Heterogeneous Reservoir Models: Local Refinement and Effective Parameters

Abstract

Heterogeneous porous media are generally characterized by many scales of variations. A methodology is required for transporting information from one scale to another. Also, grid refinement techniques require that we are able to assign effective permeabilities on grid-blocks of different sizes. Recently, methods for calculating effective permeabilities on blocks of arbitrary size have been developed for models in groundwater-flow. We have extended these methods to a two-phase model, where a new dispersion coefficient is derived. Based on operator-splitting techniques and adaptive grid-refinement, we have developed a discretization strategy able to resolve local phenomena in space and time. The solution procedure includes the concept of domain decomposition where the global solution is constructed from local computations on sub-domains. This approach allows the resolution and even the entire solution strategy to depend on local properties of the model. The algorithm is well suited for parallel computer architectures as well as integration into existing large scale simulators. In the present paper these techniques are tested for heterogeneous, two-dimensional two-phase models. Numerical experiments based on fine-scale discretization are compared with the results from the calculation based on averaged equations.

Upscaling of Biological Processes and Multiphase Flow in Highly Heterogeneous Media

“…We have positive experience with self-adaptive local grid refinement methods [19,17,55,62,70], coupled with local time-stepping techniques [59,52,60,61] and we have implemented and tested a fully adaptive refinement technique for general 3-D steady-state problems [97]. See also [2, 12-14,50, 103, 104].…”

Methods in Oil Recovery Processes and Reservoir Simulation

“…Nevertheless, at low Peclet numbers (Pe < 10) both dispersitivies are of the same order of magnitude [75]- [77]. Dispersion can represent small scale movements not captured by the REV used in the mathematical model, but according to Heimsund [28], taking this into account in the numerical model may be troublesome [78] [79]. It is worth mentioning that some numerical schemes, especially first order methods (see point 3.2), add artificial diffusion which is most of the times far greater than the physical dispersion discussed here.…”