From the pore scale to the lab scale: 3-D lab experiment and numerical simulation of drainage in heterogeneous porous media

A well-controlled 3-D experiment with pre-defined block heterogeneities is conducted, where neutron tomography is used to map 3-D water distribution after two successive drainage steps. The material and hydraulic properties of the two sands are first measured in the laboratory with multistep outflow experiments. Additionally, the pore structure of the sands is acquired by means of image analysis of synchrotron tomography data and the structure is used for pore-scale simulation of one- and two-phase flow with Lattice-Boltzmann methods. This gives us another set of material and hydraulic parameters of the sands. The two sets of hydraulic properties (from the lab scale and from the pore scale) are then used in numerical simulations of the 3-D experiment.     

Lattice-Boltzmann simulations of the capillary pressure–saturation–interfacial area relationship for porous media

Hysteresis in the relationship between capillary pressure (P_c), wetting phase saturation (S_w) and nonwetting–wetting interfacial area per volume (a_nw) is investigated using multiphase lattice-Boltzmann simulations of drainage and imbibition in a glass bead porous system. In order to validate the simulations, the P_c–S_w and a_nw–S_w main hysteresis loops were compared to experimental data reported by Culligan et al. [Culligan KA, Wildenschild D, Christensen BS, Gray WG, Rivers ML, Tompson AB. Interfacial area measurements for unsaturated flow through porous media. Water Resour Res 2004;40:W12413]. In general, the comparison shows that the simulations are reliable and capture the important physical processes in the experimental system. P_c–S_w curves, a_nw–S_w curves and phase distributions (within the pores) show good agreement during drainage, but less satisfactory agreement during imbibition. Drainage and imbibition scanning curves were simulated in order to construct P_c–S_w–a_nw surfaces. The root mean squared error (RMSE) and mean absolute error (MAE) between drainage and imbibition surfaces was 0.10 mm⁻¹ and 0.03 mm⁻¹, respectively. This small difference indicates that hysteresis is virtually nonexistent in the P_c–S_w–a_nw relationship for the multiphase system studied here. Additionally, a surface was fit to the main loop (excluding scanning curves) of the drainage and imbibition P_c–S_w–a_nw data and compared to the surface fit to all of the data. The differences between these two surfaces were small (RMSE = 0.05 mm⁻¹ and MAE = 0.01 mm⁻¹) indicating that the P_c–S_w–a_nw surface is adequately represented without the need for the scanning curve data, which greatly reduces the amount of data required to construct the non-hysteretic P_c–S_w–a_nw surface for this data.     

Monitoring water transport in sandstone using flow propagators: A quantitative comparison of nuclear magnetic resonance measurement with lattice Boltzmann and pore network simulations

A comparison of advective displacement probability distributions (flow propagators) obtained by nuclear magnetic resonance (NMR) experiment with both lattice Boltzmann (LB) and pore network (PN) simulations is presented. Here, we apply all three methods to the exact same sample for the first time: we consider water transport in a Bentheimer sandstone. The LB and PN simulations are based on X-ray micro-tomography (XMT) images of a small rock sample; the NMR experiments are conducted on a much larger rock core-plug from which the small rock sample originated. Despite the limited size of the simulation domains, good agreement is achieved between all three sets of results, verified quantitatively by comparison of the low order moments of the flow propagators. We are concerned primarily with validating the simulations at high liquid flow rates (>10 ml min⁻¹) in high permeability sandstone, ultimately for future application to geological carbon sequestration studies. Under these conditions the LB simulation is found, as expected, to be more robust than the PN model due primarily to the reduced requirement to manually tune the simulation lattice to match the petro-physical properties of the rock.     

Micromechanics of undrained response of dilative granular media using a coupled DEM-LBM model: A case of biaxial test

In this paper the Discrete Element Method (DEM) is coupled with the Lattice-Boltzmann Method (LBM) to model the undrained condition of dense granular media that display significant dilation under highly confined loading. DEM-only models are commonly used to simulate the micromechanics of an undrained specimen by applying displacements at the domain boundaries so that the specimen volume remains constant. While this approach works well for uniform strain conditions found in laboratory tests, it doesn’t realistically represent non-uniform strain conditions that exist in the majority of real geotechnical problems. The LBM offers a more realistic approach to simulate the undrained condition since the fluid can locally conserve the system volume. To investigate the ability of the DEM-LBM model to effectively represent the undrained constraint while conserving volume and accurately calculating the stress path of the system, a two dimensional biaxial test is simulated using the coupled DEM-LBM model, and the results are compared with those attained from a DEM-only constant volume simulation. The compressibility of the LBM fluid was found to play an important role in the model response. The compressibility of the fluid is expressed as an apparent Skempton’s pore pressure parameter B. The biaxial test, both with and without fluid, demonstrated particle-scale instabilities associated with shear band development. The results show that the DEM-LBM model offers a promising technique for a variety of geomechanical problems that involve particle-fluid mixtures undergoing large deformation under shear loading.     

Impact of geometrical properties on permeability and fluid phase distribution in porous media

To predict fluid phase distribution in porous media, the effect of geometric properties on flow processes must be understood. In this study, we analyze the effect of volume, surface, curvature and connectivity (the four Minkowski functionals) on the hydraulic conductivity and the water retention curve. For that purpose, we generated 12 artificial structures with 800³ voxels (the units of a 3D image) and compared them with a scanned sand sample of the same size. The structures were generated with a Boolean model based on a random distribution of overlapping ellipsoids whose size and shape were chosen to fulfill the criteria of the measured functionals. The pore structure of sand material was mapped with X-rays from synchrotrons.     

Network flow modeling via lattice-Boltzmann based channel conductance

Lattice-Boltzmann (LB) computations of single phase, pore-to-pore conductance are compared to models in which such conductances are computed via standard pore body–channel–pore body series resistance (SR), with the conductance of each individual element (pore body, channel) based on geometric shape factor measurements. The LB computations, based upon actual channel geometry derived from X-ray computed tomographic imagery, reveal that the variation in conductance for channels having similar shape factor is much larger than is adequately captured by the geometric models. Fits to the dependence of median value of conductance versus shape factor from the LB-based computations show a power law dependence of higher power than that predicted by the geometric models. We introduce two network flow models based upon the LB conductance computations: one model is based upon LB computations for each pore-to-pore connection; the second is based upon a power law fit to the relationship between computed conductance and throat shape factor. Bulk absolute permeabilities for Fontainebleau sandstone images are computed using the SR-based network models and the two LB-based models. Both LB-based network models produce bulk absolute permeability values that fit published data more accurately than the SR-based models.     

高速铁路沿线短时大风预测方法

高速铁路沿线短时大风预测对于保障列车的安全运行至关重要。运行列车振动频率与侧风频率相同时所形成的共振极端情况,极易造成列车倾覆事故。通过分析列车的振动模态与侧风频率,建立了侧风共振简化模型,并运用阻尼振动方法得出列车典型倾覆时间为10 s。通过建立铁路在山丘后方和在三座呈品字形分布的山丘之间两种标准模型,以跃阶函数表示风场来流的变化,用以考察模型对来流变化的响应和地形因素对预测的影响。结果显示：基于格子玻尔兹曼的多观测点的准三维预测方法能够反映流场在变化来流中的响应以及地形对流场的影响。这种方法可能是解决大风预测问题的有效途径,值得深入研究。     

A study of pore geometry effects on anisotropy in hydraulic permeability using the lattice-Boltzmann method

We hypothesize that anisotropy in soil properties arises from pore-scale heterogeneity caused by the alignment of aspherical soil particles. We developed a method to predict the permeability tensor from particle shape and packing structure. Digital geometry maps were created for the pore space in regular cubic and random packs of particles with various aspect ratios using a numerical packing algorithm. The lattice-Boltzmann method was used to simulate saturated flow through these packs, and the effect of particle shape and degree of alignment on the permeability tensor was characterized. Results show that the degree of anisotropy in permeability depends not only upon particle shape and alignment, but also on the three-dimensional structure of the pack. In random packs, more oblate particles and higher degrees of particle alignment lead to reduced permeability perpendicular to the direction of particle alignment compared to the direction parallel to particle alignment.