Rough discrete fracture network multi-parameter joint modeling based on improved neural spline flow

Discrete fracture network (DFN) modeling is a popular method for studying reservoir characteristics. However, on one hand of the existing DFN studies, the correlations that may exist among the multi-dimensional parameters of the fracture (dip, dip direction, trace length, aperture, and roughness) were ignored and each property was estimated independently. On the other hand, the 3D DFN models were simplified as flats without roughness. Therefore, this study proposes a simulation method for the rough discrete fracture network while considering multi-parameter joint distribution to make up for the stated deficiencies: (1) An improved deep learning model for the joint distribution estimation and joint sampling of the multi-dimensional parameters of the fracture is proposed, which is the Neural Spline Flow improved by the Multimodal Distribution (NSF-MD). The initial distribution of the Neural Spline Flow (NSF) is improved from a unimodal Gaussian to a multimodal mixed Gaussian, which enhances the fitting ability of the NSF model for the multimodal joint distribution. (2) A modeling assumption of the 3D rough fracture surface is presented to improve the conventional flat ones. In this way, a 3D rough fracture surface is generated by the NURBS tensor product of the fractal traces, and the fractal trace is simulated parametrically based on the fractal dimension. Finally, an outcrop DFN modeling application from southwest China indicates that the NSF-MD can simulate the correlations among the fracture multi-dimensional parameters and that the 3D rough discrete fracture network model (RDFN) increases the representation of the fracture roughness. The Wasserstein distance, which is an indicator quantifying the accuracy of the joint multi-parameter estimation, of the NSF-MD model was 72.4% and 81.9% better than that of the NSF model and that of the conventional method with parameters estimated independently, respectively. The relative distance error (RDE) and the global angle error (GAE) of the fractal traces were 87.9% and 88.3% more accurate than those of the conventional linear traces, respectively.