Model for fracture conductivity considering particle size distribution in a proppant monolayer

Abstract

Abstract The formation of a complex supporting fracture network by volume fracturing is the key to the development of unconventional gas reservoirs, such as shale gas reservoirs and coalbed gas reservoirs. It is critical to predict the conductivity of the supporting fractures for the optimal design of volume reconstruction. A large number of narrow fractures exist that are filled with a proppant monolayer in the fracture network. To date, an analytical model for predicting the conductivity of narrow fractures has been established. However, the proppant added in fracturing has a limited particle size distribution range, and the effect of different particle size combinations on the conductivity of narrow fractures remains unclear. Therefore, based on the mechanical contact theory, this study established a prediction model for the conductivity of monolayer-supported fractures with multi-particle size distributions. The results showed that, under the action of closure pressure, the fracture conductivity decreased sharply when proppants with large and small particle sizes were successively embedded in the rock. The higher was the proportion of proppant with a large particle size, the smaller was the sharp decline in conductivity. When the embedding process was stable, the embedding of a small particle size proppant could slow the decline in conductivity. The larger the proppant proportion was, the larger was the residual fracture width. The permeability increased linearly with an increase in the proppant proportion. It was determined that a least desirable proppant particle size ratio exists, which results in the lowest conductivity. With an increase in the large proppant size ratio, the proppant particle size ratio shifts to the right. The choice of proppant with a similar particle size has little effect on the conductivity. On the other hand, mixing with a proppant with a smaller particle size can significantly reduce the conductivity, whereas mixing with a proppant with a larger particle size plays a significant role in the conductivity. The higher the elastic modulus of the rock is, the greater is the conductivity. The findings of this study are expected to assist in the selection of proppant particle sizes in fracturing operations.