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

Abstract

Abstract:The constant-head test (CHT) is commonly employed to determine the aquifer parameters. This test is also applied to many environmental problems such as recovering light nonaqueous phase liquids (LNAPL) and controlling off-site migration of contaminated groundwater in low-transmissivity aquifers. A well skin near the wellbore may be produced due to the well construction or development and its formation properties are significantly different from the original ones. A more appropriate description for the skin effect on the aquifer system should treat the well skin as a different formation instead of using a skin factor. Thus, the aquifer system becomes a two-zone formation including the skin and formation zones. This study presents a mathematical model developed for analyzing a two-zone unconfined aquifer system and the associated solution for CHTs at partially penetrating wells under transient state. The solution of the model may be used either to identify the in situ aquifer parameters or to investigate the effects of the wellbore storage and well skin on the head changes in unconfined aquifers under constant-head pumping.

Recent advances in modeling of well hydraulics

“…For unconfined aquifers, for example, Chen and Chang [51] considered the skin effect and developed a wellhydraulic theory for CHT in unconfined aquifers. Chang et al [52,53] gave hydraulic head solutions for CHT performed at a partially penetrating well in unconfined aquifers. The review of the recent development in the literature shows that there are a limited number of researches on the CHT in leaky and multilayered aquifers.…”

“…The third is the domain decomposition method which divides the flow domain into two or several sub-regions and each region has its own flow equation and associated initial and boundary conditions [5,52,53]. The flow equations are then solved simultaneously via the continuity conditions for the hydraulic head and flow rate at the interfaces of the sub-regions.…”

On Inflow to a Tunnel in a Fractured Double‐Porosity Aquifer

“…Hwang and Lu (2007) used the image well method along with convolution‐deconvolution to obtain the semianalytical solution of discharge of a tunnel in a finite width confined fault zone. Other analytical solutions of constant head sinks, that may represent tunnels, in confined (Bennett and Patten 1962; Chang and Yeh 2010), leaky confined (Feng and Zhan 2019) or unconfined (Chang et al 2010) aquifers, are focused on the vertical wells. For more information on the constant head test in this type of wells, the reader may refer to Jiang et al (2020).…”

Hydraulics of a partially penetrating well with skin zone in a confined aquifer

“…However, in some circumstances, a zone of higher conductivity (negative skin) in the immediate vicinity of a well as compared to regions farther away from the well may also develop due to extensive spalling and fracturing of the wellbore during drilling and/or due to extensive well development [29,30,39,[41][42][43][44]. The skin hydraulics problem for an aquifer of infinite horizontal dimension was solved analytically by several investigators [5,6,11,13,14,20,29,[31][32][33]39,[41][42][43][44] utilizing different assumptions. Whereas Novakowski [29], Yang and Yeh [39], Yeh et al [43], Cimen [14] and Yeh and Yang [44] provided analytical solutions to the problem by neglecting vertical flow, Novakowski [31] provided a solution by assigning a specified head on the well face but a zero head and not a zero flux in the non-active portion of the well, and Hyder et al [20], Yang and Yeh [41], Chiu et al [13], Yeh et al [42] and Chang et al [11] presented solutions by assuming a uniform radial flux at the well screen.…”

“…The skin hydraulics problem for an aquifer of infinite horizontal dimension was solved analytically by several investigators [5,6,11,13,14,20,29,[31][32][33]39,[41][42][43][44] utilizing different assumptions. Whereas Novakowski [29], Yang and Yeh [39], Yeh et al [43], Cimen [14] and Yeh and Yang [44] provided analytical solutions to the problem by neglecting vertical flow, Novakowski [31] provided a solution by assigning a specified head on the well face but a zero head and not a zero flux in the non-active portion of the well, and Hyder et al [20], Yang and Yeh [41], Chiu et al [13], Yeh et al [42] and Chang et al [11] presented solutions by assuming a uniform radial flux at the well screen. Cassiani et al [6], using the dual integral method of Cassiani and Kabala [5], presented a semi-analytical solution to the transient skin hydraulics problem for a confined aquifer with a mixed-boundary at the well face by assuming the skin to be infinitesimal small and the aquifer to be infinite in both horizontal and vertical directions.…”