Calibrate complex fracture model for subsurface flow based on Bayesian formulation

Abstract

In practical development of unconventional reservoirs, fracture networks are a highly conductive transport media for subsurface fluid flow. Therefore, it is crucial to clearly determine the fracture properties used in production forecast. However, it is different to calibrate the properties of fracture networks because it is an inverse problem with multi-patterns and highcomplexity of fracture distribution and inherent defect of multiplicity of solution. In this paper, in order to solve the problem, the complex fracture model is divided into two sub-systems, namely "Pattern A" and "Pattern B." In addition, the generation method is grouped into two categories. Firstly, we construct each sub-system based on the probability density function of the fracture properties. Secondly, we recombine the sub-systems into an integral complex fracture system. Based on the generation mechanism, the estimation of the complex fracture from dynamic performance and observation data can be solved as an inverse problem. In this study, the Bayesian formulation is used to quantify the uncertainty of fracture properties. To minimize observation data misfit immediately as it occurs, we optimize the updated properties by a simultaneous perturbation stochastic algorithm which requires only two measurements of the loss function. In numerical experiments, we firstly visualize that small-scale fractures significantly contribute to the flow simulation. Then, we demonstrate the suitability and effectiveness of the Bayesian formulation for calibrating the complex fracture model in the following simulation.