Energetic Formulation of Large-Deformation Poroelasticity

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy-based continuum mechanics framework to model large-deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas-liquid phase-changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data-driven models in a Bayesian framework.

Temporal and spatial evolution of deepwater fold thrust belts: Implications for quantifying strain imbalance

Deepwater fold and thrust belts (DWFTBs) occur in a large number of active and passive continental margins, and their occurrence play an important role in controlling the structural configuration and stratigraphic evolution of margins. Although DWFTBs that are located on passive margins are a coupled system, in which updip extension is linked to downdip contraction, many studies have established a significant imbalance between these two domains in favor of net extensional strain. We have sequentially restored a series of parallel sections from the Orange Basin, South Africa, to quantify the amount of extension and contraction along a single collapse system. We found there to be a constant shortfall in the amount of contraction relative to extension in these features, which allowed us to quantify the lateral compaction of the margin as 5%. We also established a temporal model for the development and growth of thin shale detachment gravity collapse structures on passive margins. This model had implications not only for the kinematic and geometric evolution of these systems but also on the geomechanical process involved, in particular the accommodation of strain through compactional processes rather than discrete faulting.