Pore-Scale Level Set Simulations of Capillary-Controlled Displacement with Adaptive Mesh Refinement
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Multiphase flow simulations on imaged porous rock structures require numerical methods that are accurate and robust when applied on complex geometries. A key element in this context is to investigate how simulations behave under grid refinement. In this work, we couple an existing software for structured adaptive mesh refinement (AMR) and parallelism to a previously developed level set method for capillary-controlled displacement on the pore scale. The level set method accounts for wettability by using different evolution velocities in pore and solid space rather than implementing it as a boundary condition on the pore walls. We perform simulations with up to three nested refinement levels on idealized pore geometries to validate the AMR technology. Based on simulations, we identify suitable cell refinement criteria for our applications. We demonstrate effects of AMR in simulations relevant for drainage in porous media, such as in the computation of capillary entry pressures in pore throats with different shapes and wetting states, and obtain excellent agreement with analytic results. Finally, we investigate the effects of AMR during simulation of quasi-static drainage on sandstone. The comparison of capillary equilibrium fluid configurations, capillary pressure, and specific fluid/fluid interfacial area–saturation relationships for drainage with and without AMR shows differences that diminish for less water-wet states. The general behavior is that the capillary pressure and interfacial area for a given saturation increase in simulations with AMR. The largest deviation occurs for small water saturations, suggesting AMR can be an important component in simulation tools to describe more accurately capillary behavior in the low water saturation regime where interface curvature is high.
KeywordsAdaptive mesh refinement Level set method Capillary pressure Wettability Rock image
Financial support was provided by the Research Council of Norway under Petromaks2 project 234131/E30 “Three-phase capillary pressure, hysteresis, and trapping in mixed-wet rock” and ConocoPhillips through the research center COREC. Maša Prodanović acknowledges support from NSF EAR CAREER Grant 1255622. The computations (Sects. 4–6) were performed on resources provided by UNINETT Sigma2—the National Infrastructure for High Performance Computing and Data Storage in Norway. We acknowledge PRACE for awarding us access to MareNostrum 4 at Barcelona Supercomputing Center (BSC), Spain, which made it possible to explore scaling behavior of our code with a large number of CPUs (Appendix A). Rahul Verma (UT Austin) provided the sphere pack pore geometry files used in Sect. 5.1.
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