An integral transform approach for a mixed boundary problem involving a flowing partially penetrating well with infinitesimal well skin

Water Resources Research

Volumn 38, Issue 6, 2002, Pages 7-1-7-7

  Chang, Chien Chieh ^a   Chen, Chia Shyun ^a  

^a NATIONAL CENTRAL UNIVERSITY   (Taiwan)

Author keywords

Constant drawdown; Laplace and Fourier transforms; Mixed boundary; Partial penetration

Indexed keywords

BOUNDARY LAYER FLOW; FOURIER TRANSFORMS; NUMERICAL ANALYSIS; WELLS;

WELL BORE FLUXES;

WATER RESOURCES;

AQUIFER; GROUNDWATER FLOW; SKIN EFFECT; WELL WATER;

EID: 0036592387     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2001wr001091     Document Type: Article

References (37)

1. Abdul, A. S., A new pumping strategy for petroleum product recovery from contaminated hydrogeologic systems: Laboratory and field evaluations, Ground Water Monit. Rem., 12, 105-114, 1992.
2. Cassiani, G., and Z. J. Kabala, Hydraulics of a partially penetrating well: Solution to a mixed-type boundary value problem via dual integral equations, J. Hydrol., 211, 100-111, 1998.
3. Cassiani, G., Z. J. Kabala, and M. A. Medina, Jr., Flowing partially penetrating well: Solution to a mixed-type boundary value problem, Adv. Water Resour., 23, 59-68, 1999.
4. Clegg, M. W., Some approximate solutions of radial flow problems associated with production at constant well pressure, Soc. Pet. Eng. J., 240, 31-42, 1967.
5. Cooper, H. H., and C. E. Jacob, A generalized graphical method for evaluating formation constants and summarizing well field history, Eos. Trans. AGU, 27, 526-534, 1946.
6. Dagan, G., A note on packer, slug, and recovery tests in unconfined aquifers, Water Resour. Res., 14, 929-934, 1978.
7. Dougherty, D. E., and D. K. Babu, Flow to a partially penetrating well in a double-porosity reservoir, Water Resour. Res., 20, 1116-1122, 1984.
8. Ehlig-Economides, C. A., and H. J. Ramey Jr., Transient rate decline analysis for wells produced at constant pressure, Soc. Pet. Eng. J., 21(1), 98-104, 1981.
9. Fabrikant, V. I., Mixed Boundary Value Problems of Potential Theory and Their Application in Engineering, 451 pp., Kluwer Acad., Norwell, Mass., 1991.
10. Gradshteyn, I. S., and I. M. Ryzhik, Table of Integrals, Series, and Products, 1160 pp., Academic, San Diego, Calif., 1980.
11. Gringarten, A. C., and H. J. Ramey, Jr., An approximate infinite conductivity solution for a partially penetrating line-source well, Soc. Pet. Eng. J., 259, 140-148, 1975.
12. Hantush, M. S., Aquifer tests on partially penetrating wells, J. Hydraul. Div. Am. Soc. Civ. Eng., 87(HY5), 95-171, 1961.
13. Hantush, M. S., Hydraulics of wells, in Advances in Hydroscience, vol. 1, edited by V. T. Chow, pp. 309-343, Academic, San Diego, Calif., 1964.
14. Hiller, C. K., and B. S. Levy, Estimation of aquifer diffusivity from analysis of constant head pumping test data, Ground Water, 32(1), 47-52, 1994.
15. Huang, S. C., Unsteady-state heat conduction in semi-infinite regions with mixed-type boundary conditions, J. Heat Transfer, 107, 391-489, 1985.
16. Huang, S. C., and Y. P. Chang, Anisotropic heat conduction with mixed boundary conditions, J. Heat Transfer, 106, 646-648, 1984.
17. Hurst, W., J. D. Clark, and E. B. Brauer, The skin effect in producing wells, J. Pet. Tech., 246, 1483-1489, 1969.
18. Jacob, C. E., and S. W. Lohman, Nonsteady flow to a well of constant drawdown in extensive aquifers, Eos. Trans. AGU, 33, 559-569, 1952.
19. Javandel, I., Analytical solutions in subsurface fluid flow, Spec. Pap. Geol. Soc. Am., 189, 223-235, 1982.
20. Jones, L., A comparison of pumping and slug tests for estimating the hydraulic conductivity of unweathered Wisconsin age till in Iowa, Ground Water, 31, 896-904, 1993.
21. Jones, L., T. Lemar, and C.-T. Tsai, Results of two pumping tests in Wisconsin age weathered till in Iowa, Ground Water, 30, 529-538, 1992.
22. Marshall, S. L., Convergence acceleration of Fourier series by analytical and numerical application of Poisson's formula, J. Phys. A Math. Gen., 31, 2691-2704, 1998.
23. Mishra, S., and D. Guyonnet, Analysis of observation-well response during constant-head testing, Ground Water, 30, 523-528, 1992.
24. Moench, A. F., Transient flow to a large-diameter well in an aquifer with storative semiconfining layers, Water Resour. Res., 21, 1121-1131, 1985.
25. Murdoch, L. C., and J. Franco, The analysis of constant drawdown wells using instantaneous source functions, Water Resour. Res., 30, 117-124, 1994.
26. Noble, B., Methods Based on the Wiener-Hopf Technique, Pergamon, New York, 1958.
27. Olarewaju, J. S., and W. J. Lee, A comprehensive application of a composite reservoir model to pressure-transient analysis, SPE Reservoir Eng., 4(3), 325-331, 1989.
28. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 933 pp., Cambridge Univ. Press, New York, 1992.
29. Ruud, N. C., and Z. J. Kabala, Response of a partially penetrating well in a heterogeneous aquifer: Integrated well-face flux versus uniform well-face flux boundary conditions, J. Hydrol., 194, 76-94, 1997.
30. Schapery, R. A., Approximate methods of transform inversion for viscoelastic stress analysis, Proc. Fourth U. S. Natl. Congress Appl. Mech., 4, 1075-1085, 1961.
31. Selim, M. S., and D. Kirkham, Screen theory for wells and soil drainpipes, Water Resour. Res., 10, 1019-1030, 1974.
32. Sneddon, I. N., Mixed Boundary Value Problems in Potential Theory, North-Holland, New York, 1966.
33. Stehfest, H., Numerical inversion of Laplace transforms, Commun. ACM, 13, 39-47, 1970.
34. Streltsova, T. D., Well Testing in Heterogeneous Formations, An Exxon Monograph, 423 pp., John Wiley, New York, 1988.
35. Talbot, A., The accurate numerical inversion of Laplace transforms, J. Inst. Math. Appl., 23, 97-120, 1979.
36. van Everdingen, A. F., and W. Hurst, The application of the Laplace transformation to flow problems in reservoirs, Trans. Am. Inst. Min. Metall. Pet. Eng., 186, 305-324, 1949.
37. Wilkinson, D., and P. S. Hammond, A perturbation method for mixed boundary-value problems in pressure transient testing, Transp. Porous Media, 5(6), 609-636, 1990.