Three-dimensional poroelastic hydraulic fracture simulation using the displacement discontinuity method

Hydraulic fracturing is used extensively to stimulate oil and gas reservoirs for the purpose of enhancing hydrocarbon production. A number of numerical models have been developed for the simulation of the hydraulic fracturing process. However, most models were formulated and developed within the framework of the theory of elasticity with poroelastic effects not included. It is now well-established that the presence of a freely moving fluid alters the mechanical behavior of the formation. The diffusion process bestows a time-dependent character upon the rock behavior. This time dependency of the rock deformation is very important in hydraulic fracturing and is accounted for in the linear theory of poroelasticity. The existing models that do include the poroelastic effects are either two-dimensional or restricted to a fixed fracture geometry and in-plane fracture propagation. In addition, leak-off is generally modeled using a one-dimensional model.; The model developed in this study is fully three-dimensional. It incorporates the poroelastic effects by allowing coupling between diffusion and deformation processes. For this purpose, the displacement discontinuity method is extended to three-dimensions within the frame work of the theory of poroelasticity.; The Displacement discontinuity (DD) method is an indirect boundary integral technique which is suitable for modeling fractures. The discontinuities in displacements correspond to the actual fracture opening (normal DD) and ride (shear DD). The latter provides a basis for modeling out-of-plane fracture propagation.; Using this method, a model has been developed and used to investigate the fracture response in a poroelastic medium. The results indicate that rock dilation caused by fluid diffusion is a significant poroelastic phenomenon which reduces fracture width. Using a higher order DD formulation, a three-dimensional poroelastic simulator has been developed which takes into account this effect.; The model uses quadratic fracture elements as well as square-root tip elements. Linear source elements are used to model leak-off and fluid diffusion into the rock formation. The fluid flow in the fracture is considered as a two-dimensional, steady-state flow in a parallel plate; and is treated using the two-dimensional finite element method. The results of the application of the model indicate smaller leak-off volumes when compared to the traditional Carter's leak-off model. Additional results reveal that poroelasticity increases the net fracture pressure and decrease the fracture volume; and, that poroelastic effects are dependent upon the rate of pumping, formation properties, far-field pore pressure, and in-situ stress.