A unified approach to simulation and upscaling of single-phase flow through vuggy carbonates
Numerical modeling of flow through vuggy porous media, mainly vuggy carbonates, is a challenging endeavor. Firstly, because the presence of vugs can significantly alter the effective porosity and permeability of the medium. Secondly, because of the co-existence of porous and free flow regions within the medium and the uncertainties in defining the exact boundary between them. Traditionally, such heterogeneous systems are modeled by the coupled DarcyStokes equations. However, numerical modeling of flow through vuggy porous media using coupled DarcyStokes equations poses several numerical challenges particularly with respect to specification of correct interface condition between the porous and free-flow regions. Hence, an alternative method, a more unified approach for modeling flows through vuggy porous media, the StokesBrinkman model, is proposed here. It is a single equation model with variable coefficients, which can be used for both porous and free-flow regions. This also makes the requirement for interface condition redundant. Thus, there is an obvious benefit of using the StokesBrinkman equation, which can be reduced to Stokes or Darcy equation by the appropriate choice of parameters. At the same time, the StokesBrinkman equation provides a smooth transition between porous and free-flow region, thereby taking care of the associated uncertainties. A numerical treatment for upscaling StokesBrinkman model is presented as an approach to use StokesBrinkman model for multi-phase flow. Numerical upscaling methodology is validated by analyzing the error norm for numerical pressure convergence. StokesBrinkman single equation model is tested on a series of realistic data sets, and the results are compared with traditional coupled DarcyStokes model. Copyright (C) 2011 John Wiley & Sons, Ltd.
vugs carbonate heterogeneity stokes-brinkman stokes-darcy numerical simulation porous medium vuggy porosity darcy's law upscaling and numerical convergence