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A Simple Mathematical Model to Predict the Pressure Drop for Transport of Deformable Particles in Homogeneous Porous Media

Authors :
Víctor Matías-Pérez
Simón López-Ramírez
Elizbeth Franco-Urresti
Carlos G. Aguilar-Madera
Source :
Fluids, Vol 9, Iss 12, p 275 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

Abstract

The transport of deformable particles (TDPs) through porous media has been of considerable interest due to the multiple applications found in industrial and medical processes. The adequate design of these applications has been mainly achieved through experimental efforts, since TDPs through porous media are challenging to model because of the mechanical blockage of the pore throat due to size exclusion, deformation in order to pass through the pore throat under the driven pressure, and breakage under strong extrusion. In this work, based on the diffusivity equation and considering the TDP as a complex fluid whose viscosity and density depend on the local pressure, a simple but accurate theoretical model is proposed to describe the pressure behavior under steady- and unsteady-state flow conditions. Assuming a linear pressure dependence of the viscosity and density of the TDPs, valid for moderate pressure changes, the solution of the mathematical model yields a quantitative correlation between the pressure evolution and the parameters compressibility, viscosity coefficient, elastic modulus, particle size, and friction factor. The predictions of the model agree with experiments and allow the understanding of transport of deformable particles through a porous media.

Details

Language :
English
ISSN :
23115521
Volume :
9
Issue :
12
Database :
Directory of Open Access Journals
Journal :
Fluids
Publication Type :
Academic Journal
Accession number :
edsdoj.7baf7c53e184498c84a32765d59f9779
Document Type :
article
Full Text :
https://doi.org/10.3390/fluids9120275