Adaptive Numerical Homogenization for Upscaling Single Phase Flow & Transport

This poster presents an adaptive multiscale approach to improve the efficiency and the accuracy of numerical computations by combining upscaling and domain decomposition methods. The key objective of this research work is to develop upscaling approaches to minimize the use of fine scale information for time varying initial and boundary conditions. This includes changes in well parameter such as injection composition and specifications as well as in situ or initial conditions. A fine scale Darcy’s flow and transport problem is solved only in specific subdomains while solving a coarse scale problem in the rest of the domain. This involves special treatment of sharp interfaces associated with the transport equations. We define transient regions as subdomains where spatial changes in concentration are significant. Away from the transient regions, upscaling is performed locally by using a numerical homogenization to obtain effective equations at the macroscopic scale. A fine grid is then used in the transient regions and a coarse grid everywhere else resulting in a non-matching multi-block problem. We use the Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition approach to couple the coarse and fine subdomains. A number of numerical tests are also presented for verifying and demonstrating the capability of the adaptive numerical homogenization approach in upscaling flow and transport in porous medium. The numerical results on different layers of SPE10 also indicate that an upscaling based solely upon numerical homogenization is in good agreement with the fine scale solution for a Gaussian or periodic permeability distribution. An optimal tolerance for the adaptivity criteria is chosen to reduce computational cost without substantial loss in solution accuracy.