Groundwater pumping in head-controlled coastal systems: The role of lateral boundaries in quantifying the interface toe location and maximum pumping rate

摘要

The current study explores quantitatively the impact of lateral impermeable boundaries on groundwater pumping in head-controlled coastal systems, based on the potential theory and the image-well superposition method. We compare the interface toe location and maximum pumping rate among three scenarios that assume (S1) an infinite domain width and a finite domain length, (S2) a finite domain width and length, and (SS) an infinite domain width and length. Focusing exclusively on boundary effects, the upstream freshwater discharge is assumed the same for all scenarios, regardless of the variation in domain size. It is found that the impact from both inland and lateral boundaries could play a significant role on the interface toe location and maximum pumping rate (defined as the maximum allowable pumping rate that will not lead to pumping saltwater), depending on sizes of domain length and width. Since the impacts of inland fixed-head boundary and lateral impermeable boundaries are contrary on the maximum interface toe location (defined as the farthest inland point of the interface toe under pumping condition) and maximum pumping rate, they can be offset under certain critical conditions such that the results of the two quantitative indictors (i.e. the maximum interface toe location and maximum pumping rate) in S2 are close to those in SS. In particular, a linear equation is derived to reflect the relationship between the domain width and length under such critical conditions and expressed as L~* = 0.87W~* + 0.62 (W* > 1 or L~* > 1.5), in which W~* and L~* are the domain width and length normalized by the distance between the coastline and pumping well. When L~* > 0.87W~* + 0.62, the impact from lateral overcomes that from inland, producing a larger maximum interface toe location and a lower maximum pumping rate than those in SS. When L~* < 0.87W~* + 0.62, by contrast, the impact from inland exceeds that from lateral and hence, resulting in a smaller maximum interface toe location and a higher maximum pumping rate. It is expected that the results developed in the current study could support the design of numerical models and 3D laboratory experiments as well as the assessment of domain size impact on pumping in head-controlled coastal groundwater systems.