Modeling the Enhanced Bioremediation of Organic Contaminants in Pyrite-containing Aquifers

The bioremediation of organic contaminants in the subsurface is strongly influenced by the existing geochemical environment. In this study a coupled reactive transport and geochemical model is developed for the simulation of enhanced bioremediation of organic contamination in the presence of pyrite. The two-dimensional model allows for the simulation of both kinetically defined as well as geochemical equilibrium reactions. The model is applied to a hypothetical pyrite-containing aquifer contaminated with petroleum hydrocarbons. Oxygen injected into the aquifer to enhance contaminant biodegradation reacts with pyrite resulting in reduced oxygen availability, acidification of the subsurface environment and, subsequently, the inadvertent inhibition of the microbial activity. The reactive transport and geochemical model is used to quantify these processes. The dominance of the various chemical reactions and the sensitivity of the biodegradation on pyrite content are evaluated. Through groundwater pH manipulation, the interference of pyrite with the intended remedial action is partially mitigated. It is shown that when oxygen availability is a limiting factor, the optimal pH that would maximize hydrocarbon degradation may significantly differ from the pH value that maximizes bacterial activity.     

Modeling Variable Density Flow and Solute Transport in Porous Medium: 1. Numerical Model and Verification

A new numerical model for the resolution of density coupled flow and transport in porous media is presented. The model is based on the mixed hybrid finite elements (MHFE) and discontinuous finite elements (DFE) methods. MHFE is used to solve the flow equation and the dispersive part of the transport equation. This method is more accurate in the calculation of velocities and ensures continuity of fluxes from one element to the adjacent one. DFE is used to solve the convective part of the transport equation. Combined with a slope limiting procedure, it avoids numerical instabilities and creates a very limited numerical dispersion, even for high grid Peclet number.Flow and transport equations are coupled by a standard iterative scheme. Residual based criterion is used to stop the iterations. Simulations of an unstable equilibrium show the effects of the criteria used to stop the iterations and the stopping criterion in the solver. The effects are more important for finer grids than for coarser grids.The numerical model is verified by the simulation of standard benchmarks: the Henry and the Elder test cases. A good agreement is found between the revised semianalytical Henry solution and the numerical solution. The Elder test case was also studied. The simulations were similar to those presented in previous works but with significantly less unknowns (i.e. coarser grids). These results show the efficiency of the used numerical schemes.     

A Quasilinear Based Procedure for Saturated/Unsaturated Water Movement in Soils

The quasilinear form of Richards equation for one-dimensional unsaturated flow in soils can be readily solved for a wide variety of conditions. However, it cannot explain saturated/unsaturated flow and the constant diffusivity assumption, used to linearise the transient quasilinear equation, can introduce significant error. This paper presents a quasi-analytical solution to transient saturated/unsaturated flow based on the quasilinear equation, with saturated flow explained by a transformed Darcy's equation. The procedure presented is based on the modified finite analytic method. With this approach, the problem domain is divided into elements, with the element equations being solutions to a constant coefficient form of the governing partial differential equation. While the element equations are based on a constant diffusivity assumption, transient diffusivity behaviour is incorporated by time stepping. Profile heterogeneity can be incorporated into the procedure by allowing flow properties to vary from element to element. Two procedures are presented for the temporal solution; a Laplace transform procedure and a finite difference scheme. An advantage of the Laplace transform procedure is the ability to incorporate transient boundary condition behaviour directly into the analytical solutions. The scheme is shown to work well for two different flow problems, for three soil types. The technique presented can yield results of high accuracy if the spatial discretisation is sufficient, or alternatively can produce approximate solutions with low computational overheads by using large sized elements. Error was shown to be stable, linearly related to element size.     

A mixed finite element/finite volume approach for solving biodegradation transport in groundwater

A numerical model for the simulation of flow and transport of organic compounds undergoing bacterial oxygen- and nitrate-based respiration is presented. General assumptions regarding microbial population, bacteria metabolism and effects of oxygen, nitrogen and nutrient concentration on organic substrate rate of consumption are briefly described. The numerical solution techniques for solving both the flow and the transport are presented. The saturated flow equation is discretized using a high-order mixed finite element scheme, which provides a highly accurate estimation of the velocity field. The transport equation for a sorbing porous medium is approximated using a finite volume scheme enclosing an upwind TVD shock-capturing technique for capturing concentration-unsteady steep fronts. The performance and capabilities of the present approach in a bio-remediation context are assessed by considering a set of test problems. The reliability of the numerical results concerning solution accuracy and the computational efficiency in terms of cost and memory requirements are also estimated. © 1998 John Wiley & Sons, Ltd.     

二维任意多边形有限单元

目前常用于单晶体材料的计算细观力学分析方法是将晶体细分成许多三角形或四边形有限元，对于多晶体材料，这方法的计算量之大将难于承受，实验观测表明，多晶体材料中除角点附近局部区域外每个晶体内部的变形、滑移基本上是绶慢变化的，因此可以将每个晶体简化为一个多边形有限单元，晶界简化为界面单元，使计算量大大减少，本文导出一类任意多边形等参有限元格式，并证明这类多边形单元中的任意两个都是相互协调的，无论其边数是否相等，算例表明任意多边形单元是有效可行的．     

On the Reliability of Numerical Solutions of Brine Transport in Groundwater: Analysis of Infiltration from a Salt Lake

The density dependent flow and transport problem in groundwater is solved numerically by means of a mixed finite element scheme for the flow equation and a mixed finite element-finite volume time-splitting based technique for the transport equation. The proposed approach, spatially second order accurate, is used to address the issue of grid convergence by solving on successively refined grids the salt lake problem, a physically unstable downward convection with formation of fingers. Numerical results indicate that achievement of grid convergence is problematic due to ill-conditioning arising from the strong nonlinearities of the mathematical model.     

Modeling full-tensor anisotropy in groundwater flow via an iterative scheme for mixed finite elements

This paper presents an iterative scheme for the efficient simulation of groundwater flow in a two-dimensional, heterogeneous aquifer in which the hydraulic conductivity is anisotropic. The scheme is applicable to matrix equations arising from both mixed finite-element and cell-centered finite-difference approximations to the flow equations, and it extends readily to three space dimensions. The scheme, which generalizes an earlier technique for isotropic aquifer, admits a fast multigrid solver for hydraulic heads. Numerical experiments illustrate both the effectiveness of the scheme and the importance of accurately treating anisotropy: Small changes in the off-diagonal terms in the conductivity tensor cause relatively large changes in both the predicted heads and the Darcy velocities.     

Numerical Modeling of Hydraulic Hysteresis in Unsaturated Soils

This article presents the implementation of the constitutive model of Wheeler (Geotechnique 53(1):41–54, 2003) for coupling of hydraulic hysteresis and mechanical behavior of unsaturated soils in a fully coupled transient hydro-mechanical finite element (FE) model (computer code UNSATEX) developed by the authors. The constitutive model considers the effects of irreversible changes of degree of saturation on stress–strain behavior and the influence of plastic volumetric strains on the water retention behavior. The mathematical framework and the numerical implementation of the constitutive model are presented and discussed. The FE model is verified and validated against analytical predictions [obtained using the model of Wheeler (Geotechnique 53(1):41–54, 2003] as well as experimental results from the literature involving unsaturated soils undergoing various combinations of drying, wetting, loading, unloading, and reloading paths. Comparison of the results shows that the developed FE model can be used to predict various aspects of the behavior of unsaturated soils under drying and wetting as well as loading and unloading paths. The merits and limitations of the FE model are highlighted.     

Numerical modelling of shear-dependent mass transfer in large arteries

A numerical scheme for the simulation of blood flow and transport processes in large arteries is presented. Blood flow is described by the unsteady 3D incompressible Navier–Stokes equations for Newtonian fluids; solute transport is modelled by the advection–diffusion equation. The resistance of the arterial wall to transmural transport is described by a shear-dependent wall permeability model. The finite element formulation of the Navier–Stokes equations is based on an operator-splitting method and implicit time discretization. The streamline upwind/Petrov–Galerkin (SUPG) method is applied for stabilization of the advective terms in the transport equation and in the flow equations. A numerical simulation is carried out for pulsatile mass transport in a 3D arterial bend to demonstrate the influence of arterial flow patterns on wall permeability characteristics and transmural mass transfer. The main result is a substantial wall flux reduction at the inner side of the curved region. © 1997 John Wiley & Sons, Ltd.     

Gaussian Closure of One-Dimensional Unsaturated Flow in Randomly Heterogeneous Soils

We propose a new method for the solution of stochastic unsaturated flow problems in randomly heterogeneous soils which avoids linearizing the governing flow equations or the soil constitutive relations, and places no theoretical limit on the variance of constitutive parameters. The proposed method applies to a broad class of soils with flow properties that scale according to a linearly separable model provided the dimensionless pressure head has a near-Gaussian distribution. Upon treating as a multivariate Gaussian function, we obtain a closed system of coupled nonlinear differential equations for the first and second moments of pressure head. We apply this Gaussian closure to steady-state unsaturated flow through a randomly stratified soil with hydraulic conductivity that varies exponentially with where =(1/) is dimensional pressure head and is a random field with given statistical properties. In one-dimensional media, we obtain good agreement between Gaussian closure and Monte Carlo results for the mean and variance of over a wide range of parameters provided that the spatial variability of is small. We then provide an outline of how the technique can be extended to two- and three-dimensional flow domains. Our solution provides considerable insight into the analytical behavior of the stochastic flow problem.     

Conditional Stochastic Analysis for Multiphase Trsnsport in Randomly Heterogeneous,variably Saturated Media

Groundwater contamination of organics has recently become a problem of growing concern over the resulting health and environmental problems. In general, the multiphase system of nonaqueous phase liquid (NAPL), water and air has to be studied in order to realistically describe the movement of such materials in the subsurface. Numerous models have been developed to study multiphase flow and/or multispecies transport in porous media. However, using models to study the influence of medium heterogeneity on such flow and transport is only a recent event. It has been demonstrated for single-phase flow and transport in saturated and unsaturated media that the study of medium heterogeneity is amenable to stochastic analysis. In this paper, we extend our Eulerian–Lagrangian stochastic theory for single-phase transport to the problem of multiphase–multispecies transport in randomly heterogeneous media under the conditions that the flow is steady-state and the phases are in local chemical equilibrium. We present theoretical expressions to describe the first two conditional moments of the random concentration of any species in any phase. Though they reveal some of the fundamental properties and help gaining insight into the nature of the problem, these expressions cannot be evaluated without either high resolution Monte Carlo simulation or approximation (closure). Therefore, we propose two sets of workable approximations, one being a weak approximation and the other being a linearized pseudo-Fickian approximation. The former yields a nonlinear integro-differential equation for the first conditional moment and the latter yields a linear differential equation. Then the second moments can be computed from explicit expressions from either the weak or pseudo-Fickian approximation.     

Numerical simulation of the galvanizing process during GA to GI transition

This paper presents the application of a three‐dimensional finite element solution algorithm for the prediction of the velocity, temperature and species concentration fields in an industrial continuous galvanizing bath. Simulations were carried out using a parallel CFD software developed at IMI‐NRC. The turbulent flow, heat and mass transfer has been solved using a high Reynolds number k–ε model. Simulations were carried out for the case when the density of the molten metal depends only on the temperature and also for the case when both temperature and Al concentration affect the density. When considering the buoyancy effect of the Al concentration, differences are especially apparent during the melting of ingots with high Al content. Otherwise, thermal effects are dominant. The continuous monitoring of the temperature and the Al and Fe content in an industrial bath was used to validate the flow, temperature and compositional variations. A period of three hours, corresponding to three different ingot additions, was simulated successfully, resulting in a good agreement of the temperature and compositional variations. Copyright © 2006 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.     

N表面张力对近固壁二空化泡影响的数值研究

在忽略浮力下，用边界积分方法数值模拟了表面张力对固壁之上且靠近固壁的二轴对称空化泡生长和溃灭的影响，发现在下空泡最大等效半径为上空泡一半情形，若固壁对下空泡的Bjerknes力大于上空泡对下空泡的Bjerknes力，则表面张力的作用将使下空泡溃灭加速，使其向下的液体射流变强变宽；若固壁对下空泡的Bjerknes力小于上空泡对下空泡的Bjerknes力，则表面张力的作用将使下空泡溃灭变慢，使其向上射流变弱变细长；若这两个Bjerknes力近于相等，则表面张力将会对下空泡溃灭有重大作用，如改变下空泡射流的方向甚至形式(如由环状变向下或由向上变环状)，当上空泡等于或小于下空泡时，表面张力将不会对这两个空泡的行为产生显著影响，定性地分析了表面张力作用的机理。     

CONSTRUCTION OF MODIFIED TAYLOR－GALERKIN FINITE ELEMENTS AND ITS APPLICATION IN COMPRESSIBLE FLOW COMPUTATION

ＣＯＮＳＴＲＵＣＴＩＯＮＯＦＭＯＤＩＦＩＥＤＴＡＹＬＯＲ－ＧＡＬＥＲＫＩＮＦＩＮＩＴＥＥＬＥＭＥＮＴＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＩＮＣＯＭＰＲＥＳＳＩＢＬＥＦＬＯＷＣＯＭＰＵＴＡＴＩＯＮＣＯＮＳＴＲＵＣＴＩＯＮＯＦＭＯＤＩＦＩＥＤＴＡＹＬＯＲ...     

偏心圆柱塞状管流的数值模拟

在全面调研了国内外关于两相在管道中的偏心圆柱塞状管流的研究文献之后，发现几乎都利用经验公式或近似估计式进行水力计算，这与石油工业中两相流的广泛应用极不相适应。根据流体力学中N-S方程对层流的描述，再结合经典的力学理论分析，对两相偏心圆柱塞状管流的相界面提出严密而科学的力学耦合条件，得到了完整描述偏心环状管流的适定的偏微分方程组，然后利用双极坐标变换化不规则的区域为规则的矩形域及计算机仿真技术，得到了两相流中偏心圆柱塞状管流的流动规律，对石油工业具有重要的工程应用价值。     

玻璃态聚合物银纹化过程的数值模拟

银纹化是玻璃态聚合物材料所特有的一种现象。本文在代表体积单元中嵌入能够刻划银纹萌生与生长的银纹单元，运用有限元方法对银纹化过程进行了数值模拟。银纹化过程中的最大主应力矢量图说明计算模型以及计算方法是比较合理的。而且，本文所揭示出来的银纹化过程的规律与实验中观察到的现象是吻合的。     

Numerical simulations of laminar flow over a 3D backward-facing step

A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier–Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100⩽ Re⩽ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100⩽Re⩽ 800. © 1997 John Wiley & Sons, Ltd.     

Numerical solution of subsonic and transonic cascade flows

In this work a study of the application of the finite element method to transonic flows in axial turbomachines is undertaken. Solution techniques capable of accurately predicting flows from the incompressible regime up to the establishment of shocks in the transonic regime are presented. In the subsonic and shockless transonic regimes a local linearization method capable of very rapid convergence is used. In the full transonic regime the artificial compressibility method is employed to exclude downstream influences in the supersonic regions. The two approaches can be combined in a unified package and appropriate switches introduced to select the relevant method in any flow regime.     

Numerical Experiments with Various Formulations for Two Phase Flow in Petroleum Reservoirs*

Two phase immiscible flow in petroleum reservoirs is considered. Various formulations of the governing equations that describe this flow, including phase, global, and weighted formulations, are numerically experimented. Mixed finite element methods are used to solve these formulations. Our experiments show that the numerical results obtained using the phase and global formulations match well in terms of production rates, characterization curves, and water cuts.