An Improved Pore Network Model for the Computation of the Saturated Permeability of Porous Rock

A model to estimate the permeability of a porous sample based on a 3D image of its pore space, obtained by X-ray computed tomography (CT) and applying a threshold algorithm on the CT image, is developed. Computational fluid dynamics (CFD) can be used to directly compute the saturated fluid flow in a sample. This is called the direct method. The direct method is relatively accurate, but computationally very expensive. Therefore, a new pore network approach is presented. Pore networks simplify the pore space to a network of nodes that are hydraulically connected by links. A finite difference CFD method is then applied to simulate the fluid flow inside the links and to compute the local permeability values of the links in the network according to Darcy’s law. As these links are relatively small, this demands less computational resources than a CFD simulation on the whole sample. Once the local permeabilities in the network are known, the permeability of the entire network can be calculated.     

三维射流PIV图像处理方法的研究及其精度分析

本文利用三台照相机系统记录三维射流的流动，通过照相机系统的标定、三维空间粒子的重构、空间粒子的对应及误对应向量的判断和消除等，建立了一种三个图像记录设备组成的三维PIV图像处理算法，并对其精度进行了分析，通过对三维射流图像的处理和分析表明，该方法是切实可行的。     

Computed tomographic X-ray velocimetry for simultaneous 3D measurement of velocity and geometry in opaque vessels

Computed tomographic X-ray velocimetry has been developed for simultaneous three-dimensional measurement of flow and vessel geometry. The technique uses cross-correlation functions calculated from X-ray projection image pairs acquired at multiple viewing angles to tomographically reconstruct the flow through opaque objects with high resolution. The reconstruction is performed using an iterative, least squares approach. The simultaneous measurement of the object’s structure is performed with a limited projection tomography method. An extensive parametric study using Monte Carlo simulation reveals accurate measurements with as few as 3 projection angles, and a minimum required scan angle of only 30°. When using a single/source detector system, the technique is limited to measurement of periodic or steady flow fields; however, with the use of a multiple source/detector system, instantaneous measurement will be possible. Synchrotron experiments are conducted to demonstrate the simultaneous measurement of structure and flow in a complex geometry with strong three-dimensionality. The technique will find applications in biological flow measurement, and also in engineering applications where optical access is limited, such as in mineral processing.     

Experimental two-phase flow measurement using ultra fast limited-angle-type electron beam X-ray computed tomography

An experimental evaluation of a novel limited-angle-type ultra fast electron beam X-ray computed tomography approach for the visualization and measurement of a gas–liquid two-phase flow is reported here. With this method, a simple linear electron beam scan is used to produce instantaneous radiographic views of a two-phase flow in a pipe segment of a flow loop. Electron beam scanning can be performed very rapidly, thus a frame rate of 5 kHz is achieved. Radiographic projections are recorded by a very fast detector arc made of zink–cadmium–telluride elements. This detector records the X-ray radiation passing through the object with a sampling rate of 1 MHz. The reconstruction of slice images from the recorded detector data is a limited-angle problem since in our scanning geometry the object’s Radon space is only incompletely sampled. It was investigated here, whether this technology is able to produce accurate gas fraction data from bubbly two-phase flow. Experiments were performed both on a Perspex phantom with known geometry and an experimental flow loop operated under vacuum conditions in an electron beam processing box.     

Microtomography and Pore-Scale Modeling of Two-Phase Fluid Distribution

Synchrotron-based X-ray microtomography (micro CT) at the Advanced Light Source (ALS) line 8.3.2 at the Lawrence Berkeley National Laboratory produces three-dimensional micron-scale-resolution digital images of the pore space of the reservoir rock along with the spacial distribution of the fluids. Pore-scale visualization of carbon dioxide flooding experiments performed at a reservoir pressure demonstrates that the injected gas fills some pores and pore clusters, and entirely bypasses the others. Using 3D digital images of the pore space as input data, the method of maximal inscribed spheres (MIS) predicts two-phase fluid distribution in capillary equilibrium. Verification against the tomography images shows a good agreement between the computed fluid distribution in the pores and the experimental data. The model-predicted capillary pressure curves and tomography-based porosimetry distributions compared favorably with the mercury injection data. Thus, micro CT in combination with modeling based on the MIS is a viable approach to study the pore-scale mechanisms of CO₂ injection into an aquifer, as well as more general multi-phase flows.     

Pore-Scale Lattice Boltzmann Modeling and 4D X-ray Computed Microtomography Imaging of Fracture-Matrix Fluid Transfer

We present sequential X-ray computed microtomography (CMT) images of matrix drainage in a fractured, sintered glass-granule-pack. Sequential (4D) CMT imaging captured the capillary-dominated displacement of the oil-occupied matrix by the surfactant-brine-occupied fracture at the pore scale. The sintered glass-granule-pack was designed to have minimal pore space beyond the resolution of CMT imaging, ensuring that the pore space of the matrix connected to the fracture could be captured in its entirety. This provided an opportunity to validate the increasingly common lattice Boltzmann modeling technique against experimental images at the pore scale. Although the surfactant was found to alter the wettability of the originally weakly oil-wet glass to water-wet, the fracture-matrix fluid transfer is found to be a drainage process, showing minimal counter-current migration of the initial wetting phase (decane). The LB simulations were found to closely match experimental rates of fracture-matrix fluid transfer, and trends in the saturation profiles, but not the irreducible wetting-phase saturation behind the flooding front. The underestimation of the irreducible wetting phase saturation suggests that finer image and lattice resolutions than those reported here may be required for accurate prediction of some macroscale multiphase flow properties, at a sizable computational cost.     

In vivo blood flow and wall shear stress measurements in the vitelline network

The wall shear stress plays a key role in the interaction between blood flow and the surrounding tissue. To obtain quantitative information about this parameter, velocity measurements are required with sufficient spatial (and temporal) resolution. We present a methodology for the determination of the wall shear stress in vivo in the vitelline network of a chick embryo. Velocity data is obtained by microscopic particle image velocimetry using correlation ensemble averaging; the latter is used to increase the signal-to-noise ratio of the measurements. The temporal evolution of the pulsatile flow is reconstructed by sorting the image pairs based on a phase estimate. From these flow measurements, the wall shear stress can be derived either directly from the magnitude of the gradients or from fits to velocity profiles. Both methods give results that are in good agreement with each other, while the former method is significantly easier to implement. For more accurate studies, the full three-dimensional velocity field may be required. It is demonstrated how this velocity field can be obtained by scanning the measurement volume.

---

Image analysis of oil film interferometry — a method of measuring wall shear stress distributions

A method is described of measuring a wall shear stress distribution that varies in the direction of the flow. Variations in the height of a very thin oil film moving under the boundary layer generate interference fringes, which are recorded and digitised using image processing equipment.The evolution of the film surface in space and time can be reconstructed from the interference fringe patterns and used to calculate the shear stress field. This reconstruction is achieved by comparing the picture data with images that were calculated for prescribed heights that are adjusted iteratively, until the calculated intensities match the data.The method is applied to a flow approaching a step, and the results are compared with pulsed-wire measurements.     

An Algorithm for 3D Pore Space Reconstruction from a 2D Image Using Sequential Simulation and Gradual Deformation with the Probability Perturbation Sampler

The construction of a faithful 3D pore space model of a porous medium that could reproduce the macroscopic behavior of that medium is of great interest in various fields including medicine, material science, hydrology and petroleum engineering. A computationally efficient algorithm is developed that uses the probability perturbation method and sequential multiple-point statistics simulations to generate 3D stochastic and equiprobable representations of random porous media when only a 2D thin section image is available. By employing the probability perturbation method as a gradual deformation technique, the pore patterns of a single 2D image are deformed to generate a series of 2D stochastically simulated images. The 3D pore structure is then generated by simply stacking the 2D-simulated images. The quality of the 3D reconstruction is critically dependent on the rate of deformation and a simple general procedure for choosing this parameter is presented. Various criteria such as porosity, two-point auto-correlation function, multiple-point connectivity function, local percolation probability, absolute permeability obtained by lattice-Boltzmann method (LBM), formation factor and two-phase relative permeability calculations are used to validate the results. The method is tested on two random porous solids; Berea Sandstone and synthetic Silica, for which directly measured 3D micro-CT images are available. The stochastically reconstructed 3D pore space preserves the low- and high-order spatial statistics, the macroscopic flow properties and the microstructure of the 3D micro-CT images.     

Effect of X-ray $$\mu$$ μ CT Resolution on the Computation of Permeability and Dispersion Coefficient for Granular Soils

Transport in Porous Media - X-ray micro-computed tomography ( $$\mu$$ CT) can produce realistic 3D-images of the pore structure of a material. Extracting its geometry enables the computation of...     

Calculating the Anisotropic Permeability of Porous Media Using the Lattice Boltzmann Method and X-ray Computed Tomography

A lattice Boltzmann (LB) method is developed in this article in a combination with X-ray computed tomography to simulate fluid flow at pore scale in order to calculate the anisotropic permeability of porous media. The binary 3D structures of porous materials were acquired by X-ray computed tomography at a resolution of a few microns, and the reconstructed 3D porous structures were then combined with the LB model to calculate their permeability tensor based on the simulated velocity field at pore scale. The flow is driven by pressure gradients imposed in different directions. Two porous media, one gas diffusion porous layer used in fuel cells industry and glass beads, were simulated. For both media, we investigated the relationship between their anisotropic permeability and porosity. The results indicate that the LB model is efficient to simulate pore-scale flow in porous media, and capable of giving a good estimate of the anisotropic permeability for both media. The calculated permeability is in good agreement with the measured date; the relationship between the permeability and porosity for the two media is well described by the Kozeny–Carman equation. For the gas diffusion layer, the simulated results showed that its permeability in one direction could be one order of magnitude higher than those in other two directions. The simulation was based on the single-relaxation time LB model, and we showed that by properly choosing the relaxation time, it could give similar results to those obtained using the multiple-relaxation time (MRT) LB method, but with only one third of the computational costs of MRTLB model.     

Measured Reynolds stress distributions and energy budgets of a fully pulsed round air jet

 Most particle-tracking velocimetry (PTV) algorithms are not suitable for calculating the velocity vectors of a fluid flow subjected to strong deformation, because these algorithms deal only with flows due to translation. Accordingly, it is necessary to develop a novel algorithm applicable to flows subjected to strong deformations such as rotation, shear, expansion and compression. This paper proposes a novel particle tracking algorithm using the velocity gradient tensor (VGT) which can deal with strong deformations and demonstrates that this algorithm is applicable to some basic fluid motions (rigidly rotating flow, Couette flow, and expansion flow). Furthermore, the performance of this algorithm is compared with the binary image cross-correlation method (BICC), the four-consecutive-time-step particle tracking method (4-PTV), and the spring model particle tracking algorithm (SPG) using simulations and experimental data. As a result, it is shown that this novel algorithm is useful and applicable for the highly accurate measurement and analysis of fluid flows subjected to strong deformations. Received: 9 February 1999/Accepted: 22 November 1999     

Numerical Simulation of Diagenetic Alteration and Its Effect on Residual Gas in Tight Gas Sandstones

In this study, we numerically cemented a segmented X-ray microtomography image of a sandstone to understand changes to pore space connectivity, capillary control on gas, and water distributions, and ultimately production behavior in tight gas sandstone reservoirs. Level set method-based progressive quasi-static algorithm (a state-of-the-art direct simulation of capillarity-dominated fluid displacement) was used to find the gas/water configurations during drainage and imbibition cycles. Further, we account for gas?Cwater interfacial tension changes using 1D burial history model based on available geologic data. We have found the displacement simulation method robust, and that diagenetic changes impart a significantly larger effect on gas trapping compared with interfacial tension changes.     

Space flow geometry of the radial free, wall and liquid jets with swirl

A detailed similarity analysis of the incompressible radial free, wall, and luquid jets with swirl is presented. The analysis aims at a determination of the space flow geometry of the given generally formulated problems. The derived space flow geometry implies that the transformed formulations of the given problems are formally identical to those without swirl. Unlike the free jet, the wall and liquid jets with swirl are treated only for a Newtonian fluid but in this case the similarity analysis also provides the interpretation of a virtual origin.     

动脉分岔血管内膜增生过程的数值模拟

内膜增生从发生到阻塞血管是一个复杂的变化过程,在这个过程中,内膜的增生、血管腔体形状的改变和血流动力学之间是相互影响的。为了研究这些变化,本文提出一种单元填充方法数值模拟了三维颈动脉分岔血管在低切应力作用下血管内膜增生的过程。该方法既可以克服节点移动方法所不可避免的内膜增生的不连续性,也可以避免网格重划分的困难。结果发现,如果单纯以切应力阈值作为内膜增生的判据,低切应力的作用将无法导致血管完全阻塞,但内膜增生和血流动力学之间的相互影响是可以通过数值方法进行模拟的。在本数值模拟中,内膜增生的过程分为"增厚"(先)和"扩展"(后)两个阶段,最大狭窄率为34.4%,发生在距血管分岔5mm处动脉窦的外侧壁面。其发生位置和形状与临床观察吻合。     

外框密肋复合墙抗剪机理及承载力计算

在外框密肋复合墙低周反复荷载试验的基础上,对墙体的抗剪机理进行了分析;依据极限平衡理论引入砌体抗剪承载力影响系数和框格承载力影响系数,同时考虑RC框格与填充砌块之间的相互作用;提出了外框密肋复合墙抗剪承载力计算公式;本文公式计算结果与试验结果、有限元数值模拟结果进行了比较。研究表明:本文基于水平薄弱层破坏建立的外框密肋复合墙抗剪公式较传统基于斜截面破坏建立的抗剪公式具有更明确的物理意义;本文公式计算精度较高,与试验结果、有限元数值模拟结果相差不到10%。     

Estimating gas holdup via pressure difference measurements in a cocurrent bubble column

Estimating gas holdup via pressure difference measurements is a simple and low-cost non-invasive technique to study gas holdup in bubble columns. It is usually used in a manner where the wall shear stress effect is neglected, termed Method II in this paper. In cocurrent bubble columns, when the liquid velocity is high or the fluid is highly viscous, wall shear stress may be significant and Method II may result in substantial error. Directly including the wall shear stress term in the determination of gas holdup (Method I) requires knowledge of two-phase wall shear stress models and usually requires the solution of non-linear equations. A new gas holdup estimation method (Method III) via differential pressure measurements for cocurrent bubble columns is proposed in this paper. This method considers the wall shear stress influences on gas holdup values without calculating the wall shear stress. A detailed analysis shows that Method III always results in a smaller gas holdup error than Method II, and in many cases, the error is significantly smaller than that of Method II. The applicability of Method III in measuring gas holdup in a cocurrent air–water–fiber bubble column is examined. Analysis based on experimental data shows that with Method III, accurate gas holdup measurements can be obtained, while measurement error is significant when Method II is used for some operational conditions.     

Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows

A novel method is proposed that allows accurate estimates of the local wall shear stress from near-wall mean velocity data in fully developed pipe and channel flows. DNS databases are used to demonstrate the accuracy of the method and to provide the reliability requirements on the experimental data.To demonstrate the applicability of the method, near-wall LDA measurements in turbulent pipe and channel flows were performed. The estimated wall shear stress is shown to be accurate to within 1%. Streamwise mean velocity and turbulence intensity profiles normalized with the wall friction velocity at several Reynolds numbers are presented.The current research was funded in part by the European Community under the BRITE-EURAM program, Deutsche Forschungsgemeinschaft (Du 101/16-1,2) and Deutscher Akademischer Austauschdienst. The authors are also grateful to Professors F. Nieuwstadt, N. Kasagi, P. Moin and Drs. J. Kim and N. Gilbert for providing their direct simulation data.     

土壤水分布的孔隙尺度格子玻尔兹曼模拟研究

土壤水控制着陆地生态系统几乎所有的物理和生物化学过程,准确描述土壤中水的分布与运动状态对人类发展和生态环境保护均有重要意义.土壤水分布不仅与孔隙结构有关,而且受土壤固相表面润湿性的影响.一般对土壤水分布都是从宏观尺度进行描述,但土壤中的物理及生化过程都发生在孔隙中,从孔隙尺度分析土壤水的分布规律,有助于更准确地理解土壤...