A Dual Delineation Approach to Untangle Interferences in Well Doublets Systems

Abstract

Traditional numerical methods for the delineation of wellhead protection areas span deterministic and probabilistic approaches. They provide time‐related capture zones. However, none of the existing approaches identifies the groundwater contribution areas related to each source or sink. In this work, the worthiness of the so‐called double delineation approach was extended. This task was achieved by simple postprocessing of its dual outputs leading to a highly efficient screening tool. In the particular context of geothermal resources management through the well doublets of the Dogger aquifer in the Paris Basin (France), the approach was extended to forecast the compositional heat breakthrough at production wells. Hence, cold‐water breakthrough and temperature decline in production wells are timely assessed in low‐enthalpy geothermal reservoirs. The method quantifies how groundwater volumes are moving through space and time between any couple of source and sink. It provides unprecedented tools advancing the enhanced understanding of water resources systems functioning. It is highly recommended to implement the presented concepts in the current and future generations of community groundwater models.

On Solving Groundwater Flow and Transport Models with Algebraic Multigrid Preconditioning

“…For the forward travel time simulations, the performances of AMGCL solvers are compared with those obtained with the BiCGSTAB (Van der Vorst 1992) solver provided by MATLAB with ILU(0) preconditioning and the UMFPACK direct sparse solver based on the unsymmetrical multifrontal algorithm (Davis 2004, 2006). Because application of the dual delineation approach is quite novel in groundwater modeling (Sbai 2018, 2019) selection of the most efficient solver/preconditioner is of great interest to enhance the competitiveness of this method. Unlike in (Sbai 2018) where a multistep time integration approach was proposed to solve the underlying transport equations as a shortcut to recycle existing transient transport models, a true steady‐state one‐step solver was used in this work.…”

“…Besides these out of the box bindings, the computational geosciences group in the Department of Mathematics and Cybernetics at SINTEF Digital developed a MATLAB© exchange interface to the MATLAB Reservoir Simulation Toolbox (Lie 2019;SINTEF 2020). This interface provided a convenient means to upgrade an existing MATLAB-based groundwater flow and transport modeling toolbox (Sbai 2018(Sbai , 2019. All benchmarks presented in this note were performed within this framework by using simple MATLAB scripts where the groundwater models were simultaneously pre-processed, executed, and post-processed.…”

“…We present two test problems to evaluate the performance of the AMGCL library. The first test problem is a two-dimensional field-scale application that was published in previous works (Sbai 2018(Sbai , 2019 demonstrating the so-called dual delineation technique. It involves four well doublets in a deep geothermal reservoir where heat production from pumping wells and cold fluid injection are taking place simultaneously.…”

“…Nevertheless, scalar steady‐state transport like equations were recently proposed in the framework of the dual delineation approach. This method first introduced by Sbai (2018) and extended in (Sbai 2019) solves a total of N i + N P + 2 stationary scalar advection equations to calculate travel times, steady‐state capture zones, and other derived quantities such as the time‐related capture zones, etc. N i and N p are the total number of sources (including injection wells) and sinks (including pumping wells), respectively.…”

Optimizing Recharge Area Delineation for Small- to Medium-Sized Groundwater Systems through Coupling Methods and Numerical Modeling: A Case Study of Linfen City, China

“…This Euler grid-based method not only delineates capture zones, but also provides a steady-state well capture zone, illustrating each well's contribution area to groundwater over infinite time. It emerges as a robust and effective alternative to particle tracking methods [34,35].…”