Macroscopic behavior and random‐walk particle tracking of kinetically sorbing solutes

Macroscopic behavior and random‐walk particle tracking of kinetically sorbing solutes
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动力学吸附溶质的宏观行为和随机行走粒子追踪

DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
P. Kitanidis
P. Kitanidis
中科院分区：
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文献类型：
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作者：
A. Michalak;P. Kitanidis

文献摘要

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推导出了符合线性可逆动力学传质模型的吸附溶质的第零、一、二空间矩的解析表达式。我们确定了由于溶质在两相之间的任意初始分布而导致的吸附和水相中羽流空间矩的相变概率和闭合形式的表达式。这允许在不借助数值模拟的情况下计算均匀区域的有效速度和色散系数。利用空间矩方程和相变概率方程，发展了一种新的随机游走粒子跟踪方法。该方法针对三种不同的配方进行了测试，发现在不牺牲精度的情况下计算效率很高。我们应用新的随机游走方法研究了动力学吸附引起的水溶液溶质浓度出现双峰的可能性。双峰的出现依赖于Damköhler数的大小，其出现的时间由传质速率和延迟因子控制。确定了导致双峰的Damköhler数的两个范围。在第一个范围(DAI≤1)中，所有延迟因子都出现双峰，而在第二个范围(1≤DAI≤3)中，这一行为对R&GT；12最为显著。
Analytical expressions are derived for the zeroth, first, and second spatial moments of sorbing solutes that follow a linear reversible kinetic mass transfer model. We determine phase‐transition probabilities and closed‐form expressions for the spatial moments of a plume in both the sorbed and aqueous phases resulting from an arbitrary initial distribution of solute between the phases. This allows for the evaluation of the effective velocity and dispersion coefficient for a homogeneous domain without resorting to numerical modeling. The equations for the spatial moments and the phase‐transition probabilities are used for the development of a new random‐walk particle‐tracking method. The method is tested against three alternate formulations and is found to be computationally efficient without sacrificing accuracy. We apply the new random‐walk method to investigate the possibility of a double peak in the aqueous solute concentration resulting from kinetic sorption. The occurrence of a double peak is found to be dependent on the value of the Damköhler number, and the timing of its appearance is controlled by the mass transfer rate and the retardation factor. Two ranges of the Damköhler number leading to double peaking are identified. In the first range (DaI ≤ 1), double peaking occurs for all retardation factors, while in the second range (1 ≤ DaI ≤ 3), this behavior is most significant for R > 12.