A general reduction scheme for reactive transport in porous media

We present a method to transform the governing equations of multispecies reactive transport in porous media. The reformulation leads to a smaller problem size by decoupling of equations and by elimination of unknowns, which increases the efficiency of numerical simulations. The reformulation presented here is a generalization of earlier works. In fact, a whole class of transformations is now presented. This class is parametrized by the choice of certain transformation matrices. For specific choices, some known formulations of reactive transport can be retrieved. Hence, the software based on the presented transformation can be used to obtain efficiency comparisons of different solution approaches. For our efficiency tests, we use the MoMaS benchmark problem on reactive transport.     

A global approach to reactive transport: application to the MoMas benchmark

Water resource management involves numerical simulations in order to study contamination of groundwater by chemical species. Not only do the aqueous components move due to physical advection and dispersion processes, but they also react together and with fixed components. Therefore, the mass balance couples transport and chemistry, and reactive transport models are partial differential equations coupled with nonlinear algebraic equations. In this paper, we present a global method based on the method of lines and differential algebraic system (DAE) solvers. At each time step, nonlinear systems are solved by a Newton-LU method. We use this method to carry out numerical simulations for the reactive transport benchmark proposed by the MoMas research group. Although we study only 1D computations with a specific geochemical system, several difficulties arise. Numerical experiments show that our method can solve quite difficult problems, get accurate results and capture sharp fronts.     

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed particle hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.     

饱和水流溶质运移问题数值解法综述

本文总结了饱和水流中溶质运移方程求解的各种数值方法，分析各种方法的本质特征以及各自的优缺点，并指出了求解对流—弥散方程的各种数值方法的研究进展和值得重视的问题。研究结果表明，自适应欧拉—拉格朗日法(EM)是溶质运移问题中，求解对流—弥散方程是比较有发展潜力的方法之一。以MMOC法为基础在陡峰值高价插值和其它区域低价插值相结合的ELM法，将是未来发展的趋势。而寻求非规则网格上高精度的空间单元插值模式，已开始成为求解对流问题数值方法研究的重点和关键问题。     

A dual mortar contact method for porous media and its application to clay-core rockfill dams

The clay-core rockfill dam is a multibody contact system in which the hydromechanical response of the clay core plays a crucial role. This complex problem is highly challenging to model numerically. We present a numerical approach that considers the multibody contact, consolidation, and strong geometric and material nonlinearities for the modeling of clay-core rockfill dams. Within the framework of the dual mortar finite element method, the presented approach considers the contact bodies as independent porous media continuums. The nonlinear contact conditions are derived based on the effective contact traction on contact interfaces and pore pressure continuity. The weak forms are obtained by introducing Lagrange multipliers as additional unknowns, which are then condensed through an extended general transformation. The presented method is first validated with a patch test considering the contact between two porous media. Then, a three-dimensional analysis of the Rumei clay-core rockfill dam is performed. The main numerical analysis concerns are the two observation galleries planned for construction inside the clay core. The galleries consist of dozens of tunnel-like concrete blocks, giving rise to complex concrete-concrete and concrete-clay contacts. The discontinuous separation and sliding between concrete blocks are investigated. For the concrete-concrete contact, both hard and soft joint approaches are evaluated and compared. The pore pressure results of the concrete structures are also analyzed.     

On the velocity covariance for steady flows in heterogeneous porous formations and its application to contaminants transport

We consider groundwater steady flow in a heterogeneous porous formation of random and stationary log-conductivity Y = ln K, characterized by the mean 〈Y〉, and the two point correlation function C _Y which in turn has finite, and different horizontal and vertical integral scales I and I _v , respectively. The fluid velocity V, driven by a given head drop applied at the boundary, has constant mean value U ≡ (U, 0, 0). Approximate explicit analytical expressions for transverse velocity covariances are derived. The adopted methodology follows the approach developed by Dagan and Cvetkovic (Spatial moments of kinetically sorbing plume in a heterogeneous aquifers, Water Resour. Res. 29 (1993) 4053) to obtain a similar result for the longitudinal velocity covariance. Indeed, the approximate covariances of transverse velocities are determined by requiring that they have the exact first order variances as well as zero integral scale (G. Dagan, Flow and Transport in Porous Formations (Springer, 1989)) , and provide the exact asymptotic limits of the displacement covariance of the fluid particles obtained by Russo (On the velocity covariance and transport modeling in heterogeneous anisotropic porous formations 1. Saturated flow, Water Resour. Res., 31 (1995) 129). Comparisons with numerical results show that the proposed expressions compare quite well in the early time regime, and for Ut/I >100. Since most of the applications, like assessing the effective mobility of contaminants or quantifying the potential hazards of nuclear repositories, require predictions over higher times the proposed approximate expressions provide acceptable results. The main advantage related to such expressions is that they allow obtaining closed analytical forms of spatial moments pertaining to kinetically sorbing contaminant plumes avoiding the very heavy computational effort which is generally demanded. For illustration purposes, we consider the movement of one contaminant species, and show how our approximate spatial moments compare with the numerical simulations.     

Two-phase, partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository

We derive a compositional compressible two-phase, liquid and gas, flow model for numerical simulations of hydrogen migration in deep geological repository for radioactive waste. This model includes capillary effects and the gas high diffusivity. Moreover, it is written in variables (total hydrogen mass density and liquid pressure) chosen in order to be consistent with gas appearance or disappearance. We discuss the well possedness of this model and give some computational evidences of its adequacy to simulate gas generation in a water-saturated repository.     

Rendering technique of multi-layered domain boundaries and its application to fluid flow in porous media visualizations

Current visualization techniques for computational fluid dynamics applications are sophisticated and work well in simple geometries. For complex geometries such as pore spaces, multiple domain boundaries obstruct the view and make the studying of fluid flow fields difficult. To overcome these deficiencies, we use two-sided materials to render the domain boundaries. Using this technique, it is possible to place the camera inside the domain and have a non-obstructed view of the surrounding flow field without losing spatial reference to the domain boundaries. As a result, a larger part of fluid flow visualization is visible. Two-sided material rendering was successfully applied to display still images with Blender Cycles renderer, in a virtual reality environment, and several implementation techniques were explored for using the Visualization Toolkit.     

OpenGeoSys-ChemApp: a coupled simulator for reactive transport in multiphase systems and application to CO2 storage formation in Northern Germany

Sequestration of CO₂ into a deep geological reservoir causes a complex interaction of different processes such as multiphase flow, phase transition, multicomponent transport, and geochemical reactions between dissolved CO₂ and the mineral matrix of the porous medium. A prognosis of the reservoir behaviour and the feedback from large-scale geochemical alterations require efficient process-based numerical models. For this purpose, the multiphase flow and multicomponent transport code OpenGeoSys-Eclipse have been coupled to the geochemical model ChemApp. The newly developed coupled simulator was successfully verified for correctness and accuracy of the implemented reaction module by benchmarking tests. The code was then applied to assess the impact of geochemical reactions during CO₂ sequestration at a hypothetical but typical Bunter sandstone formation in the Northern German Basin. Injection and spreading of 1.48 × 10⁷ t of CO₂ in an anticline structure of the reservoir were simulated over a period of 20 years of injection plus 80 years of post-injection time. Equilibrium geochemical calculations performed by ChemApp show only a low reactivity to the geochemical system. The increased acidity of the aqueous solution results in dissolution of small amounts of calcite, anhydrite, and quartz. Geochemical alterations of the mineral phase composition result in slight increases in porosity and permeability, which locally may reach up to +0.02 and 0.1 %, respectively.     

高密度电阻率法二维勘探数据的三维反演及其在岩溶探测中的应用

三维高密度电阻率法可以有效地解决二维高密度电阻率法在探测空间形态上的不足.将高密度电阻率法二维勘探数据做三维反演,不仅实现了地下空间结构的三维电阻率成像,还克服了传统三维高密度电阻率法在经济成本上的限制.将此方法应用到岩溶勘探中,利用DUK-2A高密度电法仪系统采集数据;然后,把二维高密度数据拼接转化成三维可反演数据,再将反演得到的结果通过三维成像软件实现任意三维地电切片,从而获得丰富的地电结构信息;最后,结合三维切片与钻孔资料对溶洞进行解释,为工程的顺利施工提供科学依据,从而证明该方法的可行性和有效性.     

Transport in a 2-D saturated porous medium: A new method for particle tracking

A new method for solving the transport equation based on the management of a large numbe of particles in a discretized 2-D domain is presented. The method uses numerical variables to represent the number of particles in a given mesh and is more complex than the 1-D problem. The first part of the paper focuses on the specific management of particles in a 2-D problem. The method also would be valid for three dimensions as long as the medium can be modeled similar to a layered system. As the particles are no longer tracked individually, the algorithm is fast and does not depend on the number of particles present. The numerical tests show that the method is nearly numerical dispersion free and permits accurate calculations even for simulations of low-concentration transport. Because each mesh is considered as a closed system between two successive time steps, it is easy to add adsorption phenomenon without any problem of numerical stability. The model is tested under conditions that are extremely demanding for its operating mode and gives a good fit to analytical solutions. The conditions in which it can be used to best advantage are discussed.     

悬浮颗粒形状对其在多孔介质中迁移和沉积特性的影响

悬浮颗粒在多孔介质中迁移的研究在地下水回灌、地下污染物扩散、核废料处置、石油开采等领域有重要的理论意义和应用价值。为了研究形状对颗粒迁移的影响,对1组球状颗粒（10 ?m中位粒径）和2组杆状颗粒（长径比为3:1和6:1）进行了三阶段室内土柱试验,得到了不同形状颗粒在多种溶液离子强度条件下的穿透曲线。结合DLVO理论分析了悬浮颗粒沉积和释放机制,阐释了形状对颗粒迁移行为的影响。试验结果表明,颗粒形状对迁移特性有重要影响,当离子强度较低时（6 mmol/L）,DLVO势能曲线展现较高能量壁垒,各种形状颗粒沉积主要为次级势阱沉积;当离子强度较高时（150 mmol/L）,球状颗粒因能量壁垒较高,其滞留机制仍以次级势阱沉积为主,但长径比为6:1的杆状颗粒在次级势阱和初级势阱都有沉积,这和杆状颗粒的静电性能和优先方向有关。对于杆状颗粒,边位沉积比端位沉积具有更深的次级势阱和更大的影响距离,边位沉积是更加稳定的沉积方式和沉积的优先方向。基于Derjaguin近似方法的DLVO理论计算显示,DLVO理论预测结果和土柱试验结果吻合较好。     

A fracture mapping and extended finite element scheme for coupled deformation and fluid flow in fractured porous media

This paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley & Sons, Ltd.     

A finite volume approach with local adaptation scheme for the simulation of free surface flow in porous media

We present a method for solving steady‐state flow with a free surface in porous media. This method is based on a finite volume approach and is halfway between a fixed and an adaptive mesh method, taking advantage of both approaches: computational efficiency and localization accuracy. Most of the mesh remains fixed during the iterative process, while the cells in contact with the free surface (free surface cells) are being reshaped. Based on this idea, we developed two methods. In the first one, only the volumes of the free surface cells are adapted. In the second one, the computational nodes of the free surface cells are relocated exactly at the free surface. Both adaptations are designed for a better application of the free surface boundary conditions. Implementation details are given on a regular finite volume mesh for the case of homogeneous and heterogeneous rectangular dams in 2D and 3D. Accuracy and convergence properties of the proposed approach are demonstrated by comparison with an analytical solution and with existing references. Copyright © 2011 John Wiley & Sons, Ltd.     

基于灰色关联分析的综合评价模型在爆破方案选定中的应用

针对爆破方案选择的复杂性,在灰色关联分析的基础上,利用层次分析法,结合判断矩阵对各指标进行权值分配,将指标的关联系数与其权值相结合,提出了爆破方案综合评价模型,该模型以权重的形式体现各个评价指标对整体的影响程度,利用判断矩阵进行权值分配克服了以往权重赋值主观性较强的局限,最终以关联度为定量指标来对爆破方案进行比较分析,并以回坡底矿爆破方案评价为实例,具体说明了该模型的科学合理性。     

基于GPU的并行条件模拟算法及其在储量估算中的应用

条件模拟是一种计算非常耗时的高精度三维插值算法。针对串行条件模拟算法计算时间过长的问题,提出基于GPU的并行条件模拟算法,并进行储量估算。对条件模拟算法进行并行分析,利用GPU的高度并行性,构建CUDA通用计算开发环境,实现串行条件模拟算法到并行条件模拟算法的转换,使条件模拟算法的时间复杂度从O(n)降至O(logn)。并对西藏甲玛铜矿进行了储量估算。实验结果表明,在安装普通NVIDIA显卡的计算机以及估算精度不下降的情况下,GPU并行条件模拟的计算效率比CPU串行条件模拟的计算效率提高了60倍以上。     

Calculating the internodal transmissibilities using finite analytic method and its application for multi‐phase flow in heterogeneous porous media

In the traditional numerical reservoir simulations, the internodal transmissibility is usually defined as the harmonic mean of the permeabilities of the adjacent grids. This definition underestimates the phase flux and the speed of the saturation front, especially for the strong heterogeneous case. In this article, the internodal transmissibility is recalculated according to the nodal analytic solution. The redefined internodal transmissibility can be used directly to calculate the multiphase flow in the numerical reservoir simulations. Numerical examples show that, compared to the traditional numerical methods, the proposed scheme makes the convergences much faster as the refinement parameter increases, and the accuracy is independent of the heterogeneity. Copyright © 2016 John Wiley & Sons, Ltd.