Optimization of Mathematical Function-Shaped Fracture Distribution Patterns for Multi-Stage Fractured Horizontal Wells

Abstract

A conventional oil and gas well does not have a natural production capacity, which necessitates a hydraulic fracturing operation. The effectiveness of the fracturing directly impacts the economic benefit of a single well. Among the various parameters, including fracture spacing, fracture width, and conductivity, fracture half-length is one of the main influencing factors on the productivity of horizontal wells. For conventional homogeneous reservoirs, research mainly focuses on fracture patterns with equal fracture lengths. However, in actual production processes, due to mutual interference and the superimposition of drainage areas between fractures, the production distribution of each fracture is non-uniform. Typical fracture distribution patterns mainly include uniform, staggered, dumbbell, and spindle. While many believe that the dumbbell-shaped fracture distribution pattern has the best effect, there has been no quantitative study on the length of each fracture under the dumbbell-shaped pattern. Based on this, this paper proposes a modeling approach for function-shaped fracture distribution that takes advantage of the high production of edge fractures and the low output of middle fractures in horizontal wells. The influence of this approach on production capacity is studied. Constant, linear, and parabolic functions are used to establish the relationship between fracture position and fracture half-length, optimizing the fracture distribution function to achieve the best production effect. This method can guide the horizontal well fracture distribution in the block to maximize productivity. The results show that the parabolic function-shaped model is better than the linear function-shaped model and the constant function-shaped model is the least effective. The research presented in this paper offers a new idea for optimizing on-site fracturing plans. It utilizes mathematical expressions to describe the parameters that affect productivity, which provides valuable guidance for designing multi-stage fractured horizontal wells in the field. In the future, this research will be extended by exploring the optimal fracture distribution function under different formation conditions.