Large‐time behavior of concentration variance and dilution in heterogeneous formations
Large‐time behavior of concentration variance and dilution in heterogeneous formations
复制标题
异质地层中浓度变化和稀释的大时间行为
DOI：
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发表时间：
1999
期刊：
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通讯作者：
P. Kitanidis
中科院分区：
文献类型：
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作者：
M. Pannone;P. Kitanidis
考虑在空间可变但统计均匀的速度场中，保守的非吸附溶质的平流和弥散。拉格朗日方法导致浓度的大时间平均值和方差的表达式。该表达式仅需要宏观速度矢量Um、宏观色散张量Dm和附加张量Θ。宏观速度和宏观弥散度在以前的研究中是众所周知的，但Θ在这里是第一次引入。需要张量Θ来描述羽流的稀释动力学：具有相同Um和Dm的两种情况具有取决于Θ的不同稀释特性。稀释的特征时间由张量ΘD− 1 m给出。它表明，第一次通过拉格朗日的方法，在羽状中心的浓度的变化系数成比例的1/t，如以前所示的欧拉理论的Kapoor和Gelhar [1994 a，B]。导出了稀释指数和反应器比的几何平均值的表达式。数值模拟结果支持了该方法的有效性。
Consider the advection and dispersion of a conservative nonsorbing solute in a spatially variable but statistically homogeneous velocity field. A Lagrangian approach leads to expressions for the large‐time mean and variance of concentration. The expressions require only the macroscopic velocity vector Um, the macrodispersion tensor Dm, and an additional tensor Θ. The macroscopic velocities and macrodispersivities are well known from numerous previous studies, but Θ is introduced here for the first time. The tensor Θ is needed to describe the kinetics of dilution of a plume: Two cases with the same Um andDm have different dilution characteristics depending on Θ. The characteristic times of dilution are given by tensor ΘD−1m. It is demonstrated, for the first time through a Lagrangian approach, that the coefficient of variation of concentration at the center of the plume becomes proportionate to 1/t, as was previously shown in the Eulerian theory ofKapoor and Gelhar [1994a, b]. Expressions for the geometric mean of the dilution index and the reactor ratio are derived. Numerical simulations support the validity of the approach.