A Fully Implicit Single Phase T-H-M Fracture Model for Modelling Hydraulic Fracturing in Oil Sands
Authors: Pak A. , Chan D.H. 
Published: March 2010

Abstract
Enhancing oil extraction from oil sands with a hydraulic fracturing technique has been widely used in practice. Due to the complexity of the actual process, modelling of hydraulic fracturing is far behind its application. Reproducing the effects of high pore pressure and high temperature, combined with complex stress changes in the oil sand reservoir, requires a comprehensive numerical model which is capable of simulating the fracturing phenomenon. To capture all of these aspects in the problem, three partial differential equations, i.e., equilibrium, flow, and heat transfer, should be solved simultaneously in a fully implicit (coupled) manner.
A fully coupled thermo-hydro-mechanical fracture finite element model is developed to incorporate all of the above features. The model is capable of analyzing hydraulic fracture problems in axisymmetric or plane strain conditions with any desired boundary conditions, e.g., constant rate of fluid injection, pressure, temperature, and fluid flow/thermal flux. Fractures can be initiated either by excessive tensile stress or shear stress. The fracture process is simulated using a node-splitting technique. Once a fracture is formed, special fracture elements are introduced to provide in-plane transmissivity of fluid. Effectiveness of the model is evaluated by solving several examples and comparing the numerical results with analytical solutions. The model is also used to simulate large-scale laboratory hydraulic fracturing experiments.

Introduction
Hydraulic fracturing technique has been a fast growing technology since its first application in 1947. By 1988, more than one million hydraulic fracturing treatments had been performed(1), and today this technique is one of the most important methods in enhancing oil extraction from wells. Hydraulic fracturing in oil sand reservoirs plays an even more important role. Due to low temperature and low permeability of oil sand deposits and high viscosity of bitumen, oil is virtually immobile(2). Hence, any attempt for in situ oil extraction should employ one of the following techniques: cyclic steam stimulation, in situ combustion, or hydraulic fracturing.
Despite the fact that hydraulic fracturing technology has advanced significantly over the past fifty years, our ability to model the process has not changed as rapidly. As a matter of fact, this technique has been so successful that in the past, designingthe treatment with a high degree of precision was not of any interest. But as the industry moved towards applications of very high volume/rate, and highly engineered and sophisticated hydraulic fracturing treatments, the demand for more rigorous designs in order to optimize the procedure have become more important. On the other hand, without a thorough understanding of the physical process and the factors that are involved, our ability for an optimal design is limited. Modelling fluid flow combined with heat transfer in the reservoir has been used by the industry for a long time, and the fracturing process was often designed based on twodimensional closed-form solutions, such as Geertsma-de Klerk(3), or GdK in brief, and Perkins-Kern(4) and Nordgren(5), or PKN. Most of the flow and heat transfer models are based on the finite difference method, and effects of stresses and deformations in the ground, if not totally ignored, are solved in a decoupled or partially coupled manner with other elements.