Generation of Voronoi Grid Based on Vorticity for Coarse-Scale Modeling of Flow in Heterogeneous Formations

We present a novel unstructured coarse grid generation technique based on vorticity for upscaling two-phase flow in permeable media. In the technique, the fineness of the gridblocks throughout the domain is determined by vorticity distribution such that where the larger is the vorticity at a region, the finer are the gridblocks at that region. Vorticity is obtained from single-phase flow on original fine grid, and is utilized to generate a background grid which stores spacing parameter, and is used to steer generation of triangular and finally Voronoi grids. This technique is applied to two channelized and heterogeneous models and two-phase flow simulations are performed on the generated coarse grids and, the results are compared with the ones of fine scale grid and uniformly gridded coarse models. The results show a close match of unstructured coarse grid flow results with those of fine grid, and substantial accuracy compared to uniformly gridded coarse grid model.     

Dispersion Measurements in Highly Heterogeneous Laboratory Scale Porous Media

Laboratory experiments and numerical simulations investigate conservative contaminant transport in a heterogeneous porous medium. The laboratory experiments were performed in cylindrical columns 1m long and 3.5cm inside diameter filled with spherical glass beads. Concentration breakthrough curves are measured at a scale much finer than the size of the heterogeneity. Numerical simulations are based on a random walk in a known constant velocity field. The heterogeneity is a distinct, discontinuous change in the local permeability field. Fluid flow is miscible, flowing in a saturated porous medium. Previous work has shown this to be a very poorly understood phenomenon. The measurements reported here help to better understand how dispersion evolves through and past a heterogeneity.     

Concentration and Lack of Observability¶of Waves in Highly Heterogeneous Media

We construct rapidly oscillating Hölder continuous coefficients for which the corresponding 1-dimensional wave equation lacks the classical observability property guaranteeing that the total energy of solutions may be bounded above by the energy localized in an open subset of the domain where the equation holds, if the observation time is large enough. The coefficients we build oscillate arbitrarily fast around two accumulation points. This allows us to build quasi-eigenfunctions for the corresponding eigenvalue problem that concentrate the energy away from the observation region as much as we wish. This example may be extended to several space dimensions by separation of variables and illustrates why the well-known controllability and dispersive properties for wave equations with smooth coefficients fail in the class of Hölder continuous coefficients. In particular we show that for such coefficients no Strichartz-type estimate holds.     

Pressure Transient Behavior of High-Fracture-Density Reservoirs (Dual-Porosity Models)

Transport in Porous Media - Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties...     

Accurate Representation of Near-well Effects in Coarse-Scale Models of Primary Oil Production

Near-well effects can have a strong impact on many subsurface flow processes. In oil production, because dissolved gas is released from the oil phase when the pressure falls below the bubble point, the detailed pressure field in the immediate vicinity of a production well strongly impacts gas (and thus oil) production. This effect is complicated by the interplay of fine-scale heterogeneity and two-phase flow physics, and can be difficult to capture in coarse-grid simulations. In this article, we develop and apply a new upscaling (coarse-graining) procedure to capture such near-well subgrid effects in coarse-scale flow simulation models. The method entails the use of preprocessing computations over near-well domains [referred to as local well models (LWM)] for the determination of upscaled single-phase and two-phase near-well parameters. These parameters are computed by minimizing the mismatch between fine and coarse-scale flows over the LWM. Minimization is accomplished using a gradient-based optimization procedure, with gradients calculated through solution of adjoint equations. The boundary conditions applied on the LWM can impact the upscaled parameters, but these boundary conditions depend on the global flow and are not, therefore, known a priori. In order to circumvent this difficulty, an adaptive local–global procedure is applied. This entails performing a global coarse-scale simulation with initial estimates for well-block parameters. The resulting pressure and saturation fields are then used to define local boundary conditions for the near-well computations. The overall procedure is applied to several example problems and is shown to provide results in close agreement with reference fine-scale computations. Significant improvement in accuracy over existing near-well upscaling treatments is demonstrated, particularly for a heavy oil case with oil viscosity of ~10⁴ cp.     

Dual-Porosity and Dual-Fracture Model for Fractured Geothermal Reservoir Simulations

Transport in Porous Media - The dual-porosity model is widely used in fractured geothermal reservoir simulations. However, the commonly-used dual-porosity approach does not always adapt to...     

2-D Numerical Modeling of Bioremediation in Heterogeneous Saturated Soils

This paper presents a numerical solution approach for an existing model for simulating transport and biodegradation in saturated porous media. The discrete approximation makes use of an appropriate blending of mixed-hybrid finite-element and shock-capturing finite-volume schemes. The model is applied for simulating enhanced-bioremediation of highly heterogeneous porous media contaminated by organic pollutants. Injection of water enriched in dissolved oxygen (DO) is considered for accelerating contaminant degradation and concentration of both organic pollutant (substrate) and DO. Heterogeneity is found to produce pools of contaminants which strongly affect DO delivery and, then, the degradation of the organic contaminant. A set of numerical results on representative situations illustrates the effectiveness and the robustness of the present approach. The computational efficiency of the present approach is also estimated in terms of CPU costs and memory requirements.     

Continuum Mechanics Modeling and Simulation of Carbon Nanotubes

The understanding of the mechanics of atomistic systems greatly benefits from continuum mechanics. One appealing approach aims at deductively constructing continuum theories starting from models of the interatomic interactions. This viewpoint has become extremely popular with the quasicontinuum method. The application of these ideas to carbon nanotubes presents a peculiarity with respect to usual crystalline materials: their structure relies on a two-dimensional curved lattice. This renders the cornerstone of crystal elasticity, the Cauchy–Born rule, insufficient to describe the effect of curvature. We discuss the application of a theory which corrects this deficiency to the mechanics of carbon nanotubes (CNTs). We review recent developments of this theory, which include the study of the convergence characteristics of the proposed continuum models to the parent atomistic models, as well as large scale simulations based on this theory. The latter have unveiled the complex nonlinear elastic response of thick multiwalled carbon nanotubes (MWCNTs), with an anomalous elastic regime following an almost absent harmonic range.     

CT Imaging of Low-Permeability, Dual-Porosity Systems Using High X-ray Contrast Gas

Low-permeability, dual-porosity media such as coal and gas shale (i.e., mudstone) exhibit structural and chemical features across a range of scales spanning from tens of meters to nanometers. Characterization methods and efforts for these porous media are needed to understand gas in place, gas flow behavior, and storage capacity for potential CO $_{2}$ sequestration. Characterizing the structure and heterogeneity of representative samples helps determine how the physical and chemical processes associated with CO $_{2}$ transport in coal and gas shale affect injectivity and storage capacity (over long periods of time), and the ability of these media to sequester CO $_{2}$ (as both a free and adsorbed phase) for thousands of years. In this study, an imaging technique focused on the submillimeter scale is applied to shale and coal samples of interest. In particular, porosity, component matrix distribution, and evidence of gas transport through these tight media were studied.     

Numerical Simulation of Two-Phase Inertial Flow in Heterogeneous Porous Media

In this study, non-Darcy inertial two-phase incompressible and non-stationary flow in heterogeneous porous media is analyzed using numerical simulations. For the purpose, a 3D numerical tool was fully developed using a finite volume formulation, although for clarity, results are presented in 1D and 2D configurations only. Since a formalized theoretical model confirmed by experimental data is still lacking, our study is based on the widely used generalized Darcy–Forchheimer model. First, a validation is performed by comparing numerical results of the saturation front kinetics with a semi-analytical solution inspired from the Buckley–Leverett model extended to take into account inertia. Second, we highlight the importance of inertial terms on the evolution of saturation fronts as a function of a suitable Reynolds number. Saturation fields are shown to have a structure markedly different from the classical case without inertia, especially for heterogeneous media, thereby, emphasizing the necessity of a more complete model than the classical generalized Darcy’s one when inertial effects are not negligible.     

Homogenization Modeling and Parametric Study of Moisture Transfer in an Unsaturated Heterogeneous Porous Medium

The classical mass balance equation is usually used to model the transfer of humidity in unsaturated macroscopically homogeneous porous media. This equation is highly non-linear due to the pressure-dependence of the hydrodynamic characteristics. The formal homogenization method by asymptotic expansions is applied to derive the upscaled form of this equation in case of large-scale heterogeneities of periodic structure. The nature of such heterogeneities may be different, resulting in locally variable hydrodynamic parameters. The effective capillary capacity and the effective hydraulic conductivity are defined as functions of geometry and local characteristics of the porous medium. A study of a two-dimensional stone-mortar system is performed. The effect of the second medium (the mortar), on the global behavior of the system is investigated. Numerical results for the Brooks and Corey hydrodynamic model are provided. The sensitivity analysis of the parameters of the model in relation to the effective hydrodynamic parameters of the porous structure is presented.     

Experimental and Theoretical Simulation of Heterogeneous Catalysis in Aerothermochemistry (a Review)

The design of aerospace vehicles has required the solution of radically new scientific and technological problems. One of the important problems has been to create reusable heat shield materials. In [1, 2] information concerning the methods and results of solving these problems, including the development of composites from ultrathin quartz fibers and carbon-carbon materials for the “Buran” orbital vehicle heat shield, was presented. The basic thermophysical characteristics of these materials include both the rate or probability coefficients of heterogeneous nitrogen and oxygen atom recombination and the accommodation coefficients of energy recombination at high surface temperatures. In the present paper the experimental and computational aspects of determining these parameters, which are also of interest for new heat shield materials for future space transport systems, are discussed.     

Heterogeneous Fracture Simulation of Three-point Bending Plain-concrete Beam with Double Notches

Plain concrete is regarded as a two-phase material comprising randomly distributed aggregates and mortar matrix. A series of three-point bending concrete beams with symmetric or asymmetric double notches are modeled using the modified random aggregate generation and packing algorithm. The cohesive zone model is used as the fracture criterion and the cohesive elements are inserted into both the mortar matrix and the aggregate-mortar interfaces as potential micro-cracking zones. The dead and alive crack phenomena are studied experimentally and numerically; and the influences of notch location, aggregate distribution and gradation on fracture are numerically evaluated. Some important conclusions are given.     

Large Eddy Simulation of Turbulent Confined Highly Swirling Annular Flows

The present paper discusses the Large Eddy Simulation of a confined non-reacting annular swirling jet. The configuration corresponds to a well investigated flow studied experimentally by Sheen (1993). The flow field is characterised by a high swirl number resulting in relatively complex features. The challenging behaviour of the flow is governed by the interaction of several recirculation zones. The central recirculation zone formed by the swirling jet is strongly affected by the cylindrical centre body which acts as a bluff body. The flow features coherent structures such as Precessing Vortex Cores (PVCs), which create regions with high velocity fluctuations. The simulations presented comprise a detailed investigation of the parameters controlling the inert flow and a thorough comparison with the experimental data.     

Uncertainty Quantification for Flow and Transport in Highly Heterogeneous Porous Media Based on Simultaneous Stochastic Model Dimensionality Reduction

Transport in Porous Media - Groundwater flow models are usually subject to uncertainty as a consequence of the random representation of the conductivity field. In this paper, we use a Gaussian...     

电梯轿厢-导靴-导轨耦合振动建模与仿真分析

导靴是连接轿厢和导轨的纽带,本文从轿厢导靴导轮-导轨及挡板-导轨的接触出发,推导了接触刚度系数用于计算接触力．建立了一种较为实用的电梯轿厢、导靴和导轨耦合振动的动力学模型,计算了系统在导轨支架多点激励作用下的水平振动响应．结果表明,该模型可以较好的模拟导轮-导轨及挡板-导轨的接触分离现象;电梯运行时,导轨刚度变化产生的参数激励明显放大导靴与导轨的接触力及脱离量,运行速度的影响非常显著．     

Modeling and Simulation of Microbial Enhanced Oil Recovery Including Interfacial Area

The focus of this paper is the derivation of a nonstandard model for microbial enhanced oil recovery (MEOR) that includes the interfacial area (IFA) between oil and water. We consider the continuity equations for water and oil, a balance equation for the oil–water interfacial area, and advective–dispersive transport equations for bacteria, nutrients, and biosurfactants. Surfactants lower the interfacial tension (IFT), which improves oil recovery. Therefore, the parametrizations of the IFT reduction and residual oil saturation are included as a function of the surfactant concentration in the model. We consider for the first time in context of MEOR, the role of IFA in enhanced oil recovery. The motivation to include the IFA is to model the hysteresis in the capillary pressure–saturation relationship in a physically based manner, to include the effects of observed bacteria migration toward the oil–water interface and the production of biosurfactants at the oil–water interface. A comprehensive 2D implementation based on two-point flux approximation and backward Euler is proposed. An efficient and robust linearization scheme is used to solve the nonlinear systems at each time step. Illustrative numerical simulations are presented. The differences in the oil recovery profiles obtained with and without IFA are discussed. The presented model can also be used to design new experiments toward a better understanding and eventually optimization of MEOR.