Productivity model for multi-fractured horizontal wells accounting for cross-scale flow of gas and total factor characteristics of fractures

Abstract

Fractured horizontal wells are widely utilized to develop tight gas reservoirs. Accurate productivity prediction of horizontal wells intercepted by complex hydraulically induced fractures is highly challenging due to fracture branching, bending, extending, and reversing in tight rock formations. Accounting for complex tree-shaped fracture geometries in reservoirs, this study proposes a cross-scale model of gas flows from the matrix to fractures. Using the proposed framework, the well productivity can be calculated in fractured gas reservoirs with any pore size and a fracture-controlled unit. The novelty of this study is that the total factor characteristics of fractures (i.e., length ratio a, width ratio b, branching angle θ, and branching level n), pressure drop coupling between the reservoir and fracture, and gas flow regime in different scale channels can be perfectly considered in the proposed model, from which the key contributions to well productivity are derived. Subsequently, the validity of the proposed cross-scale model is evaluated in comparison with the results of Ning et al. model and field well testing. The characteristic length L0,i, fracture effective width wf, stimulated reservoir volume Vf, fracture pressure pf, pressure gradient Gf, effective permeability kf and flow conductivity Cf of tree-shaped fractures are derived using the proposed model. The results show that the well productivity is jointly determined by Gf and Cf. Moreover, the well productivity mostly depends on a and n, and it is little influenced by b. In contrast, it is almost unaffected by θ. Compared to a straight fracture, a tree-shaped fracture with characteristic parameters of a=0.9 and n=3 can dramatically enhance the productivity by 32 % (b=0.5; θ=30°). In contrast, a tree-shaped fracture slightly increases the productivity by only 3 % when b increases from 0.1 to 0.9 (a=0.2; θ=30°; n=3). Furthermore, when θ is increased from 0° to 90°, the productivity of a well with a tree-shaped fracture decreases by 3 % (a=0.2; b=0.6; n=3). Hence, the study findings will contribute to the exploitation of tight gas reservoirs.