本論文利用數學模式來描述核種與膠體在多孔性介質中的傳輸行為，並考慮核種本身的放射性衰變。透過線性平衡吸附的假設，核種與膠體在多孔性岩層的傳輸方程式，可求得解析解。由解析解中可以發現，膠體的濃度、膠體速度以及對核種的吸附係數，明顯影響核種於地下水系統之傳輸。懸浮於地下水中之膠體，對於核種的傳輸具有加速作用，而不可移動的岩層則扮演延遲核種傳輸的機制。而另一方面吸附於岩層之不可移動膠體的量越多，也將阻滯核種的傳輸。由於在地下水中，膠體的組成與成分相當複雜，因此，在本論文中，也考慮了核種與膠體間非平衡吸附機制的影響，同時，核種與多孔性岩層間的非平衡吸附作用在此也一併考慮。當核種與岩層、核種與膠體間的吸附作用考慮為非平衡時，在本論文中，以數值方法求解來討論其物理現象。由數值結果可知吸附作用的反應速率速率，對核種傳輸的影響非常明顯。
對於高階放射廢料的深地層處置，核種的遠場傳輸計算，須考慮核種於裂縫岩層中的傳輸行為。研究指出，膠體的傳輸速度與地下水的流速不同，膠體由於受到外力（靜電力、凡得瓦力等等），可能趨向通道中心，而有較高的速度分布。本論文建立理論分析模型，探討無反應的膠體顆粒在裂縫中之濃度分布情形，考慮膠體受到靜電力、凡得瓦力、慣性力以及重力。分析膠體在裂縫中的受力情形，可得到膠體在達到完全發展時之濃度分布，而進一步求得膠體在裂縫中的平均速度。在求得膠體的平均速度後，經由核種與膠體在裂縫中的傳輸方程式，將核種與膠體以及岩層間的吸附作用視為平衡吸附，可求得核種濃度之解析解。同時，膠體的傳輸參數，如：延散係數、與核種之吸附係數以及平均流速，也受到膠體顆粒大小的影響。將膠體尺寸的影響引進傳輸參數中，可以由解析解看出膠體大小對核種於裂縫岩層中傳輸之影響。膠體的顆粒大小分布，在自然界中，並不是均勻分布的單分散性的膠體，而是不同顆粒尺寸組合的多分散性膠體。本論文中採用文獻中的膠體顆粒分布，討論膠體顆粒分布對核種傳輸的影響。

This thesis investigates the colloid-facilitated migration of radionuclides with radioactive decay in porous media. The sorption processes for radionuclides with both the solid matrix and colloids are treated as equilibrium or nonequilibrium. An analytical solution is obtained from a simplified linear equilibrium interaction mechanism. In addition, the adsorption processes for radionuclides with colloids and porous rock can be assumed as nonequilibrium and modeled by the linear kinetic adsorption. The numerical method is employed to solve the coupled colloid and radionuclide transport equations under nonequilibrium sorption assumption. Although colloids act as vehicles to enhance the migration of radionuclides, the solid matrix has a retardation effect. Moreover, the reaction rates of the adsorption processes for radionuclides with the solid matrix and colloids affect the transport characteristics of radionuclides. The fast reaction rate of radionuclides with colloids causes a higher concentration of radionuclides adsorbed on colloids in a dispersed phase and enlarges acceleration caused by colloids. However, the fast reaction rate for radionuclides with solid matrix increases the retardation effect caused by the solid matrix.
The performance assessment of high level radioactive waste disposal has emphasized the role of colloids in the migration of radionuclides in the fractured rock. Previous literature indicates that owing to hydrodynamic chromatography the colloid velocity may not be equal to that of groundwater. Using hydrodynamic chromatography, this thesis also investigates the effects of the size of colloidal particles on the radionuclide migration facilitated by colloids in a single fractured porous rock. Also, a methodology is proposed to develop a predictive model to assess transport within the fracture rock as well as various other phenomenological coefficients, particularly the size of colloidal particles. In addition, a fully developed concentration profile for non-reactive colloids in the fracture is developed to elucidate hydrodynamic chromatography of colloids in geological media. The external forces acting on colloidal particles hypothesized in the model proposed herein include inertial force, van der Waals attractive force, double layer force as well as gravitational force. The dispersion coefficient of colloids and the distribution coefficient for radionuclides with colloids are also considered as they pertain to the size of the colloid. In addition, the size distributions of colloids are utilized to investigate the effects of polydispersed colloids.

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