Numerical simulation of the fracture type reservoir growth during hydraulic fracturing

Sergei Fomin, Ayumu Shimizu, Toshiyuki Hashida

Research output: Contribution to journalArticlepeer-review


Hydraulic fracturing or hydraulic stimulation is one of the most effective methods of enhancing of the hot dry rock (HDR) geothermal system productivity. The 3D structure of the fractured rock is approximated with the network models of "fractal geometry". The models of fracture networks are generated by distributing fractures randomly in space and adopting the fractal correlation Nr = Cr-D that incorporates the number of fractures Nr, fractal length r, fractal dimension D, and fracture density within the rock mass C. This procedure makes possible to characterize the geothermal reservoirs by parameters measured from the field data. On the basis of this approach the mathematical model of the hydraulic rock fracturing is proposed. The model incorporates approximations of the fracture mechanical behavior drawn from the rock mechanics literature, a very simplified analysis of the operative physical processes, and mapping of the connectivity of fracture network to a cubic regular grid. Taken together, these permit the approximate engineering resolution of the multi-parametric highly complex mechanical problem. The model has shown itself capable of reproducing many facets of the data collected during the field tests of stimulation of the Hijiori geothermal system (Yamagata, Japan). The reliability of the developed model is validated by comparison with the experimentally determined data for the Hijiori Deep Reservoir. This implicitly justifies the numerical results and conclusions drawn in the present research. In particular, a series of computations indicates that the connectivity of the fracture network is greatly affected by the fractal dimension of the fracture network. The strong effect of the fractal dimension on the reservoir’s size is also observed. The numerical results illustrate the controlling effect of the pressure and flow rate in the stimulating well for reservoir growth.

Original languageEnglish
Pages (from-to)69-77
Number of pages9
JournalStrength, Fracture and Complexity
Issue number2
Publication statusPublished - 2003 Jan 1


  • Fractal dimension
  • Fracture
  • Geothermal reservoir
  • Hydraulic stimulation
  • Simulation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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