An Efficient Complex Fracture Network Inversion Method Through Adaptative Particle Filter Based on Quadratic Programming for 3D Shale Oil Reservoir
Authors: Zhao Guoxiang , Lu Hongjun , Qi Yin , Ni Qiang , Chen Wenbin , Tao Liang , Zhang Tongwu , Xian Chen , Adenutsi Caspar Daniel , Liu Qi 
Published: August 2024

ABSTRACT:
Volume fracturing is an important means to achieve efficient development of shale reservoirs. However, the complexity of the seepage process in shale oil reservoirs due to the distribution characteristics of fracture networks makes the fracture network and reservoir parameter characterization significantly a non-linearity and non-Gaussianity problem. This limits the application of traditional automatic history matching methods. In order to balance the computational efficiency and inversion accuracy, an efficient and high-precision complex fracture network inversion method that can sample from a reconstructed continuous posterior probability density distribution adaptatively is established in this work. A reference model is established to validate the practicality of the proposed method. It was found that: (a) the real posterior probability density distribution with complex non-Gaussian multimodal distribution can be reconstructed effectively by solving a convex Quadratic programming problem so that the inversion accuracy is guaranteed and the uncertainty of each parameter to be fitted can be quantified. (b) the required number of particles at each iterative step can be adjusted according to the filter accuracy so that the computational effort is reduced significantly and the disadvantage of determining the number of particles required for different problems in standard particle filter is avoided. (c) the main features and statistical characteristics of the fracture distribution can be characterized and the effective inversion results of the reference model can be obtained. (d) the proposed method has the potential to be applied in more complex inversion problems such as the inversion problems of multiphase and multi well.

1. INTRODUCTION
Shale oil reservoirs are widely distributed and play an important role in the world energy supply chain (Yi et al., 2022; Zou et al., 2013; Liu et al., 2023). Due to the fact that these type of reservoirs are limited by complex pore structure and ultralow permeability of the shale matrix as compared to conventional reservoirs, a practical and cost-effective method commonly employed in developing shale oil reservoirs is the volume fracturing technique(He et al., 2020; Chen et al., 2021; Wu et al., 2021; Zhao et al., 2023). The complex fracture networks generated by volume fracturing have complex distribution characteristics which is difficult to accurately and directly characterize. This is due to the strong heterogeneity of the formation and the commonly developed natural fractures. This leads to high uncertainties of established numerical models which are formulated stochastically with the information of the input parameters of the model obtained mostly by indirect methods (Xue et al., 2020). Moreover, the lack of accurate estimation of reservoir physical parameters and fracture network characterization parameters bring more risks to the formulation of reasonable development plans for the volume fracturing of shale oil reservoirs. Meanwhile, the complex fracture geometry coupled with significant differences in permeability between the matrix and fracture systems may pose special challenges. Therefore, establishing an accurate, efficient, and applicable method for complex fracture network inversion in volume fractured shale reservoirs remains a challenging issue.