地下水非均質等向性場之條件模擬與水層異向性分析

Abstract

傳統上，Papadopulos’ approach (PA)常被用來推求含水層蓄水係數和異向性導水係數值，該方法基本上，是假設水層具均質、非等向性。一個現地為等向、非均質的地下水場址，若沒有經過詳細的水層特性調查，貿然假設含水層具均質、異向性，並以PA推求水層異向性參數，可能不適當，而求得的參數值，也不具代表性。前人的研究顯示，針對一個具等向性的亂數導水係數場或具空間相關的隨機導水係數場，作抽水試驗數據分析時，會得到均質而具異向性的導水係數值。 給定一些現地的地質條件，如導水係數的平均值、變異數、及相關尺度，地質統計裡的隨機場產生器，可合成出具某種特性的導水係數場，以供各種研究分析用。事實上，隨機場產生的數值是隨機的，並沒有包括或反映已知的現地值，較不具代表性；而具條件模擬的亂數隨機場，產生的非均質場，可包含水層裡某些地點已知的水文地質參數值。本文的目的，在探討具條件模擬的非均質隨機場，對含水層做均質異向性分析的影響。在分析水層異向性時，針對模擬退火演算法與循序高斯法，這兩個具條件模擬亂場產生器所產生的隨機場，作抽水試驗數據異向性分析結果的比較。本研究工作，利用MODFLOW來模擬水層抽水洩降的行為，所得的數據，進一步利用PA推求水層具異向性的水文地質參數值。 若依蒙地卡羅方法，利用模擬退火演算法或循序高斯法，可大量產生具條件模擬與非均質的導水係數場，透過MODFLOW產生洩降數據，再利用PA求異向性參數，所得結果，可探討水層導水係數場的變異數對含水層異向性的影響。本研究成果顯示，具條件模擬的產生器產生等向非均質場，若經由上述步驟作異向性分析，可求得具異向性的導水係數，且異向性程度，隨導水係數變異係數增加而增加；但具條件模擬非均質場的變異係數值，與所加入條件模擬數據之標準偏差不大時，其分析結果比不具條件模擬來的小。

Papadopulos’ approach (PA) was commonly employed to determine the aquifer anisotropic parameters for an aquifer under homogeneous and anisotropic assumptions. However, such assumptions and applications of PA are not suitable for heterogeneous and isotropic aquifers. A numerical method, named as PANM, developed based on PA and nonlinear least-squares and finite-difference Newton's method (NLN) was used to analyze the anisotropic parameters. To explore the effects of heterogeneous and isotropic aquifer on anisotropic analyses, geostatistical methods assist to generate heterogeneous conductivity fields for succeeding studies and PANM is used to analyze aquifer anisotropy. Simulated Annealing (SA) and Sequential Gaussian Simulation (SGS), used to generate conductivity fields, have the abilities of producing conditional fields without losing known geology information. The purpose of this thesis is to explore the effects of aquifer heterogeneity with conditioning information on the anisotropy analysis and discusses the analyzed results for conditional and unconditional cases. Four steps are taken in this study. First, SA and SGS were employed to generate conditional and unconditional random conductivity fields. Second, the ground-water flow model MODFLOW with heterogeneous transimissivity fields was used to simulate pumping test and generate the time-drawdown data. Third, the time-drawdown data was analyzed by PA to determine the aquifer storativity and anisotropic transmissivity. Finally, the Monte Carlo method was used to analyze the effects of the conductivity variance of generated fields on the anisotropy analysis. The results demonstrated that conditional/unconditional heterogeneous and isotropic conductivity fields also appeared anisotropic characters