Zhang Fan, Yeh Gour-Tsyh, Parker Jack C, Brooks Scott C, Pace Molly N, Kim Young-Jin, Jardine Philip M, Watson David B
Environmental Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.
J Contam Hydrol. 2007 Jun 16;92(1-2):10-32. doi: 10.1016/j.jconhyd.2006.11.007. Epub 2007 Jan 16.
This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing N(E) equilibrium reactions and a set of reactive transport equations of M-N(E) kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.
本文提出了一种基于反应的地下水流系统水质迁移模型。通过M个偏微分方程（PDEs）对具有各种化学和物理过程的化学物质迁移进行数学描述。通过反应网络的高斯 - 约旦列约简分解，将M个物种反应输运方程转化为两组方程：一组表示N(E)个平衡反应的热力学平衡方程，以及一组不涉及平衡反应的M - N(E)个动力学变量的反应输运方程（动力学变量是物种的线性组合）。从反应输运方程中消除平衡反应可实现稳健且高效的数值积分。该模型求解动力学变量的偏微分方程而非单个化学物质的方程，这减少了反应输运方程的数量并简化了方程中的反应项。研究了多种用于求解耦合输运和反应方程的数值方法。与精确解进行了模拟比较，以验证数值精度并评估各种数值策略处理不同应用情况的有效性。给出了两个涉及土壤柱中铀迁移模拟的验证示例，以评估该模型模拟具有涉及动力学和平衡反应的复杂反应网络的反应输运的能力。
