臺灣博碩士論文加值系統

以往文獻上討論海水入侵問題的方法可以分為兩種，一種是假設海水與淡水為兩種彼此不相互溶的液體，所以海水與淡水將形成一明顯交界面。另一種是將鹽分視為在密度變化地下水流中傳輸之溶質，因此海水中的鹽分會因延散作用而與淡水形成一漸變區。
本文採用後者觀點並引用解構法求解海水入侵問題。於研究過程中解構法具有可以保留非線性項的特性，且比微擾法所得到的解更迅速逼近真解之優點，因此本研究首次引用解構法於海水入侵問題，並保留上述優點進行研究。
首先推導地下水流方程式與擴散方程式之積分解，進而建立海水入侵至地下含水層之數值模式，並分析流通係數與擴散係數對海水入侵鹽分濃度分佈的影響。模擬結果顯示由於流通係數本身含有相當大的不確定性，在參數決定之過程中不論對流通係數高估或是低估，都會對模擬結果有很大的影響。

第一章 緒論1
1-1 研究動機2
1-2 研究目的3
1-3 研究內容4
第二章 文獻回顧6
2-1 採用「明顯交界面」假設下之理論分析7
2-2 採用「明顯交界面」假設下之解析解與數值解8
2-3 考慮地下水流密度變化之理論分析、解析解與數值解10
第三章 定率分析12
3-1 控制方程式13
3-2 理論推導15
第四章 定率模式驗證與數值計算分析21
4-1 模式驗證22
4-2 不同模擬時間下之鹽分濃度分佈（Case 1）23
4-3 擴散係數對鹽分濃度分佈之影響（Case 2）25
4-4 流通係數對鹽分濃度分佈之影響（Case 3）26
第五章 序率分析28
5-1 控制方程式29
5-2 序率地下水流方程式推導31
5-3 達西定律序率分析34
5-4 序率擴散方程式推導37
5-5 流通係數變異數-鹽分濃度變異數之關係式推導44
第六章 序率計算結果與分析47
6-1 時間對鹽分濃度變異數之影響(Case 4)48
6-2 鹽分濃度變異數在空間之分佈(Case 5)49
6-3 流通係數變異數與鹽分濃度變異數之關係(Case 6)50
第七章 結論與建議52
參考文獻54

[1] Badon-Gyben, W., Nota in verband met de voorgenomen putboring nabij Amsterdam, Tijdschr. Kon. Inst. Ing. 8-22, 1888.
[2] Bakr, A. A., L. W. Gelhar, A. L. Gutjahr, and J. R. McMillan, Stochastic analysis of spatial variability in subsurface flow, 1, Comparison of one — and three-dimensional flow, Water Resour. Res., 14(2), pp. 263-272, 1978.
[3] Bear, J., Hydraulics of Groundwater, McGraw-Hill International Book Company, 1979.
[4] Bear, J., G. Dagan, Some exact solution of interface problem by means of the hydrograph method, J. Geophvs. Res., 69(8), pp. 1563-1572, 1964.
[5] Bear, J., G. Dagan, Solving the problem of local interface upconing in a coastal aquifer by the method of small perturbations, J. Hydro. Res., 6(1), pp. 15-43, 1968.
[6] Bennett, Electric-Analog studies of brine coning beneath freshwater wells in the punjab region, West Pakistan, U. S. Geological Survey Water Supply Paper, 1608-J, 1968.
[7] Chandler, R. L. and D. B. Mcwhorten, Upconing of the seawater-freshwater interface beneath a pumping well, Ground Water, 13(4), pp. 354-359, 1975.
[8] Dagan, G. Amethod of determining the permeability and effective porosity of unconfined anisotropic aquifers, Water Resour. Res., 3(4), pp. 1059-1071, 1967.
[9] Diersch, H. J., D. Prochnow, and H. Thiele, Finite elementanalysis of dispersion affected saltwater upconing below a pumping well, Appl. Math. Modeling, 8, pp. 305-312,1984.
[10] Frind, E. O., Seawater intrusion in continuous coastal aquifer-aquitard systems, Adv. Water Resour., 5, pp.89-87, 1982a.
[11] Frind, E. O., Simulation of long-term transient density-dependent transport in groundwater, Adv. Water Resour., 5, pp.73-88, 1982b.
[12] Gelhar, L. W., Stochastic analysis of phreatic aquifers, Water Resour. Res., 10(3), pp. 539-545, 1974.
[13] Gelhar, L. W., P. Y. Ko, H. H. Kwai, and J. L. Wilson, Stochastic modeling of groundwater systems, Parsons Laboratory Report 189, Massachusetts Instittue of Technology, Cambridge, 1974.
[14] Gutjahr, a. L., and L. W. Gelhar, Stochastic models of subsurface flowL infinte versus finite domain and stationary, Water Resour. Res. 17(2), pp. 337-350, 1981.
[15] Haubold, R. G., Approximation for steady interface beneath a well pumping fresh water overlying salt water, Ground Water, 13(3), pp. 254-259, 1975.
[16] Henry, H. R., Effects of dispersion on salt encroachment in coastal aquifers, Sea Water in Coastal Aquifer, U.S. Geo. Surv. Water Supply, pp. 1613-C, 1964.
[17] Herzberg, A., Die Wasserversorgung Einger Nor-dseebaden, Z. Gasbeleucht. Wasserversorg., 44, pp. 815-819, pp. 824-844, 1901.
[18] Huyakorn, P. S., and C. Taylor, Finite element models for coupled groundwater and convevtion dispersion, Proceedings of the 1st International Conference on Finite Elements in Water Resources, pp. 1.131-1.151, Pentech Press, London, 1976.
[19] Huyakorn, P. S., P. F. Anderson, J. W. Mercer, and H. O. White, Saltwater intrusion in aquifers: development and testing of a three-dimensional finite element model, Water Resour. Res., 23(2), pp. 293-312, 1987.
[20] Kemblowski, M., Saltwater-freshwater transient upconing — an implicit boundary element solution, J. Hydro., 78, pp. 35-47, 1985.
[21] Lee, C. H., and R. T. Cheng, On seawater encroachment in coastal aquifers, Water Resour. Res., 10(5), pp. 1039-1043, 1974.
[22] McLaughlin, D., and E. F. Wood, A distributed parameter approach for evaluating the accuracy of groundwater model predictions, 1, Mathematical development, Water Resour, Res., 24(7), pp. 1037-1047, 1988. Mizell, S. A., A. L. Gutjahr, and L. W. Gelhar, Stochastic analysis of spatial variability in two-dimensional steady groundwater flow assuming stationary and nonstationary head, Water Resour. Res., 18(4), pp. 1053-1067, 1982.
[23] Muskat, M., The Flow of Homogeneous Fluids Through Porous Media, McGraw-Hill, Ann Arbor, 1937.
[24] Muskat, M. and R. D. Wyckoff, An approximate theory of water-coning in oil production, Trans. Am. Inst. Min. Metall. Pet. Eng., 114, pp. 144-163, 1935.
[25] Ogata, A. and R. B. Banks, A solution of the differential equation of longitudinal dispersion in porous media, USGS Professional Paper 411-a:al-A7, 1961.
[26] Pinder, G. F. and H. H. JR. Cooper, A numerical technique for calculating the transient position of the saltwater front, Water Resour. Res., (3), pp. 875-882, 1970.
[27] Reilly, T. E. and A. S. Goodman, Quantitative analysis of saltwater-freshwater relationships in groundwater systems — a historical perspective, J. Hydro. 80, pp. 125-160, 1985.
[28] Reilly, T. E. and A. S. Goodman, Analysis of steady state saltwater upcoing with application at Truro well field, Cpae Cod, Massachusetts, Ground Water, 25(2), pp. 194-206, 1987a
[29] Reilly, T. E. and A. S. Goodman, Analysis of saltwater upconing beneath a pumping well, J. Hydro., 89, pp. 169-204, 1987b.
[30] Rubin, H, and G. F. Pinder, Approximate analysis of upconing, Adv. Water Resour, 1(2), pp. 97-101, 1977.
[31] Rubin, Y., and G. Dagan, Stochastic analysis of boundary effects on head spatial variability in heterogeneous aquifer, 2, Impervious boundary, Water Resour. Res., 25(4), pp. 707-712, 1989.
[32] Rumer, R. R. and D. R. F. Haleman, Intruded salt water wedge in porous media, Proc. ASCE, 89(6), pp. 193-220, 1963.
[33] Sagar, B., Galerkin finite element procedure for analyzing flow through random media, Water Resour. Res., 14(6), pp. 1035-1044, 1978.
[34] Sahni, B. M., Salt water coning beneath fresh water wells, Colorado State University, Fort Collins, Coio., Water Management Tech. Rep. No.18, 168, pp.1972.
[35] Segol, G., G. F. Pinder, and W. G. Gray, A Galerkin finite element technique for calculating the transient position of the saltwater front, Water Resour. Res., 11(2), pp. 343-347, 1975.
[36] Serrano, S. E., and T. E. Unny, Semigroup solution to stochastic unsteady groundwater flow subject to random parameters, Stochasitic hydrol. Hydraul.., 1(4), pp. 281-296, 1987.
[37] Serrano, S. E., Analysis solution of the nonlinear groundwater flow equation in unconfined aquifers and the effect of the hetterrogeneity, Water Resour. Res., 31(11), pp. 2733-2742, 1995.
[38] Serrano, S. E., The Theis solution in heterogeneous aquifers, Gruond Water, 35(31), pp. 463-467, 1997.
[39] Shamir, U. and G. Dagan, Motion of the seawater interface in coastal aquifers: A Numerical Solution, Water Resour. Res. 7(3), pp. 644-657, 1971.
[40] Wirojanagud, J. and R. J. Charbenean, Saltwater upconing in unconfined aquifers, ASCE, 111(3), pp. 417-434, 1985.