No Arabic abstract
Porous media with hierarchical structures are commonly encountered in both natural and synthetic materials, e.g., fractured rock formations, porous electrodes and fibrous materials, which generally consist of two or more distinguishable levels of pore structure with different characteristic lengths. The multiphase flow behaviours in hierarchical porous media have remained elusive. In this study, we investigate the influences of hierarchical structures in porous media on the dynamics of immiscible fingering during fluid-fluid displacement. By conducting a series of numerical simulations, we found that the immiscible fingering can be suppressed due to the existence of secondary porous structures. To characterise the fingering dynamics in hierarchical porous media, a phase diagram is constructed by introducing a scaling parameter, i.e., the ratio of time scales considering the combined effect of characteristic pore sizes and wettability. The findings present in this work provide a basis for further research on the application of hierarchical porous media for controlling immiscible fingerings.
We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper, we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.
The motion of active polymers in a porous medium is shown to depend critically on flexibilty, activity and degree of polymerization. For given Peclet number, we observe a transition from localisation to diffusion as the stiffness of the chains is increased. Whereas stiff chains move almost unhindered through the porous medium, flexible ones spiral and get stuck. Their motion can be accounted for by the model of a continuous time random walk with a renewal process corresponding to unspiraling. The waiting time distribution is shown to develop heavy tails for decreasing stiffness, resulting in subdiffusive and ultimately caged behaviour.
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 study how the dynamics of a drying front propagating through a porous medium are affected by small-scale correlations in material properties. For this, we first present drying experiments in micro-fluidic micro-models of porous media. Here, the fluid pressures develop more intermittent dynamics as local correlations are added to the structure of the pore spaces. We also consider this problem numerically, using a model of invasion percolation with trapping, and find that there is a crossover in invasion behaviour associated with the length-scale of the disorder in the system. The critical exponents associated with large enough events are similar to the classic invasion percolation problem, whereas the addition of a finite correlation length significantly affects the exponent values of avalanches and bursts, up to some characteristic size. This implies that the even a weak local structure can interfere with the universality of invasion percolation phenomena.
Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface instability, are commonly encountered during displacement processes and somehow detrimental since such hydrodynamic instabilities can significantly reduce displacement efficiency. In this study, we report a possible adjustment in pore geometry which aims to suppress the capillary fingering in porous media with hierarchical structures. Through pore-scale simulations and theoretical analysis, we demonstrate and quantify combined effects of wettability and hierarchical geometry on displacement patterns, showing a transition from fingering to compact mode. Our results suggest that with a higher porosity of the 2nd-order porous structure, the displacement can keep compact across a wider range of wettability conditions. Combined with our previous work on viscous fingering in such media, we can provide a complete insight into the fluid-fluid displacement control in hierarchical porous media, across a wide range of flow conditions from capillary- to viscous-dominated modes. The conclusions of this work can benefit the design of microfluidic devices, as well as tailoring porous media for better fluid displacement efficiency at the field scale.