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5.6 Bad Urach  275
                         5.6.1.5 Conclusions
                         A fully coupled THM model is developed based on the general balance equations
                         for fluid mass, momentum, and thermal energy as well as constitutive equations
                         for variable fluid properties, thermoporoelastic deformation, and a phenomeno-
                         logical porosity–permeability relationship for crystalline rock, taking into account
                         hydraulic stimulation effects. The stochastic concept is a combination of the fully
                         coupled numerical THM model and the Monte Carlo method. On the basis of the
                         stochastic THM model, we present an uncertainty analysis of thermal, hydraulic,
                         and mechanical parameters on long-term geothermal reservoir evolution.
                           The most important findings using the stochastic THM model are:
                         • Accounting variable fluid properties is very important within THM analysis: the
                           most sensitive parameter is fluid viscosity.
                         • Statistical heterogeneity of geothermal reservoirs is considered: sensitivity analy-
                           sis shows that permeability and rock heat capacity are most important reservoir
                           parameters; less relevant is thermal conductivity. The variability of the mechani-
                           cal parameters in the site-specific range, porosity, Young’s modulus, and Poisson
                           ratio is negligible.
                         • Hydraulic stimulation effects: as the Urach Spa site has been hydraulically
                           stimulated several times, we included those stimulation effects by a permeability
                           enhancement factor depending on the borehole distance (Figure 5.16).
                         • Combination of parameter heterogeneity: we considered interrelated spatial
                           permeability–porosity distribution using a constitutive model by Pape et al.
                           (1999) for crystalline rock (Falkenberg site).
                         • As a result of the stochastic THM analysis we found a maximum tempera-
                           ture uncertainty range of about 40 K after 15 years of reservoir exploitation
                           (Figure 5.19).
                         • Computational efficiency: parallel computing is an important technical prerequi-
                           site for THM Monte Carlo analysis.

                         5.6.2
                         The Influence of Coupled Processes on Differential Reservoir Cooling

                         5.6.2.1 Conceptual Model
                         Processes operating during the extraction of heat in fractured rock dynamically
                         influence the fluid flow and heat transport characteristics. The incorporation of
                         pressure and temperature-dependent parameters of the rock mass coupled with
                         geomechanical deformation is particularly important for predictive modeling of
                         hard rock geothermal reservoirs as discussed above. Utilizing an experimentally
                         validated geomechanical model (McDermott and Kolditz, 2006), the changes in the
                         flow and transport parameters within crystalline fractures due to changes in local
                         effective stress were simulated by McDermott et al. (2006). The changes in local
                         effective stress are linked to the dynamic reservoir fluid pressure, in situ stress
                         conditions and the build up of thermal stresses during rock mass cooling. These
                         processes are simulated in a case study of the Spa Urach (South West Germany)
                         potential geothermal reservoir, using an FE model comprising tetrahedral elements.
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