放射性核種在多重平行裂縫系統傳輸方程式之解析解

Abstract

本論文之主要目的，在探討放射性核種於具有多重平行裂縫的破裂岩層中傳輸，分析時以多個平行且其寬度可為不等間距的裂縫岩層為對象，而單一裂縫或等間距之兩平行裂縫系統，可視為本文之特例。破裂岩層中，裂縫的透水性遠大於裂縫周遭母岩；因此，假設水流只在裂縫中發生，且裂縫表面與母岩交界面沒有擴散通量。核種在裂縫中傳輸的數學模式，考慮下列機制：傳流、縱向延散、放射性衰變、及裂縫表面的吸附。所建立的多重平行裂縫傳輸方程式，利用拉普拉斯轉換方法，可導得一個解析解，此解析解可用來分析核種在岩層裂縫中的傳輸。結果顯示，當各裂縫為等寬度且寬度總和等於單一裂縫系統之寬度時，多重平行裂縫系統中每一裂縫之核種濃度的時空分佈，與單一裂縫系統情況相同。於不等間距寬度時，核種在寬裂縫中遷移距離，均較單一裂縫系統遠，且接近污染源處，寬裂縫中核種只需在較短時間內，即可達到邊界源濃度。因此，多重平行裂縫介質中之核種傳輸，裂縫寬度大小是一個非常重要的影響因子。

This thesis is to study the effects of fracture width on the transport of radionuclide in a multiple and parallel fractured rock formation. Due to the very low hydraulic conductivity of the rock matrix, the water flow is assumed to take place only within fractures. Besides, the diffusive flux due to concentration gradient across the interfaces between the fracture surfaces and the rock matrix is neglected in the system. The equation describing the transport of radionuclide includes the following mechanisms: advection, dispersion, radioactive decay, and adsorption on the fracture surfaces. An analytical solution for this equation was derived by using the Laplace transform technique. This solution indicates that identical concentration distributions can be observed in each fracture of the equal-width fractured system. For an unequal-width fractured systems, however, the travel distances along wide fractures are substantially larger than the travel distance in a single uniform fractured system. The radionuclide concentration in the wide fracture reaches source concentration rapidly. This confirms that the fracture width plays an important role in radionuclide transport through a system of multiple and parallel fractured media.