A new mechanistic model for conductivity of hydraulic fractures with proppants embedment and compaction

To extract unconventional energy more efficiently, the hydraulic fracturing technology is widely used to create fracture network in formations and facilitate the transport of hydrocarbons to production wells. Nevertheless, fracture conductivity decreases sharply and continuously due to the increase of closure pressure (or effective stress). It is a challenging problem to maintain fracture conductivity and reduce the conductivity change rate during extraction. Therefore, it is of great significance to predict the behavior of proppant embedment and compaction within hydraulic fractures. The objective of this work is to establish a reasonable model to determine the essential controls on conductivity of hydraulic fractures (conventional fracturing and channel fracturing) under stress conditions. Compared with other models, our analytical model is not limited to elastic deformation of proppants but takes elastoplastic deformation and fully plastic deformation of proppants into account. In addition, the model also considers proppant compaction (body deformation and structural deformation) besides proppant embedment. The predictions from the proposed model agree well with the available experimental data presented in the literature. The results show that the conductivity curves can be characterized by six stages: elastic embedment and elastic compaction stage, elastoplastic embedment and elastic compaction stage, plastic embedment and elastic compaction stage (including body deformation and structural deformation of proppant packs), plastic embedment and elastic compaction stage (only containing body deformation of proppant packs), plastic embedment and elastoplastic compaction stage, plastic embedment and plastic compaction stage. Although the proppant compaction depth is smaller than the proppant embedment depth, the change of conductivity due to proppant compaction cannot be ignored. Specifically, for the studied case, the change of conductivity due to proppant compaction is larger than that due to proppant embedment during the stages 2-6. Compared to the change of conductivity in harder rocks with larger elastic modulus, conductivity changes more dramatically in softer rocks with lower hardness. To reduce the rate of conductivity change, proppants with lager elastic modulus and larger size are recommended in the field. This work presents an accurate and efficient analytical model to quantify the conductivity of hydraulic fracture under stress condition. The proposed model reveals more details of the mechanisms that affect the deformation behavior in hydraulic fractures and offer some insights for parameter design and optimization during the execution of hydraulic fracturing.

Automated summary

This work establishes a reasonable model to determine the essential controls on the conductivity of hydraulic fractures under stress conditions, showing conductivity curves characterized by six stages and emphasizing the importance of proppant compaction in conductivity changes.