Dual-porosity and dual-permeability naturally fractured reservoir models assume that the fractures in the reservoir are connected with each other and distributed uniformly. However, in some cases, the reservoir characteristics exhibits discrete fracture systems, which means that the fractures might be unconnected and their distribution is not uniform. In this work, a new computational model is developed to compute the transient pressure behavior for reservoirs with discrete fracture system. This computational model is based on Laplace transform. The fluid flow in the fracture system and reservoir are computed separately and flux and pressure equivalent conditions in Laplace space are applied in the fracture wall to couple the fluid flow in both systems.
The results suggest that the pressure response in a reservoir with a discrete fracture system has three flow regions: fluid flow nearby the wellbore, fracture-dominated fluid flow and fluid flow beyond the fracture. The fracture orientation (i.e. the distance between the fracture and the well), fracture parameters (fracture conductivity and non-Darcy effects) and fracture distribution are the main factors affecting the pressure response. In some particular situations the fracture-dominated fluid flow region in the pressure derivative curve may present two villages, which has been met in some field cases. The model provides with a tool for identifying the fracture pattern in a specific reservoir. Also, this model can be applied for optimization design of tight gas reservoir development.
Classically, the fractured reservoir is modeled with Dual porosity model(1) or dual-permeability model. Those models assume that the fractures are connected with each other and distributed uniformly. The dual-porosity model also assumes that the fluid is produced from the fractures which are intersected with the well. However, in some cases, the reservoir characteristics exhibit discrete fracture system, which means that the fractures may be unconnected and their distribution is not uniform. Such kind of reservoir system was illustrated by Gao et al.(2), as shown in Figure 1. Gao et al.(2), also pointed out that the chance for a vertical well to intersect a discrete natural fracture is extremely small, since natural fractures in a reservoir tends to be vertical. Another type of discrete fracture system is artificial fracture system in tight gas reservoirs. To obtain economical production rate, most of wells in a tight gas reservoir are hydraulically fractured. Therefore, the whole reservoir looks like an artificial discrete fracture system. In this work, it is assumed that the discrete fracture system has the following characteristics,
The fractures in the reservoir are discrete and not connected with each other;
Each fracture can be described with its orientation, geometry and diffusivity;
The well is not intersected with any fracture; and, 4. The fluid flow in fracture system obeys Forchheimer equation and the fluid flow in matrix system is Darcy flow.
Zeng and Zhao(3) presented a model for non-Darcy flow in hydraulic fractures. For a reservoir with only one fracture existed, if the fracture is close enough to the well, then the system is similar to the system with a hydraulically fracture well.
