The Laplace Transform Galerkin Technique for large‐scale simulation of mass transport in discretely fractured porous formations

TLDR

Simulating contaminant migration in large‐scale porous formations with discrete fractures is limited by traditional methods due to disparate transport time scales and the need for fine spatial discretization to capture sharp concentration gradients at fracture–matrix interfaces. The study extends the Laplace transform Galerkin method to discretely fractured media to enable large‐scale modeling of contaminant transport. The method employs Laplace domain solutions on a coarse grid, a preconditioned ORTHOMIN‑accelerated iterative solver, independent p‑space solutions, and incorporates advective‑dispersive transport and dual‑porosity theory. The technique eliminates time stepping, permits coarse grids with high accuracy, achieves computational efficiency through a preconditioned ORTHOMIN solver, is highly parallelizable, and shows that deep, undetectable fractures in clayey aquitards can severely compromise groundwater quality in underlying aquifers.

Abstract

The ability to simulate contaminant migration in large‐scale porous formations containing a complex network of discrete fractures is limited by traditional modeling approaches. One primary reason is because of vastly different transport time scales in different regions due to rapid advection along the discrete fractures and slow but persistent diffusion in the porous matrix. In addition to time‐related complexities, standard numerical methods require a fine spatial discretization in the porous matrix to represent sharp concentration gradients at the interface between the fractures and the matrix. In order to circumvent these difficulties, the Laplace transform Galerkin method is extended for application to discretely fractured media with emphasis on large‐scale modeling capabilities. The technique avoids time stepping and permits the use of a relatively coarse grid without compromising accuracy because the Laplace domain solution is relatively smooth and devoid of discontinuities even in advection‐dominated problems. Further computational efficiency for large‐grid problems is achieved by employing a preconditioned, ORTHOMIN‐accelerated iterative solver. A unique feature of the method is that each of the several needed p space solutions are independent, thus making the scheme highly parallel. Other features include the accommodation of advective‐dispersive transport in the porous matrix and the straightforward inclusion of dual‐porosity theory to represent matrix diffusion in regions where microfractures exist below the modeling scale. An example problem involving contaminant transport through an aquitard into an underlying aquifer leads to the conclusion that deep, essentially undetectable fractures in clayey aquitards can greatly compromise the quality of groundwater in the impacted aquifer.