Mathematical modeling of unconventional geomaterials

Unconventional geomaterials such as aggregated soils and sedimentary rocks are common in nature. Accurate modeling of these materials remains a significant challenge due to multiscale pore spaces, anisotropy, multi-field coupling, and various flow patterns. This thesis aims to formulate a comprehensive coupled continuum framework that adequately considers these critical characteristics. We first consider various flow patterns in a double porosity medium, motivated by shale properties. Specifically, in sedimentary rocks, fluid could flow through the micro-fracture network at the larger scale as well as through the nanometer-size pores of the rock matrix at the smaller scale. We idealize the micro-fracture network as a transversely isotropic medium with respect to fluid flow, i.e., anisotropic permeability. In addition, the nanopores of sedimentary rocks such as shale are so small that Darcy's law may not hold at this scale. To better understand the impact of non-Darcy flow on the overall flow pattern, we present a hydromechanical model for materials with two porosity scales that accommodates both transverse isotropy at the larger scale and non-Darcy flow at the smaller scale. The two scales interact within the same continuum. The overarching goal is to better understand the impacts of a full tensor permeability and non-Darcy flow on the seepage pattern in this material. Second, we derive closed-form expressions for poroelastic coefficients for anisotropic materials exhibiting single and double porosity. A novel feature of the formulation is the use of the principle of superposition to derive the governing mass conservation equations from which analytical expressions for the Biot tensor and Biot moduli, among others, are derived. For single porosity media, the mass conservation equation derived from the principle of superposition is shown to be identical to the one derived from continuum principle of thermodynamics, thus confirming the veracity of both formulations and suggesting that this conservation equation can be derived in more than one way. Third, we model the elastoplastic behavior of geomaterials with a unique anisotropic poroelastoplastic theory. For the solid constitutive model, we derive an efficient implicit return mapping algorithm accounting for the loss of stress tensor coaxiality between the trial state and the final state to obtain the updated effective stress, history parameters, and consistent tangent operator for any given strain increment. We conduct a uniaxial strain point simulation to provide benchmark results. Subsequently, 3D stress point simulations are carried out to calibrate plasticity parameters using triaxial experimental data, as well as to reproduce the strain-softening phenomenon. Initial boundary value problem simulations are conducted to analyze the impacts of fluid flow and solid constitutive model on the resulting responses of geomaterials. The "shale gas revolution" in North America has had a profound impact on global energy markets, making the exploration of shale gas one of the most popular research topics nowadays. In this thesis, we combine the anisotropic poroelasticity theory with an advanced gas transport model in both the nanopores and discrete fractures for the first time. This novel contribution considers the roles of bedding plane orientation, permeability variation due to stress change, real gas effect, viscous flow, slippage effect, Knudsen diffusion, gas adsorption/desorption, and fracture flow, in a manner that is more in sync with reality. We validate this model against field data on Barnett shale and apply the validated model to study the effect of anisotropy on the evolutions of flow and deformation fields

Advisor: Borja Ronaldo I. (Ronaldo Israel) 
Durlofsky Louis
Linder Christian (Engineering professor)