DDA belongs to the family of Discrete Element Method (DEM). It is an implicit version of DEM. Unlike its sister method, Distinct Element Method, proposed by Cundall and has been developed over the years, DDA received less attention, especially for its application to simulate fluid-solid problem. Stimulated by the development of shale gas, hydraulic fracturing simulation has come to a new era. Complex fractures are believed to occur in the stimulation of shale gas. However, traditional methods are not applicable to simulate such complex physical behavior. A pipe network model is usually used to combine with Discrete Element Method for fluid-solid coupling problem. This has been adapted in the commercial codes UDEC, PFC2 and PFC3. In this paper, a two dimensional DDA based hydraulic fracturing program is developed. Hydraulic pressures are added to DDA block boundaries as line loadings. Fracturing initiation and propagation is simulated under in-situ stresses. As a discrete element method, DDA has its advantages and disadvantages in dealing with such problem. A parametric study is conduced to test the capability of our method and computer program. In-situ stresses and joint properties are shown to be the most important factors. Results will be presented and discussed. Future development will be addressed as well.


Natural fractures are believed to play an important role for the stimulation of shale gas from shale formations (Warpinski et al. 2009). Arealistic modelwhich is able to simulate hydraulic fracturing of shales has to take consideration of natural fractures. It is very difficult to deal with several fractures simultaneously by a continuous numerical method such as finite element method (Taleghani, 2009). Discrete element method appears to be promising to conquer such a difficulty. Dr. Cundall and Itasca Consulting Group have been conducting a lot of efforts to make discrete element method a good tool to achieve this goal over the years (Cundall, 1971, Potyondy & Cundall, 2004, Lemos, 2011, Pettitt et al. 2012). Their commercial software packages including UDEC and PFC have been used by several groups to simulate hydraulic fracturing and gained some success (Zhao & Young, 2009, McLennan, et al. 2010, Zangeneh et al. 2012).

DDA is an implicit version of discrete element method (Shi, 1988). The formulation of DDAis similar to that of finite element method and the simultaneous equations are derived by the minimum energy principle. We formed the basis of simulating hydraulic fracturing by combining a pipe network model with DDA (Ben et al. 2012). This paper presents some parametric studies, concerning the response of a fractured media subject to fluid injection.

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