Speaker
Description
We develop a mathematical framework for analyzing coupled fluid flow, species transport, and heat transfer in pore-scale network models, where nonlinear interactions arise from pressure-driven flow, temperature-dependent chemical reactions along pore walls, and thermal exchange between pore fluid and solid matrix. Along each network edge, species transport undergoes diffusion and advection and is coupled to temperature through reaction kinetics, while reaction-induced mass transfer feeds back into the pressure field even under static pore geometry. Pressure gradients, in turn, drive advection of species and convection of heat (alongside conduction), yielding a fully coupled multi-physics system on the network. To enable analytical insight and reduced-order modeling, we linearize the governing equations via a small-amplitude perturbation about chemical equilibrium and show that the coupled thermal-species subsystem admits a vector-valued generalized eigenvalue problem arising from linear stability analysis. The resulting eigenstructure provides a natural spectral basis for representing interacting transport modes on the network. Projecting the linearized equations onto this basis yields a reduced-order dynamical system for modal amplitudes, coupled through vertex-based pressure, temperature, and concentration variables subject to Neumann-Kirchhoff-type continuity and flux balance conditions. We validate the spectral reduction against full PDE simulations on pore networks and analyze convergence with respect to modal resolution and key nondimensional parameters, including Biot and Damköhler numbers. The framework provides a mathematically tractable approach for reduced-order modeling of nonlinear, multi-physics transport in porous and fractured media, with applications ranging from subsurface energy storage to reactive flow in geological formations.
| Country | United States |
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