Fractal concept in numerical simulation of hydraulic fracturing of the hot dry rock geothermal reservoir

Hydraulic fracturing or hydraulic stimulation is one of the most effective methods of enhancing hot dry rock (HDR) geothermal system productivity. The 3D structure of the fractured rock is approximated by the network models of 'fractal geometry'. The models of fracture networks are generated by distributing fractures randomly in space and assuming the fractal correlation N-r = Cr-D that incorporates the number of fractures N-r, fractal length r, fractal dimension D and fracture density within the rock mass C. This procedure makes it possible to characterize the geothermal reservoirs using parameters measured from field data. Based on this approach, a mathematical model of the hydraulic rock fracturing is proposed. The model incorporates approximations of the fracture mechanical behaviour 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. Along with the fractal-type distribution of the fracture lengths, the fracture surfaces are also assumed to follow fractal geometry. The latter allows numerical simulation of the natural rock fracture dilation caused by fracture shear offset. The other problem that can be resolved by fracture surface modelling is the apparent limitation on the number of fractures that can be analysed experimentally. In this respect, the suggested mathematical model can be used to simulate fractal surfaces identical to fractures found in the natural rocks. Taken together, these tools permit the approximate engineering resolution of the multi-parametric, highly complex mechanical problem. The reliability of the developed model was validated by comparisons 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 indicate 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. Copyright (C) 2003 John Wiley Sons, Ltd.