Analytical and numerical investigations of spontaneous imbibition in porous media
| Autor: | Martin J. Blunt, Hasan A. Nooruddin |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Pressure drop
Capillary action Back pressure 0208 environmental biotechnology Thermodynamics 02 engineering and technology Mechanics 020801 environmental engineering Physics::Fluid Dynamics 020401 chemical engineering Incompressible flow Imbibition 0204 chemical engineering Relative permeability Porous medium Saturation (chemistry) Water Science and Technology Mathematics |
| Zdroj: | Water Resources Research. 52:7284-7310 |
| ISSN: | 0043-1397 |
| DOI: | 10.1002/2015wr018451 |
| Popis: | We present semi-analytical solutions for co-current displacements with some degree of counter-current flow. The solution assumes a one-dimensional horizontal displacement of two immiscible incompressible fluids with arbitrary viscosities and saturation-dependent relative permeability and capillary pressures. We address the impact of the system length on the degree of counter-current flow when there is no pressure drop in the non-wetting phase across the system, assuming negligible capillary back pressure at the inlet boundary of the system. It is shown that in such displacements, the fractional flow can be used to determine a critical water saturation, from which regions of both co-current and counter-current flow are identified. This critical saturation changes with time as the saturation front moves into the porous medium. Furthermore, the saturation profile in the approach presented here is not necessarily a function of distance divided by the square root of time. We also present approximate solutions using a perturbative approach, which is valid for a wide range of flow conditions. This approach requires less computational power and is much easier to implement than the implicit integral solutions used in previous work. Finally, a comprehensive comparison between analytical and numerical solutions is presented. Numerical computations are performed using traditional finite-difference formulations and convergence analysis shows a generally slow convergence rate for water imbibition rates and saturation profiles. This suggests that most coarsely-gridded simulations give a poor estimate of imbibition rates, while demonstrating the value of these analytical solutions as benchmarks for numerical studies, complementing Buckley-Leverett analysis. This article is protected by copyright. All rights reserved. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Plný text