Transport of Three-Phase Hyper-Saline Brines in Porous Media: Examples

This paper presents a number of applications of a new code which can simulate the transport of high temperature three-phase (gas, liquid, solid) hyper-saline fluids in a porous medium. The examples presented demonstrate that multiple phase changes occur as the fluid state evolves across the H₂O–NaCl phase diagram. Multi-phase flows occur in a variety of situations, including a horizontal domain with fluid withdrawal, a vertical counter-flowing salt-pipe, and a horizontal domain with saturation shocks and expansion waves. The code is also used to simulate heat, water and salt flows in a large scale model (10s of km) of the Taupo Volcanic Zone, New Zealand.     

Gedeon Dagan and Shlomo Neuman: Subsurface Flow and Transport: A Stochastic Approach

Transport in Porous Media -     

三维正交机织复合材料的力学性能研究

利用材料试验机装置开展了三维正交机织Kevlar/乙烯基树脂复合材料力学实验,实验表明面内经向拉伸和厚度z方向压缩时,材料具有一定的应变率效应,厚度z方向压缩强度远大于面内压缩强度,而面内经向和纬向的拉伸强度则相当.结合纤维的编织方式,对这些现象做了必要的定性分析.最后,本文基于三维正交机织复合材料的结构特点,推导了一组可用于估算三维正交机织复合材料弹性模量的公式,估算结果和实验值接近.     

Modeling of the 3D rocking problem

The rocking motion of a rigid rectangular prism on a moving base is a complex three dimensional phenomenon. Although, with very few exceptions, the previous models in the literature make the simplified assumption that this motion is planar, this is usually not true since a body will probably not be aligned with the direction of the ground motion. Thus, even in the case where the body is fully symmetric, the rocking motion involves three dimensional rotations and displacements.In this work, a three dimensional formulation is introduced for the rocking motion of a rigid rectangular prism on a deformable base. Two models are developed: the Concentrated Springs Model and the Winkler Model. Both sliding and uplift are taken into account and the fully non-linear equations of the problem are developed and solved numerically.The models developed are later used to examine the behavior of bodies subjected to general ground excitations. The contribution of phenomena neglected in previous models, such as twist, is stressed.     

Stochastic Flow Simulation and Particle Transport in a 2D Layer of Random Porous Medium

A stochastic numerical method is developed for simulation of flows and particle transport in a 2D layer of porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modeled in the layer with prescribed boundary conditions. Numerical experiments are carried out by solving the Darcy equation for each sample of the hydraulic conductivity by a direct solver for sparse matrices, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, longitudinal dispersion coefficient, and the mean displacement of Lagrangian trajectories. We discuss the effect of long-range correlations of the longitudinal velocities which we have found in our numerical simulations. The related anomalous diffusion is also analyzed.     

A Model for Predicting Effective Properties of Piezocomposites with Non-piezoelectric Inclusions

Most piezocomposites, which have been widely used in engineering, consist of piezoelectric inclusions and a non-piezoelectric matrix. Due to the limits of fabrication technology, it is hard to avoid the matrix intermingling with other non-piezoelectric inclusions, such as cavities. The non-piezoelectric inclusions can substantially affect performance of piezocomposites. In this paper we study the electromechanical fields in piezocomposites which are composed of a non-piezoelectric matrix embedded with both piezoelectric and non-piezoelectric inclusions. Closed-form relations are obtained for the effective electroelastic moduli of a piezocomposite with both piezoelectric and non-piezoelectric inclusions. The effective properties of a 1-3 type piezocomposite with non-piezoelectric spherical inclusions are analyzed carefully and explicit formulae for the effective electroelastic properties of a 1-3-0 piezocomposite are also obtained. The analysis shows that the effect of non-piezoelectric inclusions on the electroelastic properties of piezocomposites is significant and should not be neglected. The model proposed in this paper is expected to be useful for predicting and analyzing the overall electromechanical properties of piezocomposites with a non-piezoelectric matrix containing both piezoelectric and non-piezoelectric inclusions.     

Transient Stochastic Analysis of Biodegradable Contaminant Transport: First-Order Decay

A stochastic methodology was used to analyze the field-scale transport of solutes in heterogeneous aquifers with first-order biodegradation. Spectral methods and perturbation techniques were utilized to develop expressions for the field-scale effective parameters in the mean transport model. Expressions were obtained for the longitudinal and transverse macrodispersivity coefficients, and effective velocity and an effective decay parameter for statistically anisotropic, and isotropic, heterogeneous porous medium, respectively. The behavior of these parameters was described as function of time and log K correlation scale. The expressions for asymptotic values of the dispersivity coefficients and effective velocity and decay parameters were also derived for the isotropic case.     

Exact Averaging of Stochastic Equations for Transport in Random Velocity Field

We present new examples of exactly averaged multi-dimensional equation of transport of a conservative solute in a time-dependent random flow velocity field. The functional approach and a technique for decoupling the correlations are used. In general, the averaged equation is non-local. We study the special cases where the averaged equation can be localized and reduced to a differential equation of finite-order, where the problem of evolution of the initial plume (Cauchy problem) can be solved exactly. We present in detail the results of the analyses of two cases of exactly averaged problems for Gaussian and telegraph random velocity with an identical exponential correlation function, which are informative and convenient models for continuous and discontinuous random functions. The problems in which the field has sources of solute and boundaries are also examined. We study the behavior of different initial plumes for all times (evolutions and convergence) and show the manner in which they approach the same asymptotic limit for two stochastic distributions of flow-velocity. A comparison between exact solutions and solutions derived by the method of perturbation is also discussed.     

Upscaling of Stochastic Micro Model for Suspension Transport in Porous Media

Micro scale population balance equations of suspension transport in porous media with several particle capture mechanisms are derived, taking into account the particle capture by accessible pores, that were cut off the flux due to pore plugging. The main purpose of the article is to prove that the micro scale equations allow for exact upscaling (averaging) in case of filtration of mono dispersed suspensions. The averaged upper scale equations generalise the classical deep bed filtration model and its latter modifications.     

Effect of 2D Image Resolution on 3D Stochastic Reconstruction and Developing Petrophysical Trend

Multi-resolution digital rock physics (DRP) makes it possible to up-scale petrophysical properties from micron size to core sample size using two-dimensional (2D) thin section images. Resolution of 3D images and sample size are challenging problems in DRP where high-resolution images are acquired from small samples using inefficient and expensive micro-CT facilities. Three-dimensional stochastic reconstruction is an alternative approach to overcome these challenges. In this paper, we use multi-resolution images and investigate effect of 2D image resolution on 3D stochastic reconstruction and development of petrophysical trends for our two sandstone and carbonate original representative volume elements (RVEs). The proposed method includes three steps. In the first step, the spatial resolution of our original RVEs is decreased synthetically. In the second step, stochastic RVEs are realized for each resolution using two perpendicular images, correlation functions, and phase recovery algorithm. In the reconstruction method, a full set of two-point correlation functions (TPCFs) is extracted from two perpendicular 2D images. Then TPCF vectors are decomposed and averaged to realize 3D stochastic RVEs. In the third step, petrophysical properties like relative and absolute permeability as well as porosity and formation factor are computed. The output is used to develop trends for petrophysical properties in different resolutions. Experimental results illustrate that the proposed method can be used to predict petrophysical properties and reconstruct 3D RVEs for resolutions unavailable in the acquired 2D or 3D data.     

Stochastic Analysis of Reactive Solute Transport in Heterogeneous,Fractured Porous Media: A Dual-Permeability Approach

A nonlocal, first-order, Eulerian stochastic theory is developed for reactive chemical transport in a heterogeneous, fractured porous medium. A dual-permeability model is adopted to describe the flow and transport in the medium, where the solute convection and dispersion in the matrix are considered. The chemical is under linear nonequilibrium sorption and first-order degradation. The hydraulic conductivities, sorption coefficients, degradation rates in both fracture and matrix regions, and interregional mass transfer coefficient are all assumed to be random variables. The resultant theory for mean concentrations in both regions is nonlocal in space and time. Under spatial Fourier and temporal Laplace transforms, the mean concentrations are explicitly expressed. The transformed results are then numerically inverted to the real space via Fast Fourier Transform method. The theory developed in this study generalizes the stochastic studies for a reactive chemical transport in a one-domain flow field (Hu et al., 1997a) and in a mobile/immobile flow field (Huang and Hu, 2001). In comparison with one-domain transport, the dual-permeability model predicts a larger second moment in the longitudinal direction, but smaller one in the transverse direction. In addition, various simplification assumptions have been made based on the general solution. The validity of these assumptions has been tested via the spatial moments of the mean concentration in both fracture and matrix regions.     

Experimental Investigation on Transport Properties of Cement-Based Materials Incorporating 2D Crack Networks

This paper investigates the correlation between the geometry of crack networks and the altered transport properties of cement-based porous materials. Cracks were artificially introduced into slice specimens to obtain bidimensional (2D) crack networks, and the network was characterized by the crack density, orientation, connectivity and crack opening aperture. For the permeability, the water vapor sorption isotherms were measured and an algorithm was established to solve the intrinsic permeability of cracked specimens with the help of moisture transport modeling and the data of drying tests. The electrical conductivity of cracked specimens was measured using an alternative current method. The study on the specimens with percolated cracks shows that: (1) the pertinent geometry parameters for altered transport properties include average-based crack density, crack opening and local crack connectivity; (2) the water permeability of cracked specimens is correlated to the combination \(b^{1.7}\rho f\) and electrical conductivity to \(b^{0.45}\rho f\); (3) the different exponents on the crack opening/length ratio reflect the resistance of tortuosity of crack paths to the water and current flow and this resistance is stronger for current flow.     

Modeling rock specimens through 3D printing: Tentative experiments and prospects

Current developments in 3D printing (3DP) technology provide the opportunity to produce rock-like specimens and geotechnical models through additive manufacturing, that is, from a file viewed with a computer to a real object. This study investigated the serviceability of 3DP products as substitutes for rock specimens and rock-type materials in experimental analysis of deformation and failure in the laboratory. These experiments were performed on two types of materials as follows: (1) compressive experiments on printed sand-powder specimens in different shapes and structures, including intact cylinders, cylinders with small holes, and cuboids with pre-existing cracks, and (2) compressive and shearing experiments on printed polylactic acid cylinders and molded shearing blocks. These tentative tests for 3DP technology have exposed its advantages in producing complicated specimens with special external forms and internal structures, the mechanical similarity of its product to rock-type material in terms of deformation and failure, and its precision in mapping shapes from the original body to the trial sample (such as a natural rock joint). These experiments and analyses also successfully demonstrate the potential and prospects of 3DP technology to assist in the deformation and failure analysis of rock-type materials, as well as in the simulation of similar material modeling experiments.     

Study of Hydraulic Properties of Uncoated Paper: Image Analysis and Pore-Scale Modeling

In this study, uncoated paper was characterized. Three-dimensional structure of the layer was reconstructed using imaging results of micro-CT scanning with a relatively high resolution \((0.9~\upmu \hbox {m})\). Image analysis provided the pore space of the layer, which was used to determine its porosity and pore size distribution. Representative elementary volume (REV) size was determined by calculating values of porosity and permeability values for varying domain sizes. We found that those values remained unchanged for domain sizes of \(400\times 400\times 150\,\upmu \hbox {m}^{3}\) and larger; this was chosen as the REV size. The determined REV size was verified by determining capillary pressure–saturation Open image in new window imbibition curves for various domain sizes. We studied the directional dependence of Open image in new window curves by simulating water penetration into the layer from various directions. We did not find any significant difference between Open image in new window curves in different directions. We studied the effect of compression of paper on Open image in new window curves. We found that up to 30% compression of the paper layer had very small effect on the Open image in new window curve. Relative permeability as a function of saturation was also calculated. Water penetration into paper was visualized using confocal laser scanning microscopy. Dynamic visualization of water flow in the paper showed that water moves along the fibers first and then fills the pores between them.     

倾斜内锁型三维机织陶瓷基复合材料的细观力学模型

利用平均化方法提出了倾斜内锁型三维机织陶瓷基复合材料弹性性能分析的三维细观力学模型,对材料的弹性性能进行了预测。这个力学模型考虑了倾斜内锁型三维机织陶瓷基复合材料经向纤维束的弯曲和纬向纤维束的平直,纤维束的横截面形状尺寸和相邻纤维束之间的孔洞以及材料制造过程中碳纤维性能下降对弹性性能的影响。基于层合板理论,提出两种单胞应变状态假设分别对材料的九个弹性常数进行了推导计算,结果表明两种方法理论的预测值非常接近。计算结果与实验值比较吻合,表明所提出的细观力学模型是合理的,可以为纺织陶瓷基复合材料的优化设计提供有价值的参考。     

Accelerating Reactive Transport Modeling: On-Demand Machine Learning Algorithm for Chemical Equilibrium Calculations

Transport in Porous Media - During reactive transport modeling, the computing cost associated with chemical equilibrium calculations can be 10 to 10,000 times higher than that of fluid flow, heat...