Iterative method on well bore boundary in numerical modeling of variably saturated flow

Abstract

An iterative method was developed for incorporating the well bore boundary into the finite difference model of water flow in variably saturated porous media. Six cases were presented involving groundwater pumping or injection to demonstrate the advantages of the iterative method over the traditional method. For the iterative method, the total flux gradually approached the well discharge and the flux profile was non-uniform. And the iterative method took into account the variation of well bore water table. Compared to the traditional method, the iterative method can simulate the variably saturated flow caused by pumping or injection more realistically.

Keywords

iterative method / variably saturated flow / well bore boundary / flux profile

References

[1] Zhang Q., Wang Y., Xu Yongfu. Seepage analysis of landfill foundations in Shanghai Laogang landfill phase IV [J]. Journal of Hydrodynamics, Ser. B, 2006, 18(5): 613 619

[2] Zhang Q., Lan S., Wang Y., et al. A new numerical method for groundwater flow and solute transport using velocity field [J]. Journal of Hydrodynamics, Ser. B, 2008, 20(3): 356-364.

[3] Dogan A., Motz L. H. Saturated-unsaturated 3D groundwater model (I): Development [J]. Journal of Hydrologic Engineering, 2005, 10(6): 492-504.

[4] Mcdonald M. G., Harbaugh A. W. A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model [M]. 1988, Washington, USA: United States Government Printing Office.

[5] Lieuallen-Dulam K. K., Sawyer C. S. Implementing intrawell, intercell flow into finite-difference ground-water flow model[J]. Journal of Hydrologic Engineering, 1997, 2(3): 109-112.

[6] Jenny P., Lunati I. Modeling complex wells with the multiscale finite-volume method [J]. Journal of Computational Physics, 2009, 228(3): 687 702

[7] Chang Y. C., Yeh H. D. New solutions to the constant-head test performed at a partially penetrating well [J]. Journal of Hydrology, 2009, 369(1/2): 90-97.

[8] Wang X., Zhan Hongbin. A new solution of transient confined-unconfined flow driven by a pumping well [J]. Advances in Water Resources, 2009, 32(8): 1213-1222.

[9] Matthew D. C. A Refined Implementation of Wellbore Boundary Conditions in Three-Dimensional Heterogeneous Formations [D]. 2007, Ontario, Canada: Queen’s University.

[10] Yin H., Xu Z., Li Huaizheng. Numerical modeling of wastewater transport and degradation in soil aquifer[J]. Journal of Hydrodynamics, Ser. B, 2006, 18(5): 597-605.

[11] Mualem Y. Hydraulic conductivity of unsaturated porous media: Generalized macroscopic approach[J]. Water Resources Research, 1978, 14(2): 325-334.

[12] Celia M. A., Bouloutas E. T., Zarba R. L. A general massconservative numerical solution for the unsaturated flow equation[J]. Water Resources Research, 1990, 26(7): 1483-1496.

[13] Nwankwor G. I., Gillham R. W., van der Kamp G., et al. Unsaturated and saturated flow in response to pumping of an unconfined aquifer: Field evidence of delayed drainage [J]. Ground Water, 1992, 30(5): 690-700.

[14] Akindunni F. F., Gillham R. W. Unsaturated and saturated flow in response to pumping of an unconfined aquifer: Numerical investigation of delayed drainage [J]. Ground Water, 1992, 30(6): 873-884.