Two-Phase Flow in Porous Media: Predicting Its Dependence on Capillary Number and Viscosity Ratio

• Published in: Transport in porous media Vol. 86; no. 1; pp. 243 - 259
• Main Authors: Ferer, M., Anna, Shelley L., Tortora, Paul, Kadambi, J. R., Oliver, M., Bromhal, Grant S., Smith, Duane H.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-01-2011; Springer; Springer Nature B.V
• Subjects: Capillarity; Capillary flow; Carbon dioxide; Carbon sequestration; Civil Engineering; Classical and Continuum Physics; Crossovers; Dependence; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Enhanced oil recovery; Exact sciences and technology; Fractals; Geotechnical Engineering & Applied Earth Sciences; Hydrocarbons; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; MATERIALS SCIENCE; Pollution, environment geology; Porous media; Predictions; Sedimentary rocks; Two dimensional models; Two phase flow; Viscosity; Viscosity ratio; Drainage; Micro-fluidics; Viscosity ratios; Pore-level modeling; experimental studies; carbon dioxide; models; recovery; transport; lead; fractals; viscosity; Pore-level modelling; prediction; drainage; porous media
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-010-9619-3

Motivated by the need to determine the dependencies of two-phase flow in a wide range of applications from carbon dioxide sequestration to enhanced oil recovery, we have developed a standard two-dimensional, pore-level model of immiscible drainage, incorporating viscous and capillary effects. This model has been validated through comparison with several experiments. For a range of stable viscosity ratios (
M
 = 
μ
injected,nwf
/
μ
defending, wf
≥ 1), we had increased the capillary number,
N
c
and studied the way in which the flows deviate from fractal capillary fingering at a characteristic time and become compact for realistic capillary numbers. This crossover has enabled predictions for the dependence of the flow behavior upon capillary number and viscosity ratio. Our results for the crossover agreed with earlier theoretical predictions, including the universality of the leading power-law indicating its independence of details of the porous medium structure. In this article, we have observed a similar crossover from initial fractal viscous fingering (FVF) to compact flow, for large capillary numbers and unstable viscosity ratios
M
 < 1. In this case, we increased the viscosity ratio from infinitesimal values, and studied the way in which the flows deviate from FVF at a characteristic time and become compact for non-zero viscosity ratios. This crossover has been studied using both our pore-level model and micro-fluidic flow-cell experiments. The same characteristic time,
τ
= 1/
M
0.7
, satisfactorily describes both the pore-level results for a range of large capillary numbers and the micro-fluidic flow cell results. This crossover should lead to predictions similar to those mentioned above.