Presence of Nonconvexity in Groundwater Concentration Response Functions

Abstract

This study examines the presence of nonconvexity and multiple extrema in the feasible region defined by the concentration response function. The response function is defined in the context of concentration constraints imposed on groundwater quality management models and is constructed assuming that concentration constraints are imposed at every node in a numerical grid. The groundwater system is represented by a homogeneous numerical simulation model. The response function is graphically depicted as a function of pumping rates at two wells. The dependence of the response function on simulation model and management model characteristics is examined by varying dimensionless parameter values. This study shows that the response surface is nonconvex and contains multiple local extrema over a wide range of parameter values. These features of the surface are most prominent at the transitions from extraction to injection pumping, Binding constraints often occur at or near low-velocity zones.