TECHNICAL PAPERS
Feb 1, 2002

Solution for Flow Rates across the Wellbore in a Two-Zone Confined Aquifer

Publication: Journal of Hydraulic Engineering
Volume 128, Issue 2

Abstract

A closed-form solution for transient flow rates across the wellbore in a confined aquifer is derived from a two-zone radial ground-water flow equation subject to the boundary condition of keeping a constant head at the well radius. An aquifer may be considered as a two-zone system if the formation properties near the wellbore are significantly changed due to the well construction and/or well development. An efficient numerical approach is used to evaluate this newly derived solution. Values of the transient flow rate are provided in a tabular form and compared with those obtained by numerical inversion for the Laplace-domain solution. The results show that the two solutions are in good agreement. This newly derived solution can be used not only for predicting the transient flow rate across the wellbore but also for identifying the effects of a skin with a finite thickness on the estimation of transient flow rates in a ground-water system with two different formation properties.

Get full access to this article

View all available purchase options and get full access to this article.

References

Abramowitz, M., and Stegun, I. A. (1964). Handbook of mathematical functions with formulas, graphs and mathematical tables, National Bureau of Standards, Dover, Washington, D.C.
Batu, V. (1998). Aquifer hydraulics: A comprehensive guide to hydrogeologic data analysis, Wiley, New York.
Burden, R. L., and, Faires, J. D. (1989). Numerical analysis, 4th Ed., PWS-KENT, Boston.
Burnett, D. S. (1987). Finite element analysis, Addison-Wesley, Redwood City, Calif.
Carslaw, H. S., and Jaeger, J. C.(1939). “Some two-dimensional problems in conduction of heat with circular symmetry.” Some Problems in Conduction of Heat, 46, 361–388.
Carslaw, H. S., and Jaeger, J. C. (1959). Conduction of heat in solids, 2nd Ed., Clarendon, Oxford.
Chang, C. C., and Chen, C. S. (1999). “Analysis of constant-head for a two-zone radially symmetric nonuniform model.” Proc. 3rd Groundwater Resources and Water Quality Protection Conf., National Central Univ., Chung-Li, Taiwan.
Crump, K. S.(1976). “Numerical inversion of Laplace transforms using a Fourier series approximation.” J. Assoc. Comput. Mach., 23(1), 89–96.
de Hoog, F. R., Knight, J. H., and Stokes, A. N.(1982). “An improved method for numerical inversion of Laplace transforms.” Soc. Industrial Appl. Mathe. J. Sci. Stat. Comput., 3(3), 357–366.
Gerald, C. F., and Wheatley, P. O. (1989). Applied numerical analysis, 4th Ed., Addison-Wesley, Reading, Mass.
Hantush, M. S.(1962), “Flow of ground water in sands of nonuniform thickness; Park 1. Flow in a wedge-shaped aquifer.” J. Geophys. Res., 67(2), 703–709.
Harvard Problem Report (1950). “A function describing the conduction of heat in a solid medium bounded internally by a cylindrical surface,” Computation Laboratory of Harvard Univ. Rep. No. 76.
Hildebrand, F. B. (1976). Advanced calculus for applications, 2nd Ed., Prentice-Hall, Englewood Cliffs, N.J.
Ingersoll, L. R., Adler, F. T. W., Plass, H. J., and Ingersoll, A. G.(1950). “Theory of earth heat exchangers for the heat pump.” Heat./Piping/Air Cond., 113–122.
Ingersoll, L. R., Zobel, O. J., and Ingersoll, A. C. (1954). Heat conduction with engineering, geological, and other applications, 2nd Ed., University Wisconsin Press, Madison, Wis.
International Mathematics and Statistics Library, Inc. (1987). IMSL User’s Manual, 2, IMSL, Inc., Houston.
Jacob, C. E., and Lohman, S. W.(1952). “Nonsteady flow to a well of constant drawdown in an extensive aquifer.” Trans., Am. Geophys. Union, 33(4), 559–569.
Jaeger, J. C., and Clarke, M.(1942). “A short table of I(o,i;x).” Proc. R. Soc. Edinburgh, Sect. A: Math. Phys. Sci., 61, 229–230.
Markle, J. M., Rowe, R. K., and Novakowski, K. S.(1995). “A model for the constant-heat pumping test conducted in vertically fractured media.” Int. J. Numer. Analyt. Meth. Geomech., 19, 457–473.
Reddy, J. N. (1984). An introduction to the finite element method, McGraw-Hill, New York.
Reed, J. E. (1980). Type curves for selected problems of flow to wells in confined aquifers; Book 3 applications of hydraulics, United States Department of the Interior, US GPO, Washington, D.C.
Shanks, D.(1955). “Non-linear transformations of divergent and slowly convergent sequences.” J. Math. Phys., 34, 1–42.
Smith, L. P.(1937). “Heat flow in an infinite solid bounded internally by a cylinder.” J. Appl. Phys., 8(6), 45–49.
Spiegel, M. R. (1965). Laplace transforms, Schaum, New York.
Stehfest, H.(1970). “Numerical inversion of Laplace transforms.” Commun. ACM, 13(1), 47–49.
Watson, G. N. (1958). A treatise on the theory of Bessel functions, 2nd Ed., Cambridge University Press, Cambridge, U.K.
Wynn, P.(1956). “On a device for computing the em(Sn) transformation.” Math. Tables Aids Comput., 10, 91–96.

Information & Authors

Information

Published In

Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 128Issue 2February 2002
Pages: 175 - 183

History

Received: Aug 18, 2000
Accepted: Jul 25, 2001
Published online: Feb 1, 2002
Published in print: Feb 2002

Permissions

Request permissions for this article.

Authors

Affiliations

Shaw-Yang Yang
Graduate Student, Institute of Environmental Engineering, National Chiao-Tung Univ., Hsinchu, Taiwan.
Hund-Der Yeh
Professor, Institute of Environmental Engineering, National Chiao-Tung Univ., Hsinchu, Taiwan.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share