A numerical approach for pressure transient analysis of a vertical well with complex fractures

A new well test model for a vertical fractured well is developed based on a discrete-fracture model in which the fractures are discretized as one dimensional (1-D) entities. The model overcomes the weakness of complex meshing, a large number of grids, and instability in conventional stripe-fracture models. Then, the discrete-fracture model is implemented using a hybrid element finite-element method. Triangular elements are used for matrix and line elements for the fractures. The finite element formulation is validated by comparing with the semi-analytical solution of a single ver-tical fractured well. The accuracy of the approach is shown through several examples with different fracture apertures, fracture conductivity, and fracture amount. Results from the discrete-fracture model agree reasonably well with the stripe-fracture model and the analytic solutions. The advantages of the discrete-fracture model are presented in mesh gen-eration, computational improvement, and abilities to handle complex fractures like wedge-shaped fractures and fractures with branches. Analytical results show that the number of grids in the discrete-fracture model is 10%less than stripe-fracture model, and computational efficiency increases by about 50%. The more fractures there are, the more the com-putational efficiency increases.