Semi-analytical tool for optimal management of alluvial aquifers hydraulically connected to streams

Abstract

Conjunctive water resources use is becoming an important tool in water management, especially with the increase in demands in all life sectors, and the decrease in available water resources with all the evolving obstacles of climate change, growing populations in addition to the conflicts over water resources in some areas of the world. A groundwater/surface water conjunctive management problem of a hydraulically connected aquifer/stream system is addressed in this research under the prior appropriation doctrine of water allocation practiced in the western states of the USA including Colorado. One approach for applying the concept of conjunctive groundwater/surface water management is achieved by techniques of artificial recharge of aquifers, where water is injected and stored in aquifers when surface water surplus is available for that purpose and pumped in the future when there is a need. Within the prior allocation doctrine, groundwater users in Colorado historically started extracting water from the aquifers underlying their agricultural lands after surface water rights were fully allocated. Consequently, in a system of hydraulically connected aquifers and streams as in the South Platte River Basin, ground water users are junior water right holders, who are allowed to divert surface water only when all senior water right holders have had their full allocation. From this perspective, the objective of the groundwater management problem is to minimize the impact of artificial recharge injection and extraction operations on the stream connected to the targeted aquifer, meaning, when extracting water from the aquifer, the pumped amount should be equal to the injected volumes, else wise the aquifer will compensate for the difference by depleting the stream. An important effect characterizing artificial recharge and groundwater pumping is the change in aquifer head levels during operations, as excessive injection might cause water mounds and over pumping might result in a stressed aquifer. In this study, groundwater pumping and artificial recharge effects on aquifers are simulated using the semi-analytical models describing the effect of an operating well in the aquifer and the interconnected stream. These models are derived from the formulated analytical solutions for aquifer drawdown and stream depletion obtained by Theis (1935) and Glover and Balmer (1945) In the first part of this research, a number of semi-analytical models are derived and implemented in MATLAB codes to simulate the response of both the aquifer and the stream to cyclically operating wells. These models can handle the cases of laterally infinite aquifers, semi-infinite aquifers limited by a stream or an impermeable boundary, and finite aquifer comprised between an impermeable boundary and a stream or between two streams. In the second part of the research, these models are used to solve a groundwater management problem that seeks to minimize the absolute value of the volume of stream depletion/accretion over a given time period while meeting prescribed constraints on aquifer water levels, irrigation demands and injection water availability. This problem is tackled using linear programming algorithms, which is proven to be effective in providing first-hand estimations of optimal injection-extraction schemes for the management of systems characterized by large numbers of operating wells, within a reasonably small computation time.