DARSim II: ADM
"For real-field applications, the reservoir is heterogeneous, fluid flow and transport are coupled via sequential or fully-implicit formulations, and there are many resolutions to capture! ADM does it all through a general algebraic framework!"
- M. Cusini, C. van Kruijsdijk, H. Hajibeygi: Algebraic dynamic multilevel (ADM) method for fully implicit simulations of multiphase flow in porous media, J Comput. Physics, 314 (2016) 60-79. doi:10.1016/j.jcp.2016.03.007
- M. Cusini, C. van Kruijsdijk, H. Hajibeygi: Algebraic Dynamic Multilevel (ADM) Fully Implicit Method for Multiphase Flow in Heterogeneous Porous Media, 15th European Conference on the Mathematics of Oil Recovery (ECMOR XV), 29 August - 1 September 2016, Amsterdam, Netherlands.
- M. Cusini, B. Fryer, C. van Kruijsdijk, H. Hajibeygi, Algebraic Dynamic Multilevel Method for Compositional Displacements in Heterogeneous Reservoirs with Capillary and Gravitational Effects (C-ADM), SPE RSC, 20-22 Feb 2017, TX, USA.
Algebraic Dynamic Multilevel (ADM) method is developed and being extended as the core development of DARSim II project. ADM extends the formulation, methodology, and applicability of grid refinement strategies for FIM simulations of multiphase flow in homogeneous and heterogeneous subsurface geological formations. It also develops the first multilevel multiscale procedure for FIM (and sequential-coupling) simulations. Starting from the FIM linear system, the ADM hierarchical nested grid resolution is determined on the basis of an error estimate criterion. Once the grid resolution is determined, the FIM system is described on this dynamic multilevel grid by employing sequences of prolongation and restriction operators. More precisely, Rij restricts the system at level i to a system at level j and Pij prolongs (interpolates) the solution from level i to level j. ADM allows for several options for prolongation operator, namely: (1) constant, (2) bilinear and (3) multiscale-based local basis functions. This algebraic formulation allows for direct applicability of ADM for both homogeneous and heterogeneous problems.
In our recent paper, DOI: doi:10.1016/j.jcp.2016.03.007 , the performance of ADM is investigated in detail for homogeneous and heterogeneous test cases. It is shown that only a small fraction of the fine-scale grid cells are enough to provide accurate (compared with reference fine-scale) solutions. ADM can be seen as a significant step forward in the application of DLGR methods, in the sense that it is algebraic, allows for systematic map across different scales, and applicable to heterogeneous test cases without any upscaling of fine-scale high resolution quantities. Also, it is the first multiscale method which allows for obtaining FIM solutions on an arbitrary multilevel grid. Thus, it casts a promising framework for next-generation FIM simulators for multiphase flow in large-scale natural subsurface formations.