有效井管半徑模式與有限厚度模式對薄壁效應多深度微水試驗之比較

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謝頤祥(Yi-Hsiang Hsieh) 查詢紙本館藏

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論文名稱

有效井管半徑模式與有限厚度模式對薄壁效應多深度微水試驗之比較
(Comparison of Effective Well Radius Model and Finite Thickness Model for Multilevel Slug Test with Skin Effect)

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摘要(中)

多深度微水試驗(MLST)可用於測定含水層的水力傳導係數K和比儲蓄係數S，但是容易受到薄壁效應之影響。有兩種不同的模擬方法處理薄壁效應。一種假設薄壁層為井邊一環狀疏鬆介質，其厚度rs有限，水力傳導係數Ks和比儲蓄係數Ss異於K及S。另一種方法假設薄壁層厚度rs為無限薄且忽略Ss，相關之薄壁效應則利用與薄壁因子Sk相關的有效井管半徑re來處理。原則上Sk可以藉由抽水試驗推估得知，故無限薄厚度方法實際上僅有兩個未知參數K和S。此外無限薄厚度方法的數學結構較有限厚度方法簡單，更適用於資料分析。本研究之目的是調查在何種情況下，兩種方法會得到相同的結果。比較有限厚度 (FTM)和有效井管半徑(ERM)兩個不同的MLST模式以達成此目的。每一模式分別對受壓和非受壓情況進行分析。當Ss≦7×10－６ m－１時，FTM符合ERM忽略薄壁層比儲蓄係數之假設。受壓情況下，若部分貫穿比≧0.9(對正薄壁效應)及≧0.6(對負薄壁效應) FTM與ERM相合，而無關扁平比、異向比、Sk、無因次薄壁層厚度s的大小。當小於0.6時，在受壓和非受壓情況下ERM與FTM結果相合條件則隨Sk、、、s、之組合而定。對執行MLST而言，通常小於0.6，故使用ERM和FTM進行資料分析會導致不同的參數結果。由於FTM所增加的三個未知參數屬於薄壁層性質並非所需之含水層參數，再加上FTM的數學性較複雜增加資料分析困難，所以建議使用ERM進行MLST現地資料分析。

摘要(英)

The multilevel slug test (MLST) is useful to characterize aquifer hydraulic conductivity K and aquifer storativity S while is under the influence of the skin effect. In general, there are two distinct approaches in modeling the skin effect. One assumes the skin zone to be an annular porous medium surrounding the well with finite thickness rs. Its Ks and Ss are different from K and S, respectively. The other assumes rs to be infinitesimal while neglecting Ss, wherein the skin effect is dealt with by using an effective well radius re that exponentially decays with the skin factor Sk. Technically, Sk can be independently evaluated using a pumping test, leaving only two parameters K and S in the infinitesimal-thickness approach. As being mathematically much simpler than the finite-thickness approach and involving less unknown parameters, the infinitesimal-thickness approach is more practical for data analysis. The purpose of this research is to investigate the conditions under which these two distinct approaches can yield similar results. In order to achieve this goal we compare two different MLST models, a finite-thickness model (FTM), and an effective well radius model (ERM) for both the confined and unconfined aquifers. When Ss≦7×10－６ m－１, the FTM meets the assumption of neglecting skin zone storativity in the ERM. For confined conditions, if the partial penetration ratio  exceeds 0.9 (as for positive skin) and is greater than 0.6 (as for negative skin), the FTM and ERM can produce similar results, regardless the values of the aspect ratio , dimensionless skin thickness s, the skin factor Sk, and the anisotropy ratio . When  <0.4, for both confined and unconfined conditions, the conditions for FTM and ERM being the same dependent on various combinations of the parameters of Sk, ,s . Because  of the MLST is usually less than 0.6, the data analysis using FTM and ERM will produce different parameter estimates. As the FTM involves three skin zone parameters, rs, Ks and Ss, which are of little practical interest, and the data analysis method using the FTM is more complicated, we recommend that the ERM be used for analyzing MLST field data.

關鍵字(中)

★ 多深度微水試驗
★ 薄壁效應
★ 有效井管半徑

關鍵字(英)

★ multilevel slug test
★ skin effect
★ effective well radius

論文目次

中文摘要 i
英文摘要 ii
誌謝 iv
目錄 v
圖目錄 vii
表目錄 xi
符號說明 xii
第一章緒論 1
1.1 多深度微水試驗 1
1.2 薄壁效應 3
1.3 研究動機與目的 10
第二章有效井管半徑模式 12
2.1 受壓含水層有效井管半徑模式 12
2.2 非受壓含水層有效井管半徑模式 19
第三章有限厚度模式 22
3.1 受壓含水層有限厚度模式 22
3.2 非受壓含水層有限厚度模式 26
3.3 薄壁層儲蓄效應分析 28
第四章有效井管半徑模式與有限厚度模式比較 36
4.1 模式包含的無因次參數與比較方法 36
4.2 正薄壁效應比較 38
4.2.1 正薄壁效應各無因次參數之影響 38
4.2.2 正薄壁效應經驗曲線 46
4.3 負薄壁效應比較 52
4.3.1 負薄壁效應各無因次參數之影響 52
4.3.2 負薄壁效應經驗曲線 61
第五章結論與建議 66
5.1 結論 66
5.2 建議 67
參考文獻 69
附錄A 76
附錄B 78

參考文獻

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指導教授

陳家洵(Chia-Shyun Chen)

審核日期

2013-8-7

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