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Hydraulic Stimulation Modeling in Geothermal Systems

Final Report Summary - HYSM (Hydraulic Stimulation Modeling in Geothermal Systems)

Hydraulic Stimulation Modeling in Geothermal Systems


The extraction of geothermal energy is typically achieved by use of deep wells with openhole well intervals, providing a hydraulic interaction with the hot rock mass. By means of an induced circulation of water between the wells and a heat exchange between the solid and liquid phase the heat is mined from the aquifer. It is obvious that the extraction of thermal energy from the hot rock depends on the availability and sustainability of permeable fractures in which water can be circulated to mine the heat content and the possibility to connect wells with the greatest possible mass of hot rock. In order to improve the permeability of the rock and to increase the activated area of contact between wells and the far-field system, a network of fractures can be artificially opened or even created. The aim of hydraulic stimulation is obviously the maximization of productivity. It is however linked to risks, such as induced microseismicity or borehole stability, which in turn are likely to increase significantly the production costs. Therefore it is necessary to develop methods of determining the exact stimulation procedure suitable in each specific case. The present project suggests an approach to the subject from several different aspects.

From the experimental point of view, an investigation of crack propagation, coalescence and interaction was performed on gypsum specimens with predefined crack spacing and orientation. 36 specimens with 12 different crack angles were prepared with an especially designed and constructed metal mold and tested in a simple shear apparatus. The specimens were tested under a normal stress of 0.5 MPa, corresponding to less than 10% of the uniaxial strength of the material. The maximum shear stress was found to vary significantly as a function of the orientation of the cracks relative to the shearing direction. The shear resistance of the specimens with crack orientations contrary to the shear direction was found to be larger than that of specimens with crack orientations in the shear direction. Both categories showed a maximum around an inclination of 45 degrees. Comparison of the results to theory demonstrated that neither the theory of Griffith [1] nor the law of Patton [2] are suitable for the description of the mechanism. It was found that the failure mechanism seems to be essentially controlled by the material bridges rather than the cracks.

The effect of fracture orientations on the strength of rock mass during hydraulic stimulation was further investigated by means of Discrete Element simulations. A material with two fracture families was considered in two dimensions, under a given biaxial stress state. The program MechSys [3], developed by S.A. Galindo Torres, was used. As the code did not include the possibility of generating a structured mesh as the basis for the generation of the blocks, a suitable mesh generator was programmed for the needs of the project. Assemblies of blocks divided by two families of fractures were modeled in two dimensions. The control parameters were the relative lengths of the blocks and the angles formed with the principal stress axes. Subsequently the hydraulic pressure was increased in the center of the assembly up to the point where fracture propagation was observed. The maximum hydraulic pressures were thus gained for a large variety of different orientations and block shapes. It was observed that both the orientation of the preexisting fractures with respect to the principal axes and block shape play a significant role for the hydraulic pressure required for fracturing. These variations seem to be in good agreement with theoretical predictions. The dependence on the orientation is in agreement with the theoretical prediction of the shear resistance of a fracture to sliding. The theoretical dependence of the resistance to failure of a fracture on its length on the other hand is in agreement with the dependence on the block shape and thus, indirectly, on the fracture tortuosity. In addition tensile and shear failure were observed for different specimens, depending on the orientations of the preexisting fractures. For the most part the orientation of the resulting fracture was found to be independent of the block orientations and determined by the stress field and the friction angle.

Within the frame of the constitutive work package of the project the permeability of a fractured medium containing multiple fractures was evaluated in accordance with the method of Oda [4] on the basis of the probability density function of the fractures. This formulation then was modified to account for changes in permeability arising from changes in the normal and shear stresses, affecting the aperture of the fractures. The mechanical behavior of the rock itself was described by a model of the damage type. The damage in this case is governed by a set of parameters describing the fracture distribution and geometric properties. For the evolution of the fracture distribution a simplified form of the Kachanov method [5] was used, in combination with the results of the experimental and numerical tests, as it was deemed important that the model should be simple enough for application. It was deemed sufficient to use the commercial code Abaqus for the simulations, though the possibility of one way coupling to the multiphysics transport code TOUGH2 was examined and deemed feasible. A UMAT script was written for the mechanical behavior of the material and a USDEV script for the evolution of the permeability of the fracture matrix. The results show, as was expected, a very marked dependence of the pressure distribution on the distribution of the fractures. As the stimulation progresses, the permeability does not simply increase, but at the same time its principal axes are rotated, depending on the orientation of the in situ stress state.

Within the frame of HySM the mechanics of hydraulic stimulation were considered from a triple point of view, experimental, numerical and analytical. Some very interesting results were retrieved and a relatively simple model was developed for the description of the phenomenon. The most important of the conclusions to be drawn is the very strong dependence of the fracture orientation and the pressures required to achieve stimulation on the orientation and geometric properties of the preexisting fractures. The anisotropy of the in situ stresses was also found to play a very significant role in the orientation of the principal axes of the permeability after the stimulation. It is hoped that these conclusions will have a significant impact on the modeling of hydraulic stimulation, where the anisotropy of the rock mass and the permeability are often neglected.

[1] Gross D. and Seelig T. Fracture Mechanics. Springer, 2006.
[2] Brady B.H.G. and Brown E.T. Rock Mechanics, Springer, 2004.
[3] Galindo-Torres S.A. Pedroso D.M. Williams D.J. and Li L. Breaking processes in three-dimensional bonded granular materials with general shapes. Computer Physics Communications, 183:266–277, 2012.
[4] Oda M. Permeability tensor for discontinuous rock masses. Géotechnique, 35:483 – 495, 1985.
[5] Kachanov M. Elastic solids with many cracks and related problems. Advances in applied mechanics, 30:259–445, 1994.