The numerical model FRACSIM developed by the research group in Tohoku University for the hot-dry-rock (HDR) geothermal reservoir is proved to be an appropriate approximate model capable to address simultaneously the problems associated with hydraulic stimulation, fluid circulation and heat extraction. The structure of the fractured rock is approximated with the network models of "fractal geometry". The adopted procedure makes it possible to characterize geothermal reservoirs by parameters measured from the field data. As is proved both theoretically and experimentally for the fluid flows in the fractured and porous media with relatively high fluid velocities, the values of the effective thermal conductivities in the longitudinal and transverse to the flow directions are directly proportional to the values of the fluid velocity. The water/rock chemical interaction (WRCI) is the other factor that inevitably exerts an influence on the permeability of the high temperature deep HDR circulating system. In the present study the mathematical model, which accounts for the effects of thermal dispersion and WRCI (in terms rock chemical dissolution and precipitation), is proposed. The numerical analysis based on the 3D model of the reacting fluid flow within the fractured media proves the importance of the thermal dispersion and WRCI factors for the assessment of the overall reservoir thermal and hydraulic performance.