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

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