A general productivity model for optimization of multiple fractures with heterogeneous properties

The principle focus of this work is on developing a general productivity model to fill the gap in simultaneously optimizing multiple hydraulic fractures with different properties in heterogeneous spaced fracture configuration. Based on the instantaneous point source solutions, a rigorous mathematical model is established by coupling reservoir flow model with fracture flow model in a box-shaped reservoir, which takes into account fracture interaction, fracture conductivity, contacted reservoir area with fractures, and heterogeneity of fracture properties. A corresponding semi-analytical solution is further proposed to solve the model by using a new discretization algorithm called multi direct boundary element methodology (MDBEM). Based on the general model, the maximum productivity index (PI) is obtained by optimizing properties of fractures under the limitation of given proppant volume, which puts a constraint on number of fractures, fracture conductivity and fracture length. The heterogeneity effect of fracture properties on optimization is discussed in detail, and results indicate that it is more advantageous and practical to create more fractures with identical properties in homogeneous fractured configuration.