A Multiscale Framework for Hybrid Reactive-Poroelastic Porous Media Modeling

Thesis Abstract

This study addresses the challenge of accurately predicting coupled chemical reactions and mechanical deformations in porous media across multiple scales, where microscopic reaction kinetics interact with macroscale poroelastic responses under transient load and flow conditions. The aim is to develop a multiscale framework that integrates reactive transport, poroelasticity, and microstructure-informed constitutive behavior to improve predictive capability for geotechnical and energy-related applications. Specific objectives are (1) to formulate a hierarchical multiscale model that couples pore-scale reactive transport with continuum-scale poroelastic equations; (2) to derive effective constitutive relations and upscaling operators from detailed microscale simulations using homogenization and asymptotic expansion techniques; (3) to implement a hybrid reactive-poroelastic numerical solver that preserves mass conservation and energy consistency across scales; (4) to calibrate and validate the framework against experimental data from heterogeneous rock samples and surrogate porous media; (5) to demonstrate predictive capability through case studies involving time-dependent stress, mineral dissolution/precipitation, and fluid-structure interaction under varied boundary conditions. The methodology employs a mixed-methods research design rooted in computational modelling and empirical validation. The population comprises representative elementary volumes (REVs) extracted from sandstone and carbonate matrices, combined with synthetic porous media generated to control pore-scale features. A stratified sampling approach yields 12 sandstone and 8 carbonate REV datasets, supplemented by 6 tuned synthetic media. Data collection instruments include micro-CT imaging for pore geometry, high-resolution X-ray diffraction for mineralogical composition, and laboratory core flooding tests under controlled stress and chemical environments. The analytical framework integrates (i) pore-scale simulations of reactive transport using species transport equations with reaction kinetics, solved by finite-volume methods; (ii) homogenization-based upscaling to derive effective poroelastic moduli, coupling coefficients, and reaction terms; (iii) a macro-scale finite element solver incorporating Biot-type poroelasticity with embedded reaction-transport submodels; (iv) parameter estimation and model calibration via Bayesian inference and Markov Chain Monte Carlo (MCMC) techniques to quantify uncertainties in upscaled parameters. Validity and reliability are ensured through cross-validation across multiple REV samples and sensitivity analyses identifying influential microstructural features. The method of data analysis combines statistical and computational approaches regression analyses to relate microscopic mineral changes to macroscopic stiffness evolution, ANOVA to assess the impact of pore geometry categories on effective properties, and probabilistic calibration to propagate uncertainty. The model specification includes a coupled set of governing equations for momentum balance in the poroelastic medium, mass conservation with advection-diffusion-reaction for chemical species, and microstructure-informed constitutive laws derived from asymptotic homogenization. The study anticipates key findings such as quantification of scale-dependent coupling coefficients, identification of dominant reactive pathways controlling stiffness degradation or enhancement, and demonstration that the multiscale framework reduces predictive error by 25–40% relative to single-scale models under transient loading and chemical alteration. The anticipated contribution to knowledge lies in (i) delivering a rigorously derived multiscale framework that integrates chemical reactions with poroelastic deformation in porous media, (ii) providing a validated upscaling methodology linking microstructure to macro-behavior, and (iii) offering a versatile computational platform adaptable to geological carbon storage, geothermal reservoirs, and reactive filtration systems. The study concludes that a hybrid reactive-poroelastic approach is essential for capturing coupled phenomena across scales, with recommendations to extend the framework to anisotropic composites, incorporate thermo-chemo-mechanical coupling, and apply machine learning surrogates for rapid scenario analyses in real-time decision support.