Literature Review

For aquifers with low-transmissivity, CHT is more suitable to apply than CFT. The wellbore storage at the pumping well has large effect on the early time drawdown behavior at pumping and observation wells in CFT (Renard, 2005). If a CHT is established in a short period of time, the effect of wellbore storage is negligible under the situations that the aquifer has low transmissivity and the well radius is small (Chen and Chang, 2003).

In the past, many studies had been devoted to the solutions for CHT. Kirkham (1959) derived a steady-state solution for groundwater distribution in a bounded confined aquifer pumped by a partially penetrating well under CHT. They simplified the complexity of the geometry by dividing the model into two different regions. Javandel and Zaghi (1975) considered the groundwater in a confined aquifer pumped by a fully penetrating well that is radially extended at the bottom of the aquifer. The procedure used in their study is similar to that in Kirkham (1959) and the steady-state groundwater solution was obtained using separation of variables. Jones et al. (1992) and Jones (1993) discussed the practicality of CHTs on wells completed in low-conductivity glacial till deposits. Mishra and Guyonnet (1992) indicated the operational benefit of CHTs in situations where the total available

drawdown is limited by well construction and aquifer characteristics. They developed a method for analyzing observation well response under a CHT. There have been numerous studies in the literature using CHT [e.g., Wilkinson, 1968; Uraiet and Raghaven, 1980; Hiller and Levy, 1994; Chen and Chang, 2003; Singh, 2007].

Considering a CHT performed in a partially penetrating well, Yang and Yeh (2005) developed a time-domain solution to describe the drawdown in a confined aquifer with finite thickness skin. The boundary conditions along the partially penetrating well are represented by a constant-head (first kind) boundary for the screen while a no-flow (second kind) boundary for the casing. They transformed the first kind boundary along the screen into a second kind boundary with an unknown flux which is time-dependent and therefore the boundary along the partially penetrating well became uniform. The solution was then solved by the Laplace and finite Fourier cosine transforms. Chang and Yeh (2009) used the methods of dual series equations and perturbation method to solve the mixed boundary problem for the CHT at a partially penetrating well. Chang and Yeh (2010) developed a new model describing a CHT performed in flowing partially penetrating well for arbitrary location of the well screen in a finite thick aquifer in depth. However, the studies mentioned above are only applicable for confined aquifers.

For unconfined aquifers, Chen and Chang (2003) developed a well hydraulic theory for CHT performed in a fully penetrating well and established a parameter estimation method.

Chang et al. (2010) extended the work of Yang and Yeh (2005) to develop a mathematical model for an unconfined aquifer system while treating the skin as a finite thickness zone and derived the associated solution for CHT at a partially penetrating well. For other environmental applications, light nonaqueous phase liquids (LNAPLs) are usually recovered by wells held at constant drawdown (Abdul, 1992; Murdoch and Franco, 1994) and a constant-head pumping is employed to control off-site migration of contaminated groundwater (Hiller and Levy, 1994). At LNAPL contaminant sites the pollutant forms a pool of LNAPL in the subsurface on the top of water table. It is therefore to install a well with the screen goes from the top of the aquifer in unconfined aquifers.

For the research of CFT in unconfined aquifers, Neuman (1972) presented a new analytical solution for characterizing flow to a fully penetrating well in an unconfined aquifer.

He assumed the drainage above the water table occurs instantaneously. Take into account the effect of finite diameter pumping well, Moench (1997) developed a solution in Laplace-domain for the flow to a partially penetrating well in unconfined aquifers. Contrary to Neuman’s assumption, he used the free-surface boundary in Boulton (1954) under the assumption that the drainage of pores occurs as an exponential function of time in response to a step change in hydraulic head in the aquifer. Tartakovsky and Neuman (2007) presented an analytical solution for drawdown in an unconfined aquifer due to pumping at a constant rate from a partially penetrating well. They generalized the solution of Neuman (1972, 1974)

by accounting for unsaturated flow above the water table and derived the solution from a linearized Richards’ equation in which unsaturated hydraulic conductivity and water content are expressed as exponential functions of incremental capillary pressure head relative to its air entry value. Malama et al. (2007) utilized Laplace and Hankel transforms to obtain a semi-analytical solution for the problem of flow with leakage in an unconfined aquifer bounded below by an aquitard of finite or semi-infinite vertical extent. Malama et al. (2008) further extended their previous work to a system consisting of unconfined and confined aquifers, separated by an aquitard. The unconfined aquifer is pumped at a constant rate from a partially penetrating well. Pasadi et al. (2008) considered the effect of wellbore storage and finite-thickness skin and presented a Laplace-domain solution for CFT conducted in an unconfined aquifer with a partially penetrating well.

More recently, Malama et al. (2009a) developed a semi-analytic solution for a three-layered system, consisting of an aquifer and two confining units, due to constant rate pumping of the aquifer at a fully penetrating well. Their solution was successfully tested on the streaming potential data presented by Rizzo et al. (2004). Malama et al. (2009b) also developed a semi-analytic solution for a fully penetrating well in an unconfined aquifer under constant-rate pumping. Their solution was applied to estimate aquifer parameters using data recorded at the Boise Hydrogeophysical Research Site.