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Modelling Hydraulic-Fracturing in 2D

Magnus Wangen and Nina Simon
Institute of Energy Technology, Kjeller, Norway

Hydraulic fracturing is an important process for fluid flow in the subsurface. It appears in a variety of natural systems such as: a fluid release mechanism from reservoirs during pressure build-up over geological time, primary migration of hydrocarbons, melt migration in the crust, melt intrusions as sills and dykes, mud volcanoes and hydrothermal plumes. In reservoir engineering it is an important mean to increase the reservoir productivity or injectivity of wells.

We have developed a finite element procedure for the modelling of hydraulic fracturing. The procedure is so far in 2D and it has been tested with fluid injection and pressure build-up from a well. The model is based on the Biot equations for coupled fluid flow and deformations in the rock. Fractures are represented on the same grid as the rock. Two important properties of the fracture are its volume and its ability to conduct fluid, which are represented by means of “fracture porosity” and “fracture permeability”, respectively. These properties are represented on the original grid, and it is therefore possible to make a uniform finite element formulation for both the rock and the fracture on the same grid.

Fracture propagation takes place as discrete events when the fracture extends into one or more elements. The element size is therefore the smallest step a fracture can advance during propagation. The fracture volume, represented by an equivalent fracture porosity, is important because it controls the pressure drop that follows an event. A fracture event is assumed to take place instantaneously. The volume of fluid in the fracture is then the same right after an event as it was right before the event. A fracture becomes extended after an event, and a lower pressure is normally needed to keep a “long” fracture open than a “short” fracture. Furthermore, a reduced fracture width is needed after the event for the fracture to have the same volume.

The current implementation of hydraulic-fracturing is tested by fluid injected from a well. We model the pressure build-up between the fracture events and the pressure drop that follows an event. The modelling shows that the well pressure during hydraulic fracturing fluctuates around a plateau value.

AAPG Search and Discovery Article #120098©2013 AAPG Hedberg Conference Petroleum Systems: Modeling the Past, Planning the Future, Nice, France, October 1-5, 2012