Fast and robust scheme for uncertainty quantification in naturally fractured reservoirs

Abstract

The main objective of this study is to perform Uncertainty Quantification (UQ) using a detailed representation of fractured reservoirs. This is achieved by creating a simplified representation of the fracture network while preserving the main characteristics of the high-fidelity model. We include information at different scales in the UQ workflow which allows for a large reduction in the computational time while converging to the high-fidelity full ensemble statistics. Ultimately, it allows us to make accurate predictions on geothermal energy production in highly heterogeneous fractured porous media. The numerical reservoir simulation tool we use in this work is the Delft Advanced Research Terra Simulator (DARTS). It is based on Finite Volume approximation in space, fully coupled explicit approximation in time, and uses the novel linearization technique called Operator-Based Linearization (OBL) for the system of discretized nonlinear governing equations. We use a fracture network generation algorithm that uses distributions for length, angles, size of fracture sets, and connectivity as its main input. This allows us to generate a large number of complex fracture networks at the reservoir scale. We developed a pre-processing algorithm to simplify the fracture network and use graph theory to analyze the connectivity before and after pre-processing. Furthermore, we use metric space modeling methods for statistical analysis. A robust coarsening method for the Discrete Fracture Matrix model (DFM) is developed which allows for great control over the degree of simplification of the network’s topology and connectivity. We apply the framework to modeling of geothermal energy extraction. The pre-processing algorithm allows for a hierarchical representation of the fracture network, which in turn is utilized in the reduced UQ methodology. The reduced UQ workflow uses the coarser representation of the fracture networks to partition/rank the high-fidelity parameter space. Then a small subset of high-fidelity models is chosen to represent the full ensemble statistics. Hereby, the computational time of the UQ is reduced by two/three orders of magnitude, while converging to similar statistics as the high-fidelity full ensemble statistics. The methods developed in this study are part of a larger project on a prediction of energy production from carboniferous carbonates. The final goal is to perform UQ in pre-salt reservoirs which are characterized by complex reservoir architecture (i.e., large karstification and fracture networks). The UQ of fractured reservoirs is typically done in the petroleum industry using effective media models. We present a methodology that can efficiently handle a large ensemble of DFM models, which represent complex fracture networks and allow for making decisions under uncertainty using more detailed high-resolution numerical models.