Transient flow of water to a well in an unconfined aquifer: Applicability of some conceptual models

Abstract

Currently available methods for interpreting data from unconfined aquifers are based on analytical solutions which restrict attention to flow in the saturated zone and account for drainage of water from the unsaturated zone through a source term. The parameter, specific yield (Sy), is assumed to dictate the total quantity of water that is derivable through the desaturation process. It is commonly assumed that flow in the unsaturated zone has little effect on flow in the saturated zone and therefore that all the drainable water is instantly delivered at the water table as it declines in response to pumping. In a model proposed in 1954, Boulton empirically assumed that the drainable water associated with Sy is released gradually at the water table as an exponential function of time. This concept of Boulton is similar to the notion of first‐order kinetics frequently used to handle chemical transformations. Boulton's model is considered by some to have no physical basis. Numerical experiments performed on sand columns with reasonable properties suggest that vertical drainage of water at the water table due to a falling water table is a time‐dependent process which is mathematically more complex than a simple exponential relation. Although Boulton did not provide a rational physical explanation, his exponential assumption has some merit in that it implicitly provides for a time dependent drainage process which seems to occur in the unsaturated zone. However, the simple exponential approximation is not adequate to account for what is seemingly a complex process. It appears that a physically comprehensive model of radial flow in an unconfined aquifer will combine time‐dependent drainage from above the water table with vertical components of flow in the saturated zone. An additional assumption frequently made is that the well can be treated as a line source. Results from numerical experiments suggest that caution is in order before neglecting effects of well‐bore storage in interpreting data from tests on unconfined aquifers.

Flow to a well of finite diameter in a homogeneous, anisotropic water table aquifer

“…The difference is due to the fact that Boulton worked with vertically averaged heads and included the term containing a in the governing partial differential equation.) The assumption provides only a crude approximation of the actual drainage process [Narasimhan and Zhu, 1993], but it is a significant improvement over the assumption of instantaneous drainage (where a• is infinite) used by Neuman [1972Neuman [ , 1974.…”

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

“…Contrary to Neuman's assumption, some literatures indicated that the drainage above the water table in unconfined aquifer is transient and both the radial and vertical flow components occur in saturated thickness (e.g. Akindunni and Gillham, 1992;Nwankwor et al, 1992;Narasimhan and Zhu, 1993;Moench, 1994Moench, , 2004Moench, , 2008. The solutions for flow to a well in unconfined aquifers with considering the effect of unsaturated zone are also presented (e.g.…”

Recent advances in modeling of well hydraulics

“…Recently, the effect of drainage from the unsaturated zone on the unconfined flow has been mentioned in the groundwater literature [209]. To explore the importance of unsaturated zone characteristics in the analyses of unconfined aquifer test, analytical solutions for flow toward a well in an unconfined aquifer had been reported.…”