Abstract
Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone.
Highlights
The problem of filtering disperse systems in a porous medium is of big practical importance.Many technological processes, natural phenomena, production processes, etc. are associated with the flow of dispersed systems in porous [1,2] and fractured-porous media [3,4]
Where c is the concentration of the suspension (m3 /m3 ), v is the filtration velocity (m/s), m0 is the initial porosity of the medium, ρ a is the concentration of deposition in the active zone (m3 /m3 ), ρ p is the concentration of deposition in the passive zone (m3 /m3 ), β a is the coefficient characterizing the kinetics in the active zone (1/s), β p is the coefficient (1/s) associated with the effect of compaction
A mathematical model of suspension filtration in porous media is considered as a system of partial differential equations, which consists of mass balance equation, kinetic equations, Darcy’s law and Carman–Kozeny equation
Summary
The problem of filtering disperse systems in a porous medium is of big practical importance. First reversible kinetic equations given by Mints [35] mentioned and experimentally showed that during the filtration due to the increasing of pressure gradient, detachment of less strongly linked particles from grain occurs This kind of process can be described in the form ∂ρ/∂t = β att c − β det ρ, where β att and β det phenomenological attachment and detachment coefficients respectively. We consider the problem of filtering a suspension in a porous medium, taking into account the deposition of solid particles of the suspension in the pore volume and their release For this we use the well-known model of Venitsianov [23,24] and suggest its modification. The numerical algorithm developed in the present paper can be used for
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
