A new solution for a partially penetrating constant-rate pumping well with a finite-thickness skin

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 31, Issue 15, 2007, Pages 1659-1674

  Chiu, Pin Yuan ^a   Yeh, Hund Der ^a   Yang, Shaw Yang ^b  

^a NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

^b VANUNG UNIVERSITY   (Taiwan)

Author keywords

Analytical solution; Constant pumping test; Finite fourier cosine transforms; Groundwater; Heterogeneous aquifer; Laplace transforms; Partially penetrating well

Indexed keywords

AQUIFERS; FOURIER TRANSFORMS; HYDRAULICS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS;

FINITE FOURIER COSINE TRANSFORM; HANTUSH EQUATION;

WATER WELLS;

AQUIFERS; FOURIER TRANSFORMS; HYDRAULICS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; WATER WELLS;

AQUIFER; DRAWDOWN; GROUNDWATER; LAPLACE TRANSFORM; NUMERICAL MODEL;

EID: 37249064710     PISSN: 03639061     EISSN: 10969853     Source Type: Journal    
DOI: 10.1002/nag.607     Document Type: Article

References (25)

1. Theis CV. The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using ground-water storage. Transactions - American Geophysical Union 1935; 16:519-524.
2. Papadopulos IS, Cooper Jr HH. Drawdown in a well of large diameter. Water Resources Research 1967; 3(1):241-244.
3. Hantush MS. Hydraulics of wells. In Advances in Hydroscience, Chow VT (ed.). Academic Press: New York, 1964.
4. Streltsova TD, McKinley RM. Effect of flow time duration on buildup pattern for reservoirs with heterogeneous properties. Society of Petroleum Engineers Journal 1984; 24:294-306.
5. Butler Jr JJ, Liu WZ. Pumping tests in nonuniform aquifers: the radially asymmetric case. Water Resources Research 1993; 29(2):259-269.
6. Barker JA, Herbert R. Pumping tests in patchy aquifers. Ground Water 1982; 20(2):150-155.
7. Novakowski KS. A composite analytical model for analysis of pumping tests affected by wellbore storage and finite thickness skin. Water Resources Research 1989; 25(9):1937-1946.
8. Yeh HD, Yang SY, Peng HY. A new closed-form solution for a radial two-layer drawdown equation for groundwater under constant-flux pumping in a finite-radius well. Advances in Water Resources 2003; 26(7):747-757.
9. Bixel HC, van Poollen HK. Pressure drawdown and buildup in the presence of radial discontinuities. Society of Petroleum Engineers Journal 1967; 7:301-309.
10. Jargon JR. Effect of wellbore storage and wellbore damage at the active well on interference test analysis. Journal of Petroleum Technology 1976; 28:851-858.
11. Butler Jr JJ. Pumping tests in nonuniform aquifers - the radially symmetric case. Journal of Hydrology 1988; 101:15-30.
12. Cassiani G, Kabala ZJ. Hydraulics of a partially penetrating well: solution to a mixed-type boundary value problem via dual integral equations. Journal of Hydrology 1998; 211:100-111.
13. Park E, Zhan H. Hydraulic of a finite-diameter horizontal well with wellbore storage and skin effect. Advances in Water Resources 2002; 25:389-400.
14. Zhan H, Bian A. A method of calculating pumping induces leakage. Journal of Hydrology 2006; 328:659-667.
15. Markle JM, Rowe RK, Novakowski KS. A model for the constant-head pumping test conducted in vertically fractured media. International Journal for Numerical and Analytical Methods in Geomechanics 1995; 19:457-473.
16. Moench AF. Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer. Water Resources Research 1997; 33(6):1397-1407.
17. Cassiani G, Kabala ZJ, Medina Jr MA. Flowing partially penetrating well: solution to a mixed-type boundary value problem. Water Resources Research 1999; 23:59-68.
18. de Hoog FR, Knoght JH, Stokes AN. An improved method for numerical inversion of Laplace transforms. Society for Industrial and Applied Mathematics Journal on Scientific Computing 1982; 3(3):357-366.
19. IMSL. Stat/Library. Volumes 1 and 2. Visual Numerics, Inc.: Houston, Texas, 1997.
20. Neuman SP. Effect of partial penetration on flow in unconfined aquifers considering delayed gravity response. Water Resources Research 1974; 10(2):303-312.
21. Carslaw HS, Jaeger JC. Conduction of Heat in Solids (2nd edn). Clarendon Press: Oxford, 1959.
22. Stehfest H. Numerical inversion of Laplace transforms. Communications of the Association for Computing Machinery 1970; 13(1):47-49.
23. Crump KS. Numerical inversion of Laplace transforms using a Fourier series approximation. Journal of the Association for Computing Machinery 1976; 23(1):89-96.
24. Talbot A. The accurate numerical inversion of Laplace transforms. Journal of The Institute of Mathematics and its Applications 1979; 23:97-120.
25. Kreyszig E. Advanced Engineering Mathematics (7th edn). Wiley: New York, 1993.