Stress-strain response of hydrate-bearing sands: Numerical study using discrete element method simulations

Gas hydrate is a crystalline solid found within marine and subpermafrost sediments. While the presence of hydrates can have a profound effect on sediment properties, the stress-strain behavior of hydrate-bearing sediments is poorly understood due to inherent limitations in laboratory testing. In this study, we use numerical simulations to improve our understanding of the mechanical behavior of hydrate-bearing sands. The hydrate mass is simulated as either small randomly distributed bonded grains or as "ripened hydrate" forming patchy saturation, whereby sediment clusters with 100% pore-filled hydrate saturation are distributed within a hydrate-free sediment. Simulation results reveal that reduced sand porosity and higher hydrate saturation cause an increase in stiffness, strength, and dilative tendency, and the critical state line shifts toward higher void ratio and higher shear strength. In particular, the critical state friction angle increases in sands with patchy saturation, while the apparent cohesion is affected the most when the hydrate mass is distributed in pores. Sediments with patchy hydrate distribution exhibit a slightly lower strength than sediments with randomly distributed hydrate. Finally, hydrate dissociation under drained conditions leads to volume contraction and/or stress relaxation, and pronounced shear strains can develop if the hydrate-bearing sand is subjected to deviatoric loading during dissociation.

Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.