# A lattice-Boltzmann study of permeability-porosity relationships and mineral precipitation patterns in fractured porous media

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## Abstract

Mineral precipitation can drastically alter a reservoir’s ability to transmit mass and energy during various engineering/natural subsurface processes, such as geothermal energy extraction and geological carbon dioxide sequestration. However, it is still challenging to explain the relationships among permeability, porosity, and precipitation patterns in reservoirs, particularly in fracture-dominated reservoirs. Here, we investigate the pore-scale behavior of single-species mineral precipitation reactions in a fractured porous medium, using a phase field lattice-Boltzmann method. Parallel to the main flow direction, the medium is divided into two halves, one with a low-permeability matrix and one with a high-permeability matrix. Each matrix contains one flow-through and one dead-end fracture. A wide range of species diffusivity and reaction rates is explored to cover regimes from advection- to diffusion-dominated, and from transport- to reaction-limited. By employing the ratio of the Damköhler (Da) and the Peclet (Pe) number, four distinct precipitation patterns can be identified, namely (1) no precipitation (Da/Pe < 1), (2) near-inlet clogging (Da/Pe > 100), (3) fracture isolation (1 < Da/Pe < 100 and Pe > 1), and (4) diffusive precipitation (1 < Da/Pe < 100 and Pe < 0.1). Using moment analyses, we discuss in detail the development of the species (i.e., reactant) concentration and mineral precipitation fields for various species transport regimes. Finally, we establish a general relationship among mineral precipitation pattern, porosity, and permeability. Our study provides insights into the feedback loop of fluid flow, species transport, mineral precipitation, pore space geometry changes, and permeability in fractured porous media.

## Keywords

Lattice-Boltzmann method Fractured porous media Mineral precipitation patterns Permeability-porosity relationships## Preview

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## Notes

### Acknowledgements

This work was supported by ETH Grant ETH-12 15-2. The Werner Siemens Foundation (Werner Siemens-Stiftung) is further thanked by Martin Saar for its support of the Geothermal Energy and Geofluids (GEG.ethz.ch) Group at ETH Zurich. We thank the two anonymous reviewers for their helpful comments and suggestions that improved this paper.

### Compliance with ethical standards

### **Conflict of interests**

The authors declare that they have no conflict of interest.

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