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Flowing partially penetrating well: Solution to a mixed-type boundary value problem

Publication ,  Journal Article
Cassiani, G; Kabala, ZJ; Medina, MA
Published in: Advances in Water Resources
September 15, 1999

A new semi-analytic solution to the mixed-type boundary value problem for a flowing partially penetrating well with infinitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-infinite vertical extent or to packer tests with aquifer horizontal boundaries far enough from the tested area. The problem reduces to a system of dual integral equations (DE) and further to a deconvolution problem. Unlike the analogous Dagan's steady-state solution [Water Resour. Res. 1978; 14:929-34], our DE solution does not suffer from numerical oscillations. The new solution is validated by matching the corresponding finite-difference solution and is computationally much more efficient. An automated (Newton-Raphson) parameter identification algorithm is proposed for field test inversion, utilizing the DE solution for the forward model. The procedure is computationally efficient and converges to correct parameter values. A solution for the partially penetrating flowing well with no skin and a drawdown-drawdown discontinuous boundary condition, analogous to that by Novakowski [Can. Geotech. J. 1993; 30:600-6], is compared to the DE solution. The D-D solution leads to physically inconsistent infinite total flow rate to the well, when no skin effect is considered. The DE solution, on the other hand, produces accurate results.

Duke Scholars

Published In

Advances in Water Resources

DOI

ISSN

0309-1708

Publication Date

September 15, 1999

Volume

23

Issue

1

Start / End Page

59 / 68

Related Subject Headings

  • Environmental Engineering
  • 4901 Applied mathematics
  • 4005 Civil engineering
  • 3707 Hydrology
  • 0907 Environmental Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics
 

Citation

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Cassiani, G., Kabala, Z. J., & Medina, M. A. (1999). Flowing partially penetrating well: Solution to a mixed-type boundary value problem. Advances in Water Resources, 23(1), 59–68. https://doi.org/10.1016/S0309-1708(99)00002-0
Cassiani, G., Z. J. Kabala, and M. A. Medina. “Flowing partially penetrating well: Solution to a mixed-type boundary value problem.” Advances in Water Resources 23, no. 1 (September 15, 1999): 59–68. https://doi.org/10.1016/S0309-1708(99)00002-0.
Cassiani G, Kabala ZJ, Medina MA. Flowing partially penetrating well: Solution to a mixed-type boundary value problem. Advances in Water Resources. 1999 Sep 15;23(1):59–68.
Cassiani, G., et al. “Flowing partially penetrating well: Solution to a mixed-type boundary value problem.” Advances in Water Resources, vol. 23, no. 1, Sept. 1999, pp. 59–68. Scopus, doi:10.1016/S0309-1708(99)00002-0.
Cassiani G, Kabala ZJ, Medina MA. Flowing partially penetrating well: Solution to a mixed-type boundary value problem. Advances in Water Resources. 1999 Sep 15;23(1):59–68.
Journal cover image

Published In

Advances in Water Resources

DOI

ISSN

0309-1708

Publication Date

September 15, 1999

Volume

23

Issue

1

Start / End Page

59 / 68

Related Subject Headings

  • Environmental Engineering
  • 4901 Applied mathematics
  • 4005 Civil engineering
  • 3707 Hydrology
  • 0907 Environmental Engineering
  • 0905 Civil Engineering
  • 0102 Applied Mathematics