Multiscale Structures to Describe Porous Media Part I: Theoretical Background and Invasion by Fluids

A porous medium with a broad pore-size distribution is described on the basis of the Multiscale Percolation System concept. The representative structure is the superposition of several constitutive elementary networks, of which mesh sizes are proportional to the diameter of the class of pores considered. To account for the contribution of each class to the connection of the medium, a recurrent building process, involving rescaling and superposition, is defined. This process leads to an equivalent monoscale network, involving elements representative of the various classes. Mercury intrusion at increasing pressure into a finite-size sample of this equivalent network is modelled. The inverse problem is solved, leading to the identification of the representative multiscale structure of a given material from the experimental intrusion curve.     

Multiscale Structures to Describe Porous Media Part II: Transport Properties and Application to Test Materials

A renormalization method for the computation of the transport properties of a porous medium modelled as a multiscale random network is proposed. The method applies to electrical conduction, molecular diffusion, hydraulic transport under low Reynolds number, transport of condensable vapour, in the medium fully or partially saturated by one or two immiscible fluids. For 31 test materials, the method previously exposed by the authors for the reconstitution of the pore structure from the mercury intrusion curve is applied. Then, the intrinsic permeability is computed. The results are in good agreement with the measured permeability.     

Condensation and isothermal water transfer in cement mortar: Part II - transient condensation of water vapor

The transient wetting of a mortar sample swept by a flow of humid air is experimentally studied at temperatures of 30 and 55°C. The water content profile shape and evolution are found to be very different from those which were observed during imbibition. The boundary condition on the exposed wall of the sample is examined. A convenient evolution of the coefficient of diffusion with water content is explored. This coefficient is interpreted in terms of pure vapor diffusion, even at relatively high water contents. But its values at low water content and its temperature dependence are inconsistent. Additional explanations are then considered with the assumption that the vapor condensation in the medium is not an equilibrium process between vapor and liquid phases. The physical origin of such a nonequilibrium process is discussed. A tentative set of transfer and phase change coefficients is proposed in order to describe the experimental data by means of numerical simulation. Then, some aspects of the imbibition processes are re-examined, taking into account the consequences of a nonequilibrium condensation.Nomenclature volumic rate of phase change - D ₀ coefficient of free diffusion of the water vapor in air - D _hv vapor diffusion coefficient of the medium - E, E equivalent air thickness - h relative humidity of gaseous phase - h _c relative humidity at the capillary condensation threshold - h _a relative humidity of the flowing air - h ₀ relative humidity at the air-material interface - h _E equilibrium relative humidity at a given water content - J global massic flux - M molar mass of water - R gas constant - T temperature - t time - x distance from the interface - ₀ total porosity - volumetric water content - _h condensation coefficient (see Equation (8)) - _L mass density of liquid water - vs mass density of saturated water vapor     

Contribution of the Dusty Gas Model to Permeability/Diffusion Tests on Partially Saturated Clay Rocks

Gas transfer experiments on claystone and numerical simulations have been conducted to enhance the knowledge of gas transport in nuclear waste repositories in the Callovo-Oxfordian clay formation in Bure, France. Laboratory Gas transfer experiments were performed with a specific device dedicated to very low permeability measurement (10^?23 to 10^?20 m²). Experiments were performed on both dry and close to saturation claystone. The Dusty Gas Model, based on multi-component gas transfer equations with Knudsen diffusion, was used to describe the experimental results. The parameters obtained are the effective permeability, the Knudsen diffusion (Klinkenberg effect) and molecular diffusion coefficients and the porosity accessible to gas. Numerical simulations were carried with various boundary conditions and for different gases (helium vs hydrogen) and were compared with experiments to test the reliability of the model parameters and to better understand the mechanisms involved in clays close to saturation. The numerical simulation fitted the experimental data well whereas simpler models cannot describe the complexity of the Knudsen/Klinkenberg effects. Permeabilities lie between 10^?22 and 10^?20 m². Claystones close to saturation have an accessible porosity to gas transfer that is lower than 0.1?C1% of the porosity. Analysis of the Klinkenberg effect suggests that this accessible pore network should be made of 50?C200?nm diameter pores. It represents pore networks accessible at capillary pressure lower than 4?MPa.     

Condensation and isothermal water transfer in cement mortar Part I — Pore size distribution,equilibrium water condensation and imbibition

The pore size distribution of cement mortar is studied in relation to water sorption experiments with the help of mercury intrusion and nitrogen sorption. The importance of adsorbed water is pointed out. Isothermal imbibition experiments at four temperatures are presented. The temperature-dependence of the mass transfer coefficients is compared to the one predicted by the classical model. Significant discrepancies are noticed. On the basis of the knowledge of the pore structure, a modelisation of the transfer process at moderate water content is proposed. It particularly takes into account Knudsen's vapor diffusion and effects of the presence of a discontinuous capillary phase interacting with vapor diffusion.