CONCLUSIONS - 背斜受限含水層中定流量抽水試驗之解析洩降解

A mathematical model has been developed for describing the steady-state flow caused by the constant-flux pumping in an anticline aquifer. The proposed model can account for the flow in response to partially or fully penetrating wells which are of infinitesimal diameter and with uniform inflow flux along the well screen. The anticline aquifer is homogeneous, anisotropic and confined with a shape being mimicked by three consecutive blocks. The integral transform techniques FT and FFCT are applied to derive the steady-state solutions in transform space. The coefficients in the solutions require solving a system of linear equations represented in a matrix form. Finally, the Fourier inversion is applied to obtain the drawdown solution in real space.

The present solution is applicable to simulate the flow in a slab-shaped aquifer or a hillslope aquifer by assuming two or three successive blocks are of the same height.

For a slab-shaped aquifer, the simulated drawdown responses based on the present solution are identical to those evaluated by the image-well method when the well is fully penetrating and the aquifer is homogeneous, isotropic, confined and bounded by two parallel constant-head boundaries. Both the present solution and the numerical model, MODFLOW, are applied to simulate the case of flow in a hillslope aquifer.

The grid settings allow MODFLOW to simulate the slope boundary in a more realistic

manner. Small differences between these simulated results can be observed around the step-like boundary. In addition, the solution is used to investigate the influence of the aquifer geometry and anisotropy as well as the well partial penetration and location on the steady-state flow pattern. The results shown in these cases exhibit significant vertical flow around the concave corner of the top boundary for a fully penetrating well or a partially penetrating well located at the hump zone of the anticline. The constant-flux pumping in a thin-limbs or narrow-ridged anticline would cause a much sharp head drop in the ridge zone. The influence of aquifer anisotropy on the observed drawdown cannot be ignored when the pumping carries out in a partially penetrating well, especially for the well of short open screen.

When the screen length or/and the anisotropy ratio decreases, the dimensionless drawdown around the pumping well increases under the same constant pumping rate.

In addition, we suggest using the real dimensionless screen length in the simulation even if the penetration ratio may be changed in the simplified anticline aquifer.

Finally, the present solution can simulate the flow field for an arbitrarily located pumping well. Naturally the flow field will change with the location of the pumping well. The well located at the top-middle of the aquifer would produce larger drawdown around the well because of the boundary restriction on the anticline shape.

The model MODFLOW, which can provide a better approximation on the curved

boundary, is employed to simulate the flow field of the anticline aquifer. The simulated results are compared with those of the present solution for the flow toward a fully penetrating well in an anticline aquifer. The present solution gives slightly higher dimensionless drawdown than the MODFLOW while the simulation is achieved by approximating the top boundary of aquifer with multiple steps. The drawdown solution derived in this study can be further applied to identify the aquifer parameters if integrated with an optimization algorithm and to do preliminary assessment for a potential waste disposal site.

REFERENCES

Al-Mohannadi, N., Ozkan, E. and Kazemi, H., 2007. Pressure-transient responses of horizontal and curved wells in anticlines and domes. SPE Reservoir Evaluation & Engineering, 10(1): 66-76.

Ashjari, J. and Raeisi, E., 2006. Influences of anticlinal structure on regional flow, Zagros, Iran. Journal of Cave and Karst Studies, 68(3): 118-129.

Chan, Y.K., Mullineux, N. and Reed, J.R., 1976. Analytical solutions for drawdowns in rectangular artesian aquifers. Journal of Hydrology, 31: 151-160.

Chan, Y.K., Mullineux, N., Reed, J.R. and Wells, G.G., 1978. Analytic solutions for drawdowns in wedge-shaped artesian aquifers. Journal of Hydrology, 36:

233-246.

Chen, Y.J., Yeh, H.D., and Yang, S.Y., 2009. Analytical solutions for constant-flux and constant-head tests at a finite-diameter well in a wedge-shaped aquifer, Journal of Hydraulic Engineering ASCE, 135(4): 333-337.

Chiang, W.H. and Kinzelbach, W., 2001. 3D-Groundwater Modeling with PMWIN: A Simulation System for Modeling Groundwater Flow and Transport Process.

Springer-Verlag Berlin Heidelberg, New York, 346 pp.

Connell, L.D., Jayatilaka, C. and Bailey, M., 1998. A quasi-analytical solution for groundwater movement in hillslopes. Journal of Hydrology, 204(1-4):

Ferris, J.G., Knowles, D.B., Brown, R.H. and Stallman, R.W., 1962. Theory of Aquifer Tests WATER-SUPPLY PAPER 1536-E, 1962, 104 P.

Harbaugh, A.W. and McDonald, M.G., 1996a. User's Documentation for MODFLOW-96, An Update to the U.S. Geological Survey Modular Finite-Difference Ground-Water Flow Model. Open-file report 96-485. U.S.

Geological Survey.

Harbaugh, A.W. and McDonald, M.G., 1996b. Programmer's Documentation for MODFLOW-96, An Update to the U.S. Geological Survey Modular Finite-Difference Ground-Water Flow Model. Open-File Report 96-486. U.S.

Geological Survey.

IMSL. 2003. IMSL Fortran Library User’s Guide Math/Library Volume 2 of 2, version 5.0, Houston, Texas: Visual Numerics.

Javandel, I. and Zaghi, N., 1975. Analysis of flow to an extended fully penetrating well. Water Resources Research, 11(1): 159-164.

Jeffrey, A. and Dai, H.H., 2008. Handbook of Mathematical Formulas and Integrals.

4th Ed., Elsevier, 541 pp.

Kirkham, D., 1957. Potential and capacity of concentric coaxial capped cylinders.

Journal of Applied Physics, 28(6): 724-731.

Kirkham, D., 1959. Exact theory of flow into a partially penetrating well. Journal of

Geophysical Research, 64(9): 1317-1327.

Kuo, M.C.T., Wang, W.L., Lin, D.S., Lin, C.C. and Chiang, C.J., 1994. An image-well method for predicting drawdown distribution in aquifers with irregularly shaped boundaries Ground Water, 32(5): 794-804.

McDonald, M.G. and Harbaugh, A.W., 1988. A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model. Book 6, Chapter A1, Open-file report 83-875, U.S. Geological Survey.

Shanks, D., 1955. Non-linear transformations of divergent and slowly convergent sequences. Journal of Mathematics and Physics, 34: 1-42.

Streltsova, T.D., 1988. Well Testing in Heterogeneous Formations. John Wiley &

Sons, New York, 413 pp.

Theis, C.V., 1935. The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Trans.

Amer. Geophys. Union, 16(1): 519–524.

Thiem, G., 1906. Hydrologische Methoden, JM Gephardt, Leipzig.

Yeh, H.D. and Chang, Y.C., 2006. New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions.

Advances in Water Resources, 29(3): 471-480.

Yeh, H.D. and Kuo, C.C., 2010. An analytical solution for heterogeneous and

anisotropic anticline reservoirs under well injection. Advances in Water Resources, 33(4): 419-429.

APPENDIX A DERIVATION OF EQ. (22)

This appendix demonstrates the procedure for obtaining Eq. (22). Taking FT and FFCT to Eq. (10) with boundary conditions (11) to (14) results in

)

determined by conditions (6a), (7), and (15). If one takes the inversion of FFCT to Eq. (A2), the solution in Fourier domain is

)

Eq. (A3) represents the drawdown solution for zone 2 in the Fourier domain. Eq.

(22) is expressed by new coefficients in the Fourier series, which are obtained by inserting Eqs. (7) and (15) into (A3) and applying the inversion formula of the FFCT.

Similar procedure can be taken for deriving Eq. (26), i.e., the drawdown solution for zone 3 in the Fourier domain. Note that ζ defined in Eq. (26) is chosen as the _k transform variable when applying FFCT over the interval [0,

z

_Db₃].

APPENDIX B MATRIX FORMULATION FOR SOLVING COEFFICIENTS The coefficients

V

₀,

V

_n ,

W

₀ and

W

_k in Eqs. (22), (26), (38), and (39) construct a system of

i

+ j+2 linear equations, which can be expressed in matrix form as

with the elements

)

Figure 1. Schematic representation of a groundwater flow problem in an anticline aquifer with a line sink located along the z axis. The anticline aquifer is approximately divided into three blocks.

Figure 2. The dimensionless drawdown distributions predicted by the present solution and the image-well method (Ferris et al., 1962) for pumping at the middle of a slab-shaped aquifer bounded by two parallel constant-head boundaries.

Figure 3. Dimensionless drawdown contours and flow field for the pumping at a fully penetrating well in a hillslope aquifer. The simulations were carried out to a step-like aquifer by (a) the present solution, (b) MODFLOW, (c) MODFLOW with multiple steps to approximate the inclined boundary.

Figure 4. Dimensionless drawdown contours produced by the present solution for the pumping at a fully penetrating well in an isotropic anticline aquifer. The cross-sectional view on (a)

x

_D -

z

_D plane for

y

= 0

, (b)

y

_D -

z

_D plane for

_D plane for

x

= 0 . 2

, and (c)

Figure 7. Plots of dimensionless drawdown contours and flow fields for pumping at a fully penetrating well in an isotropic aquifer of (a) thin limbs and (b) narrow ridge.

Figure 8. Dimensionless drawdown responses versus

x

_D calculated at (

y ,

z

_D) = (0,1) for the base case shown in Figure 4 and the cases investigated in Figure 7.

Figure 9. A comparison of largest dimensionless drawdown at

( x

, y

) = ( 0 . 001 , 0 )

學歷 88.09-92.06 學士，私立東海大學環境科學系

92.09-94.06 碩士，國立交通大學環境工程研究所 94.09-99.08 國立交通大學環境工程研究所博士班通訊電話 03-5712121＃55526

行動電話 0915-219990

地址 408 台中市南屯區黎明東街 368 號 7 樓

電子郵件 [email protected]

PUBLICATION LIST

期刊論文

1. Yeh, H. D., S. Y. Yang, and Y. J. Chen, 2007. Discussion of “Approximate Discharge for Constant Head Test with Recharging Boundary” by Philippe Renard,

Ground Water, 45(6), 659, doi: 10.1111/j.1745-6584.2007.00386. (SCI)

2. Yeh, H. D. and Y. J. Chen. (2007). Determination of skin and aquifer parameters for a slug test with wellbore-skin effect, Journal of Hydrology, 342, 283-294.

(SCI)

3. Chen, Y. J., H. D. Yeh, and S. Y. Yang, 2007. A new semi-analytical solution for slug test in a confined aquifer under the effects of well partial penetration, Journal

of Hydroscience and Hydraulic Engineering, JSCE, 25(2), 59-74.

4. Yeh, H. D., Y. J. Chen, and S. Y. Yang, 2008. Semi-analytical solution for a slug test in partially penetrating wells including the effect of finite-thickness skin,

Hydrological Processes, 22, 3741-3748. (SCI)

5. Chen, Y. J., and H. D. Yeh, 2009. Parameter estimation/sensitivity analysis for an aquifer test with skin effect, Ground Water, 47(2), 287-299. (SCI)

6. Chen, Y. J., H. D. Yeh, and S. Y. Yang, 2009. Analytical solutions for constant-flux and constant-head tests at a finite-diameter well in a wedge-shaped aquifer, Journal of Hydraulic Engineering ASCE, 135(4), 333-337, doi:

10.1061/_ASCE_0733-9429. (SCI)

7. Yeh, H. D., and C. H. Chang, Y. J. Chen, 2009. Aquifer parameter estimation for a constant-flux test performed in a radial two-zone aquifer, Journal of Irrigation

and Drainage Engineering ASCE, 135(5), 693-703, doi:

10.1061/(ASCE)IR.1943-4774.0000064. (SCI)

8. Yeh, H. D., and Y. J. Chen, 2009. Comment on ‘‘Utilization of Weibull techniques for short-term data analysis in environmental engineering,’’ by Isaiah A. Oke, 2008, 25(7), 1099–1106. Environmental Engineering Science, 26(8), 1365-1367. doi:10.1089/ees.2008.0374. (SCI)

研討會論文

1. 陳彥如、楊紹洋、葉弘德，93 年 7 月，微水試驗在受限含水層和部分貫穿井影響下的半解析解，第十四屆水利工程研討會，國立交通大學，新竹市，論文集(下冊)F164-F169 頁。

2. 陳彥如、葉弘德、楊紹洋，93 年 10 月，微水試驗在井膚層及部分貫穿井效應下的半解析解，九十三年度農業工程研討會，中國農業工程學會，桃園，論文摘要集 243 頁，論文集光碟版 1507-1514 頁。

3. 陳彥如、葉弘德，95 年 7 月，微水試驗的井膚層厚度及水層參數推求，第十

4. 陳彥如、葉弘德、楊紹洋，95 年 10 月，考慮井徑的定流量試驗在鄰近地形邊界的解析解，九十五年度農業工程研討會，中國農業工程學會，台南市，論文摘要集 91 頁，論文集光碟版 280-290 頁。

5. 陳彥如、葉弘德、楊紹洋，95 年 11 月，考慮井徑的定水頭試驗在楔型含水層的解析解，2006 土壤與地下水研討會，中國民國環境工程學會，台中市，論文摘要集 507 頁，論文集光碟版 Soi20060060.pdf。 (優秀論文獎)

6. Chen, Y.J., H.D. Yeh, and S.Y. Yang, 2007. New solutions for constant-flux and constant-head tests in a wedge-shaped aquifer. Asia Oceania Geosciences Society (AOGS) 4th Annual Meeting, Bangkok, Thailand, HS05-A0002.

7. 陳彥如、葉弘德，97 年 10 月，定水頭試驗數據對於水文地質參數的敏感度與在參數估計上的影響，九十七年度農業工程研討會，中國農業工程學會，台北市，論文摘要集 95 頁，論文集光碟版 265-274 頁。

8. Chen, Y.J. and H.D. Yeh, 2009. Composite analysis of test-well and observation-well data during constant-head test. 7th Symposium on Groundwater, Hydrology, Quality, and Management, World Environmental and Water Resources Congress 2009, Kansas City, Missouri, 2014-2021.

9. 陳庚轅、陳彥如、葉弘德、Dong-Sheng Jeng，98 年 9 月，利用濱海觀測井水位變化推求海岸坡度與含水層參數，九十八年電子計算機於土木水利工程應用論文研討會，中華大學，新竹市，論文集 869-973 頁。

10. 陳彥如、葉弘德、郭嘉真，98 年 12 月，在背斜含水層進行定流量抽水之洩降分佈，第七屆地下水資源及水質保護研討會，台灣大學，台北市，論文集 A-1-A-7 頁。

11.葉弘德、陳彥如，98 年 12 月，低放射性廢棄物核種全系統安全評估模式之重要參數敏感度分析，第七屆地下水資源及水質保護研討會，台灣大學，台北市，論文集 L-1-L-6 頁。

12.陳彥如、葉弘德，98 年 12 月，低放射性廢棄物處置場全系統安全評估程式及重要參數之分析研究，行政院原能會委託研究計畫暨國科會與原能會科技學術合作研究計畫成果發表會，核能研究所，桃園縣，摘要集 E-3 頁。

在文檔中背斜受限含水層中定流量抽水試驗之解析洩降解 (頁 47-71)