Abstract
It is very challenging to simulate unconventional reservoirs efficiently and accurately. Transient flow can last for a long time and sharp solution (pressure, saturation, compositions) gradients are induced because of the severe permeability contrast between fracture and matrix. Although high-resolution models for well and fracture are required to achieve adequate resolution, they are computationally too demanding for practical field models with many stages of hydraulic fracture. The paper aims to innovate localization strategies that take advantage of locality on timestep and Newton iteration levels. The strategies readily accommodate to complicated flow mechanisms and multiscale fracture networks in unconventional reservoirs.
Large simulation speed-up can be obtained if performing localized computations only for the solution regions that will change. We develop an a-priori method to exploit the locality, based on the diffusive character of the Newton updates of pressure. The method makes adequate estimate of the active computational gridblock for the next iterate. The active gridblock set marks the ones need to be solved, and then the solution to local linear system is accordingly computed.
Fully Implicit Scheme is used for time discretization. We study several challenging multi-phase and compositional model cases with explicit fractures. The test results demonstrate that significant solution locality of variables exist on timestep and iteration levels. A nonlinear solution update usually has sparsity, and the nonlinear convergence is restricted by a limited fraction of the simulation model. Through aggressive localization, the proposed methods can prevent overly conservative estimate, and thus achieve significant computational speedup. In comparison to a standard Newton method, the novel solver techniques achieve greatly improved solving efficiency. Furthermore, the Newton convergence exhibits no degradation, and there is no impact on the solution accuracy.
Previous works in the literature largely relate to the meshing aspect that accommodates to horizontal wells and hydraulic fractures. We instead develop new nonlinear strategies to perform localization. In particular, the adaptive DD method produces proper domain partitions according to the fluid flow and nonlinear updates. This results in an effective strategy that maintains solution accuracy and convergence behavior.
Compositional Distributional Semantics with Syntactic Dependencies and Selectional Preferences
