Experimental study of groundwater pollution predictions based on theory of complex physics

将平流-弥散方程(ADE)模型应用于核废料地下储存中放射性核素行为的预测。然而，最近有人指出，ADE并不总是正确地复制实际现场测试或实验室实验的结果。在本研究中，我们将重点放在一种新的模型CTRW(连续时间随机行走)上，从而将我们的实验结果与CTRW进行比较。我们进行了两种实验：(1)长距离沙箱渗透实验，(2)吸附重金属的柱实验。在这两个实验中，我们发现CTRW比ADE提供了更好的结果。我们的调查结果详情如下。对于(1)，我们得到了纵向色散系数的实验值。当流动距离变大时，系数变大，并收敛到一个几乎恒定的值。我们发现这一行为与原始的CTRW不一致，而是在等待时间函数中加入了截断时间的修正CTRW。原始CTRW中的假设(=包括等待时间的无限持续时间)可能太强，不能重现真实的实验。对于(2)，我们测试了两种重金属，一种是弱吸附的，另一种是强吸附的，发现后者接近原始的CTRW，但前者更接近截止CTRW。我们认为，在放射性废物处置库的分析中，CTRW是值得考虑的。

The model of Advection-Dispersion Equation (ADE) has been used in predicting the behavior of radioactive nuclides for underground storage of nuclear wastes. Recently, however, it has been pointed out that the ADE does not always properly reproduce the results of actual field tests or laboratory experiments. In this study, we concentrate on a new model, CTRW (Continuous-time Random Walk), thereby compare our experimental results with CTRW. We performed two kinds of experiments : (1) long-distance sandbox permeation tests, and (2) column tests with adsorptive heavy metal. In both experiments, we found that CTRW gives a better result than ADE does. Details of our findings are as follows. As for (1), we obtained experimental values of the longitudinal dispersion coefficient. The coefficient becomes larger when the flow distance becomes larger, and converges to an almost constant value. We found that this behavior is not consistent with the original CTRW, but a modified CTRW with cutoff time in the waiting time function. The assumption in the original CTRW (=includes infinity duration of the waiting time) may be too strong for reproducing the real experiments. As for (2), we tested two kinds of heavy metals, one is weakly adsorbed and the other is strongly adsorbed, and found that the latter is close to the original CTRW but the former is more close to cutoff-CTRW. We conclude that, in the analysis of radioactive waste repository, CTRW is worth to be considered.