Modeling transport of charged species in pore networks: Solution of the Nernst–Planck equations coupled with fluid flow and charge conservation equations

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Modeling transport of charged species in pore networks: Solution of the Nernst–Planck equations coupled with fluid flow and charge conservation equations

Agnaou, M; Sadeghi, MA; Tranter, TG; Gostick, JT; (2020) Modeling transport of charged species in pore networks: Solution of the Nernst–Planck equations coupled with fluid flow and charge conservation equations. Computers and Geosciences , 140 , Article 104505. 10.1016/j.cageo.2020.104505. Green open access

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Abstract

A pore network modeling (PNM) framework1 for the simulation of transport of charged species, such as ions, in porous media is presented. It includes the Nernst–Planck (NP) equations for each charged species in the electrolytic solution in addition to a charge conservation equation which relates the species concentration to each other. Moreover, momentum and mass conservation equations are adopted and there solution allows for the calculation of the advective contribution to the transport in the NP equations. The proposed framework is developed by first deriving the numerical model equations (NMEs) corresponding to the partial differential equations (PDEs) based on several different time and space discretization schemes, which are compared to assess solutions accuracy. The derivation also considers various charge conservation scenarios, which also have pros and cons in terms of speed and accuracy. Ion transport problems in arbitrary pore networks were considered and solved using both PNM and finite element method (FEM) solvers. Comparisons showed an average deviation, in terms of ions concentration, between PNM and FEM below 5% with the PNM simulations being over 104 times faster than the FEM ones for a medium including about 104 pores. The improved accuracy is achieved by utilizing more accurate discretization schemes for both the advective and migrative terms, adopted from the CFD literature. The NMEs were implemented within the open-source package OpenPNM based on the iterative Gummel algorithm with relaxation. This work presents a comprehensive approach to modeling charged species transport suitable for a wide range of applications from electrochemical devices to nanoparticle movement in the subsurface.

Type:	Article
Title:	Modeling transport of charged species in pore networks: Solution of the Nernst–Planck equations coupled with fluid flow and charge conservation equations
Open access status:	An open access version is available from UCL Discovery
DOI:	10.1016/j.cageo.2020.104505
Publisher version:	https://doi.org/10.1016/j.cageo.2020.104505
Language:	English
Additional information:	This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords:	Porous media, Simulations, Nernst–Planck equations, Pore network modeling, openPNM
UCL classification:	UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Chemical Engineering
URI:	https://discovery.ucl.ac.uk/id/eprint/10107552