Theoretical conductivity analysis of surface modification agent treated proppant

Proppant embedment plays a significant role in conductivity decreasing, especially for weakly consolidated sandstones, shale and coal beds. Surface modification agent (SMA) is widely used in decreasing proppant embedment and proppant crush, increasing proppant cohesive force and long term conductivity. In this study, analytical models are derived to compute SMA treated proppant embedment and fracture conductivity. A model based on coefficient adjustment is established to match the conductivity and embedment of SMA treated proppant. Application results of this method to matching fracture stabilizer treated fracture conductivity are reasonable. Visco-elastic model is adopted to predict proppant embedment and fracture conductivity. Properties of fracture filled with visco-elastic proppant is also studied, it will take a relatively long time for conductivity to reach a steady state after fracturing. With the increase of proppant viscosity, more time will be needed for conductivity to reach a steady state. Conductivity variation increases with the increase of closure pressure. There are nearly no effect of formation rock viscosity on fracture conductivity.