An inverse problem methodology to identify flow channels in fractured media using synthetic steady-state head and geometrical data

Abstract

We present a methodology for identifying highly-localized flow channels embedded in a significantly less permeable medium using steady-state head and geometrical data. This situation is typical of fractured media where flows are often strongly channeled at the scales of interest (10 m–1 km). The objective is to identify both geometrical and hydraulic characteristics of the conducting structures. Channels are identified in decreasing order of importance by successive optimizations of an objective function. The identification strategy takes advantage of the hierarchical flow organization to restrict the dimension of the solution space of each individual optimization step. The characteristics of the secondary channels are strongly determined by the main flow channels. The latter are slightly modified by the secondary channels through the addition of a regularization term to the main channel characteristics in the objective function. As the objective function is strongly non-convex with numerous local minima, inversion is performed using a stochastic algorithm (simulated annealing). We assess the possibilities of the hierarchical identification strategy on simple synthetic steady-state flow configurations where hydraulic data are made up of 25 regularly spaced heads and of the boundary conditions. Those flow structures that are dominated by at most two simple channels can be identified with these head data only. Configurations comprising up to three complex and interconnected channels can still be identified with additional geometrical information including the distances of piezometers to their closest channel. The capabilities of the hierarchical identification strategy are limited to flow structures dominated by at most three equivalent flow channels. We finally discuss the perspectives of application of the method to transient-state data obtained on a more restricted number of piezometers.