A Mathematical Model for Estimating Fracture Permeability with Invasion Damage of Formation Sand

Fracture packing is a well-known completion technique used in the hydraulic fracturing of low-permeability reservoirs. As much as fracture packs are very effective, the proppant-pack permeability damage formed from particle intrusion reduces that effectiveness because it causes low well productivity. It is important to address the issue of permeability damage caused by formation-particle intrusion. An analytical model was developed in this study to predict the permeability of proppant packs in hydraulic fractures with consideration of different levels of invasion damage of formation sand. The accuracy of the model was verified by model comparison with data from the Eagle Ford Shale field. The model result shows that for the Eagle Ford field and the corresponding proppant size used, three blocking levels were achieved that correspond to high proppant-pack permeability. Three case studies were considered in this study: California sand, Gulf Coast sand, and South China Sea silt. The proppant-pack permeability damage was calculated using the analytical model for three levels of invasion for all case studies. The results from applying the analytical model on the three case studies showed the amount of invasion that is possible in each sand according to the proppant size used. The level of invasion is a factor of the sand distribution and the initial proppant size chosen. More analysis showed that for two of the case studies, only Levels 1 and 2 blockings can develop, while for the last case study, three blocking levels considered can develop. This study, for the first time, gives an insight into how selecting the optimal proppant size can improve sand-control performance while enhancing fracture conductivity.