A Double Porosity Model to Describe Both Permeability Change and Dissolution Processes
A Double Porosity Model to Describe Both Permeability Change and Dissolution Processes
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描述渗透率变化和溶解过程的双孔隙模型
DOI：
10.1115/icone22-30481
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
H. Mimura
中科院分区：
文献类型：
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作者：
Y. Niibori;H. Usui;Taiji Chida;H. Mimura
水泥是建造放射性废物地质处置系统的一种实用材料。然而，这些材料改变了地下水的pH值高达13的处置库周围，改变了天然屏障的渗透性。到目前为止，作者已经通过将高pH溶液（NaOH，0.1mM）流入填充有无定形二氧化硅颗粒的床中来研究渗透率变化与溶解过程的关系。这里，通过筛分将粒径调节至74至149 μm的尺寸分数。通过使用氮气的BET法估计其比表面积为350 m2/g。实验结果表明，尽管可溶性草酸不断流出填充床，但渗透率并没有立即发生变化。本研究提出了一个新的数学模型，该模型考虑了颗粒内孔的扩散和溶解过程。该模型假设每个堆积颗粒（直径74 - 149μm）由较小颗粒（直径20 nm）的球形聚集体组成。OH−离子扩散到这些小颗粒之间的孔隙中，同时通过与小颗粒的反应消耗。每个堆积颗粒（小颗粒的球形聚集体）的半径由从聚集体中心到小颗粒仍然保留的区域的长度定义。由于OH−离子的扩散过程，外部的小颗粒比内部的小颗粒更容易溶解，因此每个堆积的颗粒逐渐收缩。基本方程由一个简单的OH−离子球坐标扩散方程组成，考虑了反应项，该方程描述了小颗粒随时间的尺寸变化。在此，该模型还考虑了由小颗粒之间孔隙率的变化引起的扩散效率的变化（时间和空间）。此外，通过Kozeny-Carman方程和计算得到的填充颗粒半径，对填充床整体渗透率的变化进行了评价。采用已有文献中的溶出速率常数，计算结果能很好地描述实验结果，但与实验结果比较，没有找到合适的参数。虽然地下流体的流动路径不能简单地用填充床来模拟，但这种方法表明，天然屏障中渗透率的动态行为也取决于矿物内部孔隙（次生孔隙）溶解过程的不均匀性。
Cement is a practical material for constructing the geological disposal system of radioactive wastes. However, such materials alter groundwater up to 13 in pH around the repository, changing the permeability of natural barrier. So far, the authors have examined the relation of permeability change with dissolution process by flowing a high pH solution (NaOH, 0.1 mM) into a bed packed with amorphous silica particles. Here, the particle diameters were adjusted to a size fraction of 74 to 149 μm by sieving. Its specific surface area was estimated as 350 m2/g by the BET method using nitrogen gas. The experimental results showed that the permeability did not immediately change although the soluble silicic acid continuously flowed out of the packed bed.This study proposes a new mathematical model considering the diffusion and dissolution processes in the inner pore of the particle. This model assumed that each packed particle (74 to 149μm in diameter) consists of the sphere-shaped aggregation of smaller particles (20 nm in diameter). OH− ions diffuse into the pore between such small particles, and simultaneously consumed by the reaction with small particles. The radius of the each packed particle (sphere-shaped aggregation of small particles) was defined by the length from the center of the aggregation to the region where the small particles still remains. Since the outer small particles more easily dissolve than inner small particles because of diffusion process of OH− ions, each packed particle gradually shrinks. The fundamental equations consist of a simple diffusion equation of spherical coordinates of OH− ions considering the reaction term, which is linked by the equation to describe the size change of small particles with time. Here, this model also considered a change (time and space) of the diffusion oefficient caused by the change of the porosity between small particles. Besides, the change of over-all permeability of the packed bed was evaluated by Kozeny-Carman equation and the calculated radii of packed particles. The dissolution rate constant already reported was used.The calculated result was able to well describe the experimental result, though there was no fitting parameter in the comparison with the experiment results. While the flow paths of underground cannot be simply simulated by a packed bed, this approach suggested that the dynamic behavior of permeability in a natural barrier depends also on non-uniformity of dissolution processes in inner pores (secondary pores) of minerals.Copyright © 2014 by ASME