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A two dimensional semi-continuum model to explain wetting front instability in porous media.

ABSTRACT: Modelling fluid flow in an unsaturated porous medium is a complex problem with many practical applications. There is enough experimental and theoretical evidence that the standard continuum mechanics based modelling approach is unable to capture many important features of porous media flow. In this paper, a two-dimensional semi-continuum model is presented that combines ideas from continuum mechanics with invasion percolation models. The medium is divided into blocks of finite size that retain the nature of a porous medium. Each block is characterized by its porosity, permeability, and a retention curve. The saturation and pressure of the fluids are assumed to be uniform throughout each block. It is demonstrated that the resulting semi-continuum model is able to reproduce (1) gravity induced preferential flow with a spatially rich system of rivulets (fingers) characterized by saturation overshoot, (2) diffusion-like flow with a monotonic saturation profile, (3) the transition between the two. The model helps to explain the formation of the preferential pathways and their persistence and structure (the core and fringe of the fingers), the effect of the initial saturation of the matrix, and the saturation overshoot phenomenon.

SUBMITTER: Kmec J

PROVIDER: S-EPMC7864934 | biostudies-literature | 2021 Feb

REPOSITORIES: biostudies-literature

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A two dimensional semi-continuum model to explain wetting front instability in porous media.

Kmec Jakub J Fürst Tomáš T Vodák Rostislav R Šír Miloslav M

Scientific reports 20210205 1

Modelling fluid flow in an unsaturated porous medium is a complex problem with many practical applications. There is enough experimental and theoretical evidence that the standard continuum mechanics based modelling approach is unable to capture many important features of porous media flow. In this paper, a two-dimensional semi-continuum model is presented that combines ideas from continuum mechanics with invasion percolation models. The medium is divided into blocks of finite size that retain t ...[more]

PMID: 33547389

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Project description:Interfacial areas between nonwetting-wetting (NW-W) liquids in natural porous media were measured using a modified version of the interfacial partitioning tracer test (IPTT) method that employed simultaneous two-phase flow conditions, which allowed measurement at NW saturations higher than trapped residual saturation. Measurements were conducted over a range of saturations for a well-sorted quartz sand under three wetting scenarios of primary drainage (PD), secondary imbibition (SI), and secondary drainage (SD). Limited sets of experiments were also conducted for a model glass-bead medium and for a soil. The measured interfacial areas were compared to interfacial areas measured using the standard IPTT method for liquid-liquid systems, which employs residual NW saturations. In addition, the theoretical maximum interfacial areas estimated from the measured data are compared to specific solid surface areas measured with the N2/BET method and estimated based on geometrical calculations for smooth spheres. Interfacial areas increase linearly with decreasing water saturation over the range of saturations employed. The maximum interfacial areas determined for the glass beads, which have no surface roughness, are 32±4 and 36±5 cm-1 for PD and SI cycles, respectively. The values are similar to the geometric specific solid surface area (31±2 cm-1) and the N2/BET solid surface area (28±2 cm-1). The maximum interfacial areas are 274±38, 235±27, and 581±160 cm-1 for the sand for PD, SI, and SD cycles, respectively, and ~7625 cm-1 for the soil for PD and SI. The maximum interfacial areas for the sand and soil are significantly larger than the estimated smooth-sphere specific solid surface areas (107±8 cm-1 and 152±8 cm-1, respectively), but much smaller than the N2/BET solid surface area (1387±92 cm-1 and 55224 cm-1, respectively). The NW-W interfacial areas measured with the two-phase flow method compare well to values measured using the standard IPTT method.

Dataset Information

A two dimensional semi-continuum model to explain wetting front instability in porous media.

Publications

A two dimensional semi-continuum model to explain wetting front instability in porous media.

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