Abstract
The results from a series of well characterised, unstable, miscible displacement experiments in a Hele-Shaw cell with a quarter five-spot source-sink geometry are presented, with comparisons to detailed numerical simulation. We perform repeated experiments at adverse viscosity ratios from 1 to 20 and Peclet numbers from 10\(^4\) to 10\(^6\) capturing the transition from 2D to 3D radial fingering and experimental uncertainty. The open-access dataset provides time-lapse images of the fingering patterns, transient effluent profiles, and meta-information for use in model validation. We find the complexity of the fingering pattern increases with viscosity ratio and Peclet number, and the onset of fingering is delayed compared to linear displacements, likely due to Taylor dispersion stabilisation. The transition from 2D to 3D fingering occurs at a critical Peclet number that is consistent with recent experiments in the literature. 2D numerical simulations with hydrodynamic dispersion and different mesh orientations provide good predictions of breakthrough times and sweep efficiency obtained at intermediate Peclet numbers across the range of viscosity ratios tested, generally within the experimental uncertainty. Specific finger wavelengths, tip shapes, and growth are hard to replicate; model predictions using velocity-dependent longitudinal dispersion or simple molecular diffusion bound the fingering evolution seen in the experiments, but neither fully capture both fine-scale and macroscopic measures. In both cases, simulations predict sharper fingers than the experiment. A weaker dispersion stabilisation seems necessary to capture the experimental fingering at high viscosity ratio, which may also require anisotropic components. 3D models with varying dispersion formulations should be explored in future developments to capture the full range of effects at high viscosity ratio and Peclet number.
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Data availability
Experimental and simulation data associated with this work are hosted on Zenodo at https://doi.org/10.5281/zenodo.5567913. The matlab codes for processing the images, analysing results and generating figures, as well as example simulation datafiles are available on Github at https://github.com/sci-sjj/MiscibleViscousFingering. The Mistress simulation code is currently under-development; up to date code is available from the authors on request.
Notes
Estimated for a 20% volume fraction of glycerol using data in D’Errico et al. (2004). This is only approximate for all experiments except for those described in this paper, but it enables a rough comparison of Peclet numbers.
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Acknowledgements
Dr. Wawrzyniec Kostorz is thanked for adding several new features to the MISTRESS code that enabled this study to be performed. We thank Vincenzo Cunsolo and Henry Arthur for their help in the laboratory experiments.
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The majority of this work was undertaken as part of the MSc Petroleum Engineering degree at Imperial College London by Daniel Keable in 2018.
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Keable, D., Jones, A., Krevor, S. et al. The Effect of Viscosity Ratio and Peclet Number on Miscible Viscous Fingering in a Hele-Shaw Cell: A Combined Numerical and Experimental Study. Transp Porous Med 143, 23–45 (2022). https://doi.org/10.1007/s11242-022-01778-4
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DOI: https://doi.org/10.1007/s11242-022-01778-4