On the physical and mathematical modeling of the coupling of rivers and aquifers as sustainable water supply systems

Abstract

A physical and mathematical model is presented to simulate realistic hydrological conditions and to evaluate coupled river and aquifer as water supply system. The approach is applied to estimate the extraction effects on the river and related aquifers under different conditions, with the purpose of determining the water supply potential and sustainability of the coupled system. The model consists of the conceptual and numerical coupling of two structures that take into account different aspects of the systems being considered. The fi rst is a free-surface fl ow structure, and it carries out the balance of mass and momentum along the river course, whereas the second one is of hydrogeological type that performs the mass balance in combination with Darcy's law in each aquifer of interest for evaluation purposes. The two parts of the model are coupled by their source terms with a very simple linear relationship; the numerical implementation is carried out by using MODFLOW and ISIS codes. After calibrating the models with fi eld parameters, an iterative coupling process is given where each structure must satisfy their criteria of internal convergence. The complete model is satisfactory whenever the iterative coupling process and the hydrogeological and hydraulic models converge. The conceptual approach is applied to the real and natural system constituted by the Papagayo river and the aquifers located in the river banks locally known as Norte, Obra de Toma, and Lomas de Chapultepec, in the State of Guerrero, México to determine their sustainable water supply potential. Keywords: darcy's law, equations of Saint-Venant, fl ow balance in aquifers, stream-aquifer-coupled systems. INTRODUCTIONThere are several approaches to analyze the river and aquifer interaction. The study of the fl ow in aquifers and streams through physical-based analysis and numerical simulation models has been carried out in many occasions considering both systems separately. In the best situations when analyzing one of them, the other is considered in a simple and incomplete manner; yet each individual component constitutes a dynamic system that in turn interacts dynamically with the other. Each system is governed by its own fi eld equations of balance of mass, energy, and constitutive relationships that are related among themselves by coupling terms. The purpose of this paper is to present an approach to simultaneously evaluate the behavior of rivers and aquifers as sustainable supply systems, under realistic conditions, based on their balance equations of mass and energy coupled by physical fl ow exchange terms. The numerical implementation is carried out by using MODFLOW and ISIS models. The combined model makes possible the evaluation of availability and sustainability of water for supply aims, when underground exploitation sites are near or on river courses; furthermore, the approximation remains valid when the wells lie far from river courses; in these case the river and aquifer interaction is less intense. One special situation aris...