國內外土壤地下水常用數學模式分類彙整與基準案例評析

A Collection and Benchmark Tests of Mathematical Models for Soil Groundwater Flow and Transport Problems

倪春發(Chuen-Fa Ni) ； 李奕賢(I-Hsien Lee) ； 李唯祺(Wei-Ci Li) ； 林淇平(Chi-Ping Lin) ； 吳宛庭(Wan-Ting Wu) ； Tran Quoc Dung ； 馮嵩棣(Song-Di Fong) ； 陳昶宏(Chang-Hung Cheng)

《土壤及地下水污染整治》 3卷4期 (2016/10) Pp. 261-275

https://doi.org/10.6499/JSGR.2016.0304.002

摘要

數學模式在土壤地下水污染調查分析中可協助量化評估與提高調查效率，其基礎概念、模式選擇與適用條件與使用原則，是土壤地下水污染相關調查工作中，至為關鍵的環節。本文針對國內外常用土壤地下水相關數學模式，提出整合性的模式概念說明。此外，選用不同數值分析方法建構的模式，以一基準案例比較模式網格解析度對分析結果之影響。最後，針對數學模式在土壤地下水應用領域的重要議題，提出看法與可能的解決建議。本研究共蒐集二十三個常用土壤地下水相關的數學模式；整體而言，解析模式功能較單一，不涉及耦合分析。數值模式多數是有限元素及有限差分模式，商業化模式通常可以耦合分析複雜的物理化學機制。基準案例分析結果顯示，使用有限差分法的MODFLOW模式模擬穩態流場時，對網格大小的敏感度較FEMWATER及HYDRUS高，最大的差異處發生在土壤參數變化大的區域。污染傳輸分析時，所有模式網格解析度對污染傳輸的分析結果影響大，濃度團前緣部分差異最大。既有的土壤與地下水或水文地質資料相關網路平台多以展示資料為主，為解析污染團之時空變遷特性，土壤、水文、地質等相關資訊展示平台上，應模組化與跨平台結合地下水流與污染物傳輸模擬引擎，提高處理土壤地下水污染問題判別、應變、規劃與管理效率。

關鍵字

數學模式 ； 土壤地下水污染 ； 解析模式 ； 數值模式 ； 耦合

並列摘要

Mathematical models can improve the efficiency of characterizing soil groundwater contamination. The fundamental concepts underlying such models and selections of suitable models are crucial to achieving good characterization of the flow and contaminant transport in practical soil groundwater problems. This paper reviews the available soil groundwater models for flow and transport modeling. A benchmark case is used to evaluate the effects of cell sizes on the simulation results of three numerical models. This study then proposes potential solutions for future implementations of mathematical models in the fields of soil groundwater characterization. A total of 23 models were collected and systematically analyzed in the paper. Most analytical models are developed for relatively simple problems, while numerical models are mainly developed based on finite element and finite difference schemes. A comparison of the selected MODFLOW, FEMWATER, and HYDRUS models shows good agreement among them with regard to the results of steady state flows. The finite difference-based model is sensitive to the selection of cell size, and the cell or mesh sizes significantly influence the accuracy of transport simulations. The highest variations in the concentrations for different cell/mesh sizes are obtained in the plume front areas. Many of the available soil groundwater and geology related databases focus on the presentation of data. In order to illustrate the spatial and temporal variations of plumes it may be necessary to apply modularized mathematical models and multiple platform systems, thus integrating the available databases and improving the efficiency of characterizing practical soil groundwater problems.

並列關鍵字

mathematical model ； soil groundwater contamination ； analytical model ； numerical model ； coupling