Solute transfer during consolidation based on a solid‐fluid‐solute coupling model

The migration of contaminant through soil is usually modeled using the advection‐dispersion equation and assumes that the porous media is stationary without introducing a constitutive equation to represent soil structure. Consequently, time‐dependent deformation induced by soil consolidation or physical remediation is not considered, despite the need to consider these variables during planning for the remediation of contaminated ground, the prediction of contaminated groundwater movement, and the design of engineered landfills. This study focuses on the numerical modeling of solute transfer during consolidation as a first step to resolve some of these issues. We combine a coupling theory‐based mass conservation law for soil‐fluid‐solute phases with finite element modeling to simulate solute transfer during deformation and groundwater convection. We also assessed the sensitivity of solute transfer to the initial boundary conditions. The modeling shows the migration of solute toward the ground surface as a result of ground settlement and the dissipation of excess pore water pressure. The form of solute transport is dependent on the ground conditions, including factors such as the loading schedule, contamination depth, and water content. The results indicate that an understanding of the interaction between coupling phases is essential in predicting solute transfer in ground deformation and could provide an appropriate approach to ground management for soil remediation.     

Three dimensional simulation of fluid flow in X‐ray CT images of porous media

A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Implementation of the finite element method in the three‐dimensional discontinuous deformation analysis (3D‐DDA)

A modified three‐dimensional discontinuous deformation analysis (3D‐DDA) method is derived using four‐noded tetrahedral elements to improve the accuracy of current 3D‐DDA algorithm in practical applications. The analysis program for the modified 3D‐DDA method is developed in a C++ environment and its accuracy is illustrated through comparisons with several analytical solutions that are available for selected problems. The predicted solutions for these problems using the modified 3D‐DDA approach all show satisfactory agreement with the corresponding analytical results. Results presented in this paper demonstrate that the modified 3D‐DDA method with discontinuous modeling capabilities offers a useful computational tool to determine stresses and deformations in practical problems involving fissured elastic media with reasonable accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

Impact of range‐parallel sediment transport on 2D thermo‐mechanical models of mountain belts: Application to the Kyrgyz Tien Shan

Evolving mountain belts dynamics is very sensitive to surface processes. The surface processes affect tectonics by enhancing crust exhumation and thermal weakening, and depositing soft yet cold sediments in surrounding basins. While 2D plane strain models approximate cylindrical tectonic structures well, simple 1D mass transfer cannot capture erosion–sedimentation complexity. The Eastern Kyrgyz Tien Shan, where structures, basins and exhumation rates are well constrained, is used here to illustrate this issue. Thermo‐mechanical models demonstrate that 1D transport cannot adjust both basin geometry and Apatite Fission Track exhumation ages. When out‐of‐plane sediment transfer is considered, the amount of evacuated sediment delays or accelerates the formation of new faults, affecting the relative timing of exhumation. For our case study, lateral drainage must evacuate 80% of the sediments to match the geological constraints, which is consistent with other source to sink analyses. This indicates that lateral drainage should not be neglected in regional 2D models.     

含层间错动带岩体的破坏模式及其剪切特性研究方法探讨

层间错动带存在的普遍性,给世界上许多工程带来了岩体稳定性问题和地质灾害。通过对因层间错动带导致工程岩体结构变形失效或破坏的实例进行归纳总结,采用岩体结构控制理论的观点将含层间错动带的岩体的破坏模式分为拉裂破坏、掉块和层间剪切滑移破坏3大类。以此为基础,提出剪切力学模型是层间错动带力学模型研究的重点。对层间错动带剪切力学特性的现有试验方法和建模理论进行评述,并根据现有的研究基础,提出屈服面蠕变模型是当前层间错动带剪切蠕变模型的较好选择。     

A new computational strategy for solving two‐phase flow in strongly heterogeneous poroelastic media of evolving scales

We develop a new computational methodology for solving two‐phase flow in highly heterogeneous porous media incorporating geomechanical coupling subject to uncertainty in the poromechanical parameters. Within the framework of a staggered‐in‐time coupling algorithm, the numerical method proposed herein relies on a Petrov–Galerkin postprocessing approach projected on the Raviart–Thomas space to compute the Darcy velocity of the mixture in conjunction with a locally conservative higher order finite volume discretization of the nonlinear transport equation for the saturation and an operator splitting procedure based on the difference in the time‐scales of transport and geomechanics to compute the effects of transient porosity upon saturation. Notable features of the numerical modeling proposed herein are the local conservation properties inherited by the discrete fluxes that are crucial to correctly capture the fingering patterns arising from the interaction between heterogeneity and nonlinear viscous coupling. Water flooding in a poroelastic formation subject to an overburden is simulated with the geology characterized by multiscale self‐similar permeability and Young modulus random fields with power‐law covariance structure. Statistical moments of the poromechanical unknowns are computed within the framework of a high‐resolution Monte Carlo method. Numerical results illustrate the necessity of adopting locally conservative schemes to obtain reliable predictions of secondary recovery and finger growth in strongly heterogeneous deformable reservoirs. Copyright © 2011 John Wiley & Sons, Ltd.     

Iteratively coupled solution strategies for a four‐field mixed finite element method for poroelasticity

In this paper, we consider numerical algorithms for modeling of the time‐dependent coupling between the fluid flow and deformation in elastic porous media. Here, we employ a four‐field formulation which uses the total stress, displacement, flux, and pressure as its primary variables and satisfies Darcy's law and linear elasticity in mixed weak form. We present four different iteratively coupled methods, known as drained, undrained, fixed‐strain, and fixed‐stress splits, in which the diffusion operator is separated from the elasticity operator and the two subproblems are solved in a staggered way while ensuring convergence of the solution at each time step. A‐priori convergence results for each iterative coupling which differs from those found when using a traditional two‐field or three‐field formulation are presented. We also present some numerical results to support the convergence estimates and to show the accuracy and efficiency of the algorithms. Copyright © 2016 John Wiley & Sons, Ltd.     

A constitutive model for mechanical and chemo‐mechanical compaction in sedimentary basins and finite element analysis

Compaction and associated fluid flow are fundamental processes in sedimentary basin deformation. Purely mechanical compaction originates mainly from pore fluid expulsion and rearrangement of solid particles during burial, while chemo‐mechanical compaction results from Intergranular Pressure‐Solution (IPS) and represents a major mechanism of deformation in sedimentary basins during diagenesis. The aim of the present contribution is to provide a comprehensive 3D framework for constitutive and numerical modeling of purely mechanical and chemo‐mechanical compaction in sedimentary basins. Extending the concepts that have been previously proposed for the modeling of purely mechanical compaction in finite poroplasticity, deformation by IPS is addressed herein by means of additional viscoplastic terms in the state equations of the porous material. The finite element model integrates the poroplastic and poroviscoplastic components of deformation at large strains. The corresponding implementation allows for numerical simulation of sediments accretion/erosion periods by progressive activation/deactivation of the gravity forces within a fictitious closed material system. Validation of the numerical approach is assessed by means of comparison with closed‐form solutions derived in the context of a simplified compaction model. The last part of the paper presents the results of numerical basin simulation performed in one dimensional setting, demonstrating the ability of the modeling to capture the main features in elastoplastic and viscoplastic compaction. Copyright © 2016 John Wiley & Sons, Ltd.     

The field and microstructural signatures of deformation‐assisted melt transfer: Insights from magmatic arc lower crust,New Zealand

Melt must transfer through the lower crust, yet the field signatures and mechanisms involved in such transfer zones (excluding dykes) are still poorly understood. We report field and microstructural evidence of a deformation‐assisted melt transfer zone that developed in the lower crustal magmatic arc environment of Fiordland, New Zealand. A 30–40 m wide hornblende‐rich body comprising hornblende ± clinozoisite and/or garnet exhibits 'igneous‐like' features and is hosted within a metamorphic, two‐pyroxene–pargasite gabbroic gneiss (GG). Previous studies have interpreted the hornblende‐rich body as an igneous cumulate or a mass transfer zone. We present field and microstructural characteristics supporting the later and indicating the body has formed by deformation‐assisted, channelized, reactive porous melt flow. The host granulite facies GG contains distinctive rectilinear dykes and garnet reaction zones (GRZ) from earlier in the geological history; these form important reaction and strain markers. Field observations show that the mineral assemblages and microstructures of the GG and GRZ are progressively modified with proximity to the hornblende‐rich body. At the same time, GRZ bend systematically into the hornblende‐rich body on each side of the unit, showing apparent sinistral shearing. Within the hornblende‐rich body itself, microstructures and electron back‐scatter diffraction mapping show evidence of the former presence of melt including observations consistent with melt crystallization within pore spaces, elongate pseudomorphs of melt films along grain boundaries, minerals with low dihedral angles as small as <10° and up to <60°, and interconnected 3D melt pseudomorph networks. Reaction microstructures with highly irregular contact boundaries are observed at the field and thin‐section scale in remnant islands of original rock and replaced grains, respectively. We infer that the hornblende‐rich body was formed by modification of the host GG in situ due to reaction between an externally derived, reactive, hydrous gabbroic to intermediate melt percolating via porous melt flow through an actively deforming zone. Extensive melt–rock interaction and metasomatism occurred via coupled dissolution–precipitation, triggered by chemical disequilibrium between the host rock and the fluxing melt. As a result, the host plagioclase and pyroxene became unstable and were reacted and dissolved into the melt, while hornblende and to a lesser extent clinozoisite and garnet grew replacing the unstable phases. Our study shows that hornblendite rocks commonly observed within deep crustal sections, and attributed to cumulate fractionation processes, may instead delineate areas of deformation‐assisted, channelized reactive porous melt flow formed by melt‐mediated coupled dissolution–precipitation replacement reactions.     

计算流体地球化学研究的进展

成矿作用的化学机理可以通过实验和计算机模拟进行研究。随着计算机运算能力的不断增强 ,在地球化学中正在形成一门新兴学科———计算地球化学。其中热质输运模拟、化学质量迁移数值模拟和流体输运化学反应耦合动力学研究取得了显著进展。建立在Darcy定律和守恒方程基础上的多孔介质热质输运模拟通过流函数图、等温线图及速率矢量图等 ,从古水文学和流体地球化学方面高度动态研究成矿作用。根据化学和热力学原理进行的化学质量迁移数值模拟则通过矿物和流体中化学物种的热力学数据 ,预测多组分体系中发生的流体岩石相互作用 ,定量揭示经历了复杂化学反应进程的成矿作用的化学行为。将上述两方面结合的流体输运化学反应耦合动力学 ,可以从时间和空间上模拟真实成矿流体系统复杂的动力学行为 ,是计算流体地球化学的发展方向。     

基于贴体全交错网格的起伏地表正演模拟影响因素

贴体网格有限差分正演模拟算法不仅能够精确模拟任意起伏地形下的波场特征,且计算效率较高,是一种很有应用前景的处理西部复杂地表问题的方法;然而,目前求解波动方程时常用的同位网格和标准交错网格,在处理贴体网格起伏地表正演模拟时存在诸多问题。为此,将全交错网格引入到曲线坐标系下,避免了标准交错网格的插值误差和同位网格中奇偶失联引起的高频振荡现象,提高了模拟精度,减小了算法实现的复杂度。在自由边界条件实施时,采用牵引力镜像法计算速度分量,速度自由边界条件配合紧致交错差分格式更新应力分量,得到了较好的效果。随后,重点研究了贴体全交错网格正演模拟算法的影响因素,考虑了网格正交性、网格间距和网格拼接等的影响,并取得了如下认识：算法对网格的正交性没有过分要求;网格间距的突变会引起虚假反射的产生;不同类型的网格拼接对模拟结果不会造成明显的影响。     

A reconstruction method for three‐dimensional pore space using multiple‐point geology statistic based on statistical pattern recognition and microstructure characterization

To predict the macroscopic properties (e.g., transport, electromagnetic, and mechanical properties) of porous media, it is necessary to have a three‐dimensional (3D) representation of porous media. We reconstruct the geologically realistic 3D structure of Fontainebleau sandstone based on the two‐dimensional (2D) thin sections by using the multiple‐point statistics method. For this method, the size of template is an important parameter that reflects the perceived scale of spatial structure of porous media. In this paper, we take advantage of entropy method to obtain the appropriate size of the template, which is proven to be correct and feasible. The reconstruction method proposed by us combines successive 2D MPS simulations as well as 3D MPS simulation, which takes account into the pore structure information (e.g., heterogeneity and connectivity) both intralayer and interlayer. This reconstruction method is tested on Fontainebleau sandstone for which 3D images from micro‐CT scanning are available. Applying local percolation theory analysis, this new approach can depict the expected patterns of geological heterogeneities. In addition, it also can well reproduce a high degree of connectivity of the pore space better than other reconstruction methods based on lower‐order statistics. Copyright © 2011 John Wiley & Sons, Ltd.     

Investigation on strength and stability of jointed rock mass using three‐dimensional numerical manifold method

This paper proposes a numerical model for jointed rock masses within the 3‐D numerical manifold method (NMM) framework equipped with a customized contact algorithm. The strength of rock sample containing a few sets of discontinuities is first investigated. The results of models with simple geometries are compared with the available analytical solutions to verify the developed computer code, whereas models with complex geometries are simulated to better understand the fundamental behavior and failure mechanism of jointed rock mass. Furthermore, the stability of jointed rock mass in an underground excavation is studied, where rock failure process is determined by the 3‐D NMM simulation. The simulation results provide valuable guidance on excavation process design and stabilization design in rock engineering practice. Copyright © 2012 John Wiley & Sons, Ltd.     

可控源电磁场三维数值模拟中的散度校正方法研究

在可控源电磁场三维有限差分数值模拟过程中,低频时数值模拟的收敛速度变慢,导致获得精确结果的时间变长。引入电流密度的散度校正方法可以加快低频数值模拟时的收敛速度,提高解的精确性。笔者在研究可控源电磁场三维有限差分数值模拟算法的基础上,利用电流密度的散度为零,推导了散度校正公式并利用迭代解法实现了散度校正算法。模型试验表明,在低频时,散度校正能大幅度提高三维电磁场数值模拟的速度和精度,异常体规模越大,数值模拟的频率越低,散度校正的效果越明显。     

Modeling coupled THM processes of geological porous media with multiphase flow: Theory and validation against laboratory and field scale experiments

A FEM model for analysis of fully coupled multiphase flow, thermal transport and stress/deformation in geological porous media was developed based on the momentum, mass and energy conservation laws of the continuum mechanics and the averaging approach of the mixture theory over a three phase (solid–liquid–gas) system. Six processes (i.e. stress–strain, water flow, gas flow, vapor flow, heat transport and porosity evolution processes) and their coupling effects are considered, which not only makes the problem well-defined, but renders the governing PDEs closed, complete, compact and compatible. Displacements, pore water pressure, pore gas pressure, pore vapor pressure, temperature and porosity are selected as basic unknowns. The physical phenomena such as phase transition, gas solubility in liquid, thermo-osmosis, moisture transfer and moisture swelling are modeled. As a result, the relative humidity and other related variables in porous media can be evaluated on a sounder physical basis. A three dimensional computer code, THYME3D, was developed, with eight degrees of freedom at each node. The laboratory CEA Mock-up test and the field scale FEBEX benchmark test on bentonite performance assessment for underground nuclear waste repositories were used to validate the numerical model and the software. The coupled THM behaviors of the bentonite barriers were satisfactorily simulated, and the effects and impacts of the governing equations, constitutive relations and property parameters on the coupled THM processes were understood in terms of more straightforward interpretation of physical processes at microscopic scale of the porous media. The work developed enables further in-depth research on fully coupled THM or THMC processes in porous media.     

起伏地形下可控源音频大地电磁三维数值模拟

起伏地形对可控源音频大地电磁(CSAMT)响应具有强烈的影响,因此在CSAMT数据处理解释时需要考虑地形。同时,实际的地下地质情况和地表的地形情况通常比较复杂,地质结构和地形大部分情况下都是三维的。在水平地表三维有限差分CSAMT数值模拟算法的基础上,推导了利用地下交错网格采样点处的总磁场计算起伏地形下空气-地下介质分界面处的总电场和总磁场的表达式,从而实现了起伏地形下三维CSAMT数值模拟算法。在算法实现过程中,采用伪δ函数代替麦克斯韦方程中的场源项和直接计算总场的策略,避免了原有的将总场分离成背景场和二次场的策略在复杂地质条件下难以选择合适背景电阻率的问题。为了直接模拟总场,起伏地形下三维CSAMT数值模拟算法给出了新的三维正演方程的边界条件。将模拟水平地表三维异常体和三维山峰地形两个理论模型得到的响应结果与前人算法的计算结果进行对比,验证了所实现算法的正确性和有效性。     

A semi‐analytical modeling approach for three‐dimensional heat transfer in sparsely fractured rocks with water flow and distributed heat source

A semi‐analytical approach is developed for modeling 3D heat transfer in sparsely fractured rocks with prescribed water flow and heat source. The governing differential equations are formulated, and the corresponding integral equations over the fracture faces and the distributed heat source are established in the Laplace transformed domain using the Green function method with local systems of coordinates. The algebraic equations of the Laplace transformed temperatures of water in the fractures are formed by dividing the integrals into elemental ones; in particular, the fracture faces are discretized into rectangular elements, over which the integrations are carried out either analytically for singular integrals when the base point is involved or numerically for regular integrals when otherwise. The solutions of the algebraic equations are inverted numerically to obtain the real‐time temperatures of water in the fractures, which may be employed to calculate the temperatures at prescribed locations of the rock matrix. Three example calculations are presented to illustrate the workability of the developed approach. The calculations found that water flux in the fractures may decrease the rate of temperature rise in regions close to the distributed heat source and increase the rate of temperature rise in regions downstream away from the distributed heat source and that the temperature distribution and evolvement in a sparsely fractured rock mass may be significantly influenced by water flow exchange at intersection of fractures. Copyright © 2014 John Wiley & Sons, Ltd.     

FDwave3D: a MATLAB solver for the 3D anisotropic wave equation using the finite-difference method

Seismic modeling plays an important role in geophysics and seismology for estimating the response of seismic sources in a given medium. In this work, we present a MATLAB-based package, FDwave3D, for synthetic wavefield and seismogram modeling in 3D anisotropic media. The seismic simulation is carried out using the finite-difference method over the staggered grid, and it is applicable to both active and passive surveys. The code package allows the incorporation of arbitrary source mechanisms and offers spatial derivative operators of accuracy up to tenth-order along with different types of boundary conditions. First, the methodological aspects of finite-difference method are briefly introduced. Then, the code has been tested and verified against the analytical solutions obtained for the homogeneous model. Further, the numerical examples of layered and overthrust models are presented to demonstrate its reliability.

     

Fully coupled simulation of fluid injection into geomaterials with focus on nonlinear near‐well behavior

An important part of our global wealth depends on the extraction of fluids from porous media. More recently, sequestration of carbon dioxide (rmCO₂) into deep geological layers as a possible measure to mitigate climate change has increased interest in fluid injection into porous media. Sophisticated numerical models play an important role in managing the uncertainties related to the subsurface, and finite element methods are the most versatile tool allowing the coupling of fluid flow, geomechanics and other physical processes. This paper gives insight into two important aspects of fluid injection/extraction in porous media: the correct modeling of the bore hole through specification of initial stresses, which together with a fully coupled strategy allows simulation of nonlinear poromechanics, and the imposition of appropriate boundary conditions that allow the controlled injection/extraction of a total specified amount of fluid in an anisotropic porous medium, without exceeding a safe operating pressure. Copyright © 2011 John Wiley & Sons, Ltd.