# Implementation and validation of the F4aT laboratory for flow in rough fractures

## TL;DR

This paper introduces a new lab to study how fluid flows through rough rock fractures, focusing on the transition from linear to nonlinear flow at moderate rates.

## Contribution

The F4aT-Hydraulic Laboratory is a novel experimental setup for investigating roughness-hydraulic interactions using 3D printed fracture replicas.

## Key findings

- The lab enables systematic and stochastic investigations of fracture roughness effects on hydraulics.
- Benchmarking experiments confirm the lab's ability to measure transitions in hydraulic regimes at moderate flow rates (Re ≈ 10).

## Abstract

Accurate characterization of fracture hydraulics is crucial for optimizing subsurface systems, notably geothermal energy extraction where high flow rates are essential for efficient energy production. The precise transition from linear to nonlinear fracture hydraulics at already moderate flow rates is still undefined, due to the complexity of fracture roughness, where the influence of various roughness parameters and the comparability of individual rough fractures are still unclear. Here, we introduce the Forced Fluid Fracture Flow and Transport Laboratory (F4aT-Hydraulic Laboratory), a novel experimental laboratory designed to address this knowledge gap. It focuses on a comprehensive workflow encompassing high-resolution measurements of the rock surface roughness and the experimental investigation of fracture hydraulics at a large range of flow rates (\documentclass[12pt]{minimal}
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\begin{document}$$0.05 < Re < 100$$\end{document}). A unique feature of the F4aT-Hydraulic Laboratory is its ability to conduct systematic and stochastic investigations of roughness-hydraulic interactions through 3D printed fracture replicas with defined, statistically varied fracture roughness. In this study, we present the developed workflow in detail, provide benchmarking experiments against analytical solutions, and demonstrate the ability to measure roughness effects on the transition from linear to nonlinear hydraulic regimes at already moderate flow rates (\documentclass[12pt]{minimal}
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\begin{document}$$Re \approx 10$$\end{document}).

The online version contains supplementary material available at 10.1038/s41598-025-34648-2.