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.