Experimental determination of in-plane permeability of nonwoven thin fibrous materials

Knowledge of hydraulic properties is crucial for understanding and modeling fluid flow in thin porous media. In this work, we have developed a new simple custom-built apparatus to measure the intrinsic permeability of a single thin fibrous sheet in the in-plane direction. The permeability was measured for two types of nonwoven thin fibrous porous materials using either the water or gas phase. For each layer, the measurements have been done for different combinations of flow direction and fiber orientation. The permeability values measured using gas and water were approximately close to each other. The permeability of the two samples was found to be anisotropic and the principal permeabilities were determined based on the measurements

HYPROP measurements of the unsaturated hydraulic properties of a carbonate rock sample.

The unsaturated hydraulic properties provide important theoretical and practical information about fluid flow in soils and rocks for a range of soil, environmental and engineering applications. In this study we used the evaporation (HYPROP) and chilled-mirror dew point (WP4C) methods to estimate the water retention and unsaturated hydraulic conductivity curves of an Indiana Limestone carbonate rock sample. The obtained data were analyzed in terms of unimodal and bimodal VG (van Genuchten, 1980) and PDI (Peters et al., 2015) type functions. Bimodal functions were found to produce excellent descriptions for the unsaturated hydraulic data we measured, slightly better than the standard unimodal formulations. For our particular test using an Indiana Limestone rock sample, we did not find much improvement when accounting for film and corner flow using the PDI formulation, relative to the VG model. As far as we know, this is the first time the HYPROP methodology was applied to a rock sample

Data related to manuscript submitted to WRR

Data related to manuscript submitted to WR

The effect of dynamic capillarity in modeling saturation overshoot during infiltration

Gravity-driven fingering has been observed during downward infiltration of water into dry sand. Moreover, the water saturation profile within each finger is non-monotonic, with a saturation overshoot at the finger tip. As reported in the literature, these effects can be simulated by an extended form of the Richards equation, where a dynamic capillarity term is included. The coefficient of proportionality is called the dynamic capillarity coefficient. The dynamic capillarity coefficient may depend on saturation. However, there is no consensus on the form of this dependence. We provide a detailed traveling wave analysis of four distinctly different functional forms of the dynamic capillarity coefficient. In some forms, the coefficient increases with increasing saturation, and in some forms, it decreases. For each form, we have found an explicit expression for the maximum value of saturation in the overshoot region. In current formulations of dynamic capillarity, if the value of the capillarity coefficient is large, the value of saturation in the overshoot region may exceed unity, which is obviously nonphysical. So, we have been able to ensure boundedness of saturation regardless of the value of the dynamic capillarity coefficient by extending the capillary pressure–saturation relationship. Finally, we provide a qualitative comparison of the results of traveling wave analysis with experimental observations

The Effect of Dynamic Capillarity in Modeling Saturation Overshoot during Infiltration

Gravity-driven fingering has been observed during downward infiltration of water into dry sand. Moreover, the water saturation profile within each finger is non-monotonic, with a saturation overshoot at the finger tip. As reported in the literature, these effects can be simulated by an extended form of the Richards equation, where a dynamic capillarity term is included. The coefficient of proportionality is called the dynamic capillarity coefficient. The dynamic capillarity coefficient may depend on saturation. However, there is no consensus on the form of this dependence. We provide a detailed traveling wave analysis of four distinctly different functional forms of the dynamic capillarity coefficient. In some forms, the coefficient increases with increasing saturation, and in some forms, it decreases. For each form, we have found an explicit expression for the maximum value of saturation in the overshoot region. In current formulations of dynamic capillarity, if the value of the capillarity coefficient is large, the value of saturation in the overshoot region may exceed unity, which is obviously nonphysical. So, we have been able to ensure boundedness of saturation regardless of the value of the dynamic capillarity coefficient by extending the capillary pressure–saturation relationship. Finally, we provide a qualitative comparison of the results of traveling wave analysis with experimental observations

The effect of dynamic capillarity in modeling saturation overshoot during infiltration

Gravity-driven fingering has been observed during downward infiltration of water into dry sand. Moreover, the water saturation profile within each finger is non-monotonic, with a saturation overshoot at the finger tip. As reported in the literature, these effects can be simulated by an extended form of the Richards equation, where a dynamic capillarity term is included. The coefficient of proportionality is called the dynamic capillarity coefficient. The dynamic capillarity coefficient may depend on saturation. However, there is no consensus on the form of this dependence. We provide a detailed traveling wave analysis of four distinctly different functional forms of the dynamic capillarity coefficient. In some forms, the coefficient increases with increasing saturation, and in some forms, it decreases. For each form, we have found an explicit expression for the maximum value of saturation in the overshoot region. In current formulations of dynamic capillarity, if the value of the capillarity coefficient is large, the value of saturation in the overshoot region may exceed unity, which is obviously nonphysical. So, we have been able to ensure boundedness of saturation regardless of the value of the dynamic capillarity coefficient by extending the capillary pressure–saturation relationship. Finally, we provide a qualitative comparison of the results of traveling wave analysis with experimental observations

The effect of dynamic capillarity in modeling saturation overshoot during infiltration

Gravity-driven fingering has been observed during downward infiltration of water into dry sand. Moreover, the water saturation profile within each finger is non-monotonic, with a saturation overshoot at the finger tip. As reported in the literature, these effects can be simulated by an extended form of the Richards equation, where a dynamic capillarity term is included. The coefficient of proportionality is called the dynamic capillarity coefficient. The dynamic capillarity coefficient may depend on saturation. However, there is no consensus on the form of this dependence. We provide a detailed traveling wave analysis of four distinctly different functional forms of the dynamic capillarity coefficient. In some forms, the coefficient increases with increasing saturation, and in some forms, it decreases. For each form, we have found an explicit expression for the maximum value of saturation in the overshoot region. In current formulations of dynamic capillarity, if the value of the capillarity coefficient is large, the value of saturation in the overshoot region may exceed unity, which is obviously nonphysical. So, we have been able to ensure boundedness of saturation regardless of the value of the dynamic capillarity coefficient by extending the capillary pressure–saturation relationship. Finally, we provide a qualitative comparison of the results of traveling wave analysis with experimental observations

Spontaneous Imbibition and Drainage of Water in a Thin Porous Layer: Experiments and Modeling

The typical characteristic of a thin porous layer is that its thickness is much smaller than its in-plane dimensions. This often leads to physical behaviors that are different from three-dimensional porous media. The classical Richards equation is insufficient to simulate many flow conditions in thin porous media. Here, we have provided an alternative approach by accounting for the dynamic capillarity effect. In this study, we have presented a set of one-dimensional in-plane imbibition and subsequent drainage experiments in a thin fibrous layer. The X-ray transmission method was used to measure saturation distributions along the fibrous sample. We simulated the experimental results using Richards equation either with classical capillary equation or with a so-called dynamic capillarity term. We have found that the standard Richards equation was not able to simulate the experimental results, and the dynamic capillarity effect should be taken into account in order to model the spontaneous imbibition. The experimental data presented here may also be used by other researchers to validate their models

Spontaneous Imbibition and Drainage of Water in a Thin Porous Layer: Experiments and Modeling

The typical characteristic of a thin porous layer is that its thickness is much smaller than its in-plane dimensions. This often leads to physical behaviors that are different from three-dimensional porous media. The classical Richards equation is insufficient to simulate many flow conditions in thin porous media. Here, we have provided an alternative approach by accounting for the dynamic capillarity effect. In this study, we have presented a set of one-dimensional in-plane imbibition and subsequent drainage experiments in a thin fibrous layer. The X-ray transmission method was used to measure saturation distributions along the fibrous sample. We simulated the experimental results using Richards equation either with classical capillary equation or with a so-called dynamic capillarity term. We have found that the standard Richards equation was not able to simulate the experimental results, and the dynamic capillarity effect should be taken into account in order to model the spontaneous imbibition. The experimental data presented here may also be used by other researchers to validate their models

Experimental and numerical studies of saturation overshoot during infiltration into a dry soil

Downward infiltration of water into almost dry soil, when there is no ponding at the soil surface, often occurs in the form of fingers, with saturation overshoot at the finger tips. While this is well known, there is still uncertainty about the exact saturation pattern within fingers. We performed a series of one-dimensional water infiltration experiments into a dry soil to study the non-monotonicity of the saturation. We observed that saturation showed a non-monotonic behavior as a function of time. The overshoot was somewhat plateau shaped at relatively low flow rates but was quite sharp at higher flow rates. Two mathematical models, referred to as the extended standard (ESD) model and the interfacial area (IFA) model, were used to simulate the experimental results. Both models were based on extended forms of the Richards equation by including a dynamic capillary term. In the ESD model, standard equations for hysteresis were used. In the IFA model, the specific interfacial area was introduced to simulate hysteresis. Parameter values for both models were obtained from preliminary experiments or using empirical formulas. Only one parameter, the dynamic capillarity coefficient t, was optimized to model saturation overshoot. While the ESD model did not reproduce the form of saturation overshoot for any combination of parameter values, the IFA model could provide good agreement with the data. To our knowledge, this is the first time where a combination of the IFA model and the dynamic capillarity equation has been used to simulate a set of experiments