.     

Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media

An optical Doppler tomography (ODT) system that permits imaging of fluid flow velocity in highly scattering media is described. ODT combines Doppler velocimetry with the high spatial resolution of low-coherence optical interferometry to measure fluid flow velocity at discrete spatial locations. Tomographic imaging of particle flow velocity within a circular conduit submerged 1 mm below the surface in a highly scattering phantom of Intralipid is demonstrated.     

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.