Macroscale three-dimensional modeling of fluid flow in a thin porous layer under unsaturated conditions is a challenging task. One major issue is that such layers do not satisfy the representative elementary volume length-scale requirement. Recently, a new approach, called reduced continua model (RCM), has been developed to describe multiphase fluid flow in a stack of thin porous layers. In that approach, flow equations are formulated in terms of thickness-averaged variables and properties. In this work, we have performed a set of experiments, where a wet 260-μm-thin porous layer was placed on top of a dry layer of the same material. We measured the change of average saturation with time using a single-sided low-field nuclear magnetic resonance device known as NMR-MOUSE. We have employed both RCM and the traditional Richards equation-based models to simulate our experimental results. We found that the traditional unsaturated flow model cannot simulate experimental results satisfactorily. Very close agreement was obtained by including the dynamic capillary term as postulated by Hassanizadeh and Gray in the traditional equations. The reduced continua model was found to be in good agreement with the experimental result without adding dynamic capillarity term. Moreover, the computational effort needed for RCM simulations was one order of magnitude less than that of traditional models.

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Unsaturated fluid flow in thin porous media depends on hydraulic properties, such as the capillary pressure, P c, as a function of saturation, S. We measured this relationship for two different types of compressible thin hydrophilic fibrous layers under varying conditions. Among other factors, we changed the number of layers and the overburden pressure (i.e. the confined solid pressure applied on top of the sample) imposed on one layer or a stack of layers. Applying an overburden pressure drastically affected the [Formula: see text] curves. However, increasing the number of fibrous layers had little impact on the capillary pressure–saturation curves. We also investigated the effect of multiple imbibition–drainage cycles on the [Formula: see text] data. Measured data points were used to find general expressions for the [Formula: see text] relationships of compressible thin porous media. Existing quasi-empirical correlations used in vadose zone hydrology, notably expressions by van Genuchten (Van Genuchten MTh. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 1980; 44: 892-898) and Durner (Durner W. Hydraulic conductivity estimation for soils with heterogeneous pore structure. Water Resour Res 1994; 32: 211–223) for single- and dual-porosity media, respectively, were employed to fit the measured data points.

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