Fractal Characterization of Subsurface Fracture Network for Geothermal Energy Extraction System

As a new modeling procedure of geothermal energy extraction systems, the authors present two dimensional and three dimensional modeling techniques of subsurface fracture network, based on fractal geometry. Fluid flow in fractured rock occurs primarily through a connected network of discrete fractures. The fracture network approach, therefore, seeks to model fluid flow and heat transfer through such rocks directly. Recent geophysical investigations have revealed that subsurface fracture networks can be described by "fractal geometry". In this paper, a modeling procedure of subsurface fracture network is proposed based on fractal geometry. Models of fracture networks are generated by distributing fractures randomly, following the fractal relation between fracture length r and the number of fractures N expressed with fractal dimension D as N = C . F D , where C is a constant to signify the fracture density of the rock mass. This procedure makes it possible to characterize geothermal reservoirs by the parameters measured from field data, such as core sampling. In this characterization, the fractal dimension D and the fracture density parameter C of a geothermal reservoir are used as parameters to model the subsurface fracture network. Using this model, the transmissivities between boreholes are also obtained as a function of the fracture density parameter C, and a parameter study of system performances, such as heat extraction, is performed. The results show the dependence of thermal recovery of geothermal reservoir on fracture density parameter C. INTRODUCTION Recently, HDR(Hot Dry Rock) and HWR(Hot Wet Rock) have attracted considerable attention as new geothermal energy extraction systems. In order to evaluate the performance of these systems, it is necessary to establish a modeling procedure of fluid flow and heat exchange in fractured rock. Traditionally, models of ground water flow have used parallel fractures, or a continuum approximation such as a "permeable zone". Such models are often valid when a representative volume of rock can be defined that is much smaller than the region of interest. However, it has been becoming difficult to approximate the behavior of geothermal reservoirs by such models. In fractured rocks, ground water flow and solute transport occur predominantly through the connected network of discrete fractures. For the performance evaluation of such geothermal energy extraction systems, interest has grown in more direct models of water flow and heat exchange in fractured rock. Recent geophysical investigations have confirmed that a subsurface fracture network can be described by fractal geometry. In the field of seismology several reports are available which have characterized subsurface fractures and fault systems based on fractal geometry. Hirata [ 19891 has investigated several fault systems in Japan, and characterized them by fractal geometry. In his paper, fractal geometry was considered as a useful tool to characterize the geometry of the fault line. The fractal dimensions of those fault systems were calculated by the so called "box-counting method". Furthermore, Meredith [ 19901 has noted that subsurface fractures could also be characterized by using a methodology in which the number of fractures was related to the fracture length. In this paper, two and three dimensional modeling procedures of subsurface fractuIe network are proposed, based on the relationship between the fracture length and the number of fractures &s reported by Meredith. The importance of the parameter is discussed to describe the fracture density of rock mass. This procedure is attractive, since this parameter can be measured from field data such as the core sample, and it is also possible to characterize subsurface fracture network by the same parameter. For geothermal energy extraction systems, the transmissivity and changes in temperature of geothermal reservoir are important. So, based on this modeling procedure, the transmissivity are discussed in terms of probabilities. Finally, we present one of the results of changes in temperature at reservoir outlet as computed by our model, which suggests the strong dependence of temperature change on fracture density.