Book excerpt: Modeling the stimulated reservoir volume during hydraulic fracturing is important to geothermal and petroleum reservoir stimulation. The interaction between a hydraulic fracture and pre-existing natural fractures exerts significant control on stimulated volume and fracture network complexity. This thesis presents a boundary element and finite difference based method for modeling this interaction during hydraulic fracturing process. In addition, an improved boundary element model is developed to more accurately calculate the total stimulated reservoir volume. The improved boundary element model incorporates a patch to calculate the tangential stresses on fracture walls accurately, and includes a special crack tip element at the fracture end to capture the correct stress singularity the tips The fracture propagation model couples fluid flow to fracture deformation, and accounts for fracture propagation including the transition of a mechanically-closed natural fractures to a hydraulic fracture. The numerical model is used to analyze a number of stimulation scenarios and to study the resulting hydraulic fracture trajectory, fracture aperture, and pressures as a function of injection time. The injection pressure, fracture aperture profiles shows the complexity of the propagation process and its impact on stimulation design and proppant placement. The injection pressure is observed to decrease initially as hydraulic fracture propagates and then it either increases or decreases depending on the factors such as distance between hydraulic fracture and natural fracture, viscosity of the injected fluid, injection rate and also other factor that are discussed in detail in below sections. Also, the influence of flaws on natural fracture in its opening is modeled. Results shows flaws that are very small in length will not propagate but are influencing the opening of natural fracture. If the flaw is located near to one end tip the other end tip will likely propagate first and vice versa. This behavior is observed due to the stress shadowing effect of flaw on the natural fracture. In addition, sequential and simultaneous injection and propagation of multiple fractures is modeled. Results show that for sequential injection, the pressure needed to initiate the later fractures increases but the geometry of the fractures is less complicated than that obtained from simultaneous injection under the same fracture spacing and injection. It is also observed that when mechanical interaction is present, the fractures in sequential fracturing have a higher width reduction as the later fractures are formed.