2021/11/11 by Daniel Keable, Alistair Jones, Keable, Daniel +7
Physics and Astronomy · Economics, Econometrics and Finance · #Theoretical and Computational Physics #Complex Systems and Time Series Analysis #Complex Network Analysis Techniques
paper · pdf · doi:10.48550/arxiv.2111.06548
The results from a series of well characterised, unstable, miscible\ndisplacement experiments in a Hele Shaw cell with a quarter five-spot\nsource-sink geometry are presented, with comparisons to detailed numerical\nsimulation. We perform repeated experiments at adverse viscosity ratios from 1\n- 20 and Peclet numbers from 104 - 106 capturing the transition from 2D\nto 3D radial fingering and experimental uncertainty. The open-access dataset\nprovides time-lapse images of the fingering patterns, transient effluent\nprofiles, and meta-information for use in model validation. We find the\ncomplexity of the fingering pattern increases with viscosity ratio and Peclet\nnumber, and the onset of fingering is delayed compared to linear displacements,\nlikely due to Taylor dispersion stabilisation. The transition from 2D to 3D\nfingering occurs at a critical Peclet number that is consistent with recent\nexperiments in the literature. 2D numerical simulations with hydrodynamic\ndispersion and different mesh orientations provide good predictions of\nbreakthrough times and sweep efficiency obtained at intermediate Peclet numbers\nacross the range of viscosity ratios tested, generally within the experimental\nuncertainty. Specific finger wavelengths, tip shapes, and growth are hard to\nreplicate; model predictions using velocity dependent longitudinal dispersion\nor simple molecular diffusion bound the fingering evolution seen in the\nexperiments, but neither fully capture both fine-scale and macroscopic\nmeasures. In both cases simulations predict sharper fingers than the\nexperiment. A weaker dispersion stabilisation seems necessary to capture the\nexperimental fingering at high viscosity ratio, which may also require\nanisotropic components. 3D models with varying dispersion formulations should\nbe explored in future developments to capture the full range of effects at high\nviscosity ratio and Peclet number.\n