應用隨機產生器於裂隙中之傳輸

Abstract

地下水於裂隙中之傳輸行為往往因裂隙分佈的不易掌握使相關研究變得相當棘手且不確定，例如當有污染物洩漏時，瞭解其傳輸特性方能有效進行整治計劃。本研究應用具有碎形特性的碎形隨機布朗運動及應用地質統計所發展的兩種不同的亂數產生器產生兩組具有相同資料點及相同統計特性的裂隙寬度分佈，進而將這兩組裂隙分佈刻製於玻璃上並進行定水頭試驗，以數位式攝影機錄下染色液體在兩組模型中的傳輸分佈後進行影像分析。影像分析的結果映證了液體於不同裂隙分佈中亦有不同的傳輸特性：在具有碎形特性的裂隙中其流動軌跡之變異量為傳輸時間的次方關係(次方法則; power law)，且其冪次為代表碎形特性之赫斯特指數(Hurst exponent)的兩倍；而在具有一定相關性長度的裂隙分佈中，其傳輸軌跡的變異量則在數倍相關性長度後呈現為時間的線性關係。

The complexity of natural fracture systems does not allow the actual flow field to be completely described. Different 2-D random generators are used herein to generate natural looking random fractures on which tracer transport and dispersion processes can be studied. Two fields with random aperture distributions and different spatial structures are taken as models to study solute transport in fractures. One network has non-vanishing long range correlations and represents a fractal pattern, while the other has a finite correlation length and an exponential covariance function. Based on these fields, two physical fracture models were produced and used to record the movement of a colored solute in the both artificial models via a video-camera. The images obtained are analyzed using image processing methods. A front tracking algorithm demonstrates that the growth law of the frontal variance is a power law of time in which the exponent depends on the Hurst coefficient of he aperture distribution for the fractal pattern, and is a linear function of time for the finite correlation length. The second method introduced is a random-walk method in fractures. The hydraulic conductivity varies with apertures herein. The simple cases are processed in the both fractures networks using random-walk method. Moreover, the similar behaviors of power law of time for fractional non-Fickain random-walk, and linear function of time for the classical Fickian random-walk. This study provides that the behaviors of solute transport depend on the distribution of pure fractures.