Multiscale simulation of fractured reservoirs (FracSim)

The goal of this project is to advance simulation techniques for flows in fractured media by addressing issues related to both disparate length scales and uncertainty in fracture parameters.  Three main challenges are specified to be addressed specifically.

1. Multi-level discretizations for flow in fractured media: The main
characteristic of a fractured medium is the span in length scales involved, with fracture lengths spanning from the millimeter scale to the length of the reservoir. Fracture apertures are on the micro to millimeter scale, i.e. orders of magnitude smaller than the fracture length. The starting point for our numerical framework is a discrete fracture-matrix model, which accurately represents flow in both fractures and the matrix. A hierarchy of coarse grids is constructed by successive stages of upscaling. The coarsening is based on the multiscale finite volume method and adapted to the fractures that dominate flow on the coarse scale. We apply an inexact linear solver with the crucial property that all approximated solutions provide conservative flux fields. We will use this multi-level formulation to study the relationship between accuracy and the degree of coarsening, and to develop guidelines for the construction of multi-level simulation models in fractured media. In addition, we will further establish the suitability of inexact solvers tailored for flow in fractured media.

2. Simulation with uncertainty dependent accuracy: Ensembles of  
simulations based on realizations of the fracture network are commonly employed to estimate the impact of uncertainty in fracture properties and the range of possible outcomes for a production scenario. Due to uncertainty in the physical parameters, the accuracy in the simulation and consequently the computational cost can be reduced without affecting the quality of the forecasts. We will study how to terminate the linear solver when the error associated with parameter uncertainty is the main contributor to inaccuracy rather than the linear solver error. This approach is made possible by the design of our inexact solver, which ensures that the flux approximations are conservative, and thus do not provoke instabilities in the transport solver.

3.  Upscaling of fluid transport: Upscaled transport methods that
provide decent approximations to both flow in the fracture and the interaction between fractures and the surrounding matrix are key to estimating the sweep efficiency during production. Initial investigations indicate that hierarchy of discretizations offers an attractive alternative. To investigate reliable for realistic problems we will explore several themes. Fracture specific flow indicators will be developed to improve the quality of the coarse grids. We will investigate the possibilities of dynamic transport grids with high resolution in high-flow regions. Also, we will develop guidelines for upscaling in regimes dominated by capillary forces and by advective forces, respectively.

Publication:

Incorporating Geological Uncertainty in Error Control for Linear Solvers, A. Nissen, P. Pettersson, E. Keilegavlen, J. Nordbotten, SPE 173272-MS