Special issue “fluid dynamics, multi-phase flow, and thermal recovery methods”

Intricate fluid flow and transport phenomena in porous media are ubiquitous in natural processes and engineering systems [...

Dependency of continuum model parameters on the spatially correlated pore structure studied by pore-network drying simulations

[EN] Pore-network simulations are carried out for monomodal and bimodal pore structures with spatially correlated pore-size distributions. The internal and surface relationships between the partial vapor pressure and saturation as well as the moisture transport coefficient for these model porous structures are identified from the post-processing of the corresponding pore-network model solutions. The simulation results show that the deviation of the partial vapor pressure from the saturation vapor pressure in the presence of liquid – which is referred to as non-local equilibrium effect – in the bimodal pore structures is less pronounced than in the monomodal pore structures. For the monomodal pore structures the moisture transport coefficient profile is not unique over the entire drying process, whereas this profile depends marginally on the drying history of the bimodal pore structures. Finally the ability of the continuum model to predict the results of the pore-network simulations for multiple realizations of the pore space is assessed.This work was financed by the German Research Foundation (DFG) within the Graduate School 1554 “Micro-Macro-Interactions in Structured Media and Particulate SystemsLu, X.; Kharaghani, A.; Tsotsas, E. (2018). Dependency of continuum model parameters on the spatially correlated pore structure studied by pore-network drying simulations. En IDS 2018. 21st International Drying Symposium Proceedings. Editorial Universitat Politècnica de València. 307-314. https://doi.org/10.4995/IDS2018.2018.7417OCS30731

Determination of the moisture transport coefficient from pore network simulations of spontaneous imbibition in capillary porous media

The Richards model for spontaneous imbibition of a wetting liquid into a porous medium is revisited. Two methods are presented to determine the effective parameter in the Richards equation, i.e. the saturation-dependent moisture transport coefficient D(S), from pore network simulations: The first method employs a quasi-static pore network model (QPNM), whereas the second method uses a dynamic pore network model (DPNM) to estimate D(S) in an inverse approach. The DPNM simulation results serve as a reference to assess the quality of these two parameter estimation methods. It is found that the solution of the Richards equation is very sensitive to D(S), especially when the porous medium is close to fully saturated. While the saturation levels over time obtained from solving the Richards equation with D(S) calculated from the inverse method match well with those from the DPNM, some discrepancy is observed when the QPNM is used to estimate D(S) instead

From micro-scale to macro-scale modeling of solute transport in drying capillary porous media

Drying of capillary porous media initially saturated with saline water is central to many engineering and environmental applications. In order to predict the evolution of solute concentration in a porous medium, the macroscopic continuum models (CMs) are commonly employed. However, the predictive aptitudes of the CMs have been questioned. In this work, we solve the classical advection-diffusion equation for so- lute transport in an isothermally drying capillary porous medium for the limiting condition of capillary- dominated regime. The solution of the continuum model is compared with pore network simulations. The results of both models are analyzed in terms of local solute concentration profiles for different val- ues of network saturation. On this basis, the ability of the continuum model to reciprocate the pore network results is assessed. The degree of heterogeneity in the liquid phase structure is characterized by performing pore network Monte Carlo simulations distinguishing the percolating liquid cluster from the non-percolating isolated clusters. Based on the statistical analysis of Monte Carlo simulations, the prob- ability of first solid crystals to appear in the respective liquid phase elements is discussed. We observe that solute enrichment is more pronounced in the isolated single liquid throats and isolated clusters due to lack or significant hindrance to back-diffusion as a result of discontinuity in the liquid phase

Non-local equilibrium continuum modeling of partially saturated drying porous media: comparison with pore network simulations

A two-equation continuum model is developed to simulate the mass transfer in drying porous media. The main goal is to capture the so called non-equilibrium effect. To this end, we operate in a regime where the liquid phase is immobile so that non-equilibrium mass exchange between liquid and vapor phase dominates. The formulation of the model relies on an upscaling technique. This notably permits to formulate the non-local equilibrium phase change term on a firmer basis. The upscaling also indicates that there is no reason to consider an enhancement factor in the vapor diffusion model. The macroscopic model parameters are determined from pore network drying simulations. The same simulations are also used as a reference to compare with the predictions of the non-local equilibrium continuum model. The solution of the two-equation continuum model proves that this model simulates the non-local equilibrium effect with reasonable accuracy. Also, the simulations indicate that the non-local equilibrium effect is especially significant at the porous medium surface

Moisture transport coefficient in drying porous media

Two main approaches have been used to derive mathematical models for the drying process: The first approach considers the partially saturated porous medium as a continuum and partial differential equations are used to describe the mass, momentum and energy balances of the fluid phases. The continuum-scale models obtained by this approach involve constitutive laws which require effective material properties, such as the diffusivity, permeability, and thermal conductivity which are often determined by experiments [1]. The second approach considers the material at the pore scale, where the void space is represented by a network of pores. Micro- or nanofluidics models used in each pore give rise to a large system of ordinary differential equations with degrees of freedom at each node of the pore network [2]. The characteristic length scale of the pore network models is several orders of magnitude smaller than the practically relevant length scale. A straightforward upscaling of the micro-scale models by using large pore networks is computationally costly, but it can be used to assess the quality of any chosen continuum-scale model as well as to estimate the effective parameters. When reliable estimates for these parameters have been obtained as functions of the pore size distribution and other material properties, the computationally much cheaper continuum-scale model may be used in future simulations without the need for further micro-scale simulations or experimental measurements. In this work, the moisture transport coefficient (D), the capillary pressure (pc), the effective liquid permeability (keff,l) and the effective vapor diffusivity (Deff,v) are estimated from the post-processing of the three-dimensional pore network simulations for multiple realizations of the pore space geometry from a given probability distribution. These effective parameters are then applied to the moisture diffusion model at the continuum scale

Evaporation in capillary porous media at the perfect piston-like invasion limit: Evidence of non-local equilibrium effects

The classical continuum modeling of evaporation in capillary porous media is revisited from pore network simulations of the evaporation process. The computed moisture diffusivity is characterized by a minimum corresponding to the transition between liquid and vapor transport mechanisms confirming previous interpretations. Also the study suggests an explanation for the scattering generally observed in the moisture diffusivity obtained from experimental data. The pore network simulations indicate a noticeable nonlocal equilibrium effect leading to a new interpretation of the vapor pressure‐saturation relationship classically introduced to obtain the one‐equation continuum model of evaporation. The latter should not be understood as a desorption isotherm as classically considered but rather as a signature of a nonlocal equilibrium effect. The main outcome of this study is therefore that nonlocal equilibrium two‐equation model must be considered for improving the continuum modeling of evaporation

The Role of Discrete Capillary Rings in Mass Transfer From the Surface of a Drying Capillary Porous Medium

<jats:title>Abstract</jats:title><jats:p>The mass exchange between the surface of a model capillary porous medium and the adjacent gas-side boundary layer is studied in the limiting condition of isothermal, slow drying. In order to quantify the role and significance of liquid films in the mass exchange process, three-dimensional pore network Monte Carlo simulations are carried out systematically in the presence and absence of discrete capillary rings. The pore network simulations performed with capillary rings show a noticeable delay in transition from the capillary-supported regime to the diffusion-controlled regime. These simulation results differ significantly from the predictions of classical pore network models without liquid films, and they appear to be more consistent with the experiments conducted with real porous systems. As compared to classical pore network models, the pore network model with rings seems to predict favorably the spatiotemporal evolution of wet and dry patches at the medium surface as well as of their relative contributions to the net mass exchange rate. This is apparent when the analytical solution of the commonly used Schlünder’s model is examined against the numerical simulations conducted using classical and ring pore network models.</jats:p&gt