A fixed-stress split for the simulation of coupled pore-scale flow and grain mechanics

Abstract:

The study of coupled flow and mechanics is important in many fields of science and engineering, including the assessment of surface subsidence from groundwater extraction, induced seismicity from wastewater injection or geothermal energy production, and hydraulic fracturing. These coupled flow-geomechanics processes are usually modeled using a continuum macroscopic description such as Biot’s theory of poroelasticity and its extensions to poroplasticity and multiphase flow. Two general strategies exist for the solution of the coupled field equations: simultaneous solution methods, and sequential iterative methods. Upon convergence, both strategies solve the fully coupled problem. An important contribution to the applicability of sequential schemes was the development of the fixed-stress operator split [1], where the flow subproblem is solved by holding the volumetric stress rate constant—a scheme that has been shown to be unconditionally stable and convergent [1].

This development at the continuum scale sheds light on the flow-mechanics coupling at the pore scale. Motivated by processes involving the emergence of fracture in granular systems under different conditions of confinement and wettability, we are interested in fully coupled approaches to flow and mechanics based on discrete element modeling (DEM) of grain mechanics and pore network modeling (PNM) of flow. Previous research has shown that it is notoriously difficult to implement the fully-coupled poromechanics simulation in DEM-PNM; the mismatch in the characteristic time scales of fluid flow and grain mechanics (typically several orders of magnitude) poses a big challenge for time stepping.

Here, we devise a fixed-stress operator split for DEM-PNM and demonstrate its stability and efficiency. We employ this novel scheme to simulate fluid injection into a saturated granular pack consisting of a monolayer of spherical particles, and illustrate the ability of the method to reproduce the deformation patterns (cavity expansion and fracturing) observed experimentally.

[1] Kim, J., Tchelepi, H. A., & Juanes, R. (2011). Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits. Computer Methods in Applied Mechanics and Engineering, 200(13-16), 1591-1606.