An analytic element model for groundwater flow in multiscale discrete fracture networks

In the coming years, we face many challenges related to groundwater flow in bedrock, including climate change and the ambition to increase Europe’s mineral supply. In crystalline bedrock, groundwater flow mostly occurs in fractures. Therefore, it is important to understand how individual fractures can affect groundwater flow. Simulating groundwater flow in a discrete fracture network is challenging, and the availability of analytical models is limited. This presentation introduces an analytical model for modeling groundwater flow in interconnected three-dimensional fracture networks. The presented model is based on the analytic element method and can manage random fracture networks [1].

The analytical model consists of planar circular fractures. The flow within each fracture plane is assumed to be two-dimensional. Intersecting fractures form an intersection line where the flow between the fractures is redistributed. Along the intersection line, the hydraulic head and flow are continuous. The analytical model uses a combined direct and iterative solver, and the solution can be used to calculate, among other things, equipotentials, streamlines, and flow velocities.

A unique feature of this model is that it does not require a computational mesh. This means that both the hydraulic head and flow velocity are known everywhere in the fracture network. The model also has no theoretical limit on the number of fractures that can be included or how large or small they can be. Therefore, the model is excellent for managing a combination of flow on both large and small scales simultaneously.

This presentation covers the basic concepts, the model’s properties, and application examples. We demonstrate that it is possible to include fractures at both kilometer and meter scales within the same model, while maintaining analytical accuracy. Furthermore, we will present particle tracking for multiscale models and discuss the influence scales on flow paths.

[1] Otto D.L. Strack, Erik A.L. Toller, An analytic element model for flow in fractured impermeable rock, Journal of Hydrology, Volume 643, 2024, 131983, ISSN 0022-1694, https://doi.org/10.1016/j.jhydrol.2024.131983.