Investigation into a perfect matching between fracture transfer performance and vertical well productivity based on multi-scale and total factor characteristic models

Abstract

In fractured tight gas reservoirs, complex hydraulically induced fracture networks determine fluid flowing abilities of reservoirs. Thus, characterizing the complex fracture networks and revealing fracture transfer performances become a challenging work because of fracture branching, bending, and reversing in fractured reservoirs. In this paper, a fractal-like tree-shaped fracture model for gas transfer is proposed to optimize flow conductivity, pressure distribution at fracture intersection points, and flow transfer in such a complex fracture network considering the multi-scale effect, and total factor characteristics, including the length ratio, width ratio, branching angle, and branching level. The model is implemented to conduct validation against the experiment data in the literature. Subsequently, applying the proposed fracture model, the productivity equation for a vertical gas well intercepted by the fractal-like tree-shaped fracture network is further formulated. In addition, the good match with productivity simulation validates the accuracy of the developed productivity model for a vertical gas well. As a result, the impacts of the Knudsen number, fracture total factor characteristics, reservoir parameters, etc. on fracture transfer performances and well productivity are examined using the two proposed models. The results demonstrate that optimum fracture transfer performances do not match with the maximum well productivity. In contrast, the well productivity is jointly determined by both inlet flow volume of the fracture network and matrix permeability. Hence, a new formula considering both fracture characteristics and reservoir properties is proposed to match with the optimum fracture total length and maximum well productivity, thereby contributing to high-efficient and economic exploration of tight gas reservoirs.