A three‐dimensional stochastic rock mechanics model of engineered geothermal systems in fractured crystalline rock

Jing, Zhenzi; Willis-Richards, J.; Watanabe, Kimio; Hashida, Toshiyuki

doi:10.1029/2000jb900202

Cited by 50 publications

(32 citation statements)

References 11 publications

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“…Based on the mechanisms of reservoir fracturing discussed in Gudmundsson et al (2001), Watanabe and Takahashi (1995), Willis-Richards et al (1996), Jing et al (2000), and Fomin et al (2003b), we will assume that formation of fractures occurs only in the region around the borehole, where fluid pressure, p, exceeds the specified value p s required for initiation of the fracture shear dilation and shear offset (Willis-Richards et al, 1996) or for hydro-fractures propagation (Gudmundsson et al, 2001). Namely, it will be assumed that everywhere in stimulated area p > p s and in the rest of domain p < p s .…”

Section: Mathematical Model Of the Fractured Reservoir Hydraulic Stimmentioning

confidence: 99%

“…Dealing with the design and construction of large-scale engineering systems, and a HDR geothermal system is a particular case of this, it is always advantageous to have reliable computational instruments for predicting, at least approximately, the system evolution over time prior to field experiments. Many numerical and analytic models have been proposed for simulating the HDR systems (Hopkirk et al, 1981;Watanabe and Takahashi, 1995;Willis-Richards et al, 1996;Jing et al, 2000;Gudmundsson et al, 2001;and Fomin et al, 2003b among others). The numerical model FRACSIM-3D, developed by a research group at Tohoku University, has proven to be an appropriate approximate model capable of simultaneously addressing problems associated with hydraulic stimulation, fluid circulation, and heat extraction.…”

Section: Introductionmentioning

confidence: 98%

“…In contrast to the above approach, the real process of hydraulic stimulation is characterized by the presence of a large number of fractures within the rock volume surrounding the borehole, where fracturing predominantly occurs due to the preexisting fracture shear offset and consequent shear dilation (Fomin et al, 2003b). According to estimates made on the basis of a steady-state model (Jing et al, 2000), the permeability of stimulated areas in some cases can be up to 2 orders of magnitude higher than the original permeability of the undisturbed rock. The substantial difference in permeabilities of the stimulated and undisturbed zones is a principal feature of hydraulic stimulation, which should be represented in the mathematical model of the process.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of Stimulated Area Growth During High-Pressure Hydraulic Stimulation of Fractured Subsurface Reservoir

2006

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Hydraulic stimulation is performed by high-pressure fluid injection, which permanently increases the permeability of a volume of rock, typically transforming it from the microdarcy into the millidarcy range. After a period of stimulation, fluid injection and recovery boreholes are introduced into the stimulated rock volume, and heat is extracted by water circulation. In the present study a simplified mathematical model of nonsteady-state hydraulic stimulation is proposed and analyzed. Fluid flow is assumed to be radial, injected flow rate constant; and fluid density, rock porosity, and permeability depend on fluid pressure. The conventional boundary of the growing stimulated rock volume is introduced as a surface where the porosity and permeability of the stimulated rock exhibit a sharp decline and remain constant within the undisturbed area. The problem is solved analytically by a modified method of integral correlations. As a result, approximate close-form solutions for pressure distributions in the stimulated and nonstimulated (undisturbed) areas are obtained, and an equation for the moving boundary of the stimulated volume is derived. The correctness of the approximate solution is validated by comparison to an exact self-similar solution of the problem obtained for the particular case when the well's radius is assumed to be equal to zero.

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Section: Mathematical Model Of the Fractured Reservoir Hydraulic Stimmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Assessment of Stimulated Area Growth During High-Pressure Hydraulic Stimulation of Fractured Subsurface Reservoir

2006

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“…Many numerical models have been proposed for simulating the HDR systems (Hopkirk et al, 1981;Watanabe and Takahashi, 1995;Willis-Richards et al, 1996;Jing et al, 2000;among others). The numerical model FRACSIM-3D developed by a research group at Tohoku University has proven to be an appropriate approximate model capable of simultaneously addressing problems associated with hydraulic stimulation, fluid circulation and heat extraction.…”

Section: Introductionmentioning

confidence: 98%

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

Fomin

Hashida

Shimizu

et al. 2003

Hydrological Processes

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Abstract: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 D 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.

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“…FRACSIM-3D [90,155] is used as a prototype for many of the codes presented in this review. A 3D stochastic fracture network with elastic opening and shearing, including dilation upon hydraulic pressurisation, is implemented in this code.…”

Section: Fracture-oriented Modelsmentioning

confidence: 99%

Induced seismicity in geothermal reservoirs: A review of forecasting approaches

Gaucher

Schoenball

Heidbach

et al. 2015

Renewable and Sustainable Energy Reviews

153

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In order to reach Europe's 2020 and 2050 targets in terms of greenhouse gas emissions, geothermal resources will have to contribute substantially to meeting carbon-free energy needs. However, public opinion may prevent future large-scale application of deep geothermal power plants, because induced seismicity is often perceived as an unsolicited and uncontrollable side effect of geothermal development. In the last decade, significant advances were made in the development of models to forecast induced seismicity, which are either based on catalogues of induced seismicity, on the underlying physical processes, or on a hybrid philosophy. In this paper, we provide a comprehensive overview of the existing approaches applied to geothermal contexts. This overview will outline the advantages and drawbacks of the different approaches, identify the gaps in our understanding, and describe the needs for geothermal observations. Most of the forecasting approaches focus on the stimulation phase of enhanced geothermal systems which are most prone to generate seismic events. Besides the statistical models suited for realtime applications during reservoir stimulation, the physics-based models have the advantage of considering subsurface characteristics and estimating the impact of fluid circulation on the reservoir. Hence, to mitigate induced seismicity during major hydraulic stimulations, application of hybrid methods in a decision support system seems the best available solution. So far, however, little attention has been paid to geochemical effects on the failure process and to production periods. Quantitative modelling of induced seismicity still is a challenging and complex matter. Appropriate resources remain to be invested for the scientific community to continue its research and development efforts to successfully forecast induced seismicity in geothermal fields. This is a prerequisite for making this renewable energy resource sustainable and accessible worldwide.

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A three‐dimensional stochastic rock mechanics model of engineered geothermal systems in fractured crystalline rock

Cited by 50 publications

References 11 publications

Assessment of Stimulated Area Growth During High-Pressure Hydraulic Stimulation of Fractured Subsurface Reservoir

Assessment of Stimulated Area Growth During High-Pressure Hydraulic Stimulation of Fractured Subsurface Reservoir

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

Induced seismicity in geothermal reservoirs: A review of forecasting approaches

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