A MATHEMATICAL MODEL FOR STREAM - AQUIFER INTERACTION

Abstract

A stream, forming a boundary is often encountered in regional groundwater flow modeling. In case of a partially penetrating stream with considerable stream discharge, besides treating the stream as a prescribed head boundary, the exchange of flow between the stream and aquifer has to be introduced through the boundary nodes while modeling the groundwater flow. The recharge from a stream to an aquifer is proportional to the head difference in the level of water in the stream and in the aquifer in the vicinity of the stream. The coefficient of proportionality, recognized as reach transmissivity, depends upon aquifer characteristics and the shape of the stream cross- section. The water level in the aquifer depends on the abstractions and recharges including recharge from the stream. Such an implicit and complex stream-aquifer interaction problem has been analyzed by Morel-Seytoux and Daly (1975) who have used reach transmissivity and discrete kernel theory for finding an expression for recharge. The actual magnitude of exchange of flow depends on the local geology, particularly the hydraulic conductivity of the interface between the stream and the aquifer. Really the process of interaction over spatially varied channel boundaries is difficult to examine. The most common scenario of the interaction of groundwater is that of the interaction of streams with contiguous alluvial aquifer. This type of system has been the focus of study for more than 100 years, beginning from the work of Boussinesq (1877) to the present. In this study, it is proposed to use the variable parameter Muskingum method advocated by Perumal (1994) for routing the discharge hydrograph in stream reach. For studying stream - aquifer interaction, the stream having hydraulic connection with the underlying aquifer can be subdivided into a number of sub- reaches. Each of the sub-reach iii can be considered as a rectangular recharging reach. The stage in each of the sub-reaches varies with time due to unsteady nature of flood wave and / or due to interaction of stream with aquifer or vice versa, including the mutual interaction between the recharging sub-reaches. It is required to estimate the water level variations at different locations of the considered stream reach taking into account the stream-aquifer interaction. Further, it is required to estimate the recharge details in the interactive reaches considering (i) only a small stretch of the stream reach is interactive, and (ii) a long stretch of the stream reach is interactive. It is proposed to study the stream-aquifer interaction using the approximate analytical solution developed by Hantush (1967) by estimating the rise and fall of the water-table in an infinite unconfined aquifer in response to uniform percolation from rectangular recharging sub-reaches. Based on the study it is concluded that the use of Hantush solution may be considered as an alternative approach for studying stream-aquifer interaction. Further, the study reveals that the effect of mutual influence of interacting sub-reaches on the stream-aquifer interaction is not significant. iv