漸近型式尺度延散度之一維移流-延散方程式之Laplace轉換級數解

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：10

、訪客IP：18.217.144.32

姓名

江政昌(Zheng-Chang Jiang) 查詢紙本館藏

畢業系所

應用地質研究所

論文名稱

漸近型式尺度延散度之一維移流-延散方程式之Laplace轉換級數解
(An Laplace transform power series solution to generalizedadvection-dispersion equation with asymptotic distance-dependent dispersivity)

相關論文

★ 單井垂直循環流場追蹤劑試驗數學模式發展	★ 斷層對抽水試驗洩降反應之影響
★ 延散效應對水岩交互作用反應波前的影響	★ 異向垂直循環流場溶質傳輸分析
★ 溶解反應對碳酸岩孔隙率與水力傳導係數之影響	★ 濁水溪沖積扇地下水硝酸鹽氮污染潛勢評估與預測模式建立
★ 異向含水層部分貫穿井溶質傳輸分析	★ 溶解與沈澱反應對碳酸鈣礦石填充床孔隙率與水力傳導係數變化之影響
★ 有限長度圓形土柱實驗二維溶質傳輸之解析解	★ 第三類注入邊界條件二維圓柱座標移流-延散方程式解析解發展
★ 側向延散對雙井循環流場追蹤劑試驗溶質傳輸的影響	★ 關渡平原地下水流動模擬
★ 應用類神經網路模式推估二維徑向收斂流場追蹤劑試驗縱向及側向延散度	★ 關渡濕地沉積物中砷之地化循環與分布
★ 結合水質變異與水流模擬模式評估屏東平原地下水適合飲用之區域	★ 推估土壤傳輸參數現地試驗方法改進與數學模式發展

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

為了描述溶質在地表底下的傳輸行為，數學上常用移流-延散方程式描述控制移流和水力延散傳輸的物理機制。在延散傳輸的理論中，延散度是量測溶質分散的重要的參數。傳統數學模式預測溶質傳輸，多採用常數延散度。然而，現地研究指出延散度並非常數，而是會隨溶質傳輸的距離增加而改變，且在長距離時漸近常數。本研究中，考慮溶質傳輸問題發生於有限長度的孔隙介質中，並考慮延散度隨距離增加而趨近一常數。本研究以Laplace轉換級數方法解析漸近形式的尺度延散度之移流-延散方程式。發展之解析解與數值解進行濃度穿透曲線比較以檢驗其正確性，比較的結果顯示，在不同觀測位置的濃度穿透曲線，解析解與數值解十分吻合。然而，解析解於極限延散度小而特徵半展距大時，在小時間無法進行數值計算。此外，藉由分析解析解函數的數學行為，可了解無法進行數值計算的困難之處。

摘要(英)

To describe solute transport in a subsurface porous medium, the advection-dispersion equation is widely used to mathematically describe the physical processes governing advective and hydrodynamic dispersive transport. In the theory of dispersive transport, dispersivity is an important parameter for the measurement of the spreading of solute. Classical mathematical models for predicting solute transport are based on advection-dispersion equation with space-invariant dispersivity. However, field study indicated that dispersivity is not constant but generally increases with solute transport distance, and becomes asymptotically constant at large distance. In this study, a solute transport problem in a finite porous medium where the dispersion process depends on distance and increases up to some constant limiting value is considered. The Laplace transform power series technique is applied to analytically solve the advection-dispersion equation with asymptotic distance-dependent dispersivity. The developed analytical solution is compared to the numerical solution to examine its accuracy. Results shows that the breakthrough curve at different observation points from the power series solution have good agreements with those from the numerical solution. However, the solution can not been numerically computed at the early time when the asymptotic dispersivity is small and the characteristic length is large. In addition, the mathematical behaviors of the developed solution functions are analyzed to address the difficulty in numerical computation.

關鍵字(中)

★ Laplace轉換級數解
★ 漸近型式尺度延散度
★ 移流-延散方程式

關鍵字(英)

★ Laplace transform power series solution
★ asymptotic distance-dependent dispersivity
★ advection-dispersion equation

論文目次

目錄............................................................................................................................i
圖目錄.......................................................................................................................ii
表目錄......................................................................................................................iv
符號說明...................................................................................................................v
第一章緒論.............................................................................................................1
1.1 前言................................................................................................................1
1.2 文獻回顧........................................................................................................4
1.3 研究目的........................................................................................................6
1.4 研究方法........................................................................................................6
第二章數學模式.....................................................................................................7
2.1 移流-延散方程式建立...................................................................................7
2.1.1 延散機制介紹.........................................................................................7
2.1.2 推導一維溶質傳輸方程.......................................................................10
2.2 發展一維漸近型尺度延散度之移流-延散方程.........................................14
2.3 利用Laplace轉換級數法求解....................................................................18
第三章結果與討論...............................................................................................24
3.1 數學模式驗證..............................................................................................24
3.2 函數數學行為探討......................................................................................25
3.3 尺度延散與常數延散比較.........................................................26
第四章結論...........................................................................................................65
參考文獻.................................................................................................................66

參考文獻

Aral, M. M., and B.-Sh. Liao, 1996. Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficient. J. Hydrol. Eng., 1(1): 20-32.
Barry, D. A., and G. Sposito., 1989. Analytical solution of a convection
-dispersionmodel with time-dependent transport coefficients. Water Resour. Res., 25(12): 2407-2416.
Bear, J., 1979. Hydraulics of Groundwater, 569 pp., McGraw-Hill, New York.
Bedient P. B., Hanadi S. R., Charles J. N., 1994. Ground Water Contamonation, Prentice-Hall,Inc.,126 pp.
Bruggeman G. A., 1999. Analytical solution of geohydrological problems, Elsevier, 478 pp.
Chen, J. S., C. W. Liu, H. T. Hsu, and C. M. Liao, 2003. A Lapace transformed power series solution for solute transport in a convergent flow field with scale-dependent dispersion. Water Resour. Res., 39(8): doi: 10.1029/2003WR002299
Chen, J. S. , C. P. Liang, C. Y. Chen, and C. W. Liu., 2007. Composite analytical solutions for a soil vapor extraction system, Hydrological Processes : in press, (SCI )
Crump, K. S., 1976. Numerical inversion of Lap lace transforms using a Fourier series apporoximation. J. Assoc. Comput. Mach., 23(1): 89-96.
De hoog, F. R., J. H. Knight, and A.N. Stokes., 1982. An improved method for numerical inversion of Laplace transforms. SIAM J. Sci. Stat. Cmput., 3(3): 357-366
Domenico, P. A., and G. A. Robbins., 1984. A dispersion scale effect in model calibrations and field tracer experiments. J. Hydrol., 70: 123-132.
Fetter, C. W., 1994. Applied Hydrogeology, Macmillan College Publishing Company, Inc., 691 pp.
Freyberg, D. L., 1986. A natural gradient experiment on solute transport in a sand aquifer, 2, Spatial moments and the advection and dispersion of nonreactive tracers. Water Resour. Res., 22: 2031-2046.
Gelhar, L. W., Mantoglou, A., Welty, C. and Rehfeldt, K. R., 1985. A Review of Field-scale Physical Solute Transport Processes in Saturated and Unsaturated Porous Media. Technical Report EPRI EA-4190, Electrical Power Research Institute, Palo Alto, 116 pp.
Gelhar, L. W., 1986. Stochastic subsurface hydrology from theory to applications. Water Resour. Res., 22(9): 135–145.
Gelhar, L. W., C. Welty, and K. R. Rehfeldt., 1992. A critical review of data on field-scale dispersion in aquifer. Water Resour. Res., 28(7): 1955-1974.
Huang, K.-L., M. T. van Genuchten, and R.-D. Zhang, 1996. Exact solutions for one-dimensional transport with asymptotic scale-dependent dispersion. Appl. Math. Modelling, 20: 298-308.
Hunt, B., 1998. Contaminant source solutions with scale-dependent dispersivities. J. Hydrol. Eng., 3(4): 268-275.
Jayawardena, A. W., Lui, P. H., 1984. Numerical solution of the dispersion equation using a variable dispersion coefficient; method and applications. Hydrol. Sci. J., 29 (3): 293-309.
Jury, W. A., Shoude, P. H. and Stolzy, L. H., 1982. A field test of the transfer function model for predicting solute transport. Water Resour. Res., 18: 369-375
Kreyszig E., 1999. Advanced Engineering Mathematics, John Wily & Sons, Inc.
Logan, L. D., 1996. Solute transport in porous media with scale-dependent dispersion and periodic boundary conditions. J. Hydrol., 184: 261-276.
Mishra, S., Parker, J.C., 1990. Analysis of solute transport with a hyperbolic scale dependent dispersion model. Hydrol. Proc., 4 (1): 45-57.
Molz, F. J., O. Güven and J. G. Melville, 1983. An examination of scale-dependent dispersion coefficients. Ground Water, 21 (6): 1701-1711.
Pickens, J. F. and G. E. Grisak, 1981a. Scale-dependent dispersion in a stratified granular aquifer. Water Resour. Res., 17(4): 1191-1211.
Pickens, J. F. and G. E. Grisak, 1981b. Modelling of scale-dependent dispersion in a hydrogeological system, Water Resour. Res., 17(6): 1701-1711.
Pang, L. and M. E. Close, 1999. Field-scale physical nonrquilibrium transport in an alluvial gravel aquifer. J. Contam. Hydrol., 38(4): 447-464.
Pang, L., and B. Hunt, 2001. Solutions and verification of a scale-dependent dispersion model. J. Contam. Hydrol., 53: 21-39.
Ptak, T., and Teutsch, G., 1994. Forced and natural gradient tracer tests in a highly heterogeneous porous aquifer. Instrumentation and measurements. J. Hydrol., 159: 79-104.
Roco, M. C., J. Khadilkar, and J. Zhang, 1989. Probabilistic approach for transport of contaminants through porous media. Int. J. Numer. Methods Fluids, 9(12): 1431-1451.
Schwartz, F. W. and Zhang, Hubao, 2003. Fundamental of Groumd Water, John & Sons, Inc. 451.
Wang Z. T., 2001. An analytical solution for an exponential-type dispersion process. Appl. Math. and Mech., 22(3):368-371.
Wheatcraft, S. W. and S. W. Tyler, 1988. Explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractral geometry. Water Resour. Res., 24(4): 566-578.
Yates, S. R., 1990. An analytical solution for one-dimension transport in
heterogeneous porous media. Water Resour. Res., 26(10): 2331-2338.
Yates, S. R., 1992. An analytical solution for one-dimension transport in porous media with an exponential dispersion function. Water Resour. Res., 28(2): 149-2154.
Zhang, R., K. Huang, and J. Xiang, 1994, Solute movement through homogeneous and heterogeneous soil columns. Adv. Water Resour., 17(5): 317-324.
Visual Numerical, Inc. 1994. IMSL User’s Manual. Houston, Tex., 1:159-161

指導教授

陳瑞昇(Jui-Shen Chen)

審核日期

2007-7-23

推文