Three-Dimensional Semianalytical Solutions of Groundwater Flow to a Well in Fractured Wedge-Shaped Aquifers
Publication: Journal of Hydrologic Engineering
Volume 15, Issue 12
Abstract
The three-dimensional Laplace domain solutions of groundwater flow to a well in fractured double porosity confined, unconfined, and leaky wedge-shaped aquifers are developed. Three wedge boundary configurations: (1) two constant head zero drawdown; (2) two impermeable; and (3) one constant head zero drawdown and one impermeable wedge boundary are considered. Dimensionless drawdowns are obtained for different wedge boundary configurations to investigate flow system behavior. Lateral boundary dimensionless flux at a representative line is also calculated for two constant head zero drawdown configuration and its sensitivity to the matrix hydraulic parameters are investigated. Results of our study are presented in the form of dimensionless flux-dimensionless time and dimensionless drawdown-dimensionless time, type curves. The results are useful for evaluating the role of matrix hydraulic parameters on lateral boundary depletion rate and investigation of flow system behavior in double porosity wedge-shaped aquifers with different lateral boundary configurations. The presented analytical solutions can also be used in parameter identification, stream depletion rate estimation and numerical models verification.
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Acknowledgments
This paper was prepared while the second writer was on a sabbatical leave in the Department of Earth and Environmental Sciences at the University of Waterloo, Waterloo, ON, Canada. Constructive comments and suggestions provided by editor, subeditor, and two anonymous reviewers are acknowledged.
References
Barenblatt, G. I., Zheltov, I. P., and Kocina, I. N. (1960). “Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks.” J. Appl. Math. Mech., 24, 1286–1303.
Chan, Y. K., Mullineux, N., Reed, J. R., and Wells, G. G. (1978). “Analytic solutions for drawdowns in wedge-shaped artesian aquifers.” J. Hydrol., 36, 233–246.
Charles, D. D., Rieke, H. H., and Purushothaman, R. (2001). “Well-test characterization of wedge-shaped, faulted reservoirs.” SPE Reservoir Eval. Eng., 4(3), 221–230.
Chen, C. C., and Raghavan, R. (1995). “Computing pressure distributions in wedges and pinchouts.” Proc., SPE Annual Technical Conf. and Exhibition, SPE Paper No. 30555, SPE.
Cinco-Ley, H., and Meng, H. Z. (1988). “Pressure transient analysis of wells with finite conductivity vertical fractures in double porosity reservoirs.” Proc., 63rd Annual Technical Conf. and Exhibition, SPE Paper No. 18172, SPE.
Da Prat, G., Cinco-Ley, H., and Ramey, H. J. (1981). “Decline curve analysis using type curves for two-porosity systems.” SPE J., 21(3), 354–362.
Deruyck, B. G., Bourdet, D. P., DaPrat, G., and Ramey, H. J. (1982). “Interpretation of interference tests in reservoirs with double porosity behavior: Theory and field examples.” SPE Paper No. 11025, Society of Petroleum Engineering of AIME, Dallas.
Dougherty, D. E., and Babu, D. K. (1984). “Flow to a partially penetrating well in a double-porosity reservoir.” Water Resour. Res., 20(8), 1116–1122.
Kazemi, H. (1969). “Pressure transient analysis of naturally fractured reservoirs.” Trans. AIME, 256, 451–461.
Moench, A. F. (1984). “Double-porosity models for a fissured groundwater reservoir with fracture skin.” Water Resour. Res., 20(7), 831–846.
Moench, A. F. (1997). “Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer.” Water Resour. Res., 33(6), 1397–1407.
Ohaeri, C. U., and Vo, D. T. (1991). “Practical solutions for interactive horizontal well test analysis.” SPE Paper No. 22729, Society of Petroleum Engineering of AIME, Dallas.
Ozkan, E., and Raghavan, R. (1991). “New solutions for well-test-analysis problems. I: Analytical considerations.” Proc., SPE Formation Eval., SPE, 359–368.
Park, E., and Zhan, H. (2003). “Hydraulics of horizontal wells in fractured shallow aquifer systems.” J. Hydrol., 281, 147–158.
Rahman, N. M. A. (2001). “New analytical solutions for predicting pressure distribution and transient behavior in wedges and truncated wedges.” Proc., SPE Annual Technical Conf. and Exhibition, SPE Paper No. 71585, SPE.
Sedghi, M. M., Samani, N., and Sleep, B. (2009). “Three-dimensional semi-analytical solution to groundwater flow in confined and unconfined wedge-shaped aquifers.” Adv. Water Resour., 32(6), 925–935.
Stehfest, H. (1970). “Numerical inversion of Laplace transforms.” Commun. ACM, 13(1), 47–49.
Streltsova-Adams, T. D. (1978). “Well testing in heterogeneous aquifer formations.” Advances in hydroscience, Chow, V. T., ed., Academic, New York, 357–423.
Sun, D., and Zhan, H. (2006). “Flow to a horizontal well in an aquitard-aquifer system.” J. Hydrol., 321, 364–376.
Warren, J. E., and Root, P. J. (1963). “Behavior of naturally fractured reservoirs.” Trans. Am. Inst. Min., Metall. Pet. Eng., 228, 245–255.
Yaxley, L. M. (1987). “New stabilized equations for rectangular and wedge-shaped drainage systems.” SPE Paper No. 17082, Society of Petroleum Engineering of AIME, Dallas.
Yeh, H. D., and Chang, Y. C. (2006). “New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions.” Adv. Water Resour., 29, 471–480.
Yeh, H. D., Chang, Y. C., and Zlotnik, V. (2008). “Stream depletion rate and volume from groundwater pumping in wedge-shape aquifers.” J. Hydrol., 349, 501–511.
Zhan, H., and Park, E. (2003). “Horizontal well hydraulics in leaky aquifers.” J. Hydrol., 281, 129–146.
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© 2010 ASCE.
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Received: Jan 6, 2010
Accepted: Apr 28, 2010
Published online: May 11, 2010
Published in print: Dec 2010
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