徑向收斂流場下延散效應之分析

Abstract

本研究採用二維徑向收斂流場之追蹤劑試驗傳輸數學模式，包括常數延散模式 (constant dispersivity model, CDM)及尺度延散模式 (scale-dependent dispersivity model, SDM)，分析輔英科技大學、雲林科技大學及喬治城試驗場址之現地追蹤劑試驗之數據資料，藉由抽水井之突破曲線 (breakthrough curves)推求縱向延散係數 (longitudinal dispersivity, αL)，並由觀測井之突破曲線求得橫向延散係數 (transverse dispersivity, αT)，推算延散係數之尺度效應 (scale-dependent)及探討數學模式之適用性。由套配結果可得知縱向延散度符合 之關係式，且延散具有尺度相關性，因此模擬污染物傳輸時，將延散度視為常數並不恰當；橫向延散度套配採用各觀測井不同深度之濃度平均值進行套配，其均值之t-test檢定結果顯示在95 % 信賴區間，雲林科大注入井至4號井及喬治城注入井至21號至28號井其不同深度之濃度平均值與各井不同深度之濃度套配平均值無顯著差異 ( p-value > 0.05)，故可將該等追蹤劑所流經之含水層視為均質。經數學模式應用於現地追蹤劑試驗之數據分析，可對試驗場址水文地質條件、追蹤劑移動方式及探討試驗場址之異質程度有進一步瞭解，因此可作為日後設計與分析均質含水層追蹤劑試驗之參考指引。

This study adopted a two-dimensional mathematical model, including constant dispersivity model (CDM) and scale-dependent dispersivity model (SDM), to describe solute transport in a radially convergent flow field. This model was to determine the longitudinal dispersivities, transverse dispersivities and scale-dependent dispersion effects, by fitting breakthrough curves of extraction well and observation well in a field tracer test. Data of three different field convergent radial tracer tests including Fooyin University, Yunlin Universuty of Science & Technology, and George Town field were used to explore the scale dependent effect on longitudinal dispersivities. The results of the longitudinal dispersivities estimated in this study agree with the relation of the product of the Peclet number and the dispersivity/distance ratio (Pe × eL=4). Dispersivity increases with solute transport distance, indicating that the longitudinal dispersivities treated as constants is not suitable in the modeling of solute transport in groundwater systems. The t-test is used to evaluate the means of the breakthrough curves of observation well #4 in Yunlin Universuty of Science & Technology field and observation well #21, 28 in George Town field. The results show that the transverse dispersivities calculated by averaged concentrations of breakthrough curves are similar to those calculated by concentrations of breakthrough curves with various depths under 95 % confidence interval ( p-value > 0.05). Hence, the formation of three tracer tests can be regarded as a homogeneous aquifer. Moreover, the SDM mathematical model is suitable for the analyses of field tracer tests of the homogeneous aquifer.