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。

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.

［1］Hvorslev, M. J., Time lag and soil permeability in ground-water observations., U. S. Army Corps of Engineers, Waterways Experiment Station Bulletin No.36, Mississippi, USA, 1951.
［2］Bouwer, H., and R. C. Rice, “A slug test for determining hydraulic conductivity of unconfined aquifers with completely or partially penetrating wells”, Water Resour. Res., 12(3), 423-428, 1976.
［3］Dagan, G., “A note on packer, slug, and recovery tests in unconfined aquifers”, Water Resour. Res., 14(5), 929-934, 1978.
［4］Widdowson, M. A., F. J. Molz, and J. G. Melville, “An analysis technique for multilevel and partially penetrating slug test data”, Ground Water, 28(6), 937-945, 1990.
［5］Melville, J. G., F. J. Molz, O. Guven, and M. A. Widdowson, “Multi- level slug tests with comparisons to tracer data”, Ground Water, 29(8), 897-907, 1991.
［6］Hinsby, K., P. L. Bjerg, L. J. Andersen, B. Skov, and E. V. Clausen, “A mini slug test method for determination of a local hydraulic conductivity of an unconfined sandy aquifer”, J. Hydrol., 136, 87-106, 1992.
［7］Butler, J. J. Jr., G. C. Bohling, Z. Hyder, and C. D. McElwee, “The use of slug test to describe vertical variations in hydraulic conductivity”, J. Hydrol., 156, 137-162, 1994.
［8］Ross, H. C. and C. D. McElwee, “Multi-level slug tests to measure 3-D hydraulic conductivity distributions”, Nat. Resour. Res., 16(1), 67-79, 2007.
［9］van der Kamp, G., “Determining aquifer transmissivity by memans of well response tests: The underdamped case”, Water Resour. Res., 12(1), 71-77, 1976.
［10］Kipp, K. L. Jr., “Tyoe curve analysis of inertial effects in the response of
a well to a slug test”, Water Resour. Res., 21(9), 1397-1408, 1985.
［11］Springer, R. K., and L. W. Gelhar, Characterization of large-scale aquifer heterogeneity in glacial outwash by analysis of slug tests with oscillatory response., Cape Cod, Massachusetts. U.S. Geological Survey Water-Resources Investigations Report 91-4034, 36-40, 1991.
［12］Zlotnik, V. A., and V. L. McGuire, “Multi-level slug tests in highly permeable formations: 1. Modification of the Springer-Gelhar (SG) model”, J. Hydrol., 204, 271-282, 1998.
［13］Zlotnik, V. A., and V. L. McGuire, “Multi-level slug tests in highly permeable formations: 2. Hydraulic conductivity identification, method verification, and field applications”, J. Hydrol., 204, 283-296, 1998.
［14］Zurbuchen, B. R., V. A. Zlotnik, and J. J. Butler Jr., “Dynamic interpretation of slug test in highly permeable aquifers”, Water Resour. Res., 38(3), 1025, doi: 10.1029/2001WR000354, 2002.
［15］Butler, J. J. Jr., E. J. Garnett and J. M. Healey, “Analysis of slug tests in formations of high hydraulic conductivity”, Ground Water, 41(5), 620-630, 2003.
［16］Butler, J. J. Jr. and X. Zhan, 2004. “Hydraulic tests in highly permeable aquifers”, Water Resour. Res., 40, doi: 10.1029/2003 WR002998, 2004.
［17］Chen, C. S., and C. R. Wu, “Analysis of depth-dependent pressure head of slug tests in highly permeable aquifers”, Ground Water, 44(3), 472-477, 2006.
［18］Chen, C. S., “An analytic data analysis method for oscillatory slug tests”, Ground Water, 44(4), 604-608, 2006.
［19］Butler, J. J. Jr., The Design, Performance, and Analysis of Slug Tests., Boca Raton, Florida: Lewis Publishers, 1998.
［20］Chen, C. S., Y. C. Sie and Y. T. Lin, “A Review of the Multilevel Slug Test for Characterizing Aquifer Heterogeneity”, Terr. Atmos. Ocean. Sci., 23(2), 131-143, doi: 10.3319/TAO.2011.10.03.01(Hy), 2012.
［21］van Everdingen, A. F., “The skin effect and its influence on the productive capacity of a well”, Trans. AIME, 198, 171-176, 1953.
［22］Hurst, W., “Establishment of the skin effect and its impediment to fluid flow into a well bore”, Pet. Eng., 25(10), B-6, 1953.
［23］Hawkins Jr, M., “A note on the skin effect”, J. Pet. Tech., 8(12), 65-66, 1956.
［24］Brons, F., and W.C., Miller, “A simple method for correcting spot pressure readings”, J. Pet. Tech., 13(8), 803-805, 1961.
［25］Hurst, W., J. D. Clark, and E. B. Brauer, “The skin effect in producing wells”, J. Pet. Tech., 246, 1483-1489, 1969.
［26］Standing, M. B., “Calculating damage effects in well flow problem”, unpubl. notes, Standford Univ., 20 p., 1979.
［27］Streltsova, T. D., Well Testing in Heterogeneous Formations., John Wiley and Sons, Inc., New York, 1988.
［28］Novakowski, K. S., “A composite analytical model for analysis of pumping tests affected by well bore storage and finite thickness skin”, Water Resour. Res., 251(10), 1937-1946, 1989.
［29］Onyekonwu, M. O., “Program for designing pressure transient tests”, Computers and Geosciences, 15(7), 1067-1088, 1989.
［30］Ruud, N. C., and Z. J. Kabala, “Numerical evaluation of the flowmeter test in a layered aquifer with s skin zone”, J. Hydrol., 203, 101-108, 1997.
［31］Chen, C. S. and C. C. Chang, “Use of cumulative volume of constant-head injection test to estimate aquifer parameters with skin effect: Field experiment and data analysis”, Water Resour. Res., 38(5), 1056, doi: 10. 1029/2001WR000300, 2002.
［32］Chen C. S., and C. C. Chang, “Theoretical evaluation of non-uniform skin effect on aquifer response under constant rate pumping”, J. Hydrol., 317, 190-201, 2006.
［33］Faust , C. F. and J. M. Mercer, “Evaluation of slug tests in wells containing a finite-thickness skin”, Water Resour. Res., 20(4), 504-506, 1984.
［34］Moench, A. F. and P. A. Hsieh, “Comment on “Evaluation of slug tests in wells containing a finite-thickness skin” by C. R. Faust and J. W. Mercer”, Water Resour. Res., 21(9), 1459-1461, 1985.
［35］Yang, Y. J. and T. M. Gates, “Wellbore skin effect in slug-test data analysis for low-permeability geologic materials”, Ground Water, 35(6), 931-937, 1997.
［36］Yeh, H. D. and S. Y. Yang, “A novel analytical solution for a slug test conducted in a well with a finite thickness skin”, Water Resour. Res., 29(10), 1479-1489, 2006.
［37］Hyder, Z., J. J. Butler, Jr., C. D. McElwee, and W. Liu, “Slug test in partially penetrating well”, Water Resour. Res., 30(11), 2945 -2957, 1994.
［38］Malama, B., K. L. Kuhlman, W. Barrash, M. Cardiff, and M. Thoma, “Modelingslug tests in unconfined aquifers taking into account water table kinematics, wellbore skin and inertial effects”, J. Hydrol., 408, 113-126, 2011.
［39］Cooper, H. H., Jr., J. D. Bredehodft and I. S. Papadopulos, “Response of a finite-diameter well to an instantaneous charge of water”, Water Resour. Res., 3(1), 263-269, 1967.
［40］Chen, C. S. and C. G. Lan, “A simple data analysis method for a pumping test with the skin and wellbore storage effects”, Terr. Atmos. Ocean. Sci., 20(3), 557-562, June, 2009.
［41］Ramey, H. J., Jr., and R. G. Agarwal, “Annulus unloading rates as influenced by wellbore storage and skin”, Soc. Pet. Engr. J., 12(5), 453, 1972.
［42］Ramey, H. J., Jr., R. G. Agarwal,and I. Martin, ““Analysis of “slug test”
or DST flow period data”, J. Pet. Tech., 4(3), 37-47, 1975.
［43］Sageev, A., “Slug test analysis”, Water Resour. Res., 22(8), 1323-1333, 1986.
［44］Peres, A. M. M., M. Onur and A.C. Reynolds, “A new analysis procedure for determing aquifer properties from slug test data”, Water Resour. Res., 25(7), 1591-1602, 1989.
［45］Dougherty, D. E., and D. K. Babu, “Flow to a partially penetrating well in a double-porosity reservoir”, Water Resour. Res., 20(8), 1116-1122, 1984.
［46］Cooper, H. H., Jr., J. D. Bredehodft, I. S. Papadopulos and R. R. Bennett, “The response of well-aquifer systems to seismic waves”, J. Geophys. Res., 70, 3915-3926, 1965.
［47］Kreyszig, E., Advanced Engineering Mathematics., 8th Edition, John Wiley and Sons, Inc., New York, Oct. 23,1998.
［48］Churchill, R. V., Operational Mathematics, McGraw-Hill, New York, 1972.
［49］Haberman, R., Elementary Applied Partial Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1987.
［50］de Hoog, F.R., J. H. Knight and A. N. Stokes, “An improved method for numerical inversion of Laplace transforms”, SIAM. J. Sci. and Stat. Comput., 3(3), 357-366, 1982.