Modified G-Function and Double-Logarithmic Pressure Analysis for Complex Fractures in Volume-Fractured Tight Gas Reservoirs

Accurately assessing fracture complexity and parameter evolution after fracturing is crucial for optimizing stimulation effectiveness in tight gas reservoirs. In such reservoirs, volume fractures often interact with natural fractures, resulting in pressure-dependent changes in fracture compliance and effective fracture area during closure. Based on shut-in pressure analysis, percolation mechanics, and material balance theory, this study develops diagnostic models for naturally fractured, dynamically fractured, and multi-level closure fracture systems, together with corresponding G-function and double-logarithmic interpretations. The proposed framework characterizes fracture-closure behavior through identifiable closure stages, explicitly ordered closure-pressure intervals, and pressure-dependent evolution of fracture compliance and effective fracture area. Sensitivity analyses are conducted to evaluate the influence of key parameters on diagnostic curve responses. A field application using shut-in pressure data from a tight gas well demonstrates that variations in dominant fracture parameters produce distinct concavity or hump features in G-function superimposed pressure-derivative curves. These results indicate that the proposed method provides a structured quantitative diagnostic interpretation of shut-in pressure responses, enabling systematic identification of staged fracture-closure behavior without relying on fitting-based accuracy metrics.