Laplace-domain solutions for radial two-zone flow equations under the conditions of constant-head and partially penetrating well

Shaw Yang Yang, Hund-Der Yeh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

A mathematical model is presented for a constant-head test performed in a partially penetrating well with a finite-thickness skin. The model uses a no-flow boundary condition for the casing and a constant-head boundary condition for the screen to represent the partially penetrating well. The Laplace-domain solutions for the dimensionless flow rate at the wellbore and the hydraulic heads in the skin and formation zones are derived using the Laplace and finite Fourier cosine transforms. The solutions of hydraulic heads have been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the pressure head and flow rate at the interface of the skin zone and undisturbed formation. In addition, an efficient algorithm for evaluating those solutions is also presented. The dimensionless flow rates obtained from new solutions have been shown to be better than those of Novakowski's solutions, especially when the penetration ratio is large.

Original languageEnglish
Pages (from-to)209-216
Number of pages8
JournalJournal of Hydraulic Engineering
Volume131
Issue number3
DOIs
StatePublished - 1 Mar 2005

Keywords

  • Ground water
  • Mathematical models
  • Thickness
  • Wells

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