Well Rate and Placement for Optimal Groundwater Remediation Design with A Surrogate Model

A new surrogate-assisted optimization formulation for groundwater remediation design was developed. A stationary Eulerian travel time model was used in lieu of a conservative solute transport model. The decision variables of the management model are well locations and their flow rates. The objective function adjusts the residence time distribution between all pairs of injection-production wells in the remediation system. This goal is achieved by using the Lorenz coefficient as an effective metric to rank the relative efficiency of many remediation policies. A discrete adjoint solver was developed to provide the sensitivity of the objective function with respect to changes in decision variables. The quality management model was checked with simple solutions and then applied to hypothetical two- and three-dimensional test problems. The performance of the simulation-optimization approach was evaluated by comparing the initial and optimal remediation designs using an advective-dispersive solute transport simulator. This study shows that optimal designs simultaneously delay solute transport breakthrough at pumping wells and improve the sweep efficiency leading to smaller cleanup times. Well placement optimization in heterogeneous porous media was found to be more important than well rate optimization. Additionally, optimal designs based on two-dimensional models were found to be more optimistic suggesting a direct use of three-dimensional models in a simulation-optimization framework. The computational budget was drastically reduced because the proposed surrogate-based quality management model is generally cheaper than one single solute transport simulation. The introduced model could be used as a fast, but first-order, approximation method to estimate pump-and-treat capital remediation costs. The results show that physically based low-fidelity surrogate models are promising computational approaches to harness the power of quality management models for complex applications with practical relevance

Modelling three dimensional groundwater flow and transport by hexahedral finite elements.

This research work deals with three-dimensional modeling of groundwater flow and solute transport problems in groundwater aquifer systems, with several complexities, heterogeneities and variable conditions as encountered in the field. Finite element methods are used throughout to solve a range of different problems, using in particular the Galerkin weighted residual approach based on trilinear hexahedral elements. Special emphasis is made on transient and non-linear groundwater flow problems with moving interfaces, such as the water table and the freshwater-saltwater sharp interface. A generalized Fast Updating Procedure technique is developed for these situations, which presents a number of advantageous features in comparison to classic computational techniques used to deal with such problems. One of the important contributions is the automatic construction of the generic soils characteristic curves, which are dynamically dependent upon the overall system water status. Several test examples are successfully worked out for validating this technique in different aquifer configurations, and under different initial and boundary conditions. These test cases show that the proposed method is cheap, numerically stable and accurate. Numerical stability is guaranteed through a developed solver, which is obtained by using state of the art methods for robust preconditioning and efficient numerical implementation. The accuracy is demonstrated by comparison against analytical, other numerical approaches, and laboratory experimental solutions. The usefulness of the method is clearly shown by the application of the 3-D sharp interface finite element model 'GEO-SWIM' to the coastal aquifer system of Martil in the north of Morocco. Several efficient runs are made, leading to a calibrated management model for the study area, giving a clear picture of the salinization risk in the aquifer due to saltwater encroachment. Three-dimensional modeling of solute transport problems in groundwater aquifer systems is equally investigated. It is concluded that the standard Galerkin finite element method is computationally intensive, since the obtained system of numerical equations is very large, sparse, none symmetric and usually difficult to solve with standard iterative techniques. Hence, preconditioning is necessary to improve the convergence behavior of ill-conditioned systems. In this work, we propose an M-matrix type of transformation on the general transport matrix which guarantees the existence of the preconditioning schemes, and hence improves the overall solvers performance and robustness. The usefulness of the method is demonstrated by solving several test examples with different complexities, including hypothetical and field applications in Belgium. Different solvers are tested as the minimal residual method and the stabilized biconjugate gradient method, in combination with different preconditioning schemes, as diagonal scaling and incomplete factorization. It is concluded that M-matrix preconditioning is very simple to implement, and proves to be very efficient and robust. An effort is put on packaging the computer programs, by giving modern visual support to many modules. Therefore, several GUI programs are provided as complementary tools to support the developed models, enabling their friendly use, and the possibility for future extensions

Generalized Mixed-Cell Mass Balance Solute Transport Modeling in Pore-Scale Disordered Networks: A New Semi-Analytical Approach

International audienceAccurately predicting (non-reactive or reactive) solute transport migration, at multiple scales, in subsurface aquifers is identified among urgent societal and scientific challenges in water resources engineering and environmental pollution [1]. In particular, pore-scale models are essential tools to bridge the gap between the pore and REV scales at which observable macroscopic behavior of solute transport processes become apparent. While challenges do persist in this field, we derive cutting-edge pore scale semi-analytical formulation for solute transport modelling in disordered networks. Continuous concentration profiles along pore throats are calculated analytically, a posteriori, from time-dependent numerically simulated concentrations in neighboring pores. A double Laplace transform method is applied to governing advection-diffusion equations in network elements by enforcing mass flux continuity along their interfaces. We show that these solutions involve a time-dependent convolution product kernels or interpolating functions expressed as convergent exponentially decreasing series of locally embedded pore-throat geometrical and flow properties. Explicit dependence of interpolating kernels on the local Péclet numbers leads to a generalized numerical scheme for accurate simulation of solute transport processes in pore networks. Indeed, widely used numerical schemes in the literature [2-7] are equivalent to the asymptotic (long-time) form of our general scheme for extremely small or high Péclet numbers. Therefore, we demonstrate for the first-time that previously adopted numerical schemes for mass balance in pore networks [2-7] may overlook pore scale dynamics for a full range of intermediate Péclet numbers occurring in subsurface aquifers. These findings are illustrated by analysis of simulated concentration distributions in a benchmark pore network extracted from Berea sandstone three-dimensional pore space image. Our findings [8] provide additional insights into the understanding of pore-scale solute transport processes to further improve the predictive capability of existing mixed-cell mass balance network models