A hydraulic fracture design model that simulates the complex physical process of fracture propagation in the earth driven by the injected fluid through a wellbore. An objective in the model is to adhere with the laws of physics governing the surface deformation of the created fracture subjected to the fluid pressure, the fluid flow in the gap formed by the opposing fracture surfaces, the propagation of the fracture front, the transport of the proppant in the fracture carried by the fluid, and the leakoff of the fracturing fluid into the permeable rock. The models used in accordance with methods of the invention are typically based on the assumptions and the mathematical equations for the conventional 2D or P3D models, and further take into account the network of jointed fracture segments. For each fracture segment, the mathematical equations governing the fracture deformation and fluid flow apply. For each time step, the model predicts the incremental growth of the branch tips and the pressure and flow rate distribution in the system by solving the governing equations and satisfying the boundary conditions at the fracture tips, wellbore and connected branch joints. An iterative technique is used to obtain the solution of this highly nonlinear and complex problem.
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