Heterogeneity-controlled uncertain optimization of pump-and-treat systems explained through geological entropy

Pump-and-treat (P&T) is a widely-adopted solution for the containment of solute plumes in contaminated aquifers. A cost-effective design of P&T systems requires optimizing (minimizing) the overall pumping rates (Q). This optimization is a stochastic process, as Q is a random variable linked to the randomness of the aquifer hydraulic conductivity (K). Previously presented stochastic approaches to minimize Q adopted two-dimensional (2D) Gaussian random spatial fields (r.s.f.) of log-transformed K. Recent studies based on geological entropy have demonstrated the limited ability of Gaussian r.s.f. to reproduce extreme K patterns, which mostly control transport in heterogeneous aquifers, when compared to non-Gaussian r.s.f. Moreover, 2D models generate different flow and transport connectivity than three-dimensional (3D) models. On these premises, this work aimed at extending previous works on P&T optimization in heterogeneous aquifers through Monte-Carlo groundwater simulations of 2D and 3D Gaussian and non-Gaussian r.s.f. The results indicated that the mean (Qn) and variance (sigma Qn2) of the optimal Q distribution depend strictly on the chosen model dimensionality and r.s.f. generator. In particular, 2D models and models embedding indicator-based (i.e. non-Gaussian) r.s.f. tended to generate higher Qn and sigma Qn2 than 3D models with increasing number of model layers (K-L) and Gaussian models. This behavior can be explained considering the spatial ordering of K clusters in the simulated aquifers, which is measured through metrics derived from the concept of geological entropy. It was found that 2D models and models embedding non-Gaussian r.s.f. displayed more spatially-persistent ordered K structures than 3D models and Gaussian models, resulting in higher Qn and sigma Qn2. This is attributed to the relative amount of heterogeneity sampled by the solute source and the increased likelihood of more ordered K clusters to generate preferential flow and solute transport channeling than more disordered and chaotic systems, which enhance solute mixing. Combining P&T with physical barriers (i.e. cut-off walls) was helpful to reduce both Qn and sigma Qn2 in all tested scenarios, corroborating previous findings. However, the relative efficacy of a specific physical barrier geometry to reduce Qn and sigma Qn2 also depends on the chosen model dimensionality and r.s.f. generator.