Forward Simulation and Backward Calibration on Fracture Morphology in Shale Formation Based on Finite Element Method and Ensemble Method

Abstract In this paper, a workflow is proposed to investigate fracture morphology in shale formations, integrating two parts: forward simulation and backward calibration. Uncertainty in the forward simulation should be quantified by backward calibration, in order to get the efficient simulation results. The workflow is based on the combination of finite element method and ensemble method. Finite element method is used to establish a forward simulation to study fracture initiation and propagation under the effect of natural fracture. Ensemble method is adopted in the backward calibration process, in order to quantify the uncertain parameters, such as Young's modulus, Poisson's ratio, damage factor of cracks, and horizontal stress contrast, based on injection treatment pressure. Moreover, before the backward calibration, sensitivity analysis is conducted for each type of data misfit to find the most influential parameters. The simulation results indicate that induced hydraulic fractures prefer to propagate along the maximum horizontal stress, forming a bi-wing fracture. Under the effect of natural fractures, two different propagation behaviors, diversion and cross, could be observed, resulting in a tortuous fracture geometry in the shale formation. Sensitivity analysis claims that Young's modulus, Poisson's ratio, and damage factor of cracks are the three main influential parameters for the forward simulation. A set of ensemble models are established based on above three parameters as initial state for the data assimilation algorithm. The injection treatment pressure are matched well after model calibration by ensemble method. The highlights of this workflow: 1) the interaction between induced fractures and natural fractures is involved, resulting in a torturous fracture morphology; 2) model calibration is conducted to reduce and quantify uncertainty; 3) The calibrated fracture model could be used to do production prediction. This workflow provides the theoretical basis for fracture initiation and propagation, but also generates the more reliable fracture morphology for further research.