Pressure Transient and Production Analysis of Fractured Vertical Wells in Tight Sand Gas Reservoirs Considering Threshold Pressure Gradient, Phase-Change Phenomenon, and Stress Sensitivity

The productivity and pressure response of the tight sand gas wells are influenced by multiple flow mechanisms, such as threshold pressure gradient, phase-change phenomena, and stress sensitivity. Understanding the sensitivity of these factors is crucial for the effective development of tight sand gas reservoirs. This study aims to clarify the sensitivity of various factors affecting the productivity and pressure response of tight sand gas wells. Based on the percolation theory of tight sand gas reservoirs, we considered stress sensitivity, threshold pressure gradient, and phase-change phenomena to derive an unsteady mathematical model of a fractured well with an infinite boundary, and a point source solution was obtained. The proposed model was solved using series function properties, variable substitution, perturbation technique, Poisson superposition formula, Laplace transform, and numerical inversion. The influence of several important parameters on pressure response and productivity is discussed in detail. The results show that the threshold pressure gradient, stress sensitivity, and skin factor significantly impact gas well production and pressure response, while the wellbore storage effect and phase-change effect primarily affect the initial production and pressure response, having little effect on the cumulative gas production. The proposed model can estimate the influence of the threshold pressure gradient and stress sensitivity on productivity and pressure, providing a guide for the development of technical measures for fractured wells in tight sand gas reservoirs.