Uncoupling Electrokinetic Flow Solutions
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Uncoupling Electrokinetic Flow Solutions Kristopher L. Kuhlman1
· Bwalya Malama2
Received: 6 July 2020 / Accepted: 10 August 2020 © This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply [YEAR] 2020
Abstract The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for “intermediate” potentials subject to modified material properties and boundary conditions. The fluid pressure and electrostatic potential are then found by recombining the solutions to the two intermediate uncoupled problems in a matrix-vector multiplication. Expressions for the material properties or source terms in the intermediate uncoupled problem may require extended precision or careful rewriting to avoid numerical cancellation, but the solutions themselves can typically be computed in double precision. The approach works with analytical or gridded numerical solutions and is illustrated through two examples. The solution for flow to a pumping well is manipulated to predict streaming potential and electroosmosis, and a periodic one-dimensional analytical solution is derived and used to predict electroosmosis and streaming potential in a laboratory flow cell subjected to low frequency alternating current and pressure excitation. The examples illustrate the utility of the eigenvalue decoupling approach, repurposing existing analytical solutions or numerical models and leveraging solutions that are simpler to derive for coupled physics.
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Kristopher L. Kuhlman [email protected] Bwalya Malama [email protected]
1
Applied Systems Analysis and Research Department, Sandia National Laboratories, Albuquerque, NM, USA
2
San Luis Obispo Natural Resources Management and Environmental Sciences, California Polytechnic State University, San Luis Obispo, CA, USA
123
Math Geosci
Keywords Streaming potential · Electroosmosis · Electrokinetic · Eigenvalue · Coupled processes · Geophysics
1 Introduction Coupled physical phenomena exist at the intersection of hydrological and geophysical processes, and advanced solution methods are required to make general predictions. Radioactive waste disposal (Tsang et al. 2012), water resource management (Barthel and Banzhaf 2016), geothermal energy production (Bächler and Kohl 2005), and hydrogeophysics (Hinnell et al. 2010) are examples of applications requiring holistic approaches to multiphysics. Although several alternative commercial (Li et al. 2009) and research (Guyer et al. 2009; Gaston et al. 2009; Liu 2013) software libraries exist to solve coupled physics problems using finite element or finite volume numerical methods, we illustrate an approach allowing adaptation of existing analytical or numerical methods when certain symmetries exist in the governing equations and boundary conditions. Coupled analytical solutions derived using this approach may serve to validate solutions obtained with
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