Numerical Study on Simultaneous Propagation of Multiple Fractures: A Method to Design Nonuniform Perforation and In-Stage Diversion

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Abstract
Summary: The uneven propagation of multifractures is a key factor restricting production growth due to stress shadow and heterogeneity. To date, limited-entry fracturing techniques, nonuniform perforation, and in-stage diversion have been commonly used to promote even multifracture growth. In this study, a fully coupled multiple pseudo-3D (P3D) fracture simulator has been developed to examine the competitive propagation of multifractures during multicluster fracturing in a horizontal well. The present model considers stress interaction among multiple fractures, perforation erosion, fluid distribution among clusters, and in-stage diversion. The results of the model are validated against the reference data. Using the model, a series of numerical simulations are performed to investigate multifracture propagation with nonuniform perforation and in-stage diversion fracturing. We estimate the value of stress interaction for different fractures and time based on the approximate solution of Perkins-Kern-Nordgren (PKN) fracture in the viscosity-dominated regime and improve the dimensionless parameter that characterizes the competition between stress interaction and perforation friction. The fluid distributes evenly when the dimensionless parameter is less than unity (perforation friction is larger than stress interference). Based on this dimensionless parameter, a method to design nonuniform perforation and in-stage diversion is proposed. Results show that in the case of homogeneous in-stage stress, the perforation parameters should be selected under the condition that the dimensionless parameter is less than unity. In the case of heterogeneous in-stage stress and based on the perforation parameters selected under homogeneous stress conditions, the perforation holes in the high-stress cluster should be increased, making the reduction of perforation friction equal to the value of the in-stage stress heterogeneity. The stress heterogeneity can be balanced by decreasing the perforation friction of the high-stress clusters. In this way, nonuniform perforation under heterogeneous in-stage stress conditions can be designed quantitatively without numerical simulation. For in-stage diversion treatment, a method to design the number of ball sealers is proposed based on the results of nonuniform perforation, and only several or even zero groups of simulation are necessary to find the optimal number of ball sealers. A series of numerical simulations shows that the proposed design method is reliable and achieves a satisfactory result in an actual field case. The results can be helpful for nonuniform perforation and in-stage diversion design for multicluster fracturing in a horizontal well.

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