Identification of the pore size distribution of a porous medium by yield stress fluids using Herschel-Bulkley model

Aimad Oukhlef,Stéphane Champmartin,Abdelhak Ambari

doi:10.1051/meca/2020032

Abstract

In this paper, we present a new method to determine the pore-size distribution (PSD) in a porous medium. This innovative technique uses the rheological properties of non-Newtonian yield stress fluids flowing through the porous sample. In a first approach, the capillary bundle model will be used. The PSD is obtained from the measurement of the total flow rate of fluid as a function of the imposed pressure gradient magnitude. The mathematical processing of the experimental data, which depends on the type of yield stress fluid, provides an overview of the pore size distribution of the porous material. The technique proposed here was successfully tested analytically and numerically for usual pore size distributions such as the Gaussian mono and multimodal distributions. The study was conducted for yield stress fluids obeying the classical Bingham model and extended to the more realistic Herschel-Bulkley model. Unlike other complex methods, expensive and sometimes toxic, this technique presents a lower cost, requires simple measurements and is easy to interpret. This new method could become in the future an alternative, non-toxic and cheap method for the characterization of porous materials.

Highlights

Porous media are found almost everywhere around us [1,2,3,4], whether in living matter, inert matter or industrial materials
The phenomena related to flow through porous media have occupied and continue to stimulate a strong research activity, both fundamental and applied
Present method, we propose to use the rheological properties of yield stress fluid to scan different pore scales and determine the pore-size distribution (PSD)

Summary

Introduction

Porous media are found almost everywhere around us [1,2,3,4], whether in living matter (human skin, cartilage, bone, etc.), inert matter (soils, layers sedimentary rocks, etc.) or industrial materials (concretes, cements, powders, textiles, etc.). We can cite classical methods such as: (i) the mercury intrusion porosimetry (MIP) [1,2,3,5] This technique is based on the existence of a threshold below which the pores cannot be invaded. Present method, we propose to use the rheological properties of yield stress fluid to scan different pore scales and determine the PSD. From the curve Q = f (∇P ), it is possible to extract the PSD solving an inverse problem. This paper reports an improvement to this technique: the solution of the problem for the PSD identification using a method based on a numerical approach with yield stress fluids such as Herschel-Bulkley model

Formulation of the problem and solution

Numerical inverse method for determining PSD

Numerical approach

Numerical inversions of some distributions by using Herschel-Bulkley model

Conclusion