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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.