Semianalytical solutions for parameter estimation in diffusion cell experiments
Semianalytical solutions for parameter estimation in diffusion cell experiments
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DOI：
10.1029/1999wr900084
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发表时间：
1999-06-01
影响因子：
5.4
通讯作者：
Moridis, GJ
中科院分区：
文献类型：
--
作者：
Moridis, GJ
本文在扩散池实验条件下开发了扩散问题的半解析解，其中涉及有限液体体积和上游和下游储层随时间变化的浓度。这些解决方案解释了孔隙中的扩散、表面扩散、流动水和固定水部分之间的传质、线性吸附（平衡或动力学）和放射性衰变。在拉普拉斯空间中获得了穿透扩散和储层耗尽研究的完全解析解，随后对其进行数值反转以及时提供解。研究了平衡和动力学线性吸附下各种扩散、吸附和几何参数对溶液的影响。半解析解与参数估计的优化算法相结合，并使用实验数据确定扩散和吸附参数。半解析解被证明比传统的图形方法具有显着的优势，因为（1）它们不是基于上游浓度恒定和下游浓度可忽略不计的通常无效的假设，（2）它们使提取相关扩散和吸附参数的数据量增加了一倍，（3）它们允许区分平衡和动力学吸附。
In this paper, semianalytical solutions to the diffusion problem are developed under the conditions of diffusion cell experiments, which involve finite liquid volumes and temporally variable concentrations in the upstream and downstream reservoirs. These solutions account for diffusion in the pores, surface diffusion, mass transfer between the mobile and immobile water fractions, linear sorption (equilibrium or kinetic), and radioactive decay. Fully analytical solutions for both through-diffusion and reservoir-depletion studies are obtained in the Laplace space, which are subsequently numerically inverted to provide the solution in time. The effects of the various diffusion, sorption, and geometric parameters on the solutions under both equilibrium and kinetic linear sorption are investigated. The semianalytical solutions are coupled with an optimization algorithm for parameter estimation, and diffusion and sorption parameters are determined using experimental data. The semianalytical solutions are shown to have significant advantages over the conventional graphical approach because (1) they are not based on the often invalid assumption of constant upstream and negligible downstream concentrations, (2) they double the amount of data from which to extract the pertinent diffusion and sorption parameters, and (3) they allow differentiation between equilibrium and kinetic sorption.