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1.
Gour-Tsyh Yeh Yilin Fang Fan Zhang Jiangtao Sun Yuan Li Ming-Hsu Li Malcolm D. Siegel 《Computational Geosciences》2010,14(1):149-170
Subsurface contamination problems of metals and radionuclides are ubiquitous. Metals and radionuclides may exist in the solute
phase or may be bound to soil particles and interstitial portions of the geologic matrix. Accurate tools to reliably predict
the migration and transformation of these metals and radionuclides in the subsurface environment enhance the ability of environmental
scientists, engineers, and decision makers to analyze their impact and to evaluate the efficacy of alternative remediation
techniques prior to incurring expense in the field. A mechanistic-based numerical model could provide such a tool. This paper
communicates the development and verification of a mechanistically coupled fluid-flow thermal-reactive biogeochemical-transport
model where both fast and slow reactions occur in porous and fractured media. Theoretical bases, numerical implementations,
and numerical experiments using the model are described. A definition of the “rates” of fast/equilibrium reactions is presented
to come up with a consistent set of governing equations. Two example problems are presented. The first one is a reactive transport
problem which elucidates the non-isothermal effects on heterogeneous reactions. It also demonstrates that the rates of fast/equilibrium
reactions are not necessarily greater than that of slow/kinetic reactions in the context of reactive transport. The second
example focuses on a complicated but realistic advective–dispersive–reactive transport problem. This example exemplifies the
need for innovative numerical algorithms to solve problems involving stiff geochemical reactions. It also demonstrates that
rates of all fast/equilibrium reactions are finite and definite. Furthermore, it is noted that a species-versus-time curve
cannot be used to characterize the rate of homogeneous fast/equilibrium reaction in a reactive transport system even if one
and only one such reaction is responsible for the production of this species. 相似文献
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CORE2D V4 is a finite element code for modeling partly or fully saturated water flow, heat transport, and multicomponent reactive
solute transport under both local chemical equilibrium and kinetic conditions. It can handle coupled microbial processes and
geochemical reactions such as acid–base, aqueous complexation, redox, mineral dissolution/precipitation, gas dissolution/exsolution,
ion exchange, sorption via linear and nonlinear isotherms, and sorption via surface complexation. Hydraulic parameters may
change due to mineral precipitation/dissolution reactions. Coupled transport and chemical equations are solved by using sequential
iterative approaches. A sequential partly iterative approach (SPIA) is presented which improves the accuracy of the traditional
sequential non-iterative approach (SNIA) and is more efficient than the general sequential iterative approach (SIA). While
SNIA leads to a substantial saving of computing time, it introduces numerical errors which are especially large for cation
exchange reactions. SPIA improves the efficiency of SIA because the iteration between transport and chemical equations is
only performed in nodes with a large mass transfer between solid and liquid phases. The efficiency and accuracy of SPIA are
compared to those of SIA and SNIA using synthetic examples and a case study of reactive transport through the Llobregat Delta
aquitard in Spain. SPIA is found to be as accurate as SIA while requiring significantly less CPU time. In addition, SPIA is
much more accurate than SNIA with only a minor increase in computing time. A further enhancement of the efficiency of SPIA
is achieved by improving the efficiency of the Newton–Raphson method used for solving chemical equations. Such an improvement
is obtained by working with increments of log concentrations and ignoring the terms of the Jacobian matrix containing derivatives
of activity coefficients. A proof is given for the symmetry and non-singularity of the Jacobian matrix. Numerical analyses
performed with synthetic examples confirm that these modifications improve the efficiency and convergence of the iterative
algorithm.
Changbing Yang is now at The University of Texas at Austin, USA. 相似文献
4.
Katerina Georgiou John Harte Ali Mesbah William J. Riley 《Computational Geosciences》2018,22(3):851-865
We present a numerical method for solving a class of systems of partial differential equations (PDEs) that arises in modeling environmental processes undergoing advection and biogeochemical reactions. The salient feature of these PDEs is that all partial derivatives appear in linear expressions. As a result, the system can be viewed as a set of ordinary differential equations (ODEs), albeit each one along a different characteristic. The method then consists of alternating between equations and integrating each one step-wise along its own characteristic, thus creating a customized grid on which solutions are computed. Since the solutions of such PDEs are generally smoother along their characteristics, the method offers the potential of using larger time steps while maintaining accuracy and reducing numerical dispersion. The advantages in efficiency and accuracy of the proposed method are demonstrated in two illustrative examples that simulate depth-resolved reactive transport and soil carbon cycling. 相似文献
5.
In this paper we use a Von Mises transformation to study brine transport in porous media. The model involves mass balance
equations for fluid and salt, Darcy's law and an equation of state, relating the salt mass fraction to the fluid density.
Application of the Von Mises transformation recasts the model equations into a single nonlinear diffusion equation. A further
reduction is possible if the problem admits similarity. This yields a formulation in terms of a boundary value problem for
an ordinary differential equation which can be treated by semi‐analytical means. Three specific similarity problems are considered
in detail: (i) one‐dimensional, stable displacement of fresh water and brine in a porous column, (ii) flow of fresh water
along the surface of a salt rock, (iii) mixing of parallel layers of brine and fresh water.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
Azadeh Agah Faramarz Doulati Ardejani Hossein Ghoreishi 《Arabian Journal of Geosciences》2013,6(6):1933-1944
This paper presents a two-dimensional finite volume model to predict multi-species reactive transport processes in the saturated zone of a simulated semi-confined aquifer. A multipurpose commercial software called PHOENICS was used to solve model equations numerically. Capability of the present model was first confirmed using experimental data and the results obtained by a published one-dimensional finite element reactive transport model by other researchers taking different scenarios into consideration. The model was then expanded to a two-dimensional case to simulate reactive transport of BTX compounds with discontinuous source in the saturated zone of the groundwater flow system. In addition to the physical transport processes, the two-dimensional model also incorporates linear and nonlinear adsorption isotherms, first order and Monod kinetics. The two-dimensional model considers both static and dynamics modes into account. The results show that considering chemical reactions during reactive transport of contaminants could successfully predict the contaminated zone. The results of such studies can be used for monitoring of contaminated areas, designing methods to control pollution transport, and minimize its harmful effects on aquifer systems. 相似文献
7.
近些年来地下水中多组分反应-运移模型在地球科学及环境领域开始得到应用,但其求解较为复杂,为了提高计算效率,可以采用去耦合化方法处理,从而使模型求解得到简化。针对自然界中广泛存在的非均质地质体,提出该类条件下的去耦合化方法,即根据水-岩间、水溶组分间反应的不同,将整个研究区划分为若干子区域,获得对应的去耦合化矩阵。对化学场中各子区域间相邻边界进行设定,达到简化模型求解的目的。最后,以一维非均质介质中基于热力学平衡的反应-运移问题作为算例,基于以上方法进行求解,并与该算例经PHAST软件所示的结果较为一致。结果表明,基于去耦合化方法获得的各离子浓度随时间演变和沿空间分布特征与PHAST所示的结果较为一致,显示该方法在非均质区域模拟溶质运移等方面具有较好的适用性。 相似文献
8.
Eirik Keilegavlen Jeremy E. Kozdon Bradley T. Mallison 《Computational Geosciences》2012,16(4):1021-1042
The governing equations for multiphase flow in porous media have a mixed character, with both nearly elliptic and nearly hyperbolic variables. The flux for each phase can be decomposed into two parts: (1) a geometry- and rock-dependent term that resembles a single-phase flux; and (2) a mobility term representing fluid properties and rock–fluid interactions. The first term is commonly discretized by two- or multipoint flux approximations (TPFA and MPFA, respectively). The mobility is usually treated with single-point upstream weighting (SPU), also known as dimensional or donor cell upstream weighting. It is well known that when simulating processes with adverse mobility ratios, SPU suffers from grid orientation effects. An important example of this, which will be considered in this work, is the displacement of a heavy oil by water. For these adverse mobility ratio flows, the governing equations are unstable at the modeling scale, rendering a challenging numerical problem. These challenges must be addressed in order to avoid systematic biasing of simulation results. In this work, we present a framework for multidimensional upstream weighting for multiphase flow with buoyancy on general two-dimensional grids. The methodology is based on a dual grid, and the resulting transport methods are provably monotone. The multidimensional transport methods are coupled with MPFA methods to solve the pressure equation. Both explicit and fully implicit approaches are considered for time integration of the transport equations. The results show considerable reduction of grid orientation effects compared to SPU, and the explicit multidimensional approach allows larger time steps. For the implicit method, the total number of non-linear iterations is also reduced when multidimensional upstream weighting is used. 相似文献
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Piyang Liu Gary Douglas Couples Jun Yao Zhaoqin Huang Wenhui Song Jingsheng Ma 《Computational Geosciences》2018,22(5):1187-1201
The two-scale continuum model is widely used in simulating the reactive dissolution process and predicting the optimum injection rate for carbonate reservoir acidizing treatment. The numerical methods of this model are currently based on structured grids, which are not applicable for complicated geometries. In this study, a general numerical scheme for simulating a reactive flow problem on both structured and unstructured grids is presented based on the finite volume method (FVM). The convection and diffusion terms involved in the reactive flow model are discretized by using the upwind scheme and two-point flux approximation (TPFA), respectively. The location of the centroid node inside each control volume is moved by using an optimization algorithm to make the connections with the surrounding elements as orthogonal as possible, which systematically improves the accuracy of the TPFA scheme. Additionally, in order to avoid the computational complexity resulting from the discretization of the non-linear term, the mass balance equation is only discretized in the spatial domain to get a set of ordinary differential equations (ODEs). These ODEs are coupled with the reaction equations and then solved using the numerical algorithm on ODEs. The accuracy and efficiency of the proposed method are studied by comparing the results obtained from the proposed numerical method with previous experimental and numerical results. This comparison indicates that, compared with the previous methods, the proposed method predicts the wormhole structure more accurately. Finally, the presented method is used to check the effect of the domain geometry, and it is found that the geometry of the flow domain has no effect on the optimum injection velocity, but the radial domain requires a larger breakthrough volume than the linear domain when other parameters are fixed. 相似文献
11.
结合化学反应方程式,并应用多孔多相介质溶混污染物输运过程的数值模型,对多孔多相介质中含均相/非均相化学反应传质过程进行了数值模拟。化学反应主要包含均相快速/慢速和非均相快速/慢速等5种化学反应过程,溶质输运行为的控制机制主要考虑对流、扩散及降解、吸附等。基于原有的隐式特征线Galerkin离散化的有限元方法,求解模型控制方程的边值初值问题,求解过程中把均相化学反应物质中按照反应物和生成物分开,非均相反应物质按照固相和液相分开,对均相反应物及非均相液相物质浓度耦合求解,而均相生成物和非均相固相物质独立求解。使方程组按照其不同类型进行分类,同时可减少未知数的个数。对于含有非线性内状态变量的右端项进行迭代求解。数值例题结果验证了所提出的数值方法的有效性、计算精度和稳定性。 相似文献
12.
This paper summarizes the governing equations as implemented in the MIN3P multicomponent flow and reactive transport code (Mayer et al., Water Resour Res 38:1174, 2002) and introduces the equations in discretized form. Linearization and solution methods are presented including adaptive time stepping and update modification schemes. Code-specific details for the implementation of the GdR MoMaS benchmark simulations (Carrayrou et al., Comput Geosci, 2009) are presented. The standard version of the MIN3P code was used to solve the Easy, Medium, and Hard Test Cases, in one and two spatial dimensions, for both advection- and diffusion-dominated conditions. An analysis of the sensitivity of the solution in relation to spatial and temporal discretization parameters is provided for the Easy Test Case, selected results are presented for the Medium and Hard Test Cases, and the performance of the code as a function of discretization parameters is evaluated for all test cases. 相似文献
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Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection–diffusion
PDEs coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each
grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper, a global
solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies
the Newton–Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated
in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that
one be able to solve chemical equilibrium problems (and compute derivatives) without having to know the solution method. An
additional advantage of the Newton–Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times
vector product. The proposed method is tested on the MoMaS reactive transport benchmark. 相似文献
15.
V. M. Loskutov 《Astronomy Reports》2004,48(1):21-28
The linear polarization of resonance radiation diffusely reflected from a semi-infinite atmosphere is analyzed, including a full account of the azimuthal dependence. The radiating atom is assumed to have two levels and the radiation to be fully redistributed in frequency. A new approach to the transformation of the equations of polarized radiative transport is proposed based on factorization of the full (3×3) Rayleigh phase matrix. The emergent radiation field is expressed in terms of a matrix analog for the Chandrasekhar H function. The polarization properties of radiation at the frequencies of resonance lines diffusely reflected from a scattering atmosphere are discussed. The degree of polarization of the reflected radiation can be very high. 相似文献
16.
We present here the definition of the reactive transport benchmark of Groupement Mathematical Modeling and Numerical Simulation
for Nuclear Waste Management Problems. The aim of this benchmark is to propose a challenging test for numerical methods used
for reactive transport modeling in porous media. In order to focus on numerical methods, the problem presented here is of
quite a small size, both from a hydrodynamical and from a geochemical point of view. Though the chemical coefficients used
in this benchmark are not taken from a real chemical system, they are realistic, and the test case is quite challenging. 相似文献
17.
基于有限压缩层地基模型和Reissner板的边界积分方程,考虑柱荷载作用区域的形状和筏板的横向剪切变形效应,建立了有限压缩层地基上厚筏基础与地基相互作用分析的边界元方程和系统的数值方法。对于弹性半空间模型,其柔度方程可视为有限压缩层模型的特殊情况。把筏板作为自由边界条件处理,被剖分为一系列三角形或矩形网格,假设基底反力在网格内均匀分布,以便与现有的地基沉降计算模式相一致。计算表明,虽然基底反力在内部网格相接处不连续,但并不影响计算结果,反而消除了边界基底压力计算值过大的现象。将该方法与其他方法的计算结果进行比较,显示了该方法的有效性。计算结果表明,对于实际复杂的筏板基础,无需划分太多单元即可得到较高的计算精度 相似文献
18.
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. 相似文献
19.
An overview of numerical techniques and previous investigations related to the solution of advection‐dominated transport processes is presented. In addition a new Symmetrical Streamline Stabilization (S3) scheme is introduced. The basis of the technique is to treat the transport equation in two steps. In the first step the dispersion part is approximated by a standard Galerkin approach, while in the second step the advection is approximated by a least‐squares method. The two parts are reassembled, resulting in one system of equations. The resulting coefficients' matrix is symmetric. Only half of a sparse matrix needs to be stored. Robust iterative algorithms for symmetrical systems of equations such as the preconditioned conjugate gradient method (PCG) can be successfully used. The new method leads to an implicit introduction of an ‘artificial diffusion’ term. Solute transport with high Peclet and Courant numbers does not lead to oscillations due to an inherent upwind damping. The upwind effect acts only in flow direction. The efficiency of the new formulation in terms of accuracy and computation time is shown in comparison with the Galerkin approach for mesh parallel and mesh oblique high advective solute transport. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
20.
This paper is a prequel to that of Marchand et al. (Comput Geosci 16:691–708, 2012), where an efficient and accurate hybrid-mixed finite element approximation for a system of time-dependent nonlinear conservation equations has been formulated, implemented, and tested, which are general enough to represent most of the existing formulations for two-component liquid–gas flow in porous medium with phase exchange, also allowing for any (dis)appearance of one of the phases. Temperature variation is neglected, but capillary effects are included by extended Darcy’s law, and Fickian diffusion is taken into account. The efficiency and stability of the numerical method of Lake (1989) relies on an equivalent reformulation of the otherwise commonly used model in terms of new principal variables and subsequent static (flash) equations allowing more generally for any (dis)appearance of one of the phases without the need of variable switching or unphysical quantities. In particular, the formulation in terms of complementarity conditions allows for an efficient and stable solution by the semismooth Newton’s method. 相似文献