Numerical Simulation of Pore-scale Heterogeneity and Its Effects on Elastic, Electrical and Transport Properties

Book excerpt: This dissertation describes numerical experiments quantifying the influence of pore-scale heterogeneities and their evolution on macroscopic elastic, electrical and transport properties of porous media. We design, implement and test a computational recipe to construct granular packs and consolidated microstructures replicating geological processes and to estimate the link between process-to-property trends. This computational recipe includes five constructors: a Granular Dynamics (GD) simulation, an Event Driven Molecular Dynamics (EDMD) simulation and three computational diagenetic schemes; and four property estimators based on GD for elastic, finite-elements (FE) for elastic and electrical conductivity, and Lattice-Boltzmann method (LBM) for flow property simulations. Our implementation of GD simulation is capable of constructing realistic, frictional, jammed sphere packs under isotropic and uniaxial stress states. The link between microstructural properties in these packs, like porosity and coordination number (average number of contacts per grain), and stress states (due to compaction) is non-unique and depends on assemblage process and inter-granular friction. Stable jammed packs having similar internal stress and coordination number (CN) can exist at a range of porosities (38-42%) based on how fast they are assembled or compressed. Similarly, lower inter-grain friction during assemblage creates packs with higher coordination number and lower porosity at the same stress. Further, the heterogeneities in coordination number, spatial arrangement of contacts, the contact forces and internal stresses evolve with compaction non-linearly. These pore-scale heterogeneities impact effective elastic moduli, calculated by using infinitesimal perturbation method. Simulated stress-strain relationships and pressure-dependent elastic moduli for random granular packs show excellent match with laboratory experiments, unlike theoretical models based on Effective Medium Theory (EMT). We elaborately discuss the reasons why Effective Medium Theory (EMT) fails to correctly predict pressure-dependent elastic moduli, stress-strain relationships and stress-ratios (in uniaxial compaction) of granular packs or unconsolidated sediments. We specifically show that the unrealistic assumption of homogeneity in disordered packs and subsequent use of continuum elasticity-based homogeneous strain theory creates non-physical packs, which is why EMT fails. In the absence of a rigorous theory which can quantitatively account for heterogeneity in random granular packs, we propose relaxation corrections to amend EMT elastic moduli predictions. These pressure-dependent and compaction-dependent (isotropic or uniaxial) correction factors are rigorously estimated using GD simulation without non-physical approximations. Further, these correction factors heuristically represent the pressure-dependent heterogeneity and are also applicable for amending predictions of theoretical cementation models, which are conventionally used for granular packs. For predicting stress-ratios in uniaxial compaction scenario, we show the inappropriateness of linear elasticity-based equations, which use elastic constants only and do not account for dissipative losses like grain sliding. We further implement and test a computational recipe to construct consolidated microstructures based on different geological scenarios, like sorting, compaction, cementation types and cement materials. Our diagenetic trends of elastic, electrical and transport properties show excellent match with laboratory experiments on core plugs. This shows the feasibility of implementing a full-scale computational-rock-physics-based laboratory to construct and estimate properties based on geological processes. However, the elastic property estimator (FE simulation) shows limitations of finite resolution while computing elastic properties of unconsolidated sediments and fluid-saturated microstructures.