Marc Prat

Recent advances in pore-scale models for drying of porous media

This paper presents a review of the recent advances in pore-scale modelling of drying in capillary porous media. The development of pore network models in drying has been first motivated by several fundamental features of drying that cannot be fully explained within the framework of continuum models. These features include the dry patch phenomenon and the constant drying rate period. A second source of motivation has been the advances made in pore-scale modelling of immiscible displacements in porous media and the increasing conviction that concepts developed in this area could be utilised to model drying. These concepts are recalled. We describe how they have been used for developing a pore network model of drying driven by mass transfer. A review of the main results is made, including pattern formation, drying rates and some recent results regarding drying of a porous medium containing a binary mixture and the influence of heat transfer. The use of network models for computing effective transport properties is discussed. Open problems are discussed.

Percolation model of drying under isothermal conditions in porous media

Abstract A model of drying of capillary porous media is presented based on a modified form of invasion percolation theory. The porous medium is conceptualized as a network of pores connected by narrow throats. In addition to capillary and gravity effects, evaporation at the microscopic gas-liquid interface and vapor diffusion in the gaseous phase are taken into account. This leads to a modification of the invasion rules associated with invasion percolation. The simulations on a two-dimensional network containing 5000 ducts compare favorably with experimental results obtained by means of a two-dimensional micromodel.

Numerical and experimental network study of evaporation in capillary porous media. Drying rates

Experiments of evaporation are carried out in a two-dimensional micromodel under quasi-isothermal conditions. Three basic cases are investigated: in the absence of gravity forces, in a stabilizing gravity field and in a destabilizing gravity field. The drying rates are measured and compared to the results of numerical pore network simulations. While an excellent agreement between the simulations and the experiments were found in a previous study in terms of phase distributions, the agreement is only qualitative as far as drying rates are concerned. The poor quantitative agreement between the simulations and the experiments is explained by the existence of roughness and corner flows within the micromodel during drying. These liquid film flows are not taken into account in the simulations.

Numerical and experimental network study of evaporation in capillary porous media. Phase distributions

Experiments of evaporation are carried out in a two-dimensional micromodel under quasi-isothermal conditions. The phase distributions within the network are visualized and compared to numerical pore network simulations. Numerical simulation agrees very well with the experimental results for the three basic cases investigated, i.e. in the absence of gravity forces, in a stabilizing gravity field and in a destabilizing gravity field. The phase distributions are also compared with drainage phase distributions obtained experimentally by means of the same micromodel. The comparison between the experimental drainage and evaporation patterns confirms numerical predictions presented in a previous study. The influence of the viscous forces, which are not taken into account in the simulator, is discussed.

On the boundary conditions at the macroscopic level

We study the problem of the boundary conditions specified at the boundary of a porous domain in order to solve the macroscopic transfer equations obtained by means of the volume-averaging method. The analysis is limited to the case of conductive transport but the method can be extended to other cases. A numerical study enables us to illustrate the theoretical results in the case of a model porous medium.

Gas cluster growth by solute diffusion in porous media. Experiments and automaton simulation on pore network

Abstract The study presented in this paper deals with the liquid–gas phase change by pressure decline of supersaturated CO2 solutions in 2D porous media. The growth of the gas phase is studied experimentally and numerically as a function of supersaturation, wettability and gravity. Experiments are performed on a transparent etched network (micromodel) and simulations with a specific numerical automaton. In the experiments, the nucleation process, i.e. the occurrence of the gas bubbles, as well as the growth of these bubbles are visualised and analysed by means of a micro video camera and an image processing apparatus. The observations confirm the heterogeneous nature of nucleation and the disordered growth pattern of the gas phase. The analysis of the growth rate of a single gas cluster shows that this phenomenon is different from the compact growth of an isolated single bubble in the bulk. As previously predicted, the bubble growth by mass transfer and volume expansion in porous media is characterised by a pattern of the invasion percolation type under normal laboratory conditions. Numerical simulations of the growth pattern and the growth rate of a single gas cluster are performed with a numerical automaton. Based on a pore network modelling technique and a set of hypotheses derived from the observations, this automaton is first validated by comparing the numerical results with the experiments. Then, the automaton is used to conduct a sensitivity study. In particular, the influences of the Jakob number, pressure decline rate, Bond number, wettability and characteristics of the microstructure are investigated.

Average flow model of rough surface lubrication: Flow factors for sinusoidal surfaces

The effects of lubricant film flow, pressurized and sheared between two parallel sinusoidal wavy surfaces in sliding motion is studied analytically. Results are presented using a flow factor model which provides an average description of the surfaces roughness impact. Two distinct cases are studied in order to compare stationary or time dependent local aperture configurations. Flow factors are computed respectively for each case through spatial or spatio-temporal average, revealing striking differences. The results shed light on the relevance of the composite roughness concept. Special attention is paid to the flow factor analytical behavior when surfaces are near contact.

Modelling of Heat Transfer by Conduction in a Transition Region Between a Porous Medium and an External Fluid

We study the modelling of purely conductive heat transfer between a porous medium and an external fluid within the framework of the volume averaging method. When the temperature field for such a system is classically determined by coupling the macroscopic heat conduction equation in the porous medium domain to the heat conduction equation in the external fluid domain, it is shown that the phase average temperature cannot be predicted without a generally negligible error due to the fact that the boundary conditions at the interface between the two media are specified at the macroscopic level.Afterwards, it is presented an alternative modelling by means of a single equation involving an effective thermal conductivity which is a function of point inside the interfacial region.The theoretical results are illustrated by means of some numerical simulations for a model porous medium. In particular, temperature fields at the microscopic level are presented.

Pore network simulation of evaporation of a binary liquid from a capillary porous medium

A pore-network model of evaporation of a binary liquid mixture into a ternary gas phase is developed. The model is applied to study the influence of surface tension gradients induced by composition variations of the liquid on the phase distribution within a capillary porous medium. Numerical simulations based on the proposed model show that the surface tension gradients lead to the accumulation of liquid near the open edge of the network. This surface tension gradient effect is only significant for weakly disordered porous media.

Averaged Reynolds equation for flows between rough surfaces in sliding motion

The flow between rough surfaces in sliding motion with contacts between these surfaces, is analyzed through the volume averaging method. Assuming a Reynolds (lubrication) approximation at the roughness scale, an average flow model is obtained combining spatial and time average. Time average, which is often omitted in previous works, is specially discussed. It is shown that the effective transport coefficients, traditionally termed ‘flow factors’ in the lubrication literature, that appear in the average equations can be obtained from the solution to two closure problems. This allows for the numerical determination of flow factors on firmer bases and sheds light on some arguments to the literature. Moreover, fluid flows through fractures form an important subset of problems embodied in the present analysis, for which macroscopisation is given.