Laplace-Domain Solutions for Radial Two-Zone Flow Equations under the Conditions of Constant-Head and Partially Penetrating Well

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.

Transient solution for radial two‐zone flow in unconfined aquifers under constant‐head tests

“…This study extends the work of Yang and Yeh (2005) to develop a mathematical model for an unconfined aquifer system with treating the skin as a finite thickness zone and the associated solution for the CHT at a partially penetrating well. A numerical approach including roots finding and Shanks' transform is used to evaluate the newly derived solution.…”

“…Yang and Yeh (2002) and Yeh et al (2003) provided closed-form solutions for transient flow rate across the wellbore in a confined aquifer with a finite-thickness skin and a fully penetrating well in CHT and in CRT, respectively. Yang and Yeh (2005) presented a Laplace-domain solution for the hydraulic head in a radially confined aquifer considering a finite-thickness skin and a partially penetrating well in CHT. Perina and Lee (2006) presented a general well function for groundwater flow with a partially penetrating well in a confined, leaky or unconfined aquifer.…”

“…Rudd and Kabala, 1997;Cassiani and Kabala, 1998;Cassiani et al, 1999;Chang and Chen, 2003;Yang and Yeh, 2005). Cassiani and Kabala (1998) and Cassiani et al (1999) have developed the Laplace-domain solutions for CRT and CHT in confined aquifers, respectively, where the tests are conducted at partially penetrating wells and based on the infinite aquifer thickness assumption.…”

A General Semi-Analytical Solution for Three Types of Well Tests in Confined Aquifers with a Partially Penetrating Well

“…For the constant-head test, the early works involved in the development of solutions for confined radial aquifer systems with well partial penetration were Kirkham (1959), Novakowski (1993), Cassiani et al (1999), Chang and Chen (2002), Yang and Yeh (2005) among many others. Kirkham (1959) divided the flow model into two different regions and derived a steady-state solution for groundwater distribution in a confined aquifer when performing the constanthead test at a partially penetrating well.…”

“…Chang and Chen (2002) used the same mathematical model as Cassiani et al (1999) except that the aquifer is of finite thickness in the vertical direction and the flux entering through the well screen is a function of time and location along the screen. Yang and Yeh (2005) provided an analytical solution for a constant-head test performed at a partially penetrating well under the effect of the finite-thickness skin. An efficient numerical method for computing the solutions was also presented.…”