Analytical model for fracture conductivity with multiple particle sizes and creep deformation

Abstract

The prediction of fracture conductivity in shale reservoirs is necessary for hydraulic fracturing optimization. However, problems remain with the prediction of fracture conductivity in shale reservoirs. Shale exhibits creep deformation behavior. In addition, due to the combination of large and small particle sizes, proppant, and discontinuous distribution fractures, it is challenging to establish an embedment and fracture conductivity model that combines the creep factor and multiple particle sizes.Based on the authors’ previous work, the modified Burgers creep model was introduced into the discontinuous embedment model for multiple particle sizes, and then combined with the KC equation for multiple particle sizes to develop an embedment depth and conductivity prediction model under the conditions of creep and discontinuous distribution of multiple-particle-size proppants.The results showed that the creep time increased from 10 d to 100 d, and the critical closure pressure of the minimum particle size proppant embedded in the rock decreased from 36 MPa to 14 MPa. The closure pressure increased from 20 MPa to 40 MPa, and the critical creep time of the minimum particle size proppant embedded in the rock decreased from 30 d to 12 d. Under the condition of two-particle-size proppant combinations, there is a proppant combination ratio that minimizes the fracture conductivity, which was approximately 0.2 in this study. The longer the creep time, the greater the optimal proppant distance coefficient. The greater the viscosity of the rock and proppant, the smaller the optimal proppant distance coefficient. These research results provide a theoretical basis for optimizing the local conductivity of secondary fractures in shale reservoirs.