The Effects of Swelling and Porosity Change on Capillarity: DEM Coupled with a Pore-Unit Assembly Method.

Thomas Sweijen,S Majid Hassanizadeh,Ehsan Nikooee,Bruno Chareyre

doi:10.1007/s11242-016-0689-8

Abstract

In this study, a grain-scale modelling technique has been developed to generate the capillary pressure–saturation curves for swelling granular materials. This model employs only basic granular properties such as particles size distribution, porosity, and the amount of absorbed water for swelling materials. Using this model, both drainage and imbibition curves are directly obtained by pore-scale simulations of fluid invasion. This allows us to produce capillary pressure–saturation curves for a large number of different packings of granular materials with varying porosity and/or amount of absorbed water. The algorithm is based on combining the Discrete Element Method for generating different particle packings with a pore-unit assembly approach. The pore space is extracted using a regular triangulation, with the centres of four neighbouring particles forming a tetrahedron. The pore space within each tetrahedron is referred to as a pore unit. Thus, the pore space of a particle packing is represented by an assembly of pore units for which we construct drainage and imbibition capillary pressure–saturation curves. A case study on Hostun sand is conducted to test the model against experimental data from literature and to investigate the required minimum number of particles to have a Representative Elementary Volume. Then, the capillary pressure–saturation curves are constructed for Absorbent Gelling Material particles, for different combinations of porosity values and amounts of absorbed water. Each combination yields a different configuration of pore units, and thus distinctly different capillary pressure–saturation curves. All these curves are shown to collapse into one curve for drainage and one curve for imbibition when we normalize capillary pressure and saturation values. We have developed a formula for the Van Genuchten parameter alpha (which is related to the inverse of the entry pressure) as a function of porosity and the amount of absorbed water.

Highlights

The swelling and the deformation of granular porous media under variably saturated conditions are a common phenomenon in geotechnical problems, product engineering, and biological tissues
We test our pore-unit model by constructing capillary pressure–saturation curves for Hostun sand, for which the measured drainage and imbibition curves were found in the literature
Hostun sand was chosen instead of Absorbent Gelling Material (AGM) particles, because only few data are available on the capillary pressure–saturation curves for AGM particle beds

Summary

Introduction

The swelling and the deformation of granular porous media under variably saturated conditions are a common phenomenon in geotechnical problems, product engineering, and biological tissues. Examples are swelling clays (Murad and Cushman 1996; Bennethum and Cushman 1996; Romero et al 2011), foods (Takhar 2014), paper and tissues (Sun et al 2014; Qin and Hassanizadeh 2014), biopolymers (Singh et al 2003; Malakpoor et al 2007), and absorbent polymers in hygienic products (Diersch et al 2010). Numerical models have been employed to study the swelling and the subsequent deformation of granular materials. A numerical model was developed by Diersch et al (2010) for the simulation of partially saturated swelling granular materials, such as Absorbent Gelling Material (AGM) particles used in hygienic products. That model employs empirical equations to account for the effect of swelling and the subsequent deformation on hydraulic parameters such as capillary pressure–saturation curve, permeability, and porosity

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