This paper proposes a two-dimensional (2D), time-dependent, and tightly coupled computational algorithm for hydraulic fracturing simulations. It uses the cubic law model for computing the fluid flow in opened fractures and fluid volume caged inside the fractures. A finite element method (FEM) is used to evaluate stresses and deformation of elastic rock blocks. The Lagrange multipliers method is used to prevent penetration during contact between adjacent rock blocks while imposing fracture tip displacement constraint conditions. The propagation criterion of hydraulically induced fractures is imposed by mixed mode stress intensity factor, which is calculated using a displacement correlation method. This scheme is also coupled with tensile and shearfailure models to describe natural fracture evolution and its interaction with approaching hydraulically induced fractures. The geomechanics and fluid dynamics common components naturally lead to a tightly coupled integrative system, where its unknowns are rock block corner displacements, the Lagrange multipliers in case blocks in contact or displacement constraints applied, and fluid pressure at junctions of opened fractures. The proposed algorithm solves for all unknowns simultaneously and in a tightly coupled manner, while the general Newton algorithm is implemented for solving the overall nonlinear system of equations at each time step.
Hydraulic fracturing treatments in horizontal wells are used to produce unconventional formations, such as tight gas sands and gas shale . Although hydraulic fracturing technology has been used practically for some time, the associated numerical simulations still pose some crucial challenges. A basic review of relevant hydraulic fracturing aspects is provided . Most geomechanics models used are based on single-fracture geometry and some analytical solutions, such as the PKN  and KGD  models. However, pre-existing natural fractures in unconventional reservoirs contribute more uncertainties during the fracturing process in terms of propagation of hydraulic fractures and the interaction between natural fractures and hydraulic fractures. The interaction between hydraulic fractures and natural fractures could generate a complex fracture network (CFN) other than simple fracture geometries.