Study on Conductivity Considering Proppant Crushing - Compensation Based on Population Balance Theory

This study developed a model for predicting the conductivity of propped fractures in low-permeability tight oil and gas reservoirs, which integrates elasto-plastic mechanics and the principle of population balance. The calculation is based on the porosity, tortuosity, specific surface area, and elastic embedment of the proppant conductive layer. It comprehensively considers the impact of the compensation mass fraction rate after proppant crushing and the dynamic equilibrium between particles and fractures, so as to predict the long-term maintained conductivity of the propped fractures. The results show that: Proppant crushing has a significant impact on conductivity. Large particle size proppants can enhance conductivity under low closure stress, but are prone to crushing under high closure pressure, leading to pore throat blockage and a significant reduction in conductivity. Crushed proppants will compensate to smaller particle size ranges, which helps to maintain the long-term conductivity of the fractures. Under high closure stress, the rate of proppant crushing mass fraction increases, and the degree of conductivity reduction increases. The smaller the fracture width, the less obvious the trend of conductivity decreasing with increasing closure stress. This model provides a scientific basis for the accurate prediction and optimization of the conductivity of propped fractures.