Effects of uneven proppant distribution in multiple clusters of fractures on fracture conductivity in unconventional hydrocarbon exploitation

During the unconventional hydrocarbon development, the irregular shaping and uneven sand concentration of proppants banks in the staged multi-cluster fracturing of horizontal wells are key factors determining the fracture conductivity and post-fractured well productivity. To compensate for the limitation of small-scale sand filled core conductivity research that cannot accurately reflect the fracture conductivity at the field scale, this study used the mixture model to investigate the proppant distribution in fractures after sand carrying fluid enters the multi-cluster fractures from a horizontal well section, and divided the fractures into several regions based on different sand concentration ranges inside hydraulic fractures. The mechanical parameters and permeability of the sand embankment in each region were regressed to the entire fracture. The closure and conductivity of field-scale fractures with non-uniform sand filled were studied using elastic mechanics theory and free and porous media flow theory. Effects of fracture width and height on the conductivity of field-scale fractures were analyzed. The results indicate that reducing the fracture width, from 10 to 6 mm, and fracture height, from 12 to 6 m, can increase the proportion of fracture areas with sand concentration from 12 to 15%; Configurations of areas with different sand concentrations in fractures are irregular, and some areas without proppant filling can be closed under the closure pressure of 70 MPa, causing the surrounded sand filling areas to fail providing flowing paths; Sand banks with proppant concentration between 0 and 6% at the top part of the fracture can provide a more permeable flow channel than the bottom part during the initial closure of the fracture. While sand banks with proppant concentration between 12 and 15% at the bottom of the fracture can maintain a higher permeability than the top part when the closure pressure reaches 70 MPa; Reducing the width and height of the fracture can still maintain a larger fracture width when the closure pressure exceeds 60 MPa.