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Imbibition plays a central role in diverse energy, environmental, and industrial processes. In many cases, the medium has multiple parallel strata of different permeabilities; however, how this stratification impacts imbibition is poorly understood. We address this gap in knowledge by directly visualizing forced imbibition in three-dimensional (3D) porous media with two parallel strata. We find that imbibition is spatially heterogeneous: for small capillary number Ca, the wetting fluid preferentially invades the fine stratum, while for Ca above a threshold value, the fluid instead preferentially invades the coarse stratum. This threshold value depends on the medium geometry, the fluid properties, and the presence of residual wetting films in the pore space. These findings are well described by a linear stability analysis that incorporates crossflow between the strata. Thus, our work provides quantitative guidelines for predicting and controlling flow in stratified porous media.
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Imbibition, the displacement of a nonwetting fluid by a wetting fluid, plays a central role in diverse energy, environmental, and industrial processes. While this process is typically studied in homogeneous porous media with uniform permeabilities, in many cases, the media have multiple parallel strata of different permeabilities. How such stratification impacts the fluid dynamics of imbibition, as well as the fluid saturation after the wetting fluid breaks through to the end of a given medium, is poorly understood. We address this gap in knowledge by developing an analytical model of imbibition in a porous medium with two parallel strata, combined with a pore network model that explicitly describes fluid crossflow between the strata. By numerically solving these models, we examine the fluid dynamics and fluid saturation left after breakthrough. We find that the breakthrough saturation of nonwetting fluid is minimized when the imposed capillary number Ca is tuned to a value Ca$^*$ that depends on both the structure of the medium and the viscosity ratio between the two fluids. Our results thus provide quantitative guidelines for predicting and controlling flow in stratified porous media, with implications for water remediation, oil/gas recovery, and applications requiring moisture management in diverse materials.
We report forced radial imbibition of water in a porous medium in a Hele-Shaw cell. Washburns law is confirmed in our experiment. Radial imbibition follows scaling dynamics and shows anomalous roughening dynamics when the front invades the porous medium. The roughening dynamics depend on the flow rate of the injected fluid. The growth exponents increase linearly with an increase in the flow rate while the roughness exponents decrease with an increase in the flow rate. Roughening dynamics of radial imbibition is markedly different from one dimensional imbibition with a planar interface window. Such difference caused by geometric change suggests that universality class for the interface growth is not universal.
Diverse processes rely on the viscous flow of polymer solutions through porous media. In many cases, the macroscopic flow resistance abruptly increases above a threshold flow rate in a porous medium---but not in bulk solution. The reason why has been a puzzle for over half a century. Here, by directly visualizing the flow in a transparent 3D porous medium, we demonstrate that this anomalous increase is due to the onset of an elastic instability. We establish that the energy dissipated by the unstable flow fluctuations, which vary across pores, generates the anomalous increase in flow resistance through the entire medium. Thus, by linking the pore-scale onset of unstable flow to macroscopic transport, our work provides generally-applicable guidelines for predicting and controlling polymer solution flows.
Imbibition is a commonly encountered multiphase problem in various fields, and exact prediction of imbibition processes is a key issue for better understanding capillary flow in heterogeneous porous media. In this work, a numerical framework for describing imbibition processes in porous media with material heterogeneity is proposed to track the moving wetting front with the help of a partially saturated region at the front vicinity. A new interface treatment, named the interface integral method, is developed here, combined with which the proposed numerical model provides a complete framework for imbibition problems. After validation of the current model with existing experimental results of one-dimensional imbibition, simulations on a series of two-dimensional cases are analysed with the presences of multiple porous phases. The simulations presented here not only demonstrate the suitability of the numerical framework on complex domains but also present its feasibility and potential for further engineering applications involving imbibition in heterogeneous media.
We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. In this model, the material behaves as a viscoelastic solid when unyielded, and as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress. The porous media is made of a symmetric array of cylinders, and we solve the flow in one periodic cell. We find that the solution is time-dependent even at low Reynolds numbers as we observe oscillations in time of the unyielded region especially at high Bingham numbers. The volume of the unyielded region slightly decreases with the Reynolds number and strongly increases with the Bingham number; up to 70% of the total volume is unyielded for the highest Bingham numbers considered here. The flow is mainly shear dominated in the yielded region, while shear and elongational flow are equally distributed in the unyielded region. We compute the relation between the pressure drop and the flow rate in the porous medium and present an empirical closure as function of the Bingham and Reynolds numbers. The apparent permeability, normalized with the case of Newtonian fluids, is shown to be greater than 1 at low Bingham numbers, corresponding to lower pressure drops due to the flow elasticity, and smaller than 1 for high Bingham numbers, indicating larger dissipation in the flow owing to the presence of the yielded regions. Finally we investigate the effect of the Weissenberg number on the distribution of the unyielded regions and on the pressure gradient.
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