Modeling Production Decline for Fractured Wells with Non-Uniform Fracture Properties: A Semi-Analytical Approach Based on Double-Segment Fracture Model

Hydraulic fracturing operations can create complex fractures with spatiotemporal variations that significantly affect the transient rate performance of fractured wells. To address such heterogeneous fracture characteristics, the double-segment fracture model was adopted, allowing for distinct fracture conductivity and permeability modulus assignments to each fracture segment. A novel semi-analytical model was developed, validated, and applied to investigate the influence of non-uniform fracture properties on transient rate behavior for fractured wells. More specifically, the slab source function method and finite difference method were applied to solve the fluid flow problems in the matrix and fracture subsystems, respectively. The nonlinearity caused by the pressure-dependent fracture conductivity was tackled by the iteration method. Additionally, production type curves were constructed to assess the impact of non-uniform fracture properties on transient rate behavior. It is found that the fracture conductivity and stress-sensitivity of the fracture segment near the wellbore (FSNW) have a more significant impact on the well production rate than those of the fracture segment near the fracture tip (FSNT). As the fracture conductivity near the wellbore decreases, the production rate decreases correspondingly, whereas the fracture conductivity near the fracture tip has a negligible influence on the transient rate when fracture conductivity exceeds 10. The length of the fracture segment similarly affects the transient rate behavior, where longer high-conductivity fracture segments are associated with higher production rates. The stress-sensitivity of the FSNW greatly affects the transient rate, where higher stress-sensitivity levels result in a lower production rate. In contrast, the effect of stress-sensitivity of the FSNT on the transient rate can be neglected. The results and findings obtained in this work can help us analyze the practical production rate curves with more accurate approaches, thereby obtaining more reasonable and reliable estimation results of the fracture properties.